Numerical simulation of self-similar thermal convection from a spinning cone in anisotropic porous medium

Self-similar steady natural convection thermal boundary layer flow from a rotating vertical cone to anisotropic Darcian porous medium is investigated theoretically and numerically. The transformed non-dimensional two-point boundary value problem is reduced to a system of coupled, highly nonlinear ordinary differential equations, which are solved subject to robust surface and free stream boundary conditions with the MAPLE 17 numerical quadrature software. Validation with earlier non-rotating studies is included, and also further verification of rotating solutions is achieved with a variational finite element method(FEM). The rotational(spin) parameter emerges as an inverse function of the Grashof number. The influence of this parameter, primary Darcy number, secondary Darcy number and Prandtl number on tangential velocity and swirl velocity, temperature and heat transfer rate are studied in detail. It is found that the dimensionless tangential velocity increases whilst the dimensionless swirl velocity and temperature decrease with the swirl Darcy number, tangential Darcy number and the rotational parameters. The model finds applications in chemical engineering filtration processing, liquid coating and spinning cone distillation columns.     

THE STRUCTURAL FLOW IN PIPE CONTAINING POROUS MEDIUM SATURATED WITH POWER-LAW FLUID

In this article,the method of volume averaging of flow in porous media and averaging theorem was employed to the Navier-Stokes equations.The total drag force per unit volume was considered as the bulk damping resistance due to the porous structure(i.e.,the Darcy resistance)and the resistance due to the inertia force(i.e.,the Forchheimer resistance),then the Brinkman-Forchheimer extended Darcy model was obtained from average momentum equation.The structural flow in a pipe containing porous medium saturated with power law fluid was applied in the present study.A new theoretical analysis of fully developed non-Darcy flow in a pipe containing a fibrous medium saturated with power law fluid was conducted.Using the integration method,the boundary layer solutions were obtained for flow core velocity and its radius.These theoretical solutions were used to analyze the effects of the Darcy number and inertia parameter on the axial velocity profile in the porous medium pipe.     

Entropy generation analysis for the peristaltic flow of Cu-water nanofluid in a tube with viscous dissipation

The purpose of the current investigation is to examine the influence of different physical parameters on the entropy generation. The entropy generation number due to heat transfer and fluid friction is formulated. The velocity and temperature distributions across the tube are presented along with pressure attributes. Exact analytical solution for velocity and temperature profile is obtained. It is found that the entropy generation number attains high values in the region close to the walls of the tube, while it falls to low values near the center of the tube.     

Numerical investigation of entropy generation and heat transfer of pulsating flow in a horizontal channel with an open cavity

In this study, the entropy generation and the heat transfer of pulsating air flow in a horizontal channel with an open cavity heated from below with uniform temperature distribution are numerically investigated. A numerical method based on finite volume method is used to discretize the governing equations. At the inlet of the channel, pulsating velocity is imposed for a range of Strouhal numbers St_p from 0 to 1 and amplitude A_p from 0 to 0.5. The effects of the governing parameters, such as frequency and amplitude of the pulsation, Richardson number, Ri, and aspect ratio of the cavity, L/H, on the flow field, temperature distribution, average Nusselt number and average entropy generation, are numerically analyzed. The results indicate that the heat transfer and entropy generation are strongly affected by the frequency and amplitude of the pulsation and this depends on the Richardson number and aspect ratio of the cavity. The pulsation is more effective with the aspect ratio of the cavity L/H= 1.5 in terms of heat transfer enhancement and entropy generation minimization.     

波纹板内流体流动特性的数值模拟

以室温下的水为介质，以涡量一流函数为理论基础，运用代数变换法生成适体坐标，通过有限差分对波纹板板内流场进行了数值模拟；并以Re=500为例，求出其板内流体的速度场和压力场，进而对同一周期内和不同周期的速度场和压力场进行分析，给出了速度和压力分布变化曲线图，得出了不同雷诺数下流动阻力损失变化曲线与阻力关联式，为波纹板的强化传热研究提供了有利的参考。     

LAMINAR FLOW AND HEAT TRANSFER IN THE DEVELOPING REGION OF HELICAL SQUARE DUCTS

Simultaneous development of the laminar flow and heat transfer in helical square ducts was numerically studied. The governing equations were written in an orthogonal helical coordinate system and fully parabolized in the axial direction. Results were found out over a wide range of the governing parameters. Two axial velocity entries were taken into account. The development of secondary flow, axial velocity and temperature distribution for the large Dean number were examined in detail and the effects of different governing parameters on the friction factor and the Nusselt number were annlyzee. Many new and interesting conclusions were reached. The present results reveal the nature of fluid flow and heat transfer in the developing region of helical square ducts.     

