On the upstream length of turbulent boundary-layer separation.
Upstream length of turbulent boundary layer separation ahead of compression corner or flare
TURBULENT BOUNDARY LAYER↗
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Prediction of space shuttle fluctuating pressure environments, including rocket plume effects
Preliminary estimates of space shuttle fluctuating pressure environments have been made based on prediction techniques developed by Wyle Laboratories. Particular emphasis has been given to the transonic speed regime during launch of a parallel-burn space shuttle configuration. A baseline configuration consisting of a lightweight orbiter and monolithic SRB, together with a typical flight trajectory, have been used as models for the predictions. Critical fluctuating pressure environments are predicted at transonic Mach numbers. Comparisons between predicted environments and wind tunnel test results, in general, showed good agreement. Predicted one-third octave band spectra for the above environments were generally one of three types: (1) attached turbulent boundary layer spectra (typically high frequencies); (2) homogeneous separated flow and shock-free interference flow spectra (typically intermediate frequencies); and (3) shock-oscillation and shock-induced interference flow spectra (typically low frequencies). Predictions of plume induced separated flow environments were made. Only the SRB plumes are important, with fluctuating levels comparable to compression-corner induced separated flow shock oscillation.
Plotkin, K. J.↗
Shockwave-boundary layer interference heating analysis.
Interference heating correlations have been developed based on existing wind tunnel test data taken with simple configurations such as wedge/flat plate and compression corner models. For turbulent flow, peak interference heating was first correlated with shock strength (pressure ratio across shock wave) and then as a function of Reynolds number. The peak interference Stanton number was found to exhibit the same Reynolds number and Prandtl number characteristics as the Stanton number variation for undisturbed flow over a flat plate. Similar correlations were developed for laminar flow. Results indicated that for laminar flow at higher Reynolds number, the impinging shockwave may act as a boundary layer trip and cause boundary layer transition resulting in high interference heating. The correlations derived in this study can be used to scale wind tunnel model test data to a full-scale space vehicle at supersonic or hypersonic flight conditions.
Hung, F. T.↗
Development of relaxation turbulence models
Relaxation turbulence models have been intensively studied. The complete time dependent mass averaged Navier-Stokes equations have been solved for flow into a two dimensional compression corner. A new numerical scheme has been incorporated into the developed computed code with an attendant order of magnitude reduction in computation time. Computed solutions are compared with experimental measurements of Law for supersonic flow. Details of the relaxation process have been studied; several different relaxation models, including different relaxation processes and varying relaxation length, are tested and compared. Then a parametric study has been conducted in which both Reynolds number and wedge angle are varied. To assess effects of Reynolds number and wedge angle, the parametric study includes the comparison of computed separation location and upstream extent of pressure rise; numerical results are also compared with the measurements of surface pressure, skin friction and mean velocity field.
Hung, C. M.↗
Reynolds number effects on shock-wave turbulent boundary-layer interactions - A comparison of numerical and experimental results
An experiment is described that tests and guides computations of a shock-wave turbulent boundary-layer interaction flow over a 20-deg compression corner at Mach 2.85. Numerical solutions of the time-averaged Navier-Stokes equations for the entire flow field, employing various turbulence models, are compared with the data. Each model is critically evaluated by comparisons with the details of the experimental data. Experimental results for the extent of upstream pressure influence and separation location are compared with numerical predictions for a wide range of Reynolds numbers and shock-wave strengths.
Horstman, C. C.↗
Computational models for the analysis of three-dimensional internal and exhaust plume flowfields
This paper describes computational procedures developed for the analysis of three-dimensional supersonic ducted flows and multinozzle exhaust plume flowfields. The models/codes embodying these procedures cater to a broad spectrum of geometric situations via the use of multiple reference plane grid networks in several coordinate systems. Shock capturing techniques are employed to trace the propagation and interaction of multiple shock surfaces while the plume interface, separating the exhaust and external flows, and the plume external shock are discretely analyzed. The computational grid within the reference planes follows the trace of streamlines to facilitate the incorporation of finite-rate chemistry and viscous computational capabilities. Exhaust gas properties consist of combustion products in chemical equilibrium. The computational accuracy of the models/codes is assessed via comparisons with exact solutions, results of other codes and experimental data. Results are presented for the flows in two-dimensional convergent and divergent ducts, expansive and compressive corner flows, flow in a rectangular nozzle and the plume flowfields for exhausts issuing out of single and multiple rectangular nozzles.
