Effect of a local stationary flow disturbance on separated boundary layer stability

The separated flow past a transverse barrier on a plate surface is modeled in a wind tunnel. The linear stability of the two-dimensional laminar flow in the separation zone is investigated in the presence of a stationary disturbance imposed on the flow and concentrated in a narrow spanwise region. It is experimentally shown that the local flow nonuniformity leads to a change in the flow stability features, such as the frequencies of the growing oscillations, their growth rate, and the dispersion characteristics. As a result, the transverse velocity gradients induced in the separation zone exert a strong destabilizing influence on the flow. Novosibirsk. Translated from Izvestiya Rossiiskoi Akademii Nauk, Mekhanika Zhidkosti i Gaza, No. 1, pp. 174–178, January–February, 2000. The study was carried out with the support of the INTAS Foundation under grant No, 96-2225.     

Nonlinear development of a wave in a boundary layer

In recent years definite progress has been achieved in the construction of theoretical models of nonlinear wave processes which lead to a transition from laminar to turbulent flow [1, 2]. At the same time, there is a shortage of actual experimental material, especially for flows in a boundary layer. Fairly thorough experimental studies have been carried out only on the initial stage of the development of disturbances in a boundary layer, which is satisfactorily describable by the linear theory of hydrodynamic stability. In evaluating the theoretical models of subsequent stages of the transition, investigators have been forced to turn chiefly to much earlier experiments carried out by the United States National Bureau of Standards [3, 4], in which the main attention was concentrated on the three-dimensional structure of the transition region. The present investigation was undertaken for the purpose of obtaining detailed data on the structure of the flow in the transition region when there is disturbance in the laminar boundary layer of a two-dimensional wave. In order to make the two-dimensional nonlinear effects stand out more clearly, the amplitude of the wave was specified to be fairly large from the very outset. In contrast to earlier investigations, the main attention was centered on the study of the spectral composition of the disturbance field.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 3, pp. 49–58, May–June, 1977.     

蜿蜒边界下平面流的线性流动稳定性

为便于数值分析,蜿蜒河流水动力和演变模型中一般隐性假设二次时均流-二次涡的关系与明渠流时均流-明渠湍流的关系相同,但由于高雷诺数下的DNS算力限制和实验尺度限制,这种隐含假设是否成立目前尚无相关湍流研究来支撑.文章试图通过分析明渠湍流和二次湍流发展初期的研究,侧面揭示其湍流结构的异同.通过对曲线正交坐标系下的平面二维NS方程使用双参数摄动的方法,建立了一种求解蜿蜒边界弱非线性层流的摄动解法,并推导得出一个适用于蜿蜒边界的EOS方程以及其特征值问题的解法.蜿蜒边界下弱非线性层流解为一系列蜿蜒谐波分量的叠加,其中线性部分使得两壁产生流速差,非线性部分随着雷诺数增大呈指数增长.水流的扰动增长率特征谱的第一模态与直道流相似,由3条曲线、4个波段合成,但其长波段和短波段的扰动流场与直道流不同,所有短波段的扰动流速近似于KH涡.蜿蜒边界对内部水流扰动有一定的选择性.偏角幅值越大扰动增长越快;蜿蜒波数的影响则为先增后减,有一个使扰动增长最快的蜿蜒波数.扰动流场由一个典型的TS波和一对波包形式的二次涡叠加而成,波包只有纵向流速分量,包络线由蜿蜒波数控制,波包内是与直道扰动波参数相同的TS波.     

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.     

