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The circular cyclone separator is a commonly used device for separating solid particles from gas streams. The performance of the cyclone separator is strongly influenced by the inlet configuration, which affects the flow patterns and particle trajectories within the separator. In this numerical study, the effect of different inlet configurations on the performance of the circular cyclone separator was investigated using computational fluid dynamics (CFD). The Unsteady Reynolds Averaged Navier Stokes equation Reynolds stress turbulence model (RSTM) were solved to simulate the gas flow. The Eulerian method was used for particle trajectory analysis. CFD simulations were implemented on different inlet configurations. Computational findings showed that particle separation efficiency decreased dramatically with increase on inlet temperature because of weaker swirling flow through the cyclone. For the pressure drop decreases as inlet temperature increases because of weaker swirling flow through the cyclonic separator. These findings have important implications for the design and optimization of circular cyclone separators for industrial applications. [ABSTRACT FROM AUTHOR]

Electrospray, or Electrohydrodynamic Atomization (EHDA), is a technique in which a high voltage is applied to a liquid to create aerosols. When a fluid is subjected to an adequately strong electric field induced by high voltage, its surface deforms into a cone from whose apex a jet is formed and disintegrates into microscale or nanoscale charged droplets. This multi-physics phenomenon can be applied in various areas, such as medicine delivery, 3-D printing, space thruster design, etc., owing to its low cost, high production rate and ease of control compared with other techniques. In electrospray, spraying regime can be controlled by varying parameters such as applied voltage, liquid flow rate, spraying distance, etc., and the most desirable spraying mode is the single cone-jet due to its stability, controllability, and relatively high yield rate. In this work, the authors introduce a simulation code to investigate the characteristics of electrospray operating in the cone-jet mode utilizing OpenFOAM. In our simulations, Gauss's Law and Charge Conservation Equation are solved simultaneously with Navier-Stokes equations and VOF interface tracking method to numerically produce transient multiphase electrohydrodynamic mechanism. Computational results are validated by experimental data with close agreement. [ABSTRACT FROM AUTHOR]

A numerical model is used to explain the high-frequency surface pressure fluctuations experimentally observed during the transient impact of a supersonic jet onto a substrate. The observations are made during experiments associated with the Shockwave-Induced Spray Process. Various approximations of the experimental arrangement and operating conditions are made to simplify the model and maintain a reasonable computational cost. The model geometry is axially symmetric, and a single mean jet Mach number value is used. The selected Mach number corresponds to the transient value that occurs during the high-frequency oscillation. The steady Reynolds-Averaged Navier-Stokes equations are first solved to establish the mean velocity field, followed by an unsteady Reynolds-Averaged Navier-Stokes solution to resolve the fluctuations. Due to the presence of acoustic wave propagation, non-reflecting boundary conditions are employed on the atmospheric boundaries of the solution domain. The numerical results indicate that the substrate pressure fluctuations are due to an instability of the bow shockwave that forms ahead of the substrate. The shock experiences an axially pulsing oscillation which is consistent with that previously described in the literature. The predicted frequency of oscillation however does not agree with the experiment. This is explained by the differences in the current model geometry compared to that of the actual experimental equipment. [ABSTRACT FROM AUTHOR]

In practice, there are many works dedicated to the drastic simplification of the Navier-Stokes equations and to finding their particular solutions that are very relevant for practice. These studies are usually based either on symmetry considerations or on the theory of concreteness and dimensions. In this article, a mathematical model of the motion of an incompressible fluid in a diffusion nozzle was created and numerical results were obtained. For this, the Nave-Stokes equation was reduced to a parabolic equation with Mises substitutions. Using the obtained numerical results, the longitudinal and transverse velocities of the fluid were determined [ABSTRACT FROM AUTHOR]

The hydrodynamic problems could be solved by assisting the computational fluid dynamics software, paid or based on open-source software. An open-source CFD software, OpenFOAM, is currently at the forefront of solving fluid-related problems, competing with paid CFD software, such as ANSYS Fluent, FLOW-3D, Autodesk CFD, or PHONICS. This study aims to show how OpenFOAM solves one of the fundamental hydrodynamic problems: water flow around a cylindrical obstacle. OpenFOAM's ability to solve turbulence problems at a boundary is determined by observing the flow pattern behind a cylindrical obstacle based on velocity profiles and streamlines. Meanwhile, OpenFOAM's ability to generate the resistance of an obstacle to fluid flow is determined by calculating the drag coefficient based on nine variations of the Reynolds number (Re). 2D flow simulations have been built with OpenFOAM using a CFD approach. OpenFOAM solves the Navier-Stokes equation for incompressible flow by applying the Finite Volume Method. A Turbulent Large Eddy Simulation (LES) k-equation model was chosen to overcome the turbulence. The water velocity field around a fixed diameter cylinder has been calculated using OpenFOAM based on the variation of Re from Re=0.1 (laminar flow) to Re=107 (turbulent flow). The velocity profile of the water behind the cylinder has been compared with the theory and shows a good agreement between the numerical and theoretical results. The streamlines pattern has similarities to the scientific literature. Finally, the drag coefficient (CD) is calculated based on the velocity field generated from the OpenFOAM calculations. The values of CD have followed the drag coefficient diagram of the scientific literature. The comparison test shows that OpenFOAM performs well in solving the problems of water flow through a cylindrical obstacle. The open-source CFD software OpenFOAM could be used as an alternative low-cost option to support studies related to hydrodynamics, such as aerodynamic studies, bridge pier structure design, wind and water turbine studies, and offshore/onshore foundation structure design, and breakwater design. [ABSTRACT FROM AUTHOR]

