Drag and Lift Forces Acting on a Sphere in Shear Flow of Power-Law Fluid

Laminar flow of a power-law fluid over a sphere is considered for unbounded shear flow. The Navier–Stokes equations with power-law viscosity are solved numerically using an in-house developed CFD package. Vorticities structures downstream of particle are suppressed for powerlaw fluid. The shear rate influence on drag force is negligible for power index close to unit, and the drag force appreciably decreases with falling power index. For small Reynolds numbers, the lift force coefficient monotonically decreases against the power index and exhibits an opposite behavior for moderate values of Reynolds numbers. The results of the parametric studies are used to derive correlations for the drag force and to detect the hydrodynamic differences from uniform flow. The investigation parameters varied within the following ranges: power-law index 0.3 ≤ n ≤ 1, Reynolds number 0 < Re ≤ 150, and dimensionless shear rate 0.05 ≤ s ≤ 0.4.     

Large-eddy simulations of a forced homogeneous isotropic turbulence with polymer additives

Large-eddy simulations （LES） based on the temporal approximate deconvolution model were performed for a forced homogeneous isotropic turbulence （FHIT） with polymer additives at moderate Taylor Reynolds number. Finitely extensible nonlinear elastic in the Peterlin approximation model was adopted as the constitutive equation for the filtered conformation tensor of the polymer molecules. The LES results were verified through comparisons with the direct numerical simulation results. Using the LES database of the FHIT in the Newtonian fluid and the polymer solution flows, the polymer effects on some important parameters such as strain, vorticity, drag reduction, and so forth were studied. By extracting the vortex structures and exploring the flatness factor through a high-order correlation function of velocity derivative and wavelet analysis, it can be found that the small-scale vortex structures and small-scale intermittency in the FHIT are all inhibited due to the existence of the polymers. The extended self-similarity scaling law in the polymer solution flow shows no apparent difference from that in the Newtonian fluid flow at the currently simulated ranges of Reynolds and Weissenberg numbers.     

Numerical simulation of LBGK model for high Reynolds number flow

A principle of selecting relaxation parameter was proposed to observe the limit computational capability of the incompressible LBGK models developed by Guo ZL (Guo model) and He SY (He model) for high Reynolds number flow. To the two-dimensional driven cavity flow problem, the highest Reynolds numbers covered by Guo and He models are in the range 58000－52900 and 28000－29000, respectively, at 0.3 Mach number and 1/256 lattice space. The simulation results also show that the Guo model has stronger robustness due to its higher accuracy.     

Drag coefficient of a liquid domain in a two-dimensional membrane

Using a hydrodynamic theory that incorporates a momentum decay mechanism, we calculate the drag coefficient of a circular liquid domain of finite viscosity moving in a two-dimensional membrane. We derive an analytical expression for the drag coefficient which covers the whole range of domain sizes. Several limiting expressions are discussed. The obtained drag coefficient decreases as the domain viscosity becomes smaller with respect to the outer membrane viscosity. This is because the flow induced in the domain acts to transport the fluid in the surrounding matrix more efficiently.     

Numerical simulation of heat transfer and fluid flow of Water-CuO Nanofluid in a sinusoidal channel with a porous medium

This study has compared the convection heat transfer of Water-based fluid flow with that of Water-Copper oxide (CuO) nanofluid in a sinusoidal channel with a porous medium. The heat flux in the lower and upper walls has been assumed constant, and the flow has been assumed to be two-dimensional, steady, laminar, and incompressible. The governing equations include equations of continuity, momentum, and energy. The assumption of thermal equilibrium has been considered between the porous medium and the fluid. The effects of the parameters, Reynolds number and Darcy number on the thermal performance of the channel, have been investigated. The results of this study show that the presence of a porous medium in a channel, as well as adding nanoparticles to the base fluid, increases the Nusselt number and the convection heat transfer coefficient. Also the results show that As the Reynolds number increases, the temperature gradient increases. In addition, changes in this parameter are greater in the throat of the flow than in convex regions due to changes in the channel geometry. In addition, porous regions reduce the temperature difference, which in turn increases the convective heat transfer coefficient.     

