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U ovom radu provedene su numeričke simulacije pokusa otpora modela broda i broda u naravi u neograničenoj i plitkoj vodi za kontejnerski brod DTC. Numeričke simulacije provedene su primjenom komercijalnog programskog paketa za računalnu dinamiku fluida (RDF) STAR–CCM+. Primijenjen je matematički model nestacionarnog trodimenzijskog viskoznog strujanja fluida sa slobodnom površinom na temelju Reynoldsovih osrednjenih Navier – Stokesovih jednadžbi (eng. Reynolds Averaged Navier – Stokes, RANS). Korišten je k – ω SST model turbulencije i metoda udjela fluida u volumenu (eng. Volume of Fluid, VOF) za praćenje i određivanje položaja slobodne površine. Simulacije su provedene za dva Froudeova broja te je proveden postupak verifikacije s ciljem određivanja numeričke nesigurnosti ukupnog otpora, urona/izrona te trima modela broda i broda u naravi za jedan Froudeov broj primjenom različite gustoće mreže i vremenskog koraka za slučaj neograničene i plitke vode. Dobiveni numerički rezultati za model broda u plitkoj vodi uspoređeni su s dostupnim eksperimentalnim podacima, dok su za brod u naravi uspoređeni s ekstrapoliranim rezultatima eksperimentalnih ispitivanja. Također, dan je detaljan prikaz strujanja oko trupa modela broda i broda u naravi u plitkoj vodi te je dana usporedba povećanja ukupnog otpora u plitkoj vodi u odnosu na neograničenu dubinu za model broda i brod u naravi. In this study, numerical simulations of resistance test for DTC container ship at model and full scale in unlimited and shallow water are carried out. Numerical simulations are performed within a commercial software package for Computational Fluid Dynamics (CFD) STAR – CCM+. A mathematical model of unsteady three – dimensional viscous flow with a free surface based on Reynolds averaged Navier – Stokes (RANS) equations is applied. The k – ω SST turbulence model is used, and the Volume of Fluid (VOF) method is applied for tracking and locating the free surface. The numerical simulations are carried out for two Froude numbers. The verification study is performed to assess the numerical uncertainty of the total resistance, sinkage, and trim for the ship model and full – scale ship at one Froude number using different grid densities and time steps in unlimited and shallow water. The obtained numerical results for the ship model in shallow water are compared with the experimentally obtained data, while for the full – scale ship are compared with the extrapolated results of the experimental tests. Also, a detailed description of the flow around the ship model and full – scale ship in shallow water is given. A comparison of the increase in total resistance in shallow water and unlimited depth for the ship model and full – scale ship is provided as well.

Jedan od najvećih izazova u industriji podatkovnih centara je osiguravanje strogo propisanih mikroklimatskih zahtjeva te je stoga razvoj i optimizacija klimatizacijskih jedinica za hlađenje podatkovnih centara od ključne važnosti. Za te se svrhe u posljednje vrijeme sve češće primjenjuje računalna dinamika fluida koja omogućuje bržu i učinkovitiju analizu u odnosu na eksperimentalna mjerenja, a koja su često dugotrajan i skup proces. U ovom je radu izrađen numerički model i provedena je računalna simulacija rada klimatizacijske jedinice za hlađenje podatkovnog centra koristeći računalni program ANSYS Fluent. Klimatizacijska jedinica analizirana u radu sastoji se od mješališta te adijabatskog hladnjaka za ovlaživanje i hlađenje zraka. Posebni fokus rada bio je na stvaranju i implementaciji korisničko definiranih funkcija (eng. User Defined Functions) koje u zadanoj zoni opisuju rad adijabatskog hladnjaka. Uz pretpostavku izentalpske promjene stanja tijekom direktnog ovlaživanja struje zraka te jednakog ovlaživanja u svakoj točki hladnjaka napravljen je skup korisnički definiranih funkcija te algoritam za njihovu implementaciju u ANSYS Fluent. Procjena točnosti rezultata hlađenja provedena je usporedbom s rezultatima softvera GENESYS Munters proizvođača direktnog adijabatskog hladnjaka. Numeričke simulacije pokazale su vrlo dobre rezultate, pri čemu je odstupanje u odnosu na podatke proizvođača iznosilo 4.32% za uprosječene temperature na izlazu iz hladnjaka, te 1.59% za uprosječeni sadržaj vlage. S ciljem još točnijeg modeliranja predlaže se proširenje funkcijske ovisnosti temperature struje zraka prema stupnju zasićenja te stvaranje gušće numeričke mreže. One of the biggest challenges in the data center industry is ensuring strict microclimate requirements, making the development and optimization of air handling units for data centers crucial. Recently, computational fluid dynamics has been increasingly used for these purposes, allowing for faster and more efficient analysis compared to experimental measurements, which are often time-consuming and expensive. In this study, a numerical model was developed and a computer simulation of the operation of a data center air handling unit was performed using the ANSYS Fluent computer program. The air handling unit analyzed in the study consists of air mixing plenum and an adiabatic cooler for humidifying and cooling the air. The special focus of the study was on creating and implementing user defined functions that describe the operation of the adiabatic cooler in the specified zone. Assuming isenthalpic state changes during direct air stream humidification and equal humidification at each point of the cooler, a set of user-defined functions and an algorithm for their implementation in ANSYS Fluent were created. The accuracy of the cooling results was evaluated by comparing them with the results of the GENESYS Munters software for direct adiabatic coolers. The numerical simulations showed very good results, with deviations from the manufacturer's data of 4.32% for the averaged outlet air temperature and 1.59% for the averaged moisture content. To further improve the modeling accuracy, it is proposed to extend the functional dependence of the air stream temperature on the degree of saturation and create a denser numerical mesh.

Cilj rada je primjena modela turbulencije Reynoldsovog tenzora naprezanja kod računalnog mo- deliranja opstrujavanja zgrade oblika kocke smještene u homogenom atmosferskom graničnom sloju, kako bi se utvrdilo je li spomenutim modelom moguće bolje računalno modelirati opterećenje zgrada u usporedbi s Menterovim k−ω SST modelom. U radu je za razvoj mreže konačnih volumena i računalnu simulaciju korišten programski alat OpenFOAM® , tj. foam-extend-3.2. U radu su iz jednadžbi modela turbulencije Reynoldsovog tenzora naprezanja izvedeni rubni uvjeti koje je potrebno koristiti kako bi se pravilno računalno modeliralo strujanje homogenog atmosferskog graničnog sloja korištenjem tehnike domene preteče u praznoj dvodimenzijskoj računalnoj domeni. Pritom je strujanje u blizini nepropusne hrapave stijenke modelirano zidnom funkcijom temeljenom na aerodinamičkoj duljini hrapavosti površine. Profili fizikalnih veličina dobiveni računalnom analizom strujanja u dvodimenzijskoj domeni su potom korišteni kao rubni uvjeti na ulaznoj granici trodimenzijske računalne domene u kojoj je smješten model zgrade oblika kocke. Računalnom analizom strujanja atmosferskog graničnog sloja oko modela zgrade je pokazano da se korištenjem modela turbulencije Reynoldsovog tenzora naprezanja ne postižu bolji rezultati računalno generirane raspodjele koeficijenta tlaka po stranicama zgrade u odnosu na dostupne eksperimentalne rezultate i računalne rezultate dobivene korištenjem ostalih RANS modela turbulencije. The goal in this thesis is the application of the Reynolds stress tensor turbulence model for modelling the flow over a model of a cubic-shaped building in the atmospheric boundary layer to determine whether it yields better results than when using Menter’s k − ω SST turbulence model. The CFD software used to generate the finite volume mesh and computationally model the given problem is a fork of OpenFOAM® called foam-extend-3.2. Proper boundary conditions for a successful modelling of the homogeneous atmospheric boundary layer using the precursor domain technique in an empty two-dimensional computational domain were derived from the Reynolds stress transport equations. A wall function based on the aerodynamic surface roughness length was used to model the flow near the impermeable rough surface. The resulting profiles were subsequently applied onto the inlet boundary of the three-dimensional computational domain which includes the cubic-shaped building model. It was determined that the flow over a cubic-shaped building in the atmospheric boundary layer created using the Reynolds stress transport turbulence model does not provide a better reproduction on the experimental data of the distribution of the pressure coefficient along various lines on the cubic-shaped building model compared to other RANS turbulence models.

Mala računala (klase Arduino), poznatija kao Single-Board Computers (SBC), imaju široku primjenu u industriji, a najčešće se koriste kao ugrađene upravljačke jedinice. Zbog svojih malih dimenzija, uglavnom se ugrađuju u uređaje sa limitiranim prostorom. Kako sva dovedena električna energija unutar računala disipira u toplinu, za optimalno funkcioniranje računala, posebice u tako skučenim uvjetima, potrebno je osigurati dostatno hlađenje komponenti uz minimalni utrošak energije. U ovom radu se uz pomoć računalne dinamike fluida provela simulacija hlađenja modela Raspberry PI prirodnom konvekcijom. Cilj simulacije je ispitati efikasnost hlađenja putem slobodne konvekcije, te stvoriti podlogu za validaciju daljnjih simulacija hlađenja. Također, provedeno je ispitivanje neovisnosti geometrijske mreže s ciljem kreiranja pouzdane geometrijske mreže koja bi bila pogodna za te daljnje simulacije. Geometrijska mreža načinjena je pomoću komercijalnog programskog paketa CF-MESH+. Sva generirana toplina koncentrirana je u dvije komponente računala za koje je dokazano da se najviše zagrijavaju, a strujanje fluida ostvareno je u zatvorenoj domeni sa stijenkama konstantne temperature. Proračun je proveden pomoću programskog paketa OpenFOAM Small computers (Arduino class), known as Single-Board Computers (SBC), are widely used in industry and are very often used as embedded control units. Due to their small dimensions, they are mainly installed in devices with limited space. As all the supplied electrical energy dissipates into heat inside the computer, for the optimal functioning of the computer it is necessary to ensure sufficient cooling of the components with minimal energy consumption, especially in such cramped conditions In this thesis, a computational fluid dynamics simulation of the cooling of the Raspberry PI model by natural convection was carried out. The goal of the simulation is to test the efficiency of cooling through free convection and to create a basis for validating further cooling simulations. Also, mesh independence test was carried out with the aim of creating a reliable geometric mesh that would be suitable for further simulations. The geometric mesh was created using the commercial software package CF-MESH+. All generated heat is concentrated in two computer components that have been proven to heat up the most. Fluid flow is realized in a closed domain with constant temperature walls. The calculation was performed using OpenFOAM software package.

U ovom radu predstavljeni su povijest, dijelovi, način rada te značaj centralnih procesorskih jedinica te je modelirano pasivno hlađenje centralne procesorske jedinice. Centralna procesorska jedinica detaljno je opisana u svrhu razumijevanja njezinog načina rada te zašto je odvođenje topline izuzetno bitno. Opisano je nekoliko najčešće korištenih tehnika hlađenja. Predstavljene su osnovne jednadžbe i princip rada računalne dinamike fluida, kao i softvera Ansys Fluenta. Model hladnjaka, inspiriran je komercijalno dostupnim pasivnim hladnjakom Alpine 12 za AM4 platformu. Za procesor je odabran APU AMD Ryzen 5700G koji, zajedno sa procesorskim jezgrama sadrži i grafičke jezgre čiji je TDP pri maksimalnom opterećenju 65 W. U Ansys Meshu je generirana mreža konačnih volumena. Fluent je korišten za simulaciju stacionarnog i nestacionarnog strujanja fluida. Opisani su i razlozi za odabir pojedinih opcija u Fluentu pri prirodnoj konvekciji. Svi dobiveni rezultati zatim su prikazani, opisani i objašnjeni. Na kraju, donešen je zaključak da je pasivno hlađenje primjenjivo za procesore srednjeg i visokog TDP-a prema pretpostavkama uzetim u radu., In this thesis the history, parts, operation and the importance of CPUs were desribed. Furthermore, CFD solver Ansys Fluent was used as a tool to simulate passive cooling of a CPU. The CPU was thouroghly described in order to understand the importance of thermal control. Cooling techniques were described, as well as the governing equations of Computational Fluid Dynamics. AM4 platform Alpine 12 passive cooler was chosen as inspiration for the 3D model. APU AMD Ryzen 5700G was chosen as the heat source as it contains both processing and graphic cores, the TDP of which is rated at 65 W. Finite volume mesh was generated for both steady and unsteady fluid flow. Basics of modeling natural convection were described for the used solver and all results were shown, described and explained. In the end, it was concluded that passive cooling was applicable to medium and high TDP central processing units with described assumptions about its environment.

Izvršena je 2D analiza strujanja vjetra brzine 6 m/s kroz Darrieusovu vjetroturbinu pomoću CFD programa Ansys Fluent. Uspoređene su vrijednosti koeficijenata uzgona i koeficijenata snage za NACA0015, NACA0018 i NACA0022 aeroprofile. Izrađene su geometrije, mreže i provedena simulacija. Rezultati su uspoređeni s rezultatima iz literature te pokazuju za analizirani raspon zadovoljavajuću podudarnost., A 2D analysis of 6 m/s wind flow through the Darrieus wind turbine was preformed using the Ansys Fluent CFD program. Lift coefficient and power coefficient for NACA0015, NACA0018 and NACA0022 airfoils were compared. Geometries, meshes and simulations were created. The results were compared with the results from the literature and a show a satisfactory agreement for the analyzed range.

Težnjom za zdravijim životom dovodi do novih mjera regulacija emisija onečišćujućih tvari koje uzrokuju probleme u okolišu. Značajna količina CO2 ispušta se u atmosferu izgaranjem fosilnih goriva. Dopuštene emisije onečišćujućih tvari iz dizelskih motora regulirane su tijekom posljednjih nekoliko desetljeća, a novi, stroži propisi očekuju se idućih godina. Ti propisi uključuju europske norme emisija koje proizlaze iz vladinih politika kao mogućnost smanjenja zagađenja okoliša. Štetne emisije iz motora s unutarnjim izgaranjem ovise o procesu spreja, atomizacije goriva i postupku miješanja goriva i zraka. Stoga se može zaključiti da je detaljno razumijevanje procesa spreja od najveće važnosti za razvoj motora. U ovom radu opisan je proces spreja koji nastaje visokotlačnim ubrizgavanjem goriva kroz sapnicu malog promjera. Upravo zbog ekoloških razloga ulažu se veliki resursi u razvoj novih matematičkih modela koji bi dovoljno dobro opisati proces spreja. Nadalje, prikazana i opisana je usporedba dva pristupa modeliranja spreja a to su Euler – Lagrange i Euler – Eulerian. Razumijevanje složene prirode spreja goriva formiranog pod visokim tlakom u eskeprimentalnim istraživanjima je ograničeno i to se razumijevanje može značajno poboljšati numeričkim simulacijama. Na kraju rada prikazana je analiza rezultata simulacije procesa spreja te je izveden zaključak potrebe provođenja računalnih simulacija ubrizgavanja goriva, Seeking a healthier life leads to new measures to regulate emissions of pollutants that cause environmental problems. A significant amount of CO2 is released into the atmosphere by burning fossil fuels. Allowed emissions of pollutants from diesel engines have been regulated over the past few decades, and new, stricter regulations are expected in the coming years. These rules include European emission standards resulting from government policies as a means to reduce environmental pollution. Harmful emissions from internal combustion engines depend on the spray process, fuel atomization and the fuel-air mixing process. It can therefore be concluded that a detailed understanding of the spray process is of paramount importance for engine development. This thesis describes the spray process formed by high pressure injection of fuel through a small-diameter nozzle. It is for ecological reasons that great resources are invested in the development of new mathematical models that would sufficiently describe the spray process. Furthermore, a comparison of two spray modelling approaches, namely Euler-Lagrange and Euler-Eulerian, is presented and described. Understanding of the complex nature of spray fuels formed under high pressure in expressional research is limited and this understanding can be significantly improved by numerical simulations. At the end of the paper an analysis of spray process simulation results is presented and conclusion of the need for computation simulations of fuel injection is made.

U ovom radu provedeno je numeričko određivanje ukupnog otpora, trima i urona modela jednotrupnog broda i katamarana Delft 372 primjenom računalne dinamike fluida (eng. Computational Fluid Dynamics - CFD) s ciljem istraživanja utjecaja pojave interferencije na ukupni otpor katamarana. Numeričke simulacije provedene su primjenom komercijalnog programskog paketa STAR-CCM+. Matematički model temeljen je na Reynoldsovim osrednjenim Navier - Stokesovim jednadžbama (eng. Reynolds Averaged Navier - Stokes - RANS) uz primjenu k - ω SST (eng. Shear Stress Transport) modela turbulencije. Za potrebe provedbe numeričkih simulacija, primijenjen je model nestacionarnog, trodimenzijskog, viskoznog strujanja, dok je za praćenje i lociranje slobodne površine primijenjena metoda udjela fluida u volumenu (eng. Volume of fluid - VOF). Numeričko istraživanje provedeno je za tri vrijednosti Froudeovih brojeva: 0,3; 0,5; 0,75 te za dva razmaka između trupova katamarana, što je omogućilo ispitivanje utjecaja razmaka između trupova i Froudeovog broja na pojavu interferencije. Provedena je verifikacija dobivenih numeričkih rezultata te je izračunata nesigurnost mreže i vremenskog koraka pri određivanju otpora modela jednotrupnog broda i katamarana Delft 372. Nadalje, provedena je i validacija rezultata usporedbom dobivenih numeričkih rezultata s eksperimentalnim rezultatima dostupnim u literaturi. Pokazano je da je ukupni otpor katamarana veći od dvostruke vrijednosti otpora jednotrupnog broda, što ukazuje na pojavu nepovoljne interferencije pri ispitanim Froudeovim brojevima i razmacima između trupova. Konačno, pokazano je kako se računalna dinamika fluida može primijeniti kao koristan alat u istraživanju pojave interferencije. In this study numerical assessment of the total resistance, trim, and sinkage of monohull and Delft 372 catamaran model is performed using Computational Fluid Dynamics (CFD), to investigate the impact of interference phenomenon on the total resistance of a catamaran. Numerical simulations are carried out using the commercial software package STAR-CCM+. The mathematical model is based on Reynolds Averaged Navier-Stokes (RANS) equations and k-ω SST (Shear Stress Transport) turbulence model. Unsteady three-dimensional viscous flow is numerically simulated, and the Volume of Fluid (VOF) method is utilised for tracking and locating free surface. Numerical investigations are carried out at three Froude number values: 0.3, 0.5, and 0.75 and for two demihull separations, which enabled the investigation of the impact of demihull separation and Froude number on the interference phenomenon. The verification study is performed and grid and temporal uncertainties for the prediction of the total resistance of monohull and catamaran Delft 372 model are calculated. Thereafter, the validation study is carried out by comparison of the numerically obtained results with the experimental ones available in the literature. It has been shown that the total resistance of the catamaran is higher than the double total resistance of the monohull, which demonstrates the occurrence of the detrimental interference at investigated Froude numbers and demihull separations. Finally, it has been demonstrated that Computational Fluid Dynamics can be used as a valuable tool in the investigation of interference occurrence.

