Two-dimensional Compression Corner Research Articles

Response of hypersonic compression corner flow to upstream disturbances

Hypersonic flow over a two-dimensional compression corner is investigated using computational fluid dynamics and global resolvent analysis in this study, which is a continuation of the work done by Hao et al. (J. Fluid Mech., vol. 919, 2021, p. A4). The same baseline free-stream conditions with a Mach number of 7.7 and a unit Reynolds number of 4.2 × 106 m−1 are considered. The ramp angles range from 0° (equivalent to a flat plate) to 12° (slightly below the critical angle of global instability). During this process, the base flow evolves from no separation to incipient separation to large separation. The resolvent analysis reveals that the optimal response to upstream disturbances localised near the leading edge is in the form of steady streamwise streaks for all interaction strengths, which arise from transient growth in the flat-plate boundary layer due to the lift-up mechanism and significantly grow near the corner due to the Görtler instability. The most amplified spanwise wavelength decreases as the ramp angle is increased and scales with the incoming boundary-layer thickness.

Numerical investigation of a Mach 6 hypersonic laminar flow on two-dimensional cold-wall compression corners with controlled surface roughness

Numerical simulations are performed in order to investigate the physics of a Mach 6 hypersonic, laminar flow on different configurations of a two-dimensional compression corner. For this geometry, typically characterising control surfaces of re-entry vehicles, the interaction between the incoming boundary layer and the ramp-induced shock wave can lead to the formation of a separated-flow region. The numerical experiments, carried out under adiabatic and a cold-wall conditions, include the presence of a two-dimensional sinusoidal roughness patch, which is placed at various locations upstream of the ramp, in order to evaluate the effects of the surface waviness on the separation bubble. When the roughness elements are placed upstream of the smooth separation point, the recirculation bubble stretches towards the roughness position. This behaviour is induced by the thickening of the boundary layer downstream of the roughness patches, which cause a displacement of the laminar flow. No transition is observed downstream of the patches under the investigated geometrical and flow conditions. For a patch downstream of the smooth separation point, instead, no appreciable effects on the bubble length are noticed. However, the surface roughness inside the bubble can alter the recirculation pattern within the reverse-flow region. Hence, together with the length of the separated flow region, also the heat transfer at the wall is affected by the roughness because of the different recirculation patterns inside the bubble. In particular, the Stanton number highlights a redistribution of the heat-flux intensity between the main peak at reattachment and the secondary peaks inside the separated flow. This effect is more evident for higher ramp angles. These results highlight the importance of roughness-induced effects on the complex phenomenon that shock-wave/boundary-layer interaction is.

Occurrence of global instability in hypersonic compression corner flow

Hypersonic flow over a two-dimensional compression corner with a Mach number of 7.7 and unit Reynolds number of 4.2 × 106 m−1 is numerically investigated. Special emphasis is given to the onset of global instability with respect to three-dimensional perturbations. Global stability analysis is performed for various ramp angles and wall temperatures. It is found that the shock-induced separated flow system becomes unstable when the ramp angle is beyond a certain value. The critical ramp angle increases slightly with the wall temperature, although the length of the separation region is significantly enlarged. The global instability is shown to be closely linked with the occurrence of secondary separation beneath the primary separation bubble. A criterion is established based on a scaled ramp angle defined in the triple-deck theory to predict the global stability boundary, which depends on the free-stream conditions and geometries only.

