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Nonequilibrium molecular dynamics simulations is applied to investigate the simultaneous effect of rarefaction and wall force field on the heat conduction characteristics of nano-confined rarefied argon gas. The interactive thermal wall model is used to specify the desired temperature on the walls while the Irving– Kirkwood expression is implemented for calculating the heat flux. It is observed that as the temperature differences between the walls increases by lowering the temperature of the cold wall, the number of adsorbed gas atoms on the cold wall increases notably due to the increment in the residence time of the gas atoms. Consequently, the interfacial thermal resistance between the gas and the cold wall reduces which results in a reduction of the temperature jump. Meanwhile, the increase in the temperature of the hot wall leads to a reduction of the residence time of gas atoms in the near-wall region which decreases the number of absorbed gas atoms on the hot wall. This results in an increase in interfacial thermal resistance which leads to a higher temperature jump. It is observed that the bulk, wall force field and interface regions form approximately 10%, 45% and 45% of the total thermal resistance, respectively. Furthermore, unlike the interfacial thermal resistance, the bulk and the wall force field thermal resistance are approximately independent of the implemented temperature difference.

The structures of flow in laminar Couette-Taylor flow with periodic oscillation of the inner cylinder rotation velocity (which linearly increases from zero to a fixed maximum value and then goes to zero again in each period) for different three regimes; Couette flow, Taylor vortex and wavy vortex, with the effect of the Womersley number, Wo, for different periods and the critical Taylor number are investigated numerically. The Wo varies between. 0.38 ≤ Wo ≤ 8.59. To understand how the flow responds to a given boundary conditions, the critical Taylor number is calculated and the structure of vortices which formed in the flow field is investigated. The results show that if Wo is increased, i.e. when the slope of rotational velocity of inner cylinder is increased, more delay in changing the flow regime compare to the steady state (when the inner cylinder rotates with constant velocity) is observed. Also for large values of Wo, due to the inertia, the flow does not follow the given boundary condition so for the higher value of the Womersley number, Wo = 8.59, there is a time lag and vortices do not appear until the second period of the inner cylinder oscillations. The reason is that the time scale of the dynamics of flow is less than the time scale that is associated with the flow instability, thus the flow regime behaves like a laminar Couette flow at the initial period. Comparing the present results with that of steady state, it is appeared that for a minimum value of Wo used in this paper, i.e. Wo = 0.38, the primary critical Taylor number is 50% higher than that of steady state.

Three-dimensional unsteady flow around a finite wall mounted square cylinder subjected to a steady secondary flow (blowing and suction) from the cylinder's front face has been studied with the aid of direct numerical simulations. The aspect ratio (AR) of the cylinder was varied as AR = 2, 4 and 7 while the ratio Г of the secondary flow to the freestream velocity was changed as −4 ≤ Г ≤ 4. All simulations were carried out at a Reynolds number (Re) of 250, based on the cylinder width, to investigate the influence of Г and AR on cylinder forces, vortex shedding frequency, and mean and instantaneous wake structures. The results show that, independent of AR, both blowing and suction have the potential to reduce the time-mean forces (e.g. more than 90% pressure drag reduction), fluctuating forces and vortex shedding frequency. Furthermore, a detailed investigation of vortex evolution reveals that the suction strategy considerably affects the shedding type and wake flow topology. Increasing the suction ratio changes the shedding from symmetric to asymmetric at AR = 4. Conversely, a planar jet attenuates vortical structures in the vicinity of the wall. Jet deflection is observed at Г = 2 and 4, which plays a key role in the success of the control approach and in the determination of the wake flow structure by changing the pressure distribution on the front face. The effect of AR on the shedding of large-scale vortical structures is also examined. Two critical AR values are determined where the flow and the mean wake structure changed from steady to unsteady (2

We present molecular dynamics simulations of stationary argon gas in nanoscale confinement and under various temperature differences between walls. For a channel of 5.4 nm height, we vary the gas density and find that in addition to the temperature difference between the walls, the absolute temperature of each wall plays an important role in the determination of the gas molecule distribution regardless of the level of rarefaction. The combined effect of the wall force field, the temperature difference between the walls and the wall temperature leads to the fact that the normalized temperature profile along the channel height does not coincide for various temperature differences between the walls. As the gas density is increased, it is observed that the wall force field effect on the density and temperature profiles reduces considerably due to the increment in the magnitude of the gas force field for all implemented temperature differences. Considering the temperature profiles and the distribution of the effective local thermal conductivity (ELTC) along the channel height, it is inferred that a diffusive transport mechanism is dominant throughout the dense gas medium. Besides, as the gas becomes rarefied, ballistic transport in the bulk region and diffusive transport in the regions close to the walls are observed. Furthermore, the effective thermal conductivity is a function of the implemented temperature differences between the walls and its value at 300 K varies from 0.18 to 12 mW / mK as the bulk gas density changes from 1.95 to 196 kg / m 3 .

The effect of the wall force field and the wall physical characteristics on the interfacial phenomena of a 5.4 nm nanoconfined gas medium are investigated by applying three-dimensional molecular dynamics simulations. Assuming that a range of 1 nm from each wall is affected by the wall force field, the gas distribution changes notably in this region which covers 40% of the channel height. Therefore, a combined effect of the wall force field and the wall stiffness, its mass as well as the interaction strength determines the interfacial phenomena such as interfacial thermal resistance (ITR) at the gas/solid interface. The increment in interaction strength of the gas/solid atoms leads to an increase in the amount of adsorbed gas on the wall which reduces the temperature jump and ITR notably. When the ratio between the interaction strengths of the gas/solid to the gas/gas atoms exceeds 4, the temperature jump and the ITR reduce to zero. As the wall becomes stiffer, the temperature jump and consequently the ITR are increased considerably. Simultaneously, the temperature distribution in the gas medium along the channel height becomes more and more independent of the gas density as the wall stiffness increases. It is observed that as the ratio between the mass of the wall and the gas atoms increases up to 2, the temperature jump reduces notably. Meanwhile, as the wall atoms become heavier, an increment in the temperature jump is observed. Consequently, the minimum ITR occurs at a ratio of 2. It is also shown that the temperature profile in the bulk region of the channel is approximately independent of the wall mass. Considering several metals as the wall material, our analysis reveals that silver, copper, and nickel experience the least ITR among the others.

