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.      

SBLI control for wings and inlets

Flow control can be applied to shock wave/boundary layer interactions to achieve two different goals;the delay of shock-induced separation and/or the reduction ofstagnation pressure losses, which cause wave drag or inletinefficiencies. This paper introduces the principles and maintechniques for both approaches and assesses their relativesuitability for practical applications. While boundary layersuction is already in wide use for separation control, themost promising novel device is the micro-vortex generator,which can deliver similar benefits to traditional vortex generatorsat much reduced device drag. Shock control is notyet used on practical applications for a number of reasons,but recent research has focused on three-dimensional deviceswhich promise to deliver flow control with improved offdesignbehaviour. Furthermore, there are some indicationsthat a new generation of control devices may be able to combinethe benefits of shock and boundary layer control andreduce shock-induced stagnation pressure losses as well asdelay shock-induced separation.     

Surrogate-based aeroelastic loads prediction in the presence of shock-induced separation

A surrogate-based modeling strategy is presented for robust and efficient prediction of unsteady aeroelastic loads in the presence of shock-induced separation. Enriched piston theory predictions are extended with a data-driven nonlinear autoregressive with exogenous inputs model to account for hysteresis from the interplay of a dynamically deforming surface with the separation bubble in a shock/boundary layer interaction. The approach is evaluated for prescribed surface motion and shock-induced panel flutter responses, with good agreement observed in each scenario relative to unsteady Reynolds-averaged Navier–Stokes simulations. For the latter, excellent agreement is observed in the prediction of the stability boundary and oscillation frequency. In contrast, the oscillation amplitude conservatively deviates from the Reynolds-averaged Navier–Stokes solution with increasing dynamic pressure. The online computational cost of the extended approach is orders of magnitude less than that required for predictions using an unsteady Reynolds-averaged Navier–Stokes model.     

Study of the shock-induced acceleration of hexane droplets

An experimental study of the interaction of a shock wave with a hexane droplet is presented. The main goal of the experiments was to record images of the process and measure basic parameters describing movement, dispersion and evaporation of the droplets engulfed by a shock wave propagating in air. A shock tube with a visualization section was used for this research. Photography of the process allowed one to measure the positions, velocities and sizes of mist clouds created by the interaction processes. Analysis of the pictures shows that there is no qualitative difference between cases for different size droplets, but shock Mach number had a significant effect on the process. Quantitative analysis shows that under certain conditions, a catastrophic breakup mechanism of dispersion occurred. The droplets are shattered into a mist cloud before they achieve mechanical equilibrium with the surrounding gas. The approximate time for the complete dispersion and acceleration of the fuel droplet varies from 300 to 500 μs, and depends both on the droplet diameter and shock velocity. The dispersion time is controlled principally by the droplet diameter, and to a lesser extent, the shock Mach number. This paper is based on work that was presented at the 20th International Colloquium on the Dynamics of Explosions and Reactive Systems, Montreal, Canada, July 31–August 5, 2005.     

Normal shock wave oscillations in supersonic diffusers

The present paper describes experimental investigations for shock oscillations caused by normal shock wave/turbulent boundary layer interaction in a supersonic diffuser. An array of wall-mounted transducers and especially a line image sensor for the nonintrusive detection of shock displacements were employed to investigate the interactions at low supersonic speeds. The line image sensor was collimated with a conventional schlieren optical system and was a good indicative of capturing the shock oscillating motions in the present configuration. This study shows that the amplitude of the shock motions increases with approaching flow Mach number, and the cause of oscillation of the shock wave can, however, be independent of the Mach number. In addition, the present system employed to determine the shock wave positions and displacements can be effectively applied to a variety of practical problems.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1.0 and the AMS fonts, developed by the American Mathematical Society.     