Transient peristaltic diffusion of nanofluids: A model of micropumps in medical engineering

Peristaltic micro-pumps offer an excellent mechanism for delivery of a variety of medicines including drugs, corneal solutions etc. The surge in deployment of nanoparticles in medicine has provided new potential for such pumps. In light of this we investigate the time-dependent peristaltic flow of nanofluids with diffusive effects through a finite non-uniform channel, this geometry being more representative of real micro-pumps. Creeping flow is taken into account(inertial forces are small compared with viscous forces) i.e., Reynolds number is low(Re 1) and wavelength is also taken to be very large. The Buongiorno formulation for nanofluids is employed with an Oberbeck-Boussinesq approximation. Closed-form solutions are developed for the non-dimensional governing equations subject to physically realistic boundary conditions. Mathematica symbolic software is employed to evaluate the evolution of nanoparticle fraction, temperature, axial velocity, transverse velocity and pressure difference distribution along the length of the pump channel with variation in thermal Grashof number, basic-density(species i.e., mass) Grashof number, Brownian motion parameter and thermophoresis 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。     

考虑水的密度反转特性的二维套管自然对流模拟分析

利用热和流体流动控制方程,以温差驱动的二维同心圆环套管自然对流换热为对象,分析讨论了水在4℃附近密度反转特性对流动和传热的影响,设置了三种等温差方案,分别给出了流场和温度场,并分析了各自的传热与流动原因。分析结果表明:在不包括4℃的温度方案中,各自研究区域内均能得到一个完整的循环流动,但流动方向有所不同,同时在套管的壁面附近均存在较大的温度梯度,主流区温度梯度较小;在相同温差条件下,水的密度反转特性对于传热性能影响较大,在工程应用中,应该充分考虑水的密度反转特性。     

Kelvin-Helmholtz instability.with mass transfer through porous media： Effect of irrotational viscous pressure

This paper studies the effect of the irrotational viscous pressure on Kelvin-Helmholtz instability of the plane interface of two viscous and incompressible fluids in a fully saturated porous media with mass and heat transfers across the interface. In the earlier work, the instability of the plane interface of two viscous and streaming miscible fluids through porous media was studied by assuming that the motion and the pressure are irrotational and the viscosity enters the normal stress balance. This theory is called the viscous potential flow theory. Here, we use another irrotational theory in which the discontinuities in the irrotational tangential velocity and shear stress are eliminated in the global energy balance by considering viscous contributions of the irrotational pressure. The Darcy-Brinkman model is used in the investigation and the stability criterion is formulated in terms of a critical value of the relative velocity. It is observed that the heat and mass transfer has a destabilizing effect on the stability of the system while the irrotational shearing stresses stabilize the system.     

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.     

Lifting of a large object from a rigid porous seabed

This study investigates the flow field induced by the tilting lift of a large object from a rigid porous seabed and the induced force acting on the object using an analytical approach. In the corners between the object and the seabed, we assume the flow is a corner flow with a low Reynolds number, and the porous media flow in the seabed obeys Brinkman equations. The complete boundary conditions for viscous flow, including the continuity of velocities and stresses, are utilized at the seabed-water interface. The Helmholtz decomposition theorem, which decomposes the flow field into irrotational and rotational parts, and a perturbation expansion are employed to solve the boundary-value problem. Leading-order analytical solutions for the flow in the water and in the porous seabed are presented, indicating that the flow inside the corners is not a parallel flow, and the porous media flow inside the seabed is a Stokes boundary layer flow that does not obey Darcy’s law.