The Spalart-Allmaras (SA) turbulence models applied to the calculation of swirling flows inside a separator was studied. Two approaches using vorticity and flow function to eliminate pressure and a semi-implicit method for pressure-linked equations (SIMPLE) for solving Reynolds-averaged Navier-Stokes equations were compared in the article. For the numerical solution of both approaches, the implicit method against the flow was used. [ABSTRACT FROM AUTHOR]

This paper describes in detail the method and algorithm for calculating the numerical integration of non-stationary two-dimensional systems of Navier-Stokes equations for a compressible gas using high-order implicit (explicit) difference schemes, i.e., the Beam-Warming difference scheme. A number of mathematical transformations, such as non-dimensionalization of coordinates and physical parameters, transforming the shape of the channel into a square one, as well as thickening the integration steps with large gradients of unknowns, which make it possible to bring problems to a model one for solving similar problems. In addition to the study, as convergence in the number of calculated points, the dependence of the number of iterations on the Courant number and comparison of the results obtained by different proposed models for calculating the effective viscosity, as well as a number of numerical studies as co-occurrence, temperature inhomogeneities, non-design, the ratio of the sizes of the inlet slots of cocurrent flows and the length of the channel to the height of the main flow and the degree of expansion of the channel to the process of mixing and distribution of flows in the channel. It was revealed at what ratios of the initial parameters of the cocurrent flows and the linear dimensions of the channel a recirculation zone is formed. For a channel of constant cross section at large ratios of velocities (72, 46) and temperature (2, 33), as well as small ratios of the channel length to the height of the inlet slot of the main flow (5, 31), even at the same jet pressures in the initial section, the recirculation zone occupies more than 55% of the input section, and the length along the longitudinal coordinate reaches 20 cm. [ABSTRACT FROM AUTHOR]

This paper presents a method and algorithm for calculating the outflow of a multicomponent chemically reacting gas mixture flowing out of a rectangular nozzle with different aspect ratios and propagating into a cocurrent (flooded) flow. To describe the turbulent flow, the three-dimensional parabolic system of Navier-Stokes equations for multicomponent chemically reacting gases is used. Justified initial and boundary conditions are given. The system of equations is given after non- dimensionalization of spatial coordinates and physical parameters, as well as with the help of mathematical transformations, allowing the inlet section of the nozzle to be reduced to a unit square. To calculate the turbulent viscosity, a modified algebraic turbulence model is used that takes into account temperature inhomogeneity and velocity effects in spatial coordinates. For the numerical integration of the system of equations, a two-layer ten -point implicit finite-difference scheme was used. The continuity equation is used to calculate the mass imbalance in each computational grid. The calculation algorithm and the method for determining the boundary of jet displacement are given in detail. A number of numerical experiments have been carried out to refine the empirical Karman constant included in the turbulence moduli. Poisson's difference equation, relative to the potential function for calculating the correction for three velocities at each point in space, is solved by introducing reasonable assumptions, allowing to have a tridiagonal system of equations. This allows efficient computation. The reliability of the results was verified by comparing the numerical results with the experimental works of other authors. [ABSTRACT FROM AUTHOR]

Recently, inertial-based microfluidic systems for cell separation have gained popularity owing to their ease of use and ultra-high throughput. Hydrodynamic forces prevail at the microchannel's top and bottom, creating two counter-rotating vortices that power these devices. The vortices form due to the centrifugal force acting as a secondary force inside the spiral form of the microchannel. This study employs COMSOL Multiphysics for a numerical simulation of dean flow dynamics based on the Navier-Stokes equation. Changing the flow rate inside a spiral microchannel allows for more efficient separation of RBCs, WBCs, and platelets, the three primary cell types found in human blood. The influence of channel Reynolds number and radius of curvature on dean flow velocity is investigated. PDMS (Poly Dimethyl Siloxane) is chosen as a material because of its flexibility and biocompatibility nature. The optimized spiral microchannel can be used for effective cell focusing and separation corresponding to their size depends on lateral hydrodynamic forces. [ABSTRACT FROM AUTHOR]

The aim of this research is to study and analyze the effect of the magneto-hydrodynamic peristaltic flow of Jeffrey fluid on its temperature and concentration through a flexible porous channel with an endoscope in the center of the channel. Where a magnetic field is created by the electrical conduction of the Jeffrey fluid flow channel. Using cylindrical coordinates and assuming a very short wavelength "relative to channel width to length" and using the dimensionless equations that govern the main equations of Jeffrey's fluid in the Navier-Stokes equations, the results of the problem were obtained and through the "Mathematics 12" program these results were analyzed. It is observed that the effect of bending stiffness and longitudinal tension of the wall, as well as permeability, capacitance ratio, and Jeffrey's modulus all increase the velocity of the fluid and thus its temperature while the concentration of the fluid decreases, and this is evident in the middle of the flow channel when the velocity and temperature curve is at the highest value while the concentration is at its lowest level. It is concluded from this research that the magnetic field has a major role in decreasing the fluid velocity [ABSTRACT FROM AUTHOR]

