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At least 91 records · Page 5
All sourcesNASA NTRSDOE OSTI
NASA NTRS1972

Calculative techniques for transonic flows about certain classes of wing-body combinations, phase 2

Theoretical analysis and associated computer programs were developed for predicting properties of transonic flows about certain classes of wing-body combinations. The procedures used are based on the transonic equivalence rule and employ either an arbitrarily-specified solution or the local linerization method for determining the nonlifting transonic flow about the equivalent body. The class of wind planform shapes include wings having sweptback trailing edges and finite tip chord. Theoretical results are presented for surface and flow-field pressure distributions for both nonlifting and lifting situations at Mach number one.

Stahara, S. S.↗
NASA NTRS1990

Global convergence of inexact Newton methods for transonic flow

In computational fluid dynamics, nonlinear differential equations are essential to represent important effects such as shock waves in transonic flow. Discretized versions of these nonlinear equations are solved using iterative methods. In this paper an inexact Newton method using the GMRES algorithm of Saad and Schultz is examined in the context of the full potential equation of aerodynamics. In this setting, reliable and efficient convergence of Newton methods is difficult to achieve. A poor initial solution guess often leads to divergence or very slow convergence. This paper examines several possible solutions to these problems, including a standard local damping strategy for Newton's method and two continuation methods, one of which utilizes interpolation from a coarse grid solution to obtain the initial guess on a finer grid. It is shown that the continuation methods can be used to augment the local damping strategy to achieve convergence for difficult transonic flow problems. These include simple wings with shock waves as well as problems involving engine power effects. These latter cases are modeled using the assumption that each exhaust plume is isentropic but has a different total pressure and/or temperature than the freestream.

Young, David P.↗
NASA NTRS1975

Computational aspects of the prediction of multidimensional transonic flows in turbomachinery

The analytical prediction and description of transonic flow in turbomachinery is complicated by three fundamental effects: (1) the fluid equations describing the transonic regime are inherently nonlinear, (2) shock waves may be present in the flow, and (3) turbomachine blading is geometrically complex, possessing large amounts of curvature, stagger, and twist. A three-dimensional computation procedure for the study of transonic turbomachine fluid mechanics is described. The fluid differential equations and corresponding difference operators are presented, the boundary conditions for complex blade shapes are described, and the computational implementation and mapping procedures are developed. Illustrative results of a typical unthrottled transonic rotor are also presented.

Oliver, D. A.↗
NASA NTRS1989

Development and application of a program to calculate transonic flow around an oscillating three-dimensional wing using finite difference procedures

A finite difference method for solving the unsteady transonic flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The differential equation for the unsteady potential is linear with spatially varying coefficients and with the time variable eliminated by assuming harmonic motion. Difference equations are derived for harmonic transonic flow to include a coordinate transformation for swept and tapered planforms. A pilot program is developed for three-dimensional planar lifting surface configurations (including thickness) for the CRAY-XMP at Boeing Commercial Airplanes and for the CYBER VPS-32 at the NASA Langley Research Center. An investigation is made of the effect of the location of the outer boundaries on accuracy for very small reduced frequencies. Finally, the pilot program is applied to the flutter analysis of a rectangular wing.

Weatherill, Warren H.↗
NASA NTRS1976

Application of a multi-level grid method to transonic flow calculations

A multi-level grid method was studied as a possible means of accelerating convergence in relaxation calculations for transonic flows. The method employs a hierarchy of grids, ranging from very coarse to fine. The coarser grids are used to diminish the magnitude of the smooth part of the residuals. The method was applied to the solution of the transonic small disturbance equation for the velocity potential in conservation form. Nonlifting transonic flow past a parabolic arc airfoil is studied with meshes of both constant and variable step size.

South, J. C., Jr.↗
NASA NTRS1980

Further investigation of a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings

Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. The steady velocity potential is obtained first from the well-known nonlinear equation for steady transonic flow. The unsteady velocity potential is then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. An out-of-core direct solution procedure was developed and applied to two-dimensional sections. Results are presented for a section of vanishing thickness in subsonic flow and an NACA 64A006 airfoil in supersonic flow. Good correlation is obtained in the first case at values of Mach number and reduced frequency of direct interest in flutter analyses. Reasonable results are obtained in the second case. Comparisons of two-dimensional finite difference solutions with exact analytic solutions indicate that the accuracy of the difference solution is dependent on the boundary conditions used on the outer boundaries. Homogeneous boundary conditions on the mesh edges that yield complex eigenvalues give the most accurate finite difference solutions. The plane outgoing wave boundary conditions meet these requirements.