Development of three-dimensional disturbances in a boundary layer

In the region of transition from a two-dimensional laminar boundary layer to a turbulent one, three-dimensional flow occurs [1–3]. It has been proposed that this flow is formed as the result of nonlinear interaction of two-dimensional and three-dimensional disturbances predicted by linear hydrodynamic stability theory. Using many simplifications, [4, 5] performed a calculation of this interaction for a free boundary layer and a boundary layer on a wall with a very coarse approximation of the velocity profile. The results showed some argreement with experiment. On the other hand, it is known that disturbances of the Tollmin—Schlichting wave type can be observed at sufficiently high amplitude. This present study will use the method of successive linearization to calculate the primary two- and three-dimensional disturbances, and also the average secondary flow occurring because of nonlinear interaction of the primary disturbances. The method of calculation used is close to that of [4, 5], the disturbance parameters being calculated on the basis of a Blazius velocity profile. A detailed comparison of results with experimental data [1] is made. It developed that at large disturbance amplitude the amplitude growth rate differs from that of linear theory, while the spatial distribution of disturbances agree s well with the distribution given by the natural functions and their nonlinear interaction. In calculating the secondary flow an experimental correction was made to the amplitude growth rate.     

Boundary-layer separation on conical bodies

Some characteristics of the variation in the linear dimensions of the flow separation zones on conical bodies with expanding conical skirts and of variation of the pressure within these zones as a function of variation of the Mach number, Reynolds number, and intensity of the disturbance that causes the boundary layer separation are examined. Experiments were conducted in laminar, transitional, and turbulent flows in flow separation regions. The interaction of viscous and nearly inviscid flows is quite common. This phenomenon occurs in flow past a concave corner, when a compression shock impinges on a boundary layer, and in many other cases. The characteristics of this phenomenon in flow about two-dimensional bodies have been investigated experimentally in [1, 2] and other studies. Attempts have been made to analyze the interaction of compression shocks with the boundary layer theoretically. In “free” separated flows, when the points of separation and reattachment of the boundary layer are not fixed (for example, on a flat plate with a long wedge attached to it), theoretical studies are usually made within the framework of the boundary layer theory with use of the approximate integral methods [3, 4]. In this article we examine some results from studies of free separated flows on conical bodies with conical skirts in laminar, transitional, and turbulent flows (Fig. 1).     

Zonal RANS/LES coupling simulation of a transitional and separated flow around an airfoil near stall

The objective of the current study is to examine the course of events leading to stall just before its occurrence. The stall mechanisms are very sensitive to the transition that the boundary layer undergoes near the leading edge of the profile by a so-called laminar separation bubble (LSB). In order to provide helpful insights into this complex flow, a zonal Reynolds-averaged Navier–Stokes (RANS)/large-eddy simulation (LES) simulation of the flow around an airfoil near stall has been achieved and its results are presented and analyzed in this paper. LSB has already been numerically studied by direct numerical simulation (DNS) or LES, but for a flat plate with an adverse pressure gradient only. We intend, in this paper, to achieve a detailed analysis of the transition process by a LSB in more realistic conditions. The comparison with a linear instability analysis has shown that the numerical instability mechanism in the LSB provides the expected frequency of the perturbations. Furthermore, the right order of magnitude for the turbulence intensities at the reattachment point is found.      

Uniformly valid approximation for channel flowApproximation valable uniformément pour l'écoulement dans un canal

The flow at high Reynolds number in a two-dimensional channel whose walls are slightly deformed is considered. This Note addresses the problem of constructing a uniformly valid approximation leading to a better understanding of two-dimensional steady laminar incompressible separated flow. It is proposed to use a new asymptotic approach: the Successive Complementary Expansions Method (SCEM). The starting point is an assumed form of the approximation. The matching principle is a by-product of the method not at all necessary to construct the uniformly valid approximation. To cite this article: J. Mauss et al., C. R. Mecanique 334 (2006).     