Dash, S. M.↗
Thin-layer approximation and algebraic model for separated turbulent flows
An algebraic turbulence model for two- and three-dimensional separated flows is specified that avoids the necessity for finding the edge of the boundary layer. Properties of the model are determined and comparisons made with experiment for an incident shock on a flat plate, separated flow over a compression corner, and transonic flow over an airfoil. Separation and reattachment points from numerical Navier-Stokes solutions agree with experiment within one boundary-layer thickness. Use of law-of-the-wall boundary conditions does not alter the predictions significantly. Applications of the model to other cases are contained in companion papers.
Baldwin, B.↗
Numerical solution of a three-dimensional shock wave and turbulent boundary-layer interaction
A rapid numerical scheme is used to solve the complete mass-averaged Navier-Stokes equations for supersonic turbulent flow over a three-dimensional compression corner. A simple eddy viscosity model is developed, and the interaction of a swept shock wave and a three-dimensional turbulent boundary layer is studied. Good agreement is obtained between the present results and experimental measurements for the case of a wedge with an angle of 6 deg on a flat-plate sidewall. For the case of a 12-deg wedge angle, the computed results do not show the existence of a peak pressure found experimentally. However, the range of interaction, the plateau pressure, and the peak heat transfer are closely predicted for all cases. The high heat transfer near the axial corner is due to the thinning of the boundary layer and inflow of fresh high-momentum fluid. The heat transfer is relieved through pressure reduction and boundary-layer thickening.
Hung, C. M.↗
Comparison of multiequation turbulence models for several shock-separated 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.
Viegas, J. R.↗
Injection slot location for boundary-layer control in shock-induced separation
An experimental investigation of the effect of tangential air injection, when the injection slot is located inside of what would otherwise have been the dead air zone in a separated flow, in controlling shock-induced turbulent boundary layer separation is presented. The experiments were carried out at a free-stream Mach number of 2.5 in the separated flow induced by a compression corner with a 20 deg angle. The observations made were wall static pressures, pitot profiles, and schlieren visualizations of the flow. The results show that the present location for injection is more effective in suppressing boundary-layer separation than the more conventional one, where the slot is located upstream of where separation would occur in the absence of injection.
Viswanath, P. R.↗
Computation of viscous hypersonic flow over control surfaces
A parabolized Navier-Stokes (PNS) computer code has been used to compute hypersonic flow over control surfaces located on the aft end of generic re-entry configurations. The Beam-Warming implicit numerical algorithm as modified by Schiff and Steger is used to march in the spatial direction. The outer bow shock is treated as a sharp discontinuity; within the shock layer discontinuities are captured. Several different turbulent flow solutions were generated for flap angles varying from -7 deg to 15 deg and angles of attack varying from 0 deg to 20 deg. The present results are qualitatively correct when compared with previous compression corner studies.
Chaussee, D. S.↗
Modeling of turbulent separated flows for aerodynamic applications
Steady, high speed, compressible separated flows modeled through numerical simulations resulting from solutions of the mass-averaged Navier-Stokes equations are reviewed. Emphasis is placed on benchmark flows that represent simplified (but realistic) aerodynamic phenomena. These include impinging shock waves, compression corners, glancing shock waves, trailing edge regions, and supersonic high angle of attack flows. A critical assessment of modeling capabilities is provided by comparing the numerical simulations with experiment. The importance of combining experiment, numerical algorithm, grid, and turbulence model to effectively develop this potentially powerful simulation technique is stressed.