In this paper, a parametric study of anode channel clogging of a proton exchange membrane fuel cell (PEMFC) is presented using the numerical volume of fluid method. The droplet size distribution in the present research is considered close to reality. Therefore, three droplets with different sizes are initially placed on the anode channel wall. The droplet sizes are obtained based on the distribution of the saturated liquid water along the whole channel under a specific working condition and the amount of condensed water in the channel, using the PEMFC code. Finally, the dynamic behavior of the droplets is investigated and compared to that of a single droplet with the same total volume. Numerical results show that, in the case of three droplets, the droplets coalesce during the removal time and form a larger droplet. Also, the droplets gradually spread over the channel walls and eventually reach the upper corners of the channel and form liquid slugs. Then, the slugs move slowly toward the channel outlet, and after a while, their shapes and positions are fixed and cause the channel clogging. Changing the number of droplets does not significantly change the time of channel clogging. The numerical results show that the time-averaged pressure drop of three droplets is about 85% less than that of a single droplet.

The interactive thermal wall model is applied in three-dimensional molecular dynamics simulations to investigate the combined effect of the wall force field, the wall stiffness, the wall atom mass and the wall/gas interaction potential strength on the heat transfer characteristics of static rarefied argon gas within a nanochannel. By increasing the wall stiffness, a reduction in the heat flux through the gas medium occurs which leads to a higher temperature jump. As the wall atom mass is increased up to twice the argon atom mass, the heat flux is enhanced notably and a minimum temperature jump can be found at this point. Further increase in the wall atom mass results in reducing the heat flux and consequently increasing the temperature jump. The increment of the wall/gas interaction potential strength up to four times the one of gas/gas interactions is shown to enhance the heat flux and to reduce the temperature jump until it eventually vanishes. Furthermore, it is found that under such conditions, the density profile experiences a second peak. A further increase of this parameter is found to have a negligible effect on the heat flux through the gas medium and it only increases the second peak in the density profile.

Chaotic advection flow is one of the most useful methods to enhance mixing and heat transfer simultaneously in the laminar flow which is generated by spatially chaotic trajectories of the fluid particles. The present study aims to characterize the behavior of chaotic advection flow and heat transfer in a twisted pipe. The considered geometry consists of three 90° bends with an elliptical cross-section; the angle between curvature planes of consecutive bends is 90°. Numerical simulations are performed for both steady-state and pulsatile (unsteady) inlet velocity conditions with the Reynolds numbers in the range of 200 ≤ Re ≤ 450, wall temperatures 310 ≤ Tw (K) ≤ 340, velocity amplitude ratios (the ratio of peak oscillatory velocity component to the mean flow velocity) 1 ≤ β ≤ 3, and Womersley numbers 2.1118 ≤ α ≤ 7.9018. Mixing and heat transfer are analyzed both qualitatively and quantitatively for various considered conditions. The results revealed that the elliptical cross-section has a considerable impact besides the chaotic configuration on mixing and heat transfer enhancement. In the steady-state flow, the desirable system efficiency can be achieved either by increasing the wall temperature or decreasing the Reynolds number. Moreover, in the pulsatile flow, the Womersley numbers in the range of 2.1118 ≤ α ≤ 3.9509 provide a favorable condition to augment the mixing and heat transfer in the twisted pipe.

The aim of this paper is to use the thermo-viscous expansion-contraction effect to enhance mixing in microchannels. To do this, numerical simulation of chaos flow generated by periodic thermal boundary condition in a 2-D microchannel is considered.The main objectives are to evaluate the effect of Reynolds number, Strouhal number and thermal penetration length on chaotic mixing. The vorticity is used as a criteria evaluating the chaos. It is shown that thermo-viscous expansion-contraction effect can be used as aconsiderable potential mean for micro-scale chaotic mixingpotential mean for micro-scale chaotic mixing. The results show that, the vorticity generated by change of density and viscosity due to the temperature difference caused by periodic heat transfer at flow boundary is mainly a function of dimensionless flow velocity and film thickness.

We describe in this work a numerical simulation of chaotic heat transfer by laminar flow in a twisted pipe that consists of three bends. Observations on the secondary flow topology changed by the variation of Reynolds number and tube wall temperature as well as their coincidence with heat transfer enhancement are discussed. Both steady and pulsating flows with constant wall temperature are considered. Numerical simulations are performed for Reynolds numbers range 300 1) provide a more complex secondary flow and hence a better heat transfer. Pulsation energy consumption is higher than the energy needed for increasing Reynolds number of the steady flow to match the same heat transfer enhancement. However, a better heating uniformity is obtained in the pulsating flow, which is not the case in the steady flow.

The impinging turbulent slot jet was investigated experimentally using tomographic particle image velocimetry technique. The jet Reynolds number was considered equal to 9000 and the nozzle to plate distance was 10 times the width of the nozzle. The mean flow and turbulent statistics were evaluated at different cross-sections. Then, the dominant three-dimensional structures of the turbulent flow were identified using the Proper orthogonal decomposition (POD) method, and the contribution of different energy modes to the total energy was determined. It is observed that the first 40 POD modes can be considered as the dominant flow modes which contain about 89 % of total kinetic energy of the flow. Also, horseshoe form structures were observed in some POD modes on both sides of the jet central plane. Finally, three-dimensional vortex structures were specified using vorticity, Q and λ2 criteria, and compared with each other.

Numerical simulations are performed to investigate the fluid flow and heat transfer in a three-dimensional rotating U-shaped microchannel with a square cross-section for Reynolds numbers of 200–1000. Water is employed as working fluid. The microchannel surface is considered to be hydrophilic (no-slip flow) and hydrophobic (slip flow). Effects of slip flow, temperature jump and rotational speed in the range of 0–300 rad/s are studied on the heat transfer, pressure drop and thermal performance coefficient. Various slip lengths ranging from zero (hydrophilic surface) to 10 μm are employed and their results are compared. It is observed that the effect of slip flow results on the leading and trailing walls is not similar due to the rotational effects. It is found that the slip flow augments the heat transfer rate in comparison with that of no-slip flow while using both slip flow and temperature jump reduces the heat transfer rate in comparison with that of slip flow. A relatively large reduction on the pressure drop and an improvement on the Nusselt number are found when the slip length increases from zero to 10 μm. The thermal performance coefficient increases about 90% for 10 μm slip length in comparison with that of no-slip condition. Moreover, for a rotating microchannel (300 rad/s), the thermal performance coefficient increases about 43% for low Reynolds numbers and about 11% for large Reynolds numbers in comparison with that of the stationary microchannel.

