Hypersonic Shock Wave/Boundary Layer Interactions by a Third-Order Optimized Symmetric WENO Scheme

A novel third-order optimized symmetric weighted essentially non-oscillatory(WENO-OS3)scheme is used to simulate the hypersonic shock wave/boundary layer interactions.Firstly,the scheme is presented with the achievement of low dissipation in smooth region and robust shock-capturing capabilities in discontinuities.The Maxwell slip boundary conditions are employed to consider the rarefied effect near the surface.Secondly,several validating tests are given to show the good resolution of the WENO-OS3 scheme and the feasibility of the Maxwell slip boundary conditions.Finally,hypersonic flows around the hollow cylinder truncated flare(HCTF)and the25°/55°sharp double cone are studied.Discussions are made on the characteristics of the hypersonic shock wave/boundary layer interactions with and without the consideration of the slip effect.The results indicate that the scheme has a good capability in predicting heat transfer with a high resolution for describing fluid structures.With the slip boundary conditions,the separation region at the corner is smaller and the prediction is more accurate than that with no-slip boundary conditions.

STUDY OF SWEPT SHOCK WAVE AND BOUNDARY LAYER INTERACTIONS

This paper presents briefly the recent progress on study of swept shock wave/boundary layer interactions with emphasis on application of zonal analysis and correlation analysis to them. Based on the zonal analysis an overall framework of complicated interaction flow structure including both surface flowfield and space flowfield is discussed. Based on correlation analysis the conical interactions induced by four families of shock wave generators have been discussed in detail. Some control parameter and physical mechanism of conical interaction have been revealed. Finally some aspects of the problem and the prospects for future work are suggested.

Near-wall behaviors of oblique-shock-wave/turbulent-boundary-layer interactions

A direct numerical simulation （DNS） on an oblique shock wave with an incident angle of 33.2° impinging on a Mach 2.25 supersonic turbulent boundary layer is performed. The numerical results are confirmed to be of high accuracy by comparison with the reference data. Particular efforts have been made on the investigation of the near-wall behaviors in the interaction region, where the pressure gradient is so significant that a certain separation zone emerges. It is found that, the traditional linear and loga- rithmic laws, which describe the mean-velocity profiles in the viscous and meso sublayers, respectively, cease to be valid in the neighborhood of the interaction region, and two new laws of the wall are proposed by elevating the pressure gradient to the leading order. The new laws are inspired by the analysis on the incompressible separation flows, while the compressibility is additionally taken into account. It is verified by the DNS results that the new laws are adequate to reproduce the mean-velocity profiles both inside and outside the interaction region. Moreover, the normalization adopted in the new laws is able to regularize the Reynolds stress into an almost universal distribution even with a salient adverse pressure gradient （APG）.

Model for Asymmetry of Shock/Boundary Layer Interactions in Nozzle Flows

The reason for the asymmetry phenomenon of shock/boundary layer interactions(SBLI)in a completely symmetric nozzle with symmetric flow conditions is still an open question.A model for the asymmetry of nozzle flows was proposed based on the properties of fluid entrainment in the mixing layer and momentum conservation.The asymmetry model is deduced based on the nozzle flow with restricted shock separation,and is still applicable for free shock separation.Flow deflection angle at nozzle exit is deduced from this model.Steady numerical simulations are conducted to model the asymmetry of the SBLIs in a planar convergent-divergent nozzle tested by previous researchers.The obtained values of deflection angle based on the numerical results of forced symmetric nozzle flows can judge the asymmetry of flows in a nozzle at some operations.It shows that the entrainment of shear layer on the separation induced by SBLTs is one of the reasons for the asymmetry in the confined SBLIs.

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 practicability 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 disintegrates 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 maximum increase in aerodynamic efficiency（lift-to-drag ratio）of around 10 % happens with a rectangular shape at an angle of attack of 2.26？.

