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NASA NTRS2010

Error and Uncertainty Quantification in the Numerical Simulation of Complex Fluid Flows

The failure of numerical simulation to predict physical reality is often a direct consequence of the compounding effects of numerical error arising from finite-dimensional approximation and physical model uncertainty resulting from inexact knowledge and/or statistical representation. In this topical lecture, we briefly review systematic theories for quantifying numerical errors and restricted forms of model uncertainty occurring in simulations of fluid flow. A goal of this lecture is to elucidate both positive and negative aspects of applying these theories to practical fluid flow problems. Finite-element and finite-volume calculations of subsonic and hypersonic fluid flow are presented to contrast the differing roles of numerical error and model uncertainty. for these problems.

Barth, Timothy J.↗

NASA NTRS1987

Study of one-dimensional spectral dynamic equations of the Reynolds stresses in homogeneous anisotropic turbulence: Application to split-spectrum modeling

The CTR numerical data base generated by direct simulation of homogeneous anisotropic turbulence was used to calculate all of the terms in the spectral balance equations for the turbulent Reynolds stresses. The aim in not only to test the main closure assumptions used in the split-spectrum models, but also to try to devise improved hypotheses deduced from the statistical information. Numerical simulations of turbulent flows provide a large amount of data, a thought provoking wealth of information. The main advantage of this type of comparison is that a great variety of flows can be considered, and this is necessary to test closure hypotheses. Moreover various initial conditions can be introduced in the calculation, even if they are not experimentally feasible. All the terms in the spectral equations can be calculated. The limited Reynolds numbers of the simulations and the statistical noise caused by a small sample, particularly at the large scales, causes some difficulty in the interpretation of the results, but the method of approach proved to be a powerful tool for testing and improving spectral closures.

Schiestel, R.↗

NASA NTRS1984

Studies of new media radiation induced laser

Various lasants were investigated especially, 2-iodohepafluoropropane (i-C3F7I) for the direct solar pumped lasers. Optical pumping of iodine laser was achieved using a small flashlamp. Using i-C3F7I as a laser gain medium, threshold inversion density, small signal gain, and laser performance at the elevated temperature were measured. The experimental results and analysis are presented. The iodine laser kinetics of the C3F7I and IBr system were numerically simulated. The concept of a direct solar-pumped laser amplifier using (i-C3F7I) as the laser material was evaluated and several kinetic coefficients for i-C3F7I laser system were reexamined. The results are discussed.

Han, K. S.↗

NASA NTRS1981

Numerical experiments in homogeneous turbulence

The direct simulation methods developed by Orszag and Patternson (1972) for isotropic turbulence were extended to homogeneous turbulence in an incompressible fluid subjected to uniform deformation or rotation. The results of simulations for irrotational strain (plane and axisymmetric), shear, rotation, and relaxation toward isotropy following axisymmetric strain are compared with linear theory and experimental data. Emphasis is placed on the shear flow because of its importance and because of the availability of accurate and detailed experimental data. The computed results are used to assess the accuracy of two popular models used in the closure of the Reynolds-stress equations. Data from a variety of the computed fields and the details of the numerical methods used in the simulation are also presented.

Rogallo, R. S.↗

NASA NTRS1986

Numerical simulation of the flowfield over ice accretion shapes

The primary goals are directed toward the development of a numerical method for computing flow about ice accretion shapes and determining the influence of these shapes on flow degradation. It is expedient to investigate various aspects of icing independently in order to assess their contribution to the overall icing phenomena. The specific aspects to be examined include the water droplet trajectories with collection efficiencies and phase change on the surface, the flowfield about specified shapes including lift, drag, and heat transfer distribution, and surface roughness effects. The configurations computed were models of ice accretion shapes formed on a circular cylinder in the NASA Lewis Icing Research Tunnel. An existing Navier-Stokes program was modified to compute the flowfield over four shapes (2, 5, and 15 minute models of glaze ice, and a 15 minute accumulation of rime ice).

