Direct numerical simulation of wall turbulent flows with microbubbles

The marker‐density‐function (MDF) method has been developed to conduct direct numerical simulation (DNS) for bubbly flows. The method is applied to turbulent bubbly channel flows to elucidate the interaction between bubbles and wall turbulence. The simulation is designed to clarify the structure of the turbulent boundary layer containing microbubbles and the mechanism of frictional drag reduction. It is deduced from the numerical tests that the interaction between bubbles and wall turbulence depends on the Weber and Froude numbers. The reduction of the frictional resistance on the wall is attained and its mechanism is explained from the modulation of the three‐dimensional structure of the turbulent flow. Copyright © 2001 John Wiley & Sons, Ltd.     

湍流横掠固定颗粒的全尺度直接数值模拟

气固两相流模拟中,当固相尺度接近或大于Kolmogorov尺度时,普通的点源模型将不再适用,固体相的体积效应和表面效应将对流体相产生显著的影响。通过采用直接数值模拟方法,结合内嵌边界方法对湍流中不同湍流强度流体横掠大于Kolmogorov尺度的固相颗粒进行了全尺度模拟,讨论分析了在两种湍流度下方形颗粒对湍流的调制影响以及颗粒的受力情况。     

Direct numerical simulation of free falling sphere in creeping flow

In the present study, direct numerical simulations (DNS) are performed on single and a swarm of particles settling under the action of gravity. The simulations have been carried out in the creeping flow range of Reynolds number from 0.01 to 1 for understanding the hindrance effect, of the other particles, on the settling velocity and drag coefficient. The DNS code is a non-Lagrange multiplier-based fictitious-domain method, which has been developed and validated by Jin et al. (2008 Jin, S. A parallel algorithm for the direct numerical simulation of 3D inertial particle sedimentation. Conference proceedings of the 16th annual conference of the CFD Society of Canada. Edited by: Bergstrom, D. J. and Spiteri, R. 9–11, June. Saskatoon, Saskatchewan, , Canada [Google Scholar]; A parallel algorithm for the direct numerical simulation of 3D inertial particle sedimentation. In: Conference proceedings of the 16th annual conference of the CFD Society of Canada). It has been observed that the time averaged settling velocity of the particle in the presence of other particles, decreases with an increase in the number of particles surrounding it (from 9 particles to 245 particles). The effect of the particle volume fraction on the drag coefficient has also been studied and it has been observed that the computed values of drag coefficients are in good agreement with the correlations proposed by Richardson and Zaki (1954 Richardson, J. F. and Zaki, W. N. 1954. Sedimentation and fluidization: part I. Transactions of the Institution of Chemical Engineers, 32: 35–53.  [Google Scholar]; Sedimentation and fluidization: part I. Transactions of the Institution of Chemical Engineers, 32, 35–53) and Pandit and Joshi (1998 Pandit, A. B. and Joshi, J. B. 1998. Pressure drop in packed, expanded and fluidized beds, packed columns and static mixers – a unified approach. Reviews in Chemical Engineering, 14: 321–371. [Crossref], [Web of Science ®] , [Google Scholar]; Pressure drop in packed, expanded and fluidised beds, packed columns and static mixers – a unified approach. Reviews in Chemical Engineering, 14, 321–371). The suspension viscosity-based model of Frankel and Acrivos (1967 Frankel, N. A. and Acrivos, A. 1967. On the viscosity of a concentrated suspension of solid spheres. Chemical Engineering Science, 22: 847–853. [Crossref], [Web of Science ®] , [Google Scholar]; On the viscosity of a concentrated suspension of solid spheres. Chemical Engineering Science, 22, 847–853) shows good agreement with the DNS results.     

Calculation of two-dimensional shear-driven cavity flows at high reynolds numbers

The time-dependent Navier–Stokes equations are numerically integrated for two-dimensional incompressible viscous flow in a shear-driven square cavity. Using a time-splitting method and finite differences on a staggered mesh, the momentum and pressure equations are directly solved by a tensor product method where one finite difference direction is diagonalized by eigenvalue decomposition. The effects of increasing Reynolds number are studied and the developing boundary layer is captured by using a finely clustered mesh. At Re = 30000 the flow is in a continuously developing unsteady regime. Power spectrum plots indicate that the unsteady flow oscillates with one fundamental frequency and exhibits some characteristics of transition between laminar and turbulent states.     