In the present study, the ball-spine inverse design algorithm is developed for swirling viscous flow regime to improve the performance of an axisymmetric 90-degree bend duct between the radial and axial diffuser of a centrifugal compressor. Performance improvement of the 90-degree bend duct is accomplished to increase its pressure recovery without separation. First, the effects of geometric parameters on flow separation are numerically studied and a safe margin is obtained for prevention of flow separation and stall. Then, the safe margin is enlarged to reach a higher pressure recovery via the shape modification of duct walls. The shape modification process integrates the BSA as shape modification algorithm and an axisymmetric flow analysis code as flow solver. Shape modification process is carried out by improving the current wall pressure distribution and applying it to the inverse design algorithm. Results show merits and robustness of the BSA for duct design in swirling viscous flow regime whereby the pressure recovery coefficient of the 90-degree bend duct increases up to 7%.

Electroosmosis is the predominant mechanism for flow generation in lab-on-chip devices. Since most biofluids encountered in these devices reveal non-Newtonian behavior, a special understanding of the fundamental physics of the relevant transport phenomena seems vital for an accurate design of such miniaturized devices. In this study, a numerical analysis is presented to explore transport characteristics of typical non-Newtonian biofluids through annular microchannels under combined action of pressure and electrokinetic forces. The flow is considered steady and hydrodynamically fully developed. A finite difference method is used to solve the Poisson-Boltzmann and Cauchy momentum equations, while the classical boundary condition of no velocity-slip for the flow field is applied. The Poisson-Boltzmann equation is solved in the exact form without using the Debye-Huckel approximation. After numerically solving the governing equations, role of the key parameters in hydrodynamic behavior of the flow is analyzed and discussed.

In the present study, impinging of vertical twin jet against a horizontal plate is numerically and experimentally investigated. Four two equation RANS based turbulence models are used and their capabilities to simulate such complicated turbulent flow were examined. The two fluid jets are separated by a thin membrane. The inlet jet hydraulic diameters are the same and the Reynolds number of external flows of jets is 13500. The ratio of width of nozzles (e) to nozzle-to-plate distance (H) considered as 1:10. The turbulent models used in this work are k-e, k-e RNG, k-ω and k-ω SST. The results obtained by the models were compared with each other as well as two-dimensional PIV data to evaluate the capabilities of such models for this kind of flows. By comparing the numerical and experimental results, it is concluded that all of the models can predict acceptable results in the free jet area, but in the near wall region none of the models can predict flow characteristics with reasonable accuracy. It was observed that, at low nozzle-to-plate distances, the prediction results of the turbulence models are approximately in accordance with the experimental data, particularly for a zone near the midline separating the two jets.

In this research, a new method called elastic surface algorithm is presented for inverse design of 2-D airfoil in a viscous flow regime. In this method as an iterative one, airfoil walls are considered as flexible curved beams. The difference between the target and the current pressure distribution causes the flexible beams to deflect at each shape modification step. In modification shape algorithm, the finite element equations of two-node Timoshenko beam are solved to calculate the deflection of the beams. In order to validate the proposed method, various airfoils in subsonic and transonic regimes are studied, which show the robustness of the method in the viscous flow regime with separation and normal shock. Also, three design examples are presented here, which show the capability of the proposed method.

In this work, for better understanding of microvessels disorders, mass transfer at a stenotic and the straight capillary wall in the presence of RBC motion is investigated. The immersed boundary- lattice Boltzmann method is used for this purpose. The erythrocyte is considered as an immersed biconcave shaped tissue around the capillary as a porous media. The gamma function for input concentration, which is close to the actual stenosis brain capillary, is used. The simulated results obtained for both stenosis and straight capillaries are compared. It is shown that while the RBC motion has negligibly small effects on wall mass transfer in straight capillaries, its effect is not negligible at stenosis capillaries.

Analytical relation for slow motion thin liquid films bounded by a fixed wall and free surface for Newtonian and non-Newtonian fluids are obtained in this work. Assuming long-wave approximation, the momentum and continuity equations for thin liquid films of power-law fluids are simplified and solved analytically to derive the evolution equation of thin liquid films. The evolution equation is derived for two- and three-dimensional cases. A relation for evolution of thin films is obtained for a simple case in which the liquid film is supported from below by a solid surface and subjected to gravity and constant surface tension forces. This evolution equation of thin film has been solved numerically in order to compare the behavior of Newtonian and non-Newtonian liquids for different Bond numbers. It is shown that the power-law model at low and high strain rates is invalid and it affects the results. The Rayleigh-Taylor instability is another subject that is studied in this work. This interesting phenomena is investigated by solving the evolution equation numerically for different Bond numbers. The results show that the evolution of the free surface thin film for pseudo plastic fluids is different from that of Newtonian and dilatant fluids

Couette-Taylor flow is a type of fluid flow that occurs in the annulus between differentially concentric cylinders, when the outer cylinder is fixed and the inner cylinder rotates and the rotation rate exceeds a critical value. In this research we have studied the effect of surface roughness on the hydrodynamic structures of Couette-Taylor Flow. The PIV technique has been applied for flow visualization. At first, for a smooth surface, the different flow patterns include Couette flow, Taylor vortex flow, wavy vortex flow, modulated wavy vortex flow and turbulent flow. They are investigated numerically and experimentally. The transition Taylor number for every flow regime is also taken into consideration. The results showed that the numerical results correspond quite well to the experimental data. Then, the different surface conditions for inner cylinder which are studied are: a smooth one, a sandpaper-type P180, a canvas plastic with different wire-mesh roughness. They are used to study the effects of surface roughness on the flow structures and critical Taylor numbers. The experimental results showed that the roughness causes a delay in the appearance of the first instabilities.

