Active Control of Wave Instabilities in Three-Dimensional Compressible Flows

In many fluid flows of practical importance transition is caused by the linear growth of wave instabilities, such as Tollmien–Schlichting waves, which eventually grow to a finite size at which stage secondary instabilities come into play. If transition is to be delayed or even avoided in such flows, then the linear growth of the disturbances must be prevented since control in the nonlinear regime would be a considerably more difficult task. Here a strategy for active control of two-dimensional incompressible and compressible Tollmien–Schlichting waves and its use in controlling the more practically relevant problem of crossflow instability which arises in swept-wing flows is discussed. The control is through an active suction/blowing distribution at the wall though the same result could be achieved by variable wall heating. In order to control the instability it is assumed that the wall shear stress and pressure are known from measurements. It is shown that, certainly at finite Reynolds numbers, it is sufficient to know the flow properties at a finite number of points along the wall. The cases of high and finite Reynolds numbers are discussed using asymptotic and numerical methods respectively. It is shown that a control strategy can be developed to stop the growth of all two-dimensional Tollmien–Schlichting waves at finite and large Reynolds numbers. Some discussion of nonlinear effects in the presence of active control is given and the possible control of other instability mechanisms investigated. Received 1 May 1998 and accepted 24 September 1998     

Applications of EPSE method for predicting crossflow instability in swept-wing boundary layers

The nth-order expansion of the parabolized stability equation(EPSEn) is obtained from the Taylor expansion of the linear parabolized stability equation(LPSE) in the streamwise direction. The EPSE together with the homogeneous boundary conditions forms a local eigenvalue problem, in which the streamwise variations of the mean flow and the disturbance shape function are considered. The first-order EPSE(EPSE1) and the second-order EPSE(EPSE2) are used to study the crossflow instability in the swept NLF(2)-0415 wing boundary layer. The non-parallelism degree of the boundary layer is strong. Compared with the growth rates predicted by the linear stability theory(LST),the results given by the EPSE1 and EPSE2 agree well with those given by the LPSE.In particular, the results given by the EPSE2 are almost the same as those given by the LPSE. The prediction of the EPSE1 is more accurate than the prediction of the LST, and is more efficient than the predictions of the EPSE2 and LPSE. Therefore, the EPSE1 is an efficient e~N prediction tool for the crossflow instability in swept-wing boundary-layer flows.     

Linear stability of two-dimensional steady flow in wavy-walled channels

Linear stability of fully developed two-dimensional periodic steady flows in sinusoidal wavy-walled channels is investigated numerically. Two types of channels are considered: the geometry of wavy walls is identical and the location of the crest of the lower and upper walls coincides (symmetric channel) or the crest of the lower wall corresponds to the furrow of the upper wall (sinuous channel). It is found that the critical Reynolds number is substantially lower than that for plane channel flow and that when the non-dimensionalized wall variation amplitude is smaller than a critical value (about 0.26 for symmetric channel, 0.28 for sinuous channel), critical modes are three-dimensional stationary and for larger , two-dimensional oscillatory instabilities set in. Critical Reynolds numbers of sinuous channel flows are smaller for three-dimensional disturbances and larger for two-dimensional disturbances than those of symmetric channel flows. The disturbance velocity distribution obtained by the linear stability analysis suggests that the three-dimensional stationary instability is mainly caused by local concavity of basic flows near the reattachment point, while the critical two-dimensional mode resembles closely the Tollmien–Schlichting wave for plane Poiseuille flow.     

Amplitude method of prediction of laminar-turbulent transition on a swept-wing

The amplitudemethod of prediction of laminar-turbulent transition on a swept-wing initiated by the simultaneous action of free-stream turbulence and surface roughness is developed. Generation of growing intrinsic perturbations in the boundary layer is described by the mechanism of distributed generation, i.e., an external perturbation generates an instability mode with the same wavelength and frequency. Generation occurs in a small neighborhood of the neutral point at which the parameters of an external perturbation and the instability modes coincide. The development of proper perturbations in the boundary layer is described by the nonlinear method of parabolized stability equations (PSE). The criterion of laminar-turbulent transition is the combined amplitude. i.e., transition begins at a point at which the sum of amplitudes of steady and traveling modes reaches a critical value.     