U ovom radu razvijen je novi tip srčane pumpe. Originalnost ovog koncepta je da se mehanička energija predaje fluidu trenjem, vrtnjom ravnih diskova koji nemaju lopatice. Primjenom analitičkih, numeričkih i eksperimentalnih metoda definiraju se parametri bezlopatične srčane pumpe (BSP). Iz Navier–Stokesovih jednadžbi je izveden matematički model strujanja te su određeni glavni geometrijski parametri BSP pumpe. Prilikom određivanja parametara uvedeni su kriteriji koje konstrukcija mora zadovoljiti. Prvi i najvažniji kriterij je da pumpa dobavlja krv unutar zadanih granica protoka i prirasta tlaka da bi se osigurala normalna cirkulacija krvi. Drugi vrlo važan kriterij je visoka hemokompatibilnost te minimalan negativan utjecaj BSP na krv (bez zona zastoja i recirkulacije strujanja, unutar prihvatljivog raspona tangencijalnog naprezanja). Također je bitno postići pumpu minimalnog volumena. Definiranje parametara konstrukcije centrifugalne bezlopatične srčane pumpe izvodi se u odnosu na referentnu srčanu pumpu HeartMate II (HM2), jer se kroz kliničku praksu pokazalo da uzrokuje najmanje komplikacija i da ima dobru hemokompatibilnost. Numeričkom simulacijom je, kroz postupna poboljšanja geometrije pumpe; određena konačna konstrukcija BSP pumpe bez recirkulacije i bez zona zastoja strujanja. Za radnu točku određenu sa tlakom Δp = 65 mmHg, protokom Q = 5 l/min i brojem okretaja ω = 6000 o/min određeni su parametri BSP konstrukcije: unutarnji radijus R1 = 12 mm, vanjski radijus R2 = 15 mm, udaljenost između diskova h = 1 mm, i broj diskova n = 6. Iznos tangencijalnog naprezanja u rotoru je u rasponu 46 – 108 Pa, a vrijeme prolaska fluida je 0,0194 sekundi. Uspoređujući HM2 i BSP pumpe po kriteriju hemokompatibilnosti pri tlaku Δp = 65 mmHg i kutnoj brzini ω = 6000 o/min. Protok kroz HM2 je Q = 5 l/min, dok je za pumpu BSP protok Q = 5,43 l/min. Pumpa HM2 ima tangencijalno naprezanje na zidu u rasponu od 0 do1025 Pa te skalarno smično naprezanje u rasponu od 0,0632 do 3302 Pa. Pumpa BSP ima tangencijalno naprezanje na zidu u rasponu od 0 do 308 Pa, a skalarno smično naprezanje u rasponu od 0 do 667 Pa. U novo razvijenoj BSP pumpi nema recirkulacijskih zona, ni zona zastoja što je sa stanovišta hemokompatibilnosti jako povoljno. Uz to BSP pumpa ima tangencijalno i skalarno smično naprezanje niže nego pumpa HM2 koju možemo smatrati vrlo dobrom izvedbom u smislu hemokompatibilnosti. The main function of the heart is to ensure continuous blood circulation to support normal body functions. Many life-threatening problems emerge if function of the heart is compromised. Therefore, if the heart is not able to ensure normal blood flow, it is extremely important that the blood flow is ensured by additional pumps called heart pumps. An artificial heart, i.e., a heart pump, is used to pump blood through the body when the heart itself is unable to do so. Cardiovascular diseases are the most common cause of death in the world. In the European Union countries, 42% of all deaths are due to cardiovascular diseases. Unfortunately, vascular system diseases are the main cause of death in Croatia. In 2016, the share of cardiovascular diseases in total mortality in Croatia was 45%, which means that almost every second person who died in Croatia, died of cardiovascular disease. A reasonable desire is to reduce these numbers, which in turn requires the development of heart pumps. Heart pumps provides the opportunity for people with heart disease to have significantly more time to receive a transplant (so-called bridge to transplantation). Also, heart pumps have the potential to permanently replace the patient heart when transplantation is not possible due to general health of the patient. In this research, a new type of heart pump is developed. The uniqueness of this pump concept is that the mechanical energy is transferred to the fluid by the rotation of flat discs without blades. Volumetric heart pumps with a diaphragm that provide pulsatile flow and heart pumps with blades that have continuous flow have already been developed. Heart pumps developed so far use shape, i.e., blades or diaphragm to transfer mechanical energy, while use of a bladeless pump as a heart pump is a complete novelty. Analytical, numerical, and experimental analyses are used to define the pump parameters that affect the heart pump hemocompatibility. The design parameters of a centrifugal bladeless heart pump are defined in relation to the reference heart pump. The HeartMate II Left Ventricular Assist Device from Thoratec Corporation (HM2) was selected as the reference heart pump. Through clinical practice, it was shown that HM2 causes the least complications and has good hemocompatibility. As part of this thesis, a bladeless heart pump (BSP) is designed. Hemocompatibility parameters of the BSP are equal to or better than HM2. Experimental analysis of the HM2 heart pump was performed in the interdisciplinary Laboratory for Artificial Cardiovascular Circulation, Faculty of Mechanical Engineering and Naval Architecture. For this purpose, an open-loop MOCK circulatory system was made for testing heart pumps. The MOCK circulatory system is made of Plexiglas and consists of a large tank, control valves, straight pipes of circular cross-section, a heart pump holder and a Venturimeter. In the experimental measurements, the prescribed standards for testing pumps defined by the ISO 9906: 2012 standard are met. The measured values are flow, pressure increase in the pump and suction pressure in the pump. All measuring chains were calibrated before the measurement and the measurement uncertainty of each individual measuring chain was assessed, according to ISO GUM standard. Measurements were performed with two different fluids: water and a solution of glycerol and water used as a substitute for blood. Based on the experimental results, the h – Q characteristic curves of the HM2 pump for both fluids are presented. The estimation of the total measurement uncertainty was performed based on the measurement uncertainty of each measuring chain and the deviation of the measured values of the h – Q curve from the regression curve. For the purposes of numerical calculation of the HM2 pump, it is necessary to know its geometry. Therefore, in the Laboratory for Precise Length Measurements, a cloud of points was obtained by precise CT scanning of the HM2 heart pump. The pump was scanned with a high-resolution detector (4000 x 3000 pixels), with a maximum CT scan resolution of 54 μm. After the described data collection, the 3D volume of the HM2 pump was reconstructed. Numerical analyses of HM2 was made in ANSYS Fluent 15.0. A 3D design of HM2, that was obtained by CT scanning, was used. The computer domain was divided into 6,4·106 control volumes, with the aim of achieving quality simulation. The mesh was refined in the boundary layer and near the joints and details. k – ω SST model was used to model turbulence. The rotation of the rotor was modeled using the Moving Reference Frame method. All numerical calculations were performed with a second order scheme of accuracy, until the result convergence and sufficient accuracy of the observed parameters was achieved. Shear stress magnitudes were calculated numerically. The Δp – Q characteristic curve for the HM2 pump was also calculated in the scope of the simulation. Quality of the numerical analysis settings was assessed by comparison of experimental and numerical results. Selected simulation settings were to be used for all further numerical calculations within this thesis. Different ranges of shear stress for which acceptable numerical hemocompatibility is achieved are reported in the literature. In this thesis, the narrowest range of 30 – 140 Pa was used for the reference shear stress range. Since these ranges are general, shear stress ranges for which hemocompatibility has been clinically confirmed have been taken from the numerical simulation of the reference heart pump HM2. The stated ranges of shear stresses need to be achieved in the numerical simulation of a bladeless centrifugal heart pump. This ensures the necessary condition of acceptable hemocompatibility for the new heart pump design. The flow inside the BSP can be divided into two parts, the flow inside the pump rotor and the flow in the connecting pipes. Energy transfer from the pump to the fluid is performed inside the rotor (active part of the pump). As the geometry of the BSP rotor is simple, it is possible to analyze the flow using Navier – Stokes equations. Although blood is a multiphase non-Newtonian fluid, the theoretical analysis introduced the assumption of blood as a single-phase Newtonian fluid with a density of 1050 kg/m3 and a dynamic viscosity coefficient of 0,0035 kg/(m s). Stationary flow was assumed, although there is a non-stationary velocity profile at the pump inlet resulting from active part of the heart. The relative Reynolds number is lower than the critical Reynolds number for the flow between the two plates, and laminar flow in the rotor was assumed. In addition to the above assumptions and limitations, a mathematical model of the flow in the BSP rotor was derived using the Navier – Stokes equations. The initial assumption was made for the rectified flow model. After that, the Navier – Stokes equation in cylindrical coordinates was solved. Algebraic expressions for the pressure field, velocity field, shear stress distribution on the disc, torque and force required for rotor rotation are derived. Furthermore, Δp – Q characteristic curve of the BSP pump was derived. Using the above terms and data obtained from the analysis of the HM2 pump, the main geometrical parameters of the BSP pump were determined. When determining the parameters, additional criteria were introduced that the structure must meet. The first and most important criterion is that the pump supplies blood within strict limits to ensure normal blood circulation throughout the body. The designed operating point Δp = 65 mmHg, Q = 5 l / min was selected for the construction of the BSP pump. Another very important criterion is high hemocompatibility and minimal negative impact of BSP on the blood (minimal thrombosis and hemolysis). The acceptable shear stress is within the range of 30 – 140 Pa. The third criterion is to achieve a minimum pump volume. The fourth criterion is the high efficiency of the pump due to the longer autonomy without charging the batteries. The first parameter selected in the theoretical analysis is the angular velocity. This parameter is independent, and all other parameters will depend on it. The designed operating point is defined at ω = 6000 rpm. From the condition that the shear stress is within the given limits, the inner radius of the disc is defined. Considering the criterion of the minimum pump volume, the outer radius of the disc and the number of discs are defined. Using the equations derived by solving the Navier – Stokes equations, the following were calculated: shear stress on the disc, pump power and torque required to rotate the rotor. Main parameters of the BSP pump were defined using theoretical analysis: pressure Δp = 65 mmHg and flow Q = 5.43 l/min at the designed operating point, angular speed ω = 6000 rpm, six discs 1 mm thick with 1 mm disc spacing, internal disc radius R1 = 12 mm, outer disc radius R2 = 15 mm. The range of shear stresses is from τϴz = 115 Pa at the bottom of the disc, to τϴz = 92 Pa at the top of the disc. The power of the pump is P = 1,324 W. The analytical equation Δp = Δp (Q) was derived from which the Δp – Q characteristic curve of the BSP pump was determined. Although all the main parameters required for the construction of a BSP pump have been derived by the theoretical analysis, it is impossible to design the geometry of the pump without numerical analysis. The ANSYS Fluent 15.0 program was used for flow analysis. The pump was analyzed as five identical computer domains. The domain consists of the space between two discs with the addition of a flow separator, and part of the domain of the inlet and outlet connecting pipes. In order to achieve a quality simulation, the domain was approximated with 1,1·105 control volumes. The mesh was refined in the boundary layer as well as near the junction of the flow separator and the connecting pipes. Turbulence was modeled with k – ε and k – ω SST turbulence models. In the thesis, gradual improvements of the pump shape are presented, up to the final fifth version of the pump shape, with which flow without stagnation and recirculation zones was achieved. The Δp – Q characteristic curve of the final version of the BSP pump design was calculated using numerical simulation. A comparison of the curves obtained by theoretical and numerical analysis shows that both curves are linear and coincide. The numerical Δp – Q characteristic curve was calculated considering the flow in the computation domain (with flow separator and connecting pipes), while the theoretical Δp – Q characteristic curve was calculated only for the rotor, i.e., the space between the disks. Therefore, resulting in incomplete coincidence between theoretical and numerical Δp – Q characteristic curves. Three parameters were used to assess the quality of the structure on hemocompatibility: wall shear stress (WSS), scalar shear stress (SSS) and residence time. The WSS in the rotor is in the range of 46 to 108 Pa, which is lower than the required value of the maximum WSS. The residence time of the fluid in the BSP pump is 0.0194 s. There is a small area (5% of the total volume) at the flow separator in which the values are higher than allowed (108 – 308 Pa). Exposure time in the area in question is short, in order of 5·10-4 s. According to the Hellums diagram for fluid residence time of 5·10-4 s, the allowable WSS is 700 Pa which is significantly higher than the calculated stress. During the numerical analysis, the SSS field was calculated, which determines the stress of the particles inside the fluid. 10% of the total volume was exposed to high linear stress in the fluid (SSS ˃ 100), 10% of the total volume was exposed to medium SSS (10

Računalna dinamika fluida (RDF) postala je gotovo konvencionalnim alatom u inženjerskoj praksi. Numeričkim rješavanjem setova jednadžbi dobiva se uvid u strujanje fluida u prostoru, a dobivena rješenja inženjerima i znanstvenicima daju mogućnost kvantifikacije strujanja u smislu sila, momenata i iskoristivosti na promatranom problemu. Visoki zahtjevi za računalnim resursima te vrijeme trajanja proračuna jedni su od glavnih izazova. Kako bi se smanjilo vrijeme potrebno za simulaciju uz očuvanje vremenske rezolucije rješenja, zbog periodičnosti strujanja u turbostrojevima moguće je koristiti tzv. spektralne metode. Spektralne metode zasnivaju se na pretvorbi veličina iz vremenske domene u frekvencijsku i obrnuto. Harmonička ravnoteža jedna je od spektralnih metoda, a često je primjenjiva u turbostrojevima. Harmonička ravnoteža svodi se na rješavanje određenog broja stacionarnih jednadžbi čiji se rezultati dobivaju za cijeli period T. Veća točnost rješenja ili smanjenje trajanja simulacije postiže se ovisno o odabranom broju harmonika. U sklopu ovog rada, izložena je teorijska pozadina matematičkog modela harmoničke ravnoteže te njegova implementacija u metodi kontrolnih volumena. Simulacije su provedene u svrhu validacije korištenja metode harmoničke ravnoteže u turbostrojevima. Proučavana su dva slučaja interakcije rotirajućih lopatičnih rešetki. U prvom slučaju razmatrana je rotirajuća rešetka rotora s mirujućom rešetkom statora, a u drugom slučaju razmatrane su rotirajuće rešetke oba rotora. Provedene su iduće simulacije: simulacija harmoničke ravnoteže na primjeru hidromlaznice uz primjenu različitog broja harmonika te simulacija harmoničke ravnoteže na primjeru kontrarotirajućih propelera. Provedena je analiza rezultata navedenih simulacija na temelju dostupnih rezultata stacionarnih i tranzijentnih simulacija. Pokazano je da harmonička ravnoteža, uz korištenje niskog broja harmonika, daje detaljniji prikaz rezultata uspoređujući sa stacionarnom MRF simulacijom, dok je za dobivanje rezultata približnima rezultatima tranzijentne simulacije broj harmonika potrebno povećati. Computational Fluid Dynamics (CFD) has become almost conventional tool in engineering practice. Solving sets of equations numerically can provide insight into fluid flow, thus giving engineers and scientists opportunity to quantify flow in terms of forces, torques and the efficiency of given problem. High demands for computer resources and simulation time are one of main drawbacks. In order to reduce simulation time while preserving the time resolution of the solution, due to periodicity of the flow in turbomachines it is possible to use the so-called spectral methods. Spectral methods are based on conversion of quantities from time domain to frequency domain and vice versa. Harmonic balance is one of spectral methods and it is often used in turbomachines. Harmonic balance is based on solving a number of stationary equations whose results are obtained for the entire period $ T $. Higher accuracy of the solution or reduction of the simulation time is achieved depending on the selected number of harmonics. As a part of this thesis, the theoretical background of the mathematical model of harmonic balance and its implementation in the finite volume method are presented. The simulations were performed for the purpose of validating the use of harmonic balance method in turbomachines. Two types of rotating grids interaction were studied. In the first case, the rotating grid of the rotor and the stationary grid of the stator was considered. In the second case, the rotating grid of both rotors was considered. The following simulations were performed: simulation of harmonic balance method on the water jet with different number of harmonics and simulation of harmonic balance method on the contra-rotating propellers. The analysis of the results was based on the available results of steady-state and transient simulations. It has been shown that with the use of lower number of harmonics given results are of high accuracy and more detailed compared to steady-state simulation, while compared to transient simulation results, the number of harmonic has to be increased.