Effect of Small Bluntness on Formation of Görtler Vortices in a Supersonic Compression Corner Flow

The influence of small cylindrical bluntness of the leading edge of a flat plate on formation of spatial structures in a nominally two-dimensional supersonic compression corner flow at the Mach number M∞ ≈ 8 and a laminar state of the undisturbed boundary layer is studied by the method of temperature-sensitive paints. Streamwise vortices are found in the region of reattachment of the separated flow in a wide range of Reynolds numbers (0.15 · 106–2.55 · 106) for various angles of flow deflection and plate lengths. It is demonstrated that the existence of these vortices induces spanwise oscillations of the heat transfer coefficient; the amplitude of these oscillations may reach 30%. The maximum deviations of the Stanton number reaching 80% are observed in the case with significant roughness of the leading edge of the flat plate. Both the maximum Stanton numbers in the reattachment region and the amplitude of spanwise oscillations of the Stanton number induced by streamwise vortices are found to decrease significantly in the case of small bluntness of the leading edge. Solutions of three-dimensional Navier–Stokes equations are obtained for some test conditions. The computed results are in good agreement with experimental data, which points to a significant stabilizing effect of small bluntness on the intensity of streamwise vortices.

Numerical studies of shock wave interactions with a supersonic turbulent boundary layer in compression corner:Turning angle effects

Abstract Direct numerical simulations (DNS) were performed to investigate the interactions of a Mach 2.9 turbulent boundary layer with shock waves of varying strengths in compression corner. The supersonic turbulent boundary layer was triggered by wall blowing-and-suction perturbations. The shock waves were produced by two-dimensional compression corners of 8, 14, 20 and 24°. Compared with previous DNS results and experimental data, the numerical calculations were validated. The effects of shock wave on the boundary layer are studied by both flow visualizations and statistical analysis, and the results show that the intensity of fluctuations is amplified greatly by the shock wave. With the increasing of turning angle, three-dimensionality of separation bubble is significantly enhanced. Based on the statistics and power spectrum of the wall pressure signals, the effect of turning angle on the unsteadiness of shock motion is also studied, and the results show that the shock motions are quite different in the small and the large turning angle cases. The motion in the 8° and 14° cases is characterized by high-frequency and small-amplitude, but the low-frequency and large-scale streamwise oscillation is the main feature in the 20° and 24° cases. The effect of turning angle on the turbulence state is analyzed by using the anisotropy of Reynolds stress tensor. The coherent vortex structures are also studied qualitatively. The results indicate that the cane-like streamwise vortexes in the near-wall region are the dominant structure for the small angle cases, while the hairpin vortexes and packets in the outer layer play the leading role in the large angle cases. According to the quantitative analysis of turbulent kinetic energy budgets in the separation region, the effect of turning angle on the transport mechanism is studied. It is found that the influence of shear layer above separation bubble on the mechanism is significant.

Wall-Normal-Free Reynolds-Stress Closure for Three-Dimensional Compressible Separated Flows

A near-wall Reynolds-stress closure that is independent of the distance from the wall and of the normal to the walldirection isdevelopedandvalidated.Particularattention wasgiven intheapplicabilityofthemodeltocomplex three-dimensional e ows with shock waves and boundary-layer separation. In the separated e ow region, measurements andmodelcomputations indicatethatthe e atnessparameter Aoftheanisotropy tensor aij approaches unity. Therefore, controlofseparation isachieved in themodel through theparticularfunctional dependenceoftherapid pressure‐strain isotropization of production model coefe cienton A. Echo termsaretreated by replacing geometric normalsanddistancesbyfunctionsofthegradientsofturbulencelengthscaleandanisotropytensorinvariants.The modelisinitiallycomparedwithmeasurementsforcompressiblee at-plateboundary-layere ows.Itisthenvalidated by comparison with experimental data in a two-dimensional compression corner oblique shock-wave/boundarylayer interaction at Mach 3. Finally the model is applied to the computation of the three-dimensional interaction of a Mach 1.5‐1.8 strong shock wave with the boundary layers of a rectangular channel e tted with a swept bump on the lower wall, and results are compared with measurements. One important advantage of the proposed model is its robustness in complex three-dimensional e ows. A detailed discussion of therange of validity of the model and possible improvements is presented.