Mechanism of controlling turbulent channel flow with the effect of spanwise Lorentz force distribution

A direct numerical simulation(DNS) is performed to investigate the control effect and mechanism of turbulent channel flow with the distribution of spanwise Lorentz force. A sinusoidal distribution of constant spanwise Lorentz force is selected, of which the control effects, such as flow characters, mean Reynolds stress, and drag reductions, at different parameters of amplitude A and wave number k_x are discussed. The results indicate that the control effects vary with the parameter A and k_x. With the increase of A, the drag reduction rate D_r first increases and then decreases rapidly at low k_x,and slowly at high k_x. The low drag reduction(or even drag increase) is due to a weak suppression or even the enhancements of the random velocity fluctuation and mean Reynolds stress. The efficient drag reduction is due to the quasi-streamwise vortex structure induced by Lorentz force, which contributes to suppressing the random velocity fluctuation and mean Reynolds stress, and the negative vorticity improves the distribution of streamwise velocity. Therefore, the optimal control effect with a drag reduction of up to 58% can be obtained.     

A Reynolds stress model for turbulent flows of viscoelastic fluids

A second-order closure is developed for predicting turbulent flows of viscoelastic fluids described by a modified generalised Newtonian fluid model incorporating a nonlinear viscosity that depends on a strain-hardening Trouton ratio as a means to handle some of the effects of viscoelasticity upon turbulent flows. Its performance is assessed by comparing its predictions for fully developed turbulent pipe flow with experimental data for four different dilute polymeric solutions and also with two sets of direct numerical simulation data for fluids theoretically described by the finitely extensible nonlinear elastic – Peterlin model. The model is based on a Newtonian Reynolds stress closure to predict Newtonian fluid flows, which incorporates low Reynolds number damping functions to properly deal with wall effects and to provide the capability to handle fluid viscoelasticity more effectively. This new turbulence model was able to capture well the drag reduction of various viscoelastic fluids over a wide range of Reynolds numbers and performed better than previously developed models for the same type of constitutive equation, even if the streamwise and wall-normal turbulence intensities were underpredicted.     

Local Heating Effect of Flow Past a Circular Cylinder

Heating effects of air flows past a two-dimensional circular cylinder at low Reynolds numbers and low Mach numbers are investigated by numerical simulation. The cylinder wall is heated partially rather than heated on the whole surface as with previous researches. The heating effects are completely different for various heating locations on the cylinder surface. Heating either windward or leeward side stabilizes the flow and reduces or completely suppresses vortex shedding from the cylinder at supercritical Reynolds numbers, which is consistent with previous results of heating on the whole surface of the cylinder. However, as the lateral sides of the cylinder （perpendicular to the stream-wise direction） are heated, an adverse effect is found for the first time in that the flow is destabilized and vortex shedding can be excited at subcritical Reynolds numbers. As the lateral sides of the cylinder are cooled, the flow is stabilized.     

Numerical study of the flow around a cylinder using multi-particle collision dynamics

A novel mesoscopic simulation technique--multi-particle collision dynamics--which has been suggested very recently, is used to study the two-dimensional flow around a square and a circular cylinder. The method is described and new proper boundary conditions are proposed to deal with wall collisions. The flow is analyzed in a wide range of Reynolds numbers in order to cover both the steady and unsteady regimes, resulting in symmetric steady vortices and periodic vortex shedding, respectively. The numerical results for integral flow parameters, such as the recirculation length, the drag and lift coefficients, the Strouhal number, as well as the spatial dependence of the velocity field, are compared with previous numerical and experimental studies. The qualitative and quantitative agreement is very good, validating the method as a promising technique to describe the hydrodynamic effects of solvent on embedded particles.     

基于浸入式边界方法的串联双矩形柱绕流数值模拟

基于浸入式边界算法(Virtual Boundary Method)中力源反馈边界的思想,改进其原有内部流体处理方法以减少计算耗费,并结合非等间距网格以便工程应用计算,模拟雷诺数范围内(Re=200–10³)串联双矩形柱绕流,研究表明:Re=200–300时,前柱尾流涡脱处于双剪切层控制阶段;柱间涡街为Karman类涡街,在小间距条件下被抑制,形成涡环;前柱对后柱屏蔽效应体现为后柱阻力系数远小于前柱;临界间距时柱间涡街充分发展,后柱阻力系数等气动参数亦在此发生跃升,但仍小于前柱值;随雷诺数升高,尾流涡街尺寸缩小,临界间距及跃升幅度变小. Re=400时,前柱尾流涡脱进入冲击剪切层控制阶段,阻力系数不再呈现规律性振荡;此后随雷诺数升高,冲击剪切层逐步完善,前柱流动分离使其表面产生更多附着涡,导致尾流旋涡尺寸进一步减小,屏蔽效应消失,涡脱更为剧烈,进而对后柱产生脉动冲击效应;适当间距比条件下此类脉动冲击效应使得后柱阻力系数发生跃升,并略高于前柱. 关键词： 浸入式边界算法 串联双矩形柱 屏蔽效应 临界间距     

