Compression Corner Research Articles

Uncertainty Assessment of Hypersonic Aerothermodynamics Prediction Capability

The present paper provides the background of a focused effort to assess uncertainties in predictions of heat flux and pressure in hypersonic flight (airbreathing or atmospheric entry) using state-of-the-art aerothermodynamics codes. The assessment is performed for four mission relevant problems: (1) shock turbulent boundary layer interaction on a compression corner, (2) shock turbulent boundary layer interaction due a impinging shock, (3) high-mass Mars entry and aerocapture, and (4) high speed return to Earth. A validation based uncertainty assessment approach with reliance on subject matter expertise is used. A code verification exercise with code-to-code comparisons and comparisons against well established correlations is also included in this effort. A thorough review of the literature in search of validation experiments is performed, which identified a scarcity of ground based validation experiments at hypersonic conditions. In particular, a shortage of useable experimental data at flight like enthalpies and Reynolds numbers is found. The uncertainty was quantified using metrics that measured discrepancy between model predictions and experimental data. The discrepancy data is statistically analyzed and investigated for physics based trends in order to define a meaningful quantified uncertainty. The detailed uncertainty assessment of each mission relevant problem is found in the four companion papers.

A computational investigation of laminar shock/wave boundary layer interactions

AbstractHypersonic laminar flow past a compression corner has been numerically investigated using time-accurate computational fluid dynamics (CFD) approach. Two flow conditions were considered relevant to high and low enthalpy conditions with a total specific enthalpy of 19MJ/kg and 2·8MJ/kg. The Mach number and unit Reynolds number per metre were 7·5, 9·1 and 3·10 × 105 and 32·2 × 105 respectively. These free stream conditions provided attached, incipiently separated and fully separated flows for ramp angles between θw = 5° to 24°. A grid independence study has been carried out to estimate the sensitivity of heat flux and skin friction in the strong interaction regions of the flow. The investigation was carried out assuming the flow to be laminar throughout and high temperature effects such as thermal and chemical nonequilibrium are studied using Park’s two temperature model with finite rate chemistry. A critical comparison has been made with existing steady state computational and experimental data and the study has highlighted the importance of high temperature effects on the flow separation and reattachment.

Shockwave/Boundary-Layer Interaction Control on a Compression Ramp Using Steady Micro Jets

An experimental investigation was conducted to control the amplitude of shock unsteadiness associated with a 24 deg compression-ramp-induced interaction in a Mach 2 flow.Two control configurations in the form of an array of 1) 16 90-deg-pitched steady micro-air-jet vortex-generating devices (AJVG1), and 2) eight pairs of 45-deg-pitched steady micro-air-jet vortex-generating devices (AJVG2) were studied. EachAJVGdevice was placed upstream of the interaction region at 12:5� from the compression corner. Both micro-AJVG configurations show a reduction in separation shock strength and help considerably reduce the height of the lambda-wave triple point with increase in Poj . Pitching the microjets at 45 deg, as in the AJVG2 configuration, prevents a stronger control-generated bow shock to form ahead of the injectors and, hence, reduces the obstruction component of the interaction significantly. A well defined separation line for no control is seen to get replaced by a highly corrugated separation line with control. Significant reduction (up to 67%) in the peak rms value is observed in the intermittent region of separation with AJVG1 for Poj � 208:5 kPa while the same is achieved with AJVG2 at a much higher Poj�>500 kPa�. The spectral content of the pressure fluctuations also indicate that, relative to the AJVG2 configuration, AJVG1 is successful in reducing the amplitude of fluctuations in the range of unsteadiness by an order of magnitude as soon as Poj exceeds 208.5 kPa. The amplitude of these fluctuations is seen to further decrease with increase in Poj.

