Eddy viscosity distributions in a Mach 20 turbulent boundary layer
Shear stress and eddy viscosity distribution in Mach 20 compressible turbulent boundary layer, using mixing length flow theory
Bushnell, D. M.↗
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Studies of von Karman's similarity theory and its extension to compressible flows : a similarity theory for turbulent boundary layer over a flat plate in compressible flow
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Lin, C C↗
Calculation of nonequilibrium hypersonic turbulent boundary layers and comparisons with experimental data.
Compressible hypersonic turbulent boundary layers solution by finite difference method, relating mixing length to velocity profile shape factor
Beckwith, I. E.↗
Calculation of nonequilibrium hypersonic turbulent boundary layers and comparisons with experimental data
Compressible hypersonic turbulent boundary layers solution by finite difference method, relating mixing length to velocity profile shape factor
Beckwith, I. E.↗
The present state and the future direction of eddy viscosity models
Information is given in viewgraph form on the present state and future direction of eddy viscosity models. Topics covered include the eddy viscosity dilemma, two-equation models, equations of motion, free shear flows, incompressible free shear flows, model-predicted boundary layer structure, defect layer analysis, the effects of pressure gradients, viscous sublayer structure, wall functions and viscous damping, viscous damping for kappa-omega, the effects of compressibility, perturbation analysis of the wall layer, an alternative compressibility term, unsteady boundary layers, incompressible separation, backstep results, and compressible separation.
Wilcox, David C.↗
COSAL: A black-box compressible stability analysis code for transition prediction in three-dimensional boundary layers
A fast computer code COSAL for transition prediction in three dimensional boundary layers using compressible stability analysis is described. The compressible stability eigenvalue problem is solved using a finite difference method, and the code is a black box in the sense that no guess of the eigenvalue is required from the user. Several optimization procedures were incorporated into COSAL to calculate integrated growth rates (N factor) for transition correlation for swept and tapered laminar flow control wings using the well known e to the Nth power method. A user's guide to the program is provided.
Malik, M. R.↗
Approximate Turbulent Boundary-Layer Development in Plane Compressible Flow Along Thermally Insulated Surfaces with Application to Supersonic-Tunnel Contour Correction
Numerical solutions of the differential equation obtained from the momentum theorem for the development of a turbulent boundary layer along a thermally insulated surface in two-dimensional and in radial shock-free flow are presented in tabular form for a range of Mach numbers from 0.100 to 10. The solution can be used in a step-wise procedure with any given distribution of favorable pressure gradients and for zero pressure gradients. Solutions are also given for use with moderate adverse pressure gradients. The mean velocity in the boundary layer is approximated by a power-law profile. In view of the stepwise integration methods to be used, the exponent designated the profile shape can be varied along the surface between the integral fraction limits 1/5 and 1/11 through interpolation. Agreement obtained between theoretical and experimental boundary-layer development in a supersonic nozzle at a nominal Mach number of 2 indicates the general validity of the approximations used in the analysis - in particular, the method of extrapolating low-speed skin-friction relations to high Mach number flows. The extrapolation method used assumes that the skin-friction coefficient depend primarily on Reynolds number, provided that the density and the kinematic viscosity are evaluated at surface conditions.
BOUNDARY LAYER - WIND TUNNEL WALLS↗
Three-dimensional turbulent boundary layer development and separation in V/STOL engine inlets at incidence with small-cross flow and curvature influences
The study concerns the influence of the three-dimensional cross flows on the compressible turbulent boundary layer development and flow separation prediction around V/STOL engine inlets at high incidence. The governing equations for the three-dimensional boundary layer flow with small-cross approximation are solved numerically on an intrinsic streamline coordinate system. Results are presented to illustrate the effects of small cross-flow, compressibility and streamline curvatures on the flow. Comparisons of the results with the wind tunnel data for scaled model and with data obtained from another existing compressible axisymmetric turbulent boundary layer scheme are included in the analysis.
Chou, D. C.↗
Three-layer interactive method for computing supersonic laminar separated flows
An interactive model for numerical computation of complicated two-dimensional flowfields including regions of reversed flow is proposed. The present approach is one of dividing the flowfield into three regions, in each of which a simplified mathematical model is applied: (1) outer, supersonic flow for which the full potential equation (hyperbolic) is used; (2) viscous, laminar layer in which the compressible boundary-layer model (parabolic) is used; and (3) recirculating flow modeled by the incompressible Navier-Stokes equations (elliptic). For matching of the numerical solutions in the three layers, two interaction models are developed: one for pressure interaction, the other for interaction between the shear layer and the recirculating flow. The uniform solution for the whole flowfield is then obtained by iteration of the local solutions under the constraints imposed by matching. The three-layer interactive model is used for solution of the flowfield past an asymmetric cavity. The method is shown to be capable of dealing with backflow without encountering problems at separation, characteristic to the boundary-layer approach.
Brandeis, J.↗
Turbulence measurements in axisymmetric supersonic boundary layer flow in adverse pressure gradients
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.
Gootzait, E.↗
On the period of the coherent structure in boundary layers at large Reynolds numbers
The period of the large coherent structure in a subsonic, compressible, turbulent boundary layer was determined using the autocorrelation of the velocity and pressure fluctuations for Reynolds numbers between 5,000 and 35,000. In low Reynolds number flows the overall correlation period scaled with the outer variables - namely, the free stream velocity and the boundary layer thickness.
Narayanan, M. A. B.↗
Displacement effect of a three-dimensional boundary layer
A method is described for determining the "displacement surface" of known three-dimensional compressible boundary-layer flow in terms of the mass-flow defects associated with the profiles of the two velocity components parallel to the surface. The result is a generalization of the plane flow concept of displacement thickness introduced in order to describe how a thin boundary layer distorts the outer nonviscous flow. Numerical values are found for the known three-dimensional boundary-layer flow about a cone at a small angle of attack to a supersonic stream.