Scott, J. N.↗

NASA NTRS1987

Numerical simulation of homogeneous, isotropic, compressible turbulence

A new numerical algorithm is developed and applied to the direct simulation of compressible, homogeneous turbulent flows at low Mach numbers. A split method in time first solves a subset of the equations explicitly, followed by an implicit treatment of the pressure terms. The definition of an average sound speed over the entire field allows the implicit equations to be solved analytically, while relaxing the severe time limit imposed by the large sound speeds. Results from direct simulations on 96(3) grids provide a data base against which a new subgrid-scale model for compressible homogeneous turbulence is tested. This model reduces to the linear combination model in the absence of compressibility.

Erlebacher, G.↗

NASA NTRS1991

Hypersonic rarefied flow about a compression corner - DSMC simulation and experiment

The phenomena of shock/boundary-layer interactions and flow separation are investigated using both computational and experimental methods for low-density hypersonic flow about two-dimensional compression corners. The numerical calculations are made with the direct simulation Monte Carlo (DSMC) method. Experimental measurements provide information concerning the flowfield structure and surface flow patterns by means of gas glow discharge and oil flow pictures, respectively. Comparison of the two data sets provides a qualitative basis for assessing the ability of the DSMC method to describe such flows.

Moss, James N.↗

NASA NTRS1993

Research activities at the Center for Modeling of Turbulence and Transition

The main research activities at the Center for Modeling of Turbulence and Transition (CMOTT) are described. The research objective of CMOTT is to improve and/or develop turbulence and transition models for propulsion systems. The flows of interest in propulsion systems can be both compressible and incompressible, three dimensional, bounded by complex wall geometries, chemically reacting, and involve 'bypass' transition. The most relevant turbulence and transition models for the above flows are one- and two-equation eddy viscosity models, Reynolds stress algebraic- and transport-equation models, pdf models, and multiple-scale models. All these models are classified as one-point closure schemes since only one-point (in time and space) turbulent correlations, such as second moments (Reynolds stresses and turbulent heat fluxes) and third moments, are involved. In computational fluid dynamics, all turbulent quantities are one-point correlations. Therefore, the study of one-point turbulent closure schemes is the focus of our turbulence research. However, other research, such as the renormalization group theory, the direct interaction approximation method, and numerical simulations are also pursued to support the development of turbulence modeling.

Shih, Tsan-Hsing↗

NASA NTRS1994

Center for modeling of turbulence and transition: Research briefs, 1993

This research brief contains the progress reports of the research staff of the Center for Modeling of Turbulence and Transition (CMOTT) from June 1992 to July 1993. It is also an annual report to the Institute for Computational Mechanics in Propulsion located at Ohio Aerospace Institute and NASA Lewis Research Center. The main objectives of the research activities at CMOTT are to develop, validate, and implement turbulence and transition models for flows of interest in propulsion systems. Currently, our research covers eddy viscosity one- and two-equation models, Reynolds-stress algebraic equation models, Reynolds-stress transport equation models, nonequilibrium multiple-scale models, bypass transition models, joint scalar probability density function models, and Renormalization Group Theory and Direct Interaction Approximation methods. Some numerical simulations (LES and DNS) have also been carried out to support the development of turbulence modeling. Last year was CMOTT's third year in operation. During this period, in addition to the above mentioned research, CMOTT has also hosted the following programs: an eighteen-hour short course on 'Turbulence--Fundamentals and Computational Modeling (Part I)' given by CMOTT at the NASA Lewis Research Center; a productive summer visitor research program that has generated many encouraging results; collaborative programs with industry customers to help improve their turbulent flow calculations for propulsion system designs; a biweekly CMOTT seminar series with speakers from within and without the NASA Lewis Research Center including foreign speakers. In addition, CMOTT members have been actively involved in the national and international turbulence research activities. The current CMOTT roster and organization are listed in Appendix A. Listed in Appendix B are the abstracts of the biweekly CMOTT seminar. Appendix C lists the papers contributed by CMOTT members.