U ovom radu provedene su numeričke simulacije pokusa otpora modela broda Japan Bulk Carrier (JBC) primjenom računalne dinamike fluida (RDF) u svrhu određivanja nominalnog sustrujanja, odnosno koeficijenta nominalnog sustrujanja. Numeričke simulacije provedene su primjenom komercijalnog programskog paketa STAR-CCM+. Izvršene su tri grupe numeričkih simulacija: numeričke simulacije s modelom broda sa slobodnom površinom, numeričke simulacije s udvojenim modelom (eng. double body) bez slobodne površine te numeričke simulacije s udvojenim modelom bez slobodne površine s profinjenom geometrijskom mrežom u području gdje će biti smješten brodski vijak. Svaka grupa numeričkih simulacija sastoji se od tri simulacije različitih gustoća mreža s k-ω SST modelom turbulencije te simulacije uz primjenu fine mreže i k-ε modela turbulencije. Za prvu grupu simulacija primijenjen je model nestacionarnog trodimenzijskog viskoznog strujanja, dok je za drugu i treću grupu primijenjen stacionarni model trodimenzijskog viskoznog strujanja. Unutar numeričkih simulacija sa slobodnom površinom primijenjena je metoda udjela fluida u volumenu (eng. Volume of Fluid-VOF) za praćenje i lociranje slobodne površine. Numeričko određivanje nominalnog sustrujanja provedeno je pri jednom Froudeovom broju. Izvršena je verifikacija numeričkih rezultata te je izračunata numerička nesigurnost pri određivanju nominalnog sustrujanja primjenom metode indeksa konvergencije mreže (eng. Grid Convergence Index method-GCI). Dobiveni numerički rezultati uspoređeni su s eksperimentalnim podacima dostupnim u literaturi. Pokazano je kako računalna dinamika fluida daje zadovoljavajuće rezultate te stoga može biti vrlo koristan alat za određivanje nominalnog sustrujanja. In this study, numerical simulations of the resistance test for the Japan Bulk Carrier (JBC) model are performed using Computational Fluid Dynamics (CFD) for the assessment of the nominal wake, i.e. the nominal wake fraction. Numerical simulations are performed using the commercial software package STAR-CCM+. Three groups of numerical simulations are carried out: numerical simulations with a ship model with free surface, numerical simulations with a double body model without free surface, and numerical simulations with a double body model without free surface with the refined mesh in the area where a propeller will be placed. Each group of numerical simulations is consisted of three simulations with different mesh densities and k-ω SST turbulence model, and one simulation with the fine mesh and k-ε turbulence model. For the first group of simulations, the model based on unsteady three-dimensional viscous flow is used, while for the remaining ones, the model based on steady three-dimensional viscous flow is used. Within numerical simulations with free surface, the Volume of Fluid (VOF) method is applied for tracking and locating free surface. The numerical assessment of the nominal wake is performed at one Froude number. The obtained numerical results are verified and the numerical uncertainty in the prediction of nominal wake is calculated using the Grid Convergence Index (GCI) method. The obtained numerical results are compared with the experimental data available in the literature. It is shown that CFD can provide satisfactory results and that it can be a valuable tool in the assessment of nominal wake.

U diplomskom radu je provedena CFD analiza strujanja zraka oko rotora vjetroturbine snage 1 kW koja je oblikovana Wortmannovim aeroprofilima. Nakon analize strujanja zraka oko rotora, napravljena je usporedba s vjetroturbinom koja je izrađena od Althausovih aeroprofila čija je autorica kolegica Mihaela Erceg. Ograničenja koja su postavljena autoru su snaga rotora vjetroturbine koja mora biti 1 kW i aeroprofili koji moraju biti oznake Wortmann. Uzimajući u obzir ograničenja, kreće se u prelimirarnu fazu osnivanja i razvoja vjetroturbine iz koje se oblikuje geometrija konačnog seta aeroprofila. Sljedeća faza je oblikovanje geometrije u odgovarajućem softveru platforme Ansys. Zatim slijedi generiranje mreže vodeći računa o graničnom sloju. Nakon svega slijedi CFD simulacija u rješavaču Fluent na temelju čijih rezultata se vrši usporedba polja fizikalnih veličina kod dvije različite vjetroturbine i donosi se konačan zaključak po pitanju efikasnosti. Na kraju su navedeni prijedlozi za poboljšanje procesa osnivanja i razvitka vjetroturbine., In this master’s thesis, a CFD analysis of wind flow around 1 kW wind turbine rotor defined by Wortmann airofils was conducted. After wind flow analysis around wind turbine rotor, a comparison was made with the windturbine that was made of Althaus airfoils whose author is a colleague Mihaela Erceg. Limits set up upon author were the power of a windturbine rotor which is 1 kW and airfoils which must be a Wortmann brand. Regarding the limits, the development starts with the preliminary phase of establishing and developing windturbine which is a start point for modelling the final set of airfoils. Next step is modelling geometry in a certain software of the platform Ansys. Next comes mesh generation taking into account boundary layer. After all, next comes CFD simulation in solver Fluent whose results are used to compare field of physical quantities for two different windturbines and a final conclusion is made regarding wind turbine efficiency. Lastly, suggestions for improvement have been made for the process of founding and developing windturbine.

Regulacijski ventili su ključni elementi u procesnim postrojenjima. Služe za regulaciju tlaka i protoka, ali utječu i na druge varijable procesa. Tlak se u ventilu često smanjuje pomoću trimova, čija izvedba ovisi o intenzitetu smanjenja tlaka. U ovome je radu predložen postupak dimenzioniranja višestupanjskog cilindričnog rupičastog trima koji služi za redukciju tlaka prirodnog plina, korištenjem računalne mehanike fluida. Za provedbu numeričkih proračuna turbulentnog strujanja stlačivog fluida korišten je programski paket ANSYS/FLUENT ®. Predloženi postupak dimenzioniranja trima temelji se na provedbi numeričkih simulacija strujanja kroz parametarski model periodičkog uzorka trima, pri čemu se određuje potreban broj stupnjeva trima za traženo smanjenje tlaka, te promjeri provrta na pojedinim stupnjevima trima tako da se postigne zadani protok prirodnog plina bez zagušenja. Da bi se provjerile performanse ventila s ugrađenim višestupanjskim trimom, provedena je numerička simulacija strujanja prirodnog plina kroz ventil i nizvodnu cijev. Ventil mora obavljati svoju osnovnu funkciju tako da intenzitet buke bude ispod dozvoljenih vrijednosti. U radu je proveden analitički proračun buke prema normi IEC 60534-8-3 na temelju numerički određenih polja brzine u karakterističnim presjecima ventila. Control valves are key elements in process plants. They serve to regulate pressure and flowrate, but also affect other process variables. The pressure in the valve is usually reduced using trims, whose design depends on the intensity of the pressure reduction. In this thesis, a new sizing procedure of multistage trim for natural gas pressure reduction is proposed and it is based on application of computational fluid dynamics. Numerical simulations of turbulent flow of compressible fluid are performed using ANSYS/FLUENT ® software package. The proposed procedure of trim sizing is based on conducting numerical simulations of flow through the parametric model of the periodic trim sample, determining the required number of trim stages for the required pressure reduction, and bore diameters at individual trim stages to achieve a given natural gas flowrate without choking. To check the performance of the valve with built-in multistage trim, a numerical simulation of natural gas flow through the valve and downstream pipe was performed. The valve must perform its basic function so that the noise intensity is below the permitted values. In this thesis analitical calculation of noise according to IEC 60534-8-3 standard based on numerically determined velocity fields in the characteristic cross sections of the valve was performed.

U sklopu diplomskog zadatka provedena je numerička analiza strujanja zraka oko kotača bicikla za tri različite izvedbe oblika obruča: - Izvedba s obručem dubine 50 mm i 20 žbica, - Izvedba s obručem dubine 60 mm i 3 krute žbice (zvijezda izvedba), - Izvedba s punim obručem (disk izvedba). Geometrijski modeli kotača izrađeni su u programu SolidWorks®, prostorna domena je diskretizirana pomoću programa Ansys Fluent Meshing®, a numeričke simulacije su provedene pomoću programa Ansys Fluent® koji se temelji na primjeni metode konačnih volumena. Aerodinamičke karakteristike kotača (sila otpora, sila uzgona i bočna sila) su promatrane u ovisnosti o intenzitetu brzine i napadnom kutu strujanja zraka. Numerička analiza je provedena za intenzitete brzine od 11,11 m/s (40 km/h), 12,50 m/s (45 km/h) i 13,88 m/s (50 km/h) te napadne kutove od 0°, 5° i 10° jer se taj raspon vrijednosti brzina i napadnih kutova najčešće javlja tijekom biciklističkih utrka. Nakon provedene numeričke analize dan je komparativni pregled aerodinamičkih karakteristika kotača u ovisnosti o intenzitetu brzine, napadnom kutu i obliku obruča kotača. As a part of this master thesis numerical analysis of air flow around the bicycle wheels was conducted for three different types of bicycle wheels: - Wheel with rim cross section depth of 50 mm and 20 spokes, - Wheel with rim cross section depth of 60 mm and 3 stiff spokes (trispoke wheel), - Wheel with full rim cross section (disc wheel). Geometrical models of bicycle wheels were made in 3D modeling program SolidWorks®, discretization of spatial domain was made in program Ansys Fluent Meshing®, and numerical analysis was conducted in program Ansys Fluent® which is based on finite volume method. Aerodynamic characteristics (drag force, lift force and side force) of bicycle wheels were studied with regards to changes of velocity intensity and changes of yaw angle. Therefore numerical analysis was conducted for inlet velocities of 11,11 m/s (40 km/h), 12,5 m/s (45 km/h), 13,88 m/s (50 km/h), and yaw angles of 0°, 5° and 10° because these values resemble range that commonly occurs during bicycle races. After the conclusion of numerical analysis comparative overview of aerodynamic characteristics with regards to inlet velocities, yaw angles and types of the bicycle wheels was given.

U ovom radu su prikazane različite vrste hidrauličkih turbina u postrojenjima za proizvodnju električne energije. Analiziraju se njihove glavne karakteristike da bi se razumijelo u kojem području raspoloživih vodenih padova i protoka se mogu efikasno koristiti. Također se razmatraju cijevne turbine za postrojenja koja koriste energiju plime i oseke te turbine-pumpe za postrojenja koja skladište energiju. Prikazano je kako odabrati osnovne veličine cijevne turbine uz pomoć osnovnih projektnih parametara. Proračunavaju se komponente brzina na ulazu u rotor, izlazu iz rotora, izlazu iz statora te kutove relativne brzine β_2 i β_3 . Prikazan je i proračun pada tlaka kroz rotorske lopatice. Zadatak ovog rada bio je izraditi parametarski geometrijski model protočnog dijela cijevne turbine. Pomoću m4 kompjuterskog jezika prikazana je parametrizacija geometrijskog modela cijevne turbine unutar koje se promjenom vanjskog promjera rotora mijenja cijeloukupna geometrija cijevne turbine. Numerički proračuni cijevne turbine izvršeni su u programskom paketu OpenFOAM. Korišten je model nestlačivog stacionarnog turbulentnog strujanja te je turbulencija modelirana pomocu k-ω SST modela turbulencije. U rezultatima simulacije cijevne turbine prikazano je polje brzine te padovi tlaka kroz turbinu. This thesis presents different types of hydraulic turbines for electric power plants. Their main characteristics are analyzed to understand in which range of head and flow rate they can be used efficiently. Bulb turbines for tidal energy plants and reversible pump-turbines for pumped storage plants are also considered. The task of this thesis was to show how to choose general dimensions of bulb turbine by knowing basic design parameters. Also, velocity components at the rotor inlet, rotor outlet, stator outlet and relative velocity angles (β_2 and β_3) are calculated. The calculation of the pressure drop through the rotor blades is also shown. Numerically parameterized model is made using the m4 computer language. The parameterization of the geometric model is shown, within which the overall geometry of the bulb turbine changes by replacing the value of the rotors outer diameter. The numerical calculations for bulb turbine were made in the OpenFOAM software package. Incompressible steady-state turbulent flow model was used, and turbulence was modeled using a k - ωSST turbulence model. The analysis of the result shows velocity eld and pressure drop eld trough turbine.

Procjena dodatnog otpora broda na valovima od velike je važnosti s ekološkog i ekonomskog aspekta. Dodatni otpor uzrokuje pad brzine plovidbe te utječe na povećanje zahtijevane snage i potrošnje goriva broda, a samim time i emisije štetnih plinova. Međunarodna pomorska organizacija (engl. International Maritime Organization, IMO), uvodi sve strože propise za smanjenje i kontrolu emisije štetnih plinova u pomorskoj industriji. Tako novi brodovi moraju zadovoljiti tehničke mjere, a postojeći brodovi operativne mjere s ciljem povećanja energetske učinkovitosti brodova i smanjenja emisije CO2. Iz tog je razloga već u preliminarnoj fazi osnivanja broda vrlo važno procijeniti povećanje otpora uslijed plovidbe broda na valovima za stanja mora na kojima će brod tijekom službe ploviti. Dodatni otpor na valovima vremenski je osrednjena vrijednost sile drugog reda, koja nastaje uslijed interakcije nailaznih valova i valova generiranih odzivom broda. S obzirom na zanemarive učinke viskoznosti, dodatni otpor moguće je razmatrati kao neviskoznu pojavu što omogućuje primjenu metoda i rješavača temeljenih na teoriji potencijalnog strujanja idealnog fluida, ali i ekstrapolaciju rezultata s modela na brod bez utjecaja mjerila. Obzirom da pouzdano određivanje dodatnog otpora na valovima zahtijeva provođenje složenih hidrodinamičkih proračuna, u okviru doktorskog rada razvijen je numerički model, koji se temelji na rezultatima hidrodinamičkih proračuna i umjetnoj neuronskoj mreži. Jedna od prednosti umjetne neuronske mreže je mogućnost aproksimacije rješenja složenih nelinearnih i viševarijabilnih problema bez poznavanja fizikalnog modela. Kako bi osnovani numerički model osigurao rezultate zadovoljavajuće točnosti, proveden je proces učenja umjetne neuronske mreže na temelju rezultata hidrodinamičkih proračuna kontejnerskih brodova različitih formi i značajki te za različita stanja mora. Dodatni otpor broda na pravilnim valovima određen je metodom rubnih integralnih jednadžbi (engl. Boundary Integral Equation Method, BIEM), a primjenom spektralne analize energije nepravilnih morskih valova određene su srednje vrijednosti dodatnog otpora za različita stanja mora definirana sa značajnom valnom visinom i periodom vala. Također, proveden je postupak validacije i verifikacije dobivenih numeričkih rezultata. U radu je provedena analiza osjetljivosti dodatnog otpora na pravilnim i nepravilnim valovima na različite značajke broda, s ciljem definiranja varijabli ulaznog vektora umjetne neuronske mreže. Analizirane su različite strukture unaprijedne statičke umjetne neuronske mreže s povratnim prostiranjem pogreške i jednim skrivenim slojem, parametri te različiti algoritmi učenja mreže. Istražen je i utjecaj načina pripreme podataka za proces učenja mreže na dobivene rezultate te prednosti primjene analize glavnih komponenata kao i klasifikacije podataka za učenje. Osnovani numerički model od posebne je praktične koristi u preliminarnoj fazi projektiranja kontejnerskog broda, kako bi se u kratkom roku i s točnošću procijenio dodatni otpor broda na valovima ovisno o planiranoj ruti plovidbe za koju se brod projektira. Za postojeće kontejnerske brodove, osnovani numerički model moguće je koristiti za procjenu dodatnog otpora pri različitim brzinama plovidbe i za različita stanja mora te tako doprinijeti planiranju rute plovidbe, posebice za izraženija stanja mora, uz ograničenje valova direktno u pramac. Evaluation of the ship added resistance in waves has increased in importance, especially from an economic as well as from an environmental protection point of view. Ship added resistance in waves causes a reduction in ship speed and has an impact on the increase in the fuel consumption and CO2 emission. The International Maritime Organization, IMO subjected the emission of harmful gases to increasingly stringent regulations, via the introduction of mandatory technical measures for new ships and operational measures for existing ships, with the aim of increasing the energy efficiency of ships and reducing CO2 emissions. For that reason, it is very important to predict the increase in ship resistance due to waves and power required for the ship sailing at an actual sea state, already in the ship design phase and when planning the sailing route of existing ships. Added resistance in waves is a time-averaged second order force consisted of three parts. When sailing in waves, ship generates two systems of waves: waves due to sailing in calm water and waves caused by the ship response to incoming waves. The first and largest part of added resistance arises due to the interference of waves generated by the ship, i.e. radiation waves mainly due to heave and pitch motions, and incoming waves. It is often called the drift force, although the drift force in the longitudinal direction of a ship is equal to the added resistance in waves only in the case of zero speed. The ship relative motions become large when the length of the ship is approximately equal to the wavelength, which corresponds to peak value of added resistance. At very long waves, when relative motions are negligible, the wave force corresponds to Froude-Krylov force that would ideally act on the ship hull in the absence of a diffraction component. On the other hand, in short waves the diffraction of incoming waves on the ship hull increases the second part of added resistance, i.e. the diffraction force with emphasized nonlinear effects. The third component is related to the viscous damping of the heave and pitch motions of the ship and is negligible in relation to the hydrodynamic damping of the motions (radiation waves). Therefore, added resistance is considered as a non-viscous phenomenon, which allows the application of methods and solvers based on the potential flow theory, but also an extrapolation of the results from model scale to ship scale without the scale effects. Analytical methods, methods based on the potential flow theory and the ones based on viscous flow theory are used for the evaluation of the ship added resistance in waves. Since the determination of the ship seakeeping characteristics and added resistance in waves requires rather complex hydrodynamic calculations to ensure an acceptable accuracy of the results, within this research a model that allows simple but sufficiently accurate and reliable evaluation of the ship added resistance sailing at an actual sea state is developed. Such model can have a practical benefit both during the ship design phase or while planning a favourable sailing route of a ship in service. The basis of the developed model is the results of hydrodynamic calculations of added resistance in waves for various hull forms at different sea states and artificial neural network, which has the ability to learn from examples and to discover relationships between the input data and solutions to the nonlinear multivariable regression problems. Hull forms of modern container ships with different types of bow and stern, section type and block coefficient (prismatic coefficient) are generated in order to create a sufficiently large database for the training process. The original hull forms with different main characteristics are modified in order to extend the range of prismatic coefficients and to obtain different longitudinal positions of the center of buoyancy. The influence of the ship mass characteristics, i.e. the vertical position of the center of gravity and the pitch radius of inertia, on the added resistance in regular regular waves is investigated, while the ship design speed is determined based on the regression analysis results. The results of the regression analysis also defined the variation range of the prismatic coefficient, in respect to the limitations of the method used for the hull form modification. Hydrodynamic calculations are conducted using the Boundary Integral Equations Method, BIEM based on the potential flow theory. Generated hull forms are discretized by flat panels and hydrodynamic calculations of added resistance in regular waves are performed. The numerical results obtained using panel method are compared to the ones obtained using finite volume method, FVM based on the viscous flow theory for benchmark containership KCS. In the defined incoming wave frequency range, the sensitivity analysis is carried out in order to define the neural network input parameters. The most important parameters affecting the added resistance in waves are the ship geometry, response in waves and the characteristics of the incoming waves. Since the ship response to incoming waves is highly dependent on the hull geometry, and transfer functions are often unknown in the preliminary design phase, it is practical to define ship main characteristics as the input parameters of the neural network. The obtained numerical results are validated against the available experimental data and verified, i.e. the numerical uncertainty is assessed. Top container ship sailing routes are analyzed and sea states with the highest probability of occurrence for waves coming from all directions and head waves for a given route are extracted based on the global wave atlas (Global Wave Statistics). For the numerically obtained results of added resistance in regular waves, spectral analysis is performed using two-parameter theoretical wave energy spectra: Bretschneider spectrum for unlimited and JONSWAP spectrum for limited fetch. In this way, the results of added resistance in irregular waves, i.e. at different sea states that ship may encounter during lifetime, are obtained. Feedforward artificial neural network with error back propagation and one hidden layer of neurons is generated as the basis of the numerical model for the estimation of ship added resistance in waves. A possible significant advantage of neural networks is that they do not require a known physical model of the before mentioned complex hydrodynamic problem. Based on the analysis of different neural network architectures, i.e. by varying the number of neurons in the hidden layer, learning rate and momentum parameters, as well as by performing an analysis of the results obtained using different learning algorithms, an adequate artificial neural network is set. The training process is performed using the results of hydrodynamic calculations, which are adequately prepared and divided into data sets for learning, validation and testing. The evaluation of the accuracy and generalization property of the neural network is evaluated based on the normalized value of the root mean square error. A multivariable linear regression analysis is also performed as well as principal component analysis in order to represent the input variables of the neural network with linearly independent variables. The generalization properties of the neural network employed for the evaluation of added resistance in waves is also analyzed for different wave headings, which increases the complexity and nonlinearity of the given problem. The developed numerical model has 12 input variables, 65 neurons in one hidden layer and is based on Levenberg-Marquard learning algorithm with Bayesian regularization. The model incorporates three sub models based on the classification of data according to the wave zero crossing period.