Weatherill, W. H.↗
NASA NTRS1984

Improvements in the accuracy and stability of algorithms for the small-disturbance and full-potential equations applied to transonic flows

Numerical techniques that improve the accuracy and stability of algorithms for the small disturbance and full potential equations used to calculate transonic flows are described. For the small disturbance equation, the algorithm improvements are: (1) the use of monotone switches in the type dependent finite differencing, and (2) the use of stable and simple second order accurate spatial differencing; these improvements are for steady and unsteady transonic flows. For the steady full potential equation, the improvement is in the use of a monotone switch in the type dependent finite differencing of an approximate factorization (AF2) algorithm. All these improvements are implemented in present computer codes by making minor coding modifications.

Goorjian, P. M.↗
NASA NTRS1977

Application of a multi-level grid method to transonic flow calculations

A multi-level grid method has been studied as a possible means of accelerating convergence in relaxation calculations for transonic flows. The method employs a hierarchy of grids, ranging from very coarse (e.g., 8 x 2 mesh cells) to fine (e.g., 128 x 32); the coarser grids are used to diminish the magnitude of the smooth part of the residuals, hopefully with far less total work than would be required with, say, optimal SLOR iterations on the finest grid. The method was applied to the solution of the transonic small-disturbance equation for the velocity potential in the conservation form. Nonlifting transonic flow past a parabolic-arc airfoil is the example studied, with meshes of both constant and variable step size.

South, J. C., Jr.↗
NASA NTRS1977

Perturbation of a discontinuous transonic flow

The main difficulty in perturbing a discontinuous transonic flow is in the representation of the shift in the location of the discontinuity (shock wave). Herein presented is a method of overcoming this difficulty by using a distorted airfoil as the initial case rather than the real physical airfoil; the distortion is chosen such that the shock location is unchanged by the perturbation. The distorted airfoil is obtained by the use of a strained coordinate system. A direct consequence of the theory is the derivation of an algebraic similarity relation between related airfoils with shock waves at differing locations. Results for simple examples are shown.

Nixon, D.↗
NASA NTRS1978

Perturbations in two- and three-dimensional transonic flows

The difficulty of treating the perturbation of transonic flow, during which shock waves change position, can be overcome by using a distorted coordinate system in which the locations of all shock waves do not change; the distortion is found as part of the solution. This device leads to a relation that allows a range of flows, with differing shock locations, to be related algebraically to two known 'calibration' flows. Results for flows around finite wings, including those with multiple, intersecting shock waves, are presented. A typical computing time for such examples is 0.3 sec on a CDC 7600 computer.

Nixon, D.↗
NASA NTRS1987

Computation of viscous transonic flow over porous airfoils

The viscous effects on transonic flow past an airfoil which contains a shallow cavity beneath a porous surface are studied numerically. The porous region occupies a small portion of the total airfoil surface, and is located near the shock. Both an interactive boundary layer (IBL) algorithm and a thin-layer Navier-Stokes (TLNS) algorithm have been modified for use in studying the outer flow, whereas a stream-function formulation has been used to model the inner flow in the small cavity. The coupling procedure at the porous surface is based on Darcy's law and on the assumption of a constant total presusre in the cavity. In addition, a modified Baldwin-Lomax turbulence model is used to consider the transpired turbulent boundary layer in the TLNS approach, and the Cebeci-Smith turbulence model is used in the IBL approach. According to the present analysis, a porous surface can reduce the wave drag appreciably, but it can also increase viscous losses. As has been observed experimentally, the numerical results indicate that the total drag is reduced at higher Mach numbers and increased at lower Mach numbers when the angles of attack are small. Furthermore, the streamline patterns of passive-shock and boundary-layer interaction are revealed in this study.

