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NASA NTRS2000

Progress in the Development of a Class of Efficient Low Dissipative High Order Shock-capturing Methods

In a series of papers, Olsson (1994, 1995), Olsson & Oliger (1994), Strand (1994), Gerritsen Olsson (1996), Yee et al. (1999a,b, 2000) and Sandham & Yee (2000), the issue of nonlinear stability of the compressible Euler and Navier-Stokes Equations, including physical boundaries, and the corresponding development of the discrete analogue of nonlinear stable high order schemes, including boundary schemes, were developed, extended and evaluated for various fluid flows. High order here refers to spatial schemes that are essentially fourth-order or higher away from shock and shear regions. The objective of this paper is to give an overview of the progress of the low dissipative high order shock-capturing schemes proposed by Yee et al. (1999a,b, 2000). This class of schemes consists of simple non-dissipative high order compact or non-compact central spatial differencings and adaptive nonlinear numerical dissipation operators to minimize the use of numerical dissipation. The amount of numerical dissipation is further minimized by applying the scheme to the entropy splitting form of the inviscid flux derivatives, and by rewriting the viscous terms to minimize odd-even decoupling before the application of the central scheme (Sandham & Yee). The efficiency and accuracy of these scheme are compared with spectral, TVD and fifth- order WENO schemes. A new approach of Sjogreen & Yee (2000) utilizing non-orthogonal multi-resolution wavelet basis functions as sensors to dynamically determine the appropriate amount of numerical dissipation to be added to the non-dissipative high order spatial scheme at each grid point will be discussed. Numerical experiments of long time integration of smooth flows, shock-turbulence interactions, direct numerical simulations of a 3-D compressible turbulent plane channel flow, and various mixing layer problems indicate that these schemes are especially suitable for practical complex problems in nonlinear aeroacoustics, rotorcraft dynamics, direct numerical simulation or large eddy simulation of compressible turbulent flows at various speeds including high-speed shock-turbulence interactions, and general long time wave propagation problems. These schemes, including entropy splitting, have also been extended to freestream preserving schemes on curvilinear moving grids for a thermally perfect gas (Vinokur & Yee 2000).

Yee, H. C.↗

NASA NTRS2013

Aeroacoustic Simulation of Nose Landing Gear on Adaptive Unstructured Grids With FUN3D

Numerical simulations have been performed for a partially-dressed, cavity-closed nose landing gear configuration that was tested in NASA Langley s closed-wall Basic Aerodynamic Research Tunnel (BART) and in the University of Florida's open-jet acoustic facility known as the UFAFF. The unstructured-grid flow solver FUN3D, developed at NASA Langley Research center, is used to compute the unsteady flow field for this configuration. Starting with a coarse grid, a series of successively finer grids were generated using the adaptive gridding methodology available in the FUN3D code. A hybrid Reynolds-averaged Navier-Stokes/large eddy simulation (RANS/LES) turbulence model is used for these computations. Time-averaged and instantaneous solutions obtained on these grids are compared with the measured data. In general, the correlation with the experimental data improves with grid refinement. A similar trend is observed for sound pressure levels obtained by using these CFD solutions as input to a FfowcsWilliams-Hawkings noise propagation code to compute the farfield noise levels. In general, the numerical solutions obtained on adapted grids compare well with the hand-tuned enriched fine grid solutions and experimental data. In addition, the grid adaption strategy discussed here simplifies the grid generation process, and results in improved computational efficiency of CFD simulations.

Vatsa, Veer N.↗

NASA NTRS1987

On the subgrid-scale modeling of compressible turbulence

A subgrid-scale model recently derived for use in the large-eddy simulation of compressible turbulent flows is examined from a fundamental theoretical and computational standpoint. It is demonstrated that this model, which is applicable only to compressible turbulent flows in the limit of small density fluctuations, correlates somewhat poorly with the results of direct numerical simulations of compressible isotropic turbulence at low Mach numbers. An alternative model, based on Favre-filtered fields, is suggested which appears to reduce these limitations.

