Direct numerical simulation of compressible turbulent channel flows using the discontinuous Galerkin method

Direct numerical simulation of turbulent channel flows between isothermal walls have been carried out using discontinuous Galerkin method. Three Mach numbers are considered (0.2, 0.7, and 1.5) at a fixed Reynolds number ≈2800, based on the bulk velocity, bulk density, half channel width, and dynamic viscosity at the wall. Power law and log-law with the scaling of the mean streamwise velocity are considered to study their performance on compressible flows and their dependence on Mach numbers. It indicates that power law seems slightly better and less dependent on Mach number than the log-law in the overlap region. Mach number effects on the second-order (velocity, pressure, density, temperature, shear stress, and vorticity fluctuations) and higher-order (skewness and flatness of velocity, pressure, density, and temperature fluctuations) statistics are explored and discussed. Both inner (that is wall variables) and outer (that is global) scalings (with Mach number) are considered. It is found that for some second-order statistics (i.e. velocity, density, and temperature), the outer scaling collapses better than the inner scaling. It is also found that near-wall large-scale motions are affected by Mach number. The near-wall spanwise streak spacing increases with increasing Mach number. Iso-surfaces of the second invariant of the velocity gradient tensor are more sparsely distributed and elongated as Mach number increases, which is similar to the distribution of near-wall low speed streaks.     

Unsteady turbulence in plane channel flow

Direct numerical simulations were conducted for oscillating flow with zero time mean (reciprocating flow) in a plane channel subject to a harmonic forcing term of varying amplitude and frequency. The results confirmed the existence of four flow regimes (laminar, “disturbed laminar”, intermittently turbulent, and fully turbulent) depending on the above parameters. The flow behaviour was found to depend on the complex interplay of mean and turbulence quantities, as described by the closed loop formed by the streamwise Reynolds-averaged momentum equation in conjunction with the exact transport equations for the turbulent (Reynolds) stresses. A crucial role in this loop appeared to be played by the different time response of the mean flow to the applied forcing at different cross-stream locations, due to the laminar and turbulent diffusion of momentum from the walls and causing characteristic distortions of the cross-stream mean velocity profiles at different phases (i.e. acceleration vs. deceleration). The intrinsic inertia of turbulence quantities themselves played only a minor role, as confirmed by the fact that, in a broad range of conditions, turbulent stresses were roughly in phase with the respective production and dissipation terms. The structure of turbulence was found to depend largely on the instantaneous mean velocity profile, as confirmed by “frozen velocity” simulations.     

Resolution requirements for numerical simulations of transition

The resolution requirements for direct numerical simulations of transition to turbulence are investigated. A reliable resolution criterion is determined from the results of several detailed simulations of channel and boundary-layer transition.     

Conditional Fourier spectral method for direct numerical simulation of incompressible flows

A new method of treating incompressible flows with nonslip boundaries is proposed as an extension of the Fourier spectral method. This is characteristic in using the function subspace that is a hyperplane in the Fourier-transformed velocity space, prescribed by the boundary condition, as well as in taking the solenoidal field representation in the Fourier space so that the pressure term need not be involved in the main dynamics and then time-integration can simply be made by the high-order Runge-Kutta scheme. The method can be applied in a more complicated case with an active scalar. As examples, the flow transitions to turbulence in a channel and in a rectangular duct heated from below are treated.     

A massively parallel hybrid scheme for direct numerical simulation of turbulent viscoelastic channel flow