Tema ovog rada je numeričko istraživanje interakcije malih vodnih turbina i dinamike riječnog korita pomoću računalne dinamike fluida. Strujanje vode iza turbine je turbulentno i utječe na sedimentno dno rijeke, što može imati značajan utjecaj na ekosustav rijeke, ali i na stabilnost podvodnih struktura, zbog čega su potrebna daljnja istraživanja. U ovom radu korištene su jednadžbe za opisivanje strujanja i interakcije strujanja fluida sa sedimentom i slobodnom površinom, pomoću foam-extend-a. Proučavana je aksijalna turbina s tri lopatice, a simulacije su provedene za četiri konfiguracije turbina u kanalu: • jedna turbina na sredini kanala, • dvije turbine postavljene koaksijalno na sredini kanala, udaljene za 4dt , • dvije turbine postavljene koaksijalno na sredini kanala, udaljene za 7dt , • dvije turbine postavljene jedna uz drugu kraj bočne strana kanala. Rezultati simulacija uspoređeni su međusobno i s dostupnim rezultatima eksperimenata Računalna dinamika fluida može preuzeti značajnu ulogu u proučavanju utjecaja turbina na morfologiju dna, jer uvelike pojednostavljuje i olakšava proučavanje ove problematike. Scope of this Thesis is numerical investigation of interaction between small hydraulic turbines and river sediment dynamics. Water flow behind turbines is turbulent and affects sediment river bed, which can have significant influence on the river ecosystem, but also on underwater structures stability, and further investigation is needed. In this Thesis equations that describe fluid flow and interaction between fluid and sediment river bed and free surface are used, together with foam-extend. Axial turbine with three blades is observed, and simulations were performed for four configurations of turbines in the channel: one turbine in the centre of the channel, two coaxial turbines, in the centre of the channel, with 4dt distance, two coaxial turbines, in the centre of the channel, with 7dt distance, two turbines positioned side by side, near the channel side. The simulation results were compared mutually and with the available experimental data. Computational Fluid Dynamics can play a significant part in investigation of turbine and river morphology interactions, making the analysis of given problems easier and simpler.

Prilikom provedbe pokusa otpora broda u bazenu manjih dimenzija, moguća je pojava utjecaja bočnih stijenki na izmjerene vrijednosti. Utjecaj stijenki postaje sve izraženiji povećanjem brzine i dimenzije modela broda te je stoga potrebno korigirati izmjerenu silu otpora broda. Numeričke simulacije strujanja fluida oko trupa broda za jednotrupni Wigley-ev model te tri katamaranske konfiguracije s Wigley-evim modelom broda u neograničenoj i ograničenoj vodi provedene su primjenom komercijalnog programskog paketa za računalnu dinamiku fluida STAR-CCM+. Ispitivanja su provedena s ciljem određivanja utjecaja bočnih stijenki bazena na ukupni otpor broda. Proračunska domena diskretizirana je metodom konačnih volumena te su definirani rubni uvjeti i fizikalni model. Detaljno je prikazan matematički model temeljen na Reynoldsovim osrednjenim Navier-Stokesovim jednadžbama (RANS). U numeričkim simulacijama je primijenjen k-ω SST model turbulencije. Za praćenje i određivanje položaja slobodne površine primijenjena je metoda udjela volumena u fluidu (eng. “Volume of Fluid-VOF“). Za modeliranje strujanja u blizini stijenke primijenjene su zidne funkcije. Proveden je postupak verifikacije za gustoću geometrijske mreže i vremenski koraka za jednotrupni Wigley-ev model i katamaranske konfiguracije u neograničenoj i ograničenoj vodi. Dobiveni numerički rezultati validirani su s eksperimentalnim rezultatima dostupnim u literaturi. Određen je utjecaj razmaka između trupova katamarana na ukupni otpor preko faktora interferencije. Konačno, provedena je analiza utjecaja stijenki bazena na ukupni otpor, sliku valova, hidrodinamički tlak i tangencijalna naprezanja. When carrying out the resistance test in small towing tank the blockage effect may occur. Influence of the blockage effect becomes more and more pronounced with the increased of the ship speed and model dimension. Therefore it is necessary to correct dimension value of total resistance. Numerical simulations of flow round the ship hull for Wigley monohull and three catamaran configuration with Wigley model in unrestricted and restricted water are preformed using the commercial software package for Computational Fluid Dynamics STAR-CCM+. The investigations are performed with the aim of determining the blockage effect on ship resistance. Computational domain is discretized by the finite volume method and boundary conditions and physical model are defined. Mathematical model based on the Reyolds Averaged Navier-Stokes (RANS) equations is presented in detail. The k-ω SST turbulence model is applied in numerical simulations, the volume of fluid method is used for tracking and locating the free surface. Wall functions are applied for modelling the flow near the wall. The verification study regarding grid size and time step for Wigley monohull and three catamaran configurations in unrestriced and restricted water is carried out. The obtained numerical results are validated with the experimental available in the literature. The influence of separation between demihulls on total resistance by means of interference factor is determined. Finally, the analysis of blockage effect on total resistance, wave pattern, hydrodynamic pressure and wallocl shear stresses is carried out.

Navier-Stokesova jednadžba opisuje gibanje viskoznih fluida. Korisna je pri opisu fizikalnih procesa u problemima koji su zanimljivi u znanosti i inženjerstvu. Dinamika fluida je grana fizike koja je, uz zakone termodinamike, opisana Navier-Stokesovom jednadžbom i jednadžbom kontinuiteta. Analitičko rješenje spometnutih jednadžbi je poznato samo za jednostavne slučajeve. Stoga, u rješavanju Navier-Stokesove jednadžbe veliku ulogu imaju numeričke metode. U ovom radu se bavimo podgranom dinamike fluida koja se zove računalna dinamika fluida. Računalna dinamika fluida podrazumijeva korištenje numeričkih metoda za rješavanje problema toka fluida te se često primjenjuje kao alat za validaciju jednostavnijih modela. U ovom radu koristit ćemo računalnu dinamiku fluida u svrhu validacije modela rashladnog sustava električnog vozila. Rashladni sustav električnog vozila modeliramo na osnovi fizikalnih jednadžbi uzimajući u obzir najrelevantnije geometrijske veličine. Model, koji će biti pisan u C++ programskom jeziku, treba biti jednostavan i imati kratko vrijeme izvođenja. Zasebno modelirane komponente ćemo spojiti u rashladni sustav. Tada, cijeli rashladni sustav kao zasebnu jedinicu spajamo sa softverom AVL VSM koji služi za simulacije dinamike vozila. Pokretanjem simulacija vožnje određene putanje, promatrat ćemo utjecaj rashladnog sustava na temperaturu ćelije i posljedično performanse vozila. Rezultate za pojedinu komponentu modeliranog rashladnog sustava ćemo usporediti sa rezultatima koji se dobiju koristeći računalnu dinamiku fluida. Navier-Stokes equation describes the motion of viscous fluids. It is useful in describing physical processes in problems of interest in science and engineering. Fluid dynamics is a branch of physics which, along with the laws of thermodynamics, is described by the Navier-Stokes equation and the continuity equation. The analytical solution of the mentioned equations is known only in simple cases. Therefore, numerical methods play a major role in solving the Navier-Stokes equation. In this thesis, we deal with a sub-branch of fluid dynamics called computational fluid dynamics. Computational fluid dynamics involves the use of numerical methods to solve fluid flow problems and is often used as a tool in validating simpler models. In this thesis, we will use computational fluid dynamics for the purpose of validating a cooling system model of an electric vehicles. The cooling system of an electric vehicle is modeled on the basis of physical equations taking into account the most relevant geometric quantities. The model, which will be written in the C ++ programming language, should be simple and have a short execution time. Separately modelled components will be connected to the cooling system. Then, the entire cooling system as a separate unit is connected to the AVL VSM software, which is used to simulate vehicle dynamics. By running driving simulations of a certain maneuver, we will observe the influence of the cooling system on the cell temperature and consequently the vehicle performance. The results for each component of the modeled cooling system will be compared with the results obtained using computational fluid dynamics.

U zadnjih nekoliko desetljeća u automobilskoj industriji se sve više pažnje posvećuje učinkovitosti vozila u smislu njihove potrošnje energije. Motivi su kroz povijest bili različiti, poput rasta cijene nafte u 80-im godinama prošloga stoljeća, no danas se pojavom električnih vozila i rastom ekološke svijesti sve više resursa i vremena ulaže u optimizaciju učinkovitosti novih vozila. Područje čijom se optimizacijom može napraviti značajan pomak u učinkovitosti potrošnje energije vozila je aerodinamika. Također, razvojem sigurnosnih sustava i sustava autonomije u novim i budućim vozilima, ukida se potreba za retrovizorima koji se u tom slučaju mogu zamijeniti kamerama ugrađenim u karoseriju automobila u slučaju da vozilo nije u potpunosti autonomno. Zadatak ovog rada bio je provesti numeričku simulaciju utjecaja retrovizora na ukupnu aerodinamičku silu koja djeluje na automobil. Geometrija je preuzeta sa interneta u STEP formatu i zatim prerađena u svrhu zadatka, pa su tako izrađena dva modela za potrebe numeričke simulacije. Jedan model predstavlja klasični električni automobil, dok su na drugom modelu uklonjeni retrovizori sa bočnih strana geometrije. Numerička simulacija provedena je u OpenFOAM-u, te su rezultati post-procesirani u Paraview-u. Prikazani su ključni presjeci geometrijske mreže i raspodjela fizikalnih polja brzina i tlakova na tim presjecima, isto kao i raspodjela tlaka na samoj površini automobila. Također je izračunat aerodinamički koeficijent otpora automobila za svaki od korištenih modela pomoću kojeg je prikazano poboljšanje u aerodinamičkoj učinkovitosti automobila bez retrovizora. Nakon toga je proveden pojednostavljen proračun utjecaja takve promjene u geometriji na potrošnju energije automobila. Prikazani su dijagrami snage potrebne za svladavanje aerodinamičke sile koju stvara pojedini model pri kretanju konstantnom brzinom na konstantnoj nadmorskoj visini, te ukupni utjecaj tih promjena na snagu potrebnu za pokretanje takvog vozila. S obzirom na to da utjecaj aerodinamike postaje značajan tek pri većim brzinama, dijagrami su prikazani za brzine od 70 do 150 kilometara na sat.U zadnjih nekoliko desetljeća u automobilskoj industriji se sve više pažnje posvećuje učinkovitosti vozila u smislu njihove potrošnje energije. Motivi su kroz povijest bili različiti, poput rasta cijene nafte u 80-im godinama prošloga stoljeća, no danas se pojavom električnih vozila i rastom ekološke svijesti sve više resursa i vremena ulaže u optimizaciju učinkovitosti novih vozila. Područje čijom se optimizacijom može napraviti značajan pomak u učinkovitosti potrošnje energije vozila je aerodinamika. Također, razvojem sigurnosnih sustava i sustava autonomije u novim i budućim vozilima, ukida se potreba za retrovizorima koji se u tom slučaju mogu zamijeniti kamerama ugrađenim u karoseriju automobila u slučaju da vozilo nije u potpunosti autonomno. Zadatak ovog rada bio je provesti numeričku simulaciju utjecaja retrovizora na ukupnu aerodinamičku silu koja djeluje na automobil. Geometrija je preuzeta sa interneta u STEP formatu i zatim prerađena u svrhu zadatka, pa su tako izrađena dva modela za potrebe numeričke simulacije. Jedan model predstavlja klasični električni automobil, dok su na drugom modelu uklonjeni retrovizori sa bočnih strana geometrije. Numerička simulacija provedena je u OpenFOAM-u, te su rezultati post-procesirani u Paraview-u. Prikazani su ključni presjeci geometrijske mreže i raspodjela fizikalnih polja brzina i tlakova na tim presjecima, isto kao i raspodjela tlaka na samoj površini automobila. Također je izračunat aerodinamički koeficijent otpora automobila za svaki od korištenih modela pomoću kojeg je prikazano poboljšanje u aerodinamičkoj učinkovitosti automobila bez retrovizora. Nakon toga je proveden pojednostavljen proračun utjecaja takve promjene u geometriji na potrošnju energije automobila. Prikazani su dijagrami snage potrebne za svladavanje aerodinamičke sile koju stvara pojedini model pri kretanju konstantnom brzinom na konstantnoj nadmorskoj visini, te ukupni utjecaj tih promjena na snagu potrebnu za pokretanje takvog vozila. S obzirom na to da utjecaj aerodinamike postaje značajan tek pri većim brzinama, dijagrami su prikazani za brzine od 70 do 150 kilometara na sat. In the last few decades, the automotive industry has increasingly focused on the efficiency of vehicles in terms of their energy consumption. Motives have varied throughout history, such as the rise in the price of oil in the 1980s, but today the advent of electric vehicles and the rise of environmental awareness, more resources and time are being invested in optimizing efficiency of new vehicles. An area whose optimization can make a significant shift in vehicle energy efficiency is aerodynamics. Also, with the development of safety and autonomy systems in new and future vehicles, the need for rear-view mirrors is eliminated, because they can be replaced by cameras fitted to the car body if the car is not fully autonomous. The task of this paper wast to perform a numerical simulation of the influence of the rearview mirrors on the total aerodynamic force acting on the car. The geometry was downloaded in STEP format and hen reworked for the purpose of the task, so two models were created for the purpose of numerical simulation. One model is a classic electric car, while the other model has no side mirrors. Numerical simulation was performed in OpenFOAM and the results where post-processed in Paraview. The key sections of the mesh and the distribution of the velocity and pressure fields at these sections are shown, as well as the pressure distribution at the very surface of the car. The aerodynamic drag coefficient of the car was also calculated for each of the models used, showing the improvement in the aerodynamic efficiency of the car without the rearview mirrors. Subsequently, a simplified calculation of the effect of such a change in geometry on the energy consumption was carried out. The diagram of power required to overcome the aerodynamic force generated by an individual model at constant speed and altitude, and the diagram of the overall impact of these changes on the power required to drive such a vehicle are shown. As the impact of aerodynamics becomes significant only at higher speeds, diagrams are shown for speeds of 70 to 150 kilometers per hour.In the last few decades, the automotive industry has increasingly focused on the efficiency of vehicles in terms of their energy consumption. Motives have varied throughout history, such as the rise in the price of oil in the 1980s, but today the advent of electric vehicles and the rise of environmental awareness, more resources and time are being invested in optimizing efficiency of new vehicles. An area whose optimization can make a significant shift in vehicle energy efficiency is aerodynamics. Also, with the development of safety and autonomy systems in new and future vehicles, the need for rear-view mirrors is eliminated, because they can be replaced by cameras fitted to the car body if the car is not fully autonomous. The task of this paper wast to perform a numerical simulation of the influence of the rearview mirrors on the total aerodynamic force acting on the car. The geometry was downloaded in STEP format and hen reworked for the purpose of the task, so two models were created for the purpose of numerical simulation. One model is a classic electric car, while the other model has no side mirrors. Numerical simulation was performed in OpenFOAM and the results where post-processed in Paraview. The key sections of the mesh and the distribution of the velocity and pressure fields at these sections are shown, as well as the pressure distribution at the very surface of the car. The aerodynamic drag coefficient of the car was also calculated for each of the models used, showing the improvement in the aerodynamic efficiency of the car without the rearview mirrors. Subsequently, a simplified calculation of the effect of such a change in geometry on the energy consumption was carried out. The diagram of power required to overcome the aerodynamic force generated by an individual model at constant speed and altitude, and the diagram of the overall impact of these changes on the power required to drive such a vehicle are shown. As the impact of aerodynamics becomes significant only at higher speeds, diagrams are shown for speeds of 70 to 150 kilometers per hour.