Study of a Compression-Ramp Interaction Using Large-Eddy Simulation/Reynolds-Averaged Navier-Stokes Models

Two large-eddy simulation/Reynolds-averaged Navier–Stokes models are applied to a shock/boundary interaction generated by a 20 deg compression corner. The models are designed to transition from unsteady Reynolds-averaged Navier–Stokes to large-eddy simulation as the boundary layer shifts from its logarithmic behavior to its wakelike response, but they differ in that one model requires a preselection of a model constant for each problem, while the other computes this constant as a function of local and ensemble-averaged turbulence properties. Predictions are compared with mean-flow and second-moment experimental data obtained at Princeton University. In general, calculatedmean-flow velocity, surface-pressure, and surface skin-friction distributions agree well with the experiment, with the most noticeable discrepancy being a slight overprediction of the level of upstream influence induced by the shock wave. Comparisons with mass-flux fluctuation intensity, Reynolds axial stress, and Reynolds shear-stress profiles are also presented. These show generally good agreement with experimental trends relating to Reynolds stress amplification and anisotropy modulation. The calculations also predict the existence of a low-frequency motion of the separation shock that is probably associated with the motion of the backflow region. Higher-frequency modulations of the shock front as induced by the passage of coherent, streaklike structures through the shock also appear to contribute to the measurable intermittency effects.

Three-dimensional features of a Mach 2.1 shock/boundary layer interaction

2D particle image velocimetry was used to study the three-dimensionality of the shock-boundary layer interaction generated by a small 20° compression ramp in a low aspect ratio continuously operated wind tunnel. High-resolution data were taken in four streamwise-wallnormal planes: three planes located in the sidewall boundary layer and one near the tunnel centerline. The incoming boundary layer was found to show three-dimensionality, with significant overshoot in the velocity profiles observed near the sidewall. The size of the wedge influenced the interaction, which was weaker than that observed in the case of a large compression wedge. The flow turning angle was ≈8° near the tunnel centerline and changed significantly across the span. Measurements behind the compression wedge in the centerline plane showed that both velocity and turbulence properties were nearly fully recovered ≈14δ behind the compression corner. The shock angle varied with spanwise position, and a multi-shock structure was observed in the sidewall planes. The size of the interaction decreased in the sidewall boundary layer. Non-monotonic variations in both velocity and turbulence profiles across the sidewall planes suggest the presence of significant spanwise flows, possibly corner vortices.

Control of shock unsteadiness in shock boundary-layer interaction on a compression corner using mechanical vortex generators

An experimental study was conducted to control the unsteadiness of separation shock in a Mach 2 24° compression ramp-induced interaction using mechanical vortex generators (VG). Control devices in the form of an array of single-row delta-ramps were placed upstream of the interaction region and tested for two streamwise locations with respect to the boundary layer thickness (δ) at the interaction location and height ‘h’ of the delta-ramps, i.e., at 27.5δ or h/δ = 0.65 and at 12.5δ or h/δ = 0.26, respectively. Surface oil study revealed traces of streamwise counter-rotating vortex pairs generated downstream of these devices. Measurements using pressure-sensitive paint also showed a spanwise sinusoidal pattern of wall pressure variation indicating generation of streamwise vortices from these control devices. These vortices, on interaction with the reverse flow in the separation bubble, replaced a well-defined separation line (for no control) by a highly corrugated separation line. In the region of separation, the mean pressure distribution gets modified while the peak rms value in the intermittent region of separation showed significant changes. Additionally, the spanwise spacing ‘s’ of the vertex of the delta ramps seemed to be an important parameter in controlling the peak rms value. A decrease in this spacing, i.e., VG1 with s = 0, significantly reduced the peak rms value (by 50 and 35 %) while an increase in the spacing, i.e., VG2 with s = 1 mm, consistently showed an increase (by 12 and 30 %) in the separation shock unsteadiness relative to no control, irrespective of their placement location (of h/δ = 0.65 and 0.26, respectively).

Shock-Wave Boundary-Layer Interaction Study on a Compression Corner Using Pressure-Sensitive Paint

Experiments have been performed to study a compression corner induced turbulent boundary layer interactions in a freestream Mach number of 2.05 without and with control. Two configurations of vortex generators (VG), in the form of an array of deltaramps placed upstream of the interaction region at 27.5δ or h/δ = 0.65, have been tested to control the interaction. Pressure sensitive paint (PSP) measurements were made using a binary paint developed in-house. Reasonably good agreement of PSP results with mean static pressure measurements has been observed. The spanwise wall pressure distribution immediately downstream of the control devices show a sinusoidal pattern indicating the generation of streamwise vortices from VG devices. The interaction of these vortices with the reverse flow in the separated region replaced a well-defined separation line for no control by a highly corrugated separation line. Relative to the no-control case, the peak rms value in the intermittent region of separation with control sh...

