Numerical simulation of thermal convection of viscoelastic fluids in an open-top porous medium with constant heat flux

This paper makes a numerical study of the buoyancy-driven convection of a viscoelastic fluid saturated in an open-top porous square box under the constant heat flux boundary condition. The effects of the relaxation and retardation times on the onset of the oscillatory convection, the convection heat transfer rate and the flow pattern transition are investigated. It is shown that a large relaxation time can destabilize the fluid flow leading to an early onset of the thermal convection and a high heat transfer rate, while a large retardation time tends to stabilize the flow and suppress the convection onset and the heat transfer. After the convection sets in, the flow bifurcation appears earlier with the increase of the relaxation time and the decrease of the retardation time, resulting in more complicated flow patterns in the porous medium. Furthermore, with the increase of the ratio of the relaxation time to the retardation time, the fluid may be blocked from flowing through the open-top boundary, which may be caused by the viscoelastic effect. Finally, the comparison of our results with those under isothermal heating boundary conditions reveals that the heat transfer rate corresponding to a constant heat flux boundary is always higher.     

Thermal instability and heat transfer of viscoelastic fluids in bounded porous media with constant heat flux boundary

A numerical simulation is performed for thermal instability and heat transfer of viscoelastic fluids in bounded porous media under the bottom constant heat flux boundary condition. The results for six different combinations of relaxation and retardation times demonstrate the existence of the thermal instability induced flow bifurcation. It is found that the increase of the relaxation time can enhance the heat transfer efficiency by disturbing the fluid flow and facilitating the bifurcation. The increase of the retardation time can stabilize the flow and postpone the bifurcation, leading to simpler flow pattern and lower heat transfer rate.     

MHD flow of a visco-elastic fluid through a porous medium between infinite parallel plates with time dependent suction

This work provides a comprehensive theoretical analysis of MHD unsteady free convection viscoelastic fluid flow through a porous medium. The medium is treated as incompressible and optically transparent. The flow of the fluid is initiated by shearing action of the moving wall with time dependent suction. Radiative heat flow is considered in temperature equation. The coupled nonlinear problem has been solved asymptotically. Approximate solutions have been obtained for the mean velocity, mean temperature using multi parameter perturbation technique. The originality of the present study is to investigate the effect of viscoelastic property of the fluid(Walters B? model) on the flow and heat transfer phenomena when the flow is permeated through a porous medium with uniform porous matrix subject to transverse magnetic field and time dependent fluctuative suction at the boundary surface. The case of viscous flow has been discussed as a particular case on comparison with the result reported earlier and it is in good agreement. Flow reversal is indicated incase of viscoelastic fluid with high heat capacity in the presence of magnetic field. The higher cooling of the plate in case of viscoelastic flow also causes a flow reversal.     

UNSTEADY FLOW OF NON-NEWTONIAN VISCO-ELASTIC FLUID IN DUAL-POROSITY MEDIA WITH THE FRACTIONAL DERIVATIVE

The fractional order derivative was introduced to the seepage flow research to establish the relaxation models of non-Newtonian viscoelastic fluids in dual porous media. The flow characteristics of non-Newtonian viscoelastic fluids through a dual porous medium were studied by using the Hankel transform, the discrete Laplace transform of sequential fractional derivatives and the generalized Mittag-Leffler function. Exact solutions were obtained for arbitrary fractional order derivative. The long-time and short-time asymptotic solutions for an infinite formation were also resulted. The pressure transient behavior of non-Newtonian viscoelastic fluids flow through an infinite dual porous media was studied by using Stehfest's inversion method of the numerical Laplace transform. It shows that the characteristics of the fluid flow are appreciably affected by the order of the fractional derivative.     

MECHANISM FOR VISCOELASTIC POLYMER SOLUTION PERCOLATING THROUGH POROUS MEDIA

The pore throat of porous media is modeled as a constricted channel or expanded channel. The flow of viscoelastic polymer solution in pore throat model is studied by numerical method. Relationship between pressure drop and flow rate is developed,viscoelasticity and throat size are found to be two main factors in high flow resistance. According to pore throat model,2-D stochastic channel bundle is put forward to model porous media,which is composed of pore throat models in series -parallel connection with size and length accord to Haring -Greenkorn stochastic distribution. Percolation model of viscoelastic fluid is developed on the basis of Darcy equation and pressure drop vs. flow rate relation in 2-D stochastic channel bundle. Results indicate that the seepage ability of viscoelastic polymer solution decreases with the increase of viscoelasticity,injection rate,and heterogeneity as well as the decrease of mean pore size of porous media. The high pressure drop of viscoelastic fluid at the connection of pore to throat plays a great role in its anomalous high flow resistance through porous media.     