Currently accepted turbulence theory assumes that the flow is continuum at all length scales, including the smallest length scale of turbulence, known as the Kolmogorov scale. Kolmogorov in his celebrated 1941 theory [A. N. Kolmogorov, C. R. Acad. Sci. URSS 30, 301-305 (1941)] asserted that the fine-scale turbulent structures in the energy cascade are universal. According to Kolmogorov's theory, the energy dissipation rate and kinematic viscosity alone describe this universal behavior in terms of the Kolmogorov length, time, and velocity scales. However, it has been suggested [R. Betchov, J. Fluid Mech. 3, 205-216 (1957); D. Bandak, N. Goldenfeld, A. A. Mailybaev, and G. Eyink, Phys. Rev. E 105, 065113 (2022)] that thermal fluctuations, absent from the continuum description of gases, can terminate the energy cascade at a length scale larger than mean-free-path considerations alone would suggest. Additionally, for high-Mach-number turbulent flows, the Kolmogorov length scale can be comparable to the gas-molecule mean free path, which could induce noncontinuum molecular-level effects in the turbulent energy cascade. To investigate these two issues, compressible Taylor-Green vortex flow is simulated using the direct simulation Monte Carlo (DSMC) method and direct numerical simulations (DNS) of the Navier-Stokes equations. It is found that the molecular-gas-dynamics spectra grow quadratically with wavenumber in the dissipation range due to thermal fluctuations instead of decreasing exponentially as the continuum description predicts. Macroscopically, thermal fluctuations appear to break the flow symmetries and thereby produce different but statistically similar routes from the initial non-turbulent flow to the long-time turbulent flow. [ABSTRACT FROM AUTHOR]

Among active flow control methods, a counter-flow jet is known to be efficient in supersonic to hypersonic flow regimes for drag reduction at high-Reynolds number regime. In order to apply the counter-flow jet in various flight environments, it is necessary to investigate the effect of drag reduction at not only low and medium altitudes but also high ones with low atmospheric density. To investigate the effect of the Reynolds number on drag reduction with the counter-flow jet, the stagnation pressure ratio (PR) defined as the ratio of the stagnation pressure of the counter-flow jet to that of the free-stream flow is fixed to 1.05, at which the flow field is known to be classified as short penetration mode (SPM) in high-Reynolds number regime. The Mach numbers of the free-stream flow and counter-flow jet are 6 and 2.86, respectively. The stagnation pressure of the free-stream flow is varied from 6.9 kPa to 20 kPa and the stagnation temperature of the free-stream flow and counter-flow jet is 610 K and 294 K, respectively. The maximum Knudsen number based on the radius of the hemisphere model is 0.01. The numerical simulations were performed solving the laminar, unsteady, axisymmetric Navier-Stokes equations by the symmetric TVD scheme with the second-order accuracy in space and the explicit strong stability preserving Runge-Kutta (SSPRK) method. The numerical results show that at the same stagnation PR, shock structure, the penetration length to the flow field, and drag reduction effect are almost identical irrespective of the difference in the free-stream stagnation pressure. Moreover, by decreasing the Reynolds number, the flow field becomes more stable due to the viscosity effect. [ABSTRACT FROM AUTHOR]

The accurate prediction of the aerodynamic and aerothermodynamic data for a reentry vehicle at high altitudes is often an important guidance for the design of the thermal protection system. During the reentry process, the hypersonic vehicles will intensively experience complicated physical and chemical phenomena, primarily including the real gas effects and rarefied gas effects. In this study, the model of nonlinear coupled constitutive relations (NCCR) is introduced for the numerical simulations of hypersonic reentry flows with the effects of thermochemical nonequilibrium and rarefaction nonequilibrium, as well as Gupta's chemical kinetic model and Park's two-temperature model are employed. Two numerical examples, including hypersonic flows around the ELECTRE vehicle at 54.3 km and the Orion command model at 105 km, are used to examine the performance of the present solution. It is found that the results computed by NCCR model, especially the heat flux distributions along the solid surface, are in better agreement with those of direct simulation Monte Carlo or flight data than the conventional Navier-Stokes equations. [ABSTRACT FROM AUTHOR]

The simulation of gas flows covering a large range of Knudsen number is still challenging, as the coupling of solvers based on the Navier-Stokes equations, which become inaccurate for rarefied flows, with the DSMC method, computationally costly in dense regions, is not straightforward. However, a multiscale method capable of handling both regimes would be beneficial to numerous applications, ranging from aerospace engineering to microelectromechanical systems. The use of the BGK collision operator in the Boltzmann equation has proven efficient for both discrete velocity methods and particle-based simulations, for gas flows in a range that goes from rarefied to lower Knudsen number regimes. The latter type of solvers also has the advantage to be easily coupled with the widely used DSMC, but corresponds however to schemes that are usually limited to first order and can therefore require fine resolutions. We present here a method that achieves second order in time by integrating the BGK equation using exponential time differencing. The idea is similar to DUGKS, which reaches second order with a Crank-Nicolson integration, but in our method all prefactors remain positive regardless of the timestep. This allows its extension from a discrete velocity-type method to a particle-based scheme without introducing any negative weighted particle, hereby keeping the implementation analogous to the standard stochastic particle BGK method. The resulting exponential differencing scheme is implemented with both stochastic particle and discrete velocity approaches, and its accuracy and efficiency are compared to preexisting BGK methods on several test cases. [ABSTRACT FROM AUTHOR]

The numerical simulation of multi-scale problems and non-equilibrium gas flows is of highest interest as experimental investigations are extremely complicated or impossible. Using the well-established Direct Simulation Monte Carlo (DSMC) method, a highly accurate solution of these flows can be achieved. However, simulations are accompanied by excessive computational requirements in the transitional and continuum regime. Considering continuum simulation methods instead, the assumptions behind the Navier-Stokes equations become invalid for rarefied gas flows. An alternative approach for the simulation of multi-scale problems is the application of the Bhatnagar-Gross-Krook (BGK) collision operator. The ellipsoidal statistical BGK (ESBGK) method implemented in the open-source particle code PICLas is extended for multi-species modeling of diatomic molecules. This opens up the possibility of constructing particle-based methods for continuum flows, which can then be easily coupled to existing DSMC solvers. For the determination of the transport coefficients of the gas mixture, Wilke's mixing rules are used. The hypersonic flow around a 70° blunted cone is simulated as test case with both the ESBGK method and the DSMC method and the solutions are subsequently compared to assess the accuracy and the computational efficiency. [ABSTRACT FROM AUTHOR]

