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At least 379 records · Page 21
All sourcesNASA NTRSDOE OSTI
NASA NTRS2017

Stabilized Finite Elements in FUN3D

A Streamlined Upwind Petrov-Galerkin (SUPG) stabilized finite-element discretization has been implemented as a library into the FUN3D unstructured-grid flow solver. Motivation for the selection of this methodology is given, details of the implementation are provided, and the discretization for the interior scheme is verified for linear and quadratic elements by using the method of manufactured solutions. A methodology is also described for capturing shocks, and simulation results are compared to the finite-volume formulation that is currently the primary method employed for routine engineering applications. The finite-element methodology is demonstrated to be more accurate than the finite-volume technology, particularly on tetrahedral meshes where the solutions obtained using the finite-volume scheme can suffer from adverse effects caused by bias in the grid. Although no effort has been made to date to optimize computational efficiency, the finite-element scheme is competitive with the finite-volume scheme in terms of computer time to reach convergence.

Anderson, W. Kyle↗
NASA NTRS2019

WRLES: Wave Resolving Large-Eddy Simulation Code, Theory and Usage

A computational fluid dynamics code has been developed for large-eddy simulations (LES) of turbulent flow. The code uses high-order of accuracy and high-resolution numerical methods to minimize solution error and maximize the resolution of the turbulent structures. Spatial discretization is performed using explicit central differencing. The central differencing schemes in the code include 2nd- to 12th-order standard central difference methods as well as 7-, 9-, 11- and 13-point dispersion relation preserving schemes. Solution filtering and high-order shock capturing are included for stability. Time discretization is performed using multistage Runge-Kutta methods that are up to 4th order accurate. Several options are available to model turbulence including: Baldwin-Lomax and Spalart-Allmaras Reynolds-averaged Navier-Stokes turbulence models, and Smagorinsky, Dynamic Smagorinsky and Vreman sub-grid scale models for LES. This report presents the theory behind the numerical and physical models used in the code and provides a user's manual to the operation of the code.

High-Order↗
NASA NTRS2010

TPSAS-NF1676L-10658-DND

The systematic methodology for constructing fourth-order finite domain Energy Stable WENO schemes is developed. We prove that for hyperbolic systems, the finite domain ESWENO scheme is stable in the energy norm for both continuous and discontinuous solutions. The eigenvalues of the finite domain ESWENO dissipation operator are located in the left-half plane. Based on the rigorous truncation error analysis, the new weight functions are developed, which drastically improve the accuracy of the ESWENO scheme and provide excellent shock-capturing capabilities. Numerical experiments show that the new finite domain ESWENO scheme with the new weights outperform the conventional WENO schemes in terms of accuracy.

Travis Fisher↗
NASA NTRSDate not supplied

OVERFLOW Analysis of Supersonic Retropropulsion Testingon the CobraMRV Mars Entry Vehicle Concept

The CFD solver OVERFLOW was used to simulate the CobraMRV undergoing supersonic retropropulsion (SRP) in the Langley Unitary Plan Wind Tunnel as part of a pre-test study. Aerodynamics of the CobraMRV are summarized and the sensitivity of vehicle loads to CFD parameters at a subset of operating conditions are investigated. Specific numerical methods, boundary conditions, and turbulence modeling options have been selected after considering the complex phenomena in SRP flows. Proper shock-capturing methods and dynamic grid adaption are necessary to correctly capture vehicle loads and dynamics. Present data indicates that at particular conditions, upstream asymmetries originating from the tunnel inflow plane contribute to measurable asymmetries on the CobraMRV heatshield.

OVERFLOW↗
NASA NTRSDate not supplied

Uncertainty Quantification of CFD Model Assumptions Against Sonic Boom Noise Prediction of a Commercial Supersonic Transport

This paper presents the results of uncertainty modeling of sonic boom noise generation from commercial supersonic transport considering the Spalart-Allmaras (SA) turbulence modeling parameters as well as Mach number, angle of attack and altitude. Sample generation and analysis for this uncertainty model was performed by UQPCE, which is a software package developed at the NASA Langley Research Center. To build the uncertainty model, 42 cases of sonic boom noise calculation were performed. Computation of the ground noise can be briefly summarized in two steps. First, the near field pressure waveforms are sampled from CFD calculation using the NASA Langley’s FUN3D solver. Second, this information is passed to an atmospheric propagation code, sBOOM, which solves an augmented Burger’s equation and simulates how the near field waveforms will change while passing through the atmosphere. The ground signature is further processed to obtain the perceived loudness, PLdB. Having a high spatial resolution near the shockwave in the CFD calculation is critical in sonic boom noise prediction. Because the variation in the input parameters for the current uncertainty quantification (UQ) study is likely to lead to change in shock location, angle and strength, the grid adaptation for shock capturing is independently applied for each condition. The final mesh used in the CFD calculation consists of approximately 420 million cells. The pressure signatures are sampled at three, four and five body lengths away from the aircraft to make sure the three dimensional effects around the aircraft are resolved. The results of the UQ analysis shows that within the three aleatory variables, the angle of attack had the most impact against ground noise, followed by the altitude and the Mach number. Between the two SA model parameters, the Kármán constant (𝜅) was significantly more important than the turbulent Prandtl number (𝜎), but these two parameters were only marginally significant in the overall prediction variance in ground noise. The UQ procedure explained in this paper can be widely applied to other model parameters.