Application of binding theory for seepage of viscoelastic fluid in a variable diameter capillary

The polymer solution for polymer flooding is a viscoelastic fluid. There exist both shear flow and elongational flow when the polymer solution flows in a porous medium, where an additional dissipation is involved. The additional dissipation caused by elongational deformation is often ignored while studying the flow of the fluid in a porous medium. For a complex polymer solution, the generated elongational pressure drop cannot be ignored. In a capillary of fixed diameter, the polymer solution is only impacted by the shear force, and its rheological property is pseudoplastic. Therefore the variable diameter capillary and the converging-diverging flow model with different cross sections are required to describe the flow characteristics of the polymer solution in porous media more accurately. When the polymer solution flows through the port, we have the elongational flow and the polymer molecules undergo elongational deformation elastically. By using the mechanical energy balance principle and the minimum energy principle, a mathematical model of non-Newtonian fluid inlet flow was established by Binding. On the basis of the Binding theory, with the application of the theory of viscoelastic fluid flow in the circular capillary and the contraction-expansion tube, the relations between the viscoelastic fluid flow rate and the pressure drop are obtained.     

Effects of Navier slip on unsteady flow of a reactive variable viscosity non-Newtonian fluid through a porous saturated medium with asymmetric convective boundary conditions

A study on the effects of Navier slip, in conjunction with other flow parameters, on unsteady flow of reactive variable viscosity third-grade fluid through a porous saturated medium with asymmetric convective boundary conditions is presented. The channel walls are assumed to be subjected to asymmetric convective heat exchange with the ambient, and exothermic chemical reactions take place within the flow system. The heat exchange with the ambient obeys Newton's law of cooling. The coupled equations, arising from the law of conservation of momentum and the first law of thermodynamics, then the derived system are nondimensionalised and solved using a semi-implicit finite difference scheme. The lower wall slip parameter is observed to increase the fluid velocity profiles, whereas the upper wall slip parameter retards them because of backflow at the upper channel wall. Heat production in the fluid is seen to increase with the slip parameters. The wall shear stress increases with the slip parameters while the wall heat transfer rate is largely unaltered by the lower wall slip parameter but marginally increased by the upper wall slip parameter.     

同轴套管间涡旋流动及强化传热数值模拟

相对旋转两同轴套管间的涡旋流动,能够带来二次流强化传热传质作用,在航空、水处理、生态保护、生物工程和膜分离等领域都具有广泛的应用价值。本文使用Fluent软件,对同轴套管间涡旋流动及传热特性进行数值模拟,考察了内管转速、内外管壁面温差等操作参数变化对同轴套管间流体传热性能的影响,分析了涡旋流动与传热效率之间的关联关系。模拟结果表明:内管转速增加在流场中形成泰勒涡,涡流扰动增大了高温壁面与流体间的热流密度,增强了流体传热效率。增大内外管壁面温差,也可加强流体传热性能,但其强化作用不及内管转速的强化作用显著。受流场中泰勒涡影响,流体速度、温度及热流密度沿轴向的分布都呈正弦状周期性波动,在相邻两涡交界面处,流体传热性能最好,在涡中心处的传热性能最差。     

Numerical investigation of flow and heat transfer performances of horizontal spiral-coil pipes

The flow and heat transfer performances of horizontal spiral-coil pipes of circular and elliptical cross-sections are studied.The numerical results are compared with the experimental data,to verify the numerical method.The effects of the inlet water mass flow rate,the structural parameters,the helical pitch and the radius ratio on the heat transfer performances are investigated.Performances of the secondary fluid flow with different radius ratios are also investigated.Numerical results demonstrate that the heat transfer coefficient and the Nusselt number increase with the increase of the water mass flow rate or the helical pitch.The maximum heat transfer coefficient and the maximum Nusselt number are obtained when the radius ratio is equal to 1.00.In addition,the fluid particle moves spirally along the pipe and the velocity changes periodically.The particle flow intensity and the spiral movement frequency decrease significantly with the increase of the radius ratio.Besides,the secondary flow profile in the horizontal spiral-coil pipe contains two oppositely rotating eddies,and the eddy intensity decreases significantly along the pipe owing to the change of curvature.The decreasing tendency of the eddy intensity along the pipe increases with the increase of the radius ratio.     

