改进虚拟边界算法在超声速流动问题求解中的应用

提出了一种改进的虚拟单元浸没边界法,并与一种高阶格式的有限差分算法相结合,运用于求解超声速复杂几何绕流问题.该算法的核心思想在于在固体边界的内部和外部分别施加满足边界关系的作用点,使得几何边界离散更加细化,起到了壁面附近网格局部加密的作用.采用源空间内流体点作为反距离插值算法的重构点,有效避免了插值点数目过少而与作用点相重合情况.通过对二维激波反射现象(马赫数为2.81)和三维超声速球体绕流问题(马赫数为1.2)的数值模拟,与实验结果对比表明,本文改进算法相对一般的虚拟边界法来说能显著提高数值精度,减小计算误差.计算结果揭示了球体绕流中剪切层、压缩波系和尾迹的相互作用导致自由剪切层失稳的机理.剪切层厚度和湍流雷诺脉动经历了线性增长、大幅度震荡和小幅度波动三个阶段,导致剪切层表面褶皱因子变化呈指数规律增长.其湍流结构表现出明显的各向异性,具体在流向雷诺正应力在湍流脉动中占主导地位,激波的压缩作用对不同方向雷诺正应力的影响存在空间迟滞效应.     

高超声速激波湍流边界层干扰直接数值模拟研究

高超声速激波与湍流边界层干扰会导致飞行器表面出现局部热流峰值,严重影响飞行器气动性能和飞行安全.针对高马赫数激波干扰问题,以往数值研究多采用雷诺平均方法,而在直接数值模拟方面的相关工作较为少见.开展高超声速激波与湍流边界层干扰的直接数值模拟研究,有助于进一步提升对其复杂流动机理认识和理解,同时也将为现有湍流模型和亚格子应力模型的改进提供理论依据.采用直接数值模拟方法对来流马赫数6.0,34?压缩拐角内激波与湍流边界层的干扰问题进行了研究.基于雷诺应力各向异性张量,分析了高超声速湍流边界层在压缩拐角内的演化特性.通过对湍动能输运方程的逐项分析,系统地研究了可压缩效应对湍动能及其输运的影响机制.采用动态模态分解方法,探讨了干扰流场的非定常运动历程.研究结果表明,随着湍流边界层往下游发展,近壁湍流的雷诺应力状态由两组元轴对称状态逐渐演化为两组元状态,外层区域则由轴对称膨胀趋近于各向同性.干扰流场内存在强内在压缩性效应(声效应),其对湍动能输运的影响主要体现在压力-膨胀项,而对膨胀-耗散项影响较小.高超声速下压缩拐角内的非定常运动仍存在以分离泡膨胀/收缩为特征的低频振荡特性,其物理机制与分离泡剪切层密切相关.     

高超声速激波湍流边界层干扰直接数值模拟研究

高超声速激波与湍流边界层干扰会导致飞行器表面出现局部热流峰值,严重影响飞行器气动性能和飞行安全. 针对高马赫数激波干扰问题,以往数值研究多采用雷诺平均方法,而在直接数值模拟方面的相关工作较为少见. 开展高超声速激波与湍流边界层干扰的直接数值模拟研究,有助于进一步提升对其复杂流动机理认识和理解,同时也将为现有湍流模型和亚格子应力模型的改进提供理论依据. 采用直接数值模拟方法对来流马赫数6.0,34°压缩拐角内激波与湍流边界层的干扰问题进行了研究. 基于雷诺应力各向异性张量,分析了高超声速湍流边界层在压缩拐角内的演化特性. 通过对湍动能输运方程的逐项分析,系统地研究了可压缩效应对湍动能及其输运的影响机制. 采用动态模态分解方法,探讨了干扰流场的非定常运动历程. 研究结果表明,随着湍流边界层往下游发展,近壁湍流的雷诺应力状态由两组元轴对称状态逐渐演化为两组元状态,外层区域则由轴对称膨胀趋近于各向同性. 干扰流场内存在强内在压缩性效应(声效应),其对湍动能输运的影响主要体现在压力--膨胀项,而对膨胀--耗散项影响较小. 高超声速下压缩拐角内的非定常运动仍存在以分离泡膨胀/收缩为特征的低频振荡特性,其物理机制与分离泡剪切层密切相关.      

