Integral analysis of transonic shock wave/boundary-layer interaction in internal flow
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Engineering topics
Publications and source records attributed to Childs, M. E..
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Wall static pressure distributions, surface flow patterns, pitot pressures, and yaw angle profiles were measured in a skewed three-dimensional shock wave/turbulent boundary layer interaction region. The test section was axisymmetric with a constant diameter. The nominal freestream Mach number was 4. Upstream of the interaction, the boundary layer thickness was 0.31 in. (0.787 cm). The three-dimensional flow was produced by azimuthal pressure gradients which were generated by an 8-degree cone aligned with the primary flow direction, but with the cone axis displaced 0.3 in. (0.76 cm) from the channel centerline. The yaw angle was found to be a function of both the azimuthal angle and the distance from the beginning of the interaction. It was observed that yaw angle increased substantially near the wall. The maximum yaw angle for the whole flow field was obtained in the 90 degree azimuthal plane.
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The passive control of compressible boundary layer growth by boundary layer trips has been studied experimentally. Axisymmetric trips and three dimensional trips were used in this study. The nomial freestream Mach numbers are 1.5 and 4. The results show that trips are effective in promoting boundary layer growth. Trips are more effective for Mach 1.5 flows than for Mach 4 flows.
The mean flow results of an experimental study of compressible turbulent boundary layers in an adverse pressure gradient with and without surface curvature effects are presented. The test was conducted in an axisymmetric flow facility. The upstream Reynolds number based on boundary layer momentum thickness was 5884 and the boundary layer thickness was 0.90 cm. The curvature effects were examined by studying two flows with essentially identical adverse pressure gradients. One flow was along a concave compression surface test section, while the other was along a straight-walled test section. Mean flow measurements included wall static pressure distributions, wall temperatures, pitot pressure profiles and total temperature profiles. The mean flow results indicated that the surface curvature resulted in a definite increase of turbulent mixing in the boundary layer.
Detailed pitot, static and wall pressure measurements have been obtained for multiple shock wave/turbulent boundary layer interactions in a circular duct at a free-stream Mach number of 1.49 and at a unit Reynolds number of 4.90 x 10 to the 6th per meter. The details of the flow field show the formation of a series of normal shock waves with successively decreasing strength and with decreasing distance between the successive shock waves. The overall pressure recovery is much lower than the single normal shock pressure recovery at the same free-stream Mach number. A one-dimensional flow model based on the boundary layer displacement buildup is postulated to explain the formation of a series of normal shock waves.
An approximate integral viscous-inviscid interaction method is presented for calculating the development of a turbulent boundary layer subjected to a normal shock wave induced adverse pressure gradient in an internal axisymmetric flow. The inflow conditions and the downstream pressure are provided for the computation. In the supersonic region of shock pressure rise, the Prandtl-Meyer function is used to couple the viscous and inviscid flows. An analytical model for the coupling process is postulated and appropriate equations are defined. Downstream of the sonic point, one-dimensional inviscid flow is assumed for coupling with the viscous flow. The turbulent boundary layer is calculated using Green's integral lag-entrainment method. Comparisons of the solutions with the experimental data are made for interactions which are unseparated, near separation and separated. For comparison purposes, solutions to the time-dependent, mass-averaged, Navier-Stokes equations incorporating a two-equation, Wilcox-Rubesin turbulence model are also shown. The computed results from the integral method show good agreement with experimental data for unseparated interactions and reasonable agreement with the trend of the viscous effects when the interaction becomes increasingly separated.
Detailed pitot, static and wall pressure measurements have been obtained for a transonic normal shock wave/turbulent boundary layer interaction at free-stream Mach numbers of 1.28, 1.37 and 1.48 and at a constant unit Reynolds number of 4.92 x 10 to the 6th per meter in an axisymmetric, internal flow. Measurements have also been obtained at a unit Reynolds number of 9.84 x 10 to the 6th per meter at a free-stream Mach number of 1.29. The interaction depends very strongly on the Mach number. The effect of Reynolds number under study is small. Flow confinement due to the wind-tunnel wall boundary layer produces a weaker interaction and a much larger supersonic tongue than is observed for planar flows. Comparisons are made with solutions to the time-dependent, mass-averaged, Navier-Stokes equations incorporating a two-equation, Wilcox-Rubesin turbulence model (1980). The computations are in agreement with the experimental results.
