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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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53 records · Page 3

A split finite element algorithm for the compressible Navier-Stokes equations

An accurate and efficient numerical solution algorithm is established for solution of the high Reynolds number limit of the Navier-Stokes equations governing the multidimensional flow of a compressible essentially inviscid fluid. Finite element interpolation theory is used within a dissipative formulation established using Galerkin criteria within the Method of Weighted Residuals. An implicit iterative solution algorithm is developed, employing tensor product bases within a fractional steps integration procedure, that significantly enhances solution economy concurrent with sharply reduced computer hardware demands. The algorithm is evaluated for resolution of steep field gradients and coarse grid accuracy using both linear and quadratic tensor product interpolation bases. Numerical solutions for linear and nonlinear, one, two and three dimensional examples confirm and extend the linearized theoretical analyses, and results are compared to competitive finite difference derived algorithms.

Baker, A. J.↗

A preliminary compressible second-order closure model for high speed flows

A preliminary version of a compressible second-order closure model that was developed in connection with the National Aero-Space Plane Project is presented. The model requires the solution of transport equations for the Favre-averaged Reynolds stress tensor and dissipation rate. Gradient transport hypotheses are used for the Reynolds heat flux, mass flux, and turbulent diffusion terms. Some brief remarks are made about the direction of future research to generalize the model.

Speziale, Charles G.↗

The Physics of Turbulence in the Boundary Layer

The geometry of the velocity field in a numerically simulated incompressible turbulent boundary layer over a flat plate at Re theta=670 has been studied using the invariants of the velocity gradient tensor. These invariants are computed at every grid point in the flow and used to form the discriminant. Of primary interest are those regions in the flow where the discriminant is positive; regions where, according to the characteristic equation, the eigenvalues of the velocity gradient tensor are complex. An observer moving with a frame of reference which is attached to a fluid particle lying within such a region would see a local flow pattern of the type stable-focus-stretching or unstable-focus-compressing. When the flow is visualized this way, continuous, connected, large-scale structures are revealed that extend from the point just below the buffer layer out to the beginning of the wake region. These structures are aligned with the mean shear close to the wall and arch in the cross-stream direction away from the wall. In some cases the structures observed are very similar to to the hairpin eddy vision of boundary layer structure proposed by Theodorsen. That the structure of the flow is revealed more effectively by the discriminant rather than by the vorticity is important and adds support to recent observations of the discriminant in a channel flow simulation. Of particular importance is the fact that the procedure does not require the use of an arbitrary threshold in the discriminant. Further analysis using computer flow visualization shows a high degree of spatial correlation between regions of positive discriminant, extreme negative pressure fluctuations and large instantaneous values of Reynolds shear stress.

Kline, Stephen↗

Large eddy simulations of compressible turbulent flows

An evaluation of existing models for Large Eddy Simulations (LES) of incompressible turbulent flows has been completed. LES is a computation in which the large, energy-carrying structures to momentum and energy transfer is computed exactly, and only the effect of the smallest scales of turbulence is modeled. That is, the large eddies are computed and the smaller eddies are modeled. The dynamics of the largest eddies are believed to account for most of sound generation and transport properties in a turbulent flow. LES analysis is based on an observation that pressure, velocity, temperature, and other variables are the sum of their large-scale and small-scale parts. For instance, u(i) (velocity) can be written as the sum of bar-u(i) and u(i)-prime, where bar-u(i) is the large-scale and u(i)-prime is the subgrid-scale (SGS). The governing equations for large eddies in compressible flows are obtained after filtering the continuity, momentum, and energy equations, and recasting in terms of Favre averages. The filtering operation maintains only large scales. The effects of the small-scales are present in the governing equations through the SGS stress tensor tau(ij) and SGS heat flux q(i). The mathematical formulation of the Favre-averaged equations of motion for LES is complete.