超声速流动中非线性EASM湍流模式应用研究

针对超声速复杂流动区域精确模拟的需要,发展了基于k-ω可压缩修正形式的非线性显式代数雷诺应力模式(EASM),提高了该模式对超声速复杂流动的数值模拟精度。通过对二维超声速凹槽和三维双椭球的数值计算表明,与SA和SST常规线性涡黏性湍流模式比较,非线性的EASM模式对大分离以及剪切层流动结构的刻画能力更精细,对剪切层再附区的压力及摩擦系数分布模拟更加精确;EASM模式能够准确地模拟二次激波引起的压强和热流分布情况。     

超声速流动中非线性EASM湍流模式应用研究

针对超声速复杂流动区域精确模拟的需要,发展了基于k-ω可压缩修正形式的非线性显式代数雷诺应力模式（EASM）,提高了该模式对超声速复杂流动的数值模拟精度。通过对二维超声速凹槽和三维双椭球的数值计算表明,与SA和SST常规线性涡黏性湍流模式比较,非线性的EASM模式对大分离以及剪切层流动结构的刻画能力更精细,对剪切层再附区的压力及摩擦系数分布模拟更加精确;EASM模式能够准确地模拟二次激波引起的压强和热流分布情况。     

激波/湍流边界层干扰压力脉动特性数值研究

激波/湍流边界层干扰问题广泛存在于高速飞行器内外流动中, 激波干扰会导致局部流场出现强压力脉动, 严重影响飞行器气动性能和飞行安全. 为了考察干扰区内脉动压力的统计特性, 对来流马赫数2.25, 激波角33.2°的入射激波与平板湍流边界层相互作用问题进行了直接数值模拟研究. 在对计算结果进行细致验证的基础上, 分析比较了干扰区外层和物面脉动压力的典型统计特征, 如脉动强度、功率谱密度、两点相关和时空关联特性等, 着重探讨了两者的差异及其原因. 研究发现, 激波干扰对外层和物面压力脉动的影响差异显著. 分离区内脉动以低频特征为主, 随后再附区外层压力脉动的峰值频率往高频区偏移, 而物面压力脉动的低频能量仍相对较高. 两点相关结果表明, 外层和物面脉动压力的展向关联性均明显强于其流向, 前者积分尺度过激波急剧增长随后缓慢衰减, 而后者积分尺度整体上呈现逐步增大趋势. 此外, 时空关联分析结果指出, 脉动压力关联系数等值线仍符合经典的椭圆形分布, 干扰区下游压力脉动对流速度将减小, 外层对流速度仍明显高于物面.      

雷诺应力各向异性涡黏模型的层析TRPIV测量

利用层析TRPIV测量水洞中平板湍流边界层3D-3C速度场的高分辨率时间序列数据库. 提出了空间局部平均多尺度速度结构函数的新概念, 描述湍流多尺度涡结构的空间拉伸、压缩、剪切变形和旋转. 用空间局部平均多尺度速度结构函数对湍流脉动速度进行了空间多尺度分解. 用空间流向局部平均多尺度速度结构函数, 根据湍流多尺度涡结构在流向的拉伸和压缩物理特征, 提出了新的湍流相干结构条件采样方法, 检测并提取了层析TRPIV数据中相干结构“喷射”和“扫掠”事件中的脉动速度、平均速度变形率、雷诺应力等物理量的空间拓扑形态. 通过研究平均速度变形率各分量与雷诺应力各分量之间的空间相位差异,肯定了壁湍流相干结构雷诺应力各向异性复涡黏模型的合理性.      

各向同性湍流通过正激波的演化特征研究

激波与湍流相互作用(shock-turbulence interaction,STI)是空气动力学研究中的一个基础问题.基于格心有限差分法(cell-centered finite difference method,CCFDM)求解器Helios,采用五阶加权紧致非线性格式(weighted compact nonlinear scheme,WCNS)对各向同性湍流通过正激波的情形进行直接数值模拟(direct numerical simulation,DNS).对湍流相关物理量进行统计,分析结果表明,在湍流中波后的密度、温度和压力较无湍流情形下略小,而速度则略大,均在波后呈现短暂过冲然后缓慢向理论值逼近的变化趋势;波后流向雷诺应力突降随之快速增长又衰减,呈现非单调变化趋势,线性相互作用分析(linear interaction analysis,LIA)将其归结为波后能量从声模式转移为涡模式方式,与流向不同,横向雷诺应力突增后单调衰减,波后雷诺应力各向异性明显且随下游距离逐渐增强;波后湍动能突增后呈现非单调变化趋势;泰勒微尺度和Kolmogorov尺度过激波后均明显减小,说明波后湍流长度尺度变小,从而对波后网格的分辨率提出了更高的要求;密度、温度和压力过激波后脉动均方根均增加,密度和压力脉动强度减小,温度脉动强度增大.      