Numerical simulations of nozzle starting process

The starting process of two-dimensional nozzle flow is investigated both experimentally and numerically. Discussions are made on the comparison between experimental and numerical results. Performances of two numerical methods which are used in the present study of unsteady flow problem are also discussed and indications for future development of numerical tools to study nozzle problems are obtained. Received 16 June 1998 / Accepted 17 August 1998     

Hyperbolicity and one-dimensional waves in compressible two-phase flow models

Hyperbolic models for compressible two-phase flows including a conservative symmetric hyperbolic model are reviewed. The basis for a theory of shock waves is developed within the framework of the latter. The analysis of small amplitude discontinuities allows us to conclude that in general there are two types of shocks corresponding to two sound waves. The problem of transition between a pure phase and a mixture (the phase vacuum problem) is analysed. It is proved that for some models the smooth centred wave solution can not provide such a transition. Within the framework of our conservative model there is the possibility of constructing discontinuous solutions which can resolve the phase vacuum problem.PACS: 47.55Kf, 47.40.-xE. Romenski: On leave from Sobolev Institute of Mathematics, Russian Academy of Sciences, Novosibirsk 630090, Russia     

Two-way coupling model for shock-induced laminar boundary-layer flows of a dusty gas

The present paper describes a numerical two-way coupling model for shock-induced laminar boundary-layer flows of a dust-laden gas and studies the transverse migration of fine particles under the action of Saffman lift force. The governing equations are formulated in the dilute two-phase continuum framework with consideration of the finiteness of the particle Reynolds and Knudsen numbers. The full Lagrangian method is explored for calculating the dispersed-phase flow fields (including the number density of particles) in the regions of intersecting particle trajectories. The computation results show a significant reaction of the particles on the two-phase boundary-layer structure when the mass loading ratio of particles takes finite values. The project supported by the National Natural Science Foundation of China (90205024) and Russian Foundation for Basic Research (RFBR and (RFBR-NSFC-39004) The English text was polished by Yunming Chen     

A computational study of supersonic disk-gap-band parachutes using Large-Eddy Simulation coupled to a structural membrane

Large-scale fluid-structure interaction simulations of compressible flows over flexible supersonic disk-gap-band parachutes are compared with matching experimental results. We utilize adaptive mesh refinement, large-eddy simulation of compressible flow coupled with a thin-shell structural finite-element model. The simulations are carried out in the regime where large canopy-area oscillations are present, around and above Mach 2, where strong nonlinear coupling between the system of bow shocks, turbulent wake and canopy is observed. Comparisons of drag history and its dependence on Mach number are discussed. Furthermore, it is observed that important dynamical features of this coupled system can only be reproduced when sufficient grid resolution is used. Lack of resolution resulted in incorrect flow-physics prediction and, consequently, incorrect fluid-structure interaction coupling.     

Numerical evaluation of passive control of shock wave/boundary layer interaction on NACA0012 airfoil using jagged wall

Shock formation due to flow compressibility and its interaction with boundary layers has adverse effects on aerodynamic characteristics, such as drag increase and flow separation. The objective of this paper is to appraise the prac-ticability of weakening shock waves and, hence, reducing the wave drag in transonic flight regime using a two-dimensional jagged wall and thereby to gain an appropriate jagged wall shape for future empirical study. Different shapes of the jagged wall, including rectangular, circular, and triangular shapes, were employed. The numerical method was validated by experimental and numerical studies involving transonic flow over the NACA0012 airfoil, and the results presented here closely match previous experimental and numerical results. The impact of parameters, including shape and the length-to-spacing ratio of a jagged wall, was studied on aerodynamic forces and flow field. The results revealed that applying a jagged wall method on the upper surface of an airfoil changes the shock structure significantly and disinte-grates it, which in turn leads to a decrease in wave drag. It was also found that the maximum drag coefficient decrease of around 17%occurs with a triangular shape, while the max-imum increase in aerodynamic efficiency (lift-to-drag ratio) of around 10%happens with a rectangular shape at an angle of attack of 2.26?.     

Instantaneous fluctuation velocity and skewness distributions upstream of transition onset

The development of streamwise orientated disturbances through the boundary layer thickness prior to transition onset for zero-pressure gradient boundary layer flow under the influence %Tu = 4.2 is presented. The analysis concentrates on the development of the maximum positive and negative of the fluctuation velocity in order to gain further insight into the transition process. The average location of the peak negative fluctuation velocity over a range of Reynolds numbers was measured in the upper portion of the boundary layer at y/δ ≈ 0.6, whereas the location of the peak positive value was measured at y/δ ≈ 0.3. The disturbance magnitude of the negative fluctuation velocity increased beyond that of the positive as transition onset approached. The distribution and disturbance magnitude of the maximum positive and negative fluctuation velocities indicate that the initiation of transition may occur on the low-speed components of the flow that are lifted up to the upper region of the boundary layer. This is in qualitative agreement with recent direct numerical simulations on the breakdown of the flow on the lifted low-speed streaks near the boundary layer edge. The results presented in this investigation also demonstrate the increased physical insight gained by examining the distributions of the maximum positive and negative of the streamwise fluctuation velocity component associated with the low- and high-speed streaks, compared to time-averaged values, in determining what structures cause the breakdown to turbulence.     