Speziale, C. G.↗

NASA NTRS1988

The subgrid-scale modeling of compressible turbulence

Speziale, C. G.↗

NASA NTRS1993

Computation of the sound generated by isotropic turbulence

The acoustic radiation from isotropic turbulence is computed numerically. A hybrid direct numerical simulation approach which combines direct numerical simulation (DNS) of the turbulent flow with the Lighthill acoustic analogy is utilized. It is demonstrated that the hybrid DNS method is a feasible approach to the computation of sound generated by turbulent flows. The acoustic efficiency in the simulation of isotropic turbulence appears to be substantially less than that in subsonic jet experiments. The dominant frequency of the computed acoustic pressure is found to be somewhat larger than the dominant frequency of the energy-containing scales of motion. The acoustic power in the simulations is proportional to epsilon (M(sub t))(exp 5) where epsilon is the turbulent dissipation rate and M(sub t) is the turbulent Mach number. This is in agreement with the analytical result of Proudman (1952), but the constant of proportionality is smaller than the analytical result. Two different methods of computing the acoustic power from the DNS data bases yielded consistent results.

Sarkar, S.↗

NASA NTRS1989

Advancements in turbulence modeling

Direct simulation data are used to test newly proposed nonlinear models in the Reynolds stress anisotropy for the rapid pressure-strain terms. It is found that the nonlinear models will perform better than the linear models. In addition to testing the rapid pressure-strain models, a new k-epsilon model is proposed for near-wall flow simulation. The model is proposed for near-wall flow simulation. The model was developed by fitting low-Reynolds number data from a direct simulation of a channel flow. A new wall-correction for the eddy-viscosity as well as wall-corrections for the epsilon-equation are proposed. The model will give better predictions of the turbulent kinetic profile in the near-wall region than existing models.

Mansour, N. N.↗

NASA NTRS1997

Toward Understanding Wake Vortices and Atmospheric Turbulence Interactions Using Large-Eddy Simulation

The vortices produced by an aircraft in flight are a complex phenomena created from a 'sheet of vorticity' leaving the trailing edge of the aircraft surfaces. This sheet tends to roll-up into two counter-rotating vortices. After a few spans downstream of the aircraft, the roll-up process is complete and the vortex pair may be characterized in a simple manner for modeling purposes. Our research will focus on what happens to these post roll-up vortices in the vicinity of an airport terminal. As the aircraft wake vortices descend, they are transported by the air mass which they are embedded and are decayed by both internal and external processes. In the vicinity of the airport, these external influences are usually due to planetary boundary layer (PBL) turbulence. Using large-eddy simulation (LES), one may simulate a variety of PBL conditions. In the LES method, turbulence is generated in the PBL as a response to surface heat flux, horizontal pressure gradient, wind shear, and/or stratification, and may produce convective or unstably stratified, neutral, or stably stratified PBL's. Each of these PBL types can occur during a typical diurnal cycle of the PBL. Thus it is important to be able to characterize these conditions with the LES method. Once this turbulent environment has been generated, a vortex pair will be introduced and the interactions are observed. The objective is to be able to quantify the PBL turbulence vortex interaction and be able to draw some conclusions of vortex behavior from the various scale interactions. This research is ongoing, and we will focus on what has been accomplished to date and the future direction of this research. We will discuss the model being used, show results that validate its use in the PBL, and present a nested-grid method proposed to analyze the entire PBL and vortex pair simultaneously.

DeCroix, David↗

NASA NTRS2001

A Hybrid Numerical Method for Turbulent Mixing Layers

A hybrid method has been developed for simulations of compressible turbulent mixing layers. Such mixing layers dominate the flows in exhaust systems of modern day aircraft and also those of hypersonic vehicles currently under development. The method configurations in which a dominant structural feature provides an unsteady mechanism to drive the turbulent development in the mixing layer. The hybrid method uses a Reynolds-averaged Navier-Stokes (RANS) procedure to calculate wall bounded regions entering a mixing section, and a Large Eddy Simulation (LES) procedure to calculate the mixing dominated regions. A numerical technique was developed to enable the use of the hybrid RANS-LES method on stretched, non-Cartesian grids. Closure for the RANS equations was obtained using the Cebeci-Smith algebraic turbulence model in conjunction with the wall-function approach of Ota and Goldberg. The wall-function approach enabled a continuous computational grid from the RANS regions to the LES region. The LES equations were closed using the Smagorinsky subgrid scale model. The hybrid RANS-LES method is applied to a benchmark compressible mixing layer experiment. Preliminary two dimensional calculations are used to investigate the effects of axial grid density and boundary conditions. Vortex shedding from the base region of a splitter plate separating the upstream flows was observed to eventually transition to turbulence. The location of the transition, however, was much further downstream than indicated by experiments. Actual LES calculations, performed in three spatial directions, also indicated vortex shedding, but the transition to turbulence was found to occur much closer to the beginning of the mixing section. which is in agreement with experimental observations. These calculations demonstrated that LES simulations must be performed in three dimensions. Comparisons of time-averaged axial velocities and turbulence intensities indicated reasonable agreement with experimental data.