Spectral analysis of phase-shifting measurements of crossflow waves

Computing amplitudes of periodic components in a measured signal is commonly encountered in data analysis. When this process is hampered by low-resolution data, it is sometimes possible to exploit certain qualities of the data to mitigate these limitations. In this work, spectral analysis of crossflow vortices measured in flight tests using multi-element hotfilm sensors is accomplished despite restrictive sensor counts. The vortices are nominally steady but subject to randomly changing phase shifts that can be computed to form well-resolved sets of data. The reliability and efficiency of this analysis are tested via Monte Carlo simulation and the uncertainties in detected wavelengths are quantified. This analysis technique is applied to in-flight measurements of crossflow instabilities in swept-wing boundary layers.     

Evolution of disturbances in a laminarized supersonic boundary layer on a swept wing

Experimental data on stability of a three-dimensional supersonic boundary layer on a swept wing are presented. The experiments are performed on a swept wing model with a lenticular profile with a 40° sweep angle of the leading edge at a zero angle of attack. The supersonic boundary layer on the swept wing was laminarized with the use of distributed roughness. A pioneering study of interaction of traveling and stationary disturbances is performed. Some specific features of this interaction are identified. The main reason for turbulence emergence in a supersonic boundary layer on a swept wing is demonstrated to be secondary crossflow instability. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 40–46, March–April, 2008.     

Spatial Instabilities of the Incompressible Attachment-Line Flow Using Sparse Matrix Jacobi–Davidson Techniques

We consider the linear stability of incompressible attachment-line flow within the spatial framework. No similarity or symmetry assumptions for the instability modes are introduced and the full two-dimensional representation of the modes is used. The perturbation equations are discretized on a two-dimensional staggered grid. A high order finite difference scheme has been developed which gives rise to a large, sparse, quadratic, eigenvalue problem for the instability modes. The benefits of the Jacobi–Davidson method for the solution of this eigenvalue system are demonstrated and the approach is validated in some detail. Spatial stability results are presented subsequently. In particular, instability predictions at very high Reynolds numbers are obtained which show almost equally strong instabilities for symmetric and antisymmetric modes in this regime.     

On the Secondary Instability of Three-Dimensional Boundary Layers

One of the possible transition scenarios in three-dimensional boundary layers, the saturation of stationary crossflow vortices and their secondary instability to high-frequency disturbances, is studied using the Parabolized Stability Equations (PSE) and Floquet theory. Starting from nonlinear PSE solutions, we investigate the region where a purely stationary crossflow disturbance saturates for its secondary instability characteristics utilizing global and local eigenvalue solvers that are based on the Implicitly Restarted Arnoldi Method and a Newton–Raphson technique, respectively. Results are presented for swept Hiemenz flow and the DLR swept flat plate experiment. The main focuses of this study are on the existence of multiple roots in the eigenvalue spectrum that could explain experimental observations of time-dependent occurrences of an explosive growth of traveling disturbances, on the origin of high-frequency disturbances, as well as on gaining more information about threshold amplitudes of primary disturbances necessary for the growth of secondary disturbances. Received 13 July 1998 and accepted 7 July 2000     

Three-dimensional instabilities of laminar flow in a rough channel and the concept of hydraulically smooth wall

Flow in a channel with distributed surface roughness is considered. Results of the linear stability analysis show that the presence of the roughness destabilizes the traveling-wave instability as well as introduces a new instability that manifests itself in the form of streamwise vortices. The critical conditions for the occurrence of both instabilities are given for different classes of roughness shape. It is shown that these conditions can be predicted with a reasonable accuracy in the case of an arbitrary (but Fourier transformable) roughness by considering only the leading Fourier mode (wavy-wall model). It is argued that the onset of instabilities provides a decision mechanism that determines whether a particular rough wall can be viewed as being hydraulically smooth in the case of transitional flows.     

Heat addition effect on the instability of the crossflow in a three-dimensional boundary layer

The heat addition effect on the stability characteristics of the crossflow in the swept-wing boundary layer is investigated. The physical mechanism of the effect is established. The calculations performed illustrate the variation in the instability mode growth rates under the heating of the surface in a flow and at bulk energy addition.     

Excitation of controllable perturbations in the three-dimensional boundary layer using plasma actuators

Two versions of the structure of a multi-discharge plasma actuator intended to excite boundary layer perturbations in the neighborhood of the leading swept-wing edge are suggested. The actuator must prevent from appearance and development of the crossflow instability modes leading to laminarturbulent transition under the normal conditions. In the case of flow past a swept wing, excitation of controllable perturbations by the plasma actuator is simulated numerically in the steady-state approximation under the typical conditions of cruising flight of a subsonic aircraft. The local body force and thermal impact on the boundary layer flow which is periodic along the leading wing edge is considered. The calculations are carried out for the physical impact parameters realizable in the near-surface dielectric barrier discharge.     

