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In the present work, the performance evaluation of a low capacity pneumatic engine is shown, through modeling and simulation in order to identify the feasibility of its application in commercial vehicles for short distances. For the modeling of the pneumatic engine, the main contribution in this work is that a comprehensive approach has been used including the compressed air supply pipe, the cylinder compression-expansion chamber, and the intake and exhaust valves. The compressed air supply system is modeled using compressible fluid flow models. The fluid flow is considered adiabatic represented by the model known as Fanno flow (or nonisentropic) and it is assumed to be in a steady state. The flow in the opening and exhaust valves are evaluated as adiabatic and isentropic fluid, using a divergent-convergent compressible fluid model. The simulation results show that the feeding pressure and the pipe diameter have a great influence on the motor power. Also, the compression ratio has been found to have strong influence on the overall system efficiency. On the other hand, the simulations show that the initial pressure of the piston does not have a great influence on performance indicators, such as power or efficiency. However, from the results found in this work, it can be seen that the model and all the obtained results can be used to design and generate an optimization model that describes a pneumatic engine proposed for commercial vehicles of low capacity and short distances.

This study presents an approach to study the three-dimensional internal leakage gas flow occurring in a lubricant-free revolving vane compressor. In this study, the two-dimensional analytical analysis was first carried out using Fanno flow through the leakage paths. This is then expanded by computing the equivalent width of the leakage path which was obtained from a comprehensive three-dimensional computational fluid dynamics model, to form a three-dimensional analytical leakage flow model. Thereafter, measured data from the physical prototype was collected and used to formulate a set of effective leakage flow coefficients. The resultant three-dimensional leakage model was then used to predict the internal leakage flow in the lubricant-free compressor. The results show that the proposed three-dimensional internal leakage model was able to predict the internal leakage of the compressor within discrepancies of ±15%. Subsequent studies show that with better machining tolerance control, a practical volumetric efficiency above 90% can be achieved by the lubricant-free revolving vane compressor. Nanyang Technological University The authors would like to acknowledge Nanyang Technological University for funding.

In this chapter, we look at one-dimensional adiabatic flow in a duct with friction at the walls of the duct. This type of flow occurs, for example, when gases are transported through pipes over long distances. It is also of practical importance when equipment handling gases are connected to high-pressure reservoirs, which may be located some distance away. Knowledge of this flow will allow us to determine the mass flow rate that can be handled, pressure drop and so on.

A novel rotating piston-type compressor is presented. The conventional rolling piston architecture was redesigned to allow oil-free operation. The spring activated vane was replaced by a directly driven swinging vane to provide constant contact to the rotating piston. The model of the compressor was implemented in the AMESim simulation platform. Experiments were conducted on prototypes and the data were evaluated based on the simulation results. Directly unobservable geometric dimensions were estimated by adjusting the mathematical model parameters to the measured thermodynamic state variables with the use of a multi-parametric genetic algorithm. The simple genetic algorithm proved fast and adequate solutions. According to the collected results, the oil-free rotating piston architecture is significantly more sensitive to the sealing clearances compared to the conventional oil lubricated rolling piston compressors. Therefore, the theoretically estimated performance can only be achieved with extremely small manufacturing tolerances, which has to be maintained during the operation.

Fanno theory provides an analytical model for one-dimensional confined viscous compressible flows. The model holds under the assumptions of adiabatic flow and constant cross-section channel. From theory, the differential of every flow-related quantity is expressed as a function of Mach number and friction factor. One-dimensional flow numerical models can be derived by discretizing Fanno equations. However, theory does not assess how to evaluate friction, while the model works properly only if friction is estimated correctly. Compressibility and turbulence act by deforming the velocity profile making it flatter. Assuming the friction factor function of the Reynolds number alone, in line with incompressible flow theory, is thus not correct. Better correlations should include the Mach number to address compressibility effects. Here, the impact of turbulence and compressibility on the velocity profiles in a micro-channel is analysed by means of CFD simulations. Friction factor correlations are deduced for turbulent micro-flows. The impact of the velocity profile on other quantities, such as dynamic pressure and bulk temperature, needed for the numerical model operation, is also evaluated. Additional correlations for these quantities overcome the instrinsic limits of the one-dimensional model, necessarily unaware of local velocity profiles, in a quasi-2D fashion significantly improving its predicting capabilities.