Marvin, J. G.↗
Iterative PNS method for attached flows with upstream influence
A stable global-iteration procedure is developed by utilizing successive sweeps, from inflow to outflow boundaries, of a parabolized Navier-Stokes code for attached, steady supersonic flow. It is shown that the procedure converges in about ten or fewer iterations, and allows for the upstream influence within the subsonic region of a supersonic boundary layer. An implicit forward difference is employed in the subsonic region to evaluate the pressure-gradient term in the streamwise momentum equation. The pressure-gradient term is normally approximated in standard single-sweep parabolized methods, suppressing the upstream influence. The iterative results obtained demonstrate the validity of the single-sweep method for weak interactions. For hypersonic viscous interaction on a flat plate at a Mach number of 5.8, it is found that the single-sweep method has a small error that vanishes as the Reynolds number of the flow is increased. However, the skin friction has an error of about 10 percent for low Reynolds numbers and for hot wall conditions. The application of this method to laminar two-dimensional flow over weak expansion and compression corners shows that the pressure and skin friction results in the vicinity of the expansion corner compare favorably with a time-dependent Navier-Stokes numerical solution.
Rakich, J. V.↗
Application of the implicit MacCormack scheme to the PNS equations
The two-dimensional parabolized Navier-Stokes equations are solved using MacCormack's (1981) implicit finite-difference scheme. It is shown that this method for solving the parabolized Navier-Stokes equations does not require the inversion of block tridiagonal systems of algebraic equations and allows the original explicit scheme to be employed in those regions where implicit treatment is not needed. The finite-difference algorithm is discussed and the computational results for two laminar test cases are presented. Results obtained using this method for the case of a flat plate boundary layer are compared with those obtained using the conventional Beam-Warming scheme, as well as those obtained from a boundary layer code. The computed results for a more severe test of the method, the hypersonic flow past a 15 deg compression corner, are found to compare favorably with experiment and a numerical solution of the complete Navier-Stokes equations.
Lawrence, S. L.↗
Application of the implicit MacCormack scheme to the parabolized Navier-Stokes equations
MacCormack's implicit finite-difference scheme was used to solve the two-dimensional parabolized Navier-Stokes (PNS) equations. This method for solving the PNS equations does not require the inversion of block tridiagonal systems of algebraic equations and permits the original explicit MacCormack scheme to be employed in those regions where implicit treatment is not needed. The advantages and disadvantages of the present adaptation are discussed in relation to those of the conventional Beam-Warming scheme for a flat plate boundary layer test case. Comparisons are made for accuracy, stability, computer time, computer storage, and ease of implementation. The present method was also applied to a second test case of hypersonic laminar flow over a 15% compression corner. The computed results compare favorably with experiment and a numerical solution of the complete Navier-Stokes equations.
Lawrence, J. L.↗
Turbulence measurements in two shock-wave/shear-layer interactions
Measurements of the longitudinal component of the mass-flow fluctuations have been made in an 8-deg compression corner flow and a reattaching shear layer at a Mach number of approximately 2.9 and unit Reynolds number of about 7 x 10 to the 7th per m. The data include turbulence intensities and probability density distributions. Significant turbulence amplification occurs in both interactions. A qualitative explanation in terms of direct shock effects, extra strain rates, and their relative contribution, is suggested.
Hayakawa, K.↗
Study of the structure of turbulent shear flows at supersonic speeds and high Reynolds number
A major effort to improve the accuracies of turbulence measurement techniques is described including the development and testing of constant temperature hot-wire anemometers which automatically compensate for frequency responses. Calibration and data acquisition techniques for normal and inclined wires operated in the constant temperature mode, flow geometries, and physical models to explain the observed behavior of flows are discussed, as well as cooperation with computational groups in the calculation of compression corner flows.
Smits, A. J.↗
The behaviour of a compressible turbulent boundary layer under incipient separation conditions
This paper presents an experimental study of a turbulent boundary-layer/shock-wave interaction. The interaction was generated by a two-dimensional compression corner, and the flow was on the point of separating. Measurements were made using both normal and inclined hot wires, and the data include measurements of the longitudinal mass-flow fluctuation intensity and the mass-weighted Reynolds shear stress.
Muck, K. C.↗