A study on drag reduction of a rotationally oscillating circular cylinder at low Reynolds number

The flow field around a rotationally oscillating circular cylinder in a uniform flow is studied by using a particle image velocimetry to understand the mechanism of drag reduction and the corresponding suppression of vortex shedding in the cylinder wake at low Reynolds number. Experiments are conducted on the flow around the circular cylinder under rotational oscillation at forcing Strouhal number 1, rotational amplitude 2 and Reynolds number 2,000. It is found from the flow measurement by PIV that the width of the wake is narrowed and the velocity fluctuations are reduced by the rotational oscillation of the cylinder, which results in the drag reduction rate of 30%. The mechanism of drag reduction is studied by phase-averaged PIV measurement, which indicates the formation of periodic small-scale vortices from both sides of the cylinder. It is found from the cross-correlation measurement between the velocity fluctuations that the large-scale structure of vortex shedding is almost removed in the cylinder wake, when the small-scale vortices are generated at the unstable frequency of shear layer by the influence of rotational oscillation.     

电磁力控制湍流边界层分离圆柱绕流场特性数值分析

在亚临界区高雷诺数Re=1.4×105下,采用脱体涡模拟结合湍流分离的方法对弱电解质中电磁力作用下湍流边界层分离圆柱绕流场及其升(阻)力特性进行了数值模拟和分析.结果表明,电磁力可以提高圆柱体湍流边界层内的流体动能,延缓圆柱体湍流边界层的流动分离,减弱圆柱体湍流绕流场中在流向和展向上大尺度漩涡的强度,减小圆柱体阻力时均值及其升力脉动幅值.当电磁力作用参数大于某个临界值后,湍流边界层流动分离消失,在圆柱体尾部产生射流现象,从而电磁力对圆柱体产生净推力作用,出现负阻力现象,而且升力脉动幅值接近于零,出现圆柱体升力消失现象.     

High-definition PIV analysis on vortex shedding in the cylinder wake

A high-definition analysis based on flow topology is made on the vortex motions under natural and lock-on conditions in the near-wake region of a circular cylinder, where two-dimensional flow fields in the wake-transition regime are measured by a time-resolved PIV system. The Reynolds stress distributions are examined in view of the mean separation streamline and the trajectory ofthe vortex center. It is shown that, by the lock-on, the Reynolds stresses become stronger and their dispositions match well with the shortened wake bubble, indicating perfect synchronization of shedding to the oscillatory forcing flow in the near field, which causes increased lift and drag forces.     

Bubbly turbulent drag reduction is a boundary layer effect

In turbulent Taylor-Couette flow, the injection of bubbles reduces the overall drag. On the other hand, rough walls enhance the overall drag. In this work, we inject bubbles into turbulent Taylor-Couette flow with rough walls (with a Reynolds number up to 4 x 10(5), finding an enhancement of the dimensionless drag as compared to the case without bubbles. The dimensional drag is unchanged. As in the rough-wall case no smooth boundary layers can develop, the results demonstrate that bubbly drag reduction is a pure boundary layer effect.     

Calculation of the flow about a sphere and the drag of the sphere under laminar and strongly turbulent conditions

To investigate the influence of a strongly turbulent incoming flow on the hydrodynamic drag of a body and occurrence of the early crisis of drag, a numerical experiment is conducted in which a free gas flow about a sphere is simulated for two cases, namely, for a laminar flow and for a strongly turbulent flow. Turbulence is simulated by assuming a high kinematic coefficient of turbulent viscosity. Calculation data lead us to conclude that the early crisis of drag at Reynolds numbers near 100, which shows up as a considerable (four-to sevenfold) decrease in the hydrodynamic force and the drag coefficient of the body, can be explained by the strong turbulence of the incoming flow.     