Liou, William W.↗

NASA NTRS1995

DSMC calculations for 70-deg blunted cone at 3.2 km/s in nitrogen

Numerical results obtained with the direct simulation Monte Carlo (DSMC) method are presented for Mach 15.6 nitrogen flow about a 70-deg spherically blunted cone at zero incidence. This flow condition is one of several generated in the Large Energy National Shock (LENS) tunnel during tests of a 15.24 cm diameter model with an afterbody sting. The freestream Knudsen number, based on model diameter, is 0.0023. The focus of the DSMC calculations is to characterize the near wake flow under conditions where rarefaction effects may influence afterbody aerothermal loads. This report provides information concerning computational details along with flowfield and surface quantities. Calculations show that the flow enveloping the test model is in thermal nonequilibrium and a sizable vortex develops in the near wake. Along the model baseplane the heating rates are about 0.6 percent of the forebody stagnation value while the maximum heating along the sting is about 4.2 percent of the forebody stagnation value. Comparison of a Navier-Stokes solution with the present calculations show good agreement for surface heating, pressure, and skin friction results.

Moss, J. N.↗

NASA NTRS2020

Modeling and Control of Robot-Structure Coupling During In-Space Structure Assembly

This paper considers the problem of robot-structure coupling dynamics during in-space robotic assembly of large flexible structures. A two-legged walking robot is used as a construction agent, whose primary goal is to stably walking on the flexible structure while carrying a substructure component to a designated location. The reaction forces inserted by the structure to the walking robot are treated as bounded disturbance inputs, and a trajectory tracking robotic controller is proposed that combines the standard full state feedback motion controller and an adaptive controller to account for the disturbance inputs. In this study, a reduced-order Euler-Bernoulli beam structure model is adapted, and a finite number of co-located sensors and actuators are distributed along the span of the beam structure. The robot-structure coupling forces are treated as a bounded external forcing function to the structure, and hence an output covariance constraint problem can be formulated, in terms of linear matrix inequality, for optimal structure control by utilizing the direct output feedback controllers. The numerical simulations show the effectiveness of the proposed robot-structure modeling and control methodology.

Swei, Sean↗

NASA NTRSDate not supplied

Evaluation of Acoustic Propagation in Layered Media Using Wave Confinement

A comprehensive method for propagation of sound in layered media is discussed that involves dividing the domain into two regions, source field and far field. The source field is provided using experimentally collected data from full-scale rotorcraft acoustic flight tests, which consists of short waveforms that cannot be directly simulated on the grid without numerical errors. Instead, grid based computational waves are used to carry the details of these waveforms, including amplitude, arrival time and location of origin on source sphere. This is done by solving the scalar wave equation using the Wave Confinement (WC) method, which involves adding an extra term to produce converged solutions. WC is used to study wave propagation in two different atmospheric conditions, and the results are compared to the flight test data. Overall, WC can accurately capture the propagation effects and there is a good agreement with the flight test data.

rotorcraft acoustics↗

NASA NTRSDate not supplied

Evaluation of Acoustic Propagation in Layered Media Using Wave Confinement

rotorcraft acoustics↗

NASA NTRS1984

Numerical simulation of boundary-layer transition

The transition to turbulence in boundary layers was investigated by direct numerical solution of the nonlinear, three-dimensional, incompressible Navier-Stokes equations in the half-infinite domain over a flat plate. Periodicity was imposed in the streamwise and spanwise directions. A body force was applied to approximate the effect of a nonparallel mean flow. The numerical method was spectra, based on Fourier series and Jacobi polynomials, and used divergence-free basis functions. Extremely rapid convergence was obtained when solving the linear Orr-Sommerfeld equation. The early nonlinear and three-dimensional stages of transition, in a boundary layer disturbed by a vibrating ribbon, were successfully simulated. Excellent qualitative agreement was observed with either experiments or weakly nonlinear theories. In particular, the breakdown pattern was staggered or nonstaggered depending on the disturbance amplitude.

