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At least 379 records · Page 21

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NASA NTRS1980

On the performance of explicit and implicit algorithms for transient thermal analysis

The status of an effort to increase the efficiency of calculating transient temperature fields in complex aerospace vehicle structures is described. The advantages and disadvantages of explicit and implicit algorithms are discussed. A promising set of implicit algorithms, known as the GEAR package is described. Four test problems, used for evaluating and comparing various algorithms, have been selected and finite element models of the configurations are discribed. These problems include a space shuttle frame component, an insulated cylinder, a metallic panel for a thermal protection system and a model of the space shuttle orbiter wing. Calculations were carried out using the SPAR finite element program, the MITAS lumped parameter program and a special purpose finite element program incorporating the GEAR algorithms. Results generally indicate a preference for implicit over explicit algorithms for solution of transient structural heat transfer problems when the governing equations are stiff. Careful attention to modeling detail such as avoiding thin or short high-conducting elements can sometimes reduce the stiffness to the extent that explicit methods become advantageous.

Adelman, H. M.↗

NASA NTRS1993

Development of computational methods for heavy lift launch vehicles

The research effort has been focused on the development of an advanced flow solver for complex viscous turbulent flows with shock waves. The three-dimensional Euler and full/thin-layer Reynolds-averaged Navier-Stokes equations for compressible flows are solved on structured hexahedral grids. The Baldwin-Lomax algebraic turbulence model is used for closure. The space discretization is based on a cell-centered finite-volume method augmented by a variety of numerical dissipation models with optional total variation diminishing limiters. The governing equations are integrated in time by an implicit method based on lower-upper factorization and symmetric Gauss-Seidel relaxation. The algorithm is vectorized on diagonal planes of sweep using two-dimensional indices in three dimensions. A new computer program named CENS3D has been developed for viscous turbulent flows with discontinuities. Details of the code are described in Appendix A and Appendix B. With the developments of the numerical algorithm and dissipation model, the simulation of three-dimensional viscous compressible flows has become more efficient and accurate. The results of the research are expected to yield a direct impact on the design process of future liquid fueled launch systems.

Yoon, Seokkwan↗

NASA NTRS1992

Numerical analysis of a thermal deicer

An algorithm has been developed to numerically model the concurrent phenomena of two-dimensional transient heat transfer, ice accretion and ice shedding which arise from the use of an electrothermal pad. The Alternating Direction Implicit method is used to simultaneously solve the heat transfer and accretion equations occurring in a multilayered body covered with ice. In order to model the phase change between ice and water, a technique was used which assumes a phase for each node. This allows the equations to be linearized such that a direct solution is possible. This technique requires an iterative procedure to find the correct phase at each node. The computer program developed to find this solution has been integrated with the NASA/Lewis flow/trajectory code LEWICE.

Wright, W. B.↗

NASA NTRS1989

Navier-Stokes computations of symmetric and asymmetric vortex shedding around slender bodies

The unsteady, compressible Reynolds-averaged thin-layer Navier-Stokes equations are used to solve for symmetric and asymmetric vortical flows around slender pointed bodies of revolution. The modified Baldwin and Lomax algebraic two-layer turbulent model is used for the eddy viscosity calculation in prescribed turbulent regions. The implicit, upwind flux-difference splitting finite-volume scheme is used to obtain the solutions. Computational results are presented for a low-speed symmetrical vortical flow around a 3.5-caliber tangent-ogive cylinder for fully laminar flow. Computed results are presented for a high-speed asymmetric vortex-shedding flow around a cone at 3.286 relative incidence, using a fine computational grid. The asymmetric vortex-shedding flow has been produced through a small asymmetric transitional perturbation in the cross-flow plane.

Kandil, Osama A.↗

NASA NTRS1991

Navier-Stokes computation of wing/rotor interaction for a tilt rotor in hover

A method has been developed to analyze the wing/rotor interaction of tilt rotor aircraft in hover. The unsteady, thin-layer compressible Navier-Stokes equations are solved using an implicit, finite difference scheme that employs LU-ADI factorization. The rotor is modeled as an actuator disk which imparts a radial and azimuthal distribution of pressure rise and swirl to the flowfield. The 'chimera' approach of grid point blanking is used to update the rotor boundary conditions. Results are presented for both a rotor alone and for wing/rotor interaction where the thrust coefficient is 0.0164 and wing flap deflection is 67 degrees. Many of the complex flow features are captured including the fountain effect, leading and trailing edge separation, and the unsteady wake beneath the wing. Wing surface pressures compare fairly well with experimental data although the time-averaged download is about twenty percent higher than the measured value. This discrepancy is due to a combination of factors that are discussed.

