平面突扩流动非稳定性的大涡模拟

用ＴＧ有限元法求解二维大涡模拟的非定常Ｎ－Ｓ方程，数值模拟了平面突扩流动，计算结果展示了回流区内流动的多涡结构及其不稳定的周期振荡过程，而该振荡过程的周期时间历程平均，恰好与诸多湍流模型的计算结果及实验结果相吻合，证明了数值模拟的正确性。     

Numerical analysis of axisymmetric and planar sudden expansion flows for laminar regime

In this study, the Navier–Stokes equations are solved numerically for axisymmetric and planar sudden expansion flows. The flow is considered laminar and steady state, and the fluid is incompressible. Finite difference equations are obtained using a control volume method in a non‐staggered grid arrangement, and solved by line‐by‐line TDMA technique using the SIMPLEM (SIMPLEM‐Modified) algorithm. Calculations are performed for higher expansion ratios, β, ranging from 1.5 to 10 and Reynolds numbers from 0.1 to 500. Results are presented in terms of streamlines, relative eddy intensity, location of the eddy center, and the eddy reattachment length depending on Re number and β values for both axisymmetric and planar sudden expansions. It is aimed to provide a picture of the effects of high values of expansion ratio and Reynolds number on the sudden expansion flow. As a result, it is found that the flow characteristics keep their structure for both higher expansion ratios and higher Reynolds numbers. Further, correlations were developed for the nondimensional eddy reattachment length, location of the eddy center and the relative eddy intensity, which have agreeable results to the computed results available from the literature. Copyright © 2010 John Wiley & Sons, Ltd.     

各向同性湍流内颗粒碰撞率的直接模拟研究

对 Re_{\lambda } 约为51均匀各向同性湍流内 St_{k}(=\tau_{p}/\tau_{k}) 为 0 ~10.0 的 有限惯性颗粒的碰撞行为进行了直接数值模拟，以研究湍流对有限惯性 颗粒碰撞的影响. 结果表明，具有一定惯性颗粒的湍流碰撞率完全不同于零惯性的轻颗粒 (St_{k}=0) 和可忽略湍流作用的重颗粒 (St{k} \to \infty) , 其变化趋势极其复杂： 在Stk为 0~1.0 之间，颗粒的碰撞率随 St 的增加而近乎线性地剧烈增长，在 Stk≈1.0 3.0(对应的StE=τp/Te≈0.5)附近，颗粒碰撞率出现两个峰值，在Stk>3.0以后，颗粒的碰撞率随惯性增 大而逐渐趋向于重颗粒极限；在峰值处，有限惯性颗粒的平均碰撞率的峰值较轻颗粒增强了 30倍左右. 为进一步分析湍流作用下颗粒碰撞率的影响因素，分别使用可能发生碰撞 的颗粒对的径向分布函数和径向相对速度来量化颗粒的局部富集效应和湍流掺混效应，表明 St_{k} \approx 1.0 时局部富集效应最为强烈，使得颗粒的碰撞率出现第1个峰值； 湍流掺混效应则随着颗粒Stk的增大而渐近增大；局部富集和湍流掺混联合作用的结果， 使得颗粒碰撞率在 St_{k} \approx 3.0 附近出现另一个峰值.     

Asymmetric flows in planar symmetric channels with large expansion ratio

A continuation method has been used with a finite element grid and a geometric perturbation to compute two successive symmetry breaking flow transitions with increasing Reynolds number in flow of generalized Newtonian fluids through a sudden planar expansion. With an expansion ratio of 16, the onset Reynolds number is particularly sensitive to small geometric asymmetry and the critical Reynolds numbers for the two successive flow transitions are found to be very close. These transitions are delayed to higher onset Reynolds numbers by increasing the degree of pseudoplasticity. This trend is observed experimentally as well in this work and may be attributed to the competing effects of shear thinning and inertia on the size of the corner vortex before the symmetry breaking flow transition. After the second transition with an expansion ratio of 16, the two large staggered vortices on opposite walls occupy most of the transverse dimension so that the core flow between the vortices appears as a thin jet oscillating along the flow direction. This is more pronounced for the pseudoplastic liquid. After the second transition, the degree of flow asymmetry at a given location downstream of the expansion plane is larger for the pseudoplastic liquid than for the Newtonian liquid at comparable Reynolds numbers. The last feature is also evident in the experimentally observed velocity profiles. Copyright © 2002 John Wiley & Sons, Ltd.     