Georgiadis, Nicholas J.↗

NASA NTRS1972

A simulation of saltation dynamics with application to terrestrial and Martian model surfaces.

The feasibility of predicting the saltation threshold from a dynamic model of the saltation process is demonstrated. The model is based on mechanical equations that describe the trajectories of particles (sand grains) near the ground-atmosphere interface. The equations of particle motion are formulated in terms of forces and moments. The forces employed are based on theoretical and experimental results obtained for continuum flow. Surface structuring analytics and simulated fluid turbulence further modify the particle behavior. The model is used to predict the threshold velocities on Mars.

Andres, R. M.↗

NASA NTRS1976

Numerical simulation of supersonic and hypersonic turbulent compression corner flows using relaxation models

Relaxation turbulence eddy viscosity models are incorporated to solve the complete Navier-Stokes equations for supersonic and hypersonic flows over a two-dimensional compression corner. The system of equations is solved by a time-split, second-order accurate numerical scheme. Details of relaxation process are studied, and several relaxation models are tested and compared. Good improvement in the prediction of upstream pressure propagation is obtained for a Mach number of 2.96, and Reynolds number of 10,000,000, with wedge angle of 25 deg. However, the application of the relaxation models to hypersonic flow at Mach number 8.66 and Reynolds number of 22,000,000, with highly cooled wall, shows unfavorable effects on heat transfer and skin friction in the reattachment and recompression regions.

Hung, C. M.↗

NASA NTRS1980

Numerical method for predicting flow characteristics and performance of nonaxisymmetric nozzles. Part 2: Applications

A computer implemented numerical method for predicting the flow in and about an isolated three dimensional jet exhaust nozzle is summarized. The approach is based on an implicit numerical method to solve the unsteady Navier-Stokes equations in a boundary conforming curvilinear coordinate system. Recent improvements to the original numerical algorithm are summarized. Equations are given for evaluating nozzle thrust and discharge coefficient in terms of computed flowfield data. The final formulation of models that are used to simulate flow turbulence effect is presented. Results are presented from numerical experiments to explore the effect of various quantities on the rate of convergence to steady state and on the final flowfield solution. Detailed flowfield predictions for several two and three dimensional nozzle configurations are presented and compared with wind tunnel experimental data.

Thomas, P. D.↗

NASA NTRS1981

A three-dimensional simulation of transition and early turbulence in a time-developing mixing layer

The physics of the transition and early turbulence regimes in the time developing mixing layer was investigated. The sensitivity of the mixing layer to the disturbance field of the initial condition is considered. The growth of the momentum thickness, the mean velocity profile, the turbulence kinetic energy, the Reynolds stresses, the anisotropy tensor, and particle track pictures of computations are all examined in an effort to better understand the physics of these regimes. The amplitude, spectrum shape, and random phases of the initial disturbance field were varied. A scheme of generating discrete orthogonal function expansions on some nonuniform grids was developed. All cases address the early or near field of the mixing layer. The most significant result shows that the secondary instability of the mixing layer is produced by spanwise variations in the straining field of the primary vortex structures.