Fejtek, Ian↗

NASA NTRS1991

Transonic swirling nozzle flow

A numerical model of viscous transonic swirling flow in axisymmetric nozzles is developed. MacCormack's implicit Gauss-Seidel method is applied to the thin-layer Navier-Stokes equations in transformed coordinates. Numerical results are compared with experimental data to validate the method. The effect of swirl and viscosity on nozzle performance are demonstrated by examining wall pressures, Mach contours, and integral parameters.

Keith, Theo G., Jr.↗

NASA NTRS1993

Virtual-pulse time integral methodology: A new explicit approach for computational dynamics - Theoretical developments for general nonlinear structural dynamics

The present paper describes a new explicit virtual-pulse time integral methodology for nonlinear structural dynamics problems. The purpose of the paper is to provide the theoretical basis of the methodology and to demonstrate applicability of the proposed formulations to nonlinear dynamic structures. Different from the existing numerical methods such as direct time integrations or mode superposition techniques, the proposed methodology offers new perspectives and methodology of development, and possesses several unique and attractive computational characteristics. The methodology is tested and compared with the implicit Newmark method (trapezoidal rule) through a nonlinear softening and hardening spring dynamic models. The numerical results indicate that the proposed explicit virtual-pulse time integral methodology is an excellent alternative for solving general nonlinear dynamic problems.

Chen, Xiaoqin↗

NASA NTRS1991

Non equilibrium flow in an arc-jet

A method for simulating the flow of a nitrogen plasma in thermodynamic nonequilibrium is described. The method relies on the modeling of the relevant physical and chemical phenomena and on a fully coupled implicit finite volume upwind numerical approximation of the governing equations. The results agree with experimental data.

Rostand, P.↗

NASA NTRS2001

Integrated Thermal Response Tool for Earth Entry Vehicles

A system is presented for multi-dimensional, fully-coupled thermal response modeling of hypersonic entry vehicles. The system consists of a two-dimensional implicit thermal response, pyrolysis and ablation program (TITAN), a commercial finite-element thermal and mechanical analysis code (MARC), and a high fidelity Navier-Stokes equation solver (GIANTS). The simulations performed by this integrated system include hypersonic flow-field, fluid and solid interaction, ablation, shape change, pyrolysis gas generation and flow, and thermal response of heatshield and structure. The thermal response of the ablating and charring heatshield material is simulated using TITAN, and that of the underlying structural is simulated using MARC. The ablating heatshield is treated as an outer boundary condition of the structure, and continuity conditions of temperature and heat flux are imposed at the interface between TITAN and MARC. Aerothermal environments with fluid and solid interaction are predicted by coupling TITAN and GIANTS through surface energy balance equations. With this integrated system, the aerothermal environments for an entry vehicle and the thermal response of both the heatshield and the structure can be obtained simultaneously. Representative computations for a proposed blunt body earth entry vehicle are presented and discussed in detail.

Chen, Y.-K.↗

NASA NTRS1992

Implementation/validation of a low Reynolds number two-equation turbulence model in the Proteus Navier-Stokes code: Two-dimensional/axisymmetric

The implementation and validation of the Chien low Reynolds number k-epsilon turbulence model in the two dimensional axisymmetric version Proteus, a compressible Navier-Stokes computer code, are presented. The set of k-epsilon equations are solved by marching in time using a coupled alternating direction implicit (ADI) solution procedure with generalized first or second order time differencing. To validate Proteus and the k-epsilon turbulence model, laminar and turbulent computations were done for several benchmark test cases: incompressible fully developed 2-D channel flow; fully developed axisymmetric pipe flow; boundary layer flow over a flat plate; and turbulent Sajben subsonic transonic diffuser flows. Proteus results from these test cases showed good agreement with analytical results and experimental data. Detailed comparisons of both mean flow and turbulent quantities showed that the Chien k-epsilon turbulence model given good results over a wider range of turbulent flow than the Baldwin-Lomax turbulence model in the Proteus code with no significant CPU time penalty for more complicated flow cases.

