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At least 433 records · Page 24

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NASA NTRS1988

Application of a nonisentropic full potential method to AGARD standard airfoils

An entropy-correction method for the unsteady full potential equation is presented. The unsteady potential equation is modified to model the entropy jumps across shock waves. The conservative form of the modified equation is solved in generalized coordinates using an implicit, approximate factorization method. A flux-biasing differencing method, which generates the proper amounts of artificial viscosity in supersonic regions, is used to discretize the flow equations in space. Calculated results are presented for the NLR 7301, NACA 0012, and NACA 64A010A airfoils. Comparisons of the present method and solutions of the Euler equations are presented for the NLR 7301 airfoil, and comparisons of the present method and experimental data are presented for all three airfoils. The comparisons show that the present method more accurately models solutions of the Euler equations and experiment than does the isentropic potential formulation. In addition, it is shown that modeling shock-generated entropy extends the range of validity of the full potential method.

Whitlow, Woodrow, Jr.↗

NASA NTRS1988

Accurate solutions, parameter studies and comparisons for the Euler and potential flow equations

Parameter studies are conducted using the Euler and potential flow equation models for unsteady and steady flows in both two and three dimensions. The Euler code is an implicit, upwind, finite volume code which uses the Van Leer method of flux-vector-splitting which has been recently extended for use on dynamic meshes and maintain all the properties of the original splitting. The potential flow code is an implicit, finite difference method for solving the transonic small disturbance equations and incorporates both entropy and vorticity corrections into the solution procedures thereby extending its applicability into regimes where shock strength normally precludes its use. Parameter studies resulting in benchmark type calculations include the effects of spatial and temporal refinement, spatial order of accuracy, far field boundary conditions for steady flow, frequency of oscillation, and the use of subiterations at each time step to reduce linearization and factorization errors. Comparisons between Euler and potential flows results are made as well as with experimental data where available.

Anderson, W. Kyle↗

NASA NTRS1987

Accurate pressure gradient calculations in hydrostatic atmospheric models

A method for the accurate calculation of the horizontal pressure gradient acceleration in hydrostatic atmospheric models is presented which is especially useful in situations where the isothermal surfaces are not parallel to the vertical coordinate surfaces. The present method is shown to be exact if the potential temperature lapse rate is constant between the vertical pressure integration limits. The technique is applied to both the integration of the hydrostatic equation and the computation of the slope correction term in the horizontal pressure gradient. A fixed vertical grid and a dynamic grid defined by the significant levels in the vertical temperature distribution are employed.

Carroll, John J.↗

NASA NTRS1988

Application of a nonisentropic full potential method to AGARD standard airfoils

Whitlow, Woodrow, Jr.↗

NASA NTRS1988

Accurate solutions, parameter studies and comparisons for the Euler and potential flow equations

Parameter studies are conducted using the Euler and potential flow equation models for steady and unsteady flows in both two and three dimensions. The Euler code is an implicit, upwind, finite volume code which uses the Van Leer method of flux vector splitting which has been recently extended for use on dynamic meshes and maintain all the properties of the original splitting. The potential flow code is an implicit, finite difference method for solving the transonic small disturbance equations and incorporates both entropy and vorticity corrections into the solution procedures thereby extending its applicability into regimes where shock strength normally precludes its use. Parameter studies resulting in benchmark type calculations include the effects of spatial and temporal refinement, spatial order of accuracy, far field boundary conditions for steady flow, frequency of oscillation, and the use of subiterations at each time step to reduce linearization and factorization errors. Comparisons between Euler and potential flow results are made, as well as with experimental data where available.

Anderson, W. Kyle↗

NASA NTRS1990

Multigrid solution of unsteady Navier-Stokes equations using a pressure method

A multigrid relaxation method is applied to a pressure-based implicit procedure to solve unseady, incompressible Navier-Stokes equations. The present multigrid method is a Correction Scheme according to Brandt. This method is used to solve the scalar matrices resulting from the finite-volume formulation and uses flux averaging as the restriction operator. The accuracy and computational efficiency are demonstrated with a steady state driven cavity flow and an unsteady flow over a circular cylinder case. The results are compared with single grid results using the OrthoMin conjugate gradient method and experimental data.

Jiang, Y.↗

NASA NTRS1992

CAN-DO, CFD-based Aerodynamic Nozzle Design and Optimization program for supersonic/hypersonic wind tunnels

A design program is developed which incorporates a modern approach to the design of supersonic/hypersonic wind-tunnel nozzles. The approach is obtained by the coupling of computational fluid dynamics (CFD) with design optimization. The program can be used to design a 2D or axisymmetric, supersonic or hypersonic, wind-tunnel nozzles that can be modeled with a calorically perfect gas. The nozzle design is obtained by solving a nonlinear least-squares optimization problem (LSOP). The LSOP is solved using an iterative procedure which requires intermediate flowfield solutions. The nozzle flowfield is simulated by solving the Navier-Stokes equations for the subsonic and transonic flow regions and the parabolized Navier-Stokes equations for the supersonic flow regions. The advantages of this method are that the design is based on the solution of the viscous equations eliminating the need to make separate corrections to a design contour, and the flexibility of applying the procedure to different types of nozzle design problems.

