Comparison of three large-eddy simulations of shock-induced turbulent separation bubbles

Three different large-eddy simulation investigations of the interaction between an impinging oblique shock and a supersonic turbulent boundary layer are presented. All simulations made use of the same inflow technique, specifically aimed at avoiding possible low-frequency interferences with the shock/boundary-layer interaction system. All simulations were run on relatively wide computational domains and integrated over times greater than twenty five times the period of the most commonly reported low-frequency shock-oscillation, making comparisons at both time-averaged and low-frequency-dynamic levels possible. The results confirm previous experimental results which suggested a simple linear relation between the interaction length and the oblique-shock strength if scaled using the boundary-layer thickness and wall-shear stress. All the tested cases show evidences of significant low-frequency shock motions. At the wall, energetic low-frequency pressure fluctuations are observed, mainly in the initial part of interaction.     

Stability and modal analysis of shock/boundary layer interactions

The dynamics of oblique shock wave/turbulent boundary layer interactions is analyzed by mining a large-eddy simulation (LES) database for various strengths of the incoming shock. The flow dynamics is first analyzed by means of dynamic mode decomposition (DMD), which highlights the simultaneous occurrence of two types of flow modes, namely a low-frequency type associated with breathing motion of the separation bubble, accompanied by flapping motion of the reflected shock, and a high-frequency type associated with the propagation of instability waves past the interaction zone. Global linear stability analysis performed on the mean LES flow fields yields a single unstable zero-frequency mode, plus a variety of marginally stable low-frequency modes whose stability margin decreases with the strength of the interaction. The least stable linear modes are grouped into two classes, one of which bears striking resemblance to the breathing mode recovered from DMD and another class associated with revolving motion within the separation bubble. The results of the modal and linear stability analysis support the notion that low-frequency dynamics is intrinsic to the interaction zone, but some continuous forcing from the upstream boundary layer may be required to keep the system near a limit cycle. This can be modeled as a weakly damped oscillator with forcing, as in the early empirical model by Plotkin (AIAA J 13:1036–1040, 1975).     

激波与转捩边界层干扰非定常特性数值分析

激波与边界层干扰的非定常问题是高速飞行器气动设计中基础研究内容之一.以往研究主要针对层流和湍流干扰,在分离激波低频振荡及其内在机理方面存在着上游机制和下游机制两类截然不同的理论解释.分析激波与转捩边界层干扰下非定常运动现象有助于进一步加深理解边界层状态以及分离泡结构对低频振荡特性的影响规律,为揭示其产生机理指出新的方向.采用直接数值模拟方法对来流马赫数2.9,24?压缩拐角内激波与转捩边界层干扰下激波的非定常运动特性进行了数值分析.通过在拐角上游平板特定的流向位置添加吹吸扰动激发流动转捩,使得进入拐角的边界层处于转捩初期阶段.在验证了计算程序可靠性的基础上,详细分析了转捩干扰下激波运动的间歇性和振荡特征,着重研究了分离泡展向三维结构对激波振荡特性的影响规律,最后还初步探索了转捩干扰下激波低频振荡产生的物理机制.研究结果表明:分离激波的非定常运动仍存在强间歇性和低频振荡特征,其时间尺度约为上游无干扰区内脉动信号特征尺度的10倍量级;分离泡展向三维结构不会对分离激波的低频振荡特征产生实质影响.依据瞬态脉动流场的低通滤波结果,转捩干扰下激波低频振荡的诱因来源于拐角干扰区下游,与流场中分离泡的收缩/膨胀运动存在一定的关联.     

激波和湍流相互作用的数值模拟

本文综述了关于激波和湍流相互作用数值模拟的近期研究进展, 主要包括激波和均匀各向同性湍流、激波和湍流边界层、激波和射流以及激波和尾迹的相互作用. 激波和湍流相互作用特性受到诸多因素的影响,如激波的强度、位置、形状和流动边界以及来流的湍流状态和可压缩性等. 激波和湍流的相互作用会引起流场结构、激波特性和湍流统计特性的显著变化. 最后简要讨论了激波和湍流相互作用数值研究需要关注的一些问题.      