Cain, A. B.↗

NASA NTRS1981

International Conference on Numerical Methods in Fluid Dynamics, 7th, Stanford University, Stanford and Moffett Field, CA, June 23-27, 1980, Proceedings

Topics discussed include polygon transformations in fluid mechanics, computation of three-dimensional horseshoe vortex flow using the Navier-Stokes equations, an improved surface velocity method for transonic finite-volume solutions, transonic flow calculations with higher order finite elements, the numerical calculation of transonic axial turbomachinery flows, and the simultaneous solutions of inviscid flow and boundary layer at transonic speeds. Also considered are analytical solutions for the reflection of unsteady shock waves and relevant numerical tests, reformulation of the method of characteristics for multidimensional flows, direct numerical simulations of turbulent shear flows, the stability and separation of freely interacting boundary layers, computational models of convective motions at fluid interfaces, viscous transonic flow over airfoils, and mixed spectral/finite difference approximations for slightly viscous flows.

Reynolds, W. C.↗

NASA NTRS1982

A ground-simulation investigation of helicopter decelerating instrument approaches

In connection with the expansion of civil helicopter operations in the current era, the effect of helicopter flight and control characteristics on the flying qualities for instrument flight rules (IFR) flight have become a factor of concern, and a research program has been initiated to investigate IFR certification criteria. A description is presented of an experiment which is the sixth in a series of ground- and flight-simulation investigations. This piloted-simulator experiment was conducted to examine the influence of stability-control augmentation, display information format, and approach-task effects on helicopter flying qualities for terminal-area operations incorporating a deceleration in instrument meteorological conditions. Simulated test configurations were evaluated for precision approaches with an instrument deceleration from 60 to about 15 knots in both calm air and simulated moderate turbulence and wind shear.

Lebacqz, J. V.↗

NASA NTRS1984

Reconnection of Magnetic Fields

Spacecraft observations of steady and nonsteady reconnection at the magnetopause are reviewed. Computer simulations of three-dimensional reconnection in the geomagnetic tail are discussed. Theoretical aspects of the energization of particles in current sheets and of the microprocesses in the diffusion region are presented. Terrella experiments in which magnetospheric reconnection is simulated at both the magnetopause and in the tail are described. The possible role of reconnection in the evolution of solar magnetic fields and solar flares is discussed. A two-dimensional magnetohydrodynamic computer simulation of turbulent reconnection is examined. Results concerning reconnection in Tokamak devices are also presented.

Source record↗

NASA NTRS1985

Progress and supercomputing in computational fluid dynamics; Proceedings of U.S.-Israel Workshop, Jerusalem, Israel, December 1984

Current developments and future trends in the application of supercomputers to computational fluid dynamics are discussed in reviews and reports. Topics examined include algorithm development for personal-size supercomputers, a multiblock three-dimensional Euler code for out-of-core and multiprocessor calculations, simulation of compressible inviscid and viscous flow, high-resolution solutions of the Euler equations for vortex flows, algorithms for the Navier-Stokes equations, and viscous-flow simulation by FEM and related techniques. Consideration is given to marching iterative methods for the parabolized and thin-layer Navier-Stokes equations, multigrid solutions to quasi-elliptic schemes, secondary instability of free shear flows, simulation of turbulent flow, and problems connected with weather prediction.

Murman, E. M.↗

NASA NTRS1988

Numerical study of chemically reacting flows using an LU scheme

A new computational fluid dynamic code has been developed for the study of mixing and chemical reactions in the flow fields of ramjets and scramjets. The code employs an implicit finite volume, lower-upper symmetric successive overrelaxation scheme for solving the complete two-dimensional Navier-Stokes equations and species transport equations in a fully-coupled and very efficient manner. The combustion processes are modeled by an 8-species, 14-step finite rate chemistry model whereas turbulence is simulated by a Baldwin-Lomax algebraic model. The validity of the code is demonstrated by comparing the numerical calculations with both experimental data and previous calculations of a cold flow helium injection into a straight channel and premixed hydrogen-air reacting flows in a ramped duct. The code is then used to calculate the mixing and chemical reactions of a hydrogen jet transversely injected into a supersonic airstream. Results are presented describing the flow field, the recirculation regions in front and behind the injector, and the chemical reactions.

Shuen, Jian Shun↗

NASA NTRS1987

Modeling scalar flux and the energy and dissipation equations

Closure models derived from the Two-Scale Direct-Interaction Approximation were compared with data from direct simulations of turbulence. Attention was restricted to anisotropic scalar diffusion models, models for the energy dissipation equation, and models for energy diffusion.

Yoshizawa, A.↗