Megahertz Visualization of Compression-Corner Shock Structures

The interactions between shock waves and turbulent boundary layers in a Mach 2.5 wind tunnel have been visualized by a megahertz-rate imaging system. The shock waves were produced by two-dimensional compression corners having angles of 14 and 24 deg, and the flows were, respectively, attached and separated. At the compression corner, the sequential images clearly indicate the correlation between the shock motion and the incoming turbulent boundary layer. Some large eddies in the boundary layer cause the shock to move in the streamwise direction for distances as large as the boundary-layer thickness at a frequency as high as large-eddy frequency (U e /δ), but other eddies seem to have minor effect on the shock wave. The images also indicate how the shock waves influence the boundary-layer structures

Three-dimensional mixed explicit-implicit generalized Galerkin spectral element methods for high-speed turbulent compressible flows

In high speed flows the interactions of shock waves with turbulent boundary layers are important design considerations because of the complex flowfields resulting in increased adverse pressure gradients, skin friction and temperatures. Unsteadiness and three-dimensional flowfield structure are also characteristic of shock wave turbulent boundary layer interactions. Such physical phenomena require sophisticated numerical schemes in the solution of governing equations. The purpose of this paper, therefore, is to introduce an accurate and efficient approach—the Mixed Explicit-Implicit Generalized Galerkin Spectral Element Method (MEI-GG-SEM) with Legendre polynomial spectral elements in which flowfield dependent implicitness parameters provide automatically adequate computational requirements for compressible and incompressible flows or high speed and low speed flows. This is in contrast to the traditional approach in which all-speed-regime analysis requires a separate hyperbolic-elliptic pressure equation for pressure correction if the flow becomes incompressible. In the MEI-GG-SEM scheme, mesh refinements are carried out adaptively until shock waves are resolved, followed then by the adaptive increase of Legendre polynomial degrees until turbulence microscales are resolved, in which the traditional turbulence modeling is no longer required, aimed toward direct numerical simulation. In order to demonstrate the validity of the theory and numerical procedure, two-dimensional flat plate and compression corner high speed flows are investigated, followed by a three-dimensional sharp leading edged fin for swept shock wave turbulent boundary layer interactions. Comparisons of the present study with experimental measurements and other numerical studies show favorable agreement.

Experimental, analytical, and computational methods applied to hypersonic compression ramp flows

Experimental data fully laminar and transitional shock-wave/boundary-layer interactions in two-dimensional compression corners are provided and used for the validation of two full Navier-Stokes solvers, as well as for checking the capabilities and limitations of simple analytical prediction methods. Viscous pressure interaction, free interaction, and inviscid oblique shock theory are found to predict well the pressure levels the flat plate upstream of the interaction, within the separated region, and downstream of the interaction, respectively. The reference temperature theory is found to perform well in attached flow regimes both upstream and downstream of the interaction region and to provide the basis for a universal peak heating correlation law. Full Navier-Stokes computations are necessary, however, to predict the extent of the interaction region and the associated influence the pressure distribution (control effectiveness) as well as the detailed heat transfer distribution. To achieve this, very fine gridding coupled with the use of strict convergence criteria (based the evolution of the location of the separation point rather than standard density residuals) is shown to be necessary. It is finally shown that, although sophisticated turbulence models need to be further developed before the detailed characteristics of fully turbulent shock-wave/boundary-layer interactions may be predicted, transitional interactions (where transition typically occurs in the neighborhood of reattachment) may be adequately handled by algebraic turbulence models switched on just downstream of reattachment.

Prediction of fluctuating pressure in attached and separated turbulent boundary-layer flow

A methodology is presented that predicts the fluctuating pressure and power spectra for attached zeropressure gradient and separated turbulent boundary-layer flow on smooth and rough surfaces. Attached flow conditions use a prediction technique that employs a transformation of boundary-layer properties from the compressible to the incompressible plane where a comparison can be made to an extensive data base. For a rough wall, it is shown that the rms pressure, which scales with wall shear, can be predicted by augmenting the smooth wall value by the rough/smooth skin-friction ratio. Relative to nonattached flow, represented by two-dimensional compression corner and three-dimensional fin-generated shock/boundary-layer interactions, the rms pressure is shown to scale with approach flow conditions and the oblique shock in viscid pressure rise. For this situation, a new in viscid angle has been defined as = a + /3 sin^U/M) where a is the shock generator angle and /3 is a parameter based on two-dimensional or three-dimensional interactions. Both rms pressure and power spectra have been correlated in terms of undisturbed approach flow boundary-layer parameters and modified inviscid shock strength relations to provide engineering solutions for the design resolution to complex flow problems.