In this study, a numerical technique for solving the generalized time-fractional Navier-Stokes equation in cylindrical coordinates via cubic B-spline (CBS) basis functions is proposed. The suggested technique for solving the problem is derived from the finite difference method and the collocation method. Caputo's derivative of order 0 < α ≤ 1 and CBS functions are employed for the time and spatial discretization, respectively. The Fourier stability analysis, derived from the von Neumann method was performed and indicate unconditionally stable. The convergence analysis of the presented numerical technique is of order O(h2 + Δt2−α). [ABSTRACT FROM AUTHOR]

Water wave propagation is a complex physical phenomenon in the field of coastal and ocean engineering, and it plays an important role in the prediction of working performance for nearshore, offshore and deep-water structures such as port facilities, marine vessels, floating offshore platforms. This paper presents the formulation of Green-Naghdi level I equation from the physics conservation of mass and momentum using infinitesimal element. The governing equation are derived from the Navier-Stokes equation by following Krylov-Kantorovich method. The output will enhance the understanding of behaviour of water wave propagation. The theoretical findings will start as a basis for future investigations such as the smoothness of the transition point of the water wave propagation by changing the shape function for high level Green-Naghdi Equation. [ABSTRACT FROM AUTHOR]

This paper studied active flow control techniques like suction and injection to control the boundary layer. The steady, incompressible, and two-dimensional flow passes over the flat plate, and boundary layer formation starts at the plate's leading edge. The flow is uniform and parallel to the surface of the plate at the leading edge. The suction or injection has been applied at a distance of 0.25m from the leading edge of the flat plate to convert the problem more realistic and continue up to the trailing edge. The discrete slots or porous portion is available downstream after 0.25m for mass transpiration. A steady, two-dimensional, incompressible Navier-Stokes equations are solved using OpenFoam software using a simpleFoam solver with appropriate boundary conditions. For non-uniform suction and injection, considered two variations, the first one is linear variation, and the second is quadratic variation. However, for oblique non-uniform suction/injection variations five angles (θ=300, 600, 900, 1200, and 1500) are proposed. The codedFixedValue type code is developed for oblique non-uniform wall suction and injection in the velocity boundary condition. The results show that the wall-normal component of oblique or vectored suction/injection velocity (Vw), non-uniform suction/injection profiles, suction/injection intensity, and suction/injection angles significantly affect the boundary layer characteristics. A detailed discussion has been presented in the results and discussion section. [ABSTRACT FROM AUTHOR]

Supersonic Combustion jet engine is an engine where the combustion of the fuel inside the chamber happens at a supersonic flow velocity. Analysis is finished within the domain of the whole nozzle from entry to all the way further to exit part with Fixed Angle. A basic divergent nozzle design is considered and the moderation is done at the mid-section throughout the exit part by fixing the angles at the mid-section as per the enlargement zone proceeds up to exit. One angle is determined to get betterment inside the diffusion part of the nozzle and computational analysis is substantiated with Computational Fluid dynamics tool ANSYS fluent. Solving the density-based Navier Stokes equation and simulation is performed to obtain the numbers of pressure, temperature, density, and Mach no. by assuming the flow in the nozzle and fluid in the domain follows the ideal gas laws. Numerical analysis (MATLAB) is performed and the value of pressure, temperature, density, at every section of the divergent nozzle is calculated and compare both numerical and computational analysis to validate results. [ABSTRACT FROM AUTHOR]

The hypervelocity vehicle has a very high speed during flight and during this flight, the vehicle experiences very high wave drag on the body, with the highest pressure in the nose region of the vehicle. Therefore, it becomes necessary to reduce drag for safer and more economical flights. The retractable aero-spike is a simple and effective drag mitigation device, so it becomes imperative to use a suitable spike to increase its effectiveness. In this research, Numerical results on the effect of mechanical cut aero-spike at the stagnation point of a 60° half-angle blunt cone model in a hypersonic flow stream are presented. The commercial code of ANSYS fluent is used for the present numerical investigation. The two-dimensional Reynolds-average Navier-Stokes equation (RANS) was solved numerically using ANSYS Fluent. The k-ω two-equation turbulence model was used in this study. The length of the aerospike is taken by four different lengths to base diameter (L/D) ratios: 0.2, 0.5, 0.7, and 1.0. The numerical investigation discovered a drag reduction is about 20.6% (maximum mitigation) when using cut shape aero-spike in an axisymmetric 600 apex angle blunt cone. [ABSTRACT FROM AUTHOR]

Using the fractional Adomian decomposition approach, the time fractional Navier-Stokes equation (TFNSE) with Atangana-Baleanu fractional derivative (ABFD) is approximated analytically in this paper (FADM). The suggested technique is successful in obtaining approximate TFNSE solutions with fractional order. [ABSTRACT FROM AUTHOR]