HLLE++格式在高马赫数空腔流动模拟中的应用

空腔流动存在剪切层运动、涡脱落与破裂,以及激波与激波、激波与剪切层、激波与膨胀波和激波/涡/剪切层相互干扰等现象,流动非常复杂,特别是高马赫数(M>2)时,剪切层和激波更强,激波与激波干扰更严重,对数值格式的要求更高,既需要格式耗散小,对分离涡等有很高的模拟精度,又需要格式在激波附近具有较大的耗散,可以很好地捕捉激波,防止非物理解的出现。Roe和HLLC等近似Riemann解格式在高马赫数强激波处可能会出现红玉现象,而HLLE++格式大大改善了这种缺陷,在捕捉高超声速激波时避免了红玉现象的发生,同时还保持在光滑区域的低数值耗散特性。本文在结构网格下HLLE++格式的基础上,通过改进激波探测的求解,建立了基于非结构混合网格的HLLE++计算方法,通过无粘斜坡算例,验证了HLLE++格式模拟高马赫数流动的能力,并应用于高马赫数空腔流动的数值模拟,开展了网格和湍流模型影响研究,验证了方法模拟高马赫数空腔流动的可靠性和有效性。     

各向同性湍流通过正激波的演化特征研究

激波与湍流相互作用(shock-turbulence interaction,STI)是空气动力学研究中的一个基础问题.基于格心有限差分法(cell-centered finite difference method,CCFDM)求解器Helios,采用五阶加权紧致非线性格式(weighted compact nonlinear scheme,WCNS)对各向同性湍流通过正激波的情形进行直接数值模拟(direct numerical simulation,DNS).对湍流相关物理量进行统计,分析结果表明,在湍流中波后的密度、温度和压力较无湍流情形下略小,而速度则略大,均在波后呈现短暂过冲然后缓慢向理论值逼近的变化趋势;波后流向雷诺应力突降随之快速增长又衰减,呈现非单调变化趋势,线性相互作用分析(linear interaction analysis,LIA)将其归结为波后能量从声模式转移为涡模式方式,与流向不同,横向雷诺应力突增后单调衰减,波后雷诺应力各向异性明显且随下游距离逐渐增强;波后湍动能突增后呈现非单调变化趋势;泰勒微尺度和Kolmogorov尺度过激波后均明显减小,说明波后湍流长度尺度变小,从而对波后网格的分辨率提出了更高的要求;密度、温度和压力过激波后脉动均方根均增加,密度和压力脉动强度减小,温度脉动强度增大.     

Temporal and spatial transients in turbulent boundary layer flow over an oscillating wall

Direct numerical simulations have been performed to study the effect of an oscillating segment of the wall on a turbulent boundary layer flow. Two different oscillation amplitudes with equal oscillation period have been used, which allows a direct comparison between a relatively weak and strong forcing of the flow. The weaker forcing results in 18% drag reduction while the stronger forcing, with twice the amplitude, yields 29% drag reduction. The downstream development of the drag reduction is compared with earlier simulations and experiments. In addition, a simulation with identical oscillation parameters as in previous numerical and experimental investigations allows for an estimation of the effect of the Reynolds number on the drag reduction.Reductions in the Reynolds stresses and the important role that the edge of the Stokes layer has is explained.An estimation of the idealized power consumption shows that a positive energy budget is only possible for the weaker wall velocity case.Spatial and temporal transients are investigated and a transformation between spatial and temporal coordinates via a convection velocity is shown to facilitate a comparison between the two transients in a consistent manner. The streamwise shear exhibits a similar monotonic behavior in the spatial and temporal transients, while the non-monotinic temporal transient of the longitudinal Reynolds stress has no counterpart in the spatial development. Furthermore, the evolution in time of the spanwise Reynolds stress is very similar to previously reported channel flow data.The instantaneous spanwise velocity profile (only averaged in the homogeneous spanwise direction) will for the first time be presented from a boundary layer over an oscillating wall, and comparisons with the analytical solution to the laminar Navier–Stokes equations show very good agreement.     

An experimental study of the dynamic characteristics in boundary layer in the flow past a two-dimensional circular cylinder at subcritical reynolds numbers

An experimental study of the dynamic characteristics of flow past a two-dimensional circular cylinder is described. The fluctuationsoof wall shear stress, surface-pressure and velocity of the flow are measured with hot-film, hot-wire and pressure transducer. The frequency feature of fluctuations of wall shear stress is given. The cross-correlation functions of these fluctuations at any two points are calculated. The experimental results reveal that there is an overall syncronous fluctuation, at the shedding frequency, in boundary layer in the flow past a two-dimensional circular cylinder at subcritical Reynolds number.     