Experimental and numerical investigation of the shock-induced fluidization of a particles bed

An experimental study on unsteady two phase flow is conducted in a vertical shock tube. Shock Mach numbers range from 1.3 to 1.5 in 1 bar. The particles are initially positioned in horizontal beds of various thicknesses. Our research covers a large domain of void fraction from 1 (single particles) to 0.35 (compact beds). The experiments provide shadowgraph images for the recording of particle trajectories (effect of the gas on the particles) and side-wall pressures (action of the particles on the gas). A dense two phase flow model has been elaborated and numerically solved using a finite difference scheme with pseudoviscosity. The simulated shock-induced fluidization of a 2 cm thick bed of 1.5 mm diameter glass particles is compared to the experiment. Received 10 September 1996 / Accepted 4 January 1997     

Pseudo-schlieren CT measurement of three-dimensional flow phenomena on shock waves and vortices discharged from open ends

1A pseudo-schlieren technique is applied to the interferometric computed tomography (CT) measurement of three-dimensional (3-D) shock waves discharged from a square open end and a pair of circular open ends in a shock tube experiment. The experiment is performed for incident shock Mach numbers of 2.0 and 2.2 in nitrogen gas under supersonic post shock flow conditions at the open end. The 3-D density-gradient distributions are evaluated from the CT data of the 3-D density distributions, and are depicted in gray-scale CT images of the gradient magnitude and in pseudo-color CT images of the gradient component. The resultant pseudo-schlieren CT images clearly illustrate the 3-D flow features of shock waves, contact surfaces, and the other sharp density fronts. Their image characteristics and meaning in gas dynamics are discussed in comparison with the pseudo-color images of the density. We demonstrate that the pseudo-schlieren CT technique is a useful tool for studying 3-D problems in shock dynamics. Communicated by K. Takayama PACS 47.32.cd; 47.40.Nm; 47.80.jk     

Numerical modeling of vortex/shock wave interaction and its transformation by localized energy deposition

Three-dimensional unsteady Euler simulations are presented for the interaction of a streamwise vortex with an oblique shock of angle β = 23.3° at Mach 3 and 5. The flowfield features are analyzed for weak, moderate and strong interaction regimes. The details of the free recirculation zone at conditions of subsonic and supersonic flow on the vortex axis are considered. The vortex breakdown under conditions of a subsonic vortex core is characterized by a continuous growth and gradual degeneration of the region, unlike the supersonic core condition wherein a steady recirculation zone is achieved. The possibility of using a localized steady and pulsed periodic energy deposition on the vortex axis for stimulating the breakdown is demonstrated for various interaction regimes. It is shown that the formation of a subsonic wake downstream of an energy source lying on the vortex axis contributes to a more significant growth of the dimensions of the recirculation zone compared to the case when the vortex core remains supersonic. The possibility of achieving the effects similar to the steady case is demonstrated by the effect of a pulsed periodic energy source on the flow under consideration for corresponding equivalence parameters.      

A spectral collocation method for compressible,non-similar boundary layers

An efficient and highly accurate algorithm based on a spectral collocation method is developed for numerical solution of the compressible, two-dimensional and axisymmetric boundary layer equations. The numerical method incorporates a fifth-order, fully implicit marching scheme in the streamwise (timelike) dimension and a spectral collocation method based on Chebyshev polynomial expansions in the wall-normal (spacelike) dimension. The discrete governing equations are cast in residual form and the residuals are minimized at each marching step by a preconditioned Richardson iteration scheme which fully couples energy, momentum and continuity equations. Preconditioning on the basis of the finite difference analogues of the governing equations results in a computationally efficient iteration with acceptable convergence properties. A practical application of the algorithm arises in the area of compressible linear stability theory, in the investigation of the effects of transverse curvature on the stability of flows over axisymmetric bodies. The spectral collocation algorithm is used to derive the non-similar mean velocity and temperature profiles in the boundary layer of a ‘fuselage’ (cylinder) in a high-speed (Mach 5) flow parallel to its axis. The stability of the flow is shown to be sensitive to the gradual streamwise evolution of the mean flow and it is concluded that the effects of transverse curvature on stability should not be ignored routinely.     

