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NASA NTRS1988

Supersonic turbulent flow past a swept compression corner at Mach 3. II

The three-dimensional Mach 3.0 shock wave-turbulent boundary layer interaction generated by a swept compression corner whose geometry is characterized by the angle of streamwise compression angle alpha and the angle of sweep lambda is presently treated by the Baldwin-Lomax (1978) algebraic turbulent eddy viscosity model. The results obtained, and those previously derived by means of Cebeci and Smith (1974) and Jones and Launder (1972) models, are compared with experimental measurements. The rate of change of the mean kinetic energy along a streamline is investigated, and evidence is obtained that the flowfield structure is rotational and inviscid.

Knight, Doyle D.↗

NASA NTRS1990

Boundary layer receptivity due to three-dimensional convected gusts

Compressible fully three-dimensional interactions involving convected free-stream disturbances are analyzed by utilizing a rapid distortion theory in conjunction with triple-deck concepts. Only one class of regions where the boundary layer is receptive is considered; these regions are downstream from the leading edge, where a local feature, such as a wall hump, forces the boundary layer to make a short-scale adjustment. The results obtained are applicable to a variety of situations such as receptivity due to shallow three-dimensional roughness elements or three-dimensional wall-suction distributions. The influence of the gust orientation, frequency, and the type of mean flow disturbance on the amplitudes of the generated instability waves is demonstrated. It is found that a three-dimensional instability wave can be generated by the interaction of an oblique gust with a two-dimensional mean flow disturbance.

Choudhari, Meelan↗

NASA NTRS1945

Flight Investigation of Boundary-layer and Profile-drag Characteristics of Smooth Wing Sections of a P-47D Airplane

In Mach range of 0.25 - 0.69, boundary-layer measurements were made on upper wing surface at 25% semi-span, pressure-distribution measurements made on upper surface at 63% semi-span, and wake surveys made at 63% semi-span. The minimum profile-drag coefficient of 0.0062 was indicated for smooth section at 63% semi-span. Critical mach number was exceeded by 0.04, but no compressibility shocks appeared. In slipstream, boundary layer transition occurred as far back as 20% chord on upper surface at low lift coefficients.

PRESSURE DISTRIBUTION - WINGS - REPUBLIC P-47D↗

NASA NTRS1987

Boundary-layer instability mechanisms on a swept-leading edge at Mach 3.5

Correlations have been made in NASA Langley's Mach 3.5 Pilot Quiet Tunnel for the transitions occurring from laminar to turbulent flow, in the cases of 45-deg and 60-deg swept cylinders. While freestream noise variations had no effect on boundary layer transition, the addition of boundary layer trips to the leading edges led to transition at lower Re numbers, depending on both trip height and wind tunnel noise level. Also presented are the results of compressible linear stability calculations for the boundary layer of an infinite swept cylinder; Tollmien-Schlichting waves are found to be amplified in the attachment line boundary layer.

Creel, T. R., Jr.↗

NASA NTRS1987

Supersonic turbulent flow past a 3-D swept compression corner at Mach 3

Experimental and theoretical studies are presented on the three-dimensional shock wave-turbulent boundary layer interaction generated by a swept compression corner at Mach 3 for compression angle of 24 deg, sweep angle of 60 deg, and Reynolds numbers from 140,000 to 900,000. Two theoretical approaches were used, both of which utilize the full mass-averaged compressible three-dimensional Navier-Stokes equations but differ in the choice of turbulence model (the Baldwin-Lomax, 1978, and the Jones-Launder, 1972, model, respectively). The features of the computed mean flow structure were found to be qualitatively the same for both the Baldwin-Lomax and Jones-Launder models.

Knight, Doyle D.↗

NASA NTRS1976

Boundary layer bleed system study for a full-scale, mixed-compression inlet with 45 percent internal contraction

The results of an experimental bleed development study for a full-scale, Mach 2.5, axisymmetric, mixed-compression inlet were presented. The inlet was designed to satisfy the airflow requirements of the TF30-P-3 turbofan engine. Capabilities for porous bleed on the cowl surface and ram-scoop/flush-slot bleed on the centerbody were provided. A configuration with no bleed on the cowl achieved a minimum stable, diffuser exit, total pressure recovery of 0.894 with a centerbody-bleed mass flow ratio of 0.02. Configurations with cowl bleed had minimum stable recoveries as high as 0.900 but suffered range decrement penalties from the increased bleed mass flow removal. Limited inlet stability and unstart angle-of-attack data are presented.

Shaw, R. J.↗

NASA NTRS1991

A general approach for the prediction of localized instability generation in boundary layer flows

The present approach to the prediction of instability generation that is due to the interaction of freestream disturbances with regions of subscale variations in surface boundary conditions can account for the finite Reynolds number effects, while furnishing a framework for the study of receptivity in compressible flow and in 3D boundary layers. The approach is illustrated for the case of Tollmien-Schlichting wave generation in a Blasius boundary layer, due to the interaction of a freestream acoustic wave with a localized wall inhomogeneity. Results are presented for the generation of viscous and inviscid instabilities in adverse pressure-gradient boundary layers, supersonic boundary layer instabilities, and cross-flow vortex instabilities.