ASME Digital Collection, Proc. ASME. 58059; Volume 1B, Symposia: Fluid Measurement and Instrumentation; Fluid Dynamics of Wind Energy; Renewable and Sustainable Energy Conversion; Energy and Process Engineering; Microfluidics and Nanofluidics; International audience; In this paper, impingement of a turbulent rectangular flow to a fixed wall is investigated. The jet flows from bottom-to-top and the output jet Reynolds is 16000. The nozzle-to-plate distance is equal to 10 (H/e = 10). Five turbulence models, including k-ε, RNG k-ε, k-ω SST, RSM and v2f model have been used for two-dimensional numerical simulation of the turbulent flow. Because of the complexities of the impingement flow, such as curved streamlines, flow separation, normal strains and sudden deceleration in different areas, different turbulence models are proposed to simulate different regions of the flow. To investigate the capability of these turbulence models in simulating different regions of the impinging jet, the mean flow velocity field and turbulent kinetic energy are extracted and compared with the experimental data of a two-dimensional particle image velocimetry (PIV). The calculated error of these five turbulence models was presented for the various flow regions, while it have not been clearly investigated earlier. Results indicate the highest conformity of the v2f model with the experimental data at the jet centerline. However, this model does not predict well the flow at the shear layer and wall-jet areas. RSM Gibson and Lander model has the highest conformity with the experimental data in these regions.

Mixed convection in a inclined cavity has not been investigated by LBM in case of an imposed non zero heat flux. This type of boundary condition, representing very usual situations in physical world, is not simple to model in lattice Boltzmann schemes. In effect, the only boundary condition able to simulate an imposed temperature and an imposed heat flux at a boundary has been presented by D’Orazio et al. in previous works, where the boundary was at rest. In this work, laminar mixed convective heat transfer in two-dimensional rectangular inclined driven cavity is studied numerically by means of a double population thermal Lattice Boltzmann method. The counter-slip internal energy density boundary condition, able to simulate an imposed heat flux at the wall, is applied. Through the top moving lid the heat flux enters the cavity and it leaves the system through the bottom wall; side walls are adiabatic. Results are analyzed over a range of the Richardson numbers and tilting angles of the enclosure, encompassing the dominating forced convection, mixed convection, and dominating natural convection flow regimes. The results show that, as expected, heat transfer rate increases as increases the inclination angle, but this effect is significant for higher Richardson numbers, when buoyancy forces dominate the problem; for horizontal cavity, average Nusselt number decreases with the increase of Richardson number because of the stratified field configuration. This study shows that the counter-slip internal energy density boundary condition can be effectively used to simulate heat transfer phenomena also in case of moving walls and it makes the Lattice Boltzmann Method able to simulate a wide class of cooling process where a given thermal power must be removed.

In this study, a novel inverse design method, called Elastic Surface Algorithm (ESA), is proposed for airfoil shape design in subsonic and transonic flow regimes. ESA is a physically based iterative inverse design method that uses a flow solver to estimate the pressure distribution on the solid structure, i.e. airfoil, and a 2D solid beam finite element code to calculate the deflections due to the difference between the calculated and target pressure distribution. The proposed method is validated through the inverse design of five different airfoils. In addition, three design examples in subsonic and transonic regimes are presented to prove the effectiveness and robustness of the method. Finally, the convergence rate of the method is compared with MGM and BSA methods. The results of this study showed that not only the ESA method is an effective method for inverse design of airfoils, but also it can considerably increase the convergence rate in transonic flow regimes.

This article reports the numerical geometric optimization of three-dimensional microchannel heat sinks with rectangular, elliptic, and isosceles triangular cross sections. The cross-sectional areas of the mentioned microchannels can change according to the degrees of freedom, that is, the aspect ratio and the solid volume fraction. Actually, the purpose of geometric optimization is to determine the optimal values of these parameters in such a way that the peak temperature of the wall is minimized. The effects of solid volume fraction and pressure drop upon the aspect ratio, hydraulic diameter, and peak temperature of the microchannels are investigated. Moreover, these microchannel heat sinks are compared with each other at their optimal conditions. Considering the constraints and geometric parameters for the optimization of the present study, it is revealed that microchannel heat sinks with rectangular and elliptic cross sections have similar performances, while microchannels with isosceles triangular cro...

In this study, a new inverse design method called Elastic Surface Algorithm (ESA) is developed and enhanced for axial-flow compressor blade design in subsonic and transonic flow regimes with separation. ESA is a physically based iterative inverse design method that uses a 2D flow analysis code to estimate the pressure distribution on the solid structure, i.e. airfoil, and a 2D solid beam finite element code to calculate the deflections due to the difference between the calculated and target pressure distributions. In order to enhance the ESA, the wall shear stress distribution, besides pressure distribution, is applied to deflect the shape of the airfoil. The enhanced method is validated through the inverse design of the rotor blade of the first stage of an axial-flow compressor in transonic viscous flow regime. In addition, some design examples are presented to prove the effectiveness and robustness of the method. The results of this study show that the enhanced Elastic Surface Algorithm is an effective inverse design method in flow regimes with separation and normal shock.

In the present study, the performance of a centrifugal compressor is improved by replacing the combination of vaned radial diffuser and axisymmetric vaneless 90-degree bend by a vaned 90-degree bent diffuser. It controls the outlet flow angle and reduces the overall diameter of the compressor. The optimum number of guide vanes inside the 90-degree bent diffuser is obtained using 3-D numerical simulation. Indeed, changing flow direction simultaneous with decreasing flow velocity through the 90-degree bent diffuser will increase the possibility of secondary flow and separation. Here, the meridional plane of the 90-degree bent diffuser is modified to reduce secondary flow and separation. Geometry modification process integrates Ball-Spine inverse design method as the shape modification algorithm and a quasi-3D analysis code as the flow solver. The current quasi-3D flow solver is in fact a 3-D flow solver that solves viscous flow between two virtual guide vanes located at a very close distance with free slip condition over them. In other words, in the current quasi-3D analysis, stream surfaces are the same as the virtual guide vanes and no slip condition is just applied on the hub and shroud. Shape modification process is carried out by improving the current hub and shroud pressure distribution and applying it to the inverse design algorithm. Spines directions are specified in a way that geometry would change only in the meriodional plane and guide vanes angle remain unchanged in the blade to blade plane through the geometry modification process. Having modified the meridional plane, the new vaned 90-degree bent diffuser is examined by the 3-D flow solver. Results show not only the secondary flow is reduced in the new 90-degree bent diffuser, but also its efficiency increases up to 2%. On the other hand, the overall diameter of the compressor decreases about 24%.

