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At least 991 records · Page 55
All sourcesNASA NTRSDOE OSTI
NASA NTRS1976

Higher-order numerical methods derived from three-point polynomial interpolation

Higher-order collocation procedures resulting in tridiagonal matrix systems are derived from polynomial spline interpolation and Hermitian finite-difference discretization. The equations generally apply for both uniform and variable meshes. Hybrid schemes resulting from different polynomial approximations for first and second derivatives lead to the nonuniform mesh extension of the so-called compact or Pade difference techniques. A variety of fourth-order methods are described and this concept is extended to sixth-order. Solutions with these procedures are presented for the similar and non-similar boundary layer equations with and without mass transfer, the Burgers equation, and the incompressible viscous flow in a driven cavity. Finally, the interpolation procedure is used to derive higher-order temporal integration schemes and results are shown for the diffusion equation.

Rubin, S. G.↗
NASA NTRS1976

Effect of anisotropy and rotation on turbulence production

The dynamical equations for the Reynolds stresses in a form which is suitable for incompressible homogeneous flows are used as a starting point in the investigation. It is assumed that the mean flow is two-dimensional. The equation for the rate of change of the kinetic energy of turbulence is derived. If the turbulence is isotropic, there is no turbulence production. However, the isotropic condition is not stable. The production mechanism is found to be autocatalytic. Rotation always inhibits production because it reduces anisotropy.

Ferziger, J. H.↗
NASA NTRS1976

High-beta turbulence in two-dimensional magnetohydrodynamics

Equations of ideal magnetohydrodynamics are used to study incompressible turbulent flows in a specified geometry where all the field quantities vary with only two spatial dimensions. The procedures adopted are basically those of Kraichnan (1967), in which classical equilibrium ensembles are built around constants of the motion identified from the Fourier-transformed equations of motion. Once the constants of the motion are identified, the statistical formulation of the problem is presented in a phase space whose coordinates are the real and imaginary parts of the Fourier coefficients. Canonical ensembles are constructed in this phase space by classical arguments. The theory developed permits isolation of some qualitatively new gross physical effects which have so far not been calculated. One of the more novel physical effects is the appearance of macroscopic structures involving long-wavelength, self-generated, magnetic fields for a wide range of initial parameters.

Fyfe, D.↗
NASA NTRS1977

Generalized Theodorsen solution for singular integral equations of the airfoil class

A class of singular integral equations is considered which arise in various two-dimensional mixed boundary-value problems with simple harmonic time variation. A problem typical of this class is that of determining the lifting pressure distribution on an oscillating airfoil in an unbounded incompressible potential flow. It is shown that Theodorsen's (1935) solution to this problem, with some modification, is valid for a general class of unsteady kernel functions. The technique employed is to consider an equivalent steady problem and then show that the unsteady resolvent and unsteady homogeneous solution can be written directly in terms of the steady solutions and a single frequency-dependent function which reduces to the Theodorsen function for the steady kernel.

Williams, M. H.↗
NASA NTRS1978

A comparison of the Method of Lines to finite difference techniques in solving time-dependent partial differential equations

Steady state solutions to two time dependent partial differential systems have been obtained by the Method of Lines (MOL) and compared to those obtained by efficient standard finite difference methods: (1) Burger's equation over a finite space domain by a forward time central space explicit method, and (2) the stream function - vorticity form of viscous incompressible fluid flow in a square cavity by an alternating direction implicit (ADI) method. The standard techniques were far more computationally efficient when applicable. In the second example, converged solutions at very high Reynolds numbers were obtained by MOL, whereas solution by ADI was either unattainable or impractical. With regard to 'set up' time, solution by MOL is an attractive alternative to techniques with complicated algorithms, as much of the programming difficulty is eliminated.

Kurtz, L. A.↗
NASA NTRS1978

Lifting-line theory of oblique wings

The study extends Prandtl's lifting-line theory to planar wings involving swept and curved centerlines. Attention is focused on distinct features of such a theory, with special emphasis on an oblique wing in a steady incompressible potential flow. The analysis presented is compared with exact solutions derived from an inverse method and with results from a panel method.