U radu se analizira jednodimenzijsko, podzvučno, stlačivo strujanje plina te se daje postupak proračuna istog. Kako su jednadžbe koje opisuju takvo strujanje diferencijalnog tipa, u općem slučaju nemaju analitičko rješenje te se stoga trebaju rješavati numeričkim metodama. U ovome radu koristi se računalni program „Octave“ odnosno njegova funkcija („ode45“) numeričkog rješavanja diferencijalnih jednadžbi kako bi se došlo do rješenja. Prikazan je izvod jednadžbi stlačivog strujanja te su zatim jednadžbe pripremljene za unos u računalni kod. Prije samih rezultata simulacije, opisana je funkcija „ode45“ odnosno metoda numeričke integracije (Dormand-Prince metoda) sadržana u algoritmu funkcije. Točnost simulacije provjerena je na primjerima posebnih slučajeva stlačivog strujanja za koje su dobro poznata analitička rješenja. Adijabatsko strujanje u cijevi promjenive površine poprečnog presjeka (izentropsko strujanje) te strujanje uz utjecaj trenja (Fannoovo strujanje) i strujanje uz izmjenu topline (Rayleighovo strujanje) kroz cijev konstantne površine poprečnog presjeka, primjeri su strujanja za koja su poznata analitička rješenja. Na kraju rada riješen je problem općeg slučaja strujanja za koji ne postoje analitička rješenja te su prikazani utjecaji efekata (promjena površine poprečnog presjeka, trenje, izmjena topline) na promjenu veličina u strujanju plina. Postupak proračuna jednodimenzijskog, podzvučnog stlačivog strujanja opisan u ovome radu pokazao se iznimno točnim u slučajevima izentropskog, Fannovog i Rayleighovog strujanja. This paper analyzes one-dimensional, subsonic, compressible gas flow and gives a procedure for calculating it. Since the equations describing such a flow are of a differential type, they generally do not have an analytical solution and therefore need to be solved by numerical methods. This paper uses the computer program "Octave", that is, its function ("ode45") for numerically solving differential equations to arrive at a solution. The derivatives of the compression flow equations are presented and the equations are then prepared to be entered into the computer code. Before the simulation results, the “ode45” function is described, that is, the numerical integration method (Dormand-Prince method) contained in the function algorithm. The accuracy of the simulation has been verified by examples of special cases of compressible flow for which analytical solutions are well known. Adiabatic flow in a variable cross-section tube (isentropic flow) and friction flow (Fanno flow) and heat-exchange flow (Rayleigh flow) through a constant-cross-section tube are examples of known analytical solutions. At the end of the paper, the problem of the general case of flow for which there are no analytical solutions is solved, and the contributions of effects (change in cross-sectional area, friction, heat exchange) on the change of flow quantities are presented. The calculation procedure for one-dimensional, subsonic compressible flow described in this paper proved to be extremely accurate in the case of isentropic, Fanno and Rayleigh flows.