Tabulated data from a series of experimental studies of the interaction of a shock wave with a turbulent boundary layer in axisymmetric flow configurations is presented. The studies were conducted at the walls of circular wind tunnels and on the cylindrical centerbody of an annular flow channel. Detailed pitot pressure profiles and wall static pressure profiles upstream of, within and downstream of the interaction region are given. Results are presented for flows at nominal freestream Mach Numbers of 2, 3 and 4. For studies at the tunnel sidewalls, the shock waves were produced by conical shock generators mounted on the centerline of the wind tunnel at zero angle of attack. The annular ring generator was used to produce the shock wave at the centerbody of the annular flow channel. The effects of boundary layer bleed were examined in the investigation. Both bleed rate and bleed location were studied. Most of the bleed studies were conducted with bleed holes drilled normal to the wall surface but the effects of slot suction were also examined. A summary of the principal results and conclusions is given.
Mean flow and turbulence measurements are presented for adiabatic compressible turbulent boundary layer flow in adverse pressure gradients. The gradients were induced on the wall of an axially symmetric wind tunnel by contoured centerbodies mounted on the wind tunnel centerline. The boundary layer turbulence downstream of a boundary layer bleed section in a zero pressure gradient was also examined. The measurements were obtained using a constant temperature hot-wire anemometer. The adverse pressure gradients were found to significantly alter the turbulence properties of the boundary layer. With flow through the bleed holes there was a measureable decrease in the rms longitudinal velocity fluctuations near the wall and the turbulent shear stress in the boundary layer was reduced.
The paper suggests a new form of the wall-wake profile which is applicable to flows with heat transfer, and for which the velocity gradient at the boundary-layer edge is zero. The modified profile - which takes into account the effect of turbulent Prandtl number - is found to provide a good representation of experimental data for a wide range of Mach numbers and heat transfer. The skin friction coefficient values determined by a least squares fit of the profile to the data are in good agreement with values measured by the floating element technique. The values of boundary-layer thickness determined by the fit correspond more closely to the outer edge of the viscous flow region than those obtained with earlier versions of the wall-wake profile.
A computation procedure is described for predicting the flowfields which develop when successive interactions between oblique shock waves and a turbulent boundary layer occur. Such interactions may occur, for example, in engine inlets for supersonic aircraft. Computations are carried out for axisymmetric internal flows at M 3.82 and 2.82. The effect of boundary layer bleed is considered for the M 2.82 flow. A control volume analysis is used to predict changes in the flow field across the interactions. Two bleed flow models have been considered. A turbulent boundary layer program is used to compute changes in the boundary layer between the interactions. The results given are for flows with two shock wave interactions and for bleed at the second interaction site. In principle the method described may be extended to account for additional interactions. The predicted results are compared with measured results and are shown to be in good agreement when the bleed flow rate is low (on the order of 3% of the boundary layer mass flow), or when there is no bleed. As the bleed flow rate is increased, differences between the predicted and measured results become larger. Shortcomings of the bleed flow models at higher bleed flow rates are discussed.
Measurements have been made of the mean-flow and turbulence properties in adiabatic turbulent boundary layer flows subjected to adverse pressure gradients. In the freestream region upstream of the adverse pressure gradient the Mach number was 3.86, the unit Reynolds number 5.3 million per foot. The boundary layer developed on the wall of an axisymmetric nozzle and straight test section. The pressure gradients at the test section wall were induced by contoured centerbodies mounted on the wind tunnel centerline. The flow under study simulated that which might be found in an axially symmetric engine inlet of a supersonic aircraft. The results obtained have shown good agreement to exist between the measured normalized turbulent velocity fluctuations and the results from other recent investigations of compressible boundary layers.
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A modified form of the wall-wake profile which is applicable to flows with heat transfer is presented. The modified profile takes into account the effect of a turbulent Prandtl number; it was found to provide a good representation of the experimental data from several sources. The C sub f values which are determined by a least squares fit of the profile to the data agree well with values which were measured by the floating element technique.
A form of the wall-wake profile, which is applicable to flows with heat transfer, and for which a variation in y = O at y = delta, was suggested. The modified profile, which takes into account the effect of turbulent Prandtl number, was found to provide a good representation of experimental data for a wide range numbers and heat transfer. The Cf values which are determined by a least squares fit of the profile to the data agree well with values which were measured by the floating element technique. In addition, the values of delta determined by the fit correspond more closely to the outer edge of the viscous flow region than those obtained with earlier versions of the wall-wake profile.
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