Effect of power-law index on critical parameters for power-law flow across an unconfined circular cylinder

The conditions for the formation of a wake and for the onset of wake instability for the flow of power-law fluids over an unconfined circular cylinder are investigated numerically by solving the continuity and momentum equations using FLUENT (version 6.2). The effect of power-law index on the critical Reynolds numbers, Strouhal number and drag coefficient has been presented over a wide range of power-law index (0.3?n?1.8) thereby establishing the limits of the flow without separation and the steady symmetric flow regimes, respectively. While both the shear-thinning (n<1) and the shear-thickening (n>1) seem to lower the value of the critical Reynolds number denoting the onset of wake instability as compared to that for Newtonian fluids, the effect is seen to be more prominent for shear-thickening fluids than that for shear-thinning fluids. The corresponding values of the critical Strouhal number (St_c) and drag coefficient have also been presented for the critical values of the Reynolds number. Included here are also a series of streamline plots showing the onset of asymmetry and of the time-dependent flow regime.     

Steady flow of power-law fluids across an unconfined elliptical cylinder

The momentum transfer characteristics of the power-law fluid flow past an unconfined elliptic cylinder is investigated numerically by solving continuity and momentum equations using FLUENT (version 6.2) in the two-dimensional steady cross-flow regime. The influence of the power-law index (0.2?n?1.8), Reynolds number (0.01?Re?40) and the aspect ratio of the elliptic cylinder (0.2?E?5) on the local and global flow characteristics has been studied. In addition, flow patterns showing streamline and vorticity profiles, and the pressure distribution on the surface of the cylinder have also been presented to provide further physical insights into the detailed flow kinematics. For shear-thinning (n<1) behaviour and the aspect ratio E>1, flow separation is somewhat delayed and the resulting wake is also shorter; on the other hand, for shear-thickening (n>1) fluid behaviour and for E<1, the opposite behaviour is obtained. The pressure coefficient and drag coefficient show a complex dependence on the Reynolds number and power-law index. The decrease in the degree of shear-thinning behaviour increases the drag coefficient, especially at low Reynolds numbers. While the aspect ratio of the cylinder exerts significant influence on the detailed flow characteristics, the total drag coefficient is only weakly dependent on the aspect ratio in shear-thickening fluids. The effect of the flow behaviour index, however, diminishes gradually with the increasing Reynolds number. The numerical results have also been presented in terms of closure relations for easy use in a new application.     

Dynamics of self-organizing single-line particle trains in the channel flow of a power-law fluid

The formation of self-organizing single-line particle train in a channel flow of a power-law fluid is studied using the lattice Boltzmann method with power-law index 0.6 ≤ n ≤ 1.2,particle volume concentration 0.8% ≤Φ≤ 6.4%,Reynolds number 10 ≤ Re ≤ 100,and blockage ratio 0.2 ≤ k ≤ 0.4. The numerical method is validated by comparing the present results with the previous ones.The effect n,Φ,Re and k on the interparticle spacing and parallelism of particle train is discussed.The results showed that the randomly distributed particles would migrate towards the vicinity of the equilibrium position and form the ordered particle train in the power-law fluid.The equilibrium position of particles is closer to the channel centerline in the shear-thickening fluid than that in the Newtonian fluid and shear-thinning fluid.The particles are not perfectly parallel in the equilibrium position,hence IH is used to describe the inclination of the line linking the equilibrium position of each particle.When self-organizing single-line particle train is formed,the particle train has a better parallelism and hence benefit for particle focusing in the shearthickening fluid at high Φ,low Re and small k.Meanwhile,the interparticle spacing is the largest and hence benefit for particle separation in the shear-thinning fluid at low Φ,low Re and small k.     

