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NASA NTRS1992

Near-wall reconstruction of higher order moments and length scales using the POD

An analysis of the near-wall behavior of the proper orthogonal decomposition (POD) eigenfunctions derived from direct numerical simulation (DNS) of channel flow is performed. Consistent with previous studies, a low order multi-mode reconstruction of the kinetic energy and Reynolds shear stress suffices. A similar reconstruction of the isotropic dissipation rate is shown to be insufficient, however. An analysis is performed of the multi-mode composition of the dissipation rate in the near-wall region, and it is shown that a significant number of higher-order modes are required to achieve the correct asymptotic consistency in the near-wall region. In an attempt to avoid this problem, a length scale definition is proposed in terms of an integration of the correlation tensor which factors in the presence of the wall. The wall is accounted for by only integrating out to 2y(+) and not over the entire domain. Viscous and inviscid estimates for the dissipation were used in the near-wall and core regions respectively, in conjunction with this length scale representation to obtain an estimate of the dissipation throughout the domain. The resulting dissipation exhibits the proper behavior near the wall and in the inertial layer. A 1 POD mode estimate of the length scale is computed and found to agree quite well with the length scale obtained when the entire correlation tensor is used.

Glauser, Mark N.↗

NASA NTRS1984

Hydraulic jumps in 'viscous' accretion disks

It is proposed that the dissipative process necessary for rapid accretion disk evolution is driven by hydraulic jump waves on the surface of the disk. These waves are excited by the asymmetric nature of the central rotator (e.g., neutron star magnetosphere) and spiral out into the disk to form a pattern corotating with the central object. Disk matter in turn is slowed slightly at each encounter with the jump and spirals inward. In this process, the disk is heated by true turbulence produced in the jumps. Additional effects, such as a systematic misalignment of the magnetic moment of the neutron star until it is nearly orthogonal, and systematic distortion of the magnetosphere in such a way as to form an even more asymmetric central 'paddle wheel', may enhance the interaction with inflowing matter. The application to X-ray sources corresponds to the 'slow' solutions of Ghosh and Lamb, and therefore to rms magnetic fields of about 4 x 10 to the 10th gauss. Analogous phenomena have been proposed to act in the formation of galactic spiral structure.

Michel, F. C.↗

NASA NTRS1987

A theoretical comparison of internal gravity wave propagation and dissipation in high and low temperature thermospheres Implications for orbiting spacecraft

In this paper the propagation and dissipation characteristics of a number of individual internal gravity waves are discussed and compared by using a multilayer, time-averaged model in which the waves lose energy due to viscous, thermal conduction and ion-drag dissipation. From this both the height and horizontal distance (from an assumed 'source') at which the waves achieve a maximum density amplitude may be determined. Such calculations are performed for both a very hot and a very cold thermosphere, and the subsequent differences in the wave characteristics and their relation to the control of orbiting spacecraft for each of these is discussed.

Hickey, M. P.↗

NASA NTRS1990

A critical evaluation of two-equation models for near wall turbulence

A basic theoretical and computational study of two-equation models for near-wall turbulent flows was conducted. Two major problems established for the K-epsilon model are discussed, the lack of natural boundary conditions for the dissipation rate and the appearance of higher-order correlations in the balance of terms for the dissipation rate at the wall. The K-omega equation is shown to have two problems also: an exact viscous term is missing, and the destruction of the dissipation term is not properly damped near the wall. A new K-tau model (where tau = 1/omega is the turbulent time scale) was developed by inclusion of the exact viscous term, and by introduction of new wall damping functions with improved asymptotic behavior. A preliminary test of the new model yields improved predictions for the flat-plate turbulent boundary layer.

Speziale, Charles G.↗

NASA NTRS1987

High-Temperature Vibration Damper

Device for damping vibrations functions at temperatures up to 400 degrees F. Dampens vibrational torque loads as high as 1,000 lb-in. but compact enough to be part of helicopter rotor hub. Rotary damper absorbs energy from vibrating rod, dissipating it in turbulent motion of viscous hydraulic fluid forced by moving vanes through small orifices.

Clarke, Alan↗

NASA NTRS1989

Least-squares finite element method for fluid dynamics

An overview is given of new developments of the least squares finite element method (LSFEM) in fluid dynamics. Special emphasis is placed on the universality of LSFEM; the symmetry and positiveness of the algebraic systems obtained from LSFEM; the accommodation of LSFEM to equal order interpolations for incompressible viscous flows; and the natural numerical dissipation of LSFEM for convective transport problems and high speed compressible flows. The performance of LSFEM is illustrated by numerical examples.