Trafostanice su postrojenja u kojima se transformira napon s visokih vrijednosti na niske i obrnuto. Prilikom rada, transformatorska oprema se grije i na taj način stvar toplinsko opterećenje prostorije te je nužno projektirati sustav cjelogodišnjeg hlađenja. Kako bi se projektiranje termotehničke opreme (eng Heating, Ventilation, Air Conditioning, u daljnjem tekstu HVAC) izvršilo prema zakonskim propisima, potrebno je simulirati toplinsko opterećenje i dokazati da će zadano rješenje sustava hlađenja zadovoljiti projektne zahtjeve. U ovom slučaju dominantan mehanizam prijenosa topline, odnosno stvaranja toplinskog opterećenja, je putem prisilne konvekcije pomoću ventilatora transformatorskih ormara. Na taj način zrak iz prostorije ulazi u ormar, hladi zavojnice transformatora, a topli zrak izlazi kroz krovni ispust ormara transformatora nazad u prostoriju. Vanjsko toplinsko opterećenje putem mehanizma sunčevog zračenja i konvekcije toplog zraka na zidove je zanemarivo naspram razlika temperatura, ali je ipak modelirano kao izotermni rubni uvjet temperature stjienke s unutrašnje strane prostorije kako bi se pojednostavio proračunski model. Proračun je izvršen za najgori slučaj, pri ljetnim uvjetima, odnosno pri vanjskoj projektnoj temperaturi zraka od 35 C. Koeficijenti prolaza topline kroz stijenke zidova su preuzeti iz arhitektonskog projekta. Projektiranje položaja i količine elemenata sustava može predstavljati izazov. Uz pomoć alata računalne dinamike fluida (eng. Computational Fluid Dynamics, u tekstu CFD) i vizualizacijom rezultata analize olakšano je pozicioniranje elemenata sustava hlađenja, a samim time i proces projektiranja. Dobivanjem polja brzine i temperature, projektant može poboljšati karakteristike i učinkovitost sustava izmjenom položaja i broja dijelova termotehničkog sustava. Na temelju rezultata CFD analize se provjeravaju cirkulacijske zone toplog zraka kao i kapacitet hlađenja. Na taj način projektant može provjeriti cirkulacijske zone toplog zraka i zadovoljava li projektirani sustav projektne zahtjeve. Proračuni su izvršeni u programskom paketu OpenFOAM v7. Korišten je model nestlačivog turbulentnog strujanja s izmjenom topline. Slobodna konvekcija je modelirana pomoću aproksimacije Boussinesqa. Izvršen je stacionarni i nestacionarni proračun. Korišten je provjeren model turbulencije kwSST. Svi parametri simulacije su postavljeni prema podacima iz projekta. Electrical substations are part of electrical power systems, where transformation from high to low voltage (or reverse) occurs. Transformers generate heat during operation and at the same time create heat load of the rooms. Therefore, it is necessary to design all year round cooling system. In order to design correctly HVAC equipment according to lawful regulations, it is necessary to calculate heat load and validate that given system will satisfy project assignement. In this particular case, dominant mechanism for heat transfer is convection. Convection occurs because of transfomers fans settled inside of transformer box. In that case, air from the room flows to the transformer box and cools down the transfomer coils. During this process heat transfers to the air, and hot air is exiting from the transfomer box roof opening into the room. Environment heat via radiation and convection is rather small, but its effect on flow field is taken into consideration with isotermal boundary condition of insidewall. Calculation is performed inworst case scenario, during summer conditions with outside air temperature of 35 degrees Celsius. Thermal transmittance is used from architecture map, so that correct temperature at walls can be calcuated. Choosing the right positions for the elements of the system can be quite a challenge. Utilizing the methods of Computational Fluid Dynamics can make process of designing cooling system significantly easier. Therefore, by analyzing the fields of interest (e.g. temperature and velocity field), a designer can optimize system by changing quantity and positions of equipment elements, and therefore increase efficiency of the system. On the basis of the results of the CFD analysis, a designer can check if there are circulations zones of the hot air that are not being taken care of. Also, designer can check if designed equipment can handle heat load and fulfill design conditions. Calculations are made in open source software OpenFOAM. Incompressible, turbulent flow with heat transfer model is used. Buoyancy is modeled via Boussinesq approximation. Steady state and transient simulations is performed. Turbulence is modeled using kwSST turbulence model. All parameters of simulations are set up according to the input informations of the project.

Cilj ovog diplomskog rada je određivanje utjecaja niza parametara na strujanje zraka oko zgrade s izdignutim stambenim dijelom. Rad se temelji na simulacijama provedenim u računalnoj mehanici fluida. Za izradu računalne mreže je korišten komercijalni programski paket CF MESH+®, a za proračune je korišten programski paket otvorenog koda OpenFOAM®. U radu je korišten model stacionarnog trodimenzijskog turbulentnog strujanja nestlačivog fluida opisan osrednjenim Navier Stokesovim jednadžbama i k - ε modelom turbulencije, dok je strujanje uz zid modelirano zidnim funkcijama. Strujanje vjetra je modelirano koristeći dva tipa homogenog atmosferskog graničnog sloja pogonjenog smičnim naprezanjem i gradijentom tlaka. U radu je ispitan utjecaj parametara dimenzija i oblika izdignute zgrade na brzinu strujanja vjetra i koeficijent ugode na visinama koje odgovaraju visini pješaka u okolini zgrade. Analizirano je ukupno trideset različitih konfiguracija izdignute zgrade gdje su se mijenjale dimenzije zgrade, oblik nosivog dijela zgrade, kutovi nastrujavanja vjetra na zgradu te modeli homogenog atmosferskog graničnog sloja koji nastrujava na zgradu. Dobiveni rezultati koeficijenta ugode u okolini zgrade uspoređeni su s rezultatima dostupnim u literaturi te je postignuta vrlo dobra podudarnost (relativno odstupanje manje od 6%). Rezultati analize ukazuju na činjenicu da visina zgrade te kut nastrujavanja imaju dominantan utjecaj na strujanje zraka u blizini zgrade u odnosu na vrstu homogenog atmosferskog graničnog sloja koji nastrujava na zgradu i oblik nosivog dijela zgrade. The scope of this work is to determine the parameters that influence the airflows around lift up buildings. The study is based on the Computational Fluid Mechanics (CFD) simulations. The CF MESH+® commercial software package was used to create the volume meshes and OpenFOAM® was used to perform the CFD calculations. The stationary 3D turbulent flow model of a non compressible fluid described by the averaged Navier Stokes equations and the k - ε turbulence model were used, whereas the flow near the wall was modeled by using the wall functions. The wind flow was modeled as the atmospheric boundary layer (ABL) for two types of boundary conditions. The effect of a number of parameters on wind characteristics at the pedestrian height of 2 m was analyzed. In particular, thirty simulations were performed to analyze the effects of the building dimensions and shape and the flow incidence angle for two sets of boundary conditions at the inlet of the computational domain. The results were compared with the results that are available in the literature and a very good match was obtained with the discrepancies less than 6%. It was observed that the building height and the flow incidence angle dominate the wind characteristics at 2 m height around the lift up building compared to the effects of the inlet boundary conditions and the shape of the lowest portion (core) of the building.

Posljedice požara u podzemnim garažama mogu biti ogromne, ne samo zbog materijalne štete, već zbog opasnosti za ljudske živote. Zbog toga se u današnje vrijeme postavljaju posebni zahtjevi prilikom projektiranja na sustave kontrole i izvlačenje dima. Prilikom izbijanja požara u garaži, nastaje velika količina dimnih plinova visoke temperature, te zbog smanjene visine garaže, otežavaju regulaciju dima. Podzemne garaže moraju imati ventilaciju da bi osiguralo izvlačenje produkata izgaranja motora vozila i da bi se u slučaju požara izvukao dim. U današnje vrijeme sve više prostora u projektiranju uzimaju potisni ventilatori umjesto sustava cjevovoda. Cilj ovog rada je napraviti numeričku simluaciju strujanja fluida u garaži s potisnim ventilatorima. Koristeći se metodama računalne dinamike fluida izračunat će se i prikazati polje brzine kao glavna smjernica za postavljanje komponenata ventilacije, te temperaturno polje prema propisanoj visini. Proračun je izvršen u programskom paketu PyroSim. Underground car parks are places where fire can, not only do material damage, but take human lives. Design of HVAC (Heating, Ventilation, Air Condtitioning) and smoke regulation systems needs to satisfy fire safety conditions. When a fire breaks out in underground car park, a large amount of flue gases is generated at high temperature. Because of reduced height , flue gases control and extraction is somewhat difficult. Underground car parks need to have means of ventilation, that will provide exhaust of combustion products and flue gasses in case of fire. Jet fans are getting more attention in HVAC design instead of tradional ductwork system. Objective of this paper is to make a computational fluid dynamics (CFD) analysis of underground car park with jet fans. Utilising methods of computational fluid dynamics flow and temperature field will be calculated and visualized. CFD simulations were carried out using software PyroSim which uses freeware code (the Fire Dynamics Simulator).

U ovom radu analizirano je vrtložno strujanje u zdencu oblika valjka u koji se ubrizgava voda kroz horizontalno postavljene mlaznice. Cilj ovog rada je odrediti utjecaj kuta a kojeg zatvara svaka mlaznica u odnosu na radijalni smjer i protoka Q na kut kojeg cestica fluida opisuje na slobodnoj površini. Potrebno je i iz proračunom dobivenog polja brzine, njegovom integracijom, odrediti trajektoriju čestice fluida od izlaza iz mlaznice do izlaza iz zdenca. Proračunava se vrtložno strujanje uz pretpostavku osnosimetričnog strujanja gdje je protok iz mlaznica kontinuirano raspoređen po ulaznom presjeku (obodu). Geometrijski modeli su izrađeni u programskom paketu Salome, izrada mreža konačnih volumena učinjena je u programskom paketu cfMesh, a proračuni su izvršeni pomoću programskog paketa OpenFOAM. U radu je prikazan i proračun proveden nestacionarnim rješavačem interFoam programskog paketa OpenFOAM kako bi se modelirao položaj slobodne površine na temelju koje je određena proračunska domena za stacionarni rješavač istog programskog paketa simpleFoam. Ujedno su rezultati oba proračuna analizirana te se za određivanje navedenih ciljeva rada opravdano koristi rješavač simpleFoam. Analizom zadanog strujanja utvrđeno je da kut koji opisuje čestica fluida na slobodnoj površini raste s porastom protoka Q i kuta a zbog povećanja tangencijalne komponente brzine u odnosu na radijalnu komponentu. In this thesis vortex flow in a round well is analyzed where water is injected through horizontally placed nozzles. The aim of this thesis is to determine the influence of the relative angle between each nozzle and radial direction a and the fluid flow Q on a angle described by a fluid particle on a free surface. Another goal of this thesis is to determine the trajectory of a fluid particle from the exit of a nozzle to the exit of a well by integrating calculated velocity field. Vortex flow under the assumption of an axi-symmetric flow is calculated where the flow from the nozzles is continously distributed on an inlet surface. Geometry models are created in the software package Salome, finite volume meshes are generated in the software package cfMesh and the calculations are made in the software package OpenFOAM. A transient solver, interFoam, from the software package OpenFOAM is used, for the goals of this thesis, to model free surface to determine the computational domain for the stationary solver from the same software package, simpleFoam. Results from both solvers are analyzed but the stationary solver simpleFoam is used for further analysis.The analysis of described fluid flow determined that the angle which the fluid particle decribes on the free surface is increased as the fluid flow Q and angle a grow due to rise in circular component of velocity relative to radial component.

U ovom radu se analizira sustav za uzorkovanje zraka u svrhu detekcije dimnih plinova, odnosno požara u prostoriji ili električnim i elektroničkim ormarima, sa stajališta transportnog vremena potrebnog za putovanje uzorka zraka od usisnog otvora do analizatora. Provjerene su dosadašnje metode računanja transportnog vremena koje bi se mogle koristiti za funkcije cilja i pokazano je da te metode ne daju u svim slučajevima najbolja rješenja i da su greške u odnosu na numeričku simulaciju velike u prvom analiziranom slučaju. Isto tako je pokazano da će se dogoditi „spor“ transport ako su priključne cijevi puno manjeg promjera u odnosu na glavne vodove. Uzimajući u obzir navedeno zaključeno je da je dobro imati nešto tanje cijevi i cijevi podjednakog promjera na glavnom i priključnom vodu. U radu je prvo prikazana minimizacija transportnog vremena od najudaljenijeg mjesta uzorkovanja zraka i pokazano je da se u tom slučaju dobivaju najmanja transportna vremena, ali se dobiva velika neravnomjernost protoka. Nakon toga je provedena optimizacija specifičnog vremena transporta kako bi se postiglo približno jednako vrijeme za sve cijevi, optimiranje kako bi protoci na mjestima uzimanja uzorka bili približno jednaki, te je optimirana kombinacija prethodna dva slučaja. Najbolja rješenja je dala kombinacija optimiranja vremena i protoka. This paper analyzes the air sampling system for the purpose of fire detection in the room or electric and electronic closets, from the point of view of the transport time required to travel the air sample from the inlet to the analyzer. Existing methods for transport time calculation that could be used for the objective functions were tested and showed that these methods do not provide the best solutions for all case and that the errors in comparison to the numerical simulation are large in first analyzed case. It has also been shown that "slow" transport will occur if the connecting pipe are much smaller in diameter than the main pipe. Taking into account the above, it has come to the conclusion that it is good to use thinner pipes and pipes of the approximately same diameter on the main and the connection pipes. In this paper first was minimize transport time from the furthest air sampling point and results was shown that in this case the minimum transport times were obtained, but large unevenness of the flow was obtained. Thereafter optimization of transport time was carried out in order to achieve approximately the same specific time for all pipes and optimizing the flow to the sampling points to be approximately same. Optimization for combination of the previous two cases provided the best solution.

Ovaj rad bavi se brtvljenjem velikih sučelja između gornjeg i donjeg dijela unutarnjeg kućišta komore izgaranja u silo izvedbi. Provedena je analiza učinkovitosti hlađenja hula brtve koja bi zamijenila staru belt brtvu. Hula brtva je fleksibilna prstenasta brtva koja se koristi za kompenzaciju pomaka između dvije cilindrične komponente, a da pritom pruža učinkovitu izvedbu brtvljenja. Plinska turbina na koju će se ugraditi hula brtva je starija plinska turbina s komorom izgaranja u silo izvedbi koja koristi belt brtvu za brtvljenje sučelja između gornjeg i donjeg dijela unutarnjeg kućišta komore izgaranja. Glavni razlog za odabir ove plinske turbine je veliko trošenje i troškovi popravka same belt brtve i sučelja između gornjeg i donjeg dijela unutarnjeg kućišta komore izgaranja u odnosu na druge slične plinske turbine. U okviru ovoga rada računalna dinamika fluida korištena je za provjeru učinkovitosti hula brtve i uspoređena je sa učinkovitosti belt brtve. Za gornji i donji dio unutarnjeg kućišta komore izgaranja te za belt brtvu korišteni su već postojeći geometrijski modeli dok je model hula brtve izrađen prema patentu hula brtve. Iz tih modela sklopljena su dva slučaja, onaj sa belt brtvom i onaj sa hula brtvom. Za numeričku analizu korišten je periodički isječak iz cijele geometrije oba slučaja radi smanjenja vremena računanja. Numerička analiza uključuje volumen kroz koji struji fluid te stijenku unutarnjeg kućišta kako bi se ispitala interakcija između njih odnosno da bi se saznalo kako hlađenje zrakom utječe na toplinske uvijete komponenti. Dobiveni rezultati sadrže polja tlakova, brzina i temperatura, te strujnice kako bi se što bolje opisali toplinski uvjeti i strujanje fluida. Na temelju rezultata izveden je zaključak da hula brtva u odnosu na belt brtvu nije dovoljno učinkovita odnosno ne osigurava potrebno hlađenje kućišta komore izgaranja. Kao preporuka za povećanje učinkovitosti navedene su promjene na samoj hula brtvi. This thesis deals with large-scale cylindrical interface sealing between the hot gas path components of silo combustion chamber. Implementation of hula seal for replacing old belt seal will be checked in order to minimize the amount of cooling and leakage air, without negative impact on the lifetime of the components. Hula seal is annular flexible spring finger seal used to compensate misalignment between co-annular parts, while providing effective sealing performance. It is circumferential metal seal that is slotted in the axial direction and contoured to be spring-loaded between inner and outer diameter of the matching parts that experience relative axial motion. Long term successful implementation of the hula seal for sealing of stationary interfaces for industrial and aero gas turbine engines confirms benefits like improved lifetime of the hot gas parts, reduction of manufacture costs and on-site assembly time. The target engine type is older gas turbine that currently uses belt seal as seal for cylindrical interface between the hot gas path components of silo combustion chamber. Main reason of choosing this engine is the highest wear impact and costs of the belt seal compared to other engines. In scope of this thesis computational fluid dynamics method is used to verify the sealing performance of the hula seal and compare it with belt seal performance. Models of belt seal, combustion inner liner and hot gas casing that are used already existed, while hula seal model was designed by descriptions from patent. From this models, assembly of two cases were made, one for belt seal case and one for hula seal case. Periodic models were created from assembly models to reduce mesh generation and computational time. Numerical analysis solved conjugate heat transfer problem which means that along fluid flow, heat transfer interaction between fluid and solid was solved as well. Result which shows fluid flow and thermal condition of fluid and solid are presented. Based on result it is concluded that performance of hula seal model used in this thesis are not good enough. Compared to belt seal hula seal cooling performances are worse. Suggestions for improving hula seal performance were given.

