Interaction of oblique shock waves with regions of variable pressure, entropy, and energy
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Analysis is made of the flow field produced by oblique impingement of weak plane disturbances of arbitrary profile on a plane normal shock. Three types of disturbance are considered: (a) sound wave propagating in the gas at rest into which the shock moves; (b) sound wave overtaking the shock from behind,(The sound wave reflects as a sound wave, and a stationary vorticity wave is produced); (c) an incompressible vorticity wave stationary in the gas ahead of the shock. The incident wave refracts as a stationary vorticity wave, and either a sound wave or attenuating pressure wave is also produced. Computations are presented for the first two types of incident wave, over the range of incidence angles, for shock Mach numbers of 1, 1.5, and infinity.
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Conical shock wave-turbulent boundary layer interaction data obtained for adiabatic wall conditions at supersonic free stream Mach numbers, including suction effects
The intent of this study on micro-array flow control is to demonstrate the viability and economy of Response Surface Methodology (RSM) to determine optimal designs of micro-array actuation for controlling the shock wave turbulent boundary layer interactions within supersonic inlets and compare these concepts to conventional bleed performance. The term micro-array refers to micro-actuator arrays which have heights of 25 to 40 percent of the undisturbed supersonic boundary layer thickness. This study covers optimal control of shock wave turbulent boundary layer interactions using standard micro-vane, tapered micro-vane, and standard micro-ramp arrays at a free stream Mach number of 2.0. The effectiveness of the three micro-array devices was tested using a shock pressure rise induced by the 10 shock generator, which was sufficiently strong as to separate the turbulent supersonic boundary layer. The overall design purpose of the micro-arrays was to alter the properties of the supersonic boundary layer by introducing a cascade of counter-rotating micro-vortices in the near wall region. In this manner, the impact of the shock wave boundary layer (SWBL) interaction on the main flow field was minimized without boundary bleed.
A thin film heat transfer gauge is applied to the measurement of heat transfer coefficients in the interaction regions of incident shock waves and fully developed turbulent boundary layers. It was developed to measure heat flux with high spatial resolution and fast response for wind tunnels with long flow duration. To measure the heat transfer coefficients in the interaction region in detail, experiments were performed under the conditions of Mach number = 4, total pressure = 1.2 MPa, 0.59 to approximately 0.65. Reynolds number = 1.3 to approximately 1.5 x 10 to the 7th power and incident shock angles from 17.8 to 22.8 degrees. The results show that the heat transfer coefficient changes complicatedly in the interaction region. At the beginning the interaction region, the heat transfer coefficient decreases at first, reaches its minimum value at the point where the pressure begins to increase, and then increases sharply. When the boundary layer begins to separate, even a small separation bubble causes significant changes in the heat transfer coefficient, while the pressure does not show any changes which suggests that the boundary layer begins to separate.
Attention is directed to the acoustics research of the 1950s and 1960s for guidance in understanding and quantizing the turbulence amplification that can occur in regions of shock-wave boundary-layer interaction. Three primary turbulence amplifier-generator mechanisms are identified and shown, by linear analysis, to be responsible for turbulence amplification across a shock wave in excess of 100% of the incident turbulence intensity.
An experimental investigation has been conducted to determine the effect of bleed region geometry and bleed rate on shock wave-boundary layer interactions in an axisymmetric, mixed-compression inlet at a Mach number of 2.5. The full realizable reduction in transformed form factor is obtained by bleeding off about half the incident boundary layer mass flow. Bleeding upstream or downstream of the shock-induced pressure rise is preferable to bleeding across the shock-induced pressure rise. Slanted holes are more effective than normal holes. Two different bleed hole sizes were tested without detectable difference in performance.
A preliminary experimental investigation was conducted to study two crossing, glancing shock waves of equal strengths, interacting with the boundary-layer developed on a supersonic wind tunnel wall. This study was performed at several Mach numbers between 2.5 and 4.0. The shock waves were created by fins (shock generators), spanning the tunnel test section, that were set at angles varying from 4 to 12 degrees. The data acquired are wall static pressure measurements, and qualitative information in the form of oil flow and schlieren visualizations. The principle aim is two-fold. First, a fundamental understanding of the physics underlying this flow phenomena is desired. Also, a comprehensive data set is needed for computational fluid dynamic code validation. Results indicate that for small shock generator angles, the boundary-layer remains attached throughout the flow field. However, with increasing shock strengths (increasing generator angles), boundary layer separation does occur and becomes progressively more severe as the generator angles are increased further. The location of the separation, which starts well downstream of the shock crossing point, moves upstream as shock strengths are increased. At the highest generator angles, the separation appears to begin coincident with the generator leading edges and engulfs most of the area between the generators. This phenomena occurs very near the 'unstart' limit for the generators. The wall pressures at the lower generator angles are nominally consistent with the flow geometries (i.e. shock patterns) although significantly affected by the boundary-layer upstream influence. As separation occurs, the wall pressures exhibit a gradient that is mainly axial in direction in the vicinity of the separation. At the limiting conditions the wall pressure gradients are primarily in the axial direction throughout.
