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.     

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.     

A comparison of data reduction techniques for the aeroacoustic analysis of flow over a blunt flat plate

A large eddy simulation of flow over a forward-facing plate is performed and the resulting database analyzed with respect to sound radiation. Aeroacoustic analysis motivates an initial data compression comprising eduction of the zeroth-order spanwise Fourier mode. The space–time structure of this component of the flow is then analyzed using POD and DMD in order to probe both the energetics and dynamics of the sound-producing flow skeleton. Both data processing techniques educe flapping and shedding modes and identify a nonlinear interaction between the two. POD shows the flapping mode to be energetically unimportant, while DMD highlights its dynamic importance. The difference mode—vortex shedding modulated by flapping of the separation bubble—is found to be the most acoustically important feature of the flow.     

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.     

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.      

Numerical simulation (DNS and LES) of manipulated turbulent boundary layer flow over a surface-mounted fence

Results from numerical simulations are presented for manipulated turbulent boundary layer flow over a surface-mounted fence, for a Reynolds number of Re_h=3000 (based on fence height, h , and maximum inflow velocity, U_∞ ). First, a reference data set was provided from a Direct Numerical Simulation (DNS) using 51.6 million grid points to resolve all the relevant spatial scales of the flow. A Large-Eddy Simulation (LES), using 1.67 million grid points, was validated with this reference solution and compared with experimental data for the same Reynolds number. Then, manipulated flow cases were investigated applying time-periodic forcing through a narrow slot upstream of the flow obstacle. High-frequency forcing, with Str₁=f₁h/U_∞=0.60 , leads to about 10% reduction of the mean re-attachment length. A much stronger reduction of about 36% could be achieved by low-frequency forcing with Str₂=f₂h/U_∞=0.08 . In the latter case, large-scale coherent structures are created between the location of the disturbance and the fence, they roll over the flow obstacle (nearly unaffected) and in rolling downstream they still grow in size until they fill out the entire height of the separation zone behind the fence. In agreement with corresponding experiments of Siller and Fernholz in 1997 for a higher Reynolds number ( Re_h=10500 ) the optimum forcing Strouhal number seems to be related to the low-frequency movement of the entire separation bubble and not to the instability mode of the separating shear layer.©2000 Éditions scientifiques et médicales Elsevier SAS     

Large-eddy simulation of low-frequency unsteadiness in a turbulent shock-induced separation bubble

The need for better understanding of the low-frequency unsteadiness observed in shock wave/turbulent boundary layer interactions has been driving research in this area for several decades. We present here a large-eddy simulation investigation of the interaction between an impinging oblique shock and a Mach 2.3 turbulent boundary layer. Contrary to past large-eddy simulation investigations on shock/turbulent boundary layer interactions, we have used an inflow technique which does not introduce any energetically significant low frequencies into the domain, hence avoiding possible interference with the shock/boundary layer interaction system. The large-eddy simulation has been run for much longer times than previous computational studies making a Fourier analysis of the low frequency possible. The broadband and energetic low-frequency component found in the interaction is in excellent agreement with the experimental findings. Furthermore, a linear stability analysis of the mean flow was performed and a stationary unstable global mode was found. The long-run large-eddy simulation data were analyzed and a phase change in the wall pressure fluctuations was related to the global-mode structure, leading to a possible driving mechanism for the observed low-frequency motions.      

Vortex dynamics mechanisms of separated boundary layer in a highly loaded low pressure turbine cascade

This paper investigates the vortex dynamics in the suction-side boundary layer on an aero-engine low pressure turbine blade at two different Reynolds numbers at which short and long laminar separation bubbles occur. Different vortical patterns are observed and investigated through large eddy simulation (LES). The results show that at the higher Reynolds number, streamwise streaks exist upstream of separation line. These streaks initiate spanwise undulation in the form of vortex tubes, which roll-up and shed from the shear layer due to the Kelvin–Helmholtz instability. The vortex tubes alternately pair together and eventually distort and break down to small-scale turbulence structures near the mean reattachment location and convect into a fully turbulent boundary layer. At the lower Reynolds number, streamwise streaks are strong and the separated flow is unable to reattach to the blade surface immediately after transition to turbulence. Therefore, bursting of short bubbles into long bubbles can occur, and vortex tubes have larger diameters and cover a part of the blade span. In this case vortex pairing does not occur and vortex shedding process is promoted mainly by flapping phenomenon. Moreover, the results of dynamic mode decomposition (DMD) analysis show a breathing motion as a source of unsteadiness in the separation location, which is accompanied by the flapping phenomenon.     

