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At least 1,711 records · Page 95

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NASA NTRS1977

Computation of the inviscid supersonic flow about cones at large angles of attack by a floating discontinuity approach

The technique of floating shock fitting is adapted to the computation of the inviscid flowfield about circular cones in a supersonic free stream at angles of attack that exceed the cone half-angle. The resulting equations are applicable over the complete range of free-stream Mach numbers, angles of attack and cone half-angles for which the bow shock is attached. A finite difference algorithm is used to obtain the solution by an unsteady relaxation approach. The bow shock, embedded cross-flow shock, and vortical singularity in the leeward symmetry plane are treated as floating discontinuities in a fixed computational mesh. Where possible, the flowfield is partitioned into windward, shoulder, and leeward regions with each region computed separately to achieve maximum computational efficiency. An alternative shock fitting technique which treats the bow shock as a computational boundary is developed and compared with the floating-fitting approach. Several surface boundary condition schemes are also analyzed.

Daywitt, J.↗

NASA NTRS1977

Study of effects of injector geometry on fuel-air mixing and combustion

An implicit finite-difference method has been developed for computing the flow in the near field of a fuel injector as part of a broader study of the effects of fuel injector geometry on fuel-air mixing and combustion. Detailed numerical results have been obtained for cases of laminar and turbulent flow without base injection, corresponding to the supersonic base flow problem. These numerical results indicated that the method is stable and convergent, and that significant savings in computer time can be achieved, compared with explicit methods.

Bangert, L. H.↗

NASA NTRS1977

Influence of two-dimensional hygrothermal gradients on interlaminar stresses near free edges

Interlaminar stresses are determined for mechanical loading, uniform hygrothermal loading, and gradient moisture loading through implementation of a finite element computer code. Nonuniform two-dimensional hygroscopic gradients are obtained from a finite difference solution of the diffusion equation. It is shown that hygroscopic induced stresses can be larger than those resulting from mechanical and thermal loading, and that the distribution of the interlaminar normal stress may be changed significantly in the presence of a two-dimensional moisture gradient in the boundary layer of a composite laminate.

Farley, G. L.↗

NASA NTRS1976

Steady supersonic flowfields with embedded subsonic regions

Supersonic flow past a blunt body is considered, where the flow contains an embedded subsonic region which lies between the shock wave and the body surface and is bounded by sonic lines from the body to the shock. A numerical approach is taken, which uses a basic finite difference scheme that solves the unsteady fluid dynamic equations in integral form. The unsteady equations are everywhere hyperbolic in time so no distinction need be made between subsonic and supersonic regions. Solutions to the mixed elliptic and hyperbolic steady flow equations are approached asymptotically in time. The method is illustrated for two-dimensional flows.

Maccormack, R. W.↗

NASA NTRS1976

Improved interactive calculation procedure for supersonic flows

An interactive numerical procedure has been developed for supersonic viscous flows (either two-dimensional or axisymmetric configurations). The flow field is divided into two regions: (1) an inner region which is highly viscous and mostly subsonic, and (2) an outer region where the flow is supersonic and in which viscous effects are small, but not negligible. This paper presents a detailed description of: I. Outer Region - numerical solution obtained by applying the method of characteristics to a system of equations which includes viscous and conduction transport terms only normal to the streamlines; II. Inner Region - treated by a system of equations of the boundary-layer type that includes higher order effects, such as longitudinal and transverse curvature and normal pressure gradients (equations are coupled and solved simultaneously in physical coordinates, using an implicit finite-difference scheme); III. Interactive Procedure - in the interaction mode, the two regions are coupled iteratively along a matching line, where the Mach number is of the order of 1.2.

Tassa, Y.↗

NASA NTRS1977

Diffraction of a shock wave by a compression corner. II - Single Mach reflection

The two-dimensional time-dependent Euler equations which govern the flow field resulting from the interaction of a planar shock with a compression corner are solved for initial conditions which result in single Mach reflection of the incident planar shock. The Euler equations are first transformed to include the self-similarity of the flow field. A second transformation is employed to normalize the distances between the ramp and the reflected shock and between the wall and the Mach stem. The resulting equations in strong conservation-law form are solved using a second-order discontinuity-fitting finite-difference approach. The results are compared with experimental interferograms and existing first-order shock-capturing numerical solutions.