Chow, Chuen-Yen↗
NASA NTRS1952

On a solution of the nonlinear differential equation for transonic flow past a wave-shaped wall

The Prandtl-Busemann small-perturbation method is utilized to obtain the flow of a compressible fluid past an infinitely long wave-shaped wall. When the essential assumption for transonic flow (that all Mach numbers in the region of flow are nearly unity) is introduced, the expression for the velocity potential takes the form of a power series in the transonic similarity parameter. On the basis of this form of the solution, an attempt is made to solve the nonlinear differential equation for transonic flow past the wavy wall. The analysis utilized exhibits clearly the difficulties inherent in nonlinear-flow problems.

Kaplan, Carl↗
NASA NTRS1992

Calculation of unsteady transonic flows with mild separation by viscous-inviscid interaction

This paper presents a method for calculating viscous effects in two- and three-dimensional unsteady transonic flow fields. An integral boundary-layer method for turbulent viscous flow is coupled with the transonic small-disturbance potential equation in a quasi-steady manner. The viscous effects are modeled with Green's lag-entrainment equations for attached flow and an inverse boundary-layer method for flows that involve mild separation. The boundary-layer method is used stripwise to approximate three-dimensional effects. Applications are given for two-dimensional airfoils, aileron buzz, and a wing planform. Comparisons with inviscid calculations, other viscous calculation methods, and experimental data are presented. The results demonstrate that the present technique can economically and accurately calculate unsteady transonic flow fields that have viscous-inviscid interactions with mild flow separation.

Howlett, James T.↗
NASA NTRS1985

A review of hot wire anemometry in transonic flows

The present paper provides a review of hot wire anemometry for compressible flows, giving particular attention to the transonic flow problem. It is pointed out that the first and most important definitive work in hot wire anemometry for compressible flows was reported by Kovasznay (1953). The existence of three independent fluctuating modes in compressible flows for small perturbations was found, taking into account the vorticity mode, the entropy mode, and the sound-wave mode. A review of Kovasznays' method for supersonic flows is also presented, and advances reported by Markovin (1956) are examined. Attention is given to experiments conducted by Horstman and Rose (1977), a general solution to the hot wire problem at transonic conditions sought by Stainback et al. (1983), and some apparent problems.

Stainback, P. C.↗
NASA NTRS1986

Effects of compressibility and free-stream turbulence on boundary layer transition in high-subsonic and transonic flows

Based on the existing boundary layer transition data, the effects of compressibility, pressure fluctuations, and free-stream turbulence have been reexamined for subsonic and transonic flow speeds. It is confirmed that the compressibility effects may be adequately expressed in terms of a simple correlation with free-stream Mach number. Pressure fluctuations, especially at low levels, do not seem to significantly affect the transition phenomenon. Effects of free-stream turbulence in high-subsonic and transonic flows are similar to the trends observed for low-speed flows and the transition process is hastened. The trends, as seen from slender cone flow data, seem to suggest power law correlations between transition Reynolds number and free-stream turbulence.

Murthy, S. V.↗
NASA NTRS1985

Numerical studies of unsteady transonic flow over oscillating airfoil

A finite difference solution to the Navier-Stokes equations combined with a time varying grid generation technique was used to compute unsteady transonic flow over an oscillating airfoil. These computations were compared with experimental data (obtained at Ames Research Center) which form part of the AGARD standard configuration for aeroelastic analysis. A variety of approximations to the full Navier-Stokes equations was used to determine the effect of frequency, shock wave motion, flow separation, and airfoil geometry on unsteady pressures and overall air loads. Good agreement is shown between experiment and theory with the limiting factor being the lack of a reliable turbulence model for high Reynolds number, unsteady transonic flows.

Chyu, W. J.↗
NASA NTRS1981

Conservative full-potential calculations for axisymmetric, transonic flow

A conservative, finite-difference, full-potential relaxation code has been developed to solve transonic flow around axisymmetric or nonlifting, planar, two-dimensional bodies. The program utilizes the artificial compressibility method to provide an upwind bias in supersonic regions. Calculated examples include a wide variety of axisymmetric and planar two-dimensional shapes with various blunt, pointed and open ends in subsonic, transonic, and low supersonic free streams. Comparisons between conservative and nonconservative full-potential calculations show perfect agreement at convergence when the flow is entirely subsonic. Noticeable differences exist, however, between the conservative and nonconservative solutions for transonic flows with shocks.

Green, L. L.↗