气固两相弯管湍流场中圆柱状颗粒取向和沉积特性的研究北大核心CSCD

针对在Reynolds数Re=3000~50000、Stokes数S_(tk)=0.1~10、Dean数De=1400~2800的情况下,长径比β=2~12的圆柱状颗粒流经弯管湍流场时的取向与沉积特性进行了研究.圆柱状颗粒的运动采用细长体理论结合Newton第二定律进行描述,取向分布函数由Fokker-Planck方程给出,平均湍流场通过求解Reynolds平均运动方程结合Reynolds应力方程得到,作用在颗粒上的湍流脉动速度由动力学模拟扫掠模型描述.通过求解湍流场以及颗粒的运动方程和取向分布函数方程,得到并分析了沿流向不同截面和出口处颗粒的取向分布,讨论了各因素对颗粒沉积特性的影响.研究结果表明,随着S_(tk)和颗粒长径比β的增加、De和Re的减少,颗粒的主轴更趋向于流动方向.颗粒的沉积率随着De,Re,S_(tk)和颗粒长径比的增大而增加,所得结论对于工程实际应用具有参考价值.     

Numerical study on viscoelastic fluid flow past a rigid body

Viscoelastic non-Newtonian fluids can be achieved by adding a small amount of polymer additives to a Newtonian fluid. In this paper, numerical simulations are used to investigate the influence of such polymer additives on the behavior of flow past a circular cylinder. A numerical method is proposed that discretizes the non-linear viscoelastic system on a uniform Cartesian grid, with a penalization method to model the presence of the cylinder. The drag of the cylinder and the flow behavior under the effect of different Reynolds numbers ($\mathrm{Re}$), Weissenberg numbers (Wi) and polymer viscosity ratios (ε) are studied. Numerical results show that different flow characteristics are exhibited in different parameter zones. The polymer viscosity ratio plays an important role at low Weissenberg and Reynolds numbers, but as the Reynolds and Weissenberg numbers increase, the influence of ε weakens. The drag force of the cylinder is mostly affected by the Reynolds and Weissenberg numbers. At low Reynolds numbers, the drag of the cylinder and the flow fields are only affected by a large value of Wi when the elastic forces are strong. Non-trivial drag reduction occurs only when there is vortex shedding in the wake flow, whereas drag enhancement happens when the vortex shedding is inhibited.     

A mixing-length model for magnetohydrodynamic flows in channels and ducts with wall-parallel magnetic field

A spanwise magnetic field leads to turbulent drag reduction in channel flow of a conducting liquid due to the selective Joule damping of certain flow structures. This effect can be captured by a simple modification of Prandtl's classical mixing-length idea. The mixing length over which a turbulent fluctuation loses its momentum is not only constrained geometrically but also by magnetic damping. We therefore introduce a magnetic damping length that is proportional to friction velocity and the Joule damping time. The limitation of mixing length is implemented by using the harmonic mean between wall distance and this damping length. By combining this ansatz with the van-Driest model for turbulent stresses in channel flow we obtain a satisfactory prediction for the mean velocity distribution in magnetohydrodynamic channel flow with spanwise field for different Reynolds and Hartmann numbers. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Magnetic field effects on Newtonian and non-Newtonian ferrofluid flow past a circular cylinder

The changes in the flow properties under the action of electromagnetic body forces are investigated numerically for ferrofluid flow past a circular cylinder. Ferrofluid is modeled as both a Newtonian and a non-Newtonian Power-Law fluid. Magnetic forces are applied by placing magnets at different locations on the surface of the cylinder. The magnetostatic effects on the structure of the wake region, on drag reduction and on vortex formation length and frequency are shown and compared in terms of Reynolds number, interaction parameter, Power-Law index and magnet location. It is shown that the increase in the interaction parameter reduces drag for both Newtonian and non-Newtonian model. This decrease is observed to be higher for shear thinning and lower for shear thickening fluid compared to Newtonian case. It is also shown that vortex street formation in the wake region behind the cylinder may be delayed under high magnetic effects. The Strouhal number is higher for shear thinning case at both low and high Reynolds numbers, and lower for shear thickening case at high Reynolds numbers, compared to Newtonian fluid. The vortex formation frequency also decreases under the action of the magnetic field in all cases, however the vortex formation length increases. Placing the magnet towards the front region of the cylinder increases considerably the drag coefficient for both Newtonian and non-Newtonian model. This increase in drag coefficient is higher in the shear thinning fluid and lower in the shear thickening fluid compared to the Newtonian case.     