Moore, Franklin K↗
A general method for calculating three-dimensional compressible laminar and turbulent boundary layers on arbitrary wings
The method described utilizes a nonorthogonal coordinate system for boundary-layer calculations. It includes a geometry program that represents the wing analytically, and a velocity program that computes the external velocity components from a given experimental pressure distribution when the external velocity distribution is not computed theoretically. The boundary layer method is general, however, and can also be used for an external velocity distribution computed theoretically. Several test cases were computed by this method and the results were checked with other numerical calculations and with experiments when available. A typical computation time (CPU) on an IBM 370/165 computer for one surface of a wing which roughly consist of 30 spanwise stations and 25 streamwise stations, with 30 points across the boundary layer is less than 30 seconds for an incompressible flow and a little more for a compressible flow.
Cebeci, T.↗
On the structure of hypersonic turbulent boundary layers.
Extensive hot-wire auto- and cross-correlation measurements obtained in a fully developed compressible turbulent boundary layer are presented. A tentative mechanism of turbulence production and growth in hypersonic flow suggested by these measurements is developed. This flow model is consistent with previous observations in incompressible flows. Detailed measurements of the mean properties of the hypersonic turbulent boundary layer are also presented and compared with results from various transformation and finite-difference prediction methods. It is shown that none of the theories predict all the properties of the hypersonic turbulent boundary layer and that additional measurements are needed to provide more adequate physics of turbulent processes for use in the various theories.
Owen, F. K.↗
Additional three-dimensional boundary-layer computations for a finite swept wing
Calculations have been made of the three-dimensional, compressible, turbulent boundary layer on the finite supercritical wing of the NASA modified F-8 transonic research airplane. The calculations were based on the wing pressure distribution measured in flight at M = 0.90, instead of on wind tunnel data at M = 0.50 and 0.99. Data on the boundary-layer thickness, displacement thickness, skin-friction components, and integrated streamwise skin friction are presented for points along the streamwise stations at which pressure measurements were made.
Nash, J. F.↗
Evaluation of Equilibrium Turbulence for a Hypersonic Boundary Layer at Nonadiabatic Wall Conditions
This paper presents an experimental study to characterize the naturally developing compressible turbulent boundary layer produced along a flat plate measuring 9.7 feet long in the NASA Langley 8-Foot High Temperature Tunnel and to determine the test conditions necessary to achieve equilibrium turbulence. The measurements consist of pitot pressure, static pressure, and total temperature distributions in the boundary layer. In addition, surface measurements consisting of heat transfer and pressure distributions were obtained. The tests were conducted at a nominal free-stream Mach number of 6.5, total temperatures of 2700 and 3300 R, and angles of attack of 5 and 13 degrees. The corresponding nominal boundary-layer edge Mach numbers were 6.2 and 5.0. The nominal ratios of adiabatic wall temperature to cold wall temperature were 4.4 and 5.4 and the momentum thickness Reynolds numbers at the boundary layer probe locations ranged from 400 to 7800. The results of this study indicate that momentum thickness Reynolds numbers of at least 4000 are required to obtain an equilibrium turbulent boundary layer in the Langley 8-Foot High Temperature Tunnel. This evaluation is based primarily on the behavior of shape factors inferred from the boundary-layer measurements.
Albertson, Cindy W.↗
An algebraic model for dissipation in supersonic boundary layers
With increasing mainstream Mach number, viscous dissipation becomes a progressively important influence in high-speed compressible turbulent boundary layers. An asymptotic analysis is carried out for high Reynolds numbers and Mach numbers of order 1, and it is shown that viscous dissipation gives rise to important terms in the solution of the total enthalpy equation. For simplicity, the case of supersonic flow over an adiabatic wall is considered. An expression for the adiabatic wall temperature is derived. It is shown that the asymptotic analysis constrains the types of turbulence models that can be used to represent the effects of viscous dissipation. A simple algebraic turbulence model is proposed and comparisons with measured total enthalpy profile data show good agreement.
He, J.↗
Global Analysis of Nonlinear Second-Mode Development in a Mach-6 Boundary Layer From High-Speed Schlieren Data
The second-mode instability on a 7◦ half-angle sharp cone at Mach 6 is analyzed using high-speed calibrated schlieren imagery at a frame rate near the expected fundamental frequency. Experiments were conducted in the NASA Langley 20-Inch Mach 6 facility at unit Reynolds number between 6.56×106 and 9.71×106 m−1. Time-resolved pixel intensity signals throughout the boundary layer are reconstructed using spatially available data in the schlieren images to recover an effective sampling rate of over 10 MHz; these are then converted to quantitative density gradients using a thin-lens-based calibration technique. A global analysis is performed on the schlieren data to investigate the nonlinear growth of the second-mode fundamental and harmonic content. Point-wise measures of the auto-bicoherence are used to identify specific triadic interactions and the locations of their highest levels of quadratic phase coupling. Significant resonance interactions between the second-mode fundamental and harmonic instabilities were found along with interactions between these and the mean flow. Bispectral mode decomposition is employed to educe the flow structures associated with these interactions. A similar analysis is performed for the power spectrum, with power spectral densities computed for each pixel’s time-series and spectral proper orthogonal decomposition employed to derive the modal structure and energy of the flow at specific frequencies. Comparisons between the bispectral quantities and second-mode power show that nonlinear interactions, particularly resonance interactions, are closely correlated with space-time modulation of disturbances during the nonlinear stage of transition.
boundary layer transition↗