On the inviscid acoustic-mode instability of supersonic shear flows

The same methods used previously to study acoustic-mode instability in supersonic boundary layers are applied to free shear layers, and new calculations are made for boundary layers with cooling and suction. The objective is to obtain additional information about acoustic-mode instability, and to find what features of the instability are common to boundary layers and free shear flows. Acoustic modes exist whenever there is an embedded region of locally supersonic flow relative to the phase speed of the instability wave. Consequently, they can be found in boundary layers, wakes, and jets, but not in mixing layers unless the flow is confined. In this first part of a two-part paper, attention is directed principally to two-dimensional waves. The linear, inviscid stability theory is used to calculate spatial amplification rates at Mach number 3 for the sinuous and varicose modes of a single wake flow and a single jet flow, each made up of the same mixing-layer profile plus a central region of uniform flow. Along with sequences of sinuous and varicose unstable modes clearly identifiable as acoustic modes, both of these flows, unlike the boundary layer, have a lowest sinuous mode that is the most unstable. The unstable modes include both subsonic and radiating disturbances with large amplification rates. The latter phenomenon is also found for highly cooled boundary layers with suction. In these boundary layers, suction is generally stabilizing for nonradiating acoustic disturbances, but destabilizing for radiating disturbances.The work described in this paper was carried out at the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration (NASA). Support from the Aerodynamics Division of the Office of Aeronautics and Exploration Technology is gratefully acknowledged. A preliminary version of this paper was presented at the Fourth Symposium on Numerical and Physical Aspects of Aerodynamic Flows, California State University, Long Beach, CA, 16–19 January 1989.     

Scattering of Tollmien-Schlichting waves by localized roughness in transonic boundary layers

The laminar-turbulent transition in boundary-layer flows is often affected by wall imperfections, because the latter may interact with either the freestream perturbations or the oncoming boundary-layer instability modes, leading to a modification of the accumulation of the normal modes. The present paper particularly focuses on the latter mechanism in a transonic boundary layer, namely, the effect of a two-dimensional(2 D) roughness element on the oncoming Tollmien-Schlichting(T-S) modes when they propagate through the region of the rapid mean-flow distortion induced by the roughness. The wave scattering is analyzed by adapting the local scattering theory developed for subsonic boundary layers(WU, X. S. and DONG, M. A local scattering theory for the effects of isolated roughness on boundary-layer instability and transition: transmission coefficient as an eigenvalue. Journal of Fluid Mechanics, 794, 68–108(2006)) to the transonic regime, and a transmission coefficient is introduced to characterize the effect of the roughness. In the sub-transonic regime, in which the Mach number is close to, but less than, 1, the scattering system reduces to an eigenvalue problem with the transmission coefficient being the eigenvalue; while in the super-transonic regime, in which the Mach number is slightly greater than 1, the scattering system becomes a high-dimensional group of linear equations with the transmission coefficient being solved afterward. In the largeReynolds-number asymptotic theory, the K′arm′an-Guderley parameter is introduced to quantify the effect of the Mach number. A systematical parametric study is carried out,and the dependence of the transmission coefficient on the roughness shape, the frequency of the oncoming mode, and the K′arm′an-Guderley parameter is provided.     

Nonlinear Stability and Transition in 3-D Boundary Layers

The important recent progress in three-dimensional boundary-layer transition research is reviewed with emphasis on the crossflow instability that leads to transition on swept wings with a favorable pressure gradient. Following a brief overview of swept-wing instability mechanisms and the crossflow problem, a summary of the important findings of the 1990s is given. The discussion is presented from the experimental viewpoint, and where appropriate, relevant comparisons with CFD are drawn. The recent research conducted with distributed roughness is described in more detail in order to underscore the latest developments concerning nonlinear effects and transition control.Sommario. I recenti importanti sviluppi sullo studio della tansizione in uno strato limite tridimensionale sono esaminati con particolare attenzione alla instabilità trasversale che conduce alla transizione su ali a freccia con gradiente di pressione favorevole. Dopo una breve descrizione dei meccanismi di instabilità sulle ali a freccia viene dato un riassunto degli importanti progressi ottenuti negli anni '90. La discussione è presentata dal punto di vista sperimentale e, ove appropriato, sono riportati confronti con la simulazione numerica. La recente ricerca, condotta con rugosità distribuita,è descritta con maggiore dettaglio allo scopo di presentare gli ultimi sviluppi concernenti gli effetti non lineari ed il controllo della transizione.     