High-fidelity numerical simulation of the flow field around a NACA-0012 aerofoil from the laminar separation bubble to a full stall

In the present work, large eddy simulations of the flow field around a NACA-0012 aerofoil near stall conditions are performed at a Reynolds number of 5 × 10⁴, Mach number of 0.4, and at various angles of attack. The results show the following: at relatively low angles of attack, the bubble is present and intact; at moderate angles of attack, the laminar separation bubble bursts and generates a global low-frequency flow oscillation; and at relatively high angles of attack, the laminar separation bubble becomes an open bubble that leads the aerofoil into a full stall. Time histories of the aerodynamic coefficients showed that the low-frequency oscillation phenomenon and its associated physics are indeed captured in the simulations. The aerodynamic coefficients compared to previous and recent experimental data with acceptable accuracy. Spectral analysis identified a dominant low-frequency mode featuring the periodic separation and reattachment of the flow field. At angles of attack α ≤ 9.3°, the low-frequency mode featured bubble shedding rather than bubble bursting and reformation. The underlying mechanism behind the quasi-periodic self-sustained low-frequency flow oscillation is discussed in detail.     

Effects of free-stream turbulence on a transitional separated–reattached flow over a flat plate with a sharp leading edge

The transitional separated–reattached flow on a flat plate with a blunt leading edge under 2% free-stream turbulence (FST) is numerically simulated using the Large-eddy simulation (LES) approach. The Reynolds number based on the free-stream velocity and the plate thickness is 6500. A dynamic subgrid-scale model is employed and the LES results compare well with the available experimental data.It is well known that FST enhances shear-layer entrainment rates, reduces the mean reattachment distance, and causes early transition to turbulence leading to an early breakdown of the separated boundary layer. Many experimental studies have shown that different vortex shedding frequencies exist, specially the so called low-frequency flapping when there is a separation bubble but its mechanism is still not completely understood. The previous study by us without free-stream turbulence (NFST) did not show the existence of such a low-frequency flapping of the shear layer and it is not clear what the effects of FST will have on these shedding modes. Detailed analysis of the LES data has been presented in the present paper and the low-frequency flapping has not been detected in the current study.     

Investigation of the unsteadiness of a shock-reflection interaction with time-resolved particle image velocimetry

The spatio-temporal dynamics of an impinging shock/boundary layer interaction at Mach 2 and under incipient separation conditions, has been investigated experimentally by means of high-speed particle image velocimetry (PIV). The available PIV acquisition rate of up to 20 kHz permits a time-resolved characterization of the interaction. The dynamics of different flow regions—notably the separation region and the reflected shock—were quantified by means of temporal auto-correlation fields and pseudo-spectral analysis. The PIV data further enable to investigate the relationship between spatially extended flow features, such as shock position and bubble size, as well as the influence of the upstream boundary layer. The results confirm earlier studies that there is an important upstream effect on the present incipient interaction.     

Analysis of time-resolved PIV measurements of a confined turbulent jet using POD and Koopman modes

We present a comparative analysis of proper orthogonal decomposition (POD) and dynamic mode decomposition (DMD) computed from experimental data of a turbulent, quasi 2-D, confined jet with co-flow (Re?=?11,500, co-flow ratio inner-to-outer flow ≈2:1). The experimental data come from high-speed 2-D particle image velocimetry. The flow is fully turbulent, and it contains geometry-dependent large-scale coherent structures; thus, it provides an interesting benchmark case for the comparison between POD and DMD. In this work, we address issues related to snapshot selections (1), convergence (2) and the physical interpretation (3) of both POD and DMD modes. We found that the convergence of POD modes follows the criteria of statistical convergence of the autocovariance matrix. For the computation of DMD modes, we suggest a methodology based on two criteria: the analysis of the residuals to optimize the sampling parameters of the snapshots, and a time-shifting procedure that allows us to identify the spurious modes and retain the modes that consistently appear in the spectrum. These modes are found to be the ones with nearly null growth rate. We then present the selected modes, and we discuss the way POD and DMD rank them. POD analysis reveals that the most energetic spatial structures are related to the large-scale oscillation of the inner jet (flapping); from the temporal analysis emerges that these modes are associated with a low-frequency peak at St?=?0.02. At this frequency, DMD identifies a similar mode, where oblique structures from the walls appear together with the flapping mode. The second most energetic group of modes identified is associated with shear-layer oscillations, and to a recirculation zone near the inner jet. Temporal analysis of these modes shows that the flapping of the inner jet might be sustained by the recirculation. In the DMD, the shear-layer modes are separated from the recirculation modes. These have large amplitudes in the DMD. In conclusion, the DMD modes with eigenvalues on the unit circle are found to be similar to the most energetic POD modes, although differences appear due to the fact that DMD isolates structures associated with one frequency only.     

