Decomposition of mean skin friction in incident shock wave/turbulent boundary layer interaction flows at Mach 2.25

The evolution characteristics of the mean skin friction beneath the supersonic turbulent boundary layer that interacts with incident shock waves at Mach 2.25 are analyzed using Direct Numerical Simulation(DNS). The separated and attached boundary layers in the interaction region that respectively correspond to 33.2° and 28° incident shock angles are considered. The mean skin friction recovery rate for the separated boundary layer is much gentler and distinctly less than that for the attached case where the skin friction completes its recovery within one boundary layer thickness. The novel mean skin friction decomposition method for compressible flows proposed by the recent research is applied in the interaction region to investigate the internal evolution characteristics quantitatively. The results reveal that the three decomposition components are distinctly unequal between the two cases. The contributions of the turbulent motions at different scales to the associated term are focused on using empirical mode decomposition technology. It indicates that the outer large-scale structures dominate separation and reattachment regions, while contributions from inner small-scale structures are limited. In contrast, contributions from the outer largescale structures are dramatically reduced in the attached case, which results in the outer large-scale and inner small-scale motions being of equal importance.

Analytical solutions of turbulent boundary layer beneath forward-leaning waves

As a typical nonlinear wave,forward-leaning waves can be frequently encountered in the near-shore areas,which can impact coastal sediment transport significantly.Hence,it is of significance to describe the characteristics of the boundary layer beneath forward-leaning waves accurately,especially for the turbulent boundary layer.In this work,the linearized turbulent boundary layer model with a linear turbulent viscosity coefficient is applied,and the novel expression of the near-bed orbital velocity that has been worked out by the authors for forward-leaning waves of arbitrary forward-leaning degrees is further used to specify the free stream boundary condition of the bottom boundary layer.Then,a variable transformation is found so as to make the equation of the turbulent boundary layer model be solved analytically through a modified Bessel function.Consequently,an explicit analytical solution of the turbulent boundary layer beneath forward-leaning waves is derived by means of variable separation and variable transformation.The analytical solutions of the velocity profile and bottom shear stress of the turbulent boundary layer beneath forward-leaning waves are verified by comparing the present analytical results with typical experimental data available in the previous literature.

Scaling of interaction lengths for hypersonic shock wave/turbulent boundary layer interactions

The interaction length induced by Shock Wave/Turbulent Boundary-Layer Interactions(SWTBLIs)in the hypersonic flow was investigated using a scaling analysis,in which the interaction length normalized by the displacement thickness of boundary layer was correlated with a corrected non-dimensional separation criterion across the interaction after accounting for the wall temperature effects.A large number of hypersonic SWTBLIs were compiled to examine the scaling analysis over a wide range of Mach numbers,Reynolds numbers,and wall temperatures.The results indicate that the hypersonic SWTBLIs with low Reynolds numbers collapse on the supersonic SWTBLIs,while the hypersonic cases with high Reynolds numbers show a more rapid growth of the interaction length than that with low Reynolds numbers.Thus,two scaling relationships are identified according to different Reynolds numbers for the hypersonic SWTBLIs.The scaling analysis provides valuable guidelines for engineering prediction of the interaction length,and thus,enriches the knowledge of hypersonic SWTBLIs.

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.

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）.

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.

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.

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.

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？.

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.

INTERACTION BETWEEN COHERENT STRUCTURES IN WALL REGION OF A TURBULENT BOUNDARY LAYER

Using the idea of general resonant triad of the hydrodynamic stability, the theoretical models for coherent structures in the wall region of a turbulent boundary layer is proposed. The interaction between coherent structures in the wall region of a turbulent boundary layer is studied by combining the compact finite differences of high numerical accuracy and the Fourier spectral hybrid method for solving the three dimensional Navier Stokes equations. In this method, the third order mixed explicit implicit scheme is employed for the time integration. The fifth order upwind compact finite difference schemes for the nonlinear convection terms in the physical space, and the sixth order center compact schemes for the derivatives in spectral space are descried, respectively. The fourth order compact schemes satisfied by the velocities and pressure in spectral space is derived. As an application, the method is implemented to the wall region of a turbulent boundary to study the interaction between coherent structures. It is found that the numerical results are satisfactory.

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.

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.

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.

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.

Study on Hydrodynamic Characteristics of Wave Turbulent Bottom Boundary Layer Using A Large-Sized Wave Flume

Experimental studies were conducted in a super-large wave flume,aiming at uncovering the hydrodynamic characteristics involved in the turbulent wave boundary layer of full scale environment.An explicit formula of boundary layer thickness on rough turbulent flow was presented based on the measured velocity data of the present study and collected experimental data on wave boundary layer.It was found that the bottom wave-associated nominal stresses under the conditions of prototype scale tests suppress the vertical turbulence scattering upward over the boundary layer,which accounts for thickening of the boundary layer under wave condition.Such effect has yet not been reported in the literatures using oscillatory U-tube or small-sized wave flume.The phase inconsistency in the turbulent boundary layer to the free stream velocity(velocity immediately outside the boundary layer)is within15°,which is remarkably smaller than the results from oscillatory U-tubes,as well as the larger wave flume experiment presented by Xie et al.(2021),showing that the coarser bed would further reduce the phase lead.The intensity of the vertical turbulent component is approximately 1/2 of the horizontal component,which has larger ratio compared with the value of 1/5 reported by previous studies.Especially,it was also found that the vertical turbulent energy was approximately 3/4 of the turbulent energy in spanwise directions(y-direction).This means that the turbulent fluctuation has similar order in all three-directions(x,y,z)in a full scale environment and highlights that the turbulent components in all the three directions should not be neglected when calculating the total turbulent energy.

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.

INSTABILITY WAVES IN THE WALL REGION OF A TURBULENT BOUNDARY LAYER ON A FLAT PLATE

Coherent structures and the bursting phenomena in the wall region of a turbulent boundary layer play a very important role in determining the characteristics of the boundary layer. Yet the nature and the origin of the coherent structures are unclear until now.In this paper, nonlinear stability calculations for the wall region of a turbulent boundary layer have been made.It was found that there do exist instability waves which may be responsible for the coherent structures.

A Simple Eddy Viscosity Model of Rough Turbulent Wave Boundary Layer

A one-layer time-invariant eddy viscosity model is specified to develop a mathematical model for describing the essential features of the turbulent wave boundary layer over a rough bed. The functional form of the eddy viscosity is evaluated based on computational results from a two-equation turbulence model in which the eddy viscosity varies with time and space. The present eddy viscosity model simplifies much of the mathematical complexity in many existing models. Predictions from the present model have been compared with a wide range of experimental data. It is found that the eddy viscosity model adopted in the present study is physically reasonable.

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.