Theoretical Considerations about Near-Wall Turbulence and Resulting Flow Control Schemes

Based on analytical considerations about how near-wall turbulence needs to be modified in order to reduce the momentum loss towards solid walls and to yield lower energy losses, a mechanism of turbulent drag reduction is proposed. This mechanism suggests that drag reducing flow control at high Reynolds numbers should be designed to minimize the turbulent dissipation rate. A previously published approach on how a reduction of the turbulent dissipation in the near-wall region can be achieved is analyzed further. The obtained results provide some new insight on the parameters that need to be considered when designing flow control schemes for skin friction drag reduction. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

纤维悬浮剪切湍流中纤维旋转扩散系数的理论研究

对纤维悬浮剪切湍流中纤维旋转扩散系数进行了理论研究．首先建立了流场不同脉动速度梯度间的相关矩函数,然后推导出了纤维旋转扩散系数的表达式,该表达式依赖于特征长度、时间、速度和一个与壁面作用相关的无量纲参数．得到的纤维旋转扩散系数可以应用于非均匀和非各向同性的湍流场,此外还可以推广到三维湍流场,因而为纤维悬浮湍流场的研究提供了理论基础．     

Langevin equation of a fluid particle in wall-induced turbulence

We derive the Langevin equation describing the stochastic process of fluid particle motion in wall-induced turbulence (turbulent flow in pipes, channels, and boundary layers including the atmospheric surface layer). The analysis is based on the asymptotic behavior at a large Reynolds number. We use the Lagrangian Kolmogorov theory, recently derived asymptotic expressions for the spatial distribution of turbulent energy dissipation, and also newly derived reciprocity relations analogous to the Onsager relations supplemented with recent measurement results. The long-time limit of the derived Langevin equation yields the diffusion equation for admixture dispersion in wall-induced turbulence.     

Flow-induced anisotropic viscosity in short fiber reinforced polymers

The commonly used flow models for fiber reinforced polymers often neglect the flow induced mechanical anisotropy of the suspension. With an increasing fiber volume fraction, this plays, however, an important role. There are some models which count on this effect, they are, however, phenomenological and require a fitted model parameter. In this paper, a micromechanically based constitutive law is proposed which considers the flow induced anisotropic viscosity of the fiber suspension. The introduced viscosity tensor can handle arbitrary anisotropy of the fluid-fiber mixture depending on the actual fiber orientation distribution. A homogenization method for unidirectional structures in contribution with orientation averaging is used to determine the effective viscosity tensor. The motion of rigid ellipsoidal fibers induced by the flow of the matrix material is described by Jeffery's equation. A numerical implementation of the introduced model is applied to representative flow modes. The calculated stress values are analyzed in transient and stationary flow cases. They show a less pronounced anisotropic viscous behaviour in every investigated case compared to the results obtained by the use of the Dinh-Armstrong constitutive law. The reason for the qualitative difference is that the presented model depends on the complete orientation information, while the other one is linear in the fourth-order fiber orientation tensor. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Simulation and analysis of turbulent MHD channel flow with a streamwise magnetic field

We perform large-eddy simulations of turbulent MHD channel flow with a streamwise magnetic field using a pseudo spectral method. The streamwise magnetic field leads to turbulent drag reduction due to the selective Joule damping of certain flow structures. Near the walls, the turbulent mean velocity profile retains the logarithmic layer but the von Karman constant decreases with increasing magnetic field strength. In the outer region, the flow is characterized by persistent streaky structures of large streamwise extent, which lead to a rather flat mean velocity profile. In addition, the streamwise velocity fluctuations develop a pronounced second peak upon increasing the magnetic induction as well as a second logarithmic layer that increases in steepness. We find that Prandtl's classical mixing-length model with a variable Kármán constant can describe the modified logarithmic layer reasonably accurately in a wide range of Reynolds and Hartmann numbers. However, the flow modification near the center of the channel is not properly captured by this approach. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Forces acting on particles in separated wall‐bounded shear flow