微通道冷却器内流动和传热特性的数值模拟

为满足固体激光器用微通道冷却器的换热要求, 根据冷却器结构分别建立了二维和三维物理模型, 利用计算流体力学方法首先对比研究两者的流动特性, 然后考察雷诺数和玻片生热量对微通道流动和传热特性的影响。结果表明:对于类似大平板间的矩形微通道层流流动区域, 其流动及传热特性可直接采用二维简化模型进行模拟分析;对于重点关注的转捩区, 采用三维模型模拟分析更好;当雷诺数增大到转捩点, 流体的传热效果得到明显增强;随着雷诺数的增大, 玻片生热量对通道内最低压力需求的影响逐渐减小;不同玻片生热量对微通道流动影响不可忽略, 对努赛尔数和通道总压降基本无影响。     

滴形颗粒在通道中沉降的格子Boltzmann-虚拟区域方法模拟

采用格子Boltzmann-虚拟区域方法对滴形颗粒在垂直通道中的沉降过程进行直接数值模拟.通过格子Boltzmann方法求解N-S方程,流体与固体之间的相互作用通过虚拟区域方法描述.研究雷诺数在10^-2到100范围内颗粒形状因子对其摩擦系数和阻力系数的影响.为便于比较,给出了圆形颗粒沉降的结果.结果发现,当雷诺数小于1的时候,颗粒的摩擦系数始终保持常数,而当雷诺数大于1时摩擦系数随雷诺数的增大而增大.此外,当雷诺数小于约30时圆形颗粒的摩擦系数和阻力系数均小于滴形颗粒,而当雷诺数大于30时情况正好相反.颗粒周围的压力分布证明了这一结论.     

Vortex generation in the cross-flow around a cylinder attached to an end-wall

A cylinder attached to an end-wall normal to its axis is a common feature of many practical flow systems, e.g. in turbo-machinery or when a bridge is supported by a pillar from the bed of a river. In this situation, the nominally two-dimensional boundary layer flow incident upon the cylinder develops strong three-dimensional features and a very pronounced vortex structure may arise in the upstream flow close to the wall. For the appropriate Reynolds number range, the upstream vortical structure is nominally steady and is commonly referred to as the “horseshoe vortex system”. In contrast, the flow downstream is unsteady and periodic over a wide range of Reynolds numbers and vortices aligned with the cylinder axis are shed at a regular frequency into the wake. The generation of both these vortex systems requires energy to be extracted from the incident flow with the result that the drag force on the cylinder is increased.This paper concentrates on the upstream region of the cylinder and discusses an investigation in which two-component Particle Image Velocimetry (PIV) has been used to visualise the flow behaviour for a circular cylinder on a plane end-wall. The use of PIV has enabled two orthogonal velocity components to be measured in planes defined by the upstream flow direction and the axis of the cylinder. The third (out-of-plane) velocity component was then calculated by integrating the continuity equation. Subsequently, the velocity field information has been manipulated and converted into time-averaged information.Discussion of the measured results confirms that colour displays are an invaluable aid to understanding this complex fluid flow situation since they reveal substantially more information than grey-scale plots of the same data. In particular, the source of the horseshoe vortex system can be identified when colour plots of the time-averaged velocity and vorticity distributions are obtained. A limited amount of information on the unsteady vortex structures appearing in the end-wall region upstream of the cylinder is also presented. Finally, the experimental findings are discussed in relation to the results of previous workers.     

后台阶气固两相流动的大涡模拟

本文基于开源计算流体力学软件OpenFOAM,开发了气固两相流动双向耦合求解器,并对Re=13800、颗粒直径为150μm的玻璃球的后台阶两相流动进行了计算。其中气相采用大涡模拟方法,用盒式过滤函数对流体相控制方程过滤求解。颗粒相采用拉格朗日方法对颗粒进行跟踪。将计算结果和实验数据进行对比,以此来检验颗粒受力计算模型和亚格子气固两相求解器的准确性。     

Effect of the gas flow geometry and turbulence on the hydrodynamic drag of a body in the flow

The effect of the incoming flow geometry on the hydrodynamic drag of a body is investigated in a numerical experiment simulating a free gas flow past a sphere as well as flows in cylindrical tubes of various radii, in a confuser, and a diffuser. The results of calculations lead to the conclusion that the confinement of the flow by the tube walls, its contraction and expansion may change the hydrodynamic force and the drag acting on the body insignificantly (not more than by 30%). This cannot explain the early drag crisis, in which the values of these quantities decrease by 4–7 times for Reynolds numbers on the order of 100. This phenomenon is explained theoretically by the effect of strong turbulence of the incoming flow to the body.