On the mechanism of unsteady shock oscillation in shock wave/turbulent boundary layer interactions

An experimental investigation into the mechanism of shock wave oscillation in compression ramp-generated shock wave/turbulent boundary layer interactions is presented. Particular emphasis is focused upon documenting the respective roles played by both burst-sweep events in the turbulent boundary layer immediately upstream of the interaction and the downstream separated shear layer upon unsteady shock front motion. Unlike the majority of compression ramp experiments which involve bulk separation and large-scale shock motion, consideration is given here to comparatively “weak” interactions in which the streamwise spatial excursion of the shock front is always less than one boundary layer thickness. In this manner any shock motion due to upstream burst-sweep events should be more apparent in relation to that oscillation associated with the separated region. A discrete Hilbert transform-based conditional sampling technique is used to obtain wall pressure measurements conditioned to burst-sweep events. The conditional sampling technique forms the basis by which the instantaneous shock motion is conditioned to the occurrence of upstream bursting. The relationship between the separation bubble and shock motion is also explored in detail. The results of the experiments indicate that the separation bubble represents a first-order effect on shock oscillation. Although it is demonstrated theoretically that the burst-sweep cycle can also give rise to unsteady shock motion of much lower amplitude, the experiments clearly demonstrate that there is no discernible statistical relationship between burst events and spanwise coherent shock front motion.     

Reconstruction of velocity fields from wall pressure measurements in a shock wave/turbulent boundary layer interaction

We present here experimental results in a shock wave/turbulent boundary layer interaction at Mach number of 2.3 impinged by an oblique shock wave, with a deflection angle of 9.5°, as installed in the supersonic wind tunnel of the IUSTI laboratory, France. For such a shock intensity, strong unsteadiness are developing inside the separated zone involving very low frequencies associated with reflected shock motions.The present work consists in simultaneous PIV velocity fields and unsteady wall pressure measurements. The wall pressure and PIV measurements were used to characterize the pressure distribution at the wall in an axial direction, and the flow field associated. These results give access for the first time to the spatial-time correlation between wall pressure and velocity in a shock wave turbulent boundary layer interaction and show the feasibility of such coupling techniques in compressible flows. Linear Stochastic Estimation (LSE) coupled with Proper Orthogonal Decomposition (POD) has been applied to these measurements, and first results are presented here, showing the ability of these techniques to reproduce both the unsteady breathing of the recirculating bubble at low frequency and the Kelvin–Helmholtz instabilities developing at moderate frequency.     

Dynamic mode decomposition based analysis of flow over a sinusoidally pitching airfoil

Dynamic mode decomposition (DMD) has proven to be a valuable tool for the analysis of complex flow-fields but the application of this technique to flows with moving boundaries is not straightforward. This is due to the difficulty in accounting in the DMD formulation, for a body of non-zero thickness moving through the field of interest. This work presents a method for decomposing the flow on or near a moving boundary by a change of reference frame, followed by a correction to the computed modes that is determined by the frequency spectrum of the motion. The correction serves to recover the modes of the underlying flow dynamics, while removing the effect of change in reference frame. This method is applied to flow over sinusoidally pitching airfoils, and the DMD analysis is used to derive useful insights regarding flow-induced pitch oscillations of these airfoils.     