Numerical studies of supersonic flow over a compression corner

SummaryNumerical solutions of the Reynolds-averaged Navier-Stokes equations are presented for the shock/boundary-layer interaction which occurs with the attached, near-adiabatic, turbulent flow of air over a two-dimensional compression corner of 11° at a Mach number of 2·5.It is shown that for this near-adiabatic flow, the isenthalpic and non-isenthalpic Navier-Stokes equations produce solutions which are very similar in respect of the velocity,pressure and density fields.In the first part of the work, two different upstream, or approaching boundary-layer profiles are considered: one with a normal full velocity profile and the other with a less full velocity profile corresponding to a boundary layer that has developed in an adverse pressure gradient. Several turbulence models are compared using the isenthalpic form of the equations (because the computations are more economical). It is found that agreement with previous experiments (such as in the location of the shock and density profile predictions) is improved in the vicinity of the interaction using the non-equilibrium Johnson-King model compared to the equilibrium models of Baldwin-Lomax and Cebeci-Smith.The second part of the work examines the effects of turbulent Prandtl number (Prt) modelling for this flow using the non-isenthalpic form of the Navier-Stokes equations. Three models for the turbulent Prandtl number are tested. It is found that modelling Prt affects the velocity, pressure and density fields only very slightly, and that the main impact is on the prediction of temperatures very close to the wall. The adiabatic wall temperature variation through the interaction has been measured experimentally and compared with the predictions. The best agreement was obtained using Wassel and Catton's model for Pr, rather than the familiar assumption that Prt = 0·9 everywhere in the flow.

Turbulence structure in a shock wave/turbulent boundary-layer interaction

The boundary-layer turbulence structure in a two-dimensional 24-deg compression corner flow was investigated experimentally in the Princeton University 203 x 203-mm supersonic blowdown wind tunnel. The incoming conditions were M<» = 2.84, Re^/l = 6.5 x 10, and 60 = 26 mm. The results show that the maximum mass-flux turbulence intensity is amplified by a factor of about 5, whereas the mean mass flux increases by only 2 through compression. Probability density functions (pfd's) of the mass-flux fluctuations show that upstream the distributions are Gaussian-like and typical of a fully turbulent boundary layer. Behind the interaction, however, the distributions are bimodal, centering about a level indicative of the freestream mass flux and a lower level indicative of the mass flux near the wall. The unsteady shock motion does not appear to contribute signficantly to the turbulence amplification. It is suggested that the strong, bimodal mixing indicated in the pdf's is probably caused by the presence of large-scale motions associated with the instability of the inflectional velocity profiles observed downstream of the interaction. Space-time correlations of the mass flux and wall pressure were measured, as well as the level of intermittency of the boundary layer to further characterize the changes in the boundary-layer structure through the interaction.

The Structure of Turbulence in a Supersonic Shock-Wave/Boundary-Layer Interaction

This paper reports the experimental results from a detailed investigation of the turbulent flowfields in supersonic shock-wave/boundary-layer interactions at Af=2.25. The interactions were produced by twodimensional compression corners having angles of 8, 13, and 18 deg, the flows being respectively attached, incipiently separated, and separated. Turbulence data from a laser velocimeter and a constant-temperature, hotwire anemometer are presented along with a mean flow survey from wall and pitot-static pressures. Qualitative aspects of the turbulence deduced from spectral analysis and high-speed schlieren pictures are also discussed. It is shown that a large amount of the turbulent energy is contained in large-scale structures that are still observed downstream of the interacting region, despite the severe pressure gradient. The lateral extent of these structures is of the order of one boundary-layer thickness and is roughly half of their longitudinal scale. A low-frequency unsteadiness is associated with the existence of a separation bubble, but does not affect the rest of the flow. The Reynolds shear stress is reduced in the vicinity of the separation bubble where the spatial derivatives of the normal stresses become significant.