A ghost fluid Lattice Boltzmann method for complex geometries

A ghost fluid Lattice Boltzmann method (GF‐LBM) is developed in this study to represent complex boundaries in Lattice Boltzmann simulations of fluid flows. Velocity and density values at the ghost points are extrapolated from the fluid interior and domain boundary via obtaining image points along the boundary normal inside the fluid domain. A general bilinear interpolation algorithm is used to obtain values at image points which are then extrapolated to ghost nodes thus satisfying hydrodynamic boundary conditions. The method ensures no‐penetration and no‐slip conditions at the boundaries. Equilibrium distribution functions at the ghost points are computed using the extrapolated values of the hydrodynamic variables, while non‐equilibrium distribution functions are extrapolated from the interior nodes. The method developed is general, and is capable of prescribing Dirichlet as well as Neumann boundary conditions for pressure and velocity. Consistency and second‐order accuracy of the method are established by running three test problems including cylindrical Couette flow, flow between eccentric rotating cylinders and flow over a cylinder in a confined channel. Copyright © 2011 John Wiley & Sons, Ltd.     

High-order ghost-point immersed boundary method for viscous compressible flows based on summation-by-parts operators

A high-order immersed boundary method is devised for the compressible Navier-Stokes equations by employing high-order summation-by-parts difference operators. The immersed boundaries are treated as sharp interfaces by enforcing the solid wall boundary conditions via flow variables at ghost points. Two different interpolation schemes are tested to compute values at the ghost points and a hybrid treatment is used. The first method provides the bilinearly interpolated flow variables at the image points of the corresponding ghost points and the second method applies the boundary condition at the immersed boundary by using the weighted least squares method with high-order polynomials. The approach is verified and validated for compressible flow past a circular cylinder at moderate Reynolds numbers. The tonal sound generated by vortex shedding from a circular cylinder is also investigated. In order to demonstrate the capability of the solver to handle complex geometries in practical cases, flow in a cross-section of a human upper airway is simulated.     

Vortex reynolds number in turbulent boundary layers

The effects of vortex Reynolds number on the statistics of turbulence in a turbulent boundary layer have been investigated. Vortex Reynolds number is defined as the ratio of circulation around the vortex structure to the fluid viscosity. The vortex structure of the outer region was modeled and a full numerical simulation was then conducted using a high-order spectral method. A unit domain of the outer region of a turbulent boundary layer was assumed to be composed of essentially three elements: a wall, a Blasius mean shear, and an elliptic vortex inclined at 45° to the flow direction. The laminar base-flow Reynolds number is roughly in the same range as that of a turbulent boundary layer based on eddy viscosity, and the vortex-core diameter based on the boundary-layer thickness is nearly the same as the maximum mixing length in a turbulent boundary layer. The computational box size, namely, 500, 150, and 250 wall units in the streamwise, surface-normal, and spanwise directions, respectively, is approximately the same as the measured quasi-periodic spacings of the near-wall turbulence-producing events in a turbulent boundary layer. The effects of vortex Reynolds number and the signs of the circulation on the moments of turbulence were examined. The signs mimic the ejection and sweep types of organized motions of a turbulent boundary layer. A vortex Reynolds number of 200 describes the turbulence moments in the outer layer reasonably well.     

Numerical prediction of locally forced turbulent boundary layer

An unsteady numerical simulation was performed to analyze flow structure behind a local suction/blowing in a flat-plate turbulent boundary layer. The local forcing was given to the boundary layer flow by means of a sinusoidally oscillating jet. A version of the unsteady k––f_μ model [Fluid Dyn. Res. 26 (6) (2000) 421] was employed. The Reynolds number based on the momentum thickness was about Re_θ=1700. The forcing frequency was varied in the range 0.011f⁺0.044 with a fixed forcing amplitude A_o=0.4. The predicted results were compared and validated with the experimental data. It was shown that the unsteady locally forced boundary layer flow is predicted well by the k––f_μ model. The time-dependent numerical flow visualizations were demonstrated during one period of the local forcing. The effect of the pitch angle of local forcing on the reduction of skin friction was examined.     