Cheng, H. K.↗
NASA NTRS1979

Characteristics of lightly loaded fan rotor blade wakes

Low subsonic and incompressible wake flow downstream of lightly loaded rotor was studied. Measurements of mean velocity, turbulence intensity, Reynolds stress, and static variations across the rotor wake at various axial and radial locations were investigated. Wakes were measured at various rotor blade incidences to discern the effect of blade loading on the rotor wake. Mean velocity and turbulence measurements were carried out with a triaxial hot wire probe both rotating with the rotor and stationary behind the rotor. Results indicate that increased loading slows the decay rates of axial and tangential mean velocity defects and radial velocities in the wake. The presence of large radial velocities in the rotor wake indicate the extent of the interactions between one radius and another. Appreciable static pressure variations across the rotor wake were found in the near wake region. Similarity in the profile shape was found for the axial and tangential components of the mean velocity and in the outer layer for axial, tangential, and radial turbulence intensities.

Reynolds, B.↗
NASA NTRS1979

Classical Aerodynamic Theory

A collection of papers on modern theoretical aerodynamics is presented. Included are theories of incompressible potential flow and research on the aerodynamic forces on wing and wing sections of aircraft and on airship hulls.

Jones, R. T.↗
NASA NTRS1980

Blade loading and spanwise effects on the near and far wake characteristics of a compressor rotor blade

An experimental investigation of the blade loading and spanwise effects on the rotor wake is presented. The investigation was limited to a study of a low subsonic and incompressible wake flow found downstream of a lightly loaded rotor. Measurements were made with a tri-axial hot wire probe mounted in the stationary frame of reference at six radial and nine axial positions. At each measurement location, the rotor was run at different operating conditions to discern the effects of blade loading on the wake. Near and far wake measurements are given, including mean velocity and turbulence intensity characteristics. The loading and spanwise effects on rotor wake characteristics were found to be substantial.

Reynolds, B.↗
NASA NTRS1980

Turbulent solution of the Navier-Stokes equations

The unaveraged Navier-Stokes equations are solved numerically in order to study the nonlinear physics of incompressible turbulent flow. Initial three dimensional cosine velocity fluctuations and periodic boundary conditions are used. No mean gradients are present. The three components of the mean square velocity fluctuations are equal for the initial conditions chosen. The resulting solution shows characteristics of turbulence, such as the nonlinear excitation of small scale fluctuations. For the higher Reynolds numbers the initially nonrandom flow develops into an apparently random turbulence.

Deissler, R. G.↗
NASA NTRS1980

Turbulent solution of the Navier-Stokes equations

To study the nonlinear physics of incompressible turbulent flow, the unaveraged Navier-Stokes equations are solved numerically. Initial three-dimensional cosine velocity fluctuations and periodic boundary conditions are used. No mean gradients are present. The three components of the mean-square velocity fluctuations are equal for the initial conditions chosen. The resulting solution shows characteristics of turbulence, such as the nonlinear excitation of small-scale fluctuations. For the higher Reynolds numbers the initially nonrandom flow develops into an apparently random turbulence.

Deissler, R. G.↗
NASA NTRS1981

Interactive method for computation of viscous flow with recirculation

An interactive method is proposed for the solution of two-dimensional, laminar flow fields with identifiable regions of recirculation, such as the shear-layer-driven cavity flow. The method treats the flow field as composed of two regions, with an appropriate mathematical model adopted for each region. The shear layer is computed by the compressible boundary layer equations, and the slowly recirculating flow by the incompressible Navier-Stokes equations. The flow field is solved iteratively by matching the local solutions in the two regions. For this purpose a new matching method utilizing an overlap between the two computational regions is developed, and shown to be most satisfactory. Matching of the two velocity components, as well as the change in velocity with respect to depth is amply accomplished using the present approach, and the stagnation points corresponding to separation and reattachment of the dividing streamline are computed as part of the interactive solution. The interactive method is applied to the test problem of a shear layer driven cavity. The computational results are used to show the validity and applicability of the present approach.