Turbulent boundary-layer interaction with a shock wave at a compression corner

The local interaction of an oblique shock wave with an unseparated turbulent boundary layer at a shallow two-dimensional compression corner is described by asymptotic expansions for small values of the non-dimensional friction velocity and the flow turning angle. It is assumed that the velocity-defect law and the law of the wall, adapted for compressible flow, provide an asymptotic representation of the mean velocity profile in the undisturbed boundary layer. Analytical solutions for the local mean-velocity and pressure distributions are derived in supersonic, hypersonic and transonic small-disturbance limits, with additional intermediate limits required at distances from the corner that are small in comparison with the boundary-layer thickness. The solutions describe small perturbations in an inviscid rotational flow, and show good agreement with available experimental data in most cases where effects of separation can be neglected. Calculation of the wall shear stress requires solution of the boundary-layer momentum equation in a sublayer which plays the role of a new thinner boundary layer but which is still much thicker than the wall layer. An analytical solution is derived with a mixing-length approximation, and is in qualitative agreement with one set of measured values.

Correlation Technique for Predicting Attached Turbulent Boundary-Layer/FIap Interaction Pressures

THE method of Lees-Reeves-K lineberg has been successful for r nidly predicting a large class of interacting laminar flows. Hunter and Reeves * extended the laminar work and presented a method for calculating the two-dimensional flow separation and reattachment of a turbulent boundary layer caused by a compression corner. In this work, which is a summary of Ref. 2, a further extension is made to supersonic turbulent flows over adiabatic two-dimensional compression corners where the turning angle is such that the flow remains attached. The importance of the problem coupled with the success of the moment method for similar flows strongly suggests its development for applications where rapid calculations are essential. Contents The flow of a two-dimensional supersonic turbulent boundary layer over an adiabatic compression corner is studied. The range of compression angles is restricted to those for which the flow remains attached to the surface. The moment method is used to determine the solution with the pressure distribution as the primary quantity of interest. The equations governing the solution for this problem have been set forth by previous authors1'3 and are used in a similar form. Since the method is an integral one, a family of profiles is needed to complete the formulation. Reference 3 used a combination of experimental values, existing analytical solutions, and a power law profile in the limit 6/d*-*l to obtain the necessary family. These profile results are also used here. The outer edge boundary condition coupling the viscous and inviscid flow regions can be either a Prandtl-Meyer or tangent wedge relation. Because of the fullness of the turbulent profiles and the existence of shock waves deep within the layer, the tangent wedge relation was found more useful and was used in obtaining Figs. 1-3. The angles considered in this study are relatively small. Therefore, the flow, which starts out supercritical, remains so, and a fully supercritical interaction results. A typical calculation of such a case is shown in Fig. 1 along with the data of Roshko and Thomke.4 This is for an M=5, /^ =0.38 x 106, a = 13 deg compression. The agreement is very poor.

Comparison of Multiequation Turbulence Models for Several Shock Boundary-Layer Interaction Flows

Several multiequation eddy viscosity models of turbulence are used with the Navier-Stokes equations to compute three classes of experimentally documented shock-separated turbulent boundary-layer flows. The types of flow studied are: (1) a normal shock at transonic speeds in both a circular duct and a two-dimensional channel; (2) an incident oblique shock at supersonic speeds on a flat surface; and (3) a two-dimensional compression corner at supersonic speeds. Established zero-equation (algebraic), one-equation (kinetic energy), and two-equation (kinetic energy plus length scale) turbulence models are each utilized to describe the Reynolds shear stress for the three classes of flows. These models are assessed by comparing the calculated values of skin friction, wall pressure distribution, velocity, Mach number, and turbulent kinetic energy profiles with experimental measurements. Of the models tested the two-equation model results gave the best overall agreement with the data.