High-fidelity simulations of moving and flexible airfoils at low Reynolds numbers

The present paper highlights results derived from the application of a high-fidelity simulation technique to the analysis of low-Reynolds-number transitional flows over moving and flexible canonical configurations motivated by small natural and man-made flyers. This effort addresses three separate fluid dynamic phenomena relevant to small fliers, including: laminar separation and transition over a stationary airfoil, transition effects on the dynamic stall vortex generated by a plunging airfoil, and the effect of flexibility on the flow structure above a membrane airfoil. The specific cases were also selected to permit comparison with available experimental measurements. First, the process of transition on a stationary SD7003 airfoil section over a range of Reynolds numbers and angles of attack is considered. Prior to stall, the flow exhibits a separated shear layer which rolls up into spanwise vortices. These vortices subsequently undergo spanwise instabilities, and ultimately breakdown into fine-scale turbulent structures as the boundary layer reattaches to the airfoil surface. In a time-averaged sense, the flow displays a closed laminar separation bubble which moves upstream and contracts in size with increasing angle of attack for a fixed Reynolds number. For a fixed angle of attack, as the Reynolds number decreases, the laminar separation bubble grows in vertical extent producing a significant increase in drag. For the lowest Reynolds number considered (Re _c  = 10⁴), transition does not occur over the airfoil at moderate angles of attack prior to stall. Next, the impact of a prescribed high-frequency small-amplitude plunging motion on the transitional flow over the SD7003 airfoil is investigated. The motion-induced high angle of attack results in unsteady separation in the leading edge and in the formation of dynamic-stall-like vortices which convect downstream close to the airfoil. At the lowest value of Reynolds number (Re _c  = 10⁴), transition effects are observed to be minor and the dynamic stall vortex system remains fairly coherent. For Re _c  = 4 × 10⁴, the dynamic-stall vortex system is laminar at is inception, however shortly afterwards, it experiences an abrupt breakdown associated with the onset of spanwise instability effects. The computed phased-averaged structures for both values of Reynolds number are found to be in good agreement with the experimental data. Finally, the effect of structural compliance on the unsteady flow past a membrane airfoil is investigated. The membrane deformation results in mean camber and large fluctuations which improve aerodynamic performance. Larger values of lift and a delay in stall are achieved relative to a rigid airfoil configuration. For Re _c = 4.85 × 10⁴, it is shown that correct prediction of the transitional process is critical to capturing the proper membrane structural response.     

Higher order stability effects in a natural convection boundary layer over a vertical heated wall

 The stability of a laminar boundary layer flow under natural convection on a vertical isothermally heated wall is studied analytically. The analysis is performed by using two different two-dimensional linear models: (1) The non-parallel flow model in which the steady mean flow as well as the disturbance amplitude functions can change in the streamwise direction; (2) The parallel flow model in which the effects of the mean flow and disturbance changes in the streamwise direction are neglected. The linear non-parallel stability analysis is based on the so-called parabolised stability equations (PSEs) which have been successfully applied to the stability analysis of forced convection boundary layers. In this study the PSE equations are applied to natural convection boundary layers in order to show the difference between parallel and non-parallel stability analysis. A second part of this study deals with the effects of variable properties, which are always present in natural convection flows. They are analysed by an extended version of the Orr–Sommerfeld equation (EOSE). Received on 31 May 2000     

Determination of the magnitude of the separation criterion for a three-dimensional laminar boundary layer

A separation criterion, i.e., a definite relationship between the external flow and the boundary layer parameters [1], can be used to estimate the possibility of the origination of separation of a two-dimensional boundary layer. A functional form of the separation criterion has also been obtained for a three-dimensional boundary layer [2] on the basis of dimensional analysis. As in the case of the two-dimensional boundary layer, locally self-similar solutions can be used to determine the specific magnitude of the separation criterion as a function of the values of the governing parameters. Locally self-similar solutions of the two-dimensional laminar boundary-layer equations have been found at the separation point for a perfect gas with a linear dependence of the coefficient of viscosity on the temperature (Ω=1) and Prandtl number P=1 [3, 4]. The influence of blowing and suction has been studied for this case [5]. Self-similar solutions have been obtained for Ω=1, P=0.723 for the limit case of hypersonic perfect gas flow [6]. Locally self-similar solutions of the three-dimensional laminar boundary-layer equations at the separation point are presented in [7] for a perfect gas with Ω=1, P=1. There are no such computations for Ω≠1, P≠1; however, the results of computing several examples for a two-dimensional flow [8] show that the influence of the real properties of a gas can be significant and should be taken into account. Self-similar solutions of the two- and three-dimensional boundary-layer equations at the separation point are found in this paper for a perfect gas with a power-law dependence of the viscosity coefficient on the enthalpy (Ω=0.5, 0.75, 1.0) for different values of the Prandtl number (P=0.5, 0.7, 1.0) in a broad range of variation of the external stream velocity (v ₁ ² /2h₁* = 0–0.99) and the temperature of the streamlined surface. Magnitudes of the separation criterion for a laminar boundary layer have been obtained on the basis of these data.     