Jiang, Bo-Nan↗

NASA NTRS1989

Relaminarization of turbulent flow on a flat plate by localized surface heating

Relaminarization of a turbulent boundary layer in air on a flat plate is demonstrated experimentally using localized surface heating. Localized heating is achieved by electrically heating a wire embedded in a thermally insulated substrate (Space Shuttle Tile) on the surface. The stability of the flow downstream of the applied control point increases with decreasing stream temperature in the flow direction. The mean and perturbation velocity profiles without control show that the flow is turbulent. With control, these profiles sequentially change from intermittently turbulent to a fully laminar state. In the relaminarization stage, the turbulent energy is dissipated by molecular transport due to viscous and conductivity mechanisms. The new profile adjusts to a lower Reynolds number based on the momentum thickness than that of the previous turbulent state.

Maestrello, Lucio↗

NASA NTRS1989

Least-squares finite element method for fluid dynamics

Jiang, Bo-Nan↗

NASA NTRS2001

Laminarization of Turbulent Boundary Layer on Flexible and Rigid Surfaces

An investigation of the control of turbulent boundary layer flow over flexible and rigid surfaces downstream of a concave-convex geometry has been made. The concave-convex curvature induces centrifugal forces and a pressure gradient on the growth of the turbulent boundary layer. The favorable gradient is not sufficient to overcome the unfavorable; thus, the net effect is a destabilizing, of the flow into Gortler instabilities. This study shows that control of the turbulent boundary layer and structural loading can be successfully achieved by using localized surface heating because the subsequent cooling and geometrical shaping downstream over a favorable pressure gradient is effective in laminarization of the turbulence. Wires embedded in a thermally insulated substrate provide surface heating. The laminarized velocity profile adjusts to a lower Reynolds number, and the structure responds to a lower loading. In the laminarization, the turbulent energy is dissipated by molecular transport by both viscous and conductivity mechanisms. Laminarization reduces spanwise vorticity because of the longitudinal cooling gradient of the sublayer profile. The results demonstrate that the curvature-induced mean pressure gradient enhances the receptivity of the flow to localized surface heating, a potentially viable mechanism to laminarize turbulent boundary layer flow; thus, the flow reduces the response of the flexible structure and the resultant sound radiation.

Maestrello, Lucio↗

NASA NTRS1966

A viscous ring damper for a freely precessing satellite.

Viscous ring damper for removing wobble motion of spin-stabilized satellite analyzed by studying energy dissipation

VISCOUS DAMPING↗

NASA NTRS2002

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows

Accurate numerical simulations of complex multiscale compressible viscous flows, especially high speed turbulence combustion and acoustics, demand high order schemes with adaptive numerical dissipation controls. Standard high resolution shock-capturing methods are too dissipative to capture the small scales and/or long-time wave propagations without extreme grid refinements and small time steps. An integrated approach for the control of numerical dissipation in high order schemes for the compressible Euler and Navier-Stokes equations has been developed and verified by the authors and collaborators. These schemes are suitable for the problems in question. Basically, the scheme consists of sixth-order or higher non-dissipative spatial difference operators as the base scheme. To control the amount of numerical dissipation, multiresolution wavelets are used as sensors to adaptively limit the amount and to aid the selection and/or blending of the appropriate types of numerical dissipation to be used. Magnetohydrodynamics (MHD) waves play a key role in drag reduction in highly maneuverable high speed combat aircraft, in space weather forecasting, and in the understanding of the dynamics of the evolution of our solar system and the main sequence stars. Although there exist a few well-studied second and third-order high-resolution shock-capturing schemes for the MHD in the literature, these schemes are too diffusive and not practical for turbulence/combustion MHD flows. On the other hand, extension of higher than third-order high-resolution schemes to the MHD system of equations is not straightforward. Unlike the hydrodynamic equations, the inviscid MHD system is non-strictly hyperbolic with non-convex fluxes. The wave structures and shock types are different from their hydrodynamic counterparts. Many of the non-traditional hydrodynamic shocks are not fully understood. Consequently, reliable and highly accurate numerical schemes for multiscale MHD equations pose a great challenge to algorithm development. In addition, controlling the numerical error of the divergence free condition of the magnetic fields for high order methods has been a stumbling block. Lower order methods are not practical for the astrophysical problems in question. We propose to extend our hydrodynamics schemes to the MHD equations with several desired properties over commonly used MHD schemes.

Sjoegreen, Bjoern↗

NASA NTRS1993

A numerical study of the effect of geometry variation, turbulence models, and dissipation on the flow past control surfaces

The steady 3D viscous flow past the ONERA M6 wing and a slender delta wing-body with trailing edge control surfaces has been computed. A cell-centered finite-volume Navier-Stokes patched zonal method has been used for the numerical simulation. Both diagonalized and LUSGS schemes have been implemented. Besides the standard nonplanar zonal interfacing techniques, a new virtual zone capability has been employed. For code validation, the transonic flow past the ONERA M5 wing is calculated for angles-of-attack of 3.06 deg and 5.06 deg and compared with the available experiments. The wing-body computational results are compared with experimental data for both trailing-edge flaps deflected. The experimental flow conditions are M subinfinity = 0.4, a turbulent Reynolds number of 5.41 million based on a mean aerodynamic chord of 25.959 inches, adiabatic wall, and angles-of-attack varying from 0 deg to 23.85 deg. The computational results are presented for the 23.85 deg angle-of-attack case. The effects of the base flow due to a model sting, the varying second and fourth order numerical dissipation, and the turbulence model are all considered.