Direct Numerical Simulation of the turbulent wake behind a heated cylinder

Direct Numerical Simulations were conducted to describe a well-known and widely studied configuration, i.e. flow field development downstream from a cylinder under the mixed convection regime, which has too rarely been considered. The Richardson number studied was equal to 2.77 and the Reynolds number equal to 1000; under such conditions, thermal instability development along the cylinder was found to interact with and pronouncedly disturb upper shear-layer development. Whole flow behavior in the back of the cylinder is consequently asymmetric. The resulting flow corresponds to complex features ranging from Kelvin–Helmholtz instabilities to pure buoyant diffusion process and Von Karman alley, the latter being significantly deviated upward.     

Surface breakup of a non-turbulent liquid jet injected into a high pressure gaseous crossflow

We employ detailed numerical simulations to understand the physical mechanism underlying the surface breakup of a non-turbulent liquid jet injected transversely into a high pressure gaseous crossflow under isothermal conditions. The numerical observations reveal the existence of shear instability on the jet periphery as the primary destabilization mechanism. The temporal growth of such azimuthal instabilities leads to the formation of interface corrugations, which are eventually sheared off of the jet surface as sheet-like structures. The sheets next undergo disintegration into ligaments and drops during the surface breakup process. The proposed instability mechanism is inherently an inviscid mechanism, contrary to the previously suggested mechanism of surface breakup (known as “boundary layer stripping”), which is relied on a viscous interpretation. The numerically obtained length and time scales of the shear instabilities on the jet laterals are compared with the results of Behzad et al. (2015) on temporal linear stability analyses of a jet in crossflow at near the nozzle. The stability characteristics of the most amplified modes (i.e., the wavenumber and the corresponding growth rate) obtained from the numerical simulations and the stability analyses are in good agreement.     

Linear stability of three-dimensional boundary layers

Stability of compressible three-dimensional boundary layers on a swept wing model is studied within the framework of the linear theory. The analysis based on the approximation of local self-similarity of the mean flow was performed within the Falkner-Skan-Cooke solution extended to compressible flows. The calculated characteristics of stability for a subsonic boundary layer are found to agree well with the measured results. In the case of a supersonic boundary layer, the results calculated for a Mach number M = 2 are also in good agreement with the measured spanwise scales of nonstationary vortices of the secondary flow. The calculated growth rates of disturbances, however, are substantially different from the measured values. This difference can be attributed to a high initial amplitude of disturbances generated in the experiment, which does not allow the linear stability theory to be applied. The evolution of natural disturbances with moderate amplitudes is fairly well predicted by the theory. The effect of compressibility on crossflow instability modes is demonstrated to be insignificant. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 49, No. 2, pp. 3–14, March–April, 2008.     

可压缩横流失稳及其控制

边界层流动转捩的预测与控制一直是流体力学研究中的一个重要问题. 三维边界层流动工程中十分常见, 而横流失稳是导致三维边界层流动转捩的主要原因. 本文综述了近些年来三维边界层失稳和转捩方面的研究概况. 从机理上讨论了横流扰动的感受性、首次失稳、二次失稳和转捩控制等方面的研究进展. 在数值计算方面, 简要概述了线性稳定性理论、非线性稳定性理论和直接数值模拟方法在横流失稳和转捩方面的应用.本文对横流失稳研究当前存在的问题进行了讨论, 对今后研究的发展趋势作了相应展望.     

一种求解抛物化Navier-Stokes方程的空间推进算法

讨论了抛物化NS方程(parabolized Navier-Stokesequations, PNS)的数学性质,对比分析多种处理流向压力梯度的方法的优缺点. 以此为基础,成功地将LU-SGS隐式时间积分方法推广到PNS方程的流向空间积分上,发展了基于PNS方程的有限体积单次扫描空间推进算法(single-sweep parabolized Navier-Stokesalgorithm, SSPNS). 在该算法中,横向无黏数值通量和黏性通量分别采用混合型迎风格式和中心格式求解. 用SSPNS算法计算了4个典型流场,包括超声速平板流、15$^\circ$楔板压缩高超声速流、带攻角的高超声速锥形流和侧压式高超声速进气道流动. SSPNS计算结果与NASA UPS程序数值结果、文献提供的实验数据及理论分析结果符合得很好.对比研究表明,SSPNS 法与传统时间迭代法相比,二者计算精度相当,而SSPNS计算速度快1~2个量级,存储量至少低1个量级.关键词 抛物化NS方程;空间推进算法;LU-SGS隐式积分方法;超声速/高超声速流动