In the present study, the effects of rarefaction, viscous dissipation, aspect ratio, and accommodation coefficients on transport characteristics associated with a two-phase flow within a rotating microsystem are investigated. It is assumed that centrifugal acceleration due to rotation separates the mixture into two immiscible gas and liquid layers. The incompressible Navier–Stokes–Fourier (NSF) equations in the cylindrical reference frame are employed, while the effects of velocity slip and temperature jump phenomena for the gaseous phase are taken into account. Considering external heating influence and applying the classical thermal boundary conditions of Uniform Heat Flux and Constant Wall Temperature, three different thermal cases are constructed. Expressions for the velocity and temperature distributions of these thermal cases as well as the average entropy generation rate and the Bejan number pertained to the gas and liquid layers are presented. In addition, the criteria for evaluating the impact of the gas layer on shear and temperature reductions at the shaft and also irreversibility rise in the medium are discussed.

In the present study the mechanism of transport phenomena in a low-speed rarefied gas flow confined between a shaft and its concentric housing, namely, the cylindrical Couette problem, is investigated analytically in the slip-flow regime. The incompressible Navier–Stokes–Fourier (NSF) equations in the cylindrical polar coordinate reference frame are employed while the simultaneous effects of viscous dissipation and rarefaction phenomenon are taken into account. Two different thermal boundary conditions are considered: the Uniform Heat Flux (UHF) and the Constant Wall Temperature (CWT). Solutions for the velocity and temperature distributions, the Nusselt number and the wall heat flux are obtained for different values of the Knudsen and Brinkman numbers and curvature parameter.

In this paper, we have presented an innovative model for coupled vibrations of nanotubes conveying fluid by considering the small-size effects on the flow field. By this model, we have demonstrated that ignoring the small-size effects on flow field in a nano-scale fluid–structure interaction (FSI) problem may generate erroneous results. The nanotube has been modeled by Euler–Bernoulli plug-flow beam kinematic theory, and we have formulated the small-size effects on bulk viscosity and slip boundary conditions of nanoflow through Knudsen number ( Kn ), as a discriminant parameter. The divergence instability phenomenon has been observed, incorporating various flow regimes for liquids and gases. We have observed that including the effect of nanoflow viscosity, is not so influential on vibration of nanotubes conveying fluid, as compared with the results of vibration of nanotubes conveying an inviscid fluid; however, incorporating the nanoflow slip-boundary conditions hypothesis changes the results drastically, as compared to continuum flow models.

A parametric analytical study is carried out to scrutinize the mechanism of fluid flow, heat transfer and entropy generation in a low-speed rarefied gaseous flow confined between a shaft and its concentric housing, i.e., the cylindrical Couette flow. In the first law analysis, closed form solutions for the radial temperature profiles are obtained by incorporating the calculated velocity distribution into the energy equation. The derivations for three thermal cases, which are founded on imposing different thermal conditions, namely, the Uniform Heat Flux (UHF) and the Constant Wall Temperature (CWT) boundary conditions, are presented. In the second law analysis, the contributions of thermal diffusion and fluid friction irreversibility to the total entropy generation in the micro domain are illustrated, and the relevant expressions for the Bejan number and the entropy generation number as well as the average entropy generation rate are derived. Finally, the variations of major variables with influential parameters such as the Knudsen number, the Brinkman number and rotation mode are investigated to elucidate the associated effects of rarefaction phenomenon, viscous dissipation and geometric condition on the characteristics of the flow.

To cover a wide range of the flow regimes, a new relaxation time formulation by considering the rarefaction effect and the effective dynamic viscosity has been obtained. By using the modified lattice Boltzmann method (LBM), pressure driven flow through micro and nano channels has been modeled for wide range of Knudsen number, Kn, covering the slip, transition and to some extent the free molecular regimes. The results agree very well with existing empirical and numerical data. The velocity profile was predicted as well as the volumetric flow rate and for the first time, the well known Knudsen minimum effect has been captured about Kn = 1.

Fluid flow pattern and buoyancy force support the motion of nonmetallic inclusions toward the tundish slag. Upward molten flow was investigated. To understand the fundamentals of the process, physical modelling was carried out with the utilization of a 1 : 4 scale model. Numerical modelling was carried out in line with the physical modelling to examine details of the flow pattern and rotational effect caused by the upward flow with the commercial CFD (Computational Fluid Dynamics) package environment, FLUENT. The two-equation κ-ɛ model was used to simulate the turbulence. Multiphase fluid flow was numerically simulated by using the Volume of Fluid (VoF) method. The simulation can predict free surface waves and other phenomena, which can be used to optimize these important metallurgical operations.

Invoking the velocity slip and temperature jump, numerical simulation of Darcy–Brinkman–Forchheimer flow model and forced convection in a circular micro/nano channel filled with porous media are presented. Relating the viscosity to the local Knudsen number, Kn, a generalized diffusion coefficient is obtained in such a way that it can model wide range of Kn regimes of flow. The effect of Kn and Darcy coefficient on velocity and temperature distribution is described. It is shown that despite of the fact that in most of previous researches it is assumed that Kn is constant along the channel, the variations of Kn due to the pressure variations, have considerable effects on heat transfer and temperature distribution across the channel cross section.

A method for the application of interface force in the computational modeling of free surfaces and interfaces which uses PLIC-VOF methods is developed. This method is based on evaluation of the surface tension force only in the interfacial cells with out using the neighboring cells. The normal and the interface surface area needed for the calculation of the surface tension force are calculated more accurately. This method is applied on a staggered grid and it is referred to as Staggered Grid Interfere Pressure calculation method or SGIP. The present method is applied to a two-dimensional motionless liquid drop and a gas bubble. In addition, oscillations of a non-circular two-dimensional drop and a bubble due only to the surface tension forces are considered. It is shown that the new method predicts the pressure jump at the interface more accurately and produces less spurious currents compared to CSF, CSS and Meier's methods when applied to the same cases.