Bui, Trong T.↗

NASA NTRS1991

Numerical simulation of icing, deicing, and shedding

An algorithm has been developed to numerically model the concurrent phenomena of two-dimensional transient heat transfer, ice accretion, ice shedding and ice trajectory which arise from the use of electrothermal pad. The Alternating Direction Implicit method is used to simultaneously solve the heat transfer and accretion equations occurring in the multilayered body covered with ice. In order to model the phase change between ice and water, a technique was used which assumes a phase for each node. This allows the equations to be linearized such that a direct solution is possible. This technique requires an iterative procedure to find the correct phase at each node. The computer program developed to find this solution has been integrated with the NASA-Lewis flow/trajectory code LEWICE.

Wright, W. B.↗

NASA NTRS2014

Physics Based Model for Cryogenic Chilldown and Loading. Part I: Algorithm

We report the progress in the development of the physics based model for cryogenic chilldown and loading. The chilldown and loading is model as fully separated non-equilibrium two-phase flow of cryogenic fluid thermally coupled to the pipe walls. The solution follow closely nearly-implicit and semi-implicit algorithms developed for autonomous control of thermal-hydraulic systems developed by Idaho National Laboratory. A special attention is paid to the treatment of instabilities. The model is applied to the analysis of chilldown in rapid loading system developed at NASA-Kennedy Space Center. The nontrivial characteristic feature of the analyzed chilldown regime is its active control by dump valves. The numerical predictions are in reasonable agreement with the experimental time traces. The obtained results pave the way to the development of autonomous loading operation on the ground and space.

heat transfer↗

NASA NTRS1986

Implicit, vectorizable schemes for the flux-difference split, three-dimensional Navier-Stokes equations

Two hybrid upwind models are defined for solving the Euler equations. The algorithms both employ approximate factorization (AF) in crossplane and symmetric block Gauss-Seidel relaxation in the third direction. One approach adds an additional factorization step to lower the number of required grid point operations for inversion of the block tridiagonal matrices; however, the move permits only one third of the operations to be vectorized. Finite difference solutions are calculated on a C-H-type grid, in this case enveloping a slender, sharp-edged delta wing. Sample data are provided for the calculated vortex flow for Re of 10,000, at a 20.5 deg angle of attack, represented in a crossflow velocity vector plot and in a spanwise pressure coefficient distribution. The AF scheme, without additional factorization, when used with a grid covering 51 x 51 x 72 points provides a convergent solution with no time step lasting longer than 0.00001 sec.

Liu, C. H.↗

NASA NTRS2023

Chemical Thermodynamics and the Mathematical Integration of Reaction Kinetics

Key advances in the development of numerical methods for non-reacting compressible flows have been enabled by translating physical requirements into concrete numerical guidelines, such as the satisfaction of entropy inequalities for shock-capturing techniques [Lax, Contributions to Nonlinear Functional Analysis (1971) 603-634]. In the present work, we present nonlinear numerical analysis tools that draw from Chemical Thermodynamics , the branch of Nonequilibrium Thermodynamics that deals with chemical reactions. Through Gibbs formalism, chemical thermodynamics provides a well-known theoretical expression for the chemical equilibrium constant of a reaction in terms of reduced chemical potentials. A less-known, yet extremely valuable result, due to [Krambeck, Arch. Ration. Mech. Anal. , 38 (1970) 317], states that when this expression is implemented, mass-action kinetic models are consistent with the dynamical prescriptions of the 2nd law of thermodynamics. For fixed-temperature ordinary differential equations modeling constant-volume reacting gas mixtures, this leads to a decreasing Helmholtz free energy. If the temperature is allowed to vary in accordance with conservation of energy (1st law), this leads to the statement of increasing entropy. These nonlinear prescriptions can, and should be, used to further develop temporal integration techniques for reaction kinetics. We demonstrate that Krambeck's result holds even when the equilibrium constants are approximated from data. We prove this result by constructing the implicit free energy and the implicit entropy inherent to a given approximation. This is first done for a 5-species, 17-reaction model problem for air. With this structure established, elements of discrete entropy-stability theory [Tadmor, Acta Numer. , 12 (2003) 451] are leveraged to examine the consistency of time-integration schemes with these prescriptions. Using chemical potentials, one can compute the respective contributions of the kinetics model and of the temporal scheme to free energy/entropy variations. We introduce a nonlinear-stable version of the Discontinuous-Galerkin (DG) scheme in time which shows robustness improvements over the standard linearly-stable version. Most notably, the maximum timestep that can be resolved with the nonlinearly-stable variant tends to grow with polynomial order, in contrast to the linearly-stable variant. We generalize our constructions to arbitrary systems of reversible chemical reactions, ultimately showing that the compressible reacting Euler system admits the opposite of the implicitly constructed thermodynamic entropy as a mathematical entropy . This lays important theoretical foundations towards robust scheme development [Harten, J. Comput. Phys. 49 (1983) 151-164].