Turbulence modelling of the flow past a pitching NACA0012 airfoil at and Reynolds numbers

This paper provides a study of the NACA0012 dynamic stall at Reynolds numbers 10⁵ and 10⁶ by means of two- and three-dimensional numerical simulations. The turbulence effect on the dynamic stall is studied by statistical modelling. The results are compared with experiments concerning each test case. Standard URANS turbulence modelling have shown a quite dissipative character that attenuates the instabilities and the vortex structures related to the dynamic stall. The URANS approach Organised Eddy Simulation (OES) has shown an improved behaviour at the high Reynolds number range. Emphasis is given to the physical analysis of the three-dimensional dynamic stall structure, for which there exist few numerical results in the literature, as far as the Reynolds number range is concerned. This study has shown that the downstroke phases of the pitching motion are subjected to strong three-dimensional turbulence effects along the span, whereas the flow is practically two-dimensional during the upstroke motion.     

On the use of a phased heater array for the controlled excitation of arbitrary three-dimensional perturbations in a laminar boundary layer

Flush mounted resistive heating elements were used successfully by Liepmann, Brown and Nosenchuck (1981) to excite and control the development of two-dimensional Tollmien-Schlichting waves. Due to increased interest in the three dimensional nature of boundary-layer transition, this technique has recently been extended to provide a means for introducing arbitrary controlled three-dimensional perturbations into a laminar flow. This paper describes the design and operation of a programmable 32-element linear heater array capable of exciting a wide variety of flow disturbances hitherto unobtainable in the laboratory.     

Convergence properties of high-Reynolds-number separated flow calculations

The convergence properties of an iterative solution technique for the Reduced Navier–Stokes equations are examined for two-dimensional steady subsonic flow over bump and trough geometries. Techniques for decreasing the sensitivity to the initial pressure approximation, for fine meshes in particular, are investigated. They are shown to improve the robustness of the relaxation process and to decrease the computational work required to obtain a converged solution. A semi-coarsening multigrid technique that has previously been found to be particularly advantageous for high-Reynolds-number (Re) flows with flow separation and with highly stretched surface-normal grids is applied herein to further accelerate convergence. Solutions are obtained for the laminar flow over a trough that is more severe than has been considered to date. Sufficient axial grid refinement in this case leads to a shock-like reattachment and, for sufficiently large Re, to a local ‘divergence’ of the numerical computations. This ‘laminar flow breakdown’ appears to be related to an instability associated with high-frequency fine-grid modes that are not resolvable with the present modelling. This behaviour may be indicative of dynamic stall or of incipient transition. The breakdown or instability is shown to be controllable by suitable introduction of transition turbulence models or by laminar flow control, i.e. small amounts of wall suction. This lends further support to the hypothesis that the instability is of a physical rather than numerical character and suggests that full three-dimensional analysis is required to properly capture the flow behaviour. Another inference drawn from this investigation is that there is a need for careful grid refinement studies in high-Re flow computations, since coarser grids may yield oscillation-free solutions that cannot be obtained on finer grids.     