Theoretical and numerical studies have been carried out for establishing the novel concept of the boundary-layer induced Sanal-flow-choking in high velocity transient (HVT) solid propellant rocket motors with sudden expansion / divergent port. The Sanal-flow-choking for the diabatic flow is a unique condition of any real-fluid-flow problem at which both the thermal-choking (Rayleigh flow effect) and the wall-friction induced flow-choking (Fanno flow effect) occur in a single fluid-throat region. We proved conclusively that at the subsonic igniter jet flow condition any dual-thrust motor (DTM) with large upstream port-length-to-diameter (l/d) ratio predisposes to the deflagration-to-detonation-transition (DDT) creating pressure-overshoots leading to the catastrophic failure of the HVT DTM as a result of the Sanal-flow-choking phenomenon and generation of strong shock waves. The detonation kernel is more susceptible in HVT DTMs producing the dominant reacting species with low heat capacity ratio. We observed that the flame spread acceleration is relatively higher for the DTM cases with the high propellant loading density, within the given envelop with large l/d ratio, owing to the enhanced propellant surface heating due to the boundary-layer heat transfer effects. We concluded that the undesirable detonation in any dual-thrust combustor could be eliminated by maintaining the lower-critical-detonation-index (LCDI) always higher than the total-to-static pressure-ratio at the fluid-throat and/or at the transition region of the combustor. This could be achieved in the HVT DTMs, without reducing the propellant loading density, by breaking the boundary-layer-blockage and/or increasing the heat-capacity-ratio of the gases generating from the igniter and/or the upstream-port of the motor for prohibiting the Sanal-flow-choking condition. We concluded that the l/d ratio, the heat capacity ratio of the species, total-to-static pressure ratio at the fluid-throat and the rheology of the fluid linking together determines the boundary-layer induced internal flow choking and detonation in DTMs. The concept of a critical detonation kernel established herein throws light to the global scientific community on the fundamental mechanism of the DDT in dual-thrust rockets.

© 2019 The Authors. Micro-scale fluid systems are becoming common in many applications ranging from electronic cooling to refrigeration systems and more. One-dimensional numerical models represent a simple and fast tool for the design of such devices, yet they struggle to accurately predict the flow characteristics in compressible micro-flows. Under the adiabatic assumption, the elegant theory developed by Fanno allows models for the viscous compressible flow in constant cross-section channels to be easily built. Although reasonably accurate, these models suffer from drawbacks inherent to their being one-dimensional, as such they cannot take into account the local profiles of quantities like the velocity and the temperature. In cascade, this results into incorrect evaluations of other dependent quantities, such as the dynamic pressure and the fluid thermophysical properties. The mismatch turns large when the fluid compressibility becomes important. As the Mach number grows, the velocity profile changes, and so the friction factor, even though a reliable model for predicting this change is still missing. In fact, a constant friction factor throughout the channel is generally assumed, following the incompressible flow theory. Here, a set of correlations is proposed improving the 1D theory accuracy by taking into account the effects of the non-uniform velocity and temperature profiles in a quasi-2D fashion. A detailed analysis of the velocity profiles at different Mach numbers coming from a large set of CFD simulations results in a model for assessing the impact of compressibility on friction and other quantities. The numerical model proposed, being able to properly account for the compressibility effects, offers an improved tool for the design of micro-scale fluid systems. Extending the analysis to include heat transfer is not difficult as the effect of heat flux will be analogous to the effect of pressure drop due to friction.

From Poiseuille theory, it is known that incompressible laminar fully-developed flow of a Newtonian fluid in a constant cross-section channel is characterised by steady parabolic velocity profiles after a fully-developed flow condition is attained. In turbulent fully-developed flow the velocity profiles are non-parabolic and become more flat for higher Reynolds numbers. When the incompressible hypothesis does not hold, as in the case of high velocity ideal gas flow, the velocity profile becomes flatter, as if more turbulent, due to the superposition of compressibility and turbulence effects, if applicable. This is typical in micro-channel flows, where pressure gradients are high and the gas is rapidly accelerating, eventually up to the sound velocity. As the flow accelerates the effects of compressibility grow stronger and the velocity profile keeps changing shape. The radial velocity component does not zero as in fully-developed flow but reverses after the entrance effects have damped out and grows with the Mach number. A net mass transfer toward the walls is thus generated making the velocity profile more flat. This affects the friction factor which is no longer constant, being proportional to the normal-to-wall velocity gradient, and needs to be evaluated. In the present work, the compressible friction factor is numerically investigated and correlations are proposed based on the velocity profile shape evolution as a function of the Mach number. This, together with other considerations on the velocity profile shape change, is shown to enhance the predictive capability of the Fanno theory for compressible flows.From Poiseuille theory, it is known that incompressible laminar fully-developed flow of a Newtonian fluid in a constant cross-section channel is characterised by steady parabolic velocity profiles after a fully-developed flow condition is attained. In turbulent fully-developed flow the velocity profiles are non-parabolic and become more flat for higher Reynolds numbers. When the incompressible hypothesis does not hold, as in the case of high velocity ideal gas flow, the velocity profile becomes flatter, as if more turbulent, due to the superposition of compressibility and turbulence effects, if applicable. This is typical in micro-channel flows, where pressure gradients are high and the gas is rapidly accelerating, eventually up to the sound velocity. As the flow accelerates the effects of compressibility grow stronger and the velocity profile keeps changing shape. The radial velocity component does not zero as in fully-developed flow but reverses after the entrance effects have damped out and grows with ...

