Results for “Approximate boundary” — Page 18

NASA NTRS1972

Application of the Galerkin Method in the Design of Stable Liquid Rocket Motors

A brief description of results obtained in the continuing investigations is presented. The following areas are covered: (1) the development of the third-order, multimode theory to study the behavior of large amplitude transverse instabilities, (2) nonlinear axial mode instability, and (3) the influence of the functional form of the unsteady combustion response function upon the stability characteristics of rocket motors. Also a study was begun to improve the second order potential theory in order to provide a better approximation to the nozzle boundary condition.

Zinn, B. T.↗

NASA NTRS1974

The numerical calculation of laminar boundary-layer separation

Iterative finite-difference techniques are developed for integrating the boundary-layer equations, without approximation, through a region of reversed flow. The numerical procedures are used to calculate incompressible laminar separated flows and to investigate the conditions for regular behavior at the point of separation. Regular flows are shown to be characterized by an integrable saddle-type singularity that makes it difficult to obtain numerical solutions which pass continuously into the separated region. The singularity is removed and continuous solutions ensured by specifying the wall shear distribution and computing the pressure gradient as part of the solution. Calculated results are presented for several separated flows and the accuracy of the method is verified. A computer program listing and complete solution case are included.

Klineberg, J. M.↗

NASA NTRS1974

On laminar boundary-layer separation

Iterative finite-difference techniques are developed for integrating the boundary-layer equations, without approximation, through a region of reversed flow. The numerical procedures are used to calculate incompressible laminar separated flows and to investigate the conditions for regular behavior at the point of separation. Regular flows are shown to be characterized by an integrable saddle-type singularity that makes it difficult to obtain numerical solutions which pass continuously into the separated region. The singularity is removed and continuous solutions ensured by specifying the wall shear distribution and computing the pressure gradient as part of the solution. Calculated results are presented for a number of separated flows and the accuracy of the method is verified.

Klineberg, J. M.↗

NASA NTRS1976

Calculation of the three-dimension, supersonic, inviscid, steady flow past an arrow-winged airframe, part 1

A detailed description of the procedure used to compute three dimensional, supersonic, inviscid, steady flows past airframes is given. No limitations are imposed on the geometry of the airplane. Suitable computational grids are generated by automatic conformal mappings. The equations of motion, with pressure, entropy, and velocity direction as basic unknowns, are written and discretized in the computational space. Special rules to approximate derivatives are given. Boundary points are treated by a modified method of characteristics.

Moretti, G.↗

NASA NTRS1981

On the polarity of cyclostrophic flow in planetary atmospheres

Fluids which are completely inviscid in the mathematical sense do not exist. Thus, the concepts of gradient flow and cyclostrophic balance are interpreted as approximate solutions of a boundary value problem for small but finite viscosity. Large scale phenomena such as the superrotation of Venus and cyclones are effectively bounded by the rigidly rotating planetary surface. This polarizes the circulation and excludes so-called anomalous motions from the flow regime. With scale phenomena such as dust devils, both directions are observed which is attributed to the stochastic nature of wind systems surrounding the disturbance.

Mayr, H. G.↗

NASA NTRS1983

Flat-plate drag measurements with vortex generators in turbulent boundary layer

Direct drag measurements were obtained on a flat plate with a spanwise row of vortex generators near the leading edge, to produce an array of stream wise vortices within the approaching turbulent boundary layer. The object was to explore the possibility of modifying the large scale structure of the boundary layer through embedded longitudinal vortices with a view to obtaining a reduction in wall shear. Both obstacle and vane type vortex generators were tested at free stream velocities 40 ft/sec to 130 ft/sec corresponding to plate length Reynolds no. 0.3 million to 0.8 million with a nominal boundary layer thickness of approximately 0.6 in. at the leading edge. A few vortex generator configurations were tested both on and off the plate to measure the total drag as well as the plate drag alone. The obstacle type devices reduced the plate drag, indicating that the wake momentum defect predominated even in the presence of streamwise vortices. The vane type vortex generators however always increased the plate drag.

Rao, D. M.↗

NASA NTRS1982

Numerical methods and computers used in elastohydrodynamic lubrication

Some of the methods of obtaining approximate numerical solutions to boundary value problems that arise in elastohydrodynamic lubrication are reviewed. The highlights of four general approaches (direct, inverse, quasi-inverse, and Newton-Raphson) are sketched. Advantages and disadvantages of these approaches are presented along with a flow chart showing some of the details of each. The basic question of numerical stability of the elastohydrodynamic lubrication solutions, especially in the pressure spike region, is considered. Computers used to solve this important class of lubrication problems are briefly described, with emphasis on supercomputers.

Hamrock, B. J.↗

NASA NTRS1985

Nonlinear acoustic wave propagation in atmosphere

A model problem that simulates an atmospheric acoustic wave propagation situation that is nonlinear is considered. The model is derived from the basic Euler equations for the atmospheric flow and from the regular perturbations for the acoustic part. The nonlinear effects are studied by obtaining two successive linear problems in which the second one involves the solution of the first problem. Well posedness of these problems is discussed and approximations of the radiation boundary conditions that can be used in numerical simulations are presented.