Korte, John J.↗

NASA NTRS1994

Computation and modeling of aero-thermal fields in turbine cascades and strongly curved ducts

Advanced turbulence models are crucial for accurate prediction of rocket engine flows, due to existence of very large extra strain rates, such as strong streamline curvature. Numerical simulation of the turbulent flow in a strongly curved turn-around duct (TAD) has been carried out with a Reynolds stress model (RSM), an algebraic Reynolds stress model (ARSM) and a kappa-epsilon model. the RSM model and the ARSM model are found to capture the turbulence damping due to the convex curvature, but underpredict the turbulence enhancement caused by the concave curvature. To capture the concave curvature effects, it is necessary to modify the epsilon-equation. The modification of episilon-equation suggested by Launder, et.al, provides the correct trend, but over-corrects the curvature effects. A comparative study of two modes of transition in gas turbine, the by-pass transition and the separation-induced transition, has been carried out with several low-Reynolds-number (LRN) kappa-epsilon models. Effects of blade surface pressure gradient, freestream turbulence and Reynolds number on the blade boundary layer development, and particularly the inception of transition are examined in detail. The present study indicates that the turbine blade transition, in the presence of high freestream turbulence, is predicted well with LRN kappa-epsilon models employed.

Luo, J.↗

NASA NTRS2014

The Phoenix TECP Relative Humidity Sensor: Revised Results

The original calibration function of the RH sensor on the Phoenix mission's Thermal and Electrical Conductivity Sensor (TECP), has been revised to correct the erroneously-published original calibration equation, to demonstrate the value of this unique data set, and to improve characterization of H2O exchange between the martian regolith and atmosphere. TECP returned two data streams, the temperature of the electronics analog board (Tb) and the digital 12-bit output of the RH sensor (DN), both of which are required to uniquely specify the H2O abundance. Because the original flight instrument calibration was performed against a pair of hygrometers that measured frost point (Tf), the revised calibration equation is also cast in terms of frost point. The choice of functional form for the calibration function is minimally constrained. A series of profiles across the calibration data cloud at constant DN and Tb does not reveal any evidence of a complex functional form. Therefore, a series of polynomials in both DN and Tb was investigated, along with several non-linear functions of DN and Tb.

Phoenix mission↗

NASA NTRS2017

The Root Cause of the Overheating Problem

Previously we identified the receding flow, where two fluid streams recede from each other, as an open numerical problem, because all well-known numerical fluxes give an anomalous temperature rise, thus called the overheating problem. This phenomenon, although presented in several textbooks, and many previous publications, has scarcely been satisfactorily addressed and the root cause of the overheating problem not well understood. We found that this temperature rise was solely connected to entropy rise and proposed to use the method of characteristics to eradicate the problem. However, the root cause of the entropy production was still unclear. In the present study, we identify the cause of this problem: the entropy rise is rooted in the pressure flux in a finite volume formulation and is implanted at the first time step. It is found theoretically inevitable for all existing numerical flux schemes used in the finite volume setting, as confirmed by numerical tests. This difficulty cannot be eliminated by manipulating time step, grid size, spatial accuracy, etc, although the rate of overheating depends on the flux scheme used. Finally, we incorporate the entropy transport equation, in place of the energy equation, to ensure preservation of entropy, thus correcting this temperature anomaly. Its applicability is demonstrated for some relevant 1D and 2D problems. Thus, the present study validates that the entropy generated ab initio is the genesis of the overheating problem.

Liou, Meng-Sing↗

DOE OSTI2021

Pair Fluctuation Effects on Quasiparticle Transport in Fermi Systems

The leading corrections to Fermi liquid theory for non-equilibrium quasiparticle transport near a Cooper instability arise from the virtual emission and absorption of incipient Cooper pairs. We formulate the corrections to the Landau-Boltzmann transport equation starting from Keldysh's field theory for non-equilibrium, strongly interacting Fermions. The theory is applicable to quasiparticle transport in conventional and unconventional superconductors, dense nuclear matter and the low temperature phases of liquid $^3$He. Validation of the theory is provided by our analysis, and quantitative agreement between theory and experiment, of the excess attenuation of zero sound in liquid $^3$He near the superfluid transition. We propose an additional experimental test of the theory based on the effects of a Zeeman field on the spectrum of pairing fluctuations for the Cooper instability in spin-triplet superfluids.

Lin, Wei-Ting↗

NASA NTRS1977

Redundant integrated flight control/navigation inertial sensor complex

A redundant strapdown inertial navigation system for integrated flight control/navigation use is described. Design of the system, which consists of four tuned-gimbal gyros, eight accelerometers, and four processors, is discussed, with emphasis on its compact configuration (13 by 13 by 14 in.), based on symmetry properties of an octahedron. A matrix operator for least-squares combination of data from an arbitrary number of two-degree-of-freedom gyros is derived, and general parity equations for error analysis are given. Self-contained detection and isolation of a two-axis gyro failure is considered; system failure probability, which depends on component failure rates and self-correction capacities, is analyzed. Test data, including typical parity equation responses during motion and simulated gyro and accelerometer failures, are also presented.