Over forty years of continuous research at UTIAS on nonstationary flows and shock waves

Analytical and experimental research on non-stationary shock waves, rarefaction waves and contact surfaces has been conducted continuously at UTIAS since its inception in 1948. Some unique facilities were used to study the properties of planar, cylindrical and spherical shock waves and their interactions. Investigations were also performed on shock-wave structure and boundary layers in ionizing argon, water-vapour condensation in rarefaction waves, magnetogasdynamic flows, and the regions of regular and various types of Mach reflections of oblique shock waves. Explosively-driven implosions have been employed as drivers for projectile launchers and shock tubes, and as a means of producing industrial-type diamonds from graphite, and fusion plasmas in deuterium. The effects of sonic-boom on humans, animals and structures have also formed an important part of the investigations. More recently, interest has focussed on shock waves in dusty gases, the viscous and vibrational structure of weak spherical blast waves in air, and oblique shock-wave reflections. In all of these studies instrumentation and computational methods have played a very important role. A brief survey of this work is given herein and in more detail in the relevant references.This article was processed using Springer-Verlag T_EX Shock Waves macro package 1990.     

Prediction of the turbulent boundary layer development by the lag-entrainment method

The lag-entrainment method, which is a well-established integral method for predicting the development of turbulent boundary layers, is used in this study to predict two-dimensional turbulent separated flow. The method is used in an inverse mode, in which the displacement thickness is specified together with other integral parameters of the boundary layer. It is concluded that the prediction of two-dimensional separated flow by an integral method is feasible, but there is a need for accurate data for both equilibrium and general separated flows for making a comparison.     

Importance of unsteady contributions to force and heating for particles in compressible flows : Part 1: Modeling and analysis for shock–particle interaction

Shock–particle interaction is an important phenomenon. The interaction can be accurately resolved by direct numerical simulations. However, as the length scales of interest are much larger than the particle size in many applications, fully resolving the flow around the particle is impractical. Therefore, rigorous model for momentum and energy exchange in the interaction is very important. Shock–particle interaction is strongly time-dependent, so unsteady mechanisms play important roles in momentum and energy transfer. A model that includes unsteady contributions to force and heating is proposed. The model is used to investigate particle interactions with a planar shock wave and a spherical shock wave. The peak values and the net effects of unsteady contributions are used to measure their importance. The results show the peak values of unsteady contributions are much larger than the quasi-steady ones for a wide range of particle parameters. The net effects of unsteady contributions are important when the particle-to-gas density ratio is small. For the flow behind the spherical shock is unsteady and non-uniform, unsteady contributions have long-time influence on the particle evolution.     

抽吸激波管的性能分析与计算

为了减小由于反射激波和透射激波分叉引起的反射型激波风洞试验气体提前受到污染的现象,本文研究了一种新的具有抽吸的激波管流动,分析了抽吸缝的作用,给出了这种抽吸激波管性能参数的计算方法,同时还给出了反射激波与边界层相互作用引起的激波分叉的形状随抽吸量变化的计算公式。实验证实了边界层抽吸可以有效地减小激波与壁面边界层相互作用所产生的分离现象。计算与测量结果是一致的。     

Enhancement of shock waves

The flow field developed behind a shock wave propagating inside a constant cross-section conduit is solved numerically for two different cases. First, when the density of the ambient gas into which the shock propagates has a logarithmic change with distance. In the second, and the more practical case, the ambient gas is composed of pairs of air–helium layers having a continually decreasing width. It is shown that in both cases meaningful pressure amplification can be reached behind the transmitted shock wave. It is especially so in the second case. By proper choice of the number of air–helium layers and their width reduction ratio, pressure amplification as high as 7.5 can be obtained.