板间距对三角槽道脉动流流动阻力的影响

以水为工质对不同板间距的三角槽道脉动流流动阻力特性进行了研究。基于受力平衡方程,建立了适用于三角槽道脉动流压降的数学模型,用于理论分析流动阻力的影响因素。通过实验测试与数值模拟,校验数学模型的合理性,并且对三角槽道脉动流流动阻力进行分析。结果表明,流动阻力主要受板间距、涡旋拟“能”两方面因素影响,且与板间距呈反比,与涡旋拟“能”呈正比;板间距的缩小,会使流动阻力增加,当缩小到板间距与槽深比值为1.0时,出现流动阻力的阶越式增长,上升1个数量级;造成流动阻力骤升的主要原因在于：随着板间距的缩小,流场结构逐渐变化,三角槽道内涡旋的影响区域由“三角槽内部”逐渐转变为“整个流道”,且主流区壁面出现流动分离,出现涡旋流动与波状流共存现象,使流动阻力大幅提升。     

Non-Newtonian flow in porous media

In this article we present a review of the single-phase flow of non-Newtonian fluids in porous media. The four main approaches for describing the flow through porous media in general are examined and assessed in this context. These are: continuum models, bundle of tubes models, numerical methods and pore-scale network modeling.     

Power-law shear-thinning flow around a heated square bluff body under aiding buoyancy at low Reynolds numbers

Power-law shear-thinning fluid flow over a heated square bluff body is numerically investigated under aiding buoyancy mixed convection at low Reynolds numbers. Semi-explicit finite volume code is developed to solve the governing equations along with the appropriate boundary conditions. Both aiding buoyancy and shear-thinning natures are found to augment the heat transfer rate from the surface of the long square bar. In aiding buoyancy, the total drag coefficient is found to be more for the square cylinder than that of the circular cylinder, whereas the average cylinder Nusselt number for the square cylinder is found to be lower than the circular one on equal side/diameter basis. Maximum augmentation in heat transfer is found to be approximately 20% with respect to forced convection. Finally, a heat transfer correlation is established by using the Colburn heat transfer factor.     

Liquid re-circulation in turbulent vertical pipe flow behind a cylindrical bluff body and a ventilated cavity attached to a sparger

The turbulent flow field (Re=60024) in the wake of a cylindrical bluff body in a 0.105 m internal diameter pipe with an area blockage ratio of 82% in turbulent single-phase flow was studied using laser Doppler velocimetry (LDV). The results for the time-averaged velocity showed a toroidal vortex below the bluff body. The axial location below the bluff body where both the time-averaged radial and axial velocity components were zero (eye of the vortex) was found at approximately 0.72D. The end of the re-circulation region as defined by a stagnation point on the centreline of the pipe was found at an axial location below the bluff body of approximately 1.3D. These two locations did not change when altering the liquid superficial velocity confirming that the geometry (i.e., size) of the toroidal vortex is not dependent on the superficial liquid velocity or the speed of the vortex.Similar measurements using LDV were taken in the wake of a ventilated cavity in a vertical 0.105 m internal diameter pipe, with an area blockage ratio of 80%. The flow beneath the cavity was turbulent two-phase bubbly flow and the liquid-only flow ahead of the cavity was turbulent (Re=45618). The cavity was attached to a (central) sparger, which is a scale-up of the design used by Bacon (1995). The average gas void fraction in the wake of the cavity was 7%. The results for the time-averaged velocity confirmed the formation of a toroidal vortex remarkably similar to the vortex formed below the bluff body. The eye of the vortex and the end of the re-circulation region were found at an axial location below the ventilated cavity of 0.78 and 1.35D, respectively, i.e., almost identical to the results for the bluff body.The LDV results of the cylindrical bluff body and the ventilated cavity were compared with the fully predictive model of the velocity distribution in the vortex proposed by Thorpe et al. (2001) and good agreement was found in both cases. The model also agreed well with the data of van Hout et al. (2002) for a Taylor bubble rising in stagnant liquid in a 0.025 m internal diameter pipe. The CFX simulations of Thorpe et al. (2001) carried out for a 0.050 m internal diameter pipe, agreed well with the experimental data of the cylindrical bluff body, the ventilated cavity and the data obtained by van Hout et al. (2002) when correlating the results in the appropriate dimensionless form. Our analysis showed that the maximum axial re-circulation velocity in the centre of the vortex ring was directly proportional to the mean velocity in the annulus at the base of the cylindrical bluff body, the ventilated cavity or the Taylor bubble. The proportionality constant for all cases was found to be approximately 0.38 confirming the value proposed by Thorpe et al. (2001).     