Chaussee, Denny S.↗

NASA NTRS1980

Mechanical energy transport

The properties, generation, and dissipation mechanisms of acoustic, gravity and Alfven waves are described, whose restoring forces are pressure, buoyancy, and magnetic tension, respectively. For acoustic waves, generation by turbulent convective motions and by the Eddington Valve thermal overstability is discussed, considering the 'five-minute' oscillation; dissipation is possible either by radiation or shocks. Generation of gravity waves by penetrative convective motions and by shear arising from supergranule motions is reviewed, and dissipation due to wave breaking, interaction with the mean horizontal fluid flow, and very severe radiative damping is considered. Attention is given to Alfven wave generation by convective motions and thermal overstability, and to dissipation by mode coupling, wave decay, current dissipation, and particle collisions producing Joule or viscous heating.

Stein, R. F.↗

NASA NTRS1987

The thermal-vortex equations

The Boussinesq approximation is extended so as to explicitly account for the transfer of fluid energy through viscous action into thermal energy. Ideal and dissipative integral invariants are discussed, in addition to the general equations for thermal-fluid motion.

Shebalin, John V.↗

NASA NTRS2001

Performance of Several High Order Numerical Methods for Supersonic Combustion

The performance of two recently developed numerical methods by Yee et al. and Sjoegreen and Yee using postprocessing nonlinear filters is examined for a 2-D multiscale viscous supersonic react-live flow. These nonlinear filters can improve nonlinear instabilities and at the same time can capture shock/shear waves accurately. They do not, belong to the class of TVD, ENO or WENO schemes. Nevertheless, they combine stable behavior at discontinuities and detonation without smearing the smooth parts of the flow field. For the present study, we employ a fourth-order Runge-Kutta in time and a sixth-order non-dissipative spatial base scheme for the convection and viscous terms. We denote the resulting nonlinear filter schemes ACM466-RK4 and WAV66-RK4.

Sjoegreen, Bjoern↗

NASA NTRS1995

Large-eddy simulation of flow past a circular cylinder

Some of the most challenging applications of large-eddy simulation are those in complex geometries where spectral methods are of limited use. For such applications more conventional methods such as finite difference or finite element have to be used. However, it has become clear in recent years that dissipative numerical schemes which are routinely used in viscous flow simulations are not good candidates for use in LES of turbulent flows. Except in cases where the flow is extremely well resolved, it has been found that upwind schemes tend to damp out a significant portion of the small scales that can be resolved on the grid. Furthermore, it has been found that even specially designed higher-order upwind schemes that have been used successfully in the direct numerical simulation of turbulent flows produce too much dissipation when used in conjunction with large-eddy simulation. The objective of the current study is to perform a LES of incompressible flow past a circular cylinder at a Reynolds number of 3900 using a solver which employs an energy-conservative second-order central difference scheme for spatial discretization and compare the results obtained with those of Beaudan & Moin (1994) and with the experiments in order to assess the performance of the central scheme for this relatively complex geometry.

Mittal, R.↗

NASA NTRS2002

A New Low Dissipative High Order Schemes for MHD Equations

The goal of this talk is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls to limit the amount and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids.

Yee, H. C.↗

NASA NTRS2003

Efficient Low Dissipative High Order Schemes for Multiscale MHD Flows, I: Basic Theory

The objective of this paper is to extend our recently developed highly parallelizable nonlinear stable high order schemes for complex multiscale hydrodynamic applications to the viscous MHD equations. These schemes employed multiresolution wavelets as adaptive numerical dissipation controls t o limit the amount of and to aid the selection and/or blending of the appropriate types of dissipation to be used. The new scheme is formulated for both the conservative and non-conservative form of the MHD equations in curvilinear grids. The four advantages of the present approach over existing MHD schemes reported in the open literature are as follows. First, the scheme is constructed for long-time integrations of shock/turbulence/combustion MHD flows. Available schemes are too diffusive for long-time integrations and/or turbulence/combustion problems. Second, unlike exist- ing schemes for the conservative MHD equations which suffer from ill-conditioned eigen- decompositions, the present scheme makes use of a well-conditioned eigen-decomposition obtained from a minor modification of the eigenvectors of the non-conservative MHD equations t o solve the conservative form of the MHD equations. Third, this approach of using the non-conservative eigensystem when solving the conservative equations also works well in the context of standard shock-capturing schemes for the MHD equations. Fourth, a new approach to minimize the numerical error of the divergence-free magnetic condition for high order schemes is introduced. Numerical experiments with typical MHD model problems revealed the applicability of the newly developed schemes for the MHD equations.

Sjoegreen, Bjoern↗