Experimental Investigation on Heat Transfer Enhancement in Composite Porous Media

The method of composite porous media with mini-longitudinal channels at the surface and with beads packing between plates was put foward to improve the integated performance of flow and heat transfer in porous media. The experimental results in the corresponding porous media were reported and analyzed. The experiments indicate that with proper matching of the particle diameter dp, the mini-channel width w, the channel depth d and the distance between plates δr the heat transfer in the composite porois media is enhanced and flow resistence reduced compared with those of no mini-longitudinal channels at the surface. So this is an effective method to improve the integrated performance of flow and heat transfer in porous media.     

底部加热的复合多孔介质热-流耦合场非线性特性

针对非线性流动传热受底部加热模型骨架的影响及分叉、震荡点的非线性解析解难求的问题,采用数值模拟及实验的方法对底部加热的复合多孔介质热流耦合传热过程进行数值求解和温度测试。构建底部加热的复合多孔介质热-流耦合传热的三维模型;采用SIMPLE算法对控制方程组进行QUICK格式离散求解,并在底部加热实验台上对测点进行温度采集。在小Ra工况下,揭示了复合多孔介质内存在热流分布分层特性及确定了非线性分叉、震荡解的特征值。数值结果表明:热流场分布对初始场依赖敏感,低Ra情况下三维腔体内热流场表现出稳定的二维性质;与单层多孔介质相比,复合多孔介质内存在热流分布分层的非线性特性;非线性分叉、震荡点对应的临界Ra依赖复合多孔介质骨架高度比,高度比越大(强导热、高阻力多孔介质区所占高度越大),静态分叉及震荡所对应的临界Ra越小,越早表现出分叉、震荡等非线性特性;改变复合多孔介质内高度比可以重新优化热流场分布,实现削弱或强化传热。     

A MATHEMATICAL MODEL FOR HEAT AND MASS TRANSFER IN UNSATURATED WET POROUS MEDIA CONSIDERING EFFECT OF CAPILLARY HYSTERESIS

Based on the transport mechanism of heat and mass transfer and by using the minimum gradient theory for unsaturated flow in capillary porous media, a mathematical model is developed for heat and mass transfer in unsaturated wet porous media considering the effect of capillary hysteresis. The heat and mass transport properties in the derived differential equations are analyzed in detail. which opens new way to further develop practical methods for determining heat and mass transport properties in wet porous media.     

螺旋流混合器内部流动及换热分析

构建了一种无运动部件的螺旋流混合器三维模型,运用计算流体力学理论,采用湍流、非定常和传热模型,模拟了冷、热水在混合器中螺旋混合的过程,并通过对混合器内流线和温度分布等的分析,探讨了混合器内部流动和能量交换的规律,以及进口流速和混合器容积的变化对其出口温度的影响。计算结果表明:螺旋流混合器可以得到了比较好的混合效果;在一定的阻力下,进口速度越大越易形成旋流,混合效果越好;螺旋流混合器的容积变化对混合效果影响明显,随着容积的增大,调整时间显著增加。     

NUMERICAL SIMULATION OF FLOWS FOR SECOND-ORDER VISCOELASTIC FLUID COUPLED WITH HEAT TRANSFER BY DIFFERENTIAL QUADRATURE METHOD

The problem of two-dimensional steady flow of an incompressible second-order viscoelastic fluid coupled with heat transfer between parallel plates was considered. A viscous dissipation function was included in the energy equation.When the elastic property of the fluid is weaker, the zerothorder and first-order approximate governing equations were obtained by means of the perturbation method. To understand the behavior of flow near the tube wall, the half-domain was divided into two sub-domains, in which one is a thin layer near the wall called the inner domain and the remainder is called the outer domain. The governing equations in the inner domain and in the outer domain were discretized respectively by using the Differential Quadrature Method (DQM). The matching conditions at the interface between the inner and outer domains were presented. An iterative method for solving these discretized equations was given in this paper. The numerical results obtained agree with existing results.     