Study on Compressible Turbulent Boundary Layer Multiple Shock Wave Interaction in the Duct

The structure and trubulence phenomena of multiple shock wave /turbulent boundary layer interaction (MSW-TBLI) in a square duct were investigated using flow visualization methods and a two-component Laser Doppler Velocimeter (LDV ). First - the MSW-TBLI was visualized by schlieren photography and laser holographic interferography. Second, the time-mean and fluctuating velocities in the MSW-TBLI were explored in detail using LDV Spatial distributions of turbulence intensity,Reynolds shear stress and turbulence kinetic energy are presented.

Study of interaction between shock wave and unsteady boundary layer

This paper reports theoretical and experimental study of a new type of interaction of a moving shock wave with an unsteady boundary layer. This type of shock wave-boundary layer interaction describes a moving shock wave interaction with an unsteady boundary layer induced by another shock wave and a rarefaction wave. So it is different from the interaction of a stationary shock wave with steady boundary layer, also different from the interaction of a reflected moving shock wave at the end of a shock tube with unsteady boundary layer induced by an incident shock. Geometrical shock dynamics is used for the theoretical analysis of the shock wave-unsteady boundary layer interaction, and a double-driver shock tube with a rarefaction wave bursting diaphragm is used for the experimental investigation in this work.

THE INTERACTION OF A SHOCK WAVE WITH THE BOUNDARY LAYER IN A REFLECTED SHOCK TUNNEL

The influence of a nontotal reflection on the interaction of a reflected shock wave with the boundary layer in a reflected shock tunnel has been investigated. The calculating method of the velocity, the temperature and the Mach number profiles in the boundary layer in reflected shock fixed coordinates has been obtained. To account for equilibrium real gas effects of nitrogen, the numerical results show that the minimum Mach number in the boundary layer has been moved from the wall into the boundary layer with the increasing of the incident shock Mach number. The minimum Mach number, the shock angle in the bifurcated foot and the jet velocity along the wall to the end plate are reduced owing to the Increasing of the area of nozzle throat. The numerical results are in good agreement with measurements.

HEATING CHARACTERISTICS OF BLUNT SWEPT FIN-INDUCED SHOCK WAVE TURBULENT BOUNDARY LAYER INTERACTION

An experimental study was conducted on shock wave turbulent boundary layer interactions caused by a blunt swept fin-plate configuration at Mach numbers of 5.0, 7.8, 9.9 for a Reynolds number range of (1.0.similar to 4.7) x 10(7)/m. Detailed heat transfer and pressure distributions were measured at fin deflection angles of up to 30 degrees for a sweepback angle of 67.6 degrees. Surface oil flow patterns and liquid crystal thermograms as well as schlieren pictures of fin shock shape were taken. The study shows that the flow was separated at deflection of 10 degrees and secondary separation were detected at deflection of theta greater than or equal to 20 degrees. The heat transfer and pressure distributions on flat plate showed an extensive plateau region followed by a distinct dip and local peak close to the fin foot. Measurements of the plateau pressure and heat transfer were in good agreement with existing prediction methods, but pressure and heating peak measurements at M greater than or equal to 6 were significantly lower than predicted by the simple prediction techniques at lower Mach numbers.

Numerical Simulation of Two-Dimensional Shock/Boundary-Layer Interaction between a Rocket and Booster

A two-dimensional Reynolds-averaged Navier-Stokes solver is applied to analyze the aerodynamic behavior of the Shock/Boundary-Layer interaction of rocket with a boosted The K-ε turbulence model and a finite volume method in a unstructured body-fitted curvilinear coordinates have been used. The results indicate that the separation and the reattachment occur in the Boundary-Layer of the main rocket because of the shock interaction. The shape of the booster nose effects the flow field obviously. In the case of the hemisphere booster nose the pressure has complicate distributions and the separation is very clear. The distance between the booster and main rocket has the evident effect on the flow field. If the distance is smaller the pressure coefficient is bigger the separation zone even the separation bubble occurs.