International audience; This paper presents data reduction of average friction factor of gas flow through adiabatic micro-channels. In the case of micro-channel gas flow at high speed, the large expansion occurs near the outlet and the pressure gradient along the length is not constant with a significant increase near the outlet. This results in flow acceleration and a decease in gas temperature. Therefore the friction factor of micro-channel gas flow should be obtained with measuring both the pressure and temperature. The data reductions on friction factors were carried out under the assumption of isothermal flow for numerous experimental and numerical studies since temperature measurement International Journal of Heat and Mass Transfer 2 of micro-channel gas flow at high speed is quite difficult due to the measurement limitations. In the previous study, it was found that the gas temperature can be determined by the pressure under the assumption of one dimensional flow in an adiabatic channel (Fanno flow). Therefore in the present study data reduction to estimate friction factors between two relatively distant points considering the effect of a decrease in temperature is introduced with the temperature determined by the measured pressure at a specific location. The Friction factors obtained by using the present data reduction are examined with the available literature and the results are compared with empirical correlations on Moody chart.

This paper presents an experimental study of airflow from convergent-divergent nozzles discharged into enlarged duct, focusing attention on the flow development in the duct. To investigate the influence of active control on the flow field developed in the duct, the micro jets of 0.05 mm radius orifice placed at 900 interval along the base at 6.5 mm from the main jet were employed. The Mach number of this study was 1.3. The area ratio of the present study was 2.56. The NPR presented are from 3, 5, 7, 9, and 11 respectively. The L/D ratio of the duct was varied from 10 to 1. The level of expansion at the nozzle exit influences the wall pressure very strongly since in the present case all the NPRs of the tests are under expanded. For all the L/D the entire flow field in the duct is full of waves, the few shock wave is so powerful that the wall pressure is equal to the atmospheric pressure or more. At L/D = 3, it is seen that due to the influence of the back pressure the number of compression and expansion waves have reduced drastically. The flow field with and without control is identical.

A numerical model of the internal flow in a duct rotating about one end is described. One-dimensional Euler equations are solved inside the duct using a finite volume formulation in which the advective fluxes are calculated using the advection upwind splitting method. The model was developed as a fast design tool for helicopter rotor blades with internal spanwise flow. To this end, centrifugal as well as Coriolis effects, frictional losses, duct sweep, and time-dependent duct boundary conditions are modeled, and a spanwise flow control valve can be included. The model is used to explore the behavior of a 2-m-long duct with a circular cross section, rotating at tip speeds of up to 260 m/s. The effects of centrifugal pumping, duct friction, duct sweep, and a flow control valve on the spanwise pressure and velocity distribution, mass flow rate of air through the duct, and torque required to spin the duct are discussed.

Local friction factors of laminar and turbulent gas flows including choked flows through micro-tubes were experimentally investigated under atmospheric back pressure and variable inlet pressure. The experiments were carried out using two glass micro-tubes with D = 265.7 and 399.9 μm and a fused silica micro-tube with D = 531.2 μm. Two to three pressure tap holes were drilled into the micro-tube wall at intervals of 5 ~ 6 mm to measure local pressures. The local Mach numbers, temperatures and friction factors were obtained by using stagnation temperatures and pressures, local pressures and mass flow rates. The results for wide range of Reynolds numbers and Mach numbers were obtained including choked flows. Both the local Fanning and the local Darcy friction factors were obtained under the assumption of both Fanno flow (adiabatic wall) and isothermal flow, respectively. Since the measured values of the inner relative surface roughness of the micro-tubes were less than 0.02 %, only the effect of compressibility on friction factors was assessed. The difference between Fanning and Darcy friction factors was described and compared with the ff and fd correlation as a function of Mach number. The friction factor difference obtained under the assumption of Fanno and isothermal flows was also compared with the available literature and numerical results. In the turbulent flow region including the choked flow, the local Fanning friction factors under the assumption of Fanno flow nearly coincided with Blasius correlation.