Ebner, R. E.↗

NASA NTRS2003

General Relativistic Theory of the VLBI Time Delay in the Gravitational Field of Moving Bodies

The general relativistic theory of the gravitational VLBI experiment conducted on September 8, 2002 by Fomalont and Kopeikin is explained. Equations of radio waves (light) propagating from the quasar to the observer are integrated in the time-dependent gravitational field of the solar system by making use of either retarded or advanced solutions of the Einstein field equations. This mathematical technique separates explicitly the effects associated with the propagation of gravity from those associated with light in the integral expression for the relativistic VLBI time delay of light. We prove that the relativistic correction to the Shapiro time delay, discovered by Kopeikin (ApJ, 556, L1, 2001), changes sign if one retains direction of the light propagation but replaces the retarded for the advanced solution of the Einstein equations. Hence, this correction is associated with the propagation of gravity. The VLBI observation measured its speed, and that the retarded solution is the correct one.

Kopeikin, Sergei↗

DOE OSTI2023

Code-verification techniques for the method-of-moments implementation of the magnetic-field integral equation

For computational physics simulations, code verification plays a major role in establishing the credibility of the results by assessing the correctness of the implementation of the underlying numerical methods. In computational electromagnetics, surface integral equations, such as the method-of-moments implementation of the magnetic-field integral equation, are frequently used to solve Maxwell's equations on the surfaces of electromagnetic scatterers. These electromagnetic surface integral equations yield many code-verification challenges due to the various sources of numerical error and their possible interactions. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources. We demonstrate the effectiveness of these approaches for cases with and without coding errors.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

NASA NTRS1992

Turbulent reacting flow computations including turbulence-chemistry interactions

A two-equation (k-epsilon) turbulence model has been extended to be applicable for compressible reacting flows. A compressibility correction model based on modeling the dilatational terms in the Reynolds stress equations has been used. A turbulence-chemistry interaction model is outlined. In this model, the effects of temperature and species mass concentrations fluctuations on the species mass production rates are decoupled. The effect of temperature fluctuations is modeled via a moment model, and the effect of concentration fluctuations is included using an assumed beta-pdf model. Preliminary results obtained using this model are presented. A two-dimensional reacting mixing layer has been used as a test case. Computations are carried out using the Navier-Stokes solver SPARK using a finite rate chemistry model for hydrogen-air combustion.

Narayan, J. R.↗

DOE OSTI2026

A score-based diffusion model approach for adaptive learning of stochastic partial differential equation solutions

In this paper, we propose a novel framework for adaptively learning the time-evolving solutions of stochastic partial differential equations (SPDEs) using score-based diffusion models within a recursive Bayesian inference setting. SPDEs play a central role in modeling complex physical systems under uncertainty, but their numerical solutions often suffer from model errors and reduced accuracy due to incomplete physical knowledge and environmental variability. To address these challenges, we encode the governing physics into the score function of a diffusion model using simulation data and incorporate observational information via a likelihood-based correction in a reverse-time stochastic differential equation. This enables adaptive learning through iterative refinement of the solution as new data becomes available. To improve computational efficiency in high-dimensional settings, we introduce the ensemble score filter, a training-free approximation of the score function designed for real-time inference. Numerical experiments on benchmark SPDEs demonstrate the accuracy and robustness of the proposed method under sparse and noisy observations.

97 MATHEMATICS AND COMPUTING↗

NASA NTRS1977

Downstream boundary conditions for viscous flow problems

The problem of the specification of artificial outflow conditions in flow problems is studied. It is shown that for transport type equations incorrect outflow conditions will adversely affect the solution only in a small region near the outflow boundary, while for elliptic equations, e.g. those governing the streamfunction or pressure, a correct boundary specification is essential. In addition, integral outflow boundary conditions for fluid dynamical problems are considered. It is shown that such conditions are well posed, and their effect on the solutions of the Navier-Stokes equations is also considered.

Fix, G.↗

DOE OSTI2024

Manufactured solutions for an electromagnetic slot model

The accurate modeling of electromagnetic penetration is an important topic in computational electromagnetics. Electromagnetic penetration occurs through intentional or inadvertent openings in an otherwise closed electromagnetic scatterer, which prevent the contents from being fully shielded from external fields. To efficiently model electromagnetic penetration, aperture or slot models can be used with surface integral equations to solve Maxwell's equations. A necessary step towards establishing the credibility of these models is to assess the correctness of the implementation of the underlying numerical methods through code verification. Surface integral equations and slot models yield multiple interacting sources of numerical error and other challenges, which render traditional code-verification approaches ineffective. In this paper, we provide approaches to separately measure the numerical errors arising from these different error sources for the method-of-moments implementation of the electric-field integral equation with a slot model. Finally, we demonstrate the effectiveness of these approaches for a variety of cases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