Porter-Locklear, Freda↗

Magnetohydrodynamic Jump Conditions for Oblique Relativistic Shocks with Gyrotropic Pressure

Shock jump conditions, i.e., the specification of the downstream parameters of the gas in terms of the upstream parameters, are obtained for steady-state, plane shocks with oblique magnetic fields and arbitrary flow speeds. This is done by combining the continuity of particle number flux and the electromagnetic boundary conditions at the shock with the magnetohydrodynamic conservation laws derived from the stress-energy tensor. For ultrarelativistic and nonrelativistic shocks, the jump conditions may be solved analytically. For mildly relativistic shocks, analytic solutions are obtained for isotropic pressure using an approximation for the adiabatic index that is valid in high sonic Mach number cases. Examples assuming isotropic pressure illustrate how the shock compression ratio depends on the shock speed and obliquity. In the more general case of gyrotropic pressure, the jump conditions cannot be solved analytically with- out additional assumptions, and the effects of gyrotropic pressure are investigated by parameterizing the distribution of pressure parallel and perpendicular to the magnetic field. Our numerical solutions reveal that relatively small departures from isotropy (e.g., approximately 20%) produce significant changes in the shock compression ratio, r , at all shock Lorentz factors, including ultrarelativistic ones, where an analytic solution with gyrotropic pressure is obtained. In particular, either dynamically important fields or significant pressure anisotropies can incur marked departures from the canonical gas dynamic value of r = 3 for a shocked ultrarelativistic flow and this may impact models of particle acceleration in gamma-ray bursts and other environments where relativistic shocks are inferred. The jump conditions presented apply directly to test-particle acceleration, and will facilitate future self-consistent numerical modeling of particle acceleration at oblique, relativistic shocks; such models include the modification of the fluid velocity profile due to the contribution of energetic particles to the momentum and energy fluxes.

Double, Glen P.↗

Scaling of Magnetic Reconnection in Relativistic Collisionless Pair Plasmas

Using fully kinetic simulations, we study the scaling of the inflow speed of collisionless magnetic reconnection in electron-positron plasmas from the non-relativistic to ultra-relativistic limit. In the anti-parallel configuration, the inflow speed increases with the upstream magnetization parameter sigma and approaches the speed of light when sigma is greater than O(100), leading to an enhanced reconnection rate. In all regimes, the divergence of the pressure tensor is the dominant term responsible for breaking the frozen-in condition at the x-line. The observed scaling agrees well with a simple model that accounts for the Lorentz contraction of the plasma passing through the diffusion region. The results demonstrate that the aspect ratio of the diffusion region, modified by the compression factor of proper density, remains approximately 0.1 in both the non-relativistic and relativistic limits.

plasma↗

Scalar/Vector potential formulation for compressible viscous unsteady flows

A scalar/vector potential formulation for unsteady viscous compressible flows is presented. The scalar/vector potential formulation is based on the classical Helmholtz decomposition of any vector field into the sum of an irrotational and a solenoidal field. The formulation is derived from fundamental principles of mechanics and thermodynamics. The governing equations for the scalar potential and vector potential are obtained, without restrictive assumptions on either the equation of state or the constitutive relations or the stress tensor and the heat flux vector.

Morino, L.↗

A Continuum Damage Mechanics Model to Predict Kink-Band Propagation Using Deformation Gradient Tensor Decomposition

A new model is proposed that represents the kinematics of kink-band formation and propagation within the framework of a mesoscale continuum damage mechanics (CDM) model. The model uses the recently proposed deformation gradient decomposition approach to represent a kink band as a displacement jump via a cohesive interface that is embedded in an elastic bulk material. The model is capable of representing the combination of matrix failure in the frame of a misaligned fiber and instability due to shear nonlinearity. In contrast to conventional linear or bilinear strain softening laws used in most mesoscale CDM models for longitudinal compression, the constitutive response of the proposed model includes features predicted by detailed micromechanical models. These features include: 1) the rotational kinematics of the kink band, 2) an instability when the peak load is reached, and 3) a nonzero plateau stress under large strains.