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.      

Correlation study in shock wave�Cturbulent boundary layer interaction

Shock wave–turbulent boundary layer interaction is a critical problem in aircraft design. Therefore, a thorough understanding of the processes occurring in such flows is necessary. The most important task is to study the unsteady phenomena, in particular, the low-frequency ones, for this interaction. An experimental study of separated flow has been performed in the zone of interaction of the incident oblique shock wave with a turbulent boundary layer at Mach 2. Two-point correlation data in the separation zone and the upstream flow were obtained and showed that low-frequency oscillations of the reflected shock waves are related to pulsations in the inflow turbulent boundary layer.     

Computational analysis of impinging shock-wave boundary layer interaction under conditions of incipient separation

The interaction of an oblique shock wave with a turbulent boundary layer under conditions of incipient separation is analyzed by means of large-eddy simulation (LES) and Reynolds-averaged Navier–Stokes (RANS) turbulence models, with the objective to explore their predictive capabilities, in particular with respect to the unsteady features of the interaction. Consistent with earlier direct numerical simulations, we have found that the flow dynamics in the interaction zone is characterized by strong intermittency associated with the formation of scattered spots of flow reversal near the nominal position of the reflected shock. Comparison with experimental results (at much larger Reynolds number) show that the qualitative features of the interaction are predicted reasonably well by both LES and RANS models. RANS models supplemented with a semi-empirical closure are also found to provide reasonable estimate of the fluctuating pressure loads at the wall.     

Temporal development of turbulent boundary layers with embedded streamwise vortices

The interaction of streamwise vortices with turbulent boundary layer has been investigated using large-eddy simulation. The initial conditions are a pair of counterrotating Oseen vortices with flow between them directed toward the wall (common-flow-down), superimposed on various instantaneous realizations of a turbulent boundary layer. The time development of the vortices and their interaction with the boundary layer are studied by integrating the filtered Navier-Stokes equations in time. The most important effects of the vortices on the boundary layer are the thinning of the boundary layer between vortices (downwash region) and the thickening of the boundary layer in the upwash region. The vortices first move toward the wall as a result of the self-induced velocity, and then apart from each other because of the image vortices due to the solid wall. The Reynolds stress profiles highlight the highly three-dimensional structure of the turbulent boundary layer modified by the vortices. The presence of significant turbulent activity near the vortex center and in the upwash region suggests that localized instability mechanisms in addition to the convection of turbulent energy by the secondary flow are responsible for this effect. High levels of turbulent kinetic energy and secondary stresses in the vicinity of the vortex center are also observed. The numerical results show good agreement with experimental results.This work was supported by the Office of Naval Research under Grant N00014-89-J-1638. Computer time was supplied by the San Diego Supercomputing Center.     

Effects of Compressibility and Shock-Wave Interactions on Turbulent Shear Flows

Compressibility effects are present in many practical turbulent flows, ranging from shock-wave/boundary-layer interactions on the wings of aircraft operating in the transonic flight regime to supersonic and hypersonic engine intake flows. Besides shock wave interactions, compressible flows have additional dilatational effects and, due to the finite sound speed, pressure fluctuations are localized and modified relative to incompressible turbulent flows. Such changes can be highly significant, for example the growth rates of mixing layers and turbulent spots are reduced by factors of more than three at high Mach number. The present contribution contains a combination of review and original material. We first review some of the basic effects of compressibility on canonical turbulent flows and attempt to rationalise the differing effects of Mach number in different flows using a flow instability concept. We then turn our attention to shock-wave/boundary-layer interactions, reviewing recent progress for cases where strong interactions lead to separated flow zones and where a simplified spanwise-homogeneous problem is amenable to numerical simulation. This has led to improved understanding, in particular of the origin of low-frequency behaviour of the shock wave and shown how this is coupled to the separation bubble. Finally, we consider a class of problems including side walls that is becoming amenable to simulation. Direct effects of shock waves, due to their penetration into the outer part of the boundary layer, are observed, as well as indirect effects due to the high convective Mach number of the shock-induced separation zone. It is noted in particular how shock-induced turning of the detached shear layer results in strong localized damping of turbulence kinetic energy.     