Hariharan, S. I.↗

NASA NTRS1986

Nonlinear acoustic wave propagation in atmosphere

In this paper a model problem is considered that simulates an atmospheric acoustic wave propagation situation that is nonlinear. The model is derived from the basic Euler equations for the atmospheric flow and from the regular perturbations for the acoustic part. The nonlinear effects are studied by obtaining two successive linear problems in which the second one involves the solution of the first problem. Well-posedness of these problems is discussed and approximations of the radiation boundary conditions that can be used in numerical simulations are presented.

Hariharan, S. I.↗

NASA NTRS1986

Incompressible viscous flow simulations of the NFAC wind tunnel

The capabilities of an existing 3-D incompressible Navier-Stokes flow solver, INS3D, are extended and improved to solve turbulent flows through the incorporation of zero- and two-equation turbulence models. The two-equation model equations are solved in their high Reynolds number form and utilize wall functions in the treatment of solid wall boundary conditions. The implicit approximate factorization scheme is modified to improve the stability of the two-equation solver. Applications to the 3-D viscous flow inside the 80 by 120 feet open return wind tunnel of the National Full Scale Aerodynamics Complex (NFAC) are discussed and described.

Champney, Joelle Milene↗

NASA NTRS1987

Nonlinear acoustic wave propagation in atmosphere TLSP - Final report

In this paper a model problem is considered that simulates an atmospheric acoustic wave propagation situation that is nonlinear. The model is derived from the basic Euler equations for the atmospheric flow and from the regular perturbations for the acoustic part. The nonlinear effects are studied by obtaining two successive linear problems in which the second one involves the solution of the first problem. Well-posedness of these problems is discussed and approximations of the radiation boundary conditions that can be used in numerical simulations are presented.

Hariharan, S. I.↗

NASA NTRS1988

The dynamics of free liquid drops

The behavior of rotating and oscillating free liquid drops was studied by many investigators theoretically for many years. More recent numerical treatments have yielded predictions which are yet to be verified experimentally. The purpose is to report the results of laboratory work as well as that of the experiments carried out in space during the flight of Spacelab 3, and to compare it with the existing theoretical studies. Ground-based experiments were attempted as a first approximation to the ideal boundary conditions used by the theoretical treatments by neutralizing the overwhelming effects of the Earth's gravitational field with an outside supporting liquid and with the use of levitation technology. The viscous and inertial loading of such a suspending fluid was found to profoundly effect the results, but the information thus gathered has emphasized the uniqueness of the experimental data obtained in the low-gravity environment of space.

Wang, T. G.↗

NASA NTRS1991

Euler solutions to nonlinear acoustics of non-lifting hovering rotor blades

For the first time a computational fluid dynamics (CFD) method is used to calculate directly the high-speed impulsive (HSI) noise of a non-lifting hovering rotor blade out to a distance of over three rotor radii. In order to accurately propagate the acoustic wave in a stable and efficient manner, an implicit upwind-biased Euler method is solved on a grid with points clustered along the line of propagation. A detailed validation of the code is performed for a rectangular rotor blade at tip Mach numbers ranging from 0.88 to 0.92. The agreement with experiment is excellent at both the sonic cylinder and at 2.18 rotor radii. The agreement at 3.09 rotor radii is still very good, showing improvements over the results from the best previous method. Grid sensitivity studies indicate that with special attention to the location of the boundaries a grid with approximately 60,000 points is adequate. This results in a computational time of approximately 40 minutes on a Cray-XMP. The practicality of the method to calculate HSI noise is demonstrated by expanding the scope of the investigation to examine the rectangular blade as well as a highly swept and tapered blade over a tip Mach number range of 0.80 to 0.95. Comparisons with experimental data are excellent and the advantages of planform modifications are clearly evident. New insight is gained into the mechanisms of nonlinear propagation and the minimum distance at which a valid comparison of different rotors can be made: approximately two rotor radii from the center of rotation.

Baeder, J. D.↗

NASA NTRS1993

Characterization of cavity flow fields using pressure data obtained in the Langley 0.3-Meter Transonic Cryogenic Tunnel

Static and fluctuating pressure distributions were obtained along the floor of a rectangular-box cavity in an experiment performed in the LaRC 0.3-Meter Transonic Cryogenic Tunnel. The cavity studied was 11.25 in. long and 2.50 in. wide with a variable height to obtain length-to-height ratios of 4.4, 6.7, 12.67, and 20.0. The data presented herein were obtained for yaw angles of 0 deg and 15 deg over a Mach number range from 0.2 to 0.9 at a Reynolds number of 30 x 10(exp 6) per ft with a boundary-layer thickness of approximately 0.5 in. The results indicated that open and transitional-open cavity flow supports tone generation at subsonic and transonic speeds at Mach numbers of 0.6 and above. Further, pressure fluctuations associated with acoustic tone generation can be sustained when static pressure distributions indicate that transitional-closed and closed flow fields exist in the cavity. Cavities that support tone generation at 0 deg yaw also supported tone generation at 15 deg yaw when the flow became transitional-closed. For the latter cases, a reduction in tone amplitude was observed. Both static and fluctuating pressure data must be considered when defining cavity flow fields, and the flow models need to be refined to accommodate steady and unsteady flows.