Choudhari, Meelan↗

NASA NTRS1989

Group-kinetic theory and modeling of atmospheric turbulence

A group kinetic method is developed for analyzing eddy transport properties and relaxation to equilibrium. The purpose is to derive the spectral structure of turbulence in incompressible and compressible media. Of particular interest are: direct and inverse cascade, boundary layer turbulence, Rossby wave turbulence, two phase turbulence; compressible turbulence, and soliton turbulence. Soliton turbulence can be found in large scale turbulence, turbulence connected with surface gravity waves and nonlinear propagation of acoustical and optical waves. By letting the pressure gradient represent the elementary interaction among fluid elements and by raising the Navier-Stokes equation to higher dimensionality, the master equation was obtained for the description of the microdynamical state of turbulence.

Tchen, C. M.↗

NASA NTRS1994

Turbulence models and Reynolds analogy for two-dimensional supersonic compression ramp flow

Results of the application of turbulence models and the Reynolds analogy to the Navier-Stokes computations of Mach 2.9 two-dimensional compression ramp flows are presented. The Baldwin-Lomax eddy viscosity model and the kappa-epsilon turbulence transport equations for the turbulent momentum flux modeling in the Navier-Stokes equations are studied. The Reynolds analogy for the turbulent heat flux modeling in the energy equation was also studied. The Navier-Stokes equations and the energy equation were numerically solved for the flow properties. The Reynolds shear stress, the skin friction factor, and the surface heat transfer rate were calculated and compared with their measurements. It was concluded that with a hybrid kappa-epsilon turbulence model for turbulence modeling, the present computations predicted the skin friction factors of the 8 deg and 16 deg compression ramp flows and with the turbulent Prandtl number Pr(sub t) = 0.93 and the ratio of the turbulent thermal and momentum transport coefficients mu(sub q)/mu(sub t) = 2/Prt, the present computations also predicted the surface heat transfer rates beneath the boundary layer flow of the 16 compression ramp.

Wang, Chi R.↗

NASA NTRS1997

Airfoil Design Using a Coupled Euler and Integral Boundary Layer Method with Adjoint Based Sensitivities

The objective of this paper is to present a control theory approach for the design of airfoils in the presence of viscous compressible flows. A coupled system of the integral boundary layer and the Euler equations is solved to provide rapid flow simulations. An adjunct approach consistent with the complete coupled state equations is employed to obtain the sensitivities needed to drive a numerical optimization algorithm. Design to target pressure distribution is demonstrated on an RAE 2822 airfoil at transonic speed.

Edwards, S.↗

NASA NTRS1975

A numerical method for solving the Navier-Stokes equations with application to shock-boundary layer interactions

A numerical method for solving the compressible form of the unsteady Navier-Stokes equations is described. This method was originally presented in 1970 and has since been modified during the development of computer programs at Ames for implementing models that account for the effects of turbulence in shock-induced separated flows. Although this paper does not describe the turbulence models themselves, a complete description of the basic numerical method is given with emphasis on the choice of a computational mesh for high Reynolds number flows, finite-difference approximations for mixed partial derivatives, extension of the Courant-Friedrichs-Lewy stability condition for viscous flows, mesh boundary conditions, and numerical smoothing for strong shock-wave calculations.

Maccormack, R. W.↗

NASA NTRS1988

A transonic interactive boundary-layer theory for laminar and turbulent flow over swept wings

A 3-D laminar and turbulent boundary-layer method is developed for compressible flow over swept wings. The governing equations and curvature terms are derived in detail for a nonorthogonal, curvilinear coordinate system. Reynolds shear-stress terms are modeled by the Cebeci-Smith eddy-viscosity formulation. The governing equations are descretized using the second-order accurate, predictor-corrector finite-difference technique of Matsuno, which has the advantage that the crossflow difference formulas are formed independent of the sign of the crossflow velocity component. The method is coupled with a full potential wing/body inviscid code (FLO-30) and the inviscid-viscous interaction is performed by updating the original wing surface with the viscous displacement surface calculated by the boundary-layer code. The number of these global iterations ranged from five to twelve depending on Mach number, sweep angle, and angle of attack. Several test cases are computed by this method and the results are compared with another inviscid-viscous interaction method (TAWFIVE) and with experimental data.