Spalart, P. R.↗

NASA NTRS1998

Numerical Simulation of the Generation of Axisymmetric Mode Jet Screech Tones

An imperfectly expanded supersonic jet, invariably, radiates both broadband noise and discrete frequency sound called screech tones. Screech tones are known to be generated by a feedback loop driven by the large scale instability waves of the jet flow. Inside the jet plume is a quasi-periodic shock cell structure. The interaction of the instability waves and the shock cell structure, as the former propagates through the latter, is responsible for the generation of the tones. Presently, there are formulas that can predict the tone frequency fairly accurately. However, there is no known way to predict the screech tone intensity. In this work, the screech phenomenon of an axisymmetric jet at low supersonic Mach number is reproduced by numerical simulation. The computed mean velocity profiles and the shock cell pressure distribution of the jet are found to be in good agreement with experimental measurements. The same is true with the simulated screech frequency. Calculated screech tone intensity and directivity at selected jet Mach number are reported in this paper. The present results demonstrate that numerical simulation using computational aeroacoustics methods offers not only a reliable way to determine the screech tone intensity and directivity but also an opportunity to study the physics and detailed mechanisms of the phenomenon by an entirely new approach.

Shen, Hao↗

NASA NTRS1983

Numerically simulated two-dimensional auroral double layers

A magnetized 2 1/2-dimensional particle-in-cell system which is periodic in one direction and bounded by reservoirs of Maxwellian plasma in the other is used to numerically simulate electrostatic plasma double layers. For the cases of both oblique and two-dimensional double layers, the present results indicate periodic instability, Debye length rather than gyroradii scaling, and low frequency electrostatic turbulence together with electron beam-excited electrostatatic electron-cyclotron waves. Estimates are given for the thickness of auroral doule layers, as well as the separations within multiple auroral arcs. Attention is given to the temporal modulation of accelerated beams, and the possibilities for ion precipitation and ion conic production by the double layer are hypothesized. Simulations which include the atmospheric backscattering of electrons imply the action of an ionospheric sheath which accelerates ionospheric ions upward.

Borovsky, J. E.↗

NASA NTRS1991

Methods for direct simulation of transition in hypersonic boundary layers

An implicit numerical algorithm for the time accurate solution of the compressible Navier-Stokes equations is described. Results for steady flow past a finite flat plate are presented, together with preliminary results for the temporal simulation of second mode instability in a flat plate boundary layer at Mach 4.5.

Vandervegt, J. J. W.↗

NASA NTRS2011

Numerically Exact Computer Simulations of Light Scattering by Densely Packed, Random Particulate Media

Direct computer simulations of electromagnetic scattering by discrete random media have become an active area of research. In this progress review, we summarize and analyze our main results obtained by means of numerically exact computer solutions of the macroscopic Maxwell equations. We consider finite scattering volumes with size parameters in the range, composed of varying numbers of randomly distributed particles with different refractive indices. The main objective of our analysis is to examine whether all backscattering effects predicted by the low-density theory of coherent backscattering (CB) also take place in the case of densely packed media. Based on our extensive numerical data we arrive at the following conclusions: (i) all backscattering effects predicted by the asymptotic theory of CB can also take place in the case of densely packed media; (ii) in the case of very large particle packing density, scattering characteristics of discrete random media can exhibit behavior not predicted by the low-density theories of CB and radiative transfer; (iii) increasing the absorptivity of the constituent particles can either enhance or suppress typical manifestations of CB depending on the particle packing density and the real part of the refractive index. Our numerical data strongly suggest that spectacular backscattering effects identified in laboratory experiments and observed for a class of high-albedo Solar System objects are caused by CB.

Dlugach, Janna M.↗