The paper discusses the derivation of criteria for pollutant mineral matter in fuel that is hazardous for fuel metering equipment (FME) of aircraft jet engines. It is concerned with mechanical impurities captured during fuel transportation, pumping, draining and storage, and with quartz of various range of dimensions. With optical microscopy and the requirements for model matter to obtain a mathematical description of the aviation fuel sedimentation process based on a particular solution of the Navier-Stokes equation, a sphericity coefficient of 0.835 was adopted for a ball. Based on the data obtained, 4 criteria for matter hazardous for FME were identified: hardness, size, density, shape. [ABSTRACT FROM AUTHOR]

Numerical simulations of 3D turbulent flow over a projectile model have been performed at the angles of attack α = 4° and α = 6° at high subsonic free-stream Mach numbers M∞. The simulations are based on the unsteady Reynolds-averaged Navier-Stokes equations using the k-ω Shear Stress Transport and Detached Eddy Simulation turbulence models. The obtained solutions reveal an intricate behavior of the lift force and pitching moment as functions of M∞. Locations of shock waves and supersonic regions on the projectile are discussed, and a physical interpretation of two discontinuities in the dependence of aerodynamic coefficients on M∞ is suggested. [ABSTRACT FROM AUTHOR]

The paper presents the results of numerical simulation of the airflow as compressible viscous heat-conducting medium in the tear-off zones arising near the surface of a high-speed aircraft having a segmental-conical shape blunted frontally to the oncoming flow. The developed mathematical model is based on solving the discrete analogs of the equations of gas dynamics on a structured computational grid for compressible viscous heat-conducting chemical neutral gas. For turbulence modeling two equation of the SST k-w model were added to Navier-Stokes equations. The presented results of modeling are compared with experimental data. The conclusions are made about the correctness of the application of the presented mathematical model for the prediction of flow parameters in tear-off zones. [ABSTRACT FROM AUTHOR]

The goal of this investigation is to determine how a fluid portion's aspect ratio A1 relative to cavity height affects natural convection in a partially porous container. In the porous part, a constant heat source is introduced at bottom (300,500,700,900.1100 W/m2), top is exposed to environment and other walls kept at a constant temperature. The energy equation and the Darcy-Brinkman extension are used to modify the Navier-Stokes equations, which explain the equations for thermal transfer and hydrodynamic flow. The results are represented by an isotherm's distribution (temperature distribution), effect of modified Rayleigh number and velocity streamlines. [ABSTRACT FROM AUTHOR]

Wind tunnels and linearized turbulence and boundary-layer models have been so far necessary to simulate and approximate the stationery lift and drag forces on (base-mounted) airfoils by means of statistically determined or approximated values of the relevant situational coefficients as the drag and lift coefficients. To improve this process, we introduce transient and exact formulae to separate these forces in advance by means of the solutions found from the fluid dynamics model of the Navier Stokes differential equations. [ABSTRACT FROM AUTHOR]

In this paper we continue the study of the invariant measure (IM) of dynamical systems (DS) describing turbulence of viscous incompressible fluid, now concentrating on the particular case of the flow in a long circular pipe. In a previous paper we have proved that using the basis wI of the space of incompressible vector fields satisfying the boundary conditions and expanding the fluid velocity in a series v(x, t)=∑IvI (t) wI (x) the Navier-Stokes equation is equivalent to the simple DS d v I d t = ∑ J K a I , J K v J v K − b I v I + c I , The pressure term, zero-divergence equation and boundary conditions are all 'hidden' in the constant coefficients aI,JK, bI and cI which depend only on the geometry of the system, viscosity of the fluid and the driving volume force c and can be calculated easily. We have also shown that for real-world fluids composed of molecules this DS must have a finite dimension N, hence the summation runs over I=1, ..., N, proved that the IM density ψ(v1..., vN) exists, is unique and can be expanded in the Hermite functions series. Also, a system of linear algebraic equations has been derived for the IM mean value 〈Heµ〉 of Hermite polynomials Heµ (v1,..., vN). In this paper we present further analytical results in the process of solving this algebraic system for the pipe flow, in particular of obtaining the mean values of the first-order Hermite-polynomials 〈vI〉. If we were able to calculate these mean values numerically, then we could also calculate the long-time mean velocity 〈v(x)〉 = ∑I 〈vI〉 wI (x) (i. e. the mean velocity of the stationary turbulent flow), hence give the ab initio answer to Feynman's question he poses as the prototype of the turbulence problemml: 'to push a given amount of water through that pipe, how much pressure is needed?' [ABSTRACT FROM AUTHOR]

The ABC flow for the stationary three dimensional Navier-Stokes equations is considered. The problem is formulated on the full periodic domain. The main object of the paper is the preliminary analysis of the solution curves and location of disconnected solutions from the main branch (stationary trivial solution defined by the forcing term in the ABC problem setup). It is noted that the disconnected solutions exist for two variants of the problem parametrization: A = B = C = 1 and A = B = 1,C = 2. [ABSTRACT FROM AUTHOR]

Boussinesq equations approximate the vector field velocity, pressure, and temperature of a viscous, and incompressible fluid. Boussinesq equations in two dimensions are similar to Navier-Stokes equations. In fact, the first component of Boussinesq equations coincide with corresponding momentum term of Navier-Stokes equations. However, in the second momentum expression of Boussinesq equations appears temperature multiplied by some constants. Besides incompressibility condition, in Boussinesq equations we have a time dependent partial differential equation satisfied by temperature and both components of velocity. In this work, we consider two analytical solutions of Boussinesq equations with a source term in the energy equation. [ABSTRACT FROM AUTHOR]