This paper studies steady motion of gas in a rectilinear duct with square cross-sections,governed by the three-dimensional (3-d) non-isentropic compressible Euler equations with a friction term.Such flows are called Fanno flows in engineering. We construct respectively special subsonic flows, supersonic flows and transonic shocks in the duct.Since the 3-d steady compressible Euler equations are of quasi-linear hyperbolic-elliptic composite type for subsonic flows, and there is no generaltheory up to now, we formulate a boundary value problem arising from studies of transonic shocks, and prove the well-posednessof this problem by showing that the special subsonic flows constructed above are stable under small multi-dimensional perturbations.The proof depends on separation of the elliptic and hyperbolic parts in the Euler equations, and designation of a suitable nonlinear iteration scheme.Particularly, there are strong interactions between the elliptic part and the hyperbolic part due to the appearance of friction, and we deducea linear mixed boundary value problem of a second-order elliptic equation with an integral-type nonlocal term. Its well-posedness is establishedby applying methods of Fourier analysis and regularity theory of second-order elliptic equations.

Miniature flow passages, defined here as passages with hydraulic diameters smaller than about 1 mm, have numerous applications. Some current applications include monolith chemical reactors, inkjet print-heads, bioengineering and biochemistry (lab-on-the-chip; drug delivery with ultrathin needles, etc.), microflow devices (micropumps, micro heat exchangers, etc.), and cooling systems for microelectronic and high-power magnets, to name a few. Miniature flow passages are an essential part of microfluidic devices , in which can be broadly defined as devices in which minute quantities of fluid are applied. Cooling systems based on microchannels can provide very large volumetric heat disposal rates that are unfeasible with virtually any other cooling technology. Their widespread future applications may in fact revolutionize some branches of medicine and industry. The serious study of flow in capillaries (tubes with D ≈ 1 mm) goes back to at least the 1960s. The application of microchannels for cooling of high-power systems is relatively new, however (Tuckerman and Pease, 1981). The literature dealing with flow in microtubes is extensive. Useful reviews include those of Papautsky et al. (2001), Morini (2004), Krishnamoorthy et al. (2007), and Fan and Luo (2008). The field of flow in miniature channels, in particular with respect to very small channels (microfluidics and nanofluidics) is a rapidly developing one. In this chapter we review the flow regimes and size-based miniature flow passage categories, and we discuss the limitations of the classical convection heat and mass transfer theory with respect to its application to miniature flow passages.

In this paper, a combined numerical and experimental approach for the estimation of the average friction factor along adiabatic microchannels with compressible gas flows is presented. Pressure-drop experiments are performed for a rectangular microchannel with a hydraulic diameter of 295 &mu, m by varying Reynolds number up to 17,000. In parallel, the calculation of friction factor has been repeated numerically and results are compared with the experimental work. The validated numerical model was also used to gain an insight of flow physics by varying the aspect ratio and hydraulic diameter of rectangular microchannels with respect to the channel tested experimentally. This was done with an aim of verifying the role of minor loss coefficients for the estimation of the average friction factor. To have laminar, transitional, and turbulent regimes captured, numerical analysis has been performed by varying Reynolds number from 200 to 20,000. Comparison of numerically and experimentally calculated gas flow characteristics has shown that adiabatic wall treatment (Fanno flow) results in better agreement of average friction factor values with conventional theory than the isothermal treatment of gas along the microchannel. The use of a constant value for minor loss coefficients available in the literature is not recommended for microflows as they change from one assembly to the other and their accurate estimation for compressible flows requires a coupling of numerical analysis with experimental data reduction. Results presented in this work demonstrate how an adiabatic wall treatment along the length of the channel coupled with the assumption of an isentropic flow from manifold to microchannel inlet results in a self-sustained experimental data reduction method for the accurate estimation of friction factor values even in presence of significant compressibility effects. Results also demonstrate that both the assumption of perfect expansion and consequently wrong estimation of average temperature between inlet and outlet of a microchannel can be responsible for an apparent increase in experimental average friction factor in choked flow regime.