Effects of Number of Bleed Holes on Shock-Wave/Boundary-Layer Interactions in a Transonic Compressor Stator

An extensive numerical investigation is conducted to characterize the flow separation control in a transonic compressor cascade with a porous bleed.The bleed holes are arranged on the suction surface in a single row,two staggered rows and three staggered rows.For each bleed scheme,five bleed pressure ratios are examined at an inlet Mach number of 1.0.The results indicate that the aerodynamic performance of the cascade is significantly improved by the porous bleed.For the single-row scheme,the maximum reduction in total pressure losses is 57%.For the two-staggered-row and three-staggered-row schemes,there is an optimal bleed pressure ratio of 1.0,and the maximum reductions in total pressure loss are 68% and 75%,respectively.The low loss in the cascade is due to the well-controlled boundary layer.The new local supersonic region created by the bleed hole is the key reason for the improved boundary layer.The vortex induced by side bleeding provides another mechanism for delaying flow separation.Increasing the bleed holes could create multiple local supersonic regions,which reduce the range of the adverse pressure gradient that the boundary layer needs to withstand.This is the reason why cascades with more bleed holes perform better.

Interaction between internal solitary waves and the seafloor in the deep sea

Internal solitary wave(ISW),as a typical marine dynamic process in the deep sea,widely exists in oceans and marginal seas worldwide.The interaction between ISW and the seafloor mainly occurs in the bottom boundary layer.For the seabed boundary layer of the deep sea,ISW is the most important dynamic process.This study analyzed the current status,hotspots,and frontiers of research on the interaction between ISW and the seafloor by CiteSpace.Focusing on the action of ISW on the seabed,such as transformation and reaction,a large amount of research work and results were systematically analyzed and summarized.On this basis,this study analyzed the wave–wave interaction and interaction between ISW and the bedform or slope of the seabed,which provided a new perspective for an in‐depth understanding of the interaction between ISW and the seafloor.Finally,the latest research results of the bottom boundary layer and marine engineering stability by ISW were introduced,and the unresolved problems in the current research work were summarized.This study provides a valuable reference for further research on the hazards of ISW to marine engineering geology.

AERODYNAMIC HEATING IN THE REGION OF SHOCK AND TURBULENT BOUNDARY LAYER INTERACTION INDUCED BY A CYLINDER

Detailed distributions of heat flux in the region of shock wave and turbulent boundary layer interaction induced by a cylinder were measured in the shock tunnel Oil flow patterns and Schlieren photo- graphs were taken.Empirical relations were given for determining separation shock angle,peaks of heat flux and their locations on both cylinder leading edge and flat plate surface,and other characteristic parameters of the interaction region.

FLAT-PLATE BOUNDARY-LAYER FLOWS INDUCED BY DUSTY SHOCK WAVE

When a dusty shock wave propagates along a flat plate, laminar boundary-layer flows are formed over the solid wall. The induced boundary layer problem is numerically investigated in the present paper. Using a two-continuum medium and twoway coupling model, the governing equations for this two-phase flow system are given and then solved by the finite difference method. The calculation results indicate that the post-shock flow field is characterized by relaxation phenomenon. The effects of the relaxation structure Of the dusty shock wave on the boundary layer are discussed in detail.

Structural uncertainty quantification of Reynolds-Averaged Navier–Stokes closures for various shock-wave/boundary layer interaction flows

