基于涡粘性模型的翼型湍流流场熵产率计算

利用有限体积法实现了基于非正交同位网格的SIMPLE算法。基于熵分析方法,采用涡粘性模型求解湍流熵产方程,系统研究了湍流模型对二维翼型绕流流场熵产率的影响。通过计算NACA0012翼型在来流雷诺数为2.88×10⁶时,0°攻角~16.5°攻角范围内的翼型表面压力系数分布和升阻力特性,验证了算法及程序的正确性。结果表明,选择不同湍流模型时,翼型流场熵产的计算结果存在差异,湍流耗散是引起流场熵产的主要原因;翼型流场的熵产主要发生在翼型前缘区、壁面边界层和翼型尾流区域,流场熵产率与翼型阻力系数线性相关;当产生分离涡时,粘性耗散引起的熵产下降。     

Lie group analysis for the effect of temperature-dependent fluid viscosity with thermophoresis on magnetohydrodynamic free convective heat and mass transfer over a porous stretching surface

This article concerns with a steady two-dimensional flow of an electrically conducting incompressible fluid over a vertical stretching sheet. A scaling group of transformations is applied to the governing equations. The system remains invariant due to some relations among the parameters of the transformations. Impact of thermophoresis particle deposition in the presence of temperature-dependent fluid viscosity plays an important role on the concentration boundary layer. The results thus obtained are presented graphically and discussed.     

Mixed convective heat and mass transfer in a non-Newtonian fluid at a peristaltic surface with temperature-dependent viscosity

We investigate the problem of the unsteady mixed convection peristaltic mechanism. The flow includes a temperature-dependent viscosity with thermal diffusion and diffusion-thermo effects. The peristaltic flow is between two vertical walls, one of which is deformed in the shape of traveling transversal waves exactly like peristaltic pumping and the other of which is a parallel flat plate wall. The equations of momentum, energy, and concentration are subject to a set of appropriate boundary conditions by assuming that the solution consists of two parts: a mean part and a perturbed part. The solution of the perturbed part has been obtained by using the long-wave approximation. The mean part has been solved and coincides with the approximation of Ostrach. The mean part (zeroth order), the first order, and the total solution of the problem have been evaluated numerically for several sets of values of the parameters entering the problem. The skin friction, and the rate of heat and mass transfer at the walls are obtained and illustrated graphically.     

Combined forced and free flow in a vertical rectangular duct with prescribed wall heat flux

In this paper, combined forced and free convection is studied in a vertical rectangular duct with a prescribed uniform wall heat flux (H2 boundary condition). A different heat flux value for each plane wall is considered; the condition of a uniform wall heat flux throughout the duct results as a special case. The local momentum and energy balance equations are written in a dimensionless form and solved numerically, by means of a Galerkin finite element method. The numerical solution gives the dimensionless velocity and temperature distributions, together with the values of the Fanning friction factor, of the Nusselt number, of the momentum flux correction factor and of the kinetic energy correction factor. These dimensionless parameters are reported as functions of the aspect ratio and of the ratio between the Grashof number, Gr, and the Reynolds number, Re. The threshold values of Gr/Re for the onset of flow reversal are evaluated.     

Natural convection flow of a viscous incompressible fluid in a rectangular porous cavity heated from below with cold sidewalls

We consider the flow, which is induced by differential heating on the boundaries of a porous cavity heated from below. In particular we allow the sidewalls to have the same cold temperature as the upper surface, and thus the problem is a variant of the Darcy-Bénard convection problem, but one where there is flow at all non-zero Grashof numbers. Attention is focused on how the flow and heat transfer is affected by variations in the cavity aspect ratio, the Grashof number and the Darcy number. The flow becomes weaker as the Darcy number decreases from the pure fluid limit towards the Darcy-flow limit. In addition the number of cells which form in the cavity varies primarily with the aspect ratio and is always even due to the symmetry imposed by the cold sidewalls.     

The effect of variable viscosity on the entropy generation and pumping power in a laminar fluid flow through a duct subjected to constant heat flux

Entropy generation and pumping power required for a laminar viscous flow in a duct subjected to constant heat flux has been investigated. The temperature dependence of the viscosity is taken into consideration. The ratio of pumping power to total heat flux decreases considerably and entropy generation increases along the duct length for viscous fluids. Therefore, it is shown that an optimum duct length may be obtained which minimizes total energy losses due to both entropy generation and pumping power. For low heat-flux conditions, entropy generation due to viscous friction becomes dominant and the dependence of viscosity on temperature must be considered in order to determine entropy generation accurately. Received on 17 May 1999     