The flow in micro air vents, as those used in the plastic moulding industry, can be assimilated to a Fanno flow. Even though Fanno theory is well-established, its outcome strongly depends on the correct assessment of the friction factor term. Yet, friction factor evaluation is not straightforward since traditional fluid-dynamics formulas fail to account for the compressibility effects and are only valid when low Mach numbers are attained, which is often not the case. A numerical model implementing the non-isoentropic compressible Fanno flow theory is presented. A friction factor correlation is proposed, based on the results of a large set of CFD simulations used for calibrating the numerical model. The model is then used for characterizing micro air vent geometries under different operating stagnation pressures and temperatures. The vents characterization is finally employed for the quasi-static assessment of the mass flow rate through the vents, and of the air pressure in the mould during a typical moulding process.

Intermediate turbine duct represent the flow path between the high pressure and low pressure turbine. Caused by the complex flow mechanism, the outlet flow condition of the high pressure turbine is easily changed. Since the upstream flow condition from the high pressure turbine has a significant effect on the internal flow field of intermediate turbine duct, the study in the upstream condition is of high value. Through numerical simulation, the influence of upstream flow angle variation on intermediate turbine duct is observed. It is found that the main influence of the flow angle variation is near the hub side of the duct, and the quantitative result shows that a larger flow angle has a positive effect on the flow field and can reduce loss.

In this research, experiments are performed to study the laminar flow mixed-convection heat transfer with radiation effects for a hydrodynamically fully developed and thermally developing airflow in a horizontal duct. The duct cross section is made of two differentially heated isothermal vertical walls and two adiabatic horizontal walls with aspect ratios 1 and 0.5. The total heat transfer from the hot wall to the cold wall of the duct depends on the mixed convection and also on the surface radiation heat transfer that takes place within the duct. The analysis of experimental data for the Nusselt number from the hot wall of the duct shows that it is important to consider the effects of surface radiation, and to accounted for them, in the design and analysis of flow and heat transfer through ducts. The flow field within the duct is also made visible by a suitable smoke flow visualization method. The heated air moves upward, accumulates near the top wall adjacent to the hot wall of the duct, and gets circul...

Ejector refrigeration systems are less power intensive when compared to conventional refrigeration cycles, mainly due to their ability to use low-grade heat sources to reduce electrical power requirements. The efficiency of these systems is largely dominated by the performance of the ejector. Therefore, it is essential that the performance characteristics of the ejector are predicted using a mathematical model to aid design analysis. Though numerous mathematical models of ejectors exist, this paper improves upon the one-dimensional mathematical model of the ejector and validates its accuracy by comparing it with experimental data available in the literature for the R141b refrigerant. The novelty of this improved model is that Fanno flow concept has been applied to capture frictional compressible flow that is occurring in the mixing chamber of the ejector. In addition, rather than assuming a constant heat capacity ratio γ, the proposed model further enhances the accuracy of the model by averaging the γ between each segment of the flow within the ejector. Validations have revealed that the entrainment ratio was predicted within 4% absolute error, while the condenser operating pressure predictions have an average absolute error of 5% with respect to experimental measurements.

Numerical simulations of fully-developed turbulent flow through a straight square duct at three Reynolds numbers of 190, 300, and 550 based on the friction velocity averaged over the duct perimeter and duct half width are reported. The effect of Reynolds number on the mean and turbulence statistics and secondary flow is investigated. The mean streamwise-velocity profiles along the wall bisector are found to obey a logarithmic scaling when they are normalized by the friction velocity at the mid-wall. Magnitudes and spatial distributions of the peak production and diffusion terms in the mean streamwise-vorticity equation normalized by the wall units are found to be unaffected by the Reynolds-number variation when they are considered in wall-unit coordinates.

