Direct Numerical Simulation of Turbulent Flow over a Rectangular Trailing Edge

This paper describes a direct numerical simulation (DNS) study of turbulent flow over a rectangular trailing edge at a Reynolds number of 1000, based on the freestream quantities and the trailing edge thickness h; the incoming boundary layer displacement thickness δ^* is approximately equal to h. The time-dependent inflow boundary condition is provided by a separate turbulent boundary layer simulation which is in good agreement with existing computational and experimental data. The turbulent trailing edge flow simulation is carried out using a parallel multi-block code based on finite difference methods and using a multi-grid Poisson solver. The turbulent flow in the near-wake region of the trailing edge has been studied first for the effects of domain size and grid resolution. Then two simulations with a total of 256 × 512 × 64 (∼ 8.4×10⁶) and 512 × 1024 × 128 (∼ 6.7×10⁷) grid points in the computational domain are carried out to investigate the key flow features. Visualization of the instantaneous flow field is used to investigate the complex fluid dynamics taking place in the near-wake region; of particular importance is the interaction between the large-scale spanwise, or Kármán, vortices and the small-scale quasi-streamwise vortices contained within the inflow boundary layer. Comparisons of turbulence statistics including the mean flow quantities are presented, as well as the pressure distributions over the trailing edge. A spectral analysis applied to the force coefficient in the wall normal direction shows that the main shedding frequency is characterized by a Strouhal number based on h of approximately 0.118. Finally, the turbulence kinetic energy budget is analysed. Received 4 March 1999 and accepted 27 October 2000     

Influence of the Trailing Edge of a Cavity on the Flow Fluctuation Intensity

Unsteady supersonic turbulent gas flow over a plane cavity is simulated numerically. The solution is determined by means of the joint integration of the Reynolds equations and the two-parameter turbulence model using the law of the wall. The calculation results obtained for various cavity trailing edge contours are considered. The strong effect of the geometry of the trailing edge on the flow parameter fluctuation intensity is demonstrated. A surface shape which makes it possible considerably to reduce these oscillations is determined.     

基于动网格技术的柔性后缘自适应机翼气动特性分析

研究了带柔性后缘的可变弯度自适应机翼在自适应变弯度过程中的气动特性.自适应变弯度过程中的气动力计算采用了基于弹簧理论的非结构动网格技术,求解NS方程时采用有限体积的二阶迎风格式离散,时间推进为隐格式双时间推进方法.通过计算柔性后缘机翼的升力特性、阻力特性及升阻比特性,并与带刚性后缘机翼的气动特性进行比较,发现柔性后缘机翼在后缘偏转时,其最大升阻比对应的迎角随着偏转角增大而降低.在中等迎角及接近失速迎角情况下,柔性后缘机翼升力系数明显优于刚性后缘机翼,并且其升力线变化较为平缓,有效迎角范围更大.     

Mathematical Modeling of Time-Dependent Aerodynamic Loads on an Airfoil with Dynamic Deflection of a Control on the Trailing Edge

The linear problem of the time-dependent inviscid flow past a thin symmetric airfoil with a control on its trailing edge deflected in accordance with an arbitrary law is considered. The aerodynamic loads on the airfoil are calculated. The intensity of the vortex wake shed from the airfoil is determined by numerically solving a Volterra integral equation of the first kind. Questions of the mathematical modeling of the time-dependent aerodynamic loads in a form convenient for the joint solution of the problems of aerodynamics and flight dynamics are also considered. The results of the modeling are compared with the numerical solutions obtained.__________Translated from Izvestiya Rossiiskoi Academii Nauk, Mekhanika Zhidkosti i Gaza, No. 3, 2005, pp. 157–169.Original Russian Text Copyright © 2005 by Khrabrov.     

Structure of Averaged Flow Driven by a Vibrating Body with a Large-Curvature Edge

The averaged viscous incompressible fluid flow driven by a vibrating body with a large-curvature edge is investigated experimentally and numerically. The case of an axisymmetric body immersed in fluid and performing translational vibrations along its axis is considered. Experiments carried out on fluids of various viscosity over a wide vibration frequency and amplitude range and direct numerical calculations based on the complete time-dependent equations of viscous fluid dynamics show that the global structure of the averaged flow significantly depends on the relation between the curvature radius of the body edge and the viscous skin-layer thickness. Different averaged flow regimes are detected and the flow restructuring process is investigated as a function of the vibration amplitude and frequency.     