STMD↗

NASA NTRS1988

Element-by-element and implicit-explicit finite element formulations for computational fluid dynamics

Preconditioner algorithms to reduce the computational effort in FEM analyses of large-scale fluid-dynamics problems are presented. A general model problem is constructed on the basis of the convection-diffusion equation and the two-dimensional vorticity/stream-function formulation of the Navier-Stokes equations; this problem is then analyzed using element-by-element, implicit-explicit, and adaptive implicit-explicit approximation schemes. Numerical results for the two-dimensional advection and rigid-body rotation of a cosine hill, flow past a circular cylinder, and driven cavity flow are presented in extensive graphs and shown to be in good agreement with those obtained using implicit methods.

Tezduyar, T. E.↗

NASA NTRS1992

Navier-Stokes turbine heat transfer predictions using two-equation turbulence

Navier-Stokes calculations were carried out in order to predict the heat transfer rates on turbine blades. The calculations were performed using TRAF2D which is a two-dimensional, explicit, finite volume mass-averaged Navier-Stokes solver. Turbulence was modeled using q-omega and k-epsilon two-equation models and the Baldwin-Lomax algebraic model. The model equations along with the flow equations were solved explicitly on a non-periodic C grid. Implicit residual smoothing (IRS) or a combination of multigrid technique and IRS was applied to enhance convergence rates. Calculations were performed to predict the Stanton number distributions on the first stage vane and blade row as well as the second stage vane row of the Rocketdyne Space Shuttle Main Engine (SSME) high pressure fuel turbine. The comparison with the experimental results, although generally favorable, serves to highlight the weaknesses of the turbulence models and the possible areas of improving these models for use in turbomachinery heat transfer calculations.

Ameri, Ali A.↗

NASA NTRS1998

Development of Numerical Extended Hydrodynamics for Transition-Regime Non-Equilibrium Flows Encountered in Semiconductor Manufacturing Processes

Six months of funding was received for the proposed three year research program (funding for the period from March 1, 1997 to August 31, 1997). Although the official starting date for the project was March 1, 1997, no funding for the project was received until July 1997. In the funded research period, considerable progress was made on Phase I of the proposed research program. The initial research efforts concentrated on applying the 10-, 20-, and 35-moment Gaussian-based closures to a series of standard two-dimensional non-reacting single species test flow problems, such as the flat plate, couette, channel, and rearward facing step flows, and to some other two-dimensional flows having geometries similar to those encountered in chemical-vapor deposition (CVD) reactors. Eigensystem analyses for these systems for the case of two spatial dimensions was carried out and efficient formulations of approximate Riemann solvers have been formulated using these eigenstructures. Formulations to include rotational non-equilibrium effects into the moment closure models for the treatment of polyatomic gases were explored, as the original formulations of the closure models were developed strictly for gases composed of monatomic molecules. The development of a software library and computer code for solving relaxing hyperbolic systems in two spatial dimensions of the type arising from the closure models was also initiated. The software makes use of high-resolution upwind finite-volumes schemes, multi-stage point implicit time stepping, and automatic adaptive mesh refinement (AMR) to solve the governing conservation equations for the moment closures. The initial phase of the code development was completed and a numerical investigation of the solutions of the 10-moment closure model for the simple two-dimensional test cases mentioned above was initiated. Predictions of the 10-moment model were compared to available theoretical solutions and the results of direct-simulation Monte Carlo (DSMC) calculations. The first results of this study were presented at a meeting last year.

Groth, Clinton P. T.↗

NASA NTRSDate not supplied

Concept-based Analysis of Neural Networks via Vision-Language Models

The analysis of vision-based deep neural networks (DNNs) is highly desirable but it is very challenging due to the difficulty of expressing formal specifications for vision tasks and the lack of efficient verification procedures. In this paper, we propose to leverage emerging multimodal, vision-language, foundation models (VLMs) as a lens through which we can reason about vision models. VLMs have been trained on a large body of images accompanied by their textual description, and are thus implicitly aware of high-level, human-understandable concepts describing the images. We describe a logical specification language Con spec designed to facilitate writing specifications in terms of these concepts. To define and formally check Con spec specifications, we build a map between the internal representations of a given vision model and a VLM, leading to an efficient verification procedure of natural-language properties for vision models. We demonstrate our techniques on a ResNet-based classifier trained on the RIVAL-10 dataset using CLIP as the multimodal model.

Large Vision Language Models↗