U ovom radu istražena je promjena hidrodinamičkog otpora jedrilice klase Optimist sa promjenom bočnog nagiba. Proračun je izveden korištenjem metode konačnih volumena na nestrukturiranoj nepomaknutoj mreži. Korišten je već postojeći model jedrilice u obliku STEP datoteke. Izrađeno je 11 simulacija, po jedna za svaki kut nagiba od 0 do 20°. Modeli geometrije domene su izrađeni u programskom paketu Salome, dok je za prostornu diskretizaciju korišten paket cfMesh. Proračuni su obavljeni SIMPLE postupkom za stacionarna strujanja, pomoću programa simpleFOAM- jednog od programa biblioteke OpenFOAM, a korišteni model turbolencije je k-ω SST model. Brzina jedrilice je konstantna, a iznosi 1.5 m/s. Rezultati se naknadno obrađuju pomoću ParaView i Gnuplot programskih paketa. In this work the influence of lateral tilt angle on hull drag force of the class Optimist sailboat is studied. The calculations were performed using Finite Volume Method on unstructural grids. The sailboat geometry, being defined in previous studies, was aquired in form of STEP format file. A total of 11 simulations were performed, each for different tilt angle in range 0° - 20°. The geometry models of the domain were created using Salome software package, while for the spatial discretisation the cfMesh package was used. Steady, incompressible turbulent flow model was used and the calculations were performed using SIMPLE algorithm and k-ω SST turbulence model, as implemented in the OpenFOAM library. The sailboat velocity was kept constant, of value of 1.5 m/s. The results are post-procesing using ParaView and Gnuplot packages.

Kod natjecateljskih automobila, u cilju ostvarivanja što veće sile na podlogu, pribjegava se posebnom oblikovanju podvozja automobila, te ugradnji prednjeg i stražnjeg krila. Željeno povećanje aerodinamičke sile ostvaruje se izvedbom krila s velikim specifičnim aerodinamičkim opterećenjem i to najčešće kao krila male vitkosti. U ovom radu su istražene strujne pojave pri opstrujavanju zadanog modela stražnjeg krila natjecateljskog automobila s posebnim osvrtom na inducirani otpor. Sama geometrija stražnjeg krila natjecateljskog automobila modelirana je u programskom paketu Solidworks i preuzeta od članova FSB Racing Teama. Dorade geometrije i proračunska domena izrađene su u programskom paketu Salome. Domena je ispunjena konačnim volumenima generiranim u programskom paketu cfMesh. Mrežom dominiraju pravilni heksaedarski volumeni, uz korištenje manjeg broja prijelaznih tetraedarskih ćelija te trokutnih prizmi kako bi se sačuvala geometrijska definicija rubova. Svi proračuni provedeni su s ulaznom neporemećenom brzinom od 30 m/s (108 km/h). Simulacije su napravljene uz pomoć programskog paketa OpenFoam, koristeći program za rješavanje modela stacionarnog strujanja uz k-omegaSST model turbulencije. Izrađeno je ukupno 5 simulacija uz promjenu geometrije stražnjeg krila. U analizi rezultata dan je prikaz raspodjele tlakova i brzina, te smanjenja koeficijenta otpora, odnosno povećanja koeficijenta uzgona. When it is about race cars, it is necessary to achive as more force to the base as it can. It is done by instalation of front and rear spoilers. Wanted enlargement of aerodynamic force is realized by using great loaded wing, most with low slenderness. In this work, stream phenomenon are analyzed with opposing rear wing of the race car. The special review is on the induced resistance. Geometry of the rear wing model has been designed in Solidworks program package and it is took over from students organisation FSB Racing team. Program package Salome is used for futher work on geometry and calculations. Domain grid is filled with finite volume generated in cfMesh program package. Mesh is structured by using hexahedron cells, with small number of transitional tetrahedral cells and triangular prisms used to preserve the surfaces of the geometry model. All calculations were performed with the same freestream velocity of 30 m/s (108 km/h). For all simulations a steady-state flow model with the k-omegaSST turbulence model was used as implemented in the OpenFOAM software library. There are totally 5 simulations with changing the geometry of rear wing. In results, distribution of pressure (increase in the coefficient of lift), speed and reduced coefficient of resistance are shown.

Zbog sve strože ekološke legislative, primarne mjere kontrole ispušnih plinova, poglavito NOx-a, u velikom broju slučajeva više nisu dovoljne. Rješenje za daljnje smanjenje koncentracija NOx-a je u naknadnoj obradi ispušnih plinova. Najperspektivnija tehnologija u tom području je selektivna katalitička redukcija. Kod selektivne katalitičke redukcije (eng. Selective Catalytic Reduction) vodena otopina uree u obliku spreja ubrizga se u struju vrućih dimnih plinova prije katalizatora, pri čemu dolazi do isparavanja vode iz otopine i stvaranja amonijaka termalnom dekompozicijom uree i hidrolizom izocijanske kiseline. Pri tome rezultirajuća prostorna raspodjela amonijaka prije katalizatora predstavlja ključan faktor učinkovite konverzije NOx-a. Zbog kompleksnosti reakcija i prostorne raspodjele plinova unutar katalizatora, veliki resursi ulažu se u razvoj matematičkih modela pomoću kojih bi se dovoljno dobro opisao proces selektivne katalitičke redukcije. U ovome radu izvršena je validacija najvažnijih matematičkih modela za opis SCR procesa integriranih u komercijalni kod za računalnu dinamiku fluida FIRE na bazi rezultata dobivenih simulacijama s postojećim eksperimentalnim podacima, preuzetim iz akademskog članka. Validacijom je dokazano relativno dobro slaganje eksperimentalnih rezultata i rezultata dobivenih simulacijom po kriteriju efikasnosti pretvorbe NH3. Također je dokazano da simulacije prate trend eksperimentalnih rezultata, te da odstupanja koja su prisutna nisu značajna. Nadalje, izvršena je simulacija realne geometrije industrijskog katalizatora pri različitim radnim uvjetima. Razmatrani su radni uvjeti pri čemu se varirala veličina kapljica ubrizganog spreja, kao i smjer ubrizgavanja spreja. Pokazano je da smjer ubrizgavanja spreja vodene otopine uree u odnosu na strujanje ispušnih plinova (istosmjerno/protusmjerno) nije pokazao neki učinak na konverziju NH3, dok je kod bočnog ubrizgavanja konverzija uvjerljivo najlošija. Na kraju je dokazano da je pobjeg amonijaka kod protusmjernog ubrizgavanja znatno manji nego kod istosmjernog, pri čemu ova vrsta ubrizgavanja postaje zanimljiva za daljnja istraživanja. Due to ever stringent ecological legislation, primary measures for exhaust gases control, especially NOx, in large number of cases are not sufficient any more. The solution for further NOx concentration decrease lays in exhaust gas aftertreatment. Selective Catalytic Reduction (SCR) represents the most promising technology in that area. In the SCR Urea Water Solution (UWS) spray is injected into the hot exhaust gas stream before SCR catalyst, with simultaneous water evaporation taking place. Afterwards, ammonia is generated through thermal decomposition of urea and hydrolysis of isocyanic acid. The resulting spatial distribution of the ammonia before the catalyst is a crucial factor for the efficient conversion of NOx. Due to the complexity of the reactions and the spatial distribution of gases within the catalyst, great amount of resources is invested in the development of mathematical models which will prove sufficiently accurate to describe the process of selective catalytic reduction. In this work validation of the most important mathematical models for SCR process description integrated in the commercial Computational Fluid Dynamics (CFD) code FIRE has been conducted on the basis of existing experimental results taken from the academic paper. Validation proved relatively good agreement of simulation results with experimental data in terms of NH3 conversion efficiency. Also, it was proved that simulation results follow experimental trend without significant discrepancies. Furthermore, the simulation of real industrial catalyst geometry was conducted for different working conditions, where spray droplet size was varied together with the injection direction. It was shown that UWS spray direction relative to the exhaust gases flow (in the direction of flow and against it) doesn’t have significant impact on the NH3 conversion, whilst during the perpendicular injection, NH3 conversion is by far the worse. Finally, ammonia slip was significantly lower during counterflow injection direction, making this kind of injection interesting for future investigations.

Određivanje hidrodinamičkih značajki brodskog vijka u slobodnoj vožnji je vrlo važno provesti u ranoj fazi osnivanja broda. Hidrodinamičke značajke brodskih vijaka pouzdano se mogu odrediti ispitivanjem modela brodskih vijaka. Rezultati pokusa slobodne vožnje vijka koriste se kao osnova za projektiranje vijka za novi brod. Razvoj računalne dinamike fluida omogućio je numeričko određivanje hidrodinamičkih značajki modela brodskog vijka, što znatno skraćuje vrijeme i smanjuje troškove projektiranja brodskog vijka nove geometrije. U ovom radu su provedene numeričke simulacije slobodne vožnje brodskog vijka u svrhu ispitivanja mogućnosti primjene računalne dinamike fluida (RDF) pri projektiranju brodskog vijka. U radu je korišten programski paket otvorenog koda OpenFOAM. To je programski paket koji se zasniva na modelu viskoznog strujanja teku ́cine opisanog Reynoldsovim osrednjenim Navier - Stokesovim jednadžbama. Validacija programskog paketa OpenFOAM je provedena usporedbom rezultata dobivenih numeričkim simulacijama s eksperimentalnim podacima dostupnim u literaturi. Pri provođenju numeričkih simulacija primijenjena je metoda višestrukih referentnih koordinatnih sustava (eng. Moving Reference Frame method - MRF). MRF metoda rješava jednadžbe strujanja u rotirajućem koordinatnom sustavu brodskog vijka što omogućuje rješavanje ovog problema kao stacionarnog. Iz rezultata dobivenih numeričkim simulacijama može se zaključiti da se računalna dinamika fluida može uspješno primijeniti za simulaciju pokusa slobodne vožnje brodskog vijka te dobivanje sile poriva, momenta vijka i stupanja djelovanja vijka u slobodnoj vožnji. Determination of open water hydrodynamic characteristics of a marine propeller is very important in the early stage of ship design. Hydrodynamic characteristics of marine propellers can be reliably determined by testing propeller models. Results of open water tests are used as the basis for the design of the propeller for a new ship. The development of computational fluid dynamics enabled the numerical determination of the hydrodynamic characteristics of the marine propeller model, which significantly shortens the time and reduces the cost of designing the new marine propeller geometry. In this study, numerical simulations of open water test are carried out with the purpose of examining the possibility of applying the computational fluid dynamics for the design of the marine propeller. In this paper, the open source software package OpenFOAM is used. This is a software package that is based on the viscous fluid flow model described with Reynolds averaged Navier-Stokes equations. Validation of the software package OpenFOAM is carried out by comparing the results obtained by numerical simulations with experimental data available in the literature. Moving Reference Frame (MRF) method is used in numerical simulations. MRF method solves the flow equations in a rotating coordinate system of the propeller which allows solving this problem as stationary one. From the results obtained by numerical simulations it can be concluded that the computational fluid dynamics can be successfully applied to simulate open water test of a marine and to obtain the thrust, torque and open water efficiency.

Ovaj rad se primarno fokusira na usporedbu proračuna strujanja fluida, primjenom računalne dinamike fluida, oko dvije realne geometrije krila. Jedna geometrija je konačno ravno krilo, a druga je isto krilo s dodatkom uređaja za kontrolu intenziteta vršnog vrtloga. Na početku rada objašnjeni su osnovni problemi pojave vrtloga kod zrakoplova. Nakon toga je opisan osnovni algoritam rješavanja spregnutog sustava jednadžbi brzine i tlaka u nestlačivom strujanju. Poslije toga je na jednostavnome primjeru dvodimenzijskog strujanja evolucije Taylor-Green vrtloga prikazan način mjerenja numeričke greške uz pomoć poznavanja analitičkog rješenja Navier-Stokesovih jednadžbi. Veličine numeričkih grešaka prikazane su za različite parametre diskretizacije. Na kraju ovog rada prikazani su rezultati proračuna za dvije geometrije, koji uključuju usporedbu intenziteta simuliranih vrtloga u nizvodnome toku. This work is primarily focused on the comparison of the calculation of fluid flow, using computational fluid dynamics, between two real wing geometries. The first geometry is a final straight wing, while the other is the same wing with wingtip devices used for the control of the wingtip intensity. At the beginning of this work, the basic problems of the appearance of the wingtip vortices at the aircraft are introduced and explained. Afterwards, the basic algorithm for solving the system of equations of pressure velocity coupling for incompressible flow is described. Subsequently, a simple example of measuring the numerical errors in comparison with the analytical solution of the Navier-Stokes equations of the two-dimensional Taylor-Green vortex has been shown. The size of numerical errors is presented for various parameters of discretization. At the end of this work the results of the calculation for two geometries are presented, with comparison of the intensity of simulated vortices in downstream flow.

U ovom radu se ispituje utjecaj promjene uzdužnog nagiba i dubine urona kobilice na hidrodinami čki otpor uronjenog dijela jedrilice klase Optimist. Istisnina je izračunata za ukupnu masu jedrilice i jedriličara od 80 kg. U proračunu je uzeta brzina jedrilice od 1,5 m/s. Za sve slučajeve proračunska domena je diskretizirana korištenjem računalnih programa Salome i cfMesh. Numeri čki proračun za stacionarne uvjete strujanja uz zanemaren utjecaj valova je izvršen u programskom paketu OpenFOAM. U radu je su prikazani i analizirani rezultati te su prikazana polja brzine i tlaka za najzanimljivije slučaje. Goal of this work is to determinate the influence of pitch angle and keel depth on drag force of sail-boat class Optimist hull. Drag force is analyzed for the sail-boat cruise velocity of 1.5 m/s. Computational domain is discretizated using Salome and cfMesh program package, and various cases of pitch angle and keel depth where studied. Numerical analysis for stationary flow conditions is executed in OpenFOAM program package. The results are presented trough velocity and pressure fields of most interesting cases, so as in form of force-pitch angle diagrams.

U ovom završnom radu istražen je utjecaj položaja ruku skijaša letača na duljinu njegova skoka. Duljina skoka velikim je dijelom uvjetovana odnosom sile uzgona i otpora skijaša pa su te dvije aerodinamičke sile te njihov omjer promatrani tijekom numeričke analize. Tijelo skijaša letača modelirano je u CAD programskom paketu SolidWorks na pojednostavljeni način kako je i prethodno bilo modelirano u sličnim radovima. Modelirana su tri modela skijaša letača s različitim položajem ruku u odnosu na tijelo: a) ruke pod 0° (uz tijelo), b) ruke pod 45°, c) ruke pod 90°. Proračunska domena s jednom ravninom simetrije napravljena je u programskom paketu Salome. Domena je strukturirano ispunjena mrežom heksaedarskih konačnih volumena uz veća profinjenja u blizini tijela skijaša uz korištenje programskog paketa cfMesh. Numerički proračun proveden je u računalnom programu OpenFOAM uz stacionarne uvjete strujanja. Uz aerodinamičke sile otpora i uzgona u radu su prikazana i polja tlaka i brzine oko tijela skijaša te je provedena diskusija rezultata. In this bachelor thesis, the aerodynamic forces experienced by a generic ski jumper are studied. The focus is on the position of ski jumper’s arms with respect to his body. As the length of the jump is largely determined by the lift to drag force ratio of the ski jumper, these two aerodynamic forces are analyzed using Computational Fluid Dynamics (CFD) simulations. Ski jumper’s body is modeled in the SolidWorks CAD software package in a simplified way similar to previous studies. Three models of the ski jumper with different placement of arms with respect to his body are modeled, i.e. a) arms at 0° (close to body), b) arms at 45° , c) arms at 90° . Computational domain with one symmetry plane is created in the Salome software package. The domain is structurally filled with the grid of hexahedron cells along with refinements close to the ski jumper‘s body using the cfMesh software package. The CFD simulations are carried out using the OpenFOAM software package, SST k− ω turbulence model and stationary flow conditions. The aerodynamic drag and lift forces, as well as pressure and velocity fields around the ski jumper are reported and discussed.