In this article, the two-dimensional staggered grid interface pressure (SGIP) model is generalized and presented in three-dimensional form. The model has been used to simulate three-dimensional interfacial flows and the results have been compared with other existing models. For this purpose, various models of surface tension force for interfacial flows—CSF, CSS and PCIL models as well as the proposed model, SGIP—have been applied to simulate both static and dynamic cases. A three-dimensional motionless drop of liquid and a bubble of gas in an initially stagnant fluid with no gravity force are simulated as the static test case. The motion of small air bubbles in water is simulated as the dynamic test case. It has been demonstrated that the SGIP model produces the least maximum and norm spurious velocities in comparison with the CSF, CSS and PCIL models. Moreover, it is observed that the proposed model produces more accurate pressure jumps across the interface. Results of the dynamic case show that for both CSF and CSS models, the magnitude of spurious currents is too high to enable a successful simulation of this type of surface tension dominated flows. On the other hand, by using SGIP or PCIL models, we are able to simulate bubble rise and to obtain results which are in close agreement with the experimental data.

A three-dimensional method for the calculation of interface pressure in the computational modeling of free surfaces and interfaces is developed. The methodology is based on the calculation of the pressure force at the interfacial cell faces and is mainly designed for volume of fluid (VOF) interface capturing approach. The pressure forces at the interfacial cell faces are calculated according to the pressure imposed by each fluid on the portion of the cell face that is occupied by that fluid. Special formulations for the pressure in the interfacial cells are derived for different orientations of an interface. The present method, referred to as pressure calculation based on the interface location (PCIL), is applied to both static and dynamic cases. First, a three-dimensional motionless drop of liquid in an initially stagnant fluid with no gravity force is simulated as the static case and then two different small air bubbles in water are simulated as dynamic cases. A two-fluid, piecewise linear interface calculation VOF method is used for numerical simulation of the interfacial flow. For the static case, both the continuum surface force (CSF) and the continuum surface stress (CSS) methods are used for surface tension calculations. A wide range of Ohnesorge numbers and density and viscosity ratios of the two fluids are tested. It is shown that the presence of spurious currents (artificial velocities present in case of considerable capillary forces) is mainly due to the inaccurate calculation of pressure forces in the interfacial computational cells. The PCIL model reduces the spurious currents up to more than two orders of magnitude for the cases tested. Also for the dynamic bubble rise case, it is shown that using the numerical solver employed here, without PCIL, the magnitude of spurious currents is so high that it is not possible to simulate this type of surface tension dominated flows, while using PCIL, we are able to simulate bubble rise and obtain results in close agreement with the experimental data.

The effects of red blood cells on mass transfer in brain capillaries have been investigated using a novel hybrid method that includes the immersed boundary and lattice Boltzmann method. For simulation of the flow, the multi-relaxation-time lattice Boltzmann and for simulation of mass transfer across the capillary wall, the single-relaxation-time lattice Boltzmann is used. The present results indicate that an increase in hematocrit and biophysical characteristics such as bending and elastic modules of red blood cells, not only affects the red blood cells shapes and velocities, but also influences the mass transfer by means of diffusion in capillaries. In fact, there is a direct relation between wall shear stress and mass diffusion across the capillary wall.

Laminar forced convection heat transfer of water–Cu nanofluids in a microchannel was studied utilizing the lattice Boltzmann method (LBM). The entering flow was at a lower temperature compared to the microchannel walls. Simulations were performed for nanoparticle volume fractions of 0.00 to 0.04 and slip coefficient from 0.005 to 0.02. The model predictions were found to be in good agreement with earlier studies. The effects of wall slip velocity and temperature jump of the nanofluid were studied for the first time by using lattice Boltzmann method. Streamlines, isotherms, longitudinal variations of Nusselt number, slip velocity and temperature jump as well as velocity and temperature profiles for different cross sections were presented. The results indicate that LBM can be used to simulate forced convection for the nanofluid micro flows. Moreover, the effect of the temperature jump on the heat transfer rate is significant. Also, the results showed that decreasing the values of slip coefficient enhances the convective heat transfer coefficient and consequently the Nusselt number (Nu) but increases the wall slip velocity and temperature jump values.

A new method for the calculation of interface pressure for front capturing methods is developed. This method is based on the calculation of the pressure force at each interfacial cell face using the exact pressure due to the portion of the cell face that is occupied by each fluid. Special formulations for the pressure in the interfacial cells are derived for different orientations of an interface. This method (referred to as pressure calculation based on the interface location (PCIL)) is applied to the time evolution of a two-dimensional initially stagnant liquid drop in a gas, as well as, a gas bubble in liquid (gravity effects are not considered). A two-fluid, PLIC-VOF method is used to simulate the flow numerically. Both the continuum surface force (CSF) and the continuum surface stress (CSS) methods are used. A wide range of Ohnesorge numbers and density and viscosity ratios of two fluids are tested. It is shown that the new method reduces the spurious currents by up to three orders of magnitude for the cases tested.

The simultaneous effects of flow pulsation and geometrical perturbation on laminar mixing in curved ducts have been numerically studied by three different metrics: analysis of the secondary flow patterns, Lyapunov exponents and vorticity vector analysis. The mixer that creates the flow pulsation and geometrical perturbations in these simulations is a twisted duct consisting of three bends; the angle between the curvature planes of successive bends is 90 deg. Both steady and pulsating flows are considered. In the steady case, analysis of secondary flow patterns showed that homoclinic connections appear and become prominent at large Reynolds numbers. In the pulsatile flow, homoclinic and heteroclinic connections appear by increasing beta, the ratio of the peak oscillatory velocity component of the mean flow velocity. Moreover, sharp variations in the secondary flow structure are observed over an oscillation cycle for high values of beta. These variations are reduced and the homoclinic connections disappear at high Womersley numbers. We show that small and moderate values of the Womersley number ( 6 = 2) provide a better mixing than that in the steady flow. These results correlate closely with those obtained using two other metrics, analysis of the Lyapunov exponents and vorticity vector. It is shown that the increase in the Lyapunov exponents, and thus mixing enhancement, is due to the formation of homoclinic and heteroclinic connections.