Numerical and experimental investigation of turbulent flow in a rectangular duct

Details of the turbulent flow in a 1:8 aspect ratio rectangular duct at a Reynolds number of approximately 5800 were investigated both numerically and experimentally. The three-dimensional mean velocity field and the normal stresses were measured at a position 50 hydraulic diameters downstream from the inlet using laser doppler velocimetry (LDV). Numerical simulations were carried out for the same flow case assuming fully developed conditions by imposing cyclic boundary conditions in the main flow direction. The numerical approach was based on the finite volume technique with a non-staggered grid arrangement and the SIMPLEC algorithm. Results have been obtained with a linear and a non-linear (Speziale) k–ε model, combined with the Lam–Bremhorst damping functions for low Reynolds numbers. The secondary flow patterns, as well as the magnitude of the main flow and overall parameters predicted by the non-linear k–ε model, show good agreement with the experimental results. However, the simulations provide less anisotropy in the normal stresses than the measurements. Also, the magnitudes of the secondary velocities close to the duct corners are underestimated. © 1998 John Wiley & Sons, Ltd.     

Lie group analysis for the effect of temperature-dependent fluid viscosity and thermophoresis particle deposition on free convective heat and mass transfer under variable stream conditions

This paper examines a steady two-dimensional flow of incompressible fluid over a vertical stretching sheet. The fluid viscosity is assumed to vary as a linear function of temperature. A scaling group of transformations is applied to the governing equa- tions. The system remains invariant due to some relations among the transformation parameters. After finding three absolute invariants, a third-order ordinary differential equation corresponding to the momentum equation and two second-order ordinary differential equations corresponding to energy and diffusion equations are derived. The equations along with the boundary conditions are solved numerically. It is found that the decrease in the temperature-dependent fluid viscosity makes the velocity decrease with the increasing distance of the stretching sheet. At a particular point of the sheet, the fluid velocity decreases but the temperature increases with the decreasing viscosity. The impact of the thermophoresis particle deposition plays an important role in the concentration boundary layer. The obtained results are presented graphically and discussed.     

Effect of variable viscosity on non-Darcy free or mixed convection flow on a vertical surface in a fluid saturated porous medium

This paper analyzes the variable viscosity effects on non-Darcy free or mixed convection flow on a vertical surface in a fluid saturated porous medium. The viscosity of the fluid is assumed to be a inverse linear function of temperature. Velocity and heat transfer are found to be significantly affected by the variable viscosity parameter, Ergun number, Peclet number or Rayleigh number.     

Melting heat transfer effects on stagnation point flow of micropolar fluid saturated in porous medium with internal heat generation （absorption）

The effect of melting heat transfer on the two dimensional boundary layer flow of a micropolar fluid near a stagnation point embedded in a porous medium in the presence of internal heat generation/absorption is investigated. The governing non-linear partial differential equations describing the problem are reduced to a system of non-linear ordinary differential equations using similarity transformations solved numerically using the Chebyshev spectral method. Numerical results for velocity, angular velocity and temperature profiles are shown graphically and discussed for different values of the inverse Darcy number, the heat generation/absorption parameter, and the melting parameter. The effects of the pertinent parameters on the local skin-friction coefficient, the wall couple stress, and the local Nusselt number are tabulated and discussed. The results show that the inverse Darcy number has the effect of enhancing both velocity and temperature and suppressing angular velocity. It is also found that the local skin-friction coefficient decreases, while the local Nusselt number increases as the melting parameter increases.     

Accuracy analysis of predicted velocity profiles of laminar duct flow with entropy generation method

The objective of this work is to estimate the accuracy of a predicted velocity profile which can be gained from experimental results, in comparison with the exact ones by the methodology of entropy generation. The analysis is concerned with the entropy generation rate in hydrodynamic, steady, laminar, and incompressible flow for Newtonian fluids in the insulated channels of arbitrary cross section. The entropy generation can be calculated from two local and overall techniques. Adaptation of the results of these techniques depends on the used velocity profile. Results express that in experimental works, whatever the values of local and overall entropy generation rates are close to each other, the results are more accuracy. In order to extent the subject, different geometries have been investigated. Also, the influence studied, and the distribution of volumetric geometries is drawn. of geometry on the entropy generation rate is local entropy generation rate for the selected geometries is drawn.     

Steady flow and heat transfer of a magnetohydrodynamic Sisko fluid through porous medium in annular pipe

In this paper, the steady flow and heat transfer of a magnetohydrodynamic fluid is studied. The fluid is assumed to be electrically conducting in the presence of a uniform magnetic field and occupies the porous space in annular pipe. The governing nonlinear equations are modeled by introducing the modified Darcy's law obeying the Sisko model. The system is solved using the homotopy analysis method (HAM), which yields analytical solutions in the form of a rapidly convergent infinite series. Also, HAM is used to obtain analytical solutions of the problem for noninteger values of the power index. The resulting problem for velocity field is then numerically solved using an iterative method to show the accuracy of the analytic solutions. The obtained solutions for the velocity and temperature fields are graphically sketched and the salient features of these solutions are discussed for various values of the power index parameter. We also present a comparison between Sisko and Newtonian fluids. Copyright © 2011 John Wiley & Sons, Ltd.     