Trajectories of solid particles in laminar and turbulent flow over a backward‐facing step (BFS) were numerically computed by integrating the equation of motion for particles. The various forces acting on the particles [5],[6] were calculated for a variety of flow Reynolds numbers and for different particle characteristics such as the Stokes number and the particle‐to‐fluid density ratio. The investigation was conducted for the distinct flow regimes of the BFS flow separately. Generally, the drag and gravitation were found to be the most significant forces. The lift and history force were the next most important, mostly two orders of magnitude smaller, but in some cases closing up to the other two in importance. The pressure and virtual mass effects were very small for the majority of cases. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Variation of friction drag via spanwise transversal surface waves

Introducing spanwise velocity components into the near-wall flow field of a turbulent boundary layer has shown to be an effective mean of influencing the wall shear stress. The underlying physical mechanisms leading to the drag reduction have however not been fully understood. The presented investigation uses sinusoidal transversal travelling surface waves to influence the near-wall turbulence to achieve drag reduction. Two distinct wave configurations are analysed in detail and compared to an unactuated turbulent flat plate boundary layer flow to gain inside into the drag reducing mechanisms. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Non-Boussinesq turbulent buoyant jet of a low-density gas leaks into high-density ambient

In this article, we study the problem of low-density gas jet injected into high-density ambient numerically which is important in applications such as fuel injection and leaks. It is assumed that the local rate of entrainment is consisted of two components; one is the component of entrainment due to jet momentum while the other is the component of entrainment due to buoyancy. The integral models of the mass, momentum and concentration fluxes are obtained and transformed to a set of ordinary differential equations using some similarity transformations. The resulting system is solved to determine the centerline quantities which are used to get the mean axial velocity, mean concentration and mean density of the jet. Therefore, the centerline and mean quantities are used together with the governing equation to determine some important turbulent quantities such as, cross-stream velocity, Reynolds stress, velocity-concentration correlation, turbulent eddy viscosity and turbulent eddy diffusivity. Throughout this paper the developed model is verified by comparing the present results with experimental results and jet/plume theory from the literature.     

Turbulent Poiseuille flow with near-critical wall transpiration

An incompressible, pressure-driven, fully developed turbulent flow between two parallel walls, with an extra constant transverse velocity component, is considered. A closure condition is formulated, which relates the shear stress with the first and the second derivatives of the longitudinal mean velocity. The closure condition is derived without invoking any special hypotheses on the nature of turbulent motion, only taking advantage of the fact that the flow depends on a finite number of governing parameters. By virtue of the closure condition, the momentum equation is reduced to the boundary-value problem for a second-order differential equation, which is solved by the method of matched asymptotic expansions at high values of the logarithm of the Reynolds number based on the friction velocity. The case of near-critical transpiration, when the shear stress at the injection wall vanishes, is considered. It is shown that the maximum point on the mean velocity profile lies in a thin sublayer near the suction wall in this case. A formula for the position of the maximum point as a function of the transpiration factor is obtained. The mean velocity profiles near the suction wall are calculated. A friction law for Poiseuille flow with near-critical transpiration is found, which makes it possible to describe the relation between the shear stress at the wall, the Reynolds number, and the transpiration velocity by a single function of one variable. Direct numerical simulation of the flow for some transpiration factors is performed. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Finite element calculations of flow past a spherical bubble rising on the axis of a cylindrical tube

The velocity and pressure fields of a Newtonian fluid with homogeneous and constant physical properties flowing around a sphere on the axis of a cylindrical tube with no slip, free slip and partial slip at the sphere surface and no slip at the cylinder wall have been calculated by solving the Navier-Stokes equations and the continuity equation using the finite element technique with the penalty function method. Terminal rise velocities of spherical air bubbles in water have been calculated as function of the bubble radius and some conclusions have been drawn about the nature of the interface. Finally, the influence of the presence of a cylindrical wall on the drag force has been determined and a new empirical equation is derived for the wall correction factor for a sphere rising with free slip at its surface at low Reynolds number.     

Axisymmetric bodies of minimum drag in hypersonic flow

The problem of determining the longitudinal contour of a slender, axisymmetric body in hypersonic flow which has minimum drag is considered. The pressure distribution is assumed to be Newtonian, while the skin-friction distribution is for laminar flow and depends on body geometry. This investigation is conducted with the method of steepest descent, whose feasiblity is demonstrated by solving minimum drag problems having known analytical solutions.     