In this research, a novel inverse design algorithm called, Elastic Surface Algorithm (ESA), is developed for viscose and inviscid external flow regimes. ESA is a physically based iterative inverse design method that uses flow analysis code to estimate the pressure distribution on the solid structure, i.e. airfoil, and a 2D solid beam finite element code to calculate the deflections due to the difference between the calculated and target pressure distribution. The proposed method is validated through the inverse design of three different airfoils. In addition, two design examples are presented to prove the robustness of the method in various flow regimes. Also, the convergence rate of this method is compared with flexible membrane method (MGM) and Ball-Spine Algorithm (BSA) methods in inviscid flow regime. The results of this study showed that not only the ESA method is an effective method for inverse design of airfoils, but also it can considerably increase the convergence rate in transonic flow regimes.

This study determines the simultaneous effects of spatial disturbance and flow pulsation on micromixing by using three different metrics: concentration distribution, Lyapunov exponent and axial vorticity. Numerical simulations are performed for both steady and pulsating flows through a microchannel made up of C-curved repeating units. Moreover, a straight microchannel is analyzed to compare the effects of chaotic advection and molecular diffusion, the main mechanisms of transverse mixing in the chaotic and straight mixer respectively. Simulations are carried out in the steady flow for the Reynolds number range 1 = 2) are favorable conditions for mixing enhancement. Moreover, mixing has an oscillating trend along the microchannel due to the coexistence of regular and chaotic zones in the fluid. These results correlate closely with those obtained using two other metrics, analysis of the Lyapunov exponent and axial vorticity.

The correlation between heat transfer enhancement and secondary flow structures in laminar flows through a chaotic heat exchanger is discussed. The geometry consists of three bends; the angle between curvature planes of successive bends is 90 degrees. Numerical simulations are performed for both steady and pulsating flows when the walls are subjected to a constant temperature. The temperature profiles and secondary flow patterns at the exit of bends are compared in order to characterize the flow. Simulations are carried out for the Reynolds numbers range 300 = 2 is a sufficient condition for heat transfer enhancement. The formation and development of homoclinic connections are correlated with the heating homogenization.

In the present study, theoretical formulations for calculation of optimal bifurcation angle and relationship between the diameters of mother and daughter vessels using the power law model for non-Newtonian fluids are developed. The method is based on the distribution of wall shear stress in the mother and daughter vessels. Also, the effect of distribution of wall shear stress on the minimization of energy loss and flow resistance is considered. It is shown that constant wall shear stress in the mother and daughter vessels provides the minimum flow resistance and energy loss of biological flows. Moreover, the effects of different wall shear stresses in the mother and daughter branches, different lengths of daughter branches in the asymmetric bifurcations and non-Newtonian effect of biological fluid flows on the bifurcation angle and the relationship between the diameters of mother and daughter branches are considered. Using numerical simulations for non-Newtonian models such as power law and Carreau models, the effects of optimal bifurcation angle on the pressure drop and flow resistance of blood flow in the symmetric bifurcation are investigated. Numerical simulations show that optimal bifurcation angle decreases the pressure drop and flow resistance especially for bifurcations at large Reynolds number.

This paper aims to study the gravity effects on the mixed convection heat transfer in a microchannel using lattice Boltzmann method. To include these effects, hydrodynamic boundary condition equations are modified. In this problem, cold fluid enters the microchannel and leaves it after cooling the hot walls. For a wide range of inlet Knudsen number (Kn), computations are performed, and for validation, appropriate comparisons between present and previous available results are made. As the results, stream lines, longitudinal variations of friction coefficient, Nusselt number, slip velocity and temperature jump, and velocity and temperature profiles in different cross sections are presented. The results show that lattice Boltzmann method can be used to simulate mixed convection in a microchannel, and the effects of buoyancy forces are important for Kn 0.05, these effects can be ignored. In addition, it is observed that buoyancy forces generate a rotational cell in the microchannel flow, leading to the negative slip velocity at Kn = 0.005.

Symmetrical 30-60% stenosis in a common carotid artery under unsteady flow condition for Newtonian and six non-Newtonian viscosity models are investigated numerically. Results show power-law model produces higher deviations, in terms of velocity and wall shear stress in comparison with other models while generalized power-law and modified-Casson models are more prone to Newtonian state. Comparing separation length of recirculation region at different critical points of cardiac cycle confirms the necessity of considering blood flow in unsteady mode. Increasing stenosis intensity causes flow patterns more disturbed downstream of the stenosis and WSS appear to develop remarkably at the stenosis throat.

Formation of droplets especially in microchannels, micro-electro-mechanical systems (MEMS) and polymer electrolyte membrane fuel cells and their effects on the performance of these devises, as well as scientific aspect of the droplet behavior in the fluid flow motion, makes the subject of the droplet deformation and motion an attractive problem. In this work, we numerically simulate the deformation of a drop of water attached to the wall of a channel flow using full two-dimensional Navier–Stokes equation and the volume-of-fluid method for capturing the interface. The effects of channel inlet velocity, the density and viscosity of the surrounding fluid, and the surface tension coefficient on the flow structures both inside and outside of the droplet as well as the deformation of the droplets are examined. Several test cases, which cover rather wide range of the Reynolds and capillary numbers, based on the surrounding fluid properties and the diameter of the droplet are performed. The Reynolds number, Re, range is from 24 to 1800 and the capillary number, Ca, is from 0.014 to 0.219. It is found that the droplet shape changes and depending on the capillary and Reynolds numbers, it eventually reaches an equilibrium state when there is balance between the surface tension, inertia, and the viscous forces. It is also found that the deformation of the droplet does not depend on the capillary numbers, when Ca is small, but it is a strong function of Ca, when it is large.

In this paper, the two-dimensional stagger grid interface pressure (SGIP) model has been generalized and presented into three-dimensional form. For this purpose, various models of surface tension force for interfacial flows have been investigated and compared with each other. The VOF method has been used for tracking the interface. To show the ability of the SGIP model for three-dimensional flows in comparison with other models, pressure contours, maximum spurious velocities, norm spurious flow velocities and pressure jump error for motionless drop of liquid and bubble of gas are calculated using different models. It has been pointed out that SGIP model in comparison with the CSF, CSS and PCIL models produces the least maximum and norm spurious velocities. Additionally, the new model produces more accurate results in calculating the pressure jumps across the interface for motionless drop of liquid and bubble of gas which is generated in surface tension force.