Lattice Boltzmann Method (LBM) is very much popular for fluid flow applications due to its capability of implementing the physics of the problem as well as simple explicit governing equations unlike to implicit Navier-Stokes governing equations. LBM is extensively used in single and multiphase fluid flow problems. LBM based multiphase and multi component fluid flow analysis models have got wide acceptability amongst all CFD (Computational Fluid Dynamics) tools nowadays. In this paper we propose a LBM based model for Lid driven cavity problem. Main purpose behind our study is to showcase the capabilities and benefits of LB based model against well-established Navier-stokes based solvers. Benchmark problem of Lid driven cavity and 2-D channel flow are solved and numerical results are shown in the paper. Numerical results are in nice agreement with well-established experimental and conventional NS based numerical results. [ABSTRACT FROM AUTHOR]

The goal of this paper is to use the fractional Adomian decomposition approach to discover approximate solutions to time-fractional Navier–Stokes equations (TFNSEs). In the Atangana-Baleanu fractional derivative operator, the proposed technique is considered (ABFDO). The explicit solution of the equation has been stated in closed form using a starting value, and then its numerical solution has been visually displayed. In terms of efficiency and simplicity, the current technique is excellent. [ABSTRACT FROM AUTHOR]

The propulsive performance of a 2D flat plate dynamics, immersed in a turbulent fluid flow is presented in this paper. The flexible structure is animated by a sinusoidal pitching movement. A partitioned implicit coupling scheme is applied to take into account the Fluid-Structure Interaction (FSI) effects. The Arbitrary Lagrangian-Eulerian (ALE) formulation of the Navier-Stokes equations is applied and the anisotropic diffusion equation is solved to determine the displacements of the fluid domain mesh. The flexible plate results are compared to the one obtained with a rigid structure. The analysis of the flow fields has shown that the flexibility of the structure tends to increase the mean thrust coefficient and the load fluctuations. [ABSTRACT FROM AUTHOR]

The paper is devoted to the analysis of the regularity properties of the weak solutions to the steady Navier–Stokes equations when the viscosity μ = μ(x) depends on the point. The problem is investigated in every dimension n ≥ 2 and for weak solutions u ∈ W1,q, with suitable exponent q. [ABSTRACT FROM AUTHOR]

A two-dimensional numerical wave tank (NWT) simulated the interaction between waves and a moving surface-piercing thin plate in intermediate water with a sloping beach. Navier-Stokes equations are discretized using the finite volume method in the tank model built by ANSYS FLUENT software. We'll employ the inflow velocity approach to create the nonlinear wave, which uses five different wave steepness conditions in the testing. The researchers investigated wave-structure interaction around a moving plate. It is essential to examine the efficiency of plate wave energy converters for various relative opening ratios. This paper's primary focus is on how the drag coefficient changes as the wave steepness changes. It demonstrates that when wave steepness increases, the drag coefficient improves. A wave energy converter (WEC) is directly implemented to harvest ocean wave energy as a renewable energy source. Wave steepness and second-order stokes wave theory on an intermediate-water moving thin plate are new topics for discussion. This study gives a new idea to the researchers for developing different types of WEC in the surge direction. [ABSTRACT FROM AUTHOR]

Traditional mathematical methods fail to handle most fluid dynamics issues because they require solving non-linear partial differential equations. The simulation of turbulent flows, on the other hand, is fraught with difficulties. The direct simulation of turbulence via the time-dependent Navier-Stokes equations dubbed Direct Numerical Simulation (DNS) still quite resources intensive. An ensemble averaging approach is used to decompose the flow variables into mean and fluctuation components before using Reynolds-Averaged Navier-Stokes equations (RANS). Applying the principles of RANS, this work has been carried out on three flow phenomena. For the first phase of the study, Transition over a flat plate has been considered and SST with transition followed by Transitional k-kl-ω has predicted the transition with utmost precision whereas the other models failed to capture the onset of transition. Transonic flow over an airfoil has been considered for the second phase of the study. In the second phase, where the shockwave-boundary layer interaction and the third phase of the study where the Shockwave phenomenon was studied, Menter's SST and Realizable k-epsilon have predicted the Shock characteristics and Shock-Wave Boundary Layer Interaction Phenomenon with utmost accuracy. ICEM CFD has been used for structured grid generation and ANSYS Fluent has been used to carry out the Numerical Analysis. ANSYS CFD Post MATLAB and Microsoft Excel have been used for preliminary calculations and result interpretation. [ABSTRACT FROM AUTHOR]

A water turbine is an energy conversion machine that converts kinetic energy into mechanical energy. The free flow water turbine can be used in low river flow or free water flow. The purpose of this research is to optimize the design of free flow water turbine that can be adapted to local potential. This research is a quasi-experimental study to determine the effect of fluid velocity parameters, water depth and number of fins on turbine power. The turbine was designed using Autodesk Inventor CAD software with variations of fins numbered 14, 15 and 16. The simulation was carried out with Ansys Fluent software in three stages: pre-processing, solving, and post-processing. In the pre-processing stage determine the geometry, boundary conditions, meshing and set up. The set-up process in the control solver was selected using a k-epsilon realizable model using the Navier Stokes equation. The solving stage for the running process select number iterations with convergent conditions. In the final stage, the post-processing show reading the results of tangential velocity and torque. Based on the results of the study, it was found that the most optimal of free flow water turbine construction was the number of blades 6, the number of fins 15, the water depth was 0.3 m, the highest torque was 26.5867 Nm and the highest turbine power was 77.2030 Watt. [ABSTRACT FROM AUTHOR]