三角槽道低Reynolds数脉动流的流动特性分析

以水为工质对三角槽道低Reynolds数脉动流的流动特性进行了实验研究与理论分析。通过流动实验,分析了Reynolds数（Re）、Womersley数（W）、脉动振幅（A）等参数对流动阻力的影响。同时,建立了脉动流压降的数学模型,从理论层面解析了各脉动参数对流动阻力产生影响的作用机理,揭示了瞬时流速曲线与瞬时压降曲线之间相位差产生的原因。研究发现,相较于稳态流,脉动流会增加流动阻力,这是因为脉动流压降方程中存在三角函数项Δp_r,其周期平均值P始终大于0;就脉动参数而言,W对总压降的形阻压降部分影响较为显著,而A与总压降呈正相关;相位差的产生是由于总压降方程中存在加速度压降,而相位差的大小取决于沿程阻力、形阻压降、加速度压降三者对总压降波动的影响程度。     

Measurements of flow characteristics in a confined vortex flow

A study of air flow patterns by hot-wire anemometry is reported for a vortex chamber consisting of an upper cylindrical section 122 cm in diameter and 61 cm high and a conical bottom section 122 cm high. Quantitative data are presented for flow angles, profiles of mean tangential and axial velocities, and radial distributions of tangential and axial intensities of turbulence as a function of air entrance velocities of 1.6, 2.4 and 3.2 m/s, and axial distance from the top of the chamber. In general, the quantitative results confirm the theoretical predictions and the experimental trends reported in the literature. In particular, they fully support the conclusion that the flow pattern is relatively insensitive to the entrance volumetric flow rate. A generalized correlation is presented for the axial velocity distribution. Preliminary correlations are also presented for the tangential velocity distributions in the core and in the annular region of the vortex near the wall. These were found to be functions of the axial location and of the air entrance velocity.     

Three-dimensional modelling of Non-Newtonian fluid flow in a coat-hanger die

The three-dimensional model of isothermal flow of power-law fluid in a coat-hanger die has been developed using finite element method. The shape of coat-hanger die used in the present model was determined according to the previous analytical design equation which is based on one-dimensional flow model in the manifold and the slot. Because uniform flow rate across the die outlet is most important to achieve uniform thickness of extruded polymer sheet or film, flow rate distribution is mainly examined to determine the valid process condition for the design equation as the design parameters are changed. The effects of fluid property in terms of power-law index and process parameters not considered in one-dimensional design equation such as die inlet size and the presence of land were analyzed. Results show that the manifold angle is the most influencing design parameter on flow rate distribution. When the material of different power-law index from design value is processed, the change of power-law index affects the uniformity of flow rate appreciably.     

Mixed convection flow of a power-law fluid in horizontal ducts

The laminar mixed convection heat transfer of a non-Newtonian fluid modelled by a power-law constitutive equation is studied. The equations of motion subject to the Boussinesq approximation and an axially uniform heat flux and peripherally uniform wall temperature condition are discretized by finite difference approximation and are solved by the successive relaxation method. Dual solutions with two-cell and four-cell patterns have been observed in certain regions of the parameter space. The secondary flow caused by the buoyancy force has a shear thinning effect for pseudoplastic fluids. The Nusselt number, however, always increases with increasing Grashof number.     

有序涡旋对三角槽道脉动流强化传热的影响

以水为工质对三角槽道内单相液体充分发展层流脉动传热特性进行了研究。应用粒子图像测速技术（PIV）测得流场内涡的变化规律,从“涡及涡运动”的角度揭示了“有序”的涡生长及迁移过程对脉动流强化传热的影响。此外,应用“场协同”理论,通过数值模拟深入分析了流场特性与传热之间的关系。研究发现,“有序”的涡生长及迁移过程,破坏了流体边界层,促进了近壁区热流场与速度场的协同,同时,强化了三角槽道内流体与主流区流体的掺混,热量输运能力提升;存在最佳的Strouhal数（St）,使得涡旋既能充分发展又能在较短时间脱落进入主流,实现最大效率的壁面换热;有序涡旋对速度场、温度梯度场以及压力梯度场三者协同性的改善是换热性能提升的关键。     