Accurate prediction of Shock-Wave/Boundary Layer Interaction(SWBLI)flows has been a persistent challenge for linear eddy viscosity models.A major limitation lies in the isotropic representation of the Reynolds stress,as assumed under the Boussinesq approximation.Recent studies have shown promise in improving the prediction capability for incompressible separation flows by perturbing the Reynolds-stress anisotropy tensor.However,it remains uncertain whether this approach is effective for SWBLI flows,which involve compressibility and discontinuity.To address this issue,this study systematically quantifies the structural uncertainty of the anisotropy for oblique SWBLI flows.The eigenspace perturbation method is applied to perturb the anisotropy tensor predicted by the Menter Shear–Stress Transport(SST)model and reveal the impacts of anisotropy on the prediction of quantities of interest,such as separation and reattachment positions,wall static pressure,skin friction,and heat flux.The results demonstrate the potential and reveal the challenges of eigenspace perturbation in improving the SST model.Furthermore,a detailed analysis of turbulent characteristics is performed to identify the source of uncertainty.The findings indicate that eigenspace perturbation primarily affects turbulent shear stress,while the prediction error of the SST model is more related to turbulent kinetic energy.

Dynamic soil-tunnel interaction in layered half-space for incident plane SH waves

The dynamic soil-tunnel interaction is studied by indirect boundary element method （IBEM）, using the model of a rigid tunnel in layered half-space, which is simplified to a single soil layer on elastic bedrock, subjected to incident plane SH waves. The accuracy of the results is verified through comparison with the analytical solution. It is shown that soil-tunnel interaction in layered half-space is larger than that in homogeneous half-space and this interaction mechanism is essentially different from that of soil-foundation-superstructure interaction.

ASYMPTOTIC STABILITY OF SHOCK WAVES FOR THE OUTFLOW PROBLEM OF A HEAT-CONDUCTIVE IDEAL GAS WITHOUT VISCOSITY

This paper is concerned with an ideal polytropic model of non-viscous and heatconductive gas in a one-dimensional half space. We focus our attention on the outflow problem when the flow velocity on the boundary is negative and we prove the stability of the viscous shock wave and its superposition with the boundary layer under some smallness conditions.Our waves occur in the subsonic area. The intrinsic properties of our system are more challenging in mathematical analysis, however, in the subsonic area, the lack of a boundary condition on the density provides us with a special manner for defining the shift for the viscous shock wave, and helps us to construct the asymptotic profiles successfully. New weighted energy estimates are introduced and the perturbations on the boundary are handled by some subtle estimates.

Dynamic soil-tunnel interaction in layered half-space for incident P-and SV-waves

The dynamic soil-tunnel interaction is studied by the model of a rigid tunnel embedded in layered half-space, which is simplified as a single soil layer on elastic bedrock to the excitation of P- and SV-waves. The indirect boundary element method is used, combined with the Green＇ s function of distributed loads acting on inclined lines. It is shown that the dynamic characteristics of soil-tunnel interaction in layered half-space are different much from that in homoge- neous half-space, and that the mechanism of soil-tunnel interaction is also different much from that of soil-founda- tion-superstructure interaction. For oblique incidence, the tunnel response for in-plane incident SV-waves is com- pletely different from that for incident SH-waves, while the tunnel response for vertically incident SV-wave is very similar to that of vertically incident SH-wave.

A CALCULATING METHOD OF SHOCK WAVE OSCILLATING FREQUENCY DUE TO TURBULENT SHEAR LAYER FLUCTUATIONS IN SUPERSONIC FLOW

One of the more severe fluctuating pressure environments encountered in supersonic or hypersonic flows is the shock wave oscillation driven by interaction of a shock wave with boundary layer. The high intensity oscillating shock wave may induce structure resonance of a high speed vehicle. The research for the shock oscillation used to adopt empirical or semiempirical methods because the phenomenon is very complex. In this paper a theoretical solution on shock oscillating frequency due to turbulent shear layer fluctuations has been obtained from basic conservation equations. Moreover, we have attained the regularity of the frequency of oscillating shock varying with incoming flow Much numbers M and turning angle . The calculating results indicate excellent agreement with measurements. This paper has supplied a valuable analytical method to study aeroelastic problems produced by shock wave oscillation.

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 twophase continuum framework with consideration of the finiteness of the particle Reynolds and Knudsen numbers. The full Lagrangian method is explored for calculating the dispersedphase 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.