Supersonic Shock Wave Turbulent Boundary-Layer Interactions

Results are presented of an experimental investigation of shock wave turbulent boundary-layer interactions in supersonic flow. The experiments were conducted at a freestream Mach number of 2.96 and over a boundarylayer Reynolds number range of 10 5 to 10 6. Surface static pressure measurements, oil flow photographs, and interferograms were obtained to define the length of separation and the incipient separation angles for 1) twodimensional compression corner and 2) planar shock wave interactions with a turbulent boundary layer. The tests were conducted in a high unit Reynolds number freestream on a long flat plate with a turbulent boundarylayer thickness in the region of from 0.12 to 0.18 in. Direct comparisons were made between the compression corner and incident shock wave interactions to determine the effects of configuration on turbulent boundary-layer separation. For both configurations the length of the separated region was found to decrease and the incipient separation angle to increase with increasing Reynolds number. For constant Reynolds number, the overall pressure rise for incipient separation was approximately the same for the compression corner and the incident shock wave interaction. Turbulent boundary-layer separation was found to be of the free interaction type whereby the separation angle and pressure distribution through separation were independent of Reynolds number, overall pressure rise, and configuration. fo Nomenclature skin friction coefficient at beginning of freestream Mach number pressurepressure freestream pressure Reynolds number based on freestream condition and boundary-layer thickness at beginning of . span °f shock generator stagnation temperature wall temperature axial distance from flat plate leading edge axial location of center of axial distance from flat plate/ramp hinge line to shock generator leading edge axial location of separation point axial offset distance vertical distance between flat plate and shock generator leading edge effective incipient separation corner angle compression ramp angle shock generator angle boundary-layer thickness at beginning of

Numerical Solutions of Supersonic and Hypersonic Laminar Compression Corner Flows

An efficient time-splitting, second-order accurate, numerical scheme is used to solve the complete Navier-Stokes equations for supersonic and hypersonic laminar flow over a two-dimensional compression corner. A fine, exponentially stretched mesh spacing is used in the region near the wall for resolving the viscous layer. Good agreement is obtained between the present computed results and experimental measurement for a Mach number of 14.1 and a Reynolds number of 1.04 x 10(exp 5) with wedge angles of 15 deg, 18 deg, and 24 deg. The details of the pressure variation across the boundary layer are given, and a correlation between the leading edge shock and the peaks in surface pressure and heat transfer is observed.

Incipient Separation of a Supersonic Turbulent Boundary Layer at High Reynolds Numbers

Two-dimensional compression corner and axisymmetric flare geometries were used in this study of shock wave interaction with a compressible turbulent boundary layer. The study was carried out at a Mach number of 2.9 and over a Reynolds number range of 10 5<Re60<107 (Re^up to 10 9). Detailed surface pressure, schlieren, and oil-flow data were obtained for several corner angles. A major finding of this study is that incipient separation is a gradual rather than an abrupt phenomenon. Incipient separation corner angles were found to be within a band of about 16°-18° and essentially independent of Reynolds number over the range studied.

An experimental study of turbulent separating and reattaching flows at a high Mach number

Separating and reattaching flows in a two-dimensional compression corner were investigated experimentally at a Mach number of 7·0 and Reynolds numbers (based on the distance from the leading edge to the corner) of 4·75 × 106, 9·51 × 106and 1·55 × 107. Heat-transfer measurements and Pitot traverses in the upstream boundary layer showed that the boundary layer had become fully turbulent at the start of the interactions. Increases in the Reynolds number gave increases in the length of separated shear layers and decreases in the corner angle required for incipient, separation. The reattachment pressure coefficients gave good agreement with the criterion of Batham (1969).