Different numerical methods are employed and developed for simulating interfacial flows. A large range of applications belong to this group, e.g. two-phase flows of air bubbles in water or water drops in air. In such problems surface tension effects often play a dominant role. In this paper, various models of surface tension force for interfacial flows, the CSF, CSS, PCIL and SGIP models have been applied to simulate the motion of small air bubbles in water and the results were compared and reviewed. It has been pointed out that by using SGIP or PCIL models, we are able to simulate bubble rise and obtain results in close agreement with the experimental data., {"references":["Youngs, D.L. \"Time-dependent multi-material flow with large fluid\ndistribution\", in Numerical methods for fluid dynamics, Morton and\nNorman,Editor,187-221,1996","D. Jamet, D. Torres, J.U. Brackbill, On the theory and computation of\nsurface tension: the elimination of parasitic currents through energy\nconservation in the second-gradient method, J. Comp. Phys. 182 (2002)\n262-276.","J.U. Brackbill, D.B. Kothe, C. Zemach, A continuum method for\nmodeling surface tension, J. Comp. Phys. 100 (1992) 335-354.","Landau, L. D. and Lifshitz, E. M., \"Fluid Mechanics\", Pergoman Press,\nNew York, 1959","Kothe, D.B., W.J. Rider, S.J. Mosso, and J.S. Brock, \"Volume tracking\nof interfaces having surface tension in two and three dimensions\" AIAA\n96-0859, 1996.","Aleinov, I., and Puckett, E.G., \"Computing surface tension with highorder\nkernels\", in Dwyer, H.A., ed., Proceedings of the Sixth\nInternational Symposium on Computational Fluid dynamics, pp. 13-18,\nLake Tahoe, NV, 1995.","B. Lafaurie, C. Nardone, R. Scardovelli, S. Zaleski, G. Zanetti,\nModeling merging and fragmentation in multiphase .ows with SURFER,\nJ. Comp. Phys. 113 (1994) 134-147.","Meier, M., Yadigaroglu, H. and Smith, B.L., \"A novel technique for\nincluding surface tension in PLIC-VOF methods\", Eur. J. B/fluids, 21,\n61-73, 2002.","Shirani, E., Ashgriz, N. and Mostaghimi, J.,\" Interface pressure\ncalculation based on conservative of momentum for front tracking\nmethods\", J. Comp. Phys., 203, 153-175, 2005.\n[10] Seifollahi, M., Shirani, E. and Ashgriz, N., \"An Improved Method for\nCalculation of Interface Pressure Force in PLIC-VOF Methods\",\nEuropean Journal of Mechanics- B/Fluids, 27, 1-23, 2008.\n[11] Ahmadi nadooshan, A. and Shirani, E., \"Interface Pressure Model for\nSurface Tension Force for VOF-Based Methods in Interfacial Flows\",\nSubmitted for Publication, Engineering Applications of Computational\nFluid Mechanics journal, January 2008.\n[12] Chen L, Garimella SV, Reizes JA, Leonardi E., The development of a\nbubble rising in a viscous liquid.\", J Fluid Mech. 1999, 387:61-96.\n[13] van Wachem BGM, Schouten JC., \"Experimental validation of 3-D\nLagrangian VOF model: bubble shape and rise velocity.\", AIChE J,\n2002, 48(12):2744-2753.\n[14] Tomiyama A, Zun I, Sou A, Sakaguchi T., \"Numerical analysis of\nbubble motion with the VOF method.\" , Nuclear Eng Design\n,1993;141:69-82.\n[15] Meier M., \"Numerical and experimental study of large steam-air bubbles\ninjected in a water pool,\" Dissertation no. 13091, Swiss Federal Institute\nof Technology, Zurich, Switzerland, 1999.\n[16] Clift R, Grace JR, \"Weber ME. Bubbles, Drops and Particles,\" Academic\nPress, London,1st edition, 1978.\n[17] Martin W. and Chandler GM.,\" The local measurement of the size and\nvelocity of bubbles rising in liquids.\", in Mechanics and Physics of\nBubbles in Liquids, L. van Wijngaarden, Ed., Nijhoff Pub., 1982."]}

The Reynolds-averaged equations of motion for turbulent interfacial flows are developed. A new model for the correlation of the mean pressure with the fluctuations of the interface location is introduced. A parameter referred to as turbulent surface tension coefficient is introduced that models the effect of turbulence on increasing the surface tension force. In addition, a model for the correlation of the mean fluctuations of the volume fraction with velocity is presented. A volume-of-fluid-based model is used to simulate the dynamics of the interface between the two immiscible fluids. The new turbulence models are used to simulate a two-dimensional Kelvin-Helmholtz instability at high-Reynolds-number flows. In addition, the turbulence models are used to simulate spreading of a plane turbulent water jet in air.

In this paper, the performance of the twin-entry radial flow turbine under steady state and partial admission conditions is modeled. The method, which is developed here, is based on one-dimensional performance prediction. In one-dimensional modeling, the flow properties are assumed constant on a plane normal to the flow direction. This assumption is in contrast with the flow at the rotor entry of a twin-entry turbine under partial admission condition. In this study the one-dimensional performance prediction method for single-entry turbine is modified to analyze the twin-entry turbine. In particular, the loss coefficients due to friction, clearance and blade loading, which are already developed for single-entry turbines, are modified. Also additional losses in the rotor are considered because of twin-entry rotor inlet conditions and the rotor-mixing losses. Indeed in a single-entry turbine with symmetric volute the flow tends to move toward the shroud. A correlation for the radial velocity profile at the rotor entry for this case is obtained and is considered to be optimum. Then the rotor mixing loss is estimated. Finally a model based on the above mentioned matters is developed. The results obtained from the model are compared with experimental results and good agreements are obtained. In this paper, special behaviors of the flow in the twin-entry turbine are also investigated and some physical interpretations are presented.Copyright © 2002 by ASME