Tracy, M. B.↗

NASA NTRS1992

A powerful local shear instability in weakly magnetized disks. III - Long-term evolution in a shearing sheet. IV - Nonaxisymmetric perturbations

The nonlinear evolution of the recently identified accretion disk magnetic shear instability is investigated through a series of numerical simulations. Finite-difference computations of the equations of compressible MHD are carried out on an axisymmetric shearing sheet system with periodic boundary conditions designed to approximate a local region within an accretion disk. Initial field configurations that include some net vertical component evolve into a nonlinear, exponentially growing solution with large poloidal velocities and magnetic fields with energies comparable to the thermal energy density. The stability of a purely azimuthal field configuration is examined, and it is found that nonaxisymmetric instability is present, but with a growth time measured in tens of orbital periods. In general, the most rapid growth occurs for very small radial and azimuthal wavenumbers, leading to coherent magnetic field structure in planes parallel to the disk. It is suggested that this instability is a key ingredient for the generation of magnetic fields in disks.

Hawley, John F.↗

NASA NTRS1991

Euler solutions to nonlinear acoustics of non-lifting rotor blades

For the first time a computational fluid dynamics (CFD) method is used to calculate directly the high-speed impulsive (HSI) noise of a non-lifting hovering rotor blade out to a distance of over three rotor radii. In order to accurately propagate the acoustic wave in a stable and efficient manner, an implicit upwind-biased Euler method is solved on a grid with points clustered along the line of propagation. A detailed validation of the code is performed for a rectangular rotor blade at tip Mach numbers ranging from 0.88 to 0.92. The agreement with experiment is excellent at both the sonic cylinder and at 2.18 rotor radii. The agreement at 3.09 rotor radii is still very good, showing improvements over the results from the best previous method. Grid sensitivity studies indicate that with special attention to the location of the boundaries a grid with approximately 60,000 points is adequate. This results in a computational time of approximately 40 minutes on a Cray-XMP. The practicality of the method to calculate HSI noise is demonstrated by expanding the scope of the investigation to examine the rectangular blade as well as a highly swept and tapered blade over a tip Mach number range of 0.80 to 0.95. Comparisons with experimental data are excellent and the advantages of planform modifications are clearly evident. New insight is gained into the mechanisms of nonlinear propagation and the minimum distance at which a valid comparison of different rotors can be made: approximately two rotor radii from the center of rotation.

Baeder, J. D.↗

NASA NTRS1993

Supersonic flow visualization of a nacelle in close proximity to a simulated wing

A flow visualization study was made in the 9 x 9 inch supersonic wind tunnel at Wichita State University to examine shock and boundary layer flow interaction for a nacelle in close proximity to the lower surface of a simulated wing. The test matrix included variations of angle of attack from -2 degrees to +4 degrees, nacelle-wing gap from 0.5 to 3-nacelle inlet diameter (0.12 inch), and Reynolds number based on nacelle length (1.164 inch) from 1.16 x 10(exp 6) to 1.45 x 10(exp 6) at a nominal Mach number of 2. Schlieren pictures of wing and nacelle flowfield were recorded by a video camera during each tunnel run. Results show that the nacelle inlet shock wave remains attached to the inlet lip and its impingement does not significantly affect the wing boundary layer. At the nacelle trailing edge location, the wing boundary layer thickness is approximately one nacelle inlet diameter at alpha = 0 degrees and it decreases with increase of angle of attack.

Biber, Kasim↗

NASA NTRS1994

An axisymmetric analog two-layer convective heating procedure with application to the evaluation of Space Shuttle Orbiter wing leading edge and windward surface heating

A numerical procedure for predicting the convective heating rate of hypersonic reentry vehicles is described. The procedure, which is based on the axisymmetric analog, consists of obtaining the three-dimensional inviscid flowfield solution; then the surface streamlines and metrics are calculated using the inviscid velocity components on the surface; finally, an axisymmetric boundary layer code or approximate convective heating equations are used to evaluate heating rates. This approach yields heating predictions to general three-dimensional body shapes. The procedure has been applied to the prediction of the wing leading edge heating to the Space Shuttle Orbiter. The numerical results are compared with the results of heat transfer testing (OH66) of an 0.025 scale model of the Space Shuttle Orbiter configuration in the Calspan Hypersonic Shock Tunnel (HST) at Mach 10 and angles of attack of 30 and 40 degrees. Comparisons with STS-5 flight data at Mach 9.15 and angle of attack of 37.4 degrees and STS-2 flight data at Mach 12.86 and angle of attack of 39.7 degrees are also given.

Wang, K. C.↗