Bergan, Andrew C.↗

Solar physics applications of computer graphics and image processing

Computer graphics devices coupled with computers and carefully developed software provide new opportunities to achieve insight into the geometry and time evolution of scalar, vector, and tensor fields and to extract more information quickly and cheaply from the same image data. Two or more different fields which overlay in space can be calculated from the data (and the physics), then displayed from any perspective, and compared visually. The maximum regions of one field can be compared with the gradients of another. Time changing fields can also be compared. Images can be added, subtracted, transformed, noise filtered, frequency filtered, contrast enhanced, color coded, enlarged, compressed, parameterized, and histogrammed, in whole or section by section. Today it is possible to process multiple digital images to reveal spatial and temporal correlations and cross correlations. Data from different observatories taken at different times can be processed, interpolated, and transformed to a common coordinate system.

Altschuler, M. D.↗

The behavior of a compressible turbulent boundary layer in a shock-wave-induced adverse pressure gradient

The results of an experimental investigation of the mean- and fluctuating-flow properties of a compressible turbulent boundary layer in a shock-wave-induced adverse pressure gradient are presented. The turbulent boundary layer developed on the wall of an axially symmetric nozzle and test section whose nominal free-stream Mach number and boundary-layer thickness Reynolds number were 4 and 100,000, respectively. The adverse pressure gradient was induced by an externally generated conical shock wave. Mean and time-averaged fluctuating-flow data, including the complete experimental Reynolds stress tensor and experimental turbulent mass- and heat-transfer rates are presented for the boundary layer and external flow, upstream, within and downstream of the pressure gradient. The mean-flow data include distributions of total temperature throughout the region of interest. The turbulent mixing properties of the flow were determined experimentally with a hot-wire anemometer. The calibration of the wires and the interpretation of the data are discussed. From the results of the investigation, it is concluded that the shock-wave - boundary-layer interaction significantly alters the turbulent mixing characteristics of the boundary layer.

Rose, W. C.↗

Integrated Computational System for Aerodynamic Steering and Visualization

In February of 1994, an effort from the Fluid Dynamics and Information Sciences Divisions at NASA Ames Research Center with McDonnel Douglas Aerospace Company and Stanford University was initiated to develop, demonstrate, validate and disseminate automated software for numerical aerodynamic simulation. The goal of the initiative was to develop a tri-discipline approach encompassing CFD, Intelligent Systems, and Automated Flow Feature Recognition to improve the utility of CFD in the design cycle. This approach would then be represented through an intelligent computational system which could accept an engineer's definition of a problem and construct an optimal and reliable CFD solution. Stanford University's role focused on developing technologies that advance visualization capabilities for analysis of CFD data, extract specific flow features useful for the design process, and compare CFD data with experimental data. During the years 1995-1997, Stanford University focused on developing techniques in the area of tensor visualization and flow feature extraction. Software libraries were created enabling feature extraction and exploration of tensor fields. As a proof of concept, a prototype system called the Integrated Computational System (ICS) was developed to demonstrate CFD design cycle. The current research effort focuses on finding a quantitative comparison of general vector fields based on topological features. Since the method relies on topological information, grid matching and vector alignment is not needed in the comparison. This is often a problem with many data comparison techniques. In addition, since only topology based information is stored and compared for each field, there is a significant compression of information that enables large databases to be quickly searched. This report will (1) briefly review the technologies developed during 1995-1997 (2) describe current technologies in the area of comparison techniques, (4) describe the theory of our new method researched during the grant year (5) summarize a few of the results and finally (6) discuss work within the last 6 months that are direct extensions from the grant.

Hesselink, Lambertus↗

Towards an Automated Unstructured Grid Adaptation Workflow with VULCAN

Early work is presented for an unstructured grid adaptation workflow with VULCAN and refine. Anisotropic simplex grids are iteratively adapted to match a Riemannian metric tensor field describing desired mesh spacing. The Riemannian metric tensor field is obtained from Hessians of CFD solution output scalar sensor fields; both Mach number and static temperature sensor fields are explored. In addition, we describe a Newton-method-based solver recently implemented in VULCAN utilizing Jacobian-Free-Newton-Krylov that can be used to increase flow solver automation on early grids in the adadptation process. Hypersonic flow solutions are presented on a high Reynolds number flat plate and wall heat flux is compared against a highly resolved structured solution. Additionally, complex shock boundary-layer interaction is explored in a high Mach number compression corner and complex 3D flow phenomena are evaluated on the Boundary Layer Transition (BOLT) vehicle.