Effects of the side walls on the unsteady flow of a second-grade fluid in a duct of uniform cross-section

In this paper, the effects of the side walls on the unsteady flow of a second-grade fluid in a duct of rectangular cross-section are considered. Two types of unsteady flows are investigated. One of them is the unsteady flow in a duct of rectangular cross-section moving parallel to its length and the other is the unsteady flow due to an applied pressure gradient in a duct of rectangular cross-section whose sides are at rest. It is shown that a Newtonian fluid reaches steady-state earlier than a second-grade fluid and the effect of the side walls on a second-grade fluid is more effective than that on a Newtonian fluid.     

Effects of strong compressibility in natural convective flows through porous media with a near-critical fluid

The dynamics and heat transfer in a porous medium occupied by a liquid with parameters in the neighborhood of the critical point of “liquid-gas” transition are simulated numerically within the framework of the equations of dynamics of a porous medium with a compressible liquid phase and the Van-der-Waals equation of state. Adiabatic heating of the liquid phase in a porous layer initiated by a jump in temperature on one of the boundaries is investigated under microgravity conditions. Thermo-gravitational convection in the unsteady and steady-state regimes is simulated in rectangular domains and the effect of adiabatic heating on convection is studied. Calibration relations between the Rayleigh-Darcy and Prandtl numbers in the basic system of equations and their real analogs are obtained. A comparison is made with convection in a porous media occupied by a perfect gas.     

The rheology of Hydroxy-propylguar (HPG) solutions and its influence on the flow through a porous medium and turbulent tube flow,respectively (Part 1)

The rheology of aqueous HPG solutions in the range 100 wppm to 5000 wppm is investigated. The flow through a porous medium and turbulent tube flow, respectively, of these solutions is studied as well. Especially with respect to the higher concentrations, the data correlate nicely only after the effect of shear is extracted, i.e., after the variable viscosity is taken into account. This is accomplished by working with an apparent viscosity _c , defined such that, the Hagen Poiseuille law (with _c ) holds in laminar tube flow.     

Effects of temperature-dependence of viscosity and viscous dissipation on laminar flow heat transfer in circular tubes

Heat transfer effects of variable viscosity and viscous dissipation for heated developing laminar flows in circular tubes have been investigated. Three studies are reported covering a comprehensive range of input data for the case of constant wall heat flux. Initially the program was used to predict the effect on heat transfer of temperature-dependent viscosity via a general temperature power relation. In addition, predictions were made for nine particular fluids covering a range of Prandtl numbers from 0.025 to 12 500, and a range of Brinkman numbers from 1.8 × 10^?10 to 6.8 × 10³. A more detailed study was made for two particular oils covering a range of practical interest. For the liquids considered their viscosity temperature-dependence resulted in enhancement of heat transfer, whereas for fluids with a Prandtl number <200 the effect of viscous dissipation was negligible, and for fluids of a Brinkman number > × 10^?2 the outcome was a reduction of heat transfer. A numerical instability problem occurred for situations of very high viscous dissipation which limited the length of duct that could be examined.     

Study of visco-elastic fluid flow and heat transfer over a stretching sheet with variable viscosity

This paper deals with the study of boundary layer flow and heat transfer of a visco-elastic fluid immersed in a porous medium over a non-isothermal stretching sheet. The fluid viscosity is assumed to vary as a function of temperature. The presence of variable viscosity of the fluid leads to the coupling and the non-linearity in the boundary value problem. A numerical shooting algorithm for two unknown initial conditions with fourth-order Runge-Kutta integration scheme has been used to solve the coupled non-linear boundary value problem. An analysis has been carried out for two different cases namely (1) prescribed surface temperature (PST), and (2) prescribed heat flux (PHF), to get the effect of fluid viscosity, permeability parameter and visco-elastic parameter for various situations. The important finding of our study is that the effect of fluid viscosity parameter is to decrease the wall temperature profile significantly when flow is through a porous medium. Further, the effect of permeability parameter is to decrease the skin friction on the sheet.     

Soret and Dufour effects on heat and mass transfer by mixed convection over a vertical surface saturated porous medium with temperature dependent viscosity

The diffusion‐thermo and thermal‐diffusion effects on heat and mass transfer by mixed convection boundary layer flow over a vertical isothermal permeable surface embedded in a porous medium were studied numerically in the presence of chemical reaction with temperature‐dependent viscosity. The governing nonlinear partial differential equations are transformed into a set of coupled ordinary differential equations, which are solved numerically by using Runge–Kutta method with shooting technique. Numerical results are obtained for the velocity, temperature and concentration distributions, and the local skin friction coefficient, local Nusselt number and local Sherwood number for several values of the parameters, namely, the variable viscosity parameter, suction/injection parameter, Darcy number, chemical reaction parameter, and Dufour and Soret numbers. The obtained results are presented graphically and in tabulated form, and the physical aspects of the problem are discussed. Copyright © 2011 John Wiley & Sons, Ltd.