Due to the fact that the viscosity of non-Newtonian fluids depends on two parameters, the shear rate and the fluid temperature, it is necessary to couple the Navier-Stokes equation with the law of Conservation of Energy to get accurate results in the pressure-throughput calculation of single-screw melt-extruders. In this study a non-isothermal pressure-throughput model will be introduced, considering various parts of the law of Conservation of Energy in down and cross channel direction. The non-isothermal pressure-throughput model will be verificate by comparing velocity- and temperature-profiles over the channel height with CFD-simulation results. [ABSTRACT FROM AUTHOR]

Solving the reduced Navier-Stokes equation for the calculation of the flow of non-Newtonian polymer melts in single screw extruders numerical methods are needed. In this study, a numerical model, based on the finite difference method, for the description of the one- and two-dimensional fully developed conveying characteristics of power law fluids in the melt channel will be introduced. Furthermore, the two-dimensional model will be enhanced by considering the real cross-section of the screw channel and introducing adaption factors which approximate the fully developed three-dimensional flow behavior in the screw channel. Finally, a comprehensive comparison with CFD-Simulation results will be done. Therefore, a parametric study with three independent parameters, pitch to diameter ratio, width to height ratio and power law exponent, will be done and both, viscosity- and velocity-profiles as well as the calculated πm / πP − characteristics will be compared to CFD-Simulation results. [ABSTRACT FROM AUTHOR]

One of the oldest types of human-made hydraulic structures is known as a stepped spillway, and the main use of such structures is to control and monitor the flow of water over embankment dams. However, a common problem encountered by designers of these structures is how to measure the impact of scaling on the structures' performance. This paper thus investigates the effect of scale on the Reynolds and Froude similitudes of such structures using two-dimensional numerical models developed based on Reynolds-averaged Navier-Stokes equations. Dam break conditions were selected to simulate the experiments of this study; therefore, all the essential requirements were applied to achieve model stability. The impact of scaling ratio of 1:2 in gabion stepped spillways on the location of the inception point, the velocity distribution, turbulence intensity, and pressure distribution were explored. The results were then discussed and compared with previous research which conducted over normal stepped spillways. The current study is among the first to provide guidance for the flow properties over gabion stepped spillways which could be impact significantly by the scale effects. This comparative analysis emphasised that full-scale prototype extrapolation conditions may not be feasible based on the Reynolds and Froude similitudes. The current results could be appropriate to be adopted for additional types of water flow over porous steps. Nevertheless, more comprehensive experimental tests for the properties of the water flow at the prototype scale are required. [ABSTRACT FROM AUTHOR]

Issues regarding energy efficiency issued by IMO EEDI (Energy Efficiency Design Index) encourage researchers to study how to improve ship resistance. Interceptor is one of the performance-improving devices on a planing hull. Interceptor is a vertical plate symmetrically placed on the stern. In this study, the interceptor will be applied to planing hull to understand its effect on drag, trim, and heave. Computational Fluid Dynamics (CFD) will be used in this study, with Navier Stokes equations use DFBI (Dynamic Fluid Body Interaction) 2 DoF motions. The interceptor will be placed in varied positions and angles to observe a ship's characteristics in a calm water condition. The result shows that the interceptor position tends to cause more drag for the ship. That is caused by higher momentum force, followed by higher trim angle, leading to WSA increment. Interceptor installed 4 meters behind midship in 80° angle shows the lowest resistance compared to other interceptor variations used in the present study. [ABSTRACT FROM AUTHOR]

Knowledge of the parameters of fluid movement is essential in the designing and operation of various technological processes in a wide range of technical applications. These processes play a special role in hydro engineering where the structures of water works are directly subjected to the action of static and dynamic forces from the side of the water flow. The operation of hydraulic turbines, spillway and water transport systems and other hydraulic structures is directly connected with understanding the behavior of a fluid in various regimes of movement. This report is devoted to the study of a special type of fluid and gas flow, which is called counter-vortex flow. The report gives the comparison of the results of distribution of circumferential velocities with a laminar and turbulent pattern of fluid movement. The results of the laminar flow regime were obtained using a mathematical model and the turbulent regime on a physical model using laser technologies. Such a comparison allows one to assess two approaches in determining the kinematic structures of a complicated flow. The parameters for the viscous fluid laminar flow were determined on the basis of the traditional system of Navier-Stokes equations by determining the dependence of the circumferential component of the total velocity at the given initial circulations and angular flow velocity. To obtain the distribution of velocities in the turbulent flow a physical model was made and equipped with a set of measuring equipment. The comparison showed that the distributions of velocities for the considered flow regimes depending on the channel radius have close coincidence, while the transformation length-wise the active zone of the flow is significant. [ABSTRACT FROM AUTHOR]

A numerical study of the flow structure in a flat channel in a zone with a rectangular step is presented. The calculations are based on the complete system of nonstationary Navier-Stokes equations in the velocity-pressure variables by the differential settling method. The two-step implicit Peaceman -Rachford scheme is used for the numerical solution of the Navier-Stokes equations. As a result, the velocity and pressure fields are investigated, the vortex structure of the circulation flow in the region behind the step is studied, and the length of this zone is determined depending on the Reynolds number and the coefficient of friction on the channel wall. [ABSTRACT FROM AUTHOR]

The article presents a numerical study of the flow structure in a flat channel in the zone of its sudden expansion in the form of a ledge. The calculations are based on the numerical solution of a system of non-stationary equations using Navier-Stokes. The longitudinal velocity profiles in different sections of the channel before and after the ledge are obtained. For the difference approximation of the initial equations, the control volume method was used, and the relationship between velocities and pressure was found using the SIMPLE procedure. For the numerical solution of this problem, the schemes of QUICK, Peacemen-Rachford, McCormack, Warming - Kutler - Lomax were applied, and the results were compared with each other. [ABSTRACT FROM AUTHOR]