气固两相流场的湍流颗粒浓度理论模型

本文进行了气固两相流动颗粒湍流扩散现象的理论分析，提出了颗粒湍流扩散系数和气流弥散效应二个颗粒湍流模化新概念，在此基础上建立了气固两相流场湍流颗粒浓度模型。理论模型包括离心力和其它外加力场作用下颗粒运动和浓度分布的计算方法。运用湍流颗粒浓度模型，对直管气固两相流动、受限射流气固两相流动和９０°弯管气固两相流动等三种流动做了数值模拟，计算获得颗粒速度、颗粒浓度等主要流动参数。讨论了湍流颗粒浓度模型的适用性。     

On the performance of sudden‐expansion pipe without/with cross‐flow injection: experimental and numerical studies

The paper explores the possibilities that different turbulence closures offer, for in‐depth analysis of a complex flow. The case under investigation is steady, turbulent flow in a pipe with sudden expansion without/with normal‐to‐wall injection through jets. This is a typical geometry where generation of turbulence energy takes place, due to sudden change in boundary conditions. This study is aimed at investigating the capability of a developed computational program by the present authors with three different turbulence models to calculate the mean flow variables. Three two‐equation models are implemented, namely the standard linear k ? ε model, the low Reynolds number k ? ε model and the cubic nonlinear eddy viscosity (NLEV) k ? ε model. The performance of the chosen turbulence models is investigated with regard to the available data in the literature including velocity profiles, turbulent kinetic energy and reattachment position in a pipe expansion. In order to further assess the reliability of the turbulence models, an experimental program was conducted by the present authors also at the fluid mechanics laboratory of Menoufiya University. Preliminary measurements, including the surface pressure along the two walls of the expansion pipe and the pressure drop without and with the presence of different arrangements of wall jets produced by symmetrical or asymmetrical fluid cross‐flow injection, are introduced. The results of the present studies demonstrate the superiority of the cubic NLEV k ? ε model in predicting the flow characteristics over the entire domain. The simple low Reynolds number k ? ε model also gives good prediction, especially when the reattachment point is concerned. The evaluation of the reattachment point and the pressure‐loss coefficient is numerically addressed in the paper using the cubic NLEV k ? ε model. The results show that the injection location can control the performance of the pipe‐expansion system. It is concluded that the introduction of flow injection can increase the energy loss in the pipe expansion. The near‐field turbulence structure is also considered in the present study and it is noticed that the turbulence level is strongly affected by the cross‐flow injection and the jet location. Copyright © 2011 John Wiley & Sons, Ltd.     

The behaviour of macromolecules in the flow through a sudden planar contraction

Analytic steady-state results for FENE-P model macromolecules, in the nearly coiled-up and nearly stretched state respectively, in general two-dimensional flow fields are derived. These results are utilized in the flow through a sudden planar contraction. Special emphasis is devoted to the structure tensor R R, which furnishes, among other things, the mean square extension and the average orientation of the macromolecules.     

混凝土靶侵彻过程中空腔膨胀响应分区

利用LS-DYNA有限元软件对刚性弹正侵彻混凝土靶进行数值模拟,以混凝土极限压应变和极限拉应变两阈值为依据,对侵彻过程中混凝土靶空腔膨胀响应区域进行了识别划分,得到了侵彻过程中混凝土各响应区的区域大小。另外,还讨论了弹体侵彻速度对混凝土粉碎区和破裂区的影响,以及粉碎区和破裂区边界膨胀速度分别与侵彻速度的关系。计算结果表明,随着弹体侵彻速度的增大,混凝土粉碎区和破裂区界面速度都增大,粉碎区半径增大,而破裂区半径却减小;当侵彻速度达到某一特定值时,破裂区将会消失。     

Numerical analysis of swirling turbulent droplet-laden flow and heat transfer in a sudden pipe expansion

The effect of swirling intensity on the structure and heat transfer of a turbulent gas–droplet flow after a sudden pipe expansion has been numerically simulated. Air is used as the carrier phase, and water, ethanol, and acetone are used as the dispersed phase. The Eulerian approach is applied to simulate the dynamics and heat transfer in the dispersed phase. The gas phase is described by a system of Reynolds-averaged Navier-Stokes (RANS) equations, taking into account the effect of droplets on mean transport and turbulent characteristics in the carrier phase. Gas phase turbulence is predicted using the second-moment closure. A swirling droplet-laden flow is characterized by an increase in the number of small particles on the pipe axis due to their accumulation in the zone of flow recirculation and the action of the turbulent migration (turbophoresis) force. A rapid dispersion of fine droplets over the pipe cross-section is observed without swirling. With an increase in swirling intensity, a significant reduction in the length of the separation region occurs. The swirling of a two-phase flow with liquid droplets leads to an increase in the level of turbulence for all three types of liquid droplets investigated in this work due to their intensive evaporation. It is shown that the addition of droplets leads to a significant increase in heat transfer in comparison with a single-phase swirling flow. The greatest effect of flow swirling on heat transfer intensification in a two-phase gas-droplet flow is obtained for the droplets of ethanol and water and smallest effect is for the acetone droplets.     