Brandeis, J.↗
NASA NTRS1982

Numerical analysis and FORTRAN program for the computation of the turbulent wakes of turbomachinery rotor blades, isolated airfoils and cascade of airfoils

Turbulent wakes of turbomachinery rotor blades, isolated airfoils, and a cascade of airfoils were investigated both numerically and experimentally. Low subsonic and incompressible wake flows were examined. A finite difference procedure was employed in the numerical analysis utilizing the continuity, momentum, and turbulence closure equations in the rotating, curvilinear, and nonorthogonal coordinate system. A nonorthogonal curvilinear coordinate system was developed to improve the accuracy and efficiency of the numerical calculation. Three turbulence models were employed to obtain closure of the governing equations. The first model was comprised to transport equations for the turbulent kinetic energy and the rate of energy dissipation, and the second and third models were comprised of equations for the rate of turbulent kinetic energy dissipation and Reynolds stresses, respectively. The second model handles the convection and diffusion terms in the Reynolds stress transport equation collectively, while the third model handles them individually. The numerical results demonstrate that the second and third models provide accurate predictions, but the computer time and memory storage can be considerably saved with the second model.

Hah, C.↗
NASA NTRS1982

Subsonic panel method for the efficient analysis of multiple geometry perturbations

An accurate and efficient method was developed for the aerodynamic analysis of a series of arbitrary small geometry perturbations to a given baseline configuration. The method is appropriate for wing-fuselage configurations in incompressible potential flow. Mathematical formulations are presented for three computer programs that are employed. The first program is a conventional surface panel method for calculating the baseline singularity distribution. The second program calculates a partial derivative matrix. Each element of the matrix is the rate of change of singularity strength at one point with respect to a surface coordinate of a different point. For each baseline configuration, the calculated quantities from the first two programs establish an input file for the third. The third program calculates the surface pressure distribution and forces and moments for a series of geometry perturbations.

Bristow, D. R.↗
NASA NTRS1981

Helicopter rotor loads using a matched asymptotic expansion technique

The theoretical basis and computational feasibility of the Van Holten method, and its performance and range of validity by comparison with experiment and other approximate methods was examined. It is found that within the restrictions of incompressible, potential flow and the assumption of small disturbances, the method does lead to a valid description of the flow. However, the method begins to break down under conditions favoring nonlinear effects such as wake distortion and blade/rotor interaction.

Pierce, G. A.↗
NASA NTRS1982

Correlation of Preston-tube data with laminar skin friction (Log No. J12984)

Preston tube data within laminar boundary layers obtained on a sharp ten-degree cone in the NASA Ames eleven-foot transonic wind tunnel are correlated with the corresponding values of theoretical skin friction. Data were obtained over a Mach number range of 0.30 to 0.95 and unit Reynolds numbers of 9.84, 13.1, and 16.4 million per meter. The rms scatter of skin friction coefficient about the correlation is of the order of one percent, which is comparable to the reported accuracy for calibrations of Preston tubes in incompressible pipe flows. In contrast to previous works on Preston tube/skin friction correlations, which are based on the physical height of the probe's face, this satisfactory correlation for compressible boundary layer flows is achieved by accounting for the effects of a variable "effective" height of the probe. The coefficients, which appear in the correlation, are dependent on the particular tunnel environment. The general procedure can be used to define correlations for other wind tunnels.

Reed, T. D.↗
NASA NTRS1981

Mixing layer simulation by an improved three-dimensional vortex-in-cell algorithm

An extension is presented of the three-dimensional vortex-in-cell (VIC) method that allows for the simulation of incompressible turbulent flows such as plane mixing layers and wakes with exact boundary conditions in the normal direction. The vorticity is assumed to be confined between two parallel planes and the turbulence is assumed to be homogeneous in the two directions parallel to the planes. As an application, an analysis is presented of the evolution of the plane mixing layer subjected to random two- and three-dimensional initial disturbances.

Couet, B.↗
NASA NTRS1982

Features of a reattaching turbulent shear layer subject to an adverse pressure gradient

Experimental data have been obtained in an incompressible turbulent flow over a rearward-facing step with superimposed adverse pressure gradient. Mean velocities, Reynolds stresses and triple-products measured by a laser Doppler velocimeter are presented for two cases of adverse pressure gradient. Mixing lengths, eddy viscosities, production, convection, turbulent diffusion, and dissipation terms are extracted from the data. These data are compared with various mixing length and eddy-viscosity turbulence models. Numerical calculations incorporating the k-epsilon and the algebraic-stress turbulence models are compared with the data. When determining quantities of engineering interest, the modified algebraic-stress model (ASM) is a significant improvement over the unmodified ASM and the unmodified k-epsilon model

Driver, D. M.↗