Recently, the usage of textured surfaces, as well as the slip boundary induced by hydrophobic coating for increasing the performance of tribopairs, has received a lot of attention. The purpose of this research is to investigate the differences in bearing characteristic performance between a step texture and a slip boundary. The two-dimensional slider bearing is employed in this study by adjusting the step or slip length. In this study, the simulations are conducted by solving the Navier-Stokes equation based on the finite volume method. The numerical result indicates that step bearing outperforms hydrophobic bearing in terms of load-bearing capacity irrespective of the step length ratio. However, for friction characteristics, the hydrophobic bearing is superior for all values of slip length ratio. Another interesting finding is that for each pattern, in terms of the load support, the optimal step or slip length ratio is highlighted. [ABSTRACT FROM AUTHOR]

The research work presents the flow characteristics of the steady flow field of a rocket engine with a nozzle, the objective of the work is to consider one of the rocket engines, simulate and present the variation of Mach, Density, Temperature, Thrust deflection, change in momentum due to the thrust vectoring. A numerical analysis was carried out to characterize the nozzle flow field of secondary injection thrust vector control (SITVC), and a simulation results was set out to analyze the impact of switching the injection position on the SITVC nozzle fluid flow structure and SITVC performance. Parameters. Due to the complexity of the rocket flow investigation, most of the research works are performed using the computational tool. And due to the advent of Computational Fluid Dynamics, the studies involving the fluid flow problem for complex systems has been tremendously helpful. Therefore, the research work has solved numerically the compressible 2-D steady Reynolds Average Navier Stokes equation. [ABSTRACT FROM AUTHOR]

Noise generated by aircraft engines has been a rising cause for concern. The use of acoustic liners for noise attenuation have been extensively studied in the past. In this study, the application of an acoustic metamaterial in a grazing flow impedance tube is explored using a simulation tool to demonstrate its efficacy in the reduction of broadband noise. Numerical simulation of the Navier-Stokes equation is performed using a commercially available multi-physics software, COMSOL. Simulation results indicate that the acoustic metamaterial liners provide a reduction of 5-15 dB in low-frequency broadband noise and thus could serve as candidate materials towards an effective aircraft noise mitigation strategy. A phenomenological theory based on the breakdown of larger eddies into smaller eddies and their eventual decay is also proposed for the observation of such reduction of noise levels. [ABSTRACT FROM AUTHOR]

In the present study, the authors executed the numerical analysis on the impact of external magnetic field on the flow pattern and heat propagation in liquid metal for the multi-step channel. The numerical analysis platform used in the present study is established on the open source CFD tool OpenFOAM. The partial differential equations comprised of Navier-Stokes and Energy equation coupled with electrodynamics equations. The Reynolds number of liquid metal flow in the multi-step enclosure is regulated at Re = 1000, and the magnetic force is regulated by altering Hartmann number of Ha = 0, 500, 1000, and 1500. The numerically obtained results demonstrate that the use of magnetic field promoted the decline of eddies in the flow and permits the liquid metal to occupy the complete domain, which afterward shows the uniform temperature variation at the higher Hartmann number. [ABSTRACT FROM AUTHOR]

We have numerically simulated the unsteady heat transfer from the rotating circular cylinder heated with time-periodic pulsating temperature. The cylinder is impulsively rotating in both clockwise and anti-clockwise directions and is placed across the uniform viscous stream in an unconfined domain. The Navier-Stokes equations with energy formulation are discretized by using a higher-order compact (HOC) finite difference scheme on non-uniform polar grids. The discretized system is then solved by using the Bi-Conjugate Gradient Stabilized iterative method. The effect of various Reynolds numbers, rotational rates, and various parameters of time-periodic pulsating temperature on the forced convection is studied thoroughly. It is found that the transport phenomenon is completely different from the existing forced convection from a circular cylinder heated with a constant temperature. The rotational motion is found to influence the heat transfer drastically as compared to the fixed cylinder case. Also, the different directions of rotation added different complexity to the heat transfer. The backward heat transfer is observed and studied thoroughly within our scope. The range of parameters used for our present study are, Pr (Prandtl number) = 0.7, 60 ≤ Re (Reynolds number) ≤ 200, rotational rates, α = 1, −1, amplitude of temperature, a = 1.5 and period of temperature, 0.01 ≤ P ≤ 100.0. The study is based on isotherm patterns, local and time-averaged Nusselt numbers, and center-line temperature distribution. Overall, our present study adds several new findings related to this problem, which are not reported before. [ABSTRACT FROM AUTHOR]

In non-reacting flow conditions, the mixing characteristics of the transverse injection in a Dual Combustion Ramjet engine are investigated using both experimental and numerical analysis. The study focuses on the assessment of the supersonic flow characteristics in the vicinity of the gas generator's injection location and downstream. At two positions with varying injection pressure ratios, ranging from 1.875 to 2.125, the fuel is injected. The numerical simulations have been performed by using the Reynolds Averaged Navier Stokes equation with the SST k-ω turbulence model. The computational studies are carried out using commercial software ANSYS Fluent 18.0. The computational results have been validated with the experimental results and are in good agreement with them in terms of wall pressures. The results reveal that the transverse injection at the inlet of the supersonic combustor enhances the mixing of the coaxial jets with less stagnation pressure loss due to the counter-rotating vortices generated at the nozzle rim of the gas generator. In contrast, these inherent advantages could not be noticed with isolator injection methods. [ABSTRACT FROM AUTHOR]