Shankar, V.↗

NASA NTRS1977

Numerical solution of the viscous hypersonic flow past blunted cones at angle of attack

Hypersonic viscous flow over spherically blunted cones of large half angle is computed at small angles of attack in the plane of symmetry of the flow field. Time-dependent viscous shock-layer equations in body-oriented coordinates are used to describe the flow field. The shock wave is treated as a discontinuity, across which the Rankine-Hugoniot relations are used to compute the flow conditions behind the shock. A time-marching second-order finite-difference method is used to solve the equations for a perfect gas. The local CFL (Courant-Friedrich-Lewy) time increment is used to advance the solution in time at each grid point. A fourth-order damping is used to damp the oscillations in the flow quantities. The numerical results of the present analysis for quantities such as shock standoff distance, surface-pressure distribution, and heating rates compare well with the existing theoretical and experimental results.

Kumar, A.↗

NASA NTRS1977

Heat transfer in cooled guide vanes

A numerical study to determine the temperature distribution in the guide vanes of a radial inflow turbine is presented. A computer program has been developed to calculate the temperature distribution when the vanes are cooled internally using a combination of impingement and film cooling techniques. The study is based on the use of the finite difference method in a two dimensional heat conduction problem. The results are then compared to determine the best cooling configuration for a certain coolant to primary mass flow ratio.

Tabakoff, W.↗

NASA NTRS1977

Numerical solution of axisymmetric boattail flow fields with plume simulators

Turbulent separating flows over axisymmetric afterbody-boattail configurations with solid sting plume simulators are computed with a time-dependent finite-difference method to solve the compressible Navier-Stokes equations. The Reynolds stress terms are replaced with a two-layer eddy viscosity model including a relaxation formula to model the nonequilibrium effects of the separated flow. The mesh is alined with the boattail body through an analytic transformation which accommodates a wide variety of boattail geometries. Numerical results for a series of boattail geometries over a wide range of Reynolds number (140,000 to 140 million) are presented and, when possible, compared with experimental data or independent numerical results.

Holst, T. L.↗

NASA NTRS1976

Numerical computation of transient coaxial entry tube flows

A numerical program was developed to compute transient laminar flows in two dimensions including multicomponent mixing and chemical reaction. The program can compute both incompressible flows and compressible flows at all speeds, and it is applied to describe transient and steady state solutions for low subsonic, coaxial entry, tue flows. Single component, nonreacting flows comprise most of the solutions, but one steady state solution is presented for trace concentration constituents engaging in a second order reaction. Numerical stability was obtained by adding at each calculation point a correction for numerical diffusion errors caused by truncation of the Taylor series used to finite difference the conservation equations. Transient computations were made for fluids initially at rest, then subjected to step velocity inputs that were uniform across each region of the entry plane and were held constant throughout the computation period. For center tube to annulus velocity ratios of 0.5 and 2.0, the bulk fluid in the tube initially moved in plug flow, but strong radial flows developed near the injection plane which moved the fluid into the high shear region between the jets and away from the tube wall.

Wieber, P. R.↗

NASA NTRS1977

Supersonic flow about circular cones at large angles of attack - A floating discontinuity approach

The technique of floating shock fitting is adapted to the computation of the inviscid flowfield about circular cones in a supersonic free stream at angles of attack that exceed the cone half-angle. In those regions in which the governing conical equations are mixed elliptic-hyperbolic, the fully hyperbolic form is obtained by the addition of the temporal derivative. The resulting equations are applicable over the complete range of free-stream Mach numbers, angles of attack and cone half-angles for which the bow shock is attached. An explicit finite-difference algorithm is used to obtain the solution by an unsteady relaxation approach. The bow shock, embedded crossflow shock, and vortical singularity in the leeward symmetry plane are all treated as floating discontinuities in a fixed computational mesh. The method yields excellent results for the bow and embedded shocks, however, the solution in the leeward symmetry plane exhibits viscous-like effects and does not appear to adequately predict the behavior of the vortical singularity.