三角槽道低 Reynolds 数脉动流与柔性壁耦合特性研究

以水为工质对三角槽道低 Reynolds 数脉动流与柔性壁耦合特性进行了实验研究。通过传热与流动实验,分析了脉动频率(W)、脉动振幅(A)、柔性壁特性对脉动流传热及流动的影响。同时,通过可视化实验,研究了柔性壁与脉动流之间的响应特性,解析了柔性壁形变与振频对脉动流传热及流动的作用机制及分离贡献。研究结果表明,柔性流道脉动流可以实现强化传热与流动减阻双重效果,但强化传热效果相对较弱(传热效率提升0~50%),适用于以减阻为主要目的的换热场合;柔性壁减阻与削弱强化传热效率,源于柔性壁形变造成时均流通截面积增大(流体流速下降)、W与A的增大减弱脉动能量;W的增加将使得柔性壁振动对脉动流强化传热效率的削减逐步趋于主导地位,而A的增加将使得柔性壁变形对脉动流强化传热效率的削减逐步趋于主导地位;脉动流阻力的削减主要来自于柔性壁的变形(D₁>70%),而柔性壁振频对于脉动流能量耗散的抑制作用较为次要。     

位移钝体稳燃的旋流预混燃烧污染物生成特性

石化炉、加热炉等设备中燃烧过程的污染物控制具有重要意义。旋流预混燃烧过程具有低NO _x 排放的潜力,引发了学术界和工业界的广泛关注。结合钝体燃烧和旋流燃烧各自的优势,本文设计了带有位移钝体的旋流预混燃烧器。首先研究了不同钝体结构下的污染物的生成情况,确定了最优的钝体结构,在此基础上进一步研究了在不同旋流数下污染物生成、火焰形态和温度场分布情况。研究发现,钝体角度为30°、体积较小的倒锥形钝体具有较低的NO _x 和CO生成量。NO _x 生成量随着旋流数从0增加到0.83呈先减小后增加的趋势,并且当旋流数为0.25时,NO _x 生成量最低。在同一热功率下,火焰高度随着旋流数的增加而减小。在同一旋流数下,火焰宽度随热功率增大呈增大趋势。NO _x 生成量变化规律与其火焰温度分布规律一致,即NO _x 生成量最低的工况下火焰温度也比较低。由此推测旋流引发的温度变化是NO _x 生成量变化的主要影响因素之一。本文的研究结论对旋流预混燃烧器的设计提供了理论基础。     

Two-dimensional unsteady flow of power-law fluids over a cylinder

The unsteady flow of incompressible power-law fluids over an unconfined circular cylinder in cross-flow arrangement has been studied numerically. The two-dimensional (2-D) field equations have been solved using a finite volume method based solver (FLUENT 6.3). In particular, the effects of the power-law index (0.4?n?1.8) and Reynolds number (40?Re?140) on the detailed kinematics of the flow (streamline, surface pressure and vorticity patterns) and on the macroscopic parameters (drag and lift coefficients, Strouhal number) are presented in detail. The periodic vortex shedding and the evolution of detailed kinematics with time are also presented to provide insights into the nature of flow. The two-dimensional flow transits from steady to unsteady behaviour at a critical value of the Reynolds number Re∼(40-50) and the von-Karman vortex street is observed beyond the critical Reynolds number (Re). Obviously, both the lift coefficient and Strouhal number values are zero for the steady flow, but their values increase with the increasing Reynolds number (Re) in the unsteady flow regime. For highly shear-thickening fluids (n=1.8), the flow becomes unsteady at Re=40 and unsteadiness in the flow appears at Re=50 for all values of power-law index (n). As expected, the evolution of the kinematics and vortex shedding show a complex dependence on the flow parameters near the transition in the flow. For a fixed value of the Reynolds number (Re), the drag coefficient increases and lift coefficient decreases with increasing value of the power-law index (n). For a fixed value of the power-law index (n), the drag coefficient gradually increases with the Reynolds number (Re). Similar to the drag coefficient, lift coefficient also shows a complex dependence on the power-law index (n) near the transition zone. The value of the Strouhal number (St) decreases with the increasing value of the power-law index (n) at a fixed value of the Reynolds number (Re).     