Uncertainty Quantification↗
NASA NTRSDate not supplied

Uncertainty Quantification of CFD Model Assumptions Against Sonic Boom Noise Prediction of a Commercial Supersonic Transport

This paper presents the results of uncertainty modeling of sonic boom noise generation from commercial supersonic transport considering the Spalart-Allmaras (SA) turbulence modeling parameters as well as Mach number, angle of attack and altitude. Sample generation and analysis for this uncertainty model was performed by UQPCE, which is a software package developed at the NASA Langley Research Center. To build the uncertainty model, 42 cases of sonic boom noise calculation were performed. Computation of the ground noise can be briefly summarized in two steps. First, the near field pressure waveforms are sampled from CFD calculation using the NASA Langley’s FUN3D solver. Second, this information is passed to an atmospheric propagation code, sBOOM, which solves an augmented Burger’s equation and simulates how the near field waveforms will change while passing through the atmosphere. The ground signature is further processed to obtain the perceived loudness, PLdB. Having a high spatial resolution near the shock wave in the CFD calculation is critical in sonic boom noise prediction. Because the variation in the input parameters for the current uncertainty quantification (UQ) study is likely to lead to change in shock location, angle and strength, the grid adaptation for shock capturing is independently applied for each condition. The final mesh used in the CFD calculation consists of approximately 420 million cells. The pressure signatures are sampled at three, four and five body lengths away from the aircraft to make sure the three dimensional effects around the aircraft are resolved. The results of the UQ analysis shows that within the three aleatory variables, the angle of attack had the most impact against ground noise, followed by the altitude and the Mach number. Between the two SA model parameters, the Kármán constant (𝜅) was significantly more important than the turbulent Prandtl number (𝜎), but these two parameters were only marginally significant in the overall prediction variance in ground noise. The UQ procedure explained in this paper can be widely applied to other model parameters.

Uncertainty Quantifications↗
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↗
DOE OSTI2022

Computational Study of Variable Fuel-Air Ratio and Hydrogen Doping in a Rotating Detonation Engine

Rotating detonation engines (RDEs) hold great promise as a technology for powering aviation engines. The pressure gain that results from continuously traversing detonation waves enables high theoretical performance compared to deflagration-based combustion. However, the harsh operating conditions inside an RDE restrict the availability of suitable experimental diagnostics to study these systems in detail and the range of spatial and temporal scales render numerical simulations of these systems difficult. In this study, we have combined adaptive mesh refinement and a robust shock-capturing approach to study RDE systems computationally using the compressible, reactive solver PeleC. Multi-species transport along with compressible Navier-Stokes equations are solved in the model along with finite-rate chemistry. Complex geometries are represented using an embedded boundary method with second-order spatial accuracy and the system is evolved in time using a second-order Runge-Kutta method. We present studies of a methane-air RDE system that is doped with varying levels of hydrogen. Our analysis focusses on how fuel mixture and doping levels effect the detonation flame structure and the generation of multiple wave modes.

ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2022

Numerical Study on the Effect of Methane Doping in Hydrogen-Air Rotating Detonation Engines for Various Temperatures and Pressures

Rotating detonation engines (RDEs) have gained attention as a promising technology for future aviation engines. However, the numerical studies of these systems pose severe challenges due to the broad range of spatial and temporal scales. In this study, we use an adaptive mesh refinement based compressible, reactive solver PeleC to resolve the broad range of scales and accurately capture shock and detonation waves using high-resolution numerical schemes. Multi- species transport along with compressible Navier-Stokes equations are solved in the model along with a finite-rate based chemistry model. Embedded boundary method is used to model the complex geometry consisting of discrete fuel nozzles and the combustion chamber. The fuel consisting predominantly of hydrogen is doped with varying levels of methane while air is used as the oxidizer. For a specified total pressure and temperature, the number of stable detonation waves is found to decrease with increasing methane concentration in the fuel mixture. Additionally, no stable detonation solutions are observed for methane composition higher than 20% by volume for the range of operating conditions studied (300-900K, 10 Atm). The increased presence of high temperature zones is also indicative of higher thermal NOx emissions at low methane concentrations. The effect of fuel-air mixture composition and temperature on the detonability, detonation wave structure, mode transitions and their stability are analyzed in this study in addition to their implication on NOx emission.