Influence of a Large-Eddy-Breakup-Device on the Turbulent Interface of Boundary Layers

The effects of implementing a large-eddy break-up device (LEBU) in a turbulent boundary layer on the interaction with the boundary layer is investigated with particular emphasis on the turbulent/non-turbulent interface (TNTI). The simulation data is taken from a recent well-resolved large eddy simulation (Chin et al. Flow Turb. Combust. 98, 445–460 2017), where the LEBU was implemented at a wall-normal distance of 0.8 δ (local boundary layer thickness) from the wall. A comparison of the TNTI statistics is performed between a zero-pressure-gradient boundary layer with and without the LEBU. The LEBU is found to delay the growth of the turbulent boundary layer and also attenuates the fluctuations of the TNTI. The LEBU appears to alter the structure size at the interface, resulting in a narrower and shorter dominant structure (in an average sense). Further analysis beneath the TNTI using two-point correlations shows that the LEBU affects the turbulent structures in excess of 100 δ downstream of the LEBU.     

Vortex ring/viscous wall layer interaction model of the turbulence production process near walls

An experimental simulation of the interaction of vortex ring-like eddies with the sublayer of a turbulent boundary layer is investigated. An artificially generated vortex ring interacting with a Stokes' layer enables investigation of the interaction with reproducible initial conditions and in the absence of background turbulence. All of the observed features in the turbulent boundary layer production process such as the streaky structure, the pockets, the hairpin vortices, streak lift-up, oscillation, and breakup, have been observed to form. The model shows us that hairpin vortices can pinchoff and reconnect forming new vortex ring-like eddies. Interestingly, the model includes interactions that occur with low probability in the turbulent boundary layer, but which contribute significantly to transport, and may be the events most readily controllable.     

Reynolds stress and vorticity in turbulent wall flows

Experimental measurements in a boundary layer and a large-eddy simulation of plane channel flow have been used to study the dynamics of vorticity and mass transport in the nearwall region. It was found that Reynolds stress generation occurs in the vicinity of quasi-streamwise vortices, and that smoke particles tend to be ejected from the wall near these vortical structures.     

Computations of Interaction of an Incident Oblique Shock Wave with a Turbulent Boundary Layer on a Flat Plate

Results of numerical simulation of interaction between an oblique shock wave and a turbulent boundary layer formed in a supersonic (Mach number M =5) flow past a flat plate are presented. The computations are performed for three cases of interaction of different intensity, which result in an attached or detached flow. Numerical results are compared with experimental data. The effect of flow turbulence and shockwave unsteadiness on flow parameters is studied.     

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.      

Large-eddy simulation of wing tip vortex in the near field

Large-eddy simulation with filtered-structure-function subgrid model and implicit large-eddy simulation (ILES without explicit subgrid model) using high-order accuracy and high resolution compact scheme have been performed on the tip vortex shedding from a rectangular half-wing with a NACA 0012 airfoil section and a rounded wing tip. The formation of the tip vortex and its initial development in the boundary layer and the near field wake are investigated and analysed in detail. The physics, why the tip vortex, which is originally turbulent in the boundary layer, is re-laminarised and becomes stable and laminar rapidly after shedding in the near field, is revealed by this simulation. The computation also shows the widely used second-order subgrid model is not consistent to six-order compact scheme and would degenerate the six-order LES results to second-order. Therefore, high-order schemes, grid refinement and six-order subgrid models are critical to LES approaches.     

Shock-unsteadiness model applied to oblique shock wave/turbulent boundary-layer interaction

Reynolds-averaged Navier–Stokes prediction of shock wave/turbulent boundary layer interactions can yield significant error in terms of the size of the separation bubble. In many applications, this can alter the shock structure and the resulting surface properties. Shock-unsteadiness modification of Sinha et al. (Physics of Fluids, Vol.15, No.8, 2003) has shown potential in improving separation bubble prediction in compression corner flows. In this article, the modification is applied to oblique shock wave interacting with a turbulent boundary layer. The challenges involved in the implementation of the shock-unsteadiness correction in the presence of multiple shock waves and expansion fans are addressed in detail. The results show that a robust implementation of the model yields appreciable improvement over standard k–ω turbulence model predictions.     