Daywitt, J.↗

NASA NTRS1977

Investigations related to the inviscid-viscous interaction in transonic flows about finite 3-D wings

Inviscid small-disturbance theory has been shown to predict three-dimensional transonic flows about finite wings reasonably well as long as viscous effects are negligible. In order to include these effects, the inviscid small-disturbance solution of Bailey and Ballhaus (1975) has been combined with a finite-difference solution for Prandtl's boundary-layer equations. This solution employs the conditionally stable Krause (1968) scheme, implicit in the direction normal to the wall, to cope with the domain-of-dependence problem that arises for reverse cross flow. To be consistent with the inviscid-flow solution, the boundary layer is computed in the representative wing planform plane which is transformed into rectangular shape in the computational domain. The flow has been assumed turbulent, and a scalar eddy-viscosity model is adopted. The interaction between inviscid and viscous flow is modeled with the help of the displacement surface which is added to the geometric wing shape. Sample distributions of displacement thickness for swept wings are presented for weak and strong interaction cases.

Kordulla, W.↗

NASA NTRS1976

Numerical solutions of the triple-deck equations for laminar trailing-edge stall

The problem of determining the effect of laminar boundary layers on the lift of thin wings in subsonic flow at high Reynolds numbers is considered. The boundary value problem is formulated in the framework of the triple-deck theory of Brown and Stewartson. The resulting fourth-order boundary value was solved by an iterative finite-difference technique. An inverse iteration procedure provides proper treatment of the trailing-edge singularity, and asymptotic far-field expansions and coordinate stretchings are used to deal with the problem of the slow algebraic decay of the solution.

Chow, R.↗

NASA NTRS1977

Computation of the temperature distribution in cooled radial inflow turbine guide vanes

A two-dimensional finite-difference numerical technique is presented to determine the temperature distribution of an internally-cooled blade of radial turbine guide vanes. A simple convection cooling is assumed inside the guide vane. Such an arrangement results in relatively small cooling effectiveness at the leading edge and at the trailing edge. Heat transfer augmentation in these critical areas may be achieved by using impingement jets and film cooling. A computer program is written in Fortran IV for IBM 370/165 computer.

Tabakoff, W.↗

NASA NTRS1977

Application of the method of integral relations to laminar boundary layers in three dimensions

The method of integral relations is extended to general three-dimensional compressible laminar boundary layer flows. The transformation employed to transform the basic three-dimensional compressible boundary layer equations into quasi-incompressible form is an extension of the Howarth transformation. The resulting system of differential equations is integrated numerically by the method of integral relations as proposed by Dorodnitsyn. To demonstrate the accuracy of the method, it is applied to calculation of the parabolic flow over a flat plate and the boundary flow over an infinite yawed cylinder, for which solutions are known. It is then applied to the flow over a flat plate disturbed by a cylinder normal to the plate, for which a finite-difference solution is available for comparison. It is finally applied to calculating the crossflow velocity variation for supersonic flow over a swept wedge.

Holt, M.↗

NASA NTRS1977

Prediction of outer layer mixing lengths in turbulent boundary layers

Predictions of mixing length by Pletcher's (1976) method (using a two-layer eddy viscosity model for a turbulent boundary layer at low Reynolds numbers) are compared to some values derived from turbulent boundary-layer profiles by other authors. The model is incorporated into a finite-difference scheme, to accurately predict low Reynolds number skin friction in supersonic flow.

Watson, R. D.↗

NASA NTRS1976

Numerical problems in the advection of pollutants

Prediction of pollutant transport involves solution of the advection equation numerically. Truncation errors arising from integrating the advection equation by using finite difference schemes are discussed. Numerical errors manifest themselves in artificial dissipation and dispersion of pollutants. Criteria for measuring the dissipation and dispersion are presented, and minimization of those errors is discussed. An alternative procedure by integration in the wavenumber space is examined. Examples illustrating quantitative discrepancy in actual forecasting are also shown.

Liu, C. Y.↗

NASA NTRS1977

Improved methods for large-eddy simulations of turbulence

By using Fourier transforms for evaluating spatial derivatives, the accuracy of the large-eddy simulation of homogeneous isotropic turbulence is improved. Especially, the treatment of certain terms that arise in filtering the equations is considerably improved in both speed and accuracy. Use of vorticity as the principal variable is shown to be a viable and potentially useful alternative to the primitive variables. A method of deriving conservation properties of numerical schemes is given which is much simpler than previous methods and is widely applicable. The methods are applied to the computation of homogeneous isotropic turbulence, and it is found that the subgrid scale model is improved by using finite differences in place of 'exact' derivatives.

Mansour, N. N.↗