U radu su istražene metode za određivanje lokalnih gubitaka i zagrijanja metalnih konstrukcijskih dijelova transformatora. Tijekom istraživanja korištene su eksperimentalne i numeričke metode za određivanje iznosa gubitaka i zagrijanja na modelima. U prvom dijelu razrađena je eksperimentalna metoda za određivanje lokalnih gubitaka. Riječ je o metodi koja se temelji na mjerenju brzine početnog rasta temperature. Primjenjivost metode za određivanje gubitaka u magnetskom čeliku ocijenjena je na modelima eksperimentalnih prstenova od magnetskog čelika. Analizirani su utjecaji električne prijelazne pojave na rezultate mjerenja lokalnih gubitaka u prstenu. Također istraženi su utjecaji debljine prstena i okolnog rashladnog fluida na rezultate mjerne metode. Rezultati mjerenja gubitaka metodom početnog rasta temperature uspoređeni su s rezultatima mjerenja gubitaka vatmetrom i rezultatima proračuna u numeričkom alatu MagNet. U drugom dijelu rada prikazano je istraživanje na modelu za lokalno zagrijanje kotla. Na modelu je korištena metoda brzine početnog rasta temperature za određivanje iznosa lokalnih gubitaka. Također, na modelu su napravljeni pokusi zagrijavanja te su određeni iznosi lokalnog zagrijanja kotla. U nastavku istraživanja rezultati mjerenja lokalnih gubitaka i zagrijanja služili su za određivanje lokalnih koeficijenata prijelaza topline na strani kotla koja je hlađena uljem. Izvedeni su regresijski izrazi za lokalne koeficijente prijelaza topline kao funkcije toplinskog toka iz kotla u ulje. Također su napravljeni proračuni gubitaka i temperatura metodom konačnih elemenata u alatima MagNet i ThermNet te EleFAnT-u. Na kraju su proračuni gubitaka i temperatura spregnuti s proračunom dinamike fluida. Za određivanje temperatura kotla pomoću računalne dinamike fluida korišten je alat Ansys Fluent. Zaključno je dana usporedba rezultata mjerenja s rezultatima proračuna temperatura. In this thesis methods for determination of local losses and temperatures in structural metal parts of transformers are investigated. In the research experimental and numerical methods are used for determination of losses and temperatures. In first part of the work experimental method for determination of local losses is elaborated. This is a method based on initial rate of rise of temperature. Applicability of this method for measurement of local losses in magnetic steel is evaluated on experimental ring models. The effect of electrical transients on results of measurements of local losses is analyzed. Also, influence of ring thickness and ambient cooling conditions on results of the method is investigated. Measurement results obtained by the method of initial rate of rise of temperature are compared to losses in rings measured by wattmeter and calculation results by numerical tool MagNet. In the second part of the thesis, research on model for tank local overheating is elaborated. Local losses in the tank are evaluated by method of initial rate of rise of temperature. Also, heat-run tests are made on this model and local temperatures on the tank are measured. Measurements of losses and temperatures are used for evaluation of local heat transfer coefficients on the side of the tank cooled by oil. Obtained expressions of heat transfer coefficients are given as functions of heat flux from tank to oil. Further on, local losses and temperatures in the tank are calculated by finite element method tools MagNet&ThermNet and EleFAnT. In the end electromagnetic and thermal calculations are coupled with fluid dynamics calculation. Ansys Fluent is used for determination of tank temperatures by computational fluid dynamics. Finally measured temperatures are compared with calculation results in numerical tools.

U ovome je radu pomoću računalne dinamike fluida izvršena validacija Euler-Eulerovog višefaznog modela stvaranja spreja vršenjem simulacija unutar programskog paketa FIRE®. Verifikacija modela utvrđivana je uspoređivanjem rezultata dobivenih simulacijama s postojećim eksperimentalnim podacima, preuzetim s web stranice Engine Combustion Network grupe. Kroz rad se promatra valjanost matematičkog modela primijenjenog na proces visokotlačnog ubrizgavanja goriva u dizel motor. Na temelju ekoloških zahtjeva, zbog sve većeg zagađenja atmosfere, u industriji se obraća velika pozornost na smanjenje štetnih emisija i povećanje efikasnosti procesa izgaranja, što je usko povezano s procesima miješanja goriva i zraka te stvaranja spreja. Upravo se zbog toga veliki resursi ulažu u razvoj matematičkih modela pomoću kojih bi se dovoljno dobro opisali procesi visokotlačnog ubrizgavanja i stvaranja spreja. Prilikom visokotlačnog ubrizgavanja dolazi do raspadanja tekućeg goriva u sitne kapljice, što se naziva primarnim i sekundarnim raspadanjem, te njihovog naknadnog isparavanja. Kod računalnih simulacija ubrizgavanja goriva potrebno je voditi računa o pravilnom obliku spreja, dužini penetracije tekućeg i isparenog goriva te intenzitetu isparavanja. Višefazni sprej opisan je odabirom najboljeg seta koeficijenata već postojećih modela unutar programskog paketa FIRE® i rezultati simulacije uspoređeni su s eksperimentalnim podacima. The focus of this work is on validation of the Euler-Eulerian multiphase spray modelling approach by using the AVL’s CFD software FIRE®. Verification of the model was performed by comparing the simulation results with the existing experimental data, downloaded from the Engine Combustion Network group’s website. In this work, the multiphase spray module is used for simulating the high-pressure diesel fuel injection. Based on environmental demands, due to the increase in atmosphere pollution, there is great consideration on reduction of harmful emissions and on combustion process efficiency increasement. This is closely related to the fuel-air mixing and spray modelling processes. Because of that, a huge ammount of resources are invested in the development of mathematical models that could be used for better description of high pressure fuel injection and spray processes. During the high pressure injection the liquid core undergoes disintegration into smaller droplets which tend to disintegrate into even smaller ones. This processes are called primary and secondary break-up processes. Simultaneously, the droplets tend to evaporate. In the numerical simulations of fuel injection it is necessary to take care of the proper spray form, liquid and vaporized fuel penetration length and evaporation intensity during the computer simulation. Multiphase spray is defined by selecting the best set of coefficients of the existing models within the software package FIRE® and simulation results are compared with experimental data.

Provedena je numerička implementacija i validacija dvodimenzionalne nelinearne spektralne metode viših redova (eng. "Higher Order Spectrum", skraćeno HOS) za propagaciju trodimenzionalnih površinskih valova. Metoda je implementirana u programu otvorenog koda OpenFOAM, koji je specijaliziran za računalnu dinamiku fluida (eng. "Computational Fluid Dynamics", CFD). Radi se o pseudo--spektralnoj metodi rješavanja nelinearnih diferencijalnih jednadžbi koje opisuju problem površinskih valova u okviru modela potencijalnog strujanja. Pseudo-spektralni pristup omogućuje brzo rješavanje problema površinskih valova s proizvoljnim brojem valnih komponenti, čime se može opisati realistično stanje mora. Red nelinearnosti do kojeg se provodi HOS proračun je proizvoljan, što čini metodu prilagodljivom specifičnim primjenama. Problem se razlaže na način da se prostorni dio problema rješava u spektralnoj domeni, dok se vremenski dio problema rješava u fizičkoj domeni. Pri tome se projiciranje između spektralne i fizičke domene vrši pomoću Fourierove transformacije. Korištenje "Fast Fourier Transform" (skraćeno FFT) algoritma za provođenje Fourierove transformacije omogućuje korištenje velikog broja harmonika zahvaljujući visokoj efikasnosti algoritma. U radu je prikazana matematička pozadina metode i prateći matematički alati. Implementacija je provedena prvenstveno radi sprege sa CFD alatima za brodsku hidrodinamiku, sa naglaskom na efikasnu i točnu inicijalizaciju proizvoljnog stanja mora. Mogućnost nelinearne propagacije valnog spektra omogućuje opisivanje realističnih ekstremnih valova, koji postaju sve zanimljiviji u području brodogradnje i pučinskih objekata. Točnost metode provjerena je na tri testna proračuna. U prvom proračunu provedena je usporedba nelinearne propagacije monokromatskog vala s analitičkim rezultatima. U drugom proračunu uspoređena je propagacija spektra valova s rezultatima viskoznog, dvofaznog proračuna. Treći proračun prikazuje razvoj nelinearnih nestabilnosti monokromatskog propagirajućeg vala poznatih kao Benjamin--Feir nestabilnosti. Na posljetku su prikazane simulacije računalne dinamike fluida u kojima je simuliran trodimenzionalan ekstreman val za čiju se inicijalizaciju koristila implementirana HOS metoda. Ekstreman val se prirodno razvio u dugoj HOS simulaciji, što ga čini statistički i fizikalno realističnim. In this work Higher Order Spectral (HOS) method for three--dimensional nonlinear water wave propagation is implemented and validated. Implementation is conducted in a specialised Computational Fluid Dynamics (CFD) open--source software OpenFOAM. HOS is a pseudo--spectral method for solving nonlinear differential equations, which describe free surface wave phenomena. The pseudo-spectral approach enables fast calculation of surface wave problem with arbitrary number of wave components. The order of nonlinearity of the HOS calculation is arbitrary, making this method highly flexible. Multiple wave components, or harmonics, can reproduce a realistic sea state. The problem is divided into a spectral and a physical part, where the projection between the spectral and physical space is performed via Fourier transforms. Large number of wave components may be used due to high efficiency of the FFT algorithm. Mathematical model of the HOS method is outlined and its numerical model is shown in detail. The reason for implementation of HOS method is its coupling with high-fidelity CFD simulations regarding wave-structure interaction. The capability of low-cost, long time evolution of input spectra can be used to obtain realistic freak waves. Validity of the implemented algorithm is verified on three test cases. The first test case consists of nonlinear propagation of a monochromatic wave using HOS compared with the analytical solution. The second test case demonstrates the ability of accurate wave spectrum propagation by comparing the result with viscous two--phase simulation. In the third test case emergence of Benjamin-Feir instabilities in monochromatic wave train is observed. Finally, CFD simulations of extreme wave are presented. Extreme wave is initialized using HOS solution.

U ovom radu izvršit će se validacija numeričkog algoritma za rješavanje strujanja visokog Machovog broja. Algoritam je pisan u okruženju OpenFOAM te je nov u tom kontekstu. Prvo će se opisati glavne matematičke i numerike probleme koje se susreće u teoriji poput Riemannovog problema te načina rješavanja tog problema. Opisani su ponuđeni rješavači Riemannovog problema uz ostale diskretizacijske sheme koje su standardne u računalnoj dinamici fluida. Algoritam koji koristi gustoću kao glavnu proračunsku varijablu će se validirati na temelju slučajeva za koje se moglo naći eksperimentalne i numeričke rezultate. Pokazalo se kako djeluje profinjenje proračunske mreže na rezultate te kakve rezultate daje u odnosu na algoritme koji koriste tlak kao glavnu proračunsku varijablu. U proračunima je korišten isključivo k - omega SST model turbulencije zbog visokih iznosa Reynoldsovog broja, osim u jednom slučaju za kojeg se pretpostavilo kvazilaminarno strujanje. Slučajevi koji su uzeti su geometrije krila, jednostavni "shock tube" i kovergentno-divergentne mlaznice. Rezultati proračuna će se prikazati grafički u vidu polja primitivnih varijabli i bezdimenzijskih značajki te će ih se usporediti s postojećim eksperimentalnim i referentnim numeričkim rješenjima. In this work the validation of new algorithm was done. Algorithm is written in OpenFOAM environment and it is new in that context. Firstly, main mathematical and numerical problems were introduced as well as ways to solve those problems such as Riemann problem. Approximate Riemann solvers which are available in new code were theoretically described. This algorithm which uses density as main calculation variable was validated against cases for wich results were available in literature or internet. The impact of mesh re nement was shown and also the comparison against pressure-based algorithm. In all cases except one k - omega SST turbulence model was used because of very high Reynolds numbers. In one of cases quasi-laminar ow was assumed. Geometries in simulated cases are a transonic wing, shock-tube and convergent-deivergent nozzles, namely, cases that are of interes of industry. Results of simulations were graphically shown as elds of primitive variables and dimensionless numbers.

A computational model has been developed to determine wind characteristics in the wake of a rectangular building and validated against previous field-test results. Dimensions of the recirculation zone behind the building have been determined using the Reynolds-Averaged-Navier-Stokes (RANS) equations for two different wind incidence angles, i.e. for wind normal to the longer building side and for wind normal to the shorter building side. Obtained results show a decrease in the recirculation zone length for rougher terrains. Therefore, numerical results presented in this paper proved to be in good agreement with full-scale results indicating that the approach taken in this study can be successfully applied in calculating dimensions of recirculation zone in the wake of a rectangular building for various terrain types., U radu je postavljen model računalne simulacije strujanja vjetra oko zgrade pravokutnog presjeka s ciljem određivanja dimenzije zone recirkulacije iza zgrade u ovisnosti o hrapavosti terena na kojem se zgrada nalazi. Proračun je proveden računalnim paketom Fluent 6.2, a temelji se na rješavanju osrednjenih Navier-Stokesovih jednadžbi uz primjenu k-ε modela turbulencije, i to za dva različita kuta nastrujavanja vjetra na zgradu, tj. strujanje okomito na kraću i okomito na dulju stranicu zgrade. Određivanje dimenzije zone recirkulacije je provedeno za tri različite hrapavosti terena, pri čemu su karakteristike hrapavosti terena i strujanja vjetra u prirodi preuzete iz međunarodnog ESDU 85020 standarda. Postavljeni računalni model je validiran usporedbom s rezultatima mjerenja u prirodi za jedan tip hrapavosti terena. Dobiveni rezultati ukazuju na smanjenje duljine zone recirkulacije s povećanjem hrapavosti terena, pri čemu je postignuta zadovoljavajuća sličnost s rezultatima mjerenja u prirodi.

The research in this work aims at improving application of the simulation of fuel ignition, focusing on the low-temperature auto-ignition phenomenon. The simulation of low temperature ignition has been typically achieved by using computationally demanding calculations of complex chemistry kinetics. This work attempts to reproduce the effects of complex chemistry by developing the methodology of efficient database creation consisting of the relevant ignition data used by existing combustion models. The research was separate in several phases: pre-processing, tabulation with data post-processing, and finally the implementation in the CFD software. In the pre-processing stage, available reaction mechanisms of most popular fuels have been thoroughly investigated and compared focused on their accuracy and complexity. Criteria for low- and high-temperature ignition were discussed as implemented into the tabulation application. In the post-processing part of the tabulation, several methods of data manipulation are suggested in forms of correlation functions and repair algorithms, used on the incomplete databases. Additionally, an approach of using existing data for two fuels to calculate the ignition values for their blend dependant only on the previously stored values and the blending factor is presented for the case of a fuel with varying research octane number. Finally, the database implementation into the CFD software is presented and validated. The validation was done in two stages. Initially the implemented data was compared against the results of the homogeneous reactor calculations using a comprehensive mechanism and in the final stage the model was used in a real-life case and successfully validated proving the viability of the entire process. Glavna namjera istraživanja ovog rada je izvesti numerički učinkovite algoritme za modeliranje zapaljenja goriva s posebnim fokusom na fenomen niskotemperaturnog zapaljenja. \Numerička simulacija niskotemperaturnog zapaljenja dosad se uglavnom postizala računalno zahtjevnim izračunima složene kemijske kinetike, dok će ovaj rad pokušati razviti nove postupke učinkovite izrade baza podataka koje sadrže informacije o efektima složene kemijske kinetike potrebne za simulaciju zapaljenja goriva. Istraživanje je jasno podijeljeno u nekoliko faza: pred-procesiranje, tabelacija s post-procesiranjem podataka, te na kraju implementacija u CFD aplikaciju. U prvoj fazi, pred-procesiranju, detaljno su predstavljeni dostupni reakcijski mehanizmi za popularna goriva, te su isti međusobno uspoređeni prema njihovoj točnosti i kompleksnosti. Zatim je prikazan način modeliranja nuladimenzijskog proračuna s kriterijima određivanja nisko- i visokotemperaturnog zapaljenja. U sljedećoj fazi, post-procesiranju, predloženi su alati za manipulaciju izračunatim podacima, s posebnim fokusom na popunjavanje krnjih baza podataka korelacijskim funkcijama i matematičkim algoritmima. Dodatno, predložen je i način korištenja postojećih podataka za pojedina goriva pri izračunavanju karakterističnih veličina za njihovu smjesu. U tom se slučaju koriste samo vrijednosti za izgaranje svako goriva (čistog) i faktor miješanja. Princip je provjeren na gorivu varijacijom istraživačkog oktanskog broja. \Na kraju, prikazana je implementacija u CFD aplikaciju te je ista i validirana u dvije faze. Prvo je napravljena usporedba s proračunom homogenog kemijskog reaktora s kompleksnim reakcijskim mehanizmom a na samom kraju i primjer stvarne komore izgaranja što je pokazalo valjanost modela i cijele procedure.