Theory of unsteady separation in supersonic flow around a convex corner

A theory of unsteady separation in inviscid supersonic flow around a convex corner is developed. Within the framework of the hypothesis suggested the mechanism of separationless-to-separated flow transition is explained and the forces leading to flow separation are determined as functions of the angle θ and the oncoming flow velocity. The values of the angle θ _k at which the flow is separated from the corner vertex and the stall angle θ _s determining the separated flow direction obtained previously in experiments and by numerical simulation are confirmed.     

Nonstationary waves in the continuously stratified flow of a fluid of finite depth

A theoretical investigation is made of the development of linear two-dimensional waves in a continuously stratified flow of an ideal incompressible fluid. The waves are generated by pressures that are independent of time and that are applied at time t=0 to a bounded region on the free surface of an initially undisturbed flow. The stationary internal waves generated by such a disturbance have been investigated in [1–3]. The nonstationary waves in a continuously stratified fluid that are generated by initial disturbances or periodic surface pressures applied to the entire free surface have been studied in [4–7] in the absence of a slow.Translated from Izvestiya Akademii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 6, pp. 87–93, November–December, 1976.     

Two methods for calculating the load on the surface of a slender body executing axisymmetric vibrations in a sonic gas flow

Low-frequency axisymmetric vibrations of the surface of a slender body in a sonic flow are considered. The distribution of the stationary longitudinal velocity on the body is assumed to be linear. The linear equation with variable coefficients for the nonstationary part of the velocity potential is solved by two methods: by separation of the variables, as was done in [1] for a two-dimensional flow, and by the method of superposition of sources. Particular solutions with the required singularity are obtained.Translated from Izvestiya Akaderaii Nauk SSSR, Mekhanika Zhidkosti i Gaza, No. 2, pp. 151–154, March–April, 1980.     

Direct numerical simulation of a NACA0012 in full stall

This work aims at investigating the mechanisms of separation and the transition to turbulence in the separated shear-layer of aerodynamic profiles, while at the same time to gain insight into coherent structures formed in the separated zone at low-to-moderate Reynolds numbers. To do this, direct numerical simulations of the flow past a NACA0012 airfoil at Reynolds numbers Re = 50,000 (based on the free-stream velocity and the airfoil chord) and angles of attack AOA = 9.25° and AOA = 12° have been carried out. At low-to-moderate Reynolds numbers, NACA0012 exhibits a combination of leading-edge/trailing-edge stall which causes the massive separation of the flow on the suction side of the airfoil. The initially laminar shear layer undergoes transition to turbulence and vortices formed are shed forming a von Kármán like vortex street in the airfoil wake. The main characteristics of this flow together with its main features, including power spectra of a set of selected monitoring probes at different positions on the suction side and in the wake of the airfoil are provided and discussed in detail.     

Stabilization and evolution of parameters of a symmetric laminar flow in a plane channel with sudden expansion

A problem is formulated for computing the fields of parameters of a stationary laminar symmetric flow. A two-dimensional flow in a channel with a sudden change in the cross-sectional area is computed. The evolution of a three-dimensional perturbation inserted into the channel at the initial stage of computations is analyzed. It is demonstrated that the parameters of a two-dimensional flow in the channel at a Reynolds number Re = 50 become stabilized at a dimensionless time t > 20, whereas the steady state is reached under the same conditions at t ≈ 100. At a distance of approximately 10h (h is the channel width at the entrance), the flow becomes one-dimensional, but the streamwise component of the velocity vector remains a function of the streamwise coordinate owing to flow compressibility. __________ Translated from PrikladnayaMekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 1, pp. 35–42, January–February, 2007.     

高径比对GaAs熔体液桥热毛细对流失稳的影响

采用基于谱元法线性稳定性分析方法,研究了高径比对GaAs熔体(Pr=0.068)液桥热毛细对流失稳的影响,同时结合能量分析揭示了热毛细对流的失稳机制.研究结果表明:与典型低普朗特数(例如Pr=0.011)熔体静态失稳模式和典型高普朗特数(例如Pr>1)熔体振荡失稳模式不同,GaAs熔体热毛细对流失稳模式依赖于液桥高径比...