Matthew O'Connell↗

Turbulence Modeling for Shock Wave/Turbulent Boundary Layer Interactions

Accurate aerodynamic computational predictions are essential for the safety of space vehicles, but these computations are of limited accuracy when large pressure gradients are present in the flow. The goal of the current project is to improve the state of compressible turbulence modeling for high speed flows with shock wave / turbulent boundary layer interactions (SWTBLI). Emphasis will be placed on models that can accurately predict the separated region caused by the SWTBLI. These flows are classified as nonequilibrium boundary layers because of the very large and variable adverse pressure gradients caused by the shock waves. The lag model was designed to model these nonequilibrium flows by incorporating history effects. Standard one- and two-equation models (Spalart Allmaras and SST) and the lag model will be run and compared to a new lag model. This new model, the Reynolds stress tensor lag model (lagRST), will be assessed against multiple wind tunnel tests and correlations. The basis of the lag and lagRST models are to preserve the accuracy of the standard turbulence models in equilibrium turbulence, when the Reynolds stresses are linearly related to the mean strain rates, but create a lag between mean strain rate effects and turbulence when nonequilibrium effects become important, such as in large pressure gradients. The affect this lag has on the results for SWBLI and massively separated flows will be determined. These computations will be done with a modified version of the OVERFLOW code. This code solves the RANS equations on overset grids. It was used for this study for its ability to input very complex geometries into the flow solver, such as the Space Shuttle in the full stack configuration. The model was successfully implemented within two versions of the OVERFLOW code. Results show a substantial improvement over the baseline models for transonic separated flows. The results are mixed for the SWBLI assessed. Separation predictions are not as good as the baseline models, but the over prediction of the peak heat flux downstream of the reattachment shock that plagues many models is reduced.

Lillard, Randolph P.↗

Boundary-layer equations in generalized curvilinear coordinates

A set of higher-order boundary-layer equations is derived valid for three-dimensional compressible flows. The equations are written in a generalized curvilinear coordinate system, in which the surface coordinates are nonorthogonal; the third axis is restricted to be normal to the surface. Also, higher-order viscous terms which are retained depend on the surface curvature of the body. Thus, the equations are suitable for the calculation of the boundary layer about arbitrary vehicles. As a starting point, the Navier-Stokes equations are derived in a tensorian notation. Then by means of an order-of-magnitude analysis, the boundary-layer equations are developed. To provide an interface between the analytical partial differentiation notation and the compact tensor notation, a brief review of the most essential theorems of the tensor analysis related to the equations of the fluid dynamics is given. Many useful quantities, such as the contravariant and the covariant metrics and the physical velocity components, are written in both notations.

Panaras, Argyris G.↗

A non-linearly stable implicit finite element algorithm for hypersonic aerodynamics

A generalized curvilinear coordinate Taylor weak statement implicit finite element algorithm is developed for the two-dimensional and axisymmetric compressible Navier-Stokes equations for ideal and reacting gases. For accurate hypersonic simulation, air is modeled as a mixture of five perfect gases, i.e., molecular and atomic oxygen and nitrogen as well as nitric oxide. The associated pressure is then determined via Newton solution of the classical chemical equilibrium equation system. The directional semidiscretization is achieved using an optimal metric data Galerkin finite element weak statement, on a developed 'companion conservation law system', permitting classical test and trial space definitions. Utilizing an implicit Runge-Kutta scheme, the terminal algorithm is then nonlinearly stable, and second-order accurate in space and time on arbitrary curvilinear coordinates. Subsequently, a matrix tensor product factorization procedure permits an efficient numerical linear algebra handling for large Courant numbers. For ideal- and real-gas hypersonic flows, the algorithm generates essentially nonoscillatory numerical solutions in the presence of strong detached shocks and boundary layer-inviscid flow interactions.