Assessment of Two Turbulence Models and Some Compressibility Corrections for Hypersonic Compression Corners by High-order Difference Schemes

The Spalart-Allmaras (S-A) turbulence model, the shear-stress transport (SST) turbulence model and their compressibility corrections are revaluated for hypersonic compression corner flows by using high-order difference schemes. The compressibility effect of density gradient, pressure dilatation and turbulent Mach number is accounted. In order to reduce confusions between model uncertainties and discretization errors, the formally fifth-order explicit weighted compact nonlinear scheme (WCNS-E-5) is adopted for convection terms, and a fourth-order staggered central difference scheme is applied for viscous terms. The 15° and 34° compression corners at Mach number 9.22 are investigated. Numerical results show that the original SST model is superior to the original S-A model in the resolution of separated regions and predictions of wall pressures and wall heat-flux rates. The capability of the S-A model can be largely improved by blending Catris' and Shur's compressibility corrections. Among the three corrections of the SST model listed in the present paper, Catris' modification brings the best results. However, the dissipation and pressure dilatation corrections result in much larger separated regions than that of the experiment, and are much worse than the original SST model as well as the other two corrections. The correction of turbulent Mach number makes the separated region slightly smaller than that of the original SST model. Some results of low-order schemes are also presented. When compared to the results of the high-order schemes, the separated regions are smaller, and the peak wall pressures and peak heat-flux rates are lower in the region of the reattachment points.

Studies of Compression Corner Flowfields Using THREE Turbulent Models

This paper presents the numerical investigations on shock-wave/turbulent boundary-layer interaction flow over a compression corner using SA, SST, and WJ EASM k-ω turbulence models, and compared with experiment data. The applicability of the three different turbulence models has been estimated comprehensively for this kind of the complex flow. The results indicate that the wall pressure distribution, the friction coefficients and the positions of separation and attachment with the three models agree well with the experimental data.

812 桎超音速流れにおける30°ランプ周りの流れ場の数値解析:平板幅の影響(0S.2 圧縮性流れの基礎と応用3)

812 桎超音速流れにおける30°ランプ周りの流れ場の数値解析:平板幅の影響(0S.2 圧縮性流れの基礎と応用3)

Heat transfer effects and topology of the viscous interaction induced by surface protuberances in hypersonic flow

Surface protuberances with a height of the order of the boundary layer thickness are frequently unavoidable in the design of hypersonic vehicles. These protuberances interfere with the flow and induce complex interactions which may lead to notable increases in the local surface heating rates and cause a significant damage to the vehicle. This computational and experimental study investigated hypersonic interference heating in the vicinity of simple surface protuberances. Perfect gas and Reynolds averaged Navier–Stokes simulations were carried out based on benchmark experimental cases using the compressible commercial code Cobalt. The freestream conditions were M∞ = 8.2 and Re∞/ m = 9.35 × 106. The investigated protuberances were three-dimensional compression corners with different deflection angles (30°, 60°, and 90°) and with a relatively low profile where the height was approximately the same as the local boundary layer thickness. A comparison between numerical and experimental data shows a reasonable agreement, although there are areas where there are notable differences between the predictions and measurements. In the low-deflection case (30°), good agreement is observed and the location of the hot spot is well predicted by the different turbulence models. In the higher deflection cases (60° and 90°), in which the incoming boundary layer is separated ahead of the protuberance, the maximum heating rates are reasonably well predicted by the shear stress transport and k–ω models, but systematically overpredicted by the Spalart–Allmaras model. In terms of flow structure, the simulations enable a good understanding of the flow topology, which is marked by the occurrence of junction and separation vortices to the sides and upstream of the protuberance.