Asymptotic Behavior of Solutions to a Model for the Flow of a Reacting Fluid

We give a complete analysis of solutions of a model for the flow of a multispecies reacting fluid occupying a thin cylinder whose walls may be semipermeable with respect to some or all of the chemical species. We prove the global existence of solutions and establish a number of time-independent a priori bounds sufficient to determine the corresponding time-asymptotic steady-state. We then derive necessary conditions and sufficient conditions ensuring that this steady-state reflects complete combustion, that is, that at least one of the reactant species is depleted.     

刃型位错理论模型的实验验证

刃型位错芯周围变形场的实验测量是多年来非常困难的研究任务,它导致目前有多种位错理论模型并存。为了检验刃型位错理论模型的适用性,使用透射电子显微镜直接观察并获得了多晶金中刃型位错的高分辨电子显微图像,并采用几何相位分析方法测量了刃型位错周围的位移场和应变场。将实验测量结果与线弹性理论位错模型、Peierls-Nabarro位错模型及Fore-man(a=4)位错模型进行了比较。结果表明,三种位错理论模型在远离位错芯的区域都能描述刃型位错变形场,但在距离位错芯较近的区域,Peierls-Nabarro模型是最适当的位错理论模型。     

Numerical Approaches to Optimal Control of a Model Equation for Shear Flow Instabilities

We investigate two different discretization approaches of a model optimal-control problem, chosen to be relevant for control of instabilities in shear flows. In the first method, a fully discrete approach has been used, together with a finite-element spatial discretization, to obtain the objective function gradient in terms of a discretely-derived adjoint equation. In the second method, Chebyshev collocation is used for spatial discretization, and the gradient is approximated by discretizing the continuously-derived adjoint equation. The discrete approach always results in a faster convergence of the conjugate-gradient optimization algorithm. Due to the shear in the convective velocity, a low diffusivity in the problem complicates the structure of the computed optimal control, resulting in particularly noticeable differences in convergence rate between the methods. When the diffusivity is higher, the control becomes less complicated, and the difference in convergence rate reduces. The use of approximate gradients results in a higher sensitivity to the degrees of freedom in time. When the system contains a strong instability, it only takes a few iteration to obtain an effective control for both methods,even if there are differences in the formal convergence rate. This indicates that it is possible to use the approximative gradients of the objective function in cases where the control problem mainly consists of controlling strong instabilities. This revised version was published online in July 2006 with corrections to the Cover Date.     

俯仰振荡三角翼前缘涡破碎的流动显示

前缘后掠角为６５°和７０°的两个平板三角翼作俯仰振荡运动，前缘涡破碎的流动显示实验研究在南京航空航天大学１米低速风洞中进行。俯仰振荡运动的攻角范围为０°～６０°，折合频率为０．０３和０．０６。采用四氯化钛发烟技术显示前缘涡核轨迹及涡破碎位置。流动显示图形采用相位锁定照相记录。实验结果表明大幅俯仰振荡三角翼的动态涡破碎的弦向位置明显滞后于相应攻角下的静态位置，此滞后量随折合频率增加而增大。本文也根据测得的涡破碎位置随攻角变化曲线讨论了涡破碎位置的传播速度     

LES of Jets in Cross Flow and Its Application to a Gas Turbine Burner

LES computations of jets in cross flow (JICF) were performed. Experimental investigations reported in literature are reproduced with good agreement concerning the momentum field and the mixing of a passive scalar. The results validate the ability of the present LES approach to compute fuel injection of the type JICF. LES computations of fuel injection in an industrial gas turbine burner are presented. This revised version was published online in July 2006 with corrections to the Cover Date.     

Flow around a NACA0018 airfoil with a cavity and its dynamical response to acoustic forcing

Trapping of vortices in a cavity has been explored in recent years as a drag reduction measure for thick airfoils. If, however, trapping fails, then oscillation of the cavity flow may couple with elastic vibration modes of the airfoil. To examine this scenario, the effect of small amplitude vertical motion on the oscillation of the shear layer above the cavity is studied by acoustic forcing simulating a vertical translation of a modified NACA0018 profile. At low Reynolds numbers based on the chord (O(10⁴)), natural instability modes of this shear layer are observed for Strouhal numbers based on the cavity width of order unity. Acoustic forcing sufficiently close to the natural instability frequency induces a strong non-linear response due to lock-in of the shear layer. At higher Reynolds numbers (above 10⁵) for Strouhal number 0.6 or lower, no natural instabilities of the shear layer and only a linear response to forcing were observed. The dynamical pressure difference across the airfoil is then dominated by added mass effects, as was confirmed by numerical simulations.     