Direct numerical simulation of particulate flows with a fictitious domain method

Our works on the fictitious domain method for the direct numerical simulation of particulate flows are reviewed, and particularly our recent progresses in the simulations of the motion of particles in Poiseuille flow at moderately high Reynolds numbers are reported. The method is briefly described, and its capability to simulate the motion of spherical and non-spherical particles in Newtonian, non-Newtonian and non-isothermal fluids is demonstrated. In addition, the applications of the fictitious domain method reported in the literature are also reviewed, and some comments on the features of the fictitious domain method and the immersed boundary method are given.     

Boundary element analysis of driven cavity flow for low and moderate Reynolds numbers

A boundary element method for steady two‐dimensional low‐to‐moderate‐Reynolds number flows of incompressible fluids, using primitive variables, is presented. The velocity gradients in the Navier–Stokes equations are evaluated using the alternatives of upwind and central finite difference approximations, and derivatives of finite element shape functions. A direct iterative scheme is used to cope with the non‐linear character of the integral equations. In order to achieve convergence, an underrelaxation technique is employed at relatively high Reynolds numbers. Driven cavity flow in a square domain is considered to validate the proposed method by comparison with other published data. Copyright © 2001 John Wiley & Sons, Ltd.     

气体动理学格式与多尺度流动模拟

介绍了气体动理学格式(GKS)的基本构造原理及其在两种典型多尺度流动模拟中的应用。GKS利用介观BGK方程的跨尺度演化解来构造网格界面上的数值通量,从而发展出能随计算网格尺度变化自动切换物理模型的多尺度方法。对湍流这种宏观多尺度流动,发展了高精度GKS方法并成功用于低雷诺数湍流的直接数值模拟;为实现对高雷诺数湍流的高效精细模拟,基于拓展BGK方程和已有的RANS,LES模型建立了新型多尺度模拟框架。对跨流域稀薄流动,发展了适合大规模并行的三维统一气体动理学格式(UGKS),并建立了适合轴对称稀薄流动的UGKS。研究表明,GKS在多尺度流动高效模拟中的优异性能,具有很好的发展前景。     

Direct numerical simulation of low Reynolds number flows in an open‐channel with sidewalls

A direct numerical simulation of low Reynolds number turbulent flows in an open‐channel with sidewalls is presented. Mean flow and turbulence structures are described and compared with both simulated and measured data available from the literature. The simulation results show that secondary flows are generated near the walls and free surface. In particular, at the upper corner of the channel, a small vortex called inner secondary flows is simulated. The results show that the inner secondary flows, counter‐rotating to outer secondary flows away from the sidewall, increase the shear velocity near the free surface. The secondary flows observed in turbulent open‐channel flows are related to the production of Reynolds shear stress. A quadrant analysis shows that sweeps and ejections are dominant in the regions where secondary flows rush in toward the wall and eject from the wall, respectively. A conditional quadrant analysis also reveals that the production of Reynolds shear stress and the secondary flow patterns are determined by the directional tendency of the dominant coherent structures. Copyright © 2009 John Wiley & Sons, Ltd.     

Direct numerical simulation of compressible turbulent flows

This paper reviews the authors＇ recent studies on compressible turbulence by using direct numerical simulation （DNS）,including DNS of isotropic（decaying） turbulence, turbulent mixing-layer,turbulent boundary-layer and shock/boundary-layer interaction.Turbulence statistics, compressibility effects,turbulent kinetic energy budget and coherent structures are studied based on the DNS data.The mechanism of sound source in turbulent flows is also analyzed. It shows that DNS is a powerful tool for the mechanistic study of compressible turbulence.     

On the effects of dilute polymers on driven cavity turbulent flows

Effects of dilute polymer solutions on a lid-driven cubical cavity turbulent flow are studied via particle image velocimetry (PIV). This canonical flow is a combination of a bounded shear flow, driven at constant velocity and vortices that change their spatial distribution as a function of the lid velocity. From the two-dimensional PIV data we estimate the time averaged spatial fields of key turbulent quantities. We evaluate a component of the vorticity–velocity correlation, namely 〈ω₃v〉, which shows much weaker correlation, along with the reduced correlation of the fluctuating velocity components, u and v. There are two contributions to the reduced turbulent kinetic energy production −〈u v〉S_uv, namely the reduced Reynolds stresses, −〈u v〉, and strongly modified pointwise correlation of the Reynolds stress and the mean rate-of-strain field, S_uv. The Reynolds stresses are shown to be affected because of the derivatives of the Reynolds stresses, ∂〈u v〉/∂y that are strongly reduced in the same regions as the vorticity–velocity correlation. The results, combined with the existing evidence, support the phenomenological model of polymer effects propagating from the polymer scale to the velocity derivatives and through the mixed-type correlations and Reynolds stress derivatives up to the turbulent velocity fields. The effects are shown to be qualitatively similar in different flows regardless of forcing type, homogeneity or presence of liquid–solid boundaries.     