Woodson, Shawn H.↗

NASA NTRS1991

Heat transfer, velocity-temperature correlation, and turbulent shear stress from Navier-Stokes computations of shock wave/turbulent boundary layer interaction flows

The properties of 2-D shock wave/turbulent boundary layer interaction flows were calculated by using a compressible turbulent Navier-Stokes numerical computational code. Interaction flows caused by oblique shock wave impingement on the turbulent boundary layer flow were considered. The oblique shock waves were induced with shock generators at angles of attack less than 10 degs in supersonic flows. The surface temperatures were kept at near-adiabatic (ratio of wall static temperature to free stream total temperature) and cold wall (ratio of wall static temperature to free stream total temperature) conditions. The computational results were studied for the surface heat transfer, velocity temperature correlation, and turbulent shear stress in the interaction flow fields. Comparisons of the computational results with existing measurements indicated that (1) the surface heat transfer rates and surface pressures could be correlated with Holden's relationship, (2) the mean flow streamwise velocity components and static temperatures could be correlated with Crocco's relationship if flow separation did not occur, and (3) the Baldwin-Lomax turbulence model should be modified for turbulent shear stress computations in the interaction flows.

Wang, C. R.↗

NASA NTRS1973

Transonic laminar boundary layers with surface curvature.

The effect of surface curvature (both longitudinal and transverse) and the associated pressure gradient across the flow is investigated analytically for a laminar boundary layer subjected to pressure gradients along the flow. Property variation which results from heat transfer and compressibility is taken into account. Numerical solutions of the boundary layer equations are obtained for locally similar sonic flow through the throat of a nozzle for a range of flow conditions and for various shaped nozzle surfaces with different amounts of wall cooling. A few solutions were also obtained for the analogous flow around the shoulder of a flat-faced body in a supersonic flow. The effect of various parameters that arise in the equations upon application of the Levy-Mangler transformation are investigated and discussed with respect to their influence on the velocity and total enthalpy profiles and the corresponding profile slopes at the surface to which the shear stress and heat transfer are related. An important finding is that at throat Reynolds numbers less than 100,000 the heat transfer parameter at a nozzle throat decreases as the throat radius of curvature decreases.

Back, L. H.↗

NASA NTRS1992

An investigation of shock/turbulent boundary layer bleed interactions

A numerical investigation was conducted to determine the effect of bleed on oblique shock wave/turbulent boundary layer interactions. The numerical solution to the compressible Navier-Stokes equations reveal the flow details throughout the interaction zone and inside the normal bleed slot. Results are presented for an incident oblique shock of sufficient strength to cause boundary layer separation in the absence of bleed. Bleed is applied across the shock impingement location over a range of bleed mass flow rates corresponding to different values of plenum pressures. The results indicate a complex flow structure with large variations in both normal and tangential flow velocities across the bleed slot. The flow entrainment into the slot is accompanied by an expansion-compression wave system with a bow shock originating inside the bleed slot. Increasing the bleed mass flow by decreasing the plenum pressure caused an initial decrease then a later increase in the boundary layer momentum and displacement thickness downstream of the interaction.

Hamed, A.↗

NASA NTRS1977

Instability of a compressible circular free jet with consideration of the influence of the jet boundary layer thickness

The instability of a circular jet was investigated by means of the inviscid linearized stability theory. By variation of a jet parameter which takes the ratio of jet radius to boundary layer thickness into account, the influence of axisymmetry on the spatial growth rate and disturbance phase velocity is studied. The influence of Mach number and temperature ratio is discussed. A comparison with measurements shows that the instability of a turbulent jet boundary layer may also be explained by these results.

Michalke, A.↗

NASA NTRS1988

Stability and transition in supersonic boundary layers

The three-dimensional time-dependent, compressible Navier-Stokes equations are numerically solved by a Fourier-Chebyshev collocation algorithm to study the stability of a Mach 4.5 flow over a flat plate. Several nonlinear direct simulations suggest the existence of a secondary instability which might provide a possible route to transition. Pertinent differences in the energy content of the various Fourier modes between this instability and the more common incompressible K-type instabilities are pointed out.

Erlebacher, Gordon↗

DOE OSTI2025

On High-Order/Low-Order and Micro-Macro Methods for Implicit Time-Stepping of the BGK Model

In this paper, a high-order/low-order (HOLO) method is combined with a micro-macro (MM) decomposition to accelerate iterative solvers in fully implicit time-stepping of the Bhatnagar–Gross–Krook (BGK) equation for gas dynamics. The MM formulation represents a kinetic distribution as the sum of a local Maxwellian and a perturbation. In highly collisional regimes, the perturbation away from initial and boundary layers is small and can be compressed to reduce the overall storage cost of the distribution. The convergence behavior of the MM methods, the usual HOLO method, and the standard source iteration method is analyzed on a linear BGK model. Both the HOLO and MM methods are implemented using a discontinuous Galerkin (DG) discretization in phase space, which naturally preserves the consistency between high- and low-order models required by the HOLO approach. Furthermore, the accuracy and performance of these methods are compared on the Sod shock tube problem and a sudden wall heating boundary layer problem. Overall, the results demonstrate the robustness of the MM and HOLO approaches and illustrate the compression benefits enabled by the MM formulation when the kinetic distribution is near equilibrium.

BGK model↗