automatic mesh refinement↗
NASA NTRS2003

Finite Element Method for Capturing Ultra-relativistic Shocks

While finite element methods are used extensively by researchers solving computational fluid dynamics in fields other than astrophysics, their use in astrophysical fluid simulations has been predominantly overlooked. Current simulations using other methods such as finite difference and finite volume (based on finite difference) have shown remarkable results, but these methods are limited by their fundamental properties in aspects that are important for simulations with complex geometries and widely varying spatial and temporal scale differences. We have explored the use of finite element methods for astrophysical fluids in order to establish the validity of using such methods in astrophysical environments. We present our numerical technique applied to solving ultra-relativistic (Lorentz Factor Gamma >> 1) shocks which are prevalent in astrophysical studies including relativistic jets and gamma-ray burst studies. We show our finite element formulation applied to simulations where the Lorentz factor ranges up to 2236 and demonstrate its stability in solving ultra-relativistic flows. Our numerical method is based on the Flowfield Dependent Variation (FDV) Method, unique in that numerical diffusion is derived from physical parameters rather than traditional artificial viscosity methods. Numerical instabilities account for most of the difficulties when capturing shocks in this regime. Our method results in stable solutions and accurate results as compared with other methods.

Richardson, G. A.↗
DOE OSTI2024

A high-order, localized-artificial-diffusivity method for Eulerian simulation of multi-material elastic-plastic deformation with strain hardening

A high-order method for Eulerian simulation of material undergoing large elastic–plastic deformation is developed. Thermodynamically consistent hyperelastic constitutive relations are assumed, facilitating the treatment of solids, liquids, and gases in a unified manner. Here, the method enables the simulation of multi-material interactions using a diffuse interface approach. Numerical capturing of material interfaces, shock waves, contact surfaces, and elastic-plastic strain discontinuities using high-order compact-difference schemes is assisted by Localized Artificial Diffusivity (LAD). In the new setting involving elastic–plastic deformation, the previously established terms for the artificial properties are verified to effectively regularize normal shocks. Additional LAD terms are introduced to the elastic and plastic kinematic equations to regularize shear shocks and other strain discontinuities, improving solution stability. Other important features of the method that improve robustness include the numerical treatment of compatibility terms in the kinematic equations, and the treatment of rotation. Particular emphasis is focused toward new advancements of the methods for plastic-deformation integration and the associated strain hardening of the material, including rate-dependent plasticity. The method is demonstrated on a variety of test problems, including 1-D impacts, a variant of the Shu-Osher problem, a Taylor impact, and a Richtmyer-Meshkov instability between two elastic–plastic solids with strain hardening.

42 ENGINEERING↗
NASA NTRS1973

Steady inviscid transonic flows over planar airfoils: A search for a simplified procedure

A finite difference procedure based upon a system of unsteady equations in proper conservation form with either exact or small disturbance steady terms is used to calculate the steady flows over several classes of airfoils. The airfoil condition is fulfilled on a slab whose upstream extremity is a semi-circle overlaying the airfoil leading edge circle. The limitations of the small disturbance equations are demonstrated in an extreme example of a blunt-nosed, aft-cambered airfoil. The necessity of using the equations in proper conservation form to capture the shock properly is stressed. Ability of the steady relaxation procedures to capture the shock is briefly examined.

Magnus, R.↗
DOE OSTI2025

Planar Collisionless Shock Simulations with the Semi-implicit Particle-in-cell Model FLEKS

This study investigates the applicability of the semi-implicit particle-in-cell code FLexible Exascale Kinetic Simulator (FLEKS) to heliospheric shock simulations. We examine one- and two-dimensional local planar shock simulations, initialized using MHD states with upstream conditions representative of plasmas in the hypersonic, β ∼ 1 regime, for both quasi-perpendicular and quasi-parallel configurations. The refined algorithm in FLEKS proves robust, enabling accurate shock simulations with a grid resolution on the order of the electron inertial length d e . Our simulations successfully capture key shock features, including shock structures (foot, ramp, overshoot, and undershoot), upstream and downstream waves (fast magnetosonic, whistler, Alfvén ion-cyclotron, and mirror modes), and non-Maxwellian particle distributions. Crucially, we find that at least two spatial dimensions are critical for accurately reproducing downstream-wave physics in quasi-perpendicular shocks and capturing the complex dynamics of quasi-parallel shocks, including surface rippling, shocklets, short, large-amplitude magnetic structures, magnetic reconnection, and jets. Furthermore, our parameter studies demonstrate the impact of mass ratio and grid resolution on shock physics. This work provides valuable guidance for selecting appropriate physical and numerical parameters for shock simulations using a semi-implicit PIC method, paving the way for incorporating kinetic shock processes into large-scale collisionless plasma simulations with the MHD-AEPIC model.