This paper describes in detail a numerical scheme designed for direct numerical simulation (DNS) of turbulent drag reduction. The hybrid spatial scheme includes Fourier spectral accuracy in two directions and sixth-order compact finite differences for first and second-order wall-normal derivatives, while time marching can be up to fourth-order accurate. High-resolution and high-drag reduction viscoelastic DNS are made possible through domain decomposition with a two-dimensional MPI Cartesian grid alternatively splitting two directions of space (‘pencil’ decomposition). The resulting algorithm has been shown to scale properly up to 16384 cores on the Blue Gene/P at IDRIS–CNRS, France.Drag reduction is modeled for the three-dimensional wall-bounded channel flow of a FENE-P dilute polymer solution which mimics injection of heavy-weight flexible polymers in a Newtonian solvent. We present results for four high-drag reduction viscoelastic flows with friction Reynolds numbers Re_τ0 = 180, 395, 590 and 1000, all of them sharing the same friction Weissenberg number We_τ0 = 115 and the same rheological parameters. A primary analysis of the DNS database indicates that turbulence modification by the presence of polymers is Reynolds-number dependent. This translates into a smaller percent drag reduction with increasing Reynolds number, from 64% at Re_τ0 = 180 down to 59% at Re_τ0 = 1000, and a steeper mean current at small Reynolds number. The Reynolds number dependence is also visible in second-order statistics and in the vortex structures visualized with iso-surfaces of the Q-criterion.     

交通流多格点预估格子模型与数值仿真

考虑驾驶员对多格点交通流量预估效应,建立了新的交通流多格点预估格子模型。通过线性稳定性分析获得了改进模型的稳定性条件。通过非线性分析得到了扭结—反扭结密度波解,得到了交通流相空间的三个区域:稳定区域、亚稳定区域和不稳定区域。数值仿真验证了考虑驾驶员对多格点的预估效应,能够进一步提高交通流的稳定性。     

Transition in a 2-D lid-driven cavity flow

Direct numerical simulations about the transition process from laminar to chaotic flow in square lid-driven cavity flows are considered in this paper. The chaotic flow regime is reached after a sequence of successive supercritical Hopf bifurcations to periodic, quasi-periodic, inverse period-doubling, period-doubling, and chaotic self-sustained flow regimes. The numerical experiments are conducted by solving the 2-D incompressible Navier-Stokes equations with increasing Reynolds numbers (Re). The spatial discretization consists of a seventh-order upwind-biased method for the convection term and a sixth-order central method for the diffusive term. The numerical experiments reveal that the first Hopf bifurcation takes place at Re equal to 7402±4%, and a consequent periodic flow with the frequency equal to 0.59 is obtained. As Re is increased to 10,300, a new fundamental frequency (FF) is added to the velocity spectrum and a quasi-periodic flow regime is reached. For slightly higher Re (10,325), the new FF disappears and the flow returns to a periodic regime. Furthermore, the flow experiences an inverse period doubling at 10,325 <Re< 10,700 and a period-doubling regime at 10,600 <Re< 10,900. Eventually, for flows with Re greater than 11,000, a scenario for the onset of chaotic flow is obtained. The transition processes are illustrated by increasing Re using time-velocity histories, Fourier power spectra, and the phase-space trajectories. In view of the conducted grid independent study, the values of the critical Re presented above are estimated to be accurate within ±4%.     

交通流多预期延迟模型与数值仿真

为了更准确地描述交通流,考虑驾驶员反应延迟时间和前车信息的非均衡使用,建立一种多预期延迟跟驰模型。线性稳定性分析表明,驾驶员反应延迟时间的增加会降低交通流的稳定性,多个前车信息的使用可以提高交通流的稳定性。数值仿真的结果表明,减少司机的反映延迟时间和适当地增加前车信息都能提高交通流的稳定性。为尽可能少地引入输入变量,不均衡地利用前车的车间距和速度差信息是必要的。理论和数值模拟的结果均表明驾驶员反应延迟在交通拥堵的形成过程中起着重要作用。     

Direct numerical study of hypersonic flow about a swept parabolic body

Direct numerical simulations (DNS) of hypersonic flow about a swept parabolic body have been performed to study the global stability of flow in the leading-edge region of a swept blunt body. Previous stability investigations have been based on local models but have not fully succeeded in reproducing the established experimental findings. The current flow configuration represents a more realistic model and is thus expected to resolve some of the remaining questions. However, novel approaches like DNS-based global stability theory are necessary for such flow models and are employed in this study. As a result, boundary-layer modes have been identified by different but complementary techniques as the dominant instability mechanism. The DNS starting with small-amplitude white noise provide further evidence for the presence of non-modal effects which may be important in the subcritical regime. From a methodological point of view, the potential for quantitative flow analysis by combining numerical simulations with advanced iterative techniques represents a promising direction for investigating the governing physical processes of complex flows.     