Iannelli, G. S.↗

Nonlinear analysis for the response and failure of compression-loaded angle-ply laminates with a hole

The objective was to determine the effect of nonlinear material behavior on the response and failure of unnotched and notched angle-ply laminates under uniaxial compressive loading. The endochronic theory was chosen as the constitutive theory to model the AS4/3502 graphite-epoxy material system. Three-dimensional finite element analysis incorporating the endochronic theory was used to determine the stresses and strains in the laminates. An incremental/iterative initial strain algorithm was used in the finite element program. To increase computational efficiency, a 180 deg rotational symmetry relationship was utilized and the finite element program was vectorized to run on a supercomputer. Laminate response was compared to experimentation revealing excellent agreement for both the unnotched and notched angle-ply laminates. Predicted stresses in the region of the hole were examined and are presented, comparing linear elastic analysis to the inelastic endochronic theory analysis. A failure analysis of the unnotched and notched laminates was performed using the quadratic tensor polynomial. Predicted fracture loads compared well with experimentation for the unnotched laminates, but were very conservative in comparison with experiments for the notched laminates.

Mathison, Steven R.↗

Direct numerical simulations and modeling of a spatially-evolving turbulent wake

Understanding of turbulent free shear flows (wakes, jets, and mixing layers) is important, not only for scientific interest, but also because of their appearance in numerous practical applications. Turbulent wakes, in particular, have recently received increased attention by researchers at NASA Langley. The turbulent wake generated by a two-dimensional airfoil has been selected as the test-case for detailed high-resolution particle image velocimetry (PIV) experiments. This same wake has also been chosen to enhance NASA's turbulence modeling efforts. Over the past year, the author has completed several wake computations, while visiting NASA through the 1993 and 1994 ASEE summer programs, and also while on sabbatical leave during the 1993-94 academic year. These calculations have included two-equation (K-omega and K-epsilon) models, algebraic stress models (ASM), full Reynolds stress closure models, and direct numerical simulations (DNS). Recently, there has been mutually beneficial collaboration of the experimental and computational efforts. In fact, these projects have been chosen for joint presentation at the NASA Turbulence Peer Review, scheduled for September 1994. DNS calculations are presently underway for a turbulent wake at Re(sub theta) = 1000 and at a Mach number of 0.20. (Theta is the momentum thickness, which remains constant in the wake of a two dimensional body.) These calculations utilize a compressible DNS code written by M. M. Rai of NASA Ames, and modified for the wake by J. Cimbala. The code employs fifth-order accurate upwind-biased finite differencing for the convective terms, fourth-order accurate central differencing for the viscous terms, and an iterative-implicit time-integration scheme. The computational domain for these calculations starts at x/theta = 10, and extends to x/theta = 610. Fully developed turbulent wake profiles, obtained from experimental data from several wake generators, are supplied at the computational inlet, along with appropriate noise. After some adjustment period, the flow downstream of the inlet develops into a fully three-dimensional turbulent wake. Of particular interest in the present study is the far wake spreading rate and the self-similar mean and turbulence profiles. At the time of this writing, grid resolution studies are underway, and a code is being written to calculate turbulence statistics from these wake calculations; the statistics will be compared to those from the ongoing PIV wake measurements, those of previous experiments, and those predicted by the various turbulence models. These calculations will lead to significant long-term benefits for the turbulence modeling effort. In particular, quantities such as the pressure-strain correlation and the dissipation rate tensor can be easily calculated from the DNS results, whereas these quantities are nearly impossible to measure experimentally. Improvements to existing turbulence models (and development of new models) require knowledge about flow quantities such as these. Present turbulence models do a very good job at prediction of the shape of the mean velocity and Reynolds stress profiles in a turbulent wake, but significantly underpredict the magnitude of the stresses and the spreading rate of the wake. Thus, the turbulent wake is an ideal flow for turbulence modeling research. By careful comparison and analysis of each term in the modeled Reynolds stress equations, the DNS data can show where deficiencies in the models exist; improvements to the models can then be attempted.

Cimbala, John M.↗