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At least 343 records · Page 19

GYC: A program to compute the turbulent boundary layer on a rotating cone

A computer program, GYC, which is capable of computing the properties of a compressible turbulent boundary layer on a rotating axisymmetric cone-cylinder body, according to the principles of invariant modeling was studied. The program is extended to include the calculation of the turbulence scale by a differential equation. GYC is in operation on the CDC-7600 computer and has undergone several corrections and improvements as a result of the experience gained. The theoretical basis for the program and the method of implementation, as well as information on its operation are given.

Sullivan, R. D.↗

A similarity rule for compressibility and sidewall-boundary-layer effects in two-dimensional wind tunnels

The effect of the sidewall boundary layer on flow in two-dimensional wind tunnels is determined. The small-disturbance and isentropic approximations are made, and the sidewall-boundary-layer dynamics are modeled with the von Karman momentum-integral equation. The effects of the edge-velocity-gradient term in the sidewall momentum integral, which is usually dominant near the model, and the compressibility term are shown to be similar. It is shown that the effect of sidewall suction around the model is not similar to two-dimensional flow. Comparisons with experiment are made to verify the similarity rule.

Barnwell, R. W.↗

Supersonic turbulent boundary-layer flows with tangential slot injection.

An implicit finite-difference method has been developed for the solution of the compressible boundary-layer equations. This method is applied to tangential slot injection into supersonic turbulent boundary-layer flows. In addition, the effects induced by the interaction between the boundary-layer displacement thickness and the external pressure field are considered. Three different eddy viscosity models have been used to specify the turbulent momentum exchange. One model depends on the species concentration profile, and the species conservation equation has been included in the system of governing partial differential equations. For air injected into air, the freestream and injected gases are treated as separate species which have common fluid properties. Calculations were made and results were compared with experimental data at freestream Mach numbers of 2.4 and 6.0 and with results of another finite-difference method. Good agreement was obtained for the reduction of wall skin friction with slot injection.

Miner, E. W.↗

Computational solution of the defect stream-function equation for nonequilibrium turbulent boundary layers

The derivation of the accurate, second-order, almost linear, approximate equation governing the defect stream function for nonequilibrium compressible turbulent boundary layers is reviewed. The similarity of this equation to the heat conduction equation is exploited in the development of an unconditionally stable, tridiagonal computational method which is second-order accurate in the marching direction and fourth-order accurate in the surface-normal direction. Results compare well with experimental data. Nonlinear effects are shown to be small. This two-dimensional method is simple and has been implemented on a programmable calculator.

Barnwell, Richard W.↗

Analytical method for predicting the pressure distribution about a nacelle at transonic speeds

The formulation and development of a computer analysis for the calculation of streamlines and pressure distributions around two-dimensional (planar and axisymmetric) isolated nacelles at transonic speeds are described. The computerized flow field analysis is designed to predict the transonic flow around long and short high-bypass-ratio fan duct nacelles with inlet flows and with exhaust flows having appropriate aerothermodynamic properties. The flow field boundaries are located as far upstream and downstream as necessary to obtain minimum disturbances at the boundary. The far-field lateral flow field boundary is analytically defined to exactly represent free-flight conditions or solid wind tunnel wall effects. The inviscid solution technique is based on a Streamtube Curvature Analysis. The computer program utilizes an automatic grid refinement procedure and solves the flow field equations with a matrix relaxation technique. The boundary layer displacement effects and the onset of turbulent separation are included, based on the compressible turbulent boundary layer solution method of Stratford and Beavers and on the turbulent separation prediction method of Stratford.

Keith, J. S.↗

Supersonic turbulent boundary-layer flows with mass injection through slots and/or porous walls

An implicit finite-difference method was used to solve the compressible boundary-layer equations, and to study the effects of mass transfer through porous plates, slots, and a combination of the two. The effects of the external pressure field were also included by using a global pressure interaction scheme. Two different eddy viscosity models were used for the slot and slot-porous combination cases: one was a two-layer model with inner and outer laws, and the other was a multi-layer model with as many as five separate layers. Results of the present method were compared with experimental data at a Mach number of 2.8. Comparisons of the skin friction reduction and Mach number profiles gave good to excellent agreement. Pressure interaction had little effect on the slot injection skin friction but increased the skin friction of the porous and slot-porous combination markedly.