Active control of flow separation over an airfoil using synthetic jets

We perform large-eddy simulation of turbulent flow separation over an airfoil and evaluate the effectiveness of synthetic jets as a separation control technique. The flow configuration consists of flow over an NACA 0015 airfoil at Reynolds number of 896,000 based on the airfoil chord length and freestream velocity. A small slot across the entire span connected to a cavity inside the airfoil is employed to produce oscillatory synthetic jets. Detailed flow structures inside the synthetic-jet actuator and the synthetic-jet/cross-flow interaction are simulated using an unstructured-grid finite-volume large-eddy simulation solver. Simulation results are compared with the 2005 experimental data of Gilarranz et al., and qualitative and quantitative agreements are obtained for both uncontrolled and controlled cases. As in the experiment, the present large-eddy simulation confirms that synthetic-jet actuation effectively delays the onset of flow separation and causes a significant increase in the lift coefficient. Modification of the blade boundary layer due to oscillatory blowing and suction and its role in separation control is discussed.     

Particle image velocimetry measurements of a shock wave/turbulent boundary layer interaction

Particle image velocimetry is used to investigate the interaction between an incident shock wave and a turbulent boundary layer at Mach 2.1. A particle response assessment establishes the fidelity of the tracer particles. The undisturbed boundary layer is characterized in detail. The mean velocity field of the interaction shows the incident and reflected shock wave pattern, as well as the boundary layer distortion. Significant reversed flow is measured instantaneously, although, on average no reversed flow is observed. The interaction instantaneously exhibits a multi-layered structure, namely, a high-velocity outer region and a low-velocity inner region. Flow turbulence shows the highest intensity in the region beneath the impingement of the incident shock wave. The turbulent fluctuations are found to be highly anisotropic, with the streamwise component dominating. A distinct streamwise-oriented region of relatively large kinematic Reynolds shear stress magnitude appears within the lower half of the redeveloping boundary layer. Boundary layer recovery towards initial equilibrium conditions appears to be a gradual process.     

Large-eddy simulation of a turbulent boundary layer with blowing

The modifications of a turbulent boundary layer induced by blowing through a porous plate were investigated using large-eddy simulation. The Reynolds number (based on the length of the plate) of the main flow was about 850000. Large-eddy simulations of such a boundary layer needs a turbulent inflow condition. After a review of available turbulent inflow, we describe in details the condition we developed, which consisted of recycling the velocity fluctuations. Then we show the necessity for this inflow to be non-stationary and to be three dimensional with respect to the mass conservation equation. If these properties are not achieved, we found that the velocity fluctuations do not grow as expected along the domain. Finally, the results of simulations of the boundary layer submitted to blowing are compared with experimental measurements. The good agreement obtained validate our turbulent inflow conditions and also the blowing model used. PACS 47.27.Eq, 47.27.Te, 44.20.+b     

Compressible Turbulence and Energetic Scales: What Is Known from Experiments in Supersonic Flows?

Some properties of large-scale structures in supersonic turbulent flows are examined through experiments. The large eddies considered here include energetic scales, which contribute predominantly to, say, turbulent energy and coherent structures. Different features are presented, such as the level of energy in supersonic free shear flows, the average size of energetic structures, and their characteristic timescales. It is shown that compressibility affects the level of velocity and the size of the energetic eddies, but in many common supersonic situations, the estimation of the timescales can be made from rules valid for solenoidal turbulence. Some implications for compressible turbulence modeling are suggested. Finally, the properties of coherent structures are considered in the case of mixing layers and in a separated shock/boundary layer interaction. Some features relative to the organization of the large eddies are given and the importance of the shock motion is discussed in relation to the shock/layer interaction. This revised version was published online in August 2006 with corrections to the Cover Date.