Interaction of Two-Dimensional Trailing Vortex Pair with a Shear Layer

The basic laws governing the interaction of a two-dimensional vortex pair with a shear layer of constant thickness are considered. The main idea of the study is to develop and adapt a simplified representation of a hydrodynamic flow based on a point-vortex model simulating the actual interaction of full-scale vortex patterns over the ground surface. It is shown that vortices with vorticity opposite in sign to the shear layer may stop or even ricochet from this layer, while the other vortex may penetrate through the layer. Numerical results are presented as plots and analyzed     

可压缩气体定常非Darcy渗流的流动分析及其应用

气体通过多孔介质的非Darcy流动具有广泛的工程应用背景，因此对多孔介质中的气体非Darcy流动进行流动分析有着非常重要的意义。然而，在通常的研究中，一般都将气体考虑为不可压缩流体，很少考虑气体的压缩性。对于高压气体以较高的速度通过多孔介质的情况，在进行流动分析时，不仅要考虑非Darcy效应，还必须考虑气体的压缩性。在本文中，对可压缩气体通过多孔介质的定常非Darcy流动进行了一维流动分析，得出了多孔介质中气体的压力分布和速度分布。还进一步给出了在高压差和高流速情况下，测定多孔介质材料渗透率和惯性系数的方法，以及多孔介质材料前后压力差与材料厚度的比Δp/L和材料有气流速度u1的解析关系。     

Vortex in a Supersonic Flow and its Influence on Blunt Body Flow and Heat Transfer

The dissipation of a tip vortex generated by a rectangular wing and the stagnation pressure and temperature distributions within the vortex are experimentally investigated. The interaction of the vortex with the bow shock ahead of a sphere and the heat flux distribution over the spherical surface are studied. The experiments were carried out at the Mach number M=3 and the unit Reynolds numbers Re₁=1.1·10⁷ and 3.7·10⁷ 1/m.     

Generalization of a Prandtl Slope Flow Model with a Heavy Admixture

A Prandtl slope flow model is generalized for the case with a homogeneous stationary source of a heavy admixture that significantly changes the medium density. A stationary analytical solution for a velocity of arising flows, temperature deviations, and admixture distribution is obtained. The model describes, for example, some special features of the dynamics of a ground snowstorm above a slope surface.     

A New Model and its Application to Investigate Transpiration Cooling with Liquid Coolant Phase Change

This paper presents a new mathematical model, semi-mixing model (SMM), to describe transpiration cooling with coolant phase change from liquid into vapor through two-phase process. The local heat exchange of fluid-solid within pores is considered in this model, and therefore it is closer to real transpiration cooling condition. The differences from the separated phase model and two-phase mixture model are that SMM can overcome the trouble of tracking phase change interface and avoid the inveracious numerical phenomenon, i.e., a thermal insulating layer occurs within the porous matrix. Using SMM, the corresponding numerical method is realized to simulate the processes of coolant moving, absorbing heat and evaporating within porous matrix. To validate SMM and the numerical strategy, an experiment is conducted. Using the validated SMM and numerical strategy, the effects of two-dimensional coolant injection rate and two-dimensional heat flux on transpiration cooling characteristics are simulated and analyzed. The simulations and analysis discover several interesting and valuable phenomena.     

Synthetic Turbulence Generators for RANS-LES Interfaces in Zonal Simulations of Aerodynamic and Aeroacoustic Problems

The paper presents the detailed formulation and validation results of simple and robust procedures for the generation of synthetic turbulence aimed at providing artificial turbulent content at the RANS-to-LES interface within a zonal Wall Modelled LES of attached and mildly separated wall-bounded flows. There are two versions of the procedure. The aerodynamic version amounts to a minor modification of a synthetic turbulence generator developed by the authors previously, but the acoustically adapted version is new and includes an internal damping layer, where the pressure field is computed by “weighting” of the instantaneous pressure fields from LES and RANS. This is motivated by the need to avoid creating spurious noise as part of the turbulence generation. In terms of pure aerodynamics, the validation includes canonical shear flows (developed channel flow, zero pressure gradient boundary layer, and plane mixing layer), as well as a more complex flow over the wall-mounted hump with non-fixed separation and reattachment, with emphasis on a rapid conversion from modeled to resolved Reynolds stresses. The aeroacoustic applications include the flow past a trailing edge and over a two-element airfoil configuration. In all cases the methodology ensures a very acceptable accuracy for the mean flow, turbulent statistics and, also, the near- and far-field noise.