Murray, A. L.↗

A detailed study of attached and separated compression corner flowfields in high Reynolds number supersonic flow

An experimental study has been carried out to detail the interaction of a compressible turbulent boundary layer with shock waves of varying strengths. The interaction was produced by two-dimensional compression corners of 8, 16, 20, and 24 deg angles. The incoming boundary layer had an edge Mach number of 2.85 and a Reynolds number of 1.7 million based on overall thickness. Detailed mean-flow and surface measurements are presented for the four corner angles. The 8 deg corner flow was found to be fully attached, while the 16 deg case was near incipient separation. Both the 20 deg and 24 deg corners produced significant flow separation regions. In the discussion of these results, emphasis is placed on the development of flowfield properties from attached to separated conditions. Comparisons made with a computational solution of the Navier-Stokes equations show good agreement when the corner flow is not separated.

Settles, G. S.↗

Vectored injection into compressible laminar and turbulent boundary layers

A fundamental analysis of two-dimensional supersonic boundary layer flow, both laminar and turbulent, is presented for a wide range of normal and nonnormal mass-transfer velocities. The analysis is based on the numerical solution of the Navier-Stokes equations, and results are compared with available theoretical and experimental data. Certain cases of practical importance, for which results are not presently available, are referred to.

Degani, D.↗

Numerical solutions of the compressible 3-D boundary-layer equations for aerospace configurations with emphasis on LFC

The application of stability theory in Laminar Flow Control (LFC) research requires that density and velocity profiles be specified throughout the viscous flow field of interest. These profile values must be as numerically accurate as possible and free of any numerically induced oscillations. Guidelines for the present research project are presented: develop an efficient and accurate procedure for solving the 3-D boundary layer equation for aerospace configurations; develop an interface program to couple selected 3-D inviscid programs that span the subsonic to hypersonic Mach number range; and document and release software to the LFC community. The interface program was found to be a dependable approach for developing a user friendly procedure for generating the boundary-layer grid and transforming an inviscid solution from a relatively coarse grid to a sufficiently fine boundary-layer grid. The boundary-layer program was shown to be fourth-order accurate in the direction normal to the wall boundary and second-order accurate in planes parallel to the boundary. The fourth-order accuracy allows accurate calculations with as few as one-fifth the number of grid points required for conventional second-order schemes.

Harris, Julius E.↗

Curvature effects on the stability of three-dimensional laminar boundary layers

The linear stability equations for compressible, three-dimensional laminar boundary layer flow are derived in an orthogonal curvilinear coordinate system. The system of equations is solved using a finite difference scheme in order to study the effects of streamline and surface curvature and compressibility on the stability of the flow past a swept wing. It is known that convex surface curvature can have a stabilizing effect on the laminar boundary layer. Conversely, concave surface curvature can be destabilizing. The magnitude of these effects for swept wings is determined. Results indicate that amplification rates and hence, N-factors, for the flow over the convex upper surface of a swept wing can be reduced by about 15 to 45 percent when curvature effects are included in the linear stability analysis. The results of the calculations show that concave curvature destabilizes crossflow type disturbances with a significant increase in amplification rate. In addition, comparisons are made with some experimental results on a swept concave-convex surface. Calculated velocity vector plots show good agreement with observed disturbances in the laminar boundary layer over the concave surface.

Collier, F. S., Jr.↗

Calculation of three-dimensional laminar boundary-layer flows.

Accuracy tests have been made of the approximation, proposed recently by Wang (1971), which reduces the computation of three-dimensional, laminar, compressible, boundary-layer equations to the problem of solving two-dimensional type boundary-layer equations. The tests were made by a comparison of the results achieved using Wang's method with a fully three-dimensional boundary-layer calculation. Results of the comparison are tabulated and are found to be in good agreement.