Asymptotic study of turbulent Poiseuille flow with wall transpiration

An incompressible, pressure–driven, fully developed turbulent flow between two parallel walls, with an extra constant transverse velocity component, is considered. A closure condition is formulated, which relates the shear stress to the first and second derivatives of the longitudinal mean velocity. The closure condition is derived without invoking any special hypotheses on the nature of turbulent motion, only taking advantage of the fact that the flow depends on a finite number of governing parameters. By virtue of the closure condition, the momentum equation is reduced to the boundary–value problem for a second–order differential equation, which is solved by the method of matched asymptotic expansions at high values of the logarithm of the Reynolds number based on the friction velocity. A limiting transpiration velocity is obtained, such that the shear stress at the injection wall vanishes, while the maximum point on the velocity profile approaches the suction wall. In this case, a sublayer near the suction wall appears where the mean velocity is proportional to the square root of the distance from the wall. A friction law for Poiseuille flow with transpiration is found, which makes it possible to describe the relation between the wall shear stress, the Reynolds number, and the transpiration velocity by a function of one variable. A velocity defect law, which generalizes the classical law for the core region in a channel with impermeable walls to the case of transpiration, is also established. In similarity variables, the mean velocity profiles across the whole channel width outside viscous sublayers can be described by a one–parameter family of curves. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Hydromagnetic stability of plane Couette flow of an upper convected Maxwell fluid

Hydrodynamic stability of plane Couette flow of an upper convectedMaxwell fluid is investigated in presence of a transverse magneticfield assuming that the magnetic Prandtl number is sufficientlysmall. The resulting equation is a modified Orr–Sommerfeldequation. The equations of stability are solved numericallyusing Chebyshev collocation method with QZ algorithm. The criticalvalues of Reynolds number, wave number and wave speed are computedand the results are shown through the neutral curves. By increasingthe amount of elasticity to a certain value, it is shown that,as the Hartmann number increases, the minimum critical Reynoldsnumber decreases and it does not increase again in contrastto the Newtonian case.     

Interaction between inner and outer layer in drag-reduced turbulent flows

Effects of wall-based skin-friction drag reduction strategies on the statistical properties of large-scale motions in moderate Reynolds number turbulent flows have been investigated by exploiting Direct Numerical Simulation of turbulent channels. To educe large scales, a new efficient parallel distributed memory algorithm has been implemented which delivers data-driven modes of increasing characteristic lengthscales: the Fast and Adaptive Bidimensional Empirical Mode Decomposition (FABEMD). The influence of wall-based skin friction reduction on large scales is studied by comparing single point statistics, such as r.m.s. fluctuations, and two-point statistics, as cross-correlation functions in controlled and uncontrolled channel flow fields at constant friction Reynolds number. The traditional way of observing large-scale footprinting at the wall, as cross-correlation of the streamwise velocity components at different wall distances, has been found to be unreliable when comparing drag-reduced flows, due to the arbitrary choice of a reference plane in the logarithmic layer. A more sound way of observing the footprinting via the correlation of the streamwise velocity with the friction velocity is addressed and shows an increase of the footprinting in drag-reduced flows. (© 2016 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical simulation of generalized newtonian blood flow past a couple of irregular arterial stenoses

This paper looked at the numerical investigations of the generalized Newtonian blood flow through a couple of irregular arterial stenoses. The flow is treated to be axisymmetric, with an outline of the stenoses obtained from a three dimensional casting of a mild stenosed artery, so that the flow effectively becomes two‐dimensional. The Marker and Cell (MAC) method is developed for the governing unsteady generalized Newtonian equations in staggered grid for viscous incompressible flow in the cylindrical polar co‐ordinates system. The derived pressure‐Poisson equation was solved using Successive‐Over‐Relaxation (S.O.R.) method and the pressure‐velocity correction formulae have been derived. Computations are performed for the pressure drop, the wall shear stress distribution and the separation region. The presented computations show that in comparison to the corresponding Newtonian model the generalized Newtonian fluid experiences higher pressure drop, lower peak wall shear stress and smaller separation region. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 27: 960–981, 2011     

明渠中变密度变粘度牛顿流体紊动基本方程式

本文利用Navier－Stokes方程及雷诺时均法则,导出了变密度变粘度牛顿流体的紊动微分方程式,并进一步导出了变密度变粘度牛顿流体在明渠中紊流流动时的运动微分方程式.文中首次提出了密度紊动应力与粘度紊动应力的概念.