Non-Newtonian tangential flow in cylindrical annuli. IV

Tangential flow of a “power law” model fluid between two concentric cylinders is analyzed. A constant angular pressure gradient is imposed and one of the cylinders is rotating at a constant angular velocity. This type of flow is of interest in screw extrusion theory. The error in the superposition, i.e., linear addition of tangential pressure and drag flows, for a “power law” model fluid, is quantitatively calculated and plotted in the form of a correction factor. Tangential pressure flow is compared to a pressure flow between parallel plates and additional correction factor to account for the curvature is derived and plotted. The applicability of the “power law” model for flow of polymer melts in extruders is also discussed.     

非圆小通道内非牛顿流体-氮气二相流型研究

采用可视化手段研究了水力直径为2.886 mm和0.866 mm的等边三角形截面微小通道内非牛顿流体气液二相垂直上升流动,表观气速0.1—100 m/s,表观液速0.01—6 m/s。根据观察和测量结果,得到三角形通道内的羧甲基纤维素钠(CMC)溶液-氮气的典型流型图像和流型转变界限。通过与常规通道的空气-水二相流型图对比,发现液体的黏性、表面张力以及截面形状和水力直径等因素对流型的转变具有显著的影响。     

过渡流下钝体绕流特性的可视化实验对比

为解明钝体绕流机理,设计了开式低速循环水槽,建立了钝体绕流实验平台。采用粒子图像测速法（PIV）和染色法,对钝体绕流特性进行实验研究。采用INSIGHT 4 G进行全面调控。通过检测水槽不同高度激光面上的流动状态验证实验台稳定性。将PIV及染色法所得数据与已有模拟及实验结果进行对比,验证了实验方法正确性。选取过渡流下特定钝体（圆柱）进行周期研究,探寻钝体绕流周期性。并分析圆柱、方柱绕流在不同Reynolds数下的流动特性异同。实验表明：Re=200时,在一个周期内,圆柱周围正涡、负涡周期性脱落,正涡逐渐形成、增强、消散,负涡也在对应的位置循环发展。通过圆、方柱流动实验对比可知,圆柱绕流分离点不固定而方柱绕流分离点固定,位于其前后锐边上。     

Laminar flow of power-law fluids in the entrance region of a pipe

The study is concerned with developing laminar flow of a power-law fluid in a circular tube. The analysis extends the filled-region concept, used previously to study Newtonian fluid flow, to the more general class of power-law fluids. Flow is analyzed in both the inlet and filled regions using an integral boundary layer method. Results obtained provide the lengths of the entrance, inlet and filled regions as a function of the generalized Reynolds number and the power-law fluid index. In addition, the variations of the local friction factor, the pressure drop and the centerline velocity along the axial coordinate are also provided. The available models are compared with the present one on the basis of experimental data. The present results are found to reach asymptotically the fully developed values, and also to be in good agreement with all available experimental data.     

固体材料对微型钝体燃烧器吹熄极限的影响

通过数值模拟研究了固体材料（石英、不锈钢和SiC）对微型钝体燃烧器内氢气/空气预混火焰的吹熄极限的影响。结果表明：计量比为0.5时,3个燃烧器对应的吹熄极限分别为36、25和21 m·s^-1。理论分析揭示了微型钝体燃烧器中火焰稳定性与流动和传热之间的相互作用非常密切。当热导率较小时,通过壁面向上游传导的热量较少,壁面对未燃预混气的预热效果较差,燃烧后的气体膨胀相对较弱,从而钝体后的低速区面积较大,稳燃效果较好。对于不锈钢和SiC燃烧器,由于SiC的发射率更大,通过壁面的散热损失较大,从而使得其吹熄极限较小。为获得良好稳燃性能的微型钝体燃烧器选择合适的材料提供了指导。