能量桩传热性能影响因素的数值模拟与分析

基于数值模拟的方法,运用ＡＢＡＱＵＳ软件建立模型,分别对能量桩的桩长、桩径、换热管数、换热 液流速和土体类型进行了敏感性分析,得到不同条件下能量桩的换热量。结果表明:能量桩的单位长度 换热量与桩径、流速、土体导热系数成正比,与桩长成反比。在单Ｕ、双Ｕ、三Ｕ型能量桩中,双Ｕ型能量 桩的单位长度换热量最高。     

Electro-osmotic flow of a second-grade fluid in a porous microchannel subject to an AC electric field

Studies on electro-osmotic flows of various types of fluids in microchannel are of great importance owing to their multifold applications in the transport of liquids, particularly when the ionized liquid flows with respect to a charged surface in the presence of an external electric field. In the case of viscoelastic fluids, the volumetric flow rate differs significantly from that of Newtonian fluids, even when the flow takes place under the same pressure gradient and the same electric field. With this end in view, this paper is devoted to a study concerning the flow pattern of an electro-osmotic flow in a porous microchannel, which is under the action of an alternating electric field. The influence of various rheological and electro-osmotic parameters, e.g., the Reynolds number, Debye-Huckel parameter, shape factor and fluid viscoelasticity on the kinematics of the fluid, has been investigated for a secondgrade viscoelastic fluid. The problem is first treated by using analytical methods, but the quantitative estimates are obtained numerically with the help of the software MATHEMATICA. The results presented here are applicable to the cases where the channel height is much greater than the thickness of the electrical double layer comprising the Stern and diffuse layers. The study reveals that a larger value of the Debye-Huckel parameter creates sharper profile near the wall and also that the velocity of electro-osmotic flow increases as the permeability of the porous microchannel is enhanced. The study further shows that the electro-osmotic flow dominates at lower values of Reynolds number. The results presented here will be quite useful to validate the observations of experimental investigations on the characteristics of electro-osmotic flows and also the results of complex numerical models that are necessary to deal with more realistic situations, where electro-osmotic flows come into the picture, as in blood flow in the micro-circulatory system subject to an electric field.     

复合多孔介质流动特性的模型分析

本文针对壁面开槽复合多孔介质强化传热的实验条件 ,将整个流动区域划分为多孔介质填充区和纵向微槽区两个区域 ,通过数值计算分析了这种复合多孔介质结构的流动特性 ,考察了微槽宽度、深度等有关因素的影响 ,得到了与实验相一致的结果。     

Natural convective heat transfer and nanofluid flow in a cavity with top wavy wall and corner heater

A numerical analysis of natural convection of nanofluid in a wavy-walled enclosure with an isothermal corner heater has been carried out. The cavity is heated from the left bottom corner and cooled from the top wavy wall while the rest walls are adiabatic. Mathematical model has been formulated using the single-phase nanofluid approach. Main efforts have been focused on the effects of the dimensionless time, Rayleigh number, undulation number, nanoparticle volume fraction and length of corner heaters on the fluid flow and heat transfer inside the cavity. Numerical results have been presented in the form of streamlines, isotherms, velocity and temperature profiles, local and average Nusselt numbers. It has been found that nanoparticle volume fraction essentially affects both fluid flow and heat transfer while undulation number changes significantly only the heat transfer rate.     

双流程空冷散热器不同布置方式对散热系数影响分析

本文通过理论推导给出了散热器的冷热流体的温度分布计算公式,并计算分析了初始温差、顺逆流程及散热器高度对散热系数的影响。计算结果表明,初始温差(ITD)不会影响顺、逆流程的综合散热系数;逆流程散热系数总是大于顺流程;顺流程的散热系数随着散热器高度的增加不断减小,但散热器高度对逆流程的散热系数影响很小。此结果对工程设计具有重要的参考价值。     

NUMERICAL INVESTIGATION ON EXTRUDATE SWELL FOR VISCOELASTIC FLUID： USING MAXWELL MODEL

The numerical investigation on extrudate swell through capillary die for viscoelastic fluid characteried by integral-type Maxwell constitutive equation was conducted by employing the finite element method with the calculation of viscoelastic extra stress in the conventional finite element. The method of avoiding singularity was also adopted by integrating the strain history of the Gauss points for each element near the wall and the free surface. The convergence solutions at high Weissenberg number can be obtained by using the appropriate methods to reduce errors and improve the speed of convergence of the calculation, which include adding a relaxation factor of velocity in iteration process, or enlarging the reference viscosity, or reducing the elapsed time. The highest Weissenberg number obtained here is up to 3. 8, while the solution at the Weissenberg number of 3. 75 was given in the previous work with similar extrudate swell ratio and the exit pressure drop by using differential Maxwell model with Elastic-Viscous Stress Split (EVSS) combined with Streamline Upwind Petrov-Galerkin (SUPG) scheme. The calculations indicated that the method of dealing with integral consti- tutive equation introduced in this paper is suitable in simulating viscoelastic flow characterized by integral constitutive equation at high elastic level.