Compressible-Flow Simulations Using a New Large-Eddy Simulation/Reynolds-Averaged Navier-Stokes Model

A new hybrid large-eddy simulation/Reynolds-averaged Navier–Stokes simulation (LES/RANS) method is presented in this work. In this approach, the resolved turbulence kinetic energy, ensemble-averaged modeled turbulence kinetic energy and turbulence frequency, and time-resolved turbulence frequency are used to form an estimate of an outer-layer turbulence length scale that is nearly Reynolds-number-independent. The ratio of this outer-layer scale with an inner-layer length scale (proportional to the wall distance) is used to construct a blending function that facilitates the shift between an unsteady RANS formulation near solid surfaces and a LES formulation away from the wall. The new model is tested through simulations of compressible flat-plate boundary layers over a widerangeofReynoldsnumbersandMach2.86 flowoverasmoothcompressionramp.Theresultsshowthatthenew modelpredicts mean andsecond-moment statistics that arein goodagreement withexperiment andare comparable with those obtained using an earlier model (Edwards, J. R., Choi, J-I., and Boles, J. A., “Hybrid Large-Eddy/ Reynolds-Averaged Navier–Stokes Simulation of a Mach-5 Compression Corner Interaction,” AIAA Journal, Vol. 464, 2008, pp. 977–991.) which required a case-by-case calibration of a model constant.

Development of A Two-Equation Turbulence Model for Hypersonic Shock Wave and Turbulent Boundary Layer Interaction

For hypersonic compressible turbulence, the correlations with respect to the density fluctuation must not be neglected. A Reynolds averaged K-ε model is proposed in the present paper to include these correlations, together with the Reynolds averaged Navier-Stokes equations to describe the mean flowfield. The K-equation is obtained from Reynolds averaged single-point second moment equations which are deduced from the instantaneous compressible Navier-Stokes equations. Under certain hypotheses and scales estimation of the compressible terms, the K-equation is simplified. The correlation terms of the fluctuation field appearing in the resulting K-equation, together with a conventional form of the ε-equation, are thus correlated with the variables in the average field. The new modeling coefficients of closure terms are optimized by computing the hypersonic turbulent flat-plate measured by Coleman and Stollery [J. Fliud Mech., Vol. 56 (1972), p. 741]. The proposed model is then applied to simulate hypersonic turbulent flows over a wedge compression corner angle of 34 degree. The predicting results compare favorably with the experimental results. Also, comparisons are made with other turbulence models. Additionally, an entropy modification function of Harten-Yee’s TVD scheme is introduced to reduce artificial diffusion near boundary layers and provide the required artificial diffusion to capture the shockwaves simultaneously.

Steady longitudinal vortices in supersonic turbulent separated flows

Large-scale longitudinal vortices in high-speed turbulent separated flows caused by relatively small irregularities at the model leading edges or at the model surfaces are investigated in this paper. Oil-flow visualization and infrared thermography techniques were applied in the wind tunnel tests at Mach numbers 3 and 5 to investigate the nominally 2-D ramp flow at deflection angles of 20°, 25° and 30°. The surface contour anomalies have been artificially simulated by very thin strips (vortex generators) of different shapes and thicknesses attached to the model surface. It is shown that the introduced streamwise vortical disturbances survive over very large downstream distances of the order of 104 vortex-generator heights in turbulent supersonic flows without pressure gradients. It is demonstrated that each vortex pair induced in the reattachment region of the ramp is definitely a child of a vortex pair, which was generated originally, for instance, by the small roughness element near the leading edge. The dependence of the spacing and intensity of the observed longitudinal vortices on the introduced disturbances (thickness and spanwise size of vortex generators) and on the flow parameters (Reynolds numbers, boundary-layer thickness, compression corner angles, etc.) has been shown experimentally.

A High Order Compact-Flowfield Dependent Variation (HOC-FDV) Method for Inviscid Flows

In this paper, a single high-order compact flowfield-dependent variation (HOC-FDV) method is developed, valid for twodimensional inviscid compressible as well as incompressible flow problems. The method has third-order accuracy in time and fourth-order accuracy in space. The FDV scheme is used for time discretization and the fourth-order compact Pade scheme is used for spatial derivatives. The solution procedure consists of a number of tri-diagonal matrix operations and produces an accurate solver. Numerical examples are solved to demonstrate the accuracy and convergence characteristics of the high-resolution scheme. The test cases are flow over a compression corner, a channel flow with compression/expansion, and a flow past NACA 0012 airfoil. The numerical results show an excellent agreement with analytical and published numerical results and they clearly demonstrate the higher accuracy of a single HOC-FDV scheme for both incompressible and compressible flows.