Spectral analysis of turbulence based on the DNS of a channel flow

The development and assessment of spectral turbulence models requires knowledge of the spectral turbulent kinetic energy distribution as well as an understanding of the terms which determine the energy distribution in physical and wave number space. Direct numerical simulation (DNS) of turbulent channel flow yields numerical “data” that can be, and was, analyzed using a spatial Fast Fourier Transform (FFT) to obtain the various spectral turbulent kinetic energy balance terms, including the production, dissipation, diffusion, and the non-linear convective transfer terms.     

槽流拟颗粒模型的并行算法

将流体处理为离散粒子,应用拟颗粒硬球模型来研究槽流中的流动现象,与分子动力学模拟的算法类似,是研究槽流机理的一种行之有效的方法。为了作大规模的模拟,本文采用区域分解算法和消息传递编程模型技术,将该模型串行程序并行化,应用一维划分、单相传递的方法简化了并行算法,采用轮换搜索法来避免硬球碰撞次序对结果的影响。在可扩展的机群系统上用实例计算,通过与串行程序的对比,验证了并行程序的正确性,表明本文设计的并行算法取得了较高的并行计算效率。     

A parallelized eno procedure for direct numerical simulation of compressible turbulence

In this paper, a finite-difference based ENO (essentially nonoscillatory) procedure has been chosen for the direct numerical simulation (DNS) of compressible turbulence. The implementation of the ENO scheme follows the relatively efficient procedure in Shuet al. (1992), but the latter has been modified in the present paper to admit scalar conservation equations and to run on the iPSC/860 Paragon parallel supercomputer. DNS results with our procedure are in excellent agreement with pseudo-spectral and Padé approximation calculations in two and three dimensions. This is the case for a variety of initial conditions for compressible turbulence. The parallel algorithms presented are simple but quite efficient for DNS, with a speedup that approaches the theoretical value. Some of the attractive features include 1) minimum communication whereby a processor only communicates with two neighbors, 2) almost one hundred percent load balancing, 3) a checker-board approach to solve the Poisson equation reduces communication by a factor of approximately 2, and, 4) obtaining turbulence statistics is based on a global collect approach, which is implemented to ensure that a single number, rather than a large matrix of numbers, is communicated between processors. The ENO code presented in this paper should be quite useful in its own right, while the parallel implementation should allow the simulation of fairly realistic problems.     

输水工程取水头部水流特性三维数值模拟研究

首先阐述三维紊流的计算方法,针对输水工程进水口水流特性,采用标准k-ε模型对三维水流运动进行计算,选取VOF法对自由表面进行处理,利用有限体积法对计算区域进行离散化,并采用无滑移的固壁边界条件,模拟进水口水流的复杂流动状态,并将数值模拟的结果与试验资料进行详细比对,验证数学模型的可靠性,在进水口工程设计研究中有较大参考价值。     

Numerical simulation of turbulent spots in channel and boundary layer flows

The initiation and early growth of spots in channel and boundary layer flows is simulated using a three-dimensional spectral code. The simulated spots show significant agreement with available experimental data for such quantities as growth rates and spreading angles. Disturbances are introduced into the center and edge of the developing channel spots to investigate the relative sensitivity of spots.     

地下水流可视化多尺度数值模拟系统设计与实现

将多尺度有限元法（MsFEM）与地理信息系统（GIS）进行有机集成,开发出基于组件式地理信息技术的地下水流多尺度数值模拟系统,实现求解区域的多重尺度离散、参数的可视化赋值、稳定/非稳定水流的多尺度数值模拟、粗尺度解的重构以及模拟结果的多方案显示等功能,使得MsFEM数值模型具有了图形表达能力,模拟结果更以矢量的形式存储,可供进一步决策分析。通过数值实例测试了系统性能,结果表明：以MsFEM为核心研发的集成系统为地下水流多尺度数值模拟提供了高效的可视化界面。     