Konstrukcija i određivanje radnih karakteristika pumpi je i dalje složen zadatak, prvenstveno zbog velikog broja slobodnih geometrijskih parametara čiji se utjecaj ne može direktno procijeniti. Značajna cijena koštanja konstruiranja pumpi na temelju eksperimentalnih istraživanja, tj. mjerenjima na prototipovima čini računalne simulacije temeljene na računalnoj mehanici fluida (engl. Computational fluid dynamics - CFD) najprihvatljivijim alatom pri konstruiranju i analizi radnih karakteristika pumpi. Međutim, nestacionarne pojave pri međudjelovanju rotora i statora, te nestabilnosti strujanja i dalje nužno zahtijevaju validaciju i verifikaciju dobivenih rezultata eksperimentalnim putem. Istraživanje energetske pretvorbe u centrifugalno vrtložnoj pumpi u ovom radu je provedeno numeričkim simulacijama strujanja u centrifugalnoj pumpi, centrifugalno vrtložnoj pumpi i vrtložnom dijelu centrifugalno vrtložne pumpe, te mjerenjima relevantnih parametara koji opisuju radne karakteristike pumpi na njihovim fizikalnim modelima. Rezultati mjerenja poslužili su kao eksperimentalna validacija numeričkih simulacija, ali i obrnuto, vizualizacija strujanja proizašla iz numeričke simulacije korištena je za interpretaciju mjerenja. Validacija numeričkog modela provedena je usporedbom dobivenih integralnih veličina, (protoka, visine dobave i snage) s izmjerenima na istovjetnim fizikalnim modelima. Također je provedena usporedba dobivenih veličina kod centrifugalne, centrifugalno vrtložne pumpe i vrtložnog dijela u cilju njihove usporedbe. Za potrebe provođenja eksperimentalnih istraživanja, u Laboratoriju za hidrodinamiku i hidrauličke strojeve Fakulteta strojarstva i brodogradnje u Zagrebu, izrađeni su fizikalni modeli centrifugalne i centrifugalno vrtložne pumpe koji odgovaraju numeričkim te eksperimentalna linija s pripadajućom opremom koja je omogućila promjenu broja okretaja, odabir radne točke te mjerenje trenutnog protoka, prirasta tlaka i snage pogonskog elektromotora. Numerička simulacija nestacionarnog strujanja u centrifugalnoj pumpi i centrifugalno vrtložnoj pumpi provedena je korištenjem aplikacijskog komercijalnog programskog paketa ANSYS Fluent za računalnu dinamiku fluida koji se temelji na metodi konačnih volumena. IV Provedena istraživanja su pridonijela pojašnjenju mehanizama energetske pretvorbe u centrifugalno vrtložnoj pumpi te potvrdila povoljni utjecaj vrtložnog vijenca na karakteristike iste (protok, tlak, iskoristivost, kavitacijska karakteristika). The design and performance prediction of pumps is still a complex task, mainly due to a large number of free geometrical parameters whose influence cannot be directly evaluated. The significant financial cost of pump design by trial and error methods and the cost of experimental prototype testing, renders the computational fluid dynamics (CFD computer simulation) as the most acceptable tool in the design and performance analysis of pumps. However, unsteady phenomena in the form of interaction of rotor and stator and other flow instabilities continue to make accurate prediction of the pump characteristics a difficult and time-consuming task, which still requires validation and verification of the experimentally obtained results. In this paper the research of the energy transformations in centrifugal vortex pump has been performed by numerical simulation of flow in centrifugal pumps, centrifugal vortex pumps and vortex part of centrifugal vortex pump, as well as by the measurements of relevant parameters that describe the performance of pumps on their physical models. The results of experimental measurements served primarily as experimental validation of numerical simulation, and vice versa, the visualization of the flow arising from numerical simulations was used for the interpretation of measurements. The validation of the numerical model was conducted by comparing the integrated quantities, flow rate, the head and the power consumption with those obtained by measurements on identical physical models. Also, a comparison of the obtained physical values was conducted with the aim of making a conclusion about the diversity of integral parameters of centrifugal pumps, centrifugal vortex pump and the vortex part of the centrifugal vortex part. During the preparation of this research, at the Laboratory for Hydrodynamics and hydraulic machinery, Faculty of Mechanical Engineering and Naval Architecture University of Zagreb, physical models of centrifugal pump and centrifugal vortex pump were made, that correspond to numerical models and the experimental line with the respective equipment that allowed the change of angular velocity, setting of the working point and measuring of current flow, increment of pressure and propulsion power. The numerical simulation of unsteady flow in centrifugal pumps and centrifugal vortex pumps VI were conducted using commercial software package ANSYS Fluent for Computational fluid dynamics which is based on the finite volume method. The research results have contributed to clarify the mechanisms of energy conversion in a centrifugal vortex pump and confirmed the favorable impact of a vortex ring on the pump characteristics (flow, pressure, efficiency, cavitation characteristics).

U radu je razvijena metoda konačnih volumena za rješavanje Navier-Stokesovih jednadžbi za slučaj laminarnog nestlačivog strujanja. Metoda se temelji na novom algoritmu za povezivanje polja brzine i tlaka. Osnovna razlika novog algoritma u odnosu na danas najčešće korišteni SIMPLE algoritam, sastoji se u tome da je u njemu jednadžba kontinuiteta zadovoljena u svakoj iteraciji, a konačnom se rješenju približava korigiranjem masenih protoka kroz stranice konačnih volumena sve dok polje gradijenta tlaka ne postane bezcirkulacijsko. Brzina konvergencije novog algoritma (primijenjena u vlastito razvijenom računalnom programu) uspoređena je s brzinom konvergencije algoritma SIMPLE (primijenjenom u komercijalnom računalnom programu FLUENT) u nekoliko tipičnih slučaja strujanja fluida pri niskim i visokim vrijednostima Reynoldsova broja, te za slučaj slobodne konvekcije pri niskim i visokim vrijednostima Rayleighova broja. Temeljem dobivenih rezultata zaključuje se da je u primjerima neviskoznog i viskoznog strujanja: (1) brzina konvergencije novog algoritma značajno veća, pri čemu korisnik ne treba zadavati podrelaksacijske faktore za brzinu i tlak o kojima bi ta brzina ovisila, kao u slučaju algoritma SIMPLE. (2) Brzina konvergencije novog algoritma praktično ne ovisi o gustoći mreže, za razliku od brzine konvergencije algoritma SIMPLE koja opada s porastom gustoće mreže. Brzina konvergencije novog algoritma blago opada s porastom složenosti slike strujanja u konačnom rješenju (pojava vrtloga, tj. odvajanja strujanja) i primjenom sheme višeg reda točnosti (zbog primjene „deferred correction“ postupka). Kod primjene sheme višeg reda, s porastom gustoće mreže brzina konvergencije raste. (3) Učinkovitost novog algoritma (u smislu utroška računalnog vremena za postizanje željene točnosti rješenja) pokazala se većom, unatoč manje optimalnoj implementaciji novog algoritma u usporedbi s implementacijom algoritma SIMPLE u komercijalnom paketu FLUENT. U primjerima slobodne konvekcije broj potrebnih iteracija za postizanje rješenja zadane točnosti raste obzirom na slučaj neviskoznog i viskoznog strujanja, zbog nepotpune implicitnosti u obračunu uzgonskih sila. Brzina konvergencije novog algoritma bi se povećala kad bi se jednadžbe za korekcije protoka i temperature rješavale simultano. Primijećeno je da broj potrebnih iteracija raste s porastom Rayleighova broja, ali u svim slučajevima novi algoritam brže konvergira od algoritma SIMPLE. Novi algoritam rezultira sustavom linearnih algebarskih jednadžbi s manje nepoznanica, ali je matrica sustava gušće popunjena, tako da je sa stajališta zauzeća memorije zahtjevniji. Daljnji nedostatak novog algoritma se ogleda u činjenici da ova matrica nema svojstva poznate M-matrice, kao u slučaju SIMPLE algoritma, što zahtijeva dodatna istraživanja na razvoju efikasnih iterativnih rješavača za takav tip matrice sustava. A finite volume method for solving Navier-Stokes equations in cases of laminar incompressible flows was developed. The method is based on a new-proposed pressure-velocity coupling algorithm. The fundamental difference of the new algorithm, compared to the most frequently used SIMPLE algorithm, is that in the new algorithm, the continuity equation is satisfied in each iteration. Within the new algorithm, the final solution is approached by correcting the cell face mass flux until the pressure gradient field becomes irrotational. The new algorithm (implemented in a in-house computer code) and the SIMPLE algorithm (implemented in the commercial software package, FLUENT) are compared in terms of convergence rate in few typical cases of laminar flow ranging from low to high Reynolds number, and in cases of natural convection covering the range from low to high Rayleigh number. In accordance with the obtained results, it is concluded that in the cases of inviscid and viscous flow: (1) The convergence rate of the new algorithm is significantly higher, and the user need not to prescribe pressure and velocity under-relaxation factors on which this rate would depend, as is the case with the SIMPLE algorithm; (2) The convergence rate of the new algorithm is practically independent on mesh density (mesh size), in contrast to the convergence rate of the SIMPLE algorithm, which decreases with increasing mesh density. Rate of convergence of the new algorithm slightly decreases with increasing complexity of flow pattern (the appearance of vortices and zones of flow separation) and with applying a higher order differencing scheme (due to deferred correction approach). Here, when applying the higher order scheme, the convergence rate increases with increasing mesh density; (3) The new algorithm shows better efficiency than SIMPLE, regardless to possibly suboptimal coding of the new algorithm when compared to the SIMPLE algorithm, professionally coded within the FLUENT software package. In cases of natural convection the number of iterations required to achieve the prescribed solution accuracy is greater with respect to the cases of pure inviscid and laminar flows, due to partially explicit treatment of the buoyancy force. Here, in order to increase the convergence rate of the new algorithm, the equations for the mass flux and temperature corrections should be treated in a coupled manner. The number of iterations required in new algorithm increases with the Rayleigh number, but here also, throughout the whole range of Rayleigh number, the new algorithm shows better performance than the SIMPLE algorithm. The new algorithm results in a linear system with less unknowns, but with a denser matrix than in the case of SIMPLE algorithm, thus it is more memory demanding. The drawback of the new algorithm is that this matrix does not possess the properties of the well known M-matrix, as in the case of the SIMPLE algorithm, which requires additional research in finding of an efficient iterative solver for such type of matrix.

U radu je razvijen računalni program za analizu dvodimenzijskog turbulentnog strujanja fluida. Program se temelji na metodi konačnih volumena na lokalno ortogonalnoj nestrukturiranoj geometrijskoj mreži u kojoj se brzine i tlakovi računaju u istim čvorovima (nepomaknuta mreža). U korištenoj lokalno ortogonalnoj mreži je svaka stranica konačnog volumena okomita na spojnicu susjednih čvorova i dijeli ju na dva jednaka dijela. Definirane su dvije varijante metode konačnih volumena. U prvoj varijanti se za povezivanje polja brzine i polja tlaka koristi algoritam SIMPLE, a u drugoj algoritam SIMPLER, koji se do sada nije koristio na nestrukturiranoj nepomaknutoj mreži. U program su ugrađene: uzvodna shema diferencije, shema centralne diferencije, kombinacija uzvodne i sheme centralne diferencije, eksponencijalna shema i vlastita varijanta unaprijeđene eksponencijalne shema diferencije. Brzina konvergencije algoritama u vlastitom programu uspoređena je s brzinom konvergencije algoritma SIMPLE u javno dostupnom programu CAFFA autora M. Perića, u kojem se primjenjuje strukturirana neortogonalna mreža. Zaključeno je da se zbog neortogonalnosti mreže povećava potreban broj iteracija numeričkog postupka, te da neortogonalnost geometrijske mreže smanjuje područje vrijednosti faktora podrelaksacije u kojem algoritam SIMPLE konvergira. Pokazano je da su numerički rezultati na lokalno ortogonalnoj mreži točniji od rezultata na neortogonalnoj mreži. U slučaju nestrukturirane mreže, lokalna ortogonalnost je omogućila formulaciju algoritma SIMPLER, koji je u većini provedenih testova brže konvergirao od algoritma SIMPLE. U slučaju turbulentnog strujanja veliki utjecaj na brzinu konvergencije ukupnog numeričkog postupka ima brzina konvergencije jednadžbi modela turbulencije, pa prednosti algoritma SIMPLER u odnosu na algoritam SIMPLE nisu izražene u velikoj mjeri. Općenito se može zaključiti da predložena lokalno ortogonalna mreža omogućuje dobru diskretizaciju geometrijski složenih područja i omogućuje definiranje stabilnih i točnih numeričkih metoda. A computer program for the analysis of two-dimensional turbulent fluid flow has been developed. The program is based on the finite volume method on unstructured locally orthogonal grid with the same nodes for all variables (collocated grid). In the used grid each cell face is orthogonal to the connection line of two adjacent nodes and divides it in two equal parts. Two variants of finite volume method have been proposed: one using the SIMPLE algorithm and the other using the SIMPLER algorithm which has not been used on the unstructured collocated grids yet. The following differencing schemes have been implemented: first order Upwind Differencing Scheme – UDS, Central Differencing Scheme – CDS, the combination of UDS and CDS, Exponential Differencing Scheme – EDS and Exponential Differencing Scheme Improved – EDSI. Results of proposed variants of the finite volume method have been compared with the results obtained with the public CFD program CAFFA on a structured non-orthogonal grid (author M. Perić) in terms of convergence rate and accuracy. It is concluded that the grid non-orthogonality increases the number of iterations needed to achieve prescribed accuracy. Due to the grid non-orthogonality the domain of under relaxation factors, in which SIMPLE algorithm converges, becomes smaller. It has been demonstrated that the numerical results obtained on locally orthogonal grid are more accurate than the corresponding results obtained on non-orthogonal grid. In the case of the unstructured grid, local orthogonality enables the application of the SIMPLER algorithm which is superior to the SIMPLE algorithm with respect to rate of convergence in most test cases without turbulence. In case of turbulent flow, the convergence of numerical method is mainly influenced by the convergence of turbulence model equations. Consequently, the superiority of the SIMPLER over SIMPLE algorithm is abated. A general conclusion is that the proposed locally orthogonal grid enables good discretisation of complex geometries and a robust and accurate numerical procedure.

U ovom radu napravljen je trodimenzionalni model IB prostorija na elevaciji 100.3 metara nuklearne elektrane Krško koje su pod utjecajem loma u sustavu za čišćenje parogeneratora. Od vitalnog je značaja za sigurnost elektrane osiguranje točno propisanih uvjeta u prostorijama s akumulatorskim baterijama i punjačima koje se nalaze na ovoj elevaciji u IB zgradi jer se na taj način osigurava i napajanje kompletne nuklearne instrumentacije. Za propisani maseni protok ispuštenog fluida i za različite scenarije otvaranja komunikacije prema turbinskoj zgradi i okolišu, te izolacije mjesta loma, uz pomoć CFD programa FLUENT određena je trodimenzionalna raspodjela temperature i identificirane su povoljne lokacije za ugradnju temperaturnih senzora. U prvoj fazi rada su se zbog što je moguće bolje komparacije s programom GOTHIC ali i zbog upoznavanja mogućnosti programa FLUENT napravili proračuni u relativno jednostavnoj geometriji. Upravo su iskustva stečena na ovim tzv. jednostavnijim modelima predstavljala značajan doprinos kasnijem, kvalitetnijem, modeliranju te proračunu strujanja u složenoj geometriji IB prostora. U uvodim poglavljima ovog rada napravljen je pregled osnovnih značajki analize (Grgić, 2001) koja je trasirala put i postavila temelje analizi napravljenoj u ovom radu. Također, predstavljene su osnove jednadžbe dinamike i mogućnosti CFD programa FLUENT. Kroz analizu dobivenih rezultata na modelu IB prostorija, neovisno o analiziranom scenariju, pokazalo se je da je najpovoljnija lokacija za ugradnju temperaturnih senzora prostorija IB010 i to njezini zidovi prema zgradi kontejmenta i prema prostoriji IB007. Kao zaključak može se reći da je i uz sva nužno uvedena pojednostavljenja uvođenje CFD programa FLUENT u rješavanje ove klase problema sigurno opravdalo svoju svrhu. Naime, po prvi su se put vidjele lokalne raspodjele temperature i brzine strujanja koje su jako nedostajale proračunima s modelima s distribuiranim volumenima. Također, i sama nestacionarnost i trodimenzionalnost problema zahtijevala je softverski paket koji je najučinkovitiji upravo u tom dijelu. Korištenjem CFD programa FLUENT se po prvi put kroz rezultate uspjela potvrditi činjenica da prilikom uspostavljanja dominantnog strujanja prema turbinskoj zgradi na vratima IB010-IB001 dolazi do reverziranja smjera strujanja. Međutim, nikako se ne smije zanemariti i jako velika kompleksnost modeliranja dvofaznih strujanja kroz program FLUENT, te čak i uz dosta pojednostavljenja jako dugo vrijeme izračuna. Upravo u zadnje navedenim činjenicama leži najveća prednost programa GOTHIC u odnosu na program FLUENT, brže vrijeme izračuna i jednostavnije modeliranje dvofaznih strujanja. Kombiniranjem ova sva programska paketa dobrim dijelom su se anulirale mane svakog od njih te dobiveni rezultati čine jednu, kompaktnu, cjelinu. Budući rad u ovom području upravo je determiniran kombiniranim korištenjem CFD programa i programa s distribuiranim volumenima koji bi bili alat za validaciju rezultata dobivenih CFD analizom. In this master thesis three dimensional model of Nuclear power plant Krsko IB rooms on the elevation of 100.3 meters which could be under influence of the break in the blowdown processing system was built. It is essential for the safety operation of the nuclear power plant to preserve very strictly defined environmental condition in rooms with DC batteries and their chargers. If the batteries and chargers are preserved in good operating condition we have the strongest guarantee for the safety of nuclear instrumentation power supply. For the defined mass flow of discharged fluid and for the different scenarios of break point isolation and communication with environment, via turbine building or via IB001 room, with the CFD code FLUENT three dimensional contours of temperature were calculated. Also based on the results of this analysis optimal locations for temperature sensors were defined. In the first phase of the master thesis work with the aim to get a better comparison with results obtained with GOTHIC code first calculations with FLUENT were made on a simple geometry models. Results and experience obtained on this simple geometry models were essential for the quality of the calculation in quite complicated model of IB rooms. In the first chapters of this paper basic overview of the past analysis (Grgić, 2001) were made. This past analysis (Grgic, 2001) was the base and input for the analysis that was made in this paper. Also in the first, so called introducing chapters key set of fluid dynamics equations and basic capabilities of the CFD code FLUENT were presented. Through the analysis of the results obtained on the model of IB room optimal location for the temperature sensors were defined. Based on all scenarios, wall between room IB010 and containment building and wall between IB010 and IB007 which are in the room IB010 were declared to be optimal location for the sensors. As global conclusion after these analysis we may say that even regarding all simplifications of the model that were necessary to make introduction of the CFD code FLUENT in this class of problem was very valuable. Results of analysis preformed with FLUENT clearly present local distribution of temperature and velocity vectors. Also unsteadiness and three dimensionality of the resolving problem was ideal place for the implementation of CFD code FLUENT. Results of the analysis confirmed for the first time that in the moment when communication via turbine building would be opened, on the door between rooms IB001 and IB010 would occur a reverse flow. Also we can not neglect the fact that modelling multi-phase phenomena with FLUENT is a very complex problem. Very good advantage of GOTHIC code is defined in this last sentence that describes disadvantage of FLUENT. GOTHIC code has very good capabilities for the multi-phase phenomena modelling but limited three dimensional capabilities. Combination of these codes provides the best results when applied to the analysis of this class of problems. Perspectives for the future work in this field are underlined with the combined usage of CFD codes and codes with distributed volumes for the validation of the results obtained with CFD codes.