Direct numerical simulation of a NACA0012 in full stall

This work aims at investigating the mechanisms of separation and the transition to turbulence in the separated shear-layer of aerodynamic profiles, while at the same time to gain insight into coherent structures formed in the separated zone at low-to-moderate Reynolds numbers. To do this, direct numerical simulations of the flow past a NACA0012 airfoil at Reynolds numbers Re = 50,000 (based on the free-stream velocity and the airfoil chord) and angles of attack AOA = 9.25° and AOA = 12° have been carried out. At low-to-moderate Reynolds numbers, NACA0012 exhibits a combination of leading-edge/trailing-edge stall which causes the massive separation of the flow on the suction side of the airfoil. The initially laminar shear layer undergoes transition to turbulence and vortices formed are shed forming a von Kármán like vortex street in the airfoil wake. The main characteristics of this flow together with its main features, including power spectra of a set of selected monitoring probes at different positions on the suction side and in the wake of the airfoil are provided and discussed in detail.     

Discussions on driven cavity flow

The widely studied benchmark problem, two‐dimensional‐driven cavity flow problem is discussed in detail in terms of physical and mathematical and also numerical aspects. A very brief literature survey on studies on the driven cavity flow is given. On the basis of several numerical and experimental studies, the fact of the matter is that physically the flow in a driven cavity is not two‐dimensional above moderate Reynolds numbers. However, there exist numerical solutions for two‐dimensional‐driven cavity flow at high Reynolds numbers. Copyright © 2008 John Wiley & Sons, Ltd.     

Direct numerical simulation of free and forced square jets

Direct numerical simulation (DNS) of incompressible, spatially developing square jets in the Reynolds number range of 500–2000 is reported. The three-dimensional unsteady Navier–Stokes equations are solved using high order spatial and temporal discretization. The objective of the present work is to understand the evolution of free and forced square jets by examining the formation of large-scale structures. Coherent structures and related interactions of free jets suggest control strategies that can be used to achieve enhanced spreading and mixing of the jet with the surrounding fluid. The critical Reynolds number for the onset on unsteadiness in an unperturbed free square jet is found to be 875–900 while it reduces to the range 500–525 in the presence of small-scale perturbations. Disturbances applied at the flow inlet cause saturation of KH-instability and early transition to turbulence. Forced jet calculations have been carried out using varicose perturbation with amplitude of 15%, while frequency is independently varied. Simulations show that the initial development of the square jet is influenced by the four corners leading to the appearance hairpin structures along with the formation of vortex rings. Farther downstream, adjacent vortices strongly interact leading to their rapid breakup. Excitation frequencies in the range 0.4–0.6 cause axis-switching of the jet cross-section. Results show that square jets achieve greater spreading but are less controllable in comparison to the circular ones.     

Numerical study of flow and thermal behaviour of lid‐driven flows in cavities of small aspect ratios

Numerical study has been performed to investigate the effects of cavity shape on flow and heat transfer characteristics of the lid‐driven cavity flows. Dependence of flow and thermal behaviour on the aspect ratio of the cavities is also evaluated. Three types of the cross‐sectional shape, namely, circular, triangular, and rectangular, and four aspect ratios, 0.133, 0.207, 0.288, and 0.5, are taken into account to construct twelve possible combinations; however, attention is focused on the small‐aspect‐ratio situations. Value of the Reynolds number considered in this study is varied between 100 and 1800. For the cases considered in this study a major clockwise vortex driven by the moving lid prevailing in the cavity is always observed. When the Reynolds number is fixed, the rectangular cavity produces strongest lid‐driven flow, and the triangular cavity weakest. For the cases at small aspect ratio and low Reynolds number, the streamlines appear symmetric fore‐and‐aft with respect to the central line at x/L = 0.5. Data for the local and average Nusselt numbers are also provided. For rectangular cavities, it is observed that case 1/5R produces the highest average Nusselt number at any Reynolds number. Among the twelve possible geometric cases considered herein, the highest and lowest average Nusselt numbers are found with cases 1/6T and 1/2C, respectively. Copyright © 2006 John Wiley & Sons, Ltd.     