plasma astrophysics↗
NASA NTRS1985

Numerical studies of 2-dimensional flows

A formulation of the lambda scheme for the analysis of two dimensional inviscid, compressible, unsteady transonic flows is presented. The scheme uses generalized Riemann variables to determine the appropriate two point, one sided finite difference approximation for each derivative in the unsteady Euler equations. These finite differences are applied at the predictor and corrector levels with shock updating at each level. The weaker oblique shocks are captured, but strong near normal shocks are fitted into the flow using the Rankine-Hugoniot relations. This code is demonstrated with a numerical example of a duct flow problem with developing normal and oblique shock waves. The technique is implemented in a code which has been made efficient by streamlining to a minimal number of operations and by eliminating branch statements. The scheme is shown to provide an accurate analysis of the flow, including formation, motions, and interactions of shocks; the results obtained on a relatively coarse mesh are comparable to those obtained by other methods on much finer meshes.

Moretti, G.↗
NASA NTRS1993

A generic efficient adaptive grid scheme for rocket propulsion modeling

The objective of this research is to develop an efficient, time-accurate numerical algorithm to discretize the Navier-Stokes equations for the predictions of internal one-, two-dimensional and axisymmetric flows. A generic, efficient, elliptic adaptive grid generator is implicitly coupled with the Lower-Upper factorization scheme in the development of ALUNS computer code. The calculations of one-dimensional shock tube wave propagation and two-dimensional shock wave capture, wave-wave interactions, shock wave-boundary interactions show that the developed scheme is stable, accurate and extremely robust. The adaptive grid generator produced a very favorable grid network by a grid speed technique. This generic adaptive grid generator is also applied in the PARC and FDNS codes and the computational results for solid rocket nozzle flowfield and crystal growth modeling by those codes will be presented in the conference, too. This research work is being supported by NASA/MSFC.

Mo, J. D.↗
NASA NTRS1979

Supercritical flow about a thick circular-arc airfoil

The supercritical flow about a biconvex circular-arc airfoil is being thoroughly documented at Ames Research Center in order to provide experimental test cases suitable for guiding and evaluating current and future computer codes. The effects of angle of attack, effects of leading and trailing-edge splitter plates, additional unsteady pressure fluctuation (buffeting) measurements and glow-field shadowgraphs, and application of an oil-film technique to display separated-wake streamlines were studied. Computed and measured pressure distributions for steady and unsteady flows, using a recent computer code representative of current methodology, are compared. It was found that the numerical solutions are often fundamentally incorrect in that only strong (shock-polar terminology) shocks are captured, whereas experimentally, both strong and weak shock waves appear.

Mcdevitt, J. B.↗
DOE OSTI2021

A reactive flow model for the 3,3'-diamino-4,4'-azoxyfurazan based plastic bonded explosive (PBX 9701)

Here, this paper describes the calibration of the Arrhenius Wescott–Stewart–Davis (AWSD) reactive flow model for the recently developed high explosive PBX 9701, which consists of 97% 3,3'-diamino-4,4'-azoxyfurazan (DAAF) and 3% FK-800 binder by weight. DAAF-based explosive formulations have several desirable qualities as they are relatively insensitive to non-shock insults but have higher performance than triaminotrinitrobenzene based formulations. Equations of state for the explosive reactants and products are calibrated using a combination of existing and new experimental data and theoretical calculations. The AWSD rate law calibration utilizes both one-dimensional shock-to-detonation and multidimensional rate stick experiments to capture the shock initiation and propagating detonation regimes. Validation of the calibrated model is demonstrated through comparison with recent gas-gun experiments.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
NASA NTRS1992

PNS predictions for supersonic/hypersonic flows over finned missile configurations

Finned missile design entails accurate and computationally fast numerical techniques for predicting viscous flows over complex lifting configurations at small to moderate angles of attack and over Mach 3 to 15; these flows are often characterized by strong embedded shocks, so that numerical algorithms are also required to capture embedded shocks. The recent real-gas Flux Vector Splitting technique is here extended to investigate the Mach 3 flow over a typical finned missile configuration with/without side fin deflections. Elliptic grid-generation techniques for Mach 15 flows are shown to be inadequate for Mach 3 flows over finned configurations and need to be modified. Fin-deflection studies indicate that even small amounts of missile fin deflection can substantially modify vehicle aerodynamics. This 3D parabolized Navier-Stokes scheme is also extended into an efficient embedded algorithm for studying small axially separated flow regions due to strong fin and control surface deflections.

Bhutta, Bilal A.↗