The method of energy separation in a high-speed flow proposed by A.I. Leontyev is investigated numerically. The adiabatic compressible gas flow (of a helium-xenon mixture) with a low Prandtl number in a planar narrow duct and a flow with heat exchange in a duct partitioned by a heat-conducting wall are analysed. The temperature recovery factor on the adiabatic wall, degree of cooling the low-speed flow part, temperature efficiency, and the adiabatic efficiency in a duct with heat exchange are estimated. The data are obtained for the first time, which make it possible to compare the efficiency of energy separation in a high-speed flow with the efficiency of similar processes in vortex tubes and other setups of gas-dynamic energy separation.

Experimental studies of turbulent flow through a triangular duct with small apex angle of 11.5° performed by Eckert and Irvine (1956) show flow laminarisation in the corner region of the duct. This effect is re-investigated using direct numerical simulation (DNS). In order to analyze the impact of duct corners on the flow behavior, results for the friction factor and the mean velocity profiles arising from different non-circular duct geometries, namely a square duct, an equilateral triangular duct and isosceles triangular ducts with an apex angle of 11.5° and 4° are compared with the results for circular pipe flow. Within the cross-sections of the ducts with the small apex angles, regions of essentially laminar and turbulent properties are found to exist simultaneously. From analysis of the turbulent quantities performed exemplary for the 11.5°-triangle we gain further insights into the mechanisms responsible for flow laminarization which are supported by analytical considerations for statistically axisymmetric turbulence.

The aim of this note is to obtain a flow rate equation for subsonic Fanno flow, which has a form similar to the flow rate equation for isothermal flow. When pipe dimensions and the proper values of pressures and temperatures at two sections along a pipe, namely P1, P2, T1 and T2 are given, the mass flow rate is obtained by simple substitution into the obtained formula. However, only three of the above four quantities are independently given, since the steady Fanno flow problem involves three first-order differential equations. Therefore, the problem has three degrees of freedom. The theory in this note shows an algebraic equation that determines the fourth quantity by using the given three quantities. The method for finding the mass flow rate and state variables of the gas in the pipe are substantially simplified compared with the commonly distributed method. The relative difference of mass flow rates between the subsonic Fanno and isothermal flows is smaller than 1% in practical combinations of P2 /P1 and the pipe-friction parameter fL/D.

Full-bore decompression of an initially highly pressurized pipe has been studied extensively in recent years. The main aim of this effort has been to estimate the speed of the decompression wave and its relationship to the speed of a travelling fracture in the pipe wall. It has been demonstrated that the speed of the decompression wave is influenced by the friction at the gas-solid interface, and also by the pipe size (diameter). The numerical value of the friction factor has been traditionally estimated using known relationships such as the Haaland formula. However, it has also been noticed that the friction factor calculated in this way has to be increased many-fold to achieve agreement between theory and experiment. To date, there is no physical justification for this increase. The present paper proposes an explanation by modelling the full-bore decompression as a ‘transient Fanno’ flow. The model development is based on the observation that the flow at the exit plane always tends to approach a ‘choked’ condition (sonic velocity). It is shown that a re-interpretation of the Fanno flow formula allows an estimation of the irreversibility, and therefore the friction factor, in the evolving flow. When averaged over space and time, the friction factor attains a value that need not be artificially adjusted. This value of the friction factor can be used in one-dimensional models of the decompression process. Also, the role of the ‘second coefficient of viscosity’ during the initial instants of the highly transient flow is examined.

A recent paper of Ockendon et al. discusses the Fanno model for quasi-one-dimensional flow of gas in a tube, in situations where the flow is turbulent and the tube is long enough for wall drag to be important. Based on appropriate scalings and with associated boundary conditions they derive equations for similarity solutions and make predictions about travelling and evolving waves. In this paper the existence, uniqueness and asymptotic behaviour of these wave forms is proved rigorously. Techniques include shooting methods (both one- and two-parameter), appropriate changes of variables, and comparison techniques.