Effect of air jet vortex generators on a shock wave boundary layer interaction

The effect of upstream injection by means of continuous air jet vortex generators (AJVGs) on a shock wave turbulent boundary layer interaction is experimentally investigated. The baseline interaction is of the impinging type, with a flow deflection angle of 9.5° and a Mach number M _e  = 2.3. Considered are the effects of the AJVGs on the upstream boundary layer flow topology and on the spatial and dynamical characteristics of the interaction. To this aim, Stereoscopic Particle Image Velocimetry has been employed, in addition to hot-wire anemometry (HWA) for the investigation of the unsteady characteristics of the reflected shock. The AJVGs cause a reduction of the separation bubble length and height. In addition, the energetic frequency range of the reflected shock is increased by approximately 50%, which is in qualitative agreement with the smaller separation bubble size.     

PIV study on a shock-induced separation in a transonic flow

A transonic interaction between a steady shock wave and a turbulent boundary layer in a Mach 1.4 channel flow is experimentally investigated by means of particle image velocimetry (PIV). In the test section, the lower wall is equipped with a contour profile shaped as a bump allowing flow separation. The transonic interaction, characterized by the existence in the outer flow of a lambda shock pattern, causes the separation of the boundary layer, and a low-speed recirculating bubble is observed downstream of the shock foot. Two-component PIV velocity measurements have been performed using an iterative gradient-based cross-correlation algorithm, providing high-speed and flexible calculations, instead of the classic multi-pass processing with FFT-based cross-correlation. The experiments are performed discussing all the hypotheses linked to the experimental set-up and the technique of investigation such as the two-dimensionality assumption of the flow, the particle response assessment, the seeding system, and the PIV correlation uncertainty. Mean velocity fields are presented for the whole interaction with particular attention for the recirculating bubble downstream of the detachment, especially in the mixing layer zone where the effects of the shear stress are most relevant. Turbulence is discussed in details, the results are compared to previous study, and new results are given for the turbulent production term and the return to isotropy mechanism. Finally, using different camera lens, a zoom in the vicinity of the wall presents mean and turbulent velocity fields for the incoming boundary layer.     

Dynamic Mode Decomposition of a Wing-Body Junction Flow

Junction flows are subject to an intense adverse pressure gradient and three-dimensional separation when encountering a wall-mounted obstacle. A dynamically rich horseshoe vortex system is formed in this region. In this study the junction flow at the interaction of a wing and a flat plate is investigated. The numerical modelling is carried out using the three-dimensional large eddy simulation (LES) approach at the Reynolds number Re = 1.15×10⁵ based on the wing’s maximum thickness T and the free stream velocity U_ref. The comparison with the experimental results shows that the numerical simulations fairly accurately reproduce the phenomenon under study. The dynamic mode decomposition (DMD) of the resolved flow field is employed to obtain the coherent dynamics of the flow. To clearly demonstrate the oscillation characteristics and the horseshoe vortex structures of junction flow the velocity field in the plane of symmetry is decomposed with eduction of two dominant DMDmodes. These two DMDmodes are reconstituted and developed, together with the mean flow mode to explain the latent dynamics. Mode 1 reveals the merging of the horseshoe vortices and mode 2 is responsible for the process of fission and stretching.     

Numerical computations of supersonic inlet flow

Air‐breathing propulsion systems for high‐speed space travel applications are studied. Ramjets and scramjets have been identified as potential candidates. The flow inlets of such systems are modelled with a simulation that can predict all complex inlet flow features, including shock due to forebody, multiple shock reflections, normal shock, shock–boundary layer interaction and associated separation for two‐dimensional and axisymmetric inlets. Computed values are in good agreement with experimental data. Copyright © 2001 John Wiley & Sons, Ltd.     

Enhanced delayed DES of shock wave/boundary layer interaction in a planar transonic nozzle

An enhanced delayed detached eddy simulation of a shock wave/boundary layer interaction in an over-expanded planar transonic nozzle has been carried out to predict the fundamental features of shock low-frequency unsteadiness. The modification of the sub-grid length-scale proposed in Shur et al. (2015) has been implemented to attenuate some well-known problems of detached eddy simulation: the modeled-stress depletion in the switch region between RANS and LES and the consequent delay of transition to turbulence at the onset of separation. The comparison of the computational results with the experimental data shows that the enhanced DDES leads to significant improvements in the estimation of some flow features with respect to a different DDES version, even though some discrepancies are still observable in the distribution of the mean wall pressure, and additional work is needed to further improve the transition from modeled to resolved turbulence.