Critical Transonic Shock and Supersonic Bubble in Oblique Rarefaction Wave Reflection along a Compressive Corner

The oblique rarefaction wave reflection along a compressive corner is considered by using the numerical generalized characteristic analysis method (NGCAM). We have clarified that there are two patterns: regular reflection-like and Mach reflection-like. In both patterns, the reflection wave is always a compression simple wave, which ultimately forms a critical transonic shock. The critical transonic shock is a special kind of transonic shock, and the flow at the back bank of the shock is just sonic. A supersonic bubble near the compression corner grows in the second pattern and will break through as the rarefaction wave size increases.

Experimental investigation of hypersonic flow induced separation over double wedges

Flow separation occurs over the compression corners generated by deflected control surfaces on hypersonic re-entry vehicles and in the inlet of scram jet engines. Configurations like a double wedge and double cone model are useful for studying the separated flow features. Flow fields around concave corners are relatively complicated and produce several classical viscous flow features depending on the combination of the first and second wedge or cone half apex angles. Particularly characteristic phenomena are mainly shock/boundary layer, shock/shock interaction, unsteady shear layers and non-linear shock oscillations. Although most of these basic gas dynamics characteristics are well known, it is not clear what happens at high enthalpy conditions. This paper reports a result of flow fields over a double wedge at a stagnation enthalpy of 4.8 MJ/kg. The experiment was carried out in a free piston shock tunnel at a nominal Mach number of 6.99. Schlieren and double exposure holographic interferometry were applied to visualize the flow field over the double wedge.

Effect of streamwise structures on heat transfer in a hypersonic flow in a compression corner

Coefficients of heat transfer to the surface in a laminar hypersonic flow (M∞ = 21) over plane and axisymmetric models with a compression corner are presented. These coefficients are measured by an infrared camera. The parameters varied in the experiments are the angle of the compression corner and the distance to the corner point. Characteristics of the flow with and without separation in the corner configuration are obtained. The measured results are compared with direct numerical simulations performed by solving the full unsteady Navier-Stokes equations. Experiments with controlled streamwise structures inserted into the flow are described. A substantial increase in the maximum values of the heat-transfer coefficient in the region of flow reattachment after developed laminar separation is demonstrated.

Shock-Wave/Boundary-Layer Interactions in a Model Scramjet Intake

An air intake for a Mach 8 flight vehicle concept has been studied using large-eddy simulation with flow conditions corresponding to typical wind-tunnel tests. The flow contains several types of shock-wave/boundary-layer interaction for which large-eddy simulation has advantages over conventional Reynolds-averaged Navier-Stokes approaches. Laminar-to-turbulent transition was triggered using localized blowing trips in the first external ramp surface close to the intake leading edge. The trips lead to turbulent spots that propagate within an otherwise laminar flow, with a lateral spreading angle consistent with previous studies. The transitional/turbulent shock interaction near the. first compression corner was found to enhance the transition to turbulence, leading to a fully turbulent boundary layer after the interaction. Further downstream, a large separation zone forms due to the cowl-lip shock wave impinging on the vehicle-side boundary layer. Perturbations from the vehicle-side turbulent boundary layer were found to enter the cowl-side boundary layer. The final transition of this boundary layer occurred at the end of a separation bubble created by the first cowl-side compression ramp. Statistics for the turbulent How entering the combustor inlet show thick nonequilibrium turbulent boundary layers and trapped compression waves.

Formulation of the k-w Turbulence Model Revisited

This paper presents a reformulated version of the author'sk-ω model of turbulence. Revisions include the addition of just one new closure coefficient and an adjustment to the dependence of eddy viscosity on turbulence properties. The result is a significantly improved model that applies to both boundary layers and free shear flows and that has very little sensitivity to finite freestream boundary conditions on turbulence properties. The improvements to the k-ω model facilitate a significant expansion of its range of applicability. The new model, like preceding versions, provides accurate solutions for mildly separated flows and simple geometries such as that of a backward-facing step. The model's improvement over earlier versions lies in its accuracy for even more complicated separated flows. This paper demonstrates the enhanced capability for supersonic flow into compression corners and a hypersonic shock-wave/ boundary-layer interaction. The excellent agreement is achieved without introducing any compressibility modifications to the turbulence model.