Direct numerical simulation of turbulent Taylor–Couette flow

The direct numerical simulation (DNS) of the Taylor–Couette flow in the fully turbulent regime is described. The numerical method extends the work by Quadrio and Luchini [M. Quadrio, P. Luchini, Eur. J. Mech. B/Fluids 21 (2002) 413–427], and is based on a parallel computer code which uses mixed spatial discretization (spectral schemes in the homogeneous directions, and fourth-order, compact explicit finite-difference schemes in the radial direction). A DNS is carried out to simulate for the first time the turbulent Taylor–Couette flow in the turbulent regime. Statistical quantities are computed to complement the existing experimental information, with a view to compare it to planar, pressure-driven turbulent flow at the same value of the Reynolds number. The main source for differences in flow statistics between plane and curved-wall flows is attributed to the presence of large-scale rotating structures generated by curvature effects.     

Numerical solution of incompressible flows by discrete singular convolution

A discrete singular convolution (DSC) solver is developed for treating incompressible flows. Three different two‐dimensional benchmark problems, the Taylor problem, the driven cavity flow, and a periodic shear layer flow, are utilized to test the accuracy, to explore the reliability and to demonstrate the efficiency of the present approach. Solution of extremely high accuracy is attained in the analytically solvable Taylor problem. The results of treating the other problems are in excellent agreement with those in the literature. Copyright © 2002 John Wiley & Sons, Ltd.     

基于DES的高雷诺数空腔噪声数值模拟

发展出一套基于SA-DES和SST—DES模型,对三维超音速空腔流动进行数值模拟的方法和程序。采用混合网格有限体积方法求解非定常流场,时间离散采用基于LU—SGS隐式格式的双时间步长方法。采用可压缩物面函数来减少进行高雷诺数数值模拟时物面粘性网格的数量。对比了一方程SA-DES和两方程SST—DES计算得到的涡量和压强...     

Direct numerical simulation of the near field dynamics of a rectangular reactive plume

Spatial direct numerical simulation (DNS) is used to study the near field dynamics of a buoyant diffusion flame established on a rectangular nozzle with an aspect ratio of 2:1. Combustion is represented by a one-step finite-rate Arrhenius chemistry. Without applying external perturbations at the inflow boundary, large vortical structures develop naturally in the flow field, which interact with the flame and temporally create localized holes within the reaction zone in which no chemical reactions take place. The interaction between density gradients and gravity plays a major role in the vorticity generation of the buoyant plume. At the downstream of the reactive plume, a more disorganized flow regime characterized by small scales has been observed, following the breakdown of the large vortical structures due to three-dimensional (3D) vortex interactions. Analysis of energy spectra shows that the spatially developing reactive plume has a tendency of transition to turbulence under the effects of combustion-induced buoyancy. The buoyancy effects are found to be very important to the formation, development, interaction, and breakdown of vortices in reactive plumes. In contrast with the relaminarization effects of chemical exothermicity via viscous damping and volumetric expansion on non-buoyant jet diffusion flames, the tendency towards transition to turbulence in reactive plumes is greatly enhanced by the buoyancy effects.     

高阶谱元区域分解算法求解定常方腔驱动流

主要利用Jacobian-free的Newton-Krylov方法求解定常不可压缩Navier-Stokes方程,将基于高阶谱元法的区域分解Stokes算法的非定常时间推进步作为Newton迭代的预处理,回避了传统Newton方法Jacobian矩阵的显式装配,节省了程序内存,同时降低了Newton迭代线性系统的条件数,且没有非线性对流项的隐式求解,大大加快了收敛速度。对有分析解的Kovasznay流动的计算结果表明,本高阶谱元法在空间上有指数收敛的谱精度,且对定常解的Newton迭代是二次收敛的。本文模拟了二维方腔顶盖一致速度驱动流,同基准解符合得很好,表明本文方法是准确可靠的。本文还考虑了Re=800时方腔顶盖正弦速度驱动流,除得到已知的一个稳定对称解和一对稳定非对称解外,还获得了一对新的不稳定的非对称解。     

时刻追踪多介质界面运动的动网格方法

在对可压缩多介质流动的数值模拟中,定义介质界面为一种内部边界,由网格的边组成,界面边两侧对应两种不同介质中的网格。通过求解Riemann问题追踪介质界面上网格节点的运动,同时采用局部重构的动网格技术处理介质界面的大变形问题,并将介质界面定义为网格变形边界,以防止该边界上网格体积为负。运用HLLC格式求解ALE方程组得到整个多介质流场的数值解。最后从几个多介质流模型的计算结果可以看出,本文的动网格方法是可行的,而且可以时刻追踪介质界面的运动状态。