Effect of local forcing on a turbulent boundary layer

An experimental study is performed to analyze flow structures behind local suction and blowing in a flat-plate turbulent boundary layer. The local forcing is given to the boundary layer flow by means of a sinusoidally oscillating jet issuing from a thin spanwise slot at the wall. The Reynolds number based on the momentum thickness is about Re _θ =1700. The effects of local forcing are scrutinized by altering the forcing frequency (0.011 ≤ f ⁺≤ 0.044). The forcing amplitude is fixed at A ₀=0.4. It is found that a small local forcing reduces the skin friction and the skin friction reduction increases with the forcing frequency. A phase-averaging technique is employed to capture the large-scale vortex evolution. An organized spanwise vortical structure is generated by the local forcing. The cross-sectional area of vortex and the time fraction of vortex are examined by changing the forcing frequency. An investigation of the random fluctuation components reveals that turbulent energy is concentrated near the center of vortical structures. Received: 17 March 2000/Accepted: 3 April 2001     

FLOW STRUCTURE IN THE TURBULENT BOUNDARY LAYER OVER DIRECTIONAL RIBLETS SURFACES

本文采用时间解析的二维粒子图像测速技术,对零压力梯度光滑以及汇聚和发散沟槽表面平板湍流边界层统计特性和流动结构进行了研究.结果表明在垂直于汇聚和发散沟槽表面的对称平面内,相对于光滑壁面,发散沟槽壁面使当地边界层厚度、壁面摩擦阻力、湍流脉动、雷诺应力等明显减小;而汇聚沟槽壁面对湍流边界层特性和流动结构的影响正好相反,汇聚沟槽使壁面流体有远离壁面向上运动的趋势,因而导致边界层厚度增加了约43%;同时,在汇聚沟槽表面情况下流向大尺度相干结构更容易形成,这对减阻是不利的.此外,顺向涡数量在湍流边界层的对数区均存在一个极大值,发散沟槽表面所对应的极大值位置更靠近沟槽壁面,而在汇聚沟槽表面则有远离壁面的趋势,由顺向涡诱导产生的较强的喷射和扫掠运动会在湍流边界层中产生较强的剪切作用,顺向涡数量的减少是发散沟槽壁面当地摩擦阻力降低的主要原因.     

A comparative study of lattice Boltzmann methods using bounce‐back schemes and immersed boundary ones for flow acoustic problems

In order to find applicable treatments of moving boundary conditions based on the lattice Boltzmann method in flow acoustic problems, three bounce‐back (BB) methods and four kinds of immersed boundary (IB) methods are compared. We focused on fluid–solid boundary conditions for flow acoustic problems especially the simulations of sound waves from moving boundaries. BB methods include link bounce‐back, interpolation bounce‐back and unified interpolation bounce‐back methods. Five IB methods are explicit and implicit direct‐forcing (Explicit‐IB and Implicit‐IB), two kinds of partially saturated computational methods and ghost fluid method. In order to reduce the spurious pressure generated by the fresh grid node changing from solid domain to fluid domain for BB methods and sharp IB methods, we proposed two new kinds of treatments and compared them with two existing ones. Simulations of the benchmark problems prove that the local evolutionary iteration (LI) is the best one in treatments of the fresh nodes. In addition, for standing boundary problems, although BB methods have a little higher accuracy, all the methods have similar accuracy. However, for moving boundary problems, IB methods are more appropriate than BB methods, because IB methods' smooth interpolation of pressure eld produces less disturbing spurious pressure waves. With improved treatments of fresh nodes, BB methods are also acceptable for moving boundary acoustic problems. In comparative tests in respective type, unified interpolation bounce‐back with LI, Implicit‐IB, and ghost fluid with LI are the best choices. Copyright © 2013 John Wiley & Sons, Ltd.     

Control of a three-dimensional turbulent shear layer by means of oblique vortices

The effect of local forcing on the separated, three-dimensional shear layer downstream of a backward-facing step is investigated by means of large-eddy simulation for a Reynolds number based on the step height of 10,700. The step edge is either oriented normal to the approaching turbulent boundary layer or swept at an angle of \(40^\circ \). Oblique vortices with different orientation and spacing are generated by wavelike suction and blowing of fluid through an edge parallel slot. The vortices exhibit a complex three-dimensional structure, but they can be characterized by a wavevector in a horizontal section plane. In order to determine the step-normal component of the wavevector, a method is developed based on phase averages. The dependence of the wavevector on the forcing parameters can be described in terms of a dispersion relation, the structure of which indicates that the disturbances are mainly convected through the fluid. The introduced vortices reduce the size of the recirculation region by up to 38%. In both the planar and the swept case, the most efficient of the studied forcings consists of vortices which propagate in a direction that deviates by more than \(50^\circ \) from the step normal. These vortices exhibit a spacing in the order of 2.5 step heights. The upstream shift of the reattachment line can be explained by increased mixing and momentum transport inside the shear layer which is reflected in high levels of the Reynolds shear stress \(-\rho \overline{u'v'}\). The position of the maximum of the coherent shear stress is found to depend linearly on the wavelength, similar to two-dimensional free shear layers.