Particle dispersion in a single-sided backward-facing step flow

The paper describes the particle dispersion in a single-sided backward-facing step flow. Particles of well-known sizes in the diameter range from 1 to 70 μm were suspended in an air flow and the particle motion over a step was measured by mean of a laser-Doppler anemometer. Thus, the local and integral flow quantities, i.e. the mean and turbulent velocity data could be measured precisely. In the experiments, monodispersed particle size distributions were used to exclude particle size related information ambiguity, known as triggering effects or size bias. The results of this study show qualitatively and quantitatively the difference in time-averaged particle dynamics for selected particle sizes in a backward-facing step flow. The experiments show, for different sizes, the changes in the particle velocity field in comparison with the velocity field of the continuous phase deduced from the 1 μm particles, and also imply the strong influences which different particle sizes have on flow data evaluation when size effects are not taken into account with particle-related optical measuring techniques.     

Heat transfer characteristics in a sudden expansion pipe equipped with swirl generators

This investigation is aimed at studying the heat transfer characteristics and pressure drop for turbulent airflow in a sudden expansion pipe equipped with propeller type swirl generator or spiral spring with several pitch ratios. The investigation is performed for the Reynolds number ranging from 7500 to 18,500 under a uniform heat flux condition. The experiments are also undertaken for three locations for the propeller fan (N = 15 blades and blade angle of 65°) and three pitch ratios for the spiral spring (P/D = 10, 15 and 20). The influences of using the propeller rotating freely and inserted spiral spring on heat transfer enhancement and pressure drop are reported. In the experiments, the swirl generator and spiral spring are used to create a swirl in the tube flow. Mean and relative mean Nusselt numbers are determined and compared with those obtained from other similar cases. The experimental results indicate that the tube with the propeller inserts provides considerable improvement of the heat transfer rate over the plain tube around 1.69 times for X/H = 5. While for the tube with the spiral spring inserts, an improvement of the heat transfer rate over the plain tube around 1.37 times for P/d = 20. Thus, because of strong swirl or rotating flow, the propeller location and the spiral spring pitch become influential on the heat transfer enhancement. The increase in pressure drop using the propeller is found to be three times and for spiral spring 1.5 times over the plain tube. Correlations for mean Nusselt number, fan location and spiral spring pitch are provided.     

Numerical study of a piston-driven unsteady flow in a pipe with sudden expansion

This paper presents results of the numerical study of a piston-driven unsteady flow in a pipe with sudden expansion. The piston closes the larger-diameter pipe and moves between two limiting positions with strong acceleration or deceleration at the beginning and end of each stroke and constant velocity in between. The piston velocity in the exhaust stroke is about four times higher than in the intake stroke. Periodic piston movement in this fashion creates a complex unsteady flow between the piston head and the plane of sudden expansion. The numerical method is implicit and of finite volume type, using a moving grid and a collocated arrangement of variables. Second-order spatial discretization, fine grids and a multigrid solution method were used to ensure high accuracy and good efficiency. Spatial and temporal discretization errors were of the order of 1% and 0.1% respectively. The features of the flow are discussed and the velocity profiles are compared with experimental data, showing good qualitative and quantitative agreement.     

Relative particle velocity in a turbulent flow

On the basis of a statistical approach using a probability density function for the coordinates of two particles in a turbulent flow, the parameters of the relative particle motion are investigated. For the functions describing particle entrainment in the turbulence, rigorous results are obtained using a 3D turbulence spectrum. A method of calculating the particle relative-velocity rate with account for particle trajectory correlation is presented. The effects of particle inertia and velocity slip on the parameters of the relative particle motion are studied. Simple approximating formulas for calculating the relative particle motion in a turbulent flow are proposed. The calculation results are compared with the data of direct numerical simulation of stochastic particle trajectories in an isotropic turbulent field.     