Fillo, J. A.↗

Comparison of theoretical and experimental boundary-layer development in a Mach 2.5 mixed-compression inlet

An analytical investigation was made of the boundary layer flow in an axisymmetric Mach 2.5 mixed compression inlet, and the results were compared with experimental measurements. The inlet tests were conducted in the Lewis 10- by 10-foot supersonic wind tunnel at a unit Reynolds number of 8.2 million/m. The inlet incorporated porous bleed regions for boundary layer control, and the effect of this bleed was taken into account in the analysis. The experimental boundary layer data were analyzed by using similarity laws from which the skin friction coefficient was obtained. The boundary layer analysis included predictions of laminar and turbulent boundary layer growth, transition, and the effects of the shock boundary layer interactions. In addition, the surface static pressures were compared with those obtained from an inviscid characteristics program. The results of investigation showed that the analytical techniques gave satisfactory predictions of the boundary layer flow except in regions that were badly distorted by the terminal shock.

Hingst, W. R.↗

HADY-I, a FORTRAN program for the compressible stability analysis of three-dimensional boundary layers

A computer program HADY-I for calculating the linear incompressible or compressible stability characteristics of the laminar boundary layer on swept and tapered wings is described. The eigenvalue problem and its adjoint arising from the linearized disturbance equations with the appropriate boundary conditions are solved numerically using a combination of Newton-Raphson interative scheme and a variable step size integrator based on the Runge-Kutta-Fehlburh fifth-order formulas. The integrator is used in conjunction with a modified Gram-Schmidt orthonormalization procedure. The computer program HADY-I calculates the growth rates of crossflow or streamwise Tollmien-Schlichting instabilities. It also calculates the group velocities of these disturbances. It is restricted to parallel stability calculations, where the boundary layer (meanflow) is assumed to be parallel. The meanflow solution is an input to the program.

El-Hady, N. M.↗

An experimental examination of the effects of incoming boundary layer modifications on the dynamics of a turbulent compression corner interaction

This experimental study examines the effects of modifications to the incoming turbulent boundary layer on the highly separated shock wave/boundary layer interaction generated by an unswept compression corner. Particular focus is placed on the motion of the unsteady separation shock wave. The flowfield was generated by a 28 deg ramp in a Mach 5 flow with a freestream Reynolds number of 50 x 10 exp 6/m. The incoming turbulent boundary layer transitioned naturally and developed under near-adiabatic wall conditions. Modification of the flow entering the interaction was effected through either a single plate boundary layer manipulator (BLM) or riblets. The BLM reduced the length of separation by 35-45 percent and reduced the streamwise extent of the separation shock motion by 36-74 percent. Examination of the flowfield downstream of the BLM showed this result to be due to the inviscid preturning of the flow by the BLM, and not by changes to the boundary layer dynamics. The riblets had no measurable effect on the compression corner interaction.

Mcclure, W. B.↗

Near-wall variable-Prandtl-number turbulence model for compressible flows

A near-wall four-equation turbulence model is developed for the calculation of high-speed compressible turbulent boundary layers. The four equations used are the k-epsilon equations and the theta(exp 2)-epsilon (sub theta) equations. These equations are used to define the turbulent diffusivities for momentum and heat fluxes, thus allowing the assumption of dynamic similarity between momentum and heat transport to be relaxed. The Favre-averaged equations of motion are solved in conjunction with the four transport equations. Calculations are compared with measurements and with another model's predictions where the assumption of the constant turbulent Prandtl number is invoked. Compressible flat plate turbulent boundary layers with both adiabatic and constant temperature wall boundary conditions are considered. Results for the range of low Mach numbers and temperature ratios investigated are essentially the same as those obtained using an identical near-wall k-epsilon model. In general, there are significant improvements in the predictions of mean flow properties at high Mach numbers.

Sommer, T. P.↗

Flow separation in shear-layer-driven cavities

A study of the shear-layer flow over a range of open-top cavity configurations is reported. Emphasis is placed on the effect that altering the cavity's span length and aspect ratio has on the development of the shear layer. Computational results are obtained using an interactive method which adapts the compressible boundary-layer model for the flow above the cavity and incompressible Navier-Stokes equations within the enclosure. Interaction of this composite model with the outer, inviscid supersonic flow is also considered in one case. The results show that the location of the stagnation points is sensitive primarily to the variation of the span. When the span was fixed and the aspect ratio varied, the shear layer was nearly unaffected except at aspect ratios less than 0.5. Interaction with the outer flow had a smoothing effect on the shape of the dividing streamline but did not significantly affect the location of the stagnation points.

Brandeis, J.↗