The phenomenon of choked flow has been recognized and understood for many decades. These flows also have a variety of practical applications, such as pneumatic systems, oil and gas well blowouts, and vents in high-pressure systems, among others. According to some recent experiment data carried out in a straight pipe, the flow Mach number exceeds unity at the exit of pipe. This conflicts the Fanno flow theory that has long been applied to the one-dimensional gas dynamics area. At present, it is not clear whether this comes from experimental errors or any other reasoning that was not yet disclosed. There may be a suspected possibility of boundary layer thinning near the duct exit, which accounts for a divergent flow passage. The main objective of the present effort is to understand the flow mechanism by which the main flow Mach number exceeds unity near the exit of a straight duct. Both computational and theoretical analyses have been performed to investigate the detailed choking phenomenon at the vicinity of duct exit. The results obtained show that boundary layer thinning is produced by the flow at the vicinity of duct exit, with subsonic inlet conditions, consequently leading to the divergent flow passage. The sonic conductance is analysed in terms of pressure loss and boundary layer blockage with different duct sizes.

This paper investigates the inertial and creeping flow of a second-order fluid in a curved duct with a square cross-section. Numerical modeling is employed to analyze fluid flow, and the governing equations are discretized using the finite difference method on a staggered mesh. The marker-and-cell method is employed to allocate the parameters on the staggered mesh, and static pressure is calculated using the artificial compressibility approach. The effect of centrifugal force due to the curvature of the duct and the opposing effects of the first and second normal stress difference on the flow field are investigated. In addition, the order-of-magnitude technique is used to derive the force balance relations for the core region of flow. Based on these relations, the performance mechanism of centrifugal force and normal stress differences on the generation of secondary flows is considered. We also present an analytical relation for the axial velocity profile and flow resistance ratio of creeping flow. For this kind of flow, previous studies have investigated the effect of the first normal stress difference on the transition from one pair to two pairs of vortices while we show that the negative second normal stress difference has the opposite effect on this transition and can stabilize the flow.

In this paper, we consider the unsteady flow of an incompressible second grade fluid in a circular duct with a given volume flow rate variation. The effects of Hall current are taken into account. The governing equations are solved analytically using Laplace transform method. The velocity profiles are constructed for the four cases: (a) constant accelerated flow (b) sudden started flow (c) the flow rate has a trapezoidal variation with time (d) starting from rest the volume flow rate oscillates sinusoidally. The present analysis is more general than any previous investigation.

Properties of fully developed viscous flow through a super-elliptic duct are reported. The cross section resembles rectangular ducts with rounded corners. The effect of corner rounding depends on the aspect ratio, and in general decreases both flow and convective (H1) heat transfer but increases minimum wall shear stress. An accurate, efficient Ritz method is used.

Three-dimensional simulations of laminar buoyancy assisting mixed convection in a vertical duct with a plane symmetric sudden expansion are presented to illustrate the effects of the buoyancy assisting force and the duct’s aspect ratio on the flow and heat transfer. This geometry and flow conditions appear in many engineering applications, but 3-D heat transfer results have not appeared in the literature. This study focuses on the regime where the flow and thermal fields are symmetric in this geometry. The buoyancy force is varied by changing the heat flux on the stepped walls that are downstream from the sudden expansion, and the duct’s aspect ratio is varied by changing the width of the duct while keeping the expansion ratio constant. Results are presented for duct’s aspect ratio of 4, 8, 12, 16, and ∞ (2-D flow), and for wall heat fluxes between 5–35 W/m 2 . The Reynolds number and the range of wall heat flux are selected to insure that the flow remains laminar and symmetric in this geometry and reverse flow does not develop at the exit section of the duct. Results for the velocity, temperature, and the Nusselt number distributions are presented, and the effects of the buoyancy force and the duct’s aspect ratio on these results are discussed.