     

混水角对强迫对流混水过程影响的熵产数值分析

以两入口流速相同情况下强迫对流混水过程这一物理问题为研究对象,采用计算流体力学、数值传热学理论进行数值计算,分析讨论了对流混水角在30°、45°、60°、90°条件下速度、温度、熵产的分布以及变化关系.计算、分析结果表明:熵产主要分布在两根进水管的交汇区域,及混水后的出水管区域,最大值发生在混水交点处,而两进口支管区域...     

椭圆管外流动熵产及放热系数的数值分析

以椭圆管加热水流动为研究对象,对椭圆管加热水流动系统进行了二维数值模拟。通过联立求解流体力学基本方程和熵产方程,获得了熵产、放热系数与雷诺数和纵、横向间距的变化关系。数值分析结果表明:熵产主要发生在管壁表面附近,而在系统内部区域熵产较小,可以忽略;熵产随雷诺数的增大而增大,随纵、横向间距增加而减小,熵产与雷诺数、纵、横向间距存在对应关系,纵、横向间距宜在1.75～2.0间;在相同的雷诺数值时,熵产、放热系数沿流动方向呈现单调减小的趋势;不同的雷诺数值,熵产、放热系数不同,单调减小的趋势相同。放热系数随Re的增大而增大,且与雷诺数存在对应关系。纵向总放热系数随纵、横向间距增大而减小,且存在对应关系。     

FLOW AND HEAT TRANSFER OF OLDROYD-B FLUIDS IN A ROTATING CURVED PIPE

The flow and convected heat transfer of the Oldroyd-B fluids in a rotating curved pipe with circular cross-section were investigated by employing a perturbation method. A perturbation solution up to the second order was obtained for a small curvature ratio, κ. The variations of axial velocity distribution and secondary flow structure with F, Re and We were discussed in detail in order to investigate the combined effects of the three parameters on flow structure. The combined effects of the Coriolis force, inertia force and elastic force on the temperature distribution were also analyzed, which are greater than the adding independent effects of the three forces. The variations of the flow rate and Nusselt number with the rotation, inertia and elasticity were examined as well. The results show the characteristics of the heat and mass transfer of the Oldroyd-B fluids in a rotating curved pipe.     

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.     

ANALYSIS OF SEEPAGE FLOW IN A CONFINED AQUIFER WITH A STANDING COLUMN WELL

The standing column well for ground source heat pump systems is a promising technology with high efficiency and environmental benefit, where groundwater is drawn from the bottom of a well and then re-injected to its top after transferring heat with heat pumps. Heat transfer analysis of great significance and aquifer involves complex problems. Determining the groundwater seepage flow is a precondition to solve the energy equation describing the heat transfer of the system. Only when piezometric head is obtained, the seepage velocity can be determined according to Darcy’s law. In this article the groundwater seepage flow in an axial symmetrical geometry was studied under the assumption that gross groundwater flow is neglected. An analytical solution of the groundwater seepage flow for a confined aquifer was acquired by using the integral transform method, which may provide a foundation for heat transfer analysis of the standing column well system.     

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.     

Analytic solutions of the interstitial fluid flow models

In this paper, we present the analytic solutions of several continuum porous media models that describe the interstitial fluid flow in the interosseous membrane. We first compare the results of the Bri...     

Experimental study of the transition from non-Darcian to Darcy behavior for flow through a single fracture

Laboratory experiments are designed in this paper using single fractures made of cement and coarse sand for a series of hydraulic tests under the conditions of different fracture apertures, and for the simulation of the evolution of the flow pattern at places far from the outlet. The relationship between the hydraulic gradient and the flow velocity at different points, and the proportion evolution of the linear and nonlinear portions in the Forchheimer formula are then discussed. Three major conclusions are obtained. First, the non-Darcian flow exists in a single fracture in different laboratory tests. Better fitting accuracy is obtained by using the Forchheimer formula than by using the Darcy law. Second, the proportion of the Darcy flow increases with the increase of the observation scale. In places far enough, the Darcy flow prevails, and the critical velocity between the non-Darcian flow and the Darcy flow decreases as the fracture aperture increases. Third, when the fracture aperture increases, the critical Reynolds number between the non-Darcian flow and the Darcy flow decreases.