Asymptotic solutions are derived for the pressure distribution in the interaction of a weak normal shock wave with a turbulent boundary layer. The undisturbed boundary layer is characterized by the law of the wall and the law of the wake for compressible flow. In the limiting case considered, for 'high' transonic speeds, the sonic line is very close to the wall. Comparisons with experiment are shown, with corrections included for the effect of longitudinal wall curvature and for the boundary-layer displacement effect in a circular pipe.
A three-dimensional computational fluid dynamics code, RPLUS3D, which was developed for the reactive propulsive flows of ramjets and scramjets, was validated for glancing shock wave-boundary layer interactions. Both laminar and turbulent flows were studied. A supersonic flow over a wedge mounted on a flat plate was numerically simulated. For the laminar case, the static pressure distribution, velocity vectors, and particle traces on the flat plate were obtained. For turbulent flow, both the Baldwin-Lomax and Chien two-equation turbulent models were used. The static pressure distributions, pitot pressure, and yaw angle profiles were computed. In addition, the velocity vectors and particle traces on the flat plate were also obtained from the computed solution. Overall, the computed results for both laminar and turbulent cases compared very well with the experimentally obtained data.
An asymptotic description is derived for the interaction between a shock wave and a turbulent boundary layer in transonic flow, for a particular limiting case. The dimensionless difference between the external flow velocity and critical sound speed is taken to be much smaller than one, but large in comparison with the dimensionless friction velocity. The basic results are derived for a flat plate, and corrections for longitudinal wall curvature and for flow in a circular pipe are also shown. Solutions are given for the wall pressure distribution and the shape of the shock wave. Solutions for the wall shear stress are obtained, and a criterion for incipient separation is derived. Simplified solutions for both the wall pressure and skin friction distributions in the interaction region are given. These results are presented in a form suitable for use in computer programs.
A theoretical basis for the scaling of broadband shock noise intensity In supersonic jets was formulated considering linear shock-shear wave interaction. Modeling of broadband shock noise with the aid of shock-turbulence interaction with special reference to linear theories is briefly reviewed. An hypothesis has been postulated that the peak angle of incidence (closer to the critical angle) for the shear wave primarily governs the generation of sound in the interaction process with the noise generation contribution from off-peak incident angles being relatively unimportant. The proposed hypothesis satisfactorily explains the well-known scaling law for the broadband shock-associated noise in supersonic jets.
Fluctuating surface pressure measurements have been made to investigate the effectiveness of boundary layer separators (BLS's) in reducing the fluctuating pressure loads produced by separated shock wave turbulent boundary layer interactions. Measurements have been made under unswept and swept compression corner interactions in a Mach 5 flow. BLS's fix the separation location and eliminate the large-amplitude, low-frequency fluctuating pressure loads upstream of the compression corners. The loads on the unswept compression corner face are reduced by as much as 59%. The BLS's also shift the mean pressure distribution on the unswept corner face in the streamwise direction. Results show that the loads on the corner face vary with the BLS height and the distance between the BLS and the compression corner. Suggestions for the optimum placement and the use of the BLS's are also made.
Asymptotic methods are used to calculate the shear stress at the wall for the interaction between a normal shock wave and a turbulent boundary layer on a flat plate. A mixing length model is used for the eddy viscosity. The shock wave is taken to be strong enough that the sonic line is deep in the boundary layer and the upstream influence is thus very small. It is shown that unlike the result found for laminar flow an asymptotic criterion for separation is not found; however, conditions for incipient separation are computed numerically using the derived solution for the shear stress at the wall. Results are compared with available experimental measurements.
The transition Reynolds number for shear layers produced by interactions between weak and strong shock waves is determined on the basis of experiments performed in a 20-in. (Mach 6) and an 11-in. (Mach 6.9) hypersonic tunnel. A variable angle wedge was used to generate a planar shock wave which interacted with the bow wave of a blunt body. An average value of the transition length (defined as the length along the shear layer from the shock interaction to the point where turbulence became visible on schlieren photographs) was used to determine the transition Reynolds number.