Non-isothermal polymer melt flow in sudden expansions

This paper presents numerical results for laminar, incompressible and non-isothermal polymer melt flow in sudden expansions. The mathematical model includes the mass, momentum and energy conservation laws within the framework of a generalized Newtonian formulation. Two constitutive relations are adopted to describe the non-Newtonian behavior of the flow, namely Cross and Modified Arrhenius Power-Law models. The governing equations are discretized using the finite difference method based on central, second-order accurate formulas for both convective and diffusive terms. The pressure–velocity coupling is treated by solving a Poisson equation for pressure. The results are presented for two commercial polymers and demonstrate that important flow parameters, such as pressure drop and viscosity distribution, are strongly affected by heat transfer features.     

Measurement of bubble size, velocity and concentration in flashing flow behind a sudden constriction

In the present paper the results of investigations in flashing flow behind a sudden constriction in vertical upflow are described. Flow visualization, laser-Doppler and phase-Doppler anemometry have been used to measure local bubble and fluid velocities, local bubble sizes and void fractions. The measurements were performed in the midplane of a two-dimensional channel with a 2:1 stepwise constriction.It was found that bubble nucleation takes place in the recirculation zone immediately behind the constriction, which is the location of the lowest static pressure. These bubbles are transported downstream by the mean flow field, while undergoing further growth. No additional nucleation was observed downstream of the recirculation zone. A periodic, cloudwise behaviour of the bubble formation was found which could be explained by the interaction between the bubble growth and the mean flow field. This interaction results in strong disturbances of the mean flow field, which show up as an increase of the fluctuating bubble velocity by a factor of 3 compared to single-phase measurements in a region of 10 step heights behind the constriction. However, these fluctuations appear more like a periodic change in the mean velocity rather than a higher turbulence level. The measured arithmetic mean bubble diameters rise from approx. 50 μm in the recirculation region to about 70–80 μm 50 step heights downstream. Maximum local bubble number density and void fraction were found to be 160001/cm³ and 0.8%, respectively.     

Two-dimensional planar flow of a viscoelastic plastic medium

The present study is concerned with finite element simulation of the planar entry flow of a viscoelastic plastic medium exhibiting yield stress. The numerical scheme is based on the Galerkin formulation. Flow experiments are carried out on a carbon black filled rubber compound. Steady-state pressure drops are measured on two sets of contraction or expansion dies having different lengths and a constant contraction or expansion ratio of 4:1 with entrance angles of 90, 45 and 15 degrees. The predicted and measured pressure drops are compared. The predicted results indicate that expansion flow has always a higher pressure drop than contraction flow. This prediction is in agreement with experimental data only at low flow rates, but not at high flow rates. The latter disagreement is possibly an indication that the assumption of fully-developed flow in the upstream and downstream regions is not realistic at high flow rates, even for the large length-to-thickness ratio channels employed. The evolution of the velocity, shear stress, and normal stress fields in the contraction or expansion flow and the location of pseudo-yield surfaces are also calculated.     

A corrected particle method with high-order Taylor expansion for solving the viscoelastic fluid flow

In this paper, a corrected particle method based on the smoothed particle hydrodynamics (SPH) method with high-order Taylor expansion (CSPH-HT) for solving the vis-coelastic flow is proposed and investigated. The validity and merits of the CSPH-HT method are first tested by solv-ing the nonlinear high order Kuramoto-Sivishinsky equation and simulating the drop stretching, respectively. Then the flow behaviors behind two stationary tangential cylinders of polymer melt, which have been received little attention, are investigated by the CSPH-HT method. Finally, the CSPH-HT method is extended to the simulation of the filling process of the viscoelastic fluid. The numerical results show that the CSPH-HT method possesses higher accuracy and stability than other corrected SPH methods and is more reliable than other corrected SPH methods.     

A study of the recirculating flow in planar,symmetrical branching channels

A numerical method is employed to examine the flow in symmetrical, two‐dimensional branches of Y shape and Tee shape. The methodology is based on a pressure‐correction procedure within the frame of unstructured grids. Specified pressures are imposed at the outlets of the two branches. The area ratio of the branch is allowed to vary in the range of 2–3. Separation of the flow in the bifurcating region is inevitable. With equal outlet pressures, symmetrical flow patterns prevail except for the Y type branch under the conditions of high Reynolds numbers and large area ratios. This implies that the Y‐branch flow is more sensitive to small disturbances. It is shown that with a slightly higher pressure imposed on one of the two branches the structure of the recirculating flow for the Y type is greatly affected and the flow rate is reduced dramatically in the high‐pressure branch channel. In contrast, the influence on the Tee type branch is much lower since the flow behaves like a jet impinging on a confined duct. Copyright © 2005 John Wiley & Sons, Ltd.