Direct numerical simulations of localized disturbances in pipe Poiseuille flow

We consider pipe Poiseuille flow subjected to a disturbance which is highly localized in space. Experiments by Peixinho and Mullin have shown this disturbance to be efficient in triggering turbulence, yielding a threshold dependence on the required amplitude as R^-1.5 on the Reynolds number, R. The experiments also indicate an initial formation of hairpin vortices, with each hairpin having a length of approximately one pipe radius, independent of the Reynolds number in the range of R=2000-3000. We perform direct numerical simulations for R=5000. The results show a packet of hairpin vortices traveling downstream, each having a length of approximately one pipe radius. The perturbation remains highly localized in space while being advected downstream for approximately 10 pipe diameters. Beyond that distance from the disturbance origin, the flow becomes severely disordered.     

Comfort design and optimization of direct expansion multi-connected radiant air conditioning based on 3D flow field simulation

The air conditioning method based on radiation heat exchange has the characteristics of small vertical temperature gradient, high thermal comfort and energy saving, and has become a hot spot of attention. The Fluent numerical simulation, the experiment in this paper studies the direct expansion multi-line radiant air conditioner under the artificially simulated climate environment in winter heating, summer cooling and dehumidification. The temperature difference of the radiation + fresh air mode at the same time indoors under heating conditions is less than 2.5 °C, and the time to reach the indoor set temperature of 24 °C is about 2–3 h. Under cooling conditions, the temperature difference of the radiation + fresh air mode at the same time in the room is about 0.5–2 °C, and the time to reach the indoor set temperature of 26 °C is about 1–3 h. In the fresh air mode, the indoor temperature difference and response time at the same time are slightly larger than the radiation + fresh air mode. The freezing and dehumidification effect of fresh air is obvious, the moisture content of dehumidifying fresh air is between 6.3 and 10.5 g/kg, and the dehumidification efficiency can reach 50%. Under the same artificial simulated climate environment, the consumption of the three modes is not much different. When the outdoor temperature in heating conditions is higher than 9 °C, the fresh air mode can get better, and the radiation + fresh air mode can achieve better comfort when running indoors under various conditions.     

微流控芯片中电渗流的数值模拟与仿真研究

从电渗流形成的基本理论入手,推导了电场和流场双物理场耦合的控制方程.运用多物理场数值计算分析软件建立了长为1000μm,宽为100μm的二维流道,在微流道中间250~750μm的区域施加了直流电压,并在数值模拟中还原了微流道内壁和微流体的物理属性,计算得出了各段流体的速度场,进而得出了各段流体的流型.通过二维流道压力分布分析了微流道中各段产生不同流型的原因.对微流控芯片中的电动流动的功能原理分析及优化设计具有借鉴意义.     

Falkner–Skan wedge flow of a power-law fluid with mixed convection and porous medium

This article describes the mixed convection flow of a non-Newtonian fluid past a wedge. An incompressible power-law fluid occupies the porous space. The arising mathematical problem has been solved by homotopy analysis method (HAM). Convergence of the derived solution is checked. The local skin friction coefficient and Nusselt number are also discussed.     

Parallelization and scalability of a spectral element channel flow solver for incompressible Navier–Stokes equations

Direct numerical simulation (DNS) of turbulent flows is widely recognized to demand fine spatial meshes, small timesteps, and very long runtimes to properly resolve the flow field. To overcome these limitations, most DNS is performed on supercomputing machines. With the rapid development of terascale (and, eventually, petascale) computing on thousands of processors, it has become imperative to consider the development of DNS algorithms and parallelization methods that are capable of fully exploiting these massively parallel machines. A highly parallelizable algorithm for the simulation of turbulent channel flow that allows for efficient scaling on several thousand processors is presented. A model that accurately predicts the performance of the algorithm is developed and compared with experimental data. The results demonstrate that the proposed numerical algorithm is capable of scaling well on petascale computing machines and thus will allow for the development and analysis of high Reynolds number channel flows. Copyright © 2007 John Wiley & Sons, Ltd.