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At least 1,117 records · Page 62

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NASA NTRS2003

Protoplanetary Nebula Evolution using the Beta Viscosity Model

The evolutionary dynamics of a protoplanetary disk is an important component of the planet formation process. In particular, the dynamic and thermodynamic field plays a critical role in chemical evolution, the migration of dust particles in the nebula, and the radial transport of meteoritic components. The dynamic evolution is investigated using analytical solutions of the surface density transport equations using a turbulence model based on hydrodynamic generation of turbulence. It captures the major properties of the disk including region of separation between radial inflow and-outflow and the evolution of the central plane temperature. The analytical formulas are compared with available numerical solutions based on the alpha viscosity model. The beta viscosity model, heretofore used for steady-state disks, is shown to be a useful approximation for unsteady problems.

Davis, Sanford S.↗

DOE OSTI2021

Charge Transport and Space-Charge Formation in Cd 1 - x Zn x Te 1 - y Se y Radiation Detectors

The electron- and hole-transport properties in cadmium zinc telluride selenide (CZTS) crystals are studied using a laser-induced transient-current technique with pulsed and dc bias. The internal electric field profile and velocity of surface recombination are determined by Monte Carlo simulations of electron and hole transient currents combined with a numerical solution of the drift-diffusion equation coupled with Poisson’s equation. Electron and hole drift mobilities of μe = 830 cm 2 /Vs and μh = 40 cm 2 /Vs, respectively, are determined. We also develop a simple technique for evaluating surface recombination directly from measured current waveforms without the need for numerical simulation. The good quality of the prepared detector at pulsed bias, with electron- and hole-mobility-lifetime products of (μτ)e = 1.9 × 10 -3 cm 2 /V and (μτ)h = 1.4 × 10 -4 cm 2 /V, respectively, are observed. The formation of a positive space charge, originating from hole injection combined with a recombination level, is found. We observe a significant position dependence of the lifetime of electrons and holes in dc bias due to hole injection. The experiment is successfully fitted by a simple model dominated by a single deep recombination level with an energy of E t =E C -0.73eV; concentration of 7.3 × 10 11 cm -3 ; and electron- and hole-capture cross sections of 3.5 × 10 -14 cm 2 and 6.5 × 10 -14 cm 2 , respectively.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

NASA NTRS1979

Direct control of the grid point distribution in meshes generated by elliptic equations

The generation of computational grids suitable for obtaining accurate numerical solutions to the three-dimensional Navier-Stokes equations is the subject of intensive research. For a wide class of nozzle configurations, a three-dimensional grid can be constructed by a sequence of two-dimensional grids in successive cross-sectional planes. The present paper is concerned with numerical generation of two-dimensional grids. An effective method of interior grid control is presented based on a modified elliptic system containing free parameters. For a simply connected region, the free parameters are computed from the Dirichlet boundary values. The resulting interior grid point distribution is controlled entirely by a priori selection of the grid point distribution along the boundaries of the section.

Middlecoff, J. F.↗

NASA NTRS1980

A Navier-Stokes fast solver for turbulence modeling applications

A computer code for the evaluation and/or optimization of the predicative potential of second order turbulent closure models in simple two dimensional flow configurations is discussed. A procedure for the numerical solution of the steady constant property Navier-Stokes equations are described together with algebraic, one dimensional and two dimensional equations of turbulence closure models. Four turbulence models are compared with several sets of experimental data. The effects of initial conditions and boundary conditions are also described. The effects of purely numerical parameters, such as mesh size, boundary locations, and convergence criteria are presented.

Murphy, J. D.↗

NASA NTRS2000

Prediction of Sound Waves Propagating Through a Nozzle Without/With a Shock Wave Using the Space-Time CE/SE Method

The benchmark problems in Category 1 (Internal Propagation) of the third Computational Aeroacoustics (CAA) Work-shop sponsored by NASA Glenn Research Center are solved using the space-time conservation element and solution element (CE/SE) method. The first problem addresses the propagation of sound waves through a nearly choked transonic nozzle. The second one concerns shock-sound interaction in a supersonic nozzle. A quasi one-dimension CE/SE Euler solver for a nonuniform mesh is developed and employed to solve both problems. Numerical solutions are compared with the analytical solution for both problems. It is demonstrated that the CE/SE method is capable of solving aeroacoustic problems with/without shock waves in a simple way. Furthermore, the simple nonreflecting boundary condition used in the CE/SE method which is not based on the characteristic theory works very well.

Wang, Xiao-Yen↗

NASA NTRS1984

Rocket injector anomalies study. Volume 1: Description of the mathematical model and solution procedure

The capability of simulating three dimensional two phase reactive flows with combustion in the liquid fuelled rocket engines is demonstrated. This was accomplished by modifying an existing three dimensional computer program (REFLAN3D) with Eulerian Lagrangian approach to simulate two phase spray flow, evaporation and combustion. The modified code is referred as REFLAN3D-SPRAY. The mathematical formulation of the fluid flow, heat transfer, combustion and two phase flow interaction of the numerical solution procedure, boundary conditions and their treatment are described.

Przekwas, A. J.↗

NASA NTRS1986

Solution of elliptic partial differential equations by fast Poisson solvers using a local relaxation factor. 2: Two-step method

A two-step semidirect procedure is developed to accelerate the one-step procedure described in NASA TP-2529. For a set of constant coefficient model problems, the acceleration factor increases from 1 to 2 as the one-step procedure convergence rate decreases from + infinity to 0. It is also shown numerically that the two-step procedure can substantially accelerate the convergence of the numerical solution of many partial differential equations (PDE's) with variable coefficients.

Chang, S. C.↗

NASA NTRS1985

Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

In the optimal linear quadratic regulator problem for finite dimensional systems, the method known as an alpha-shift can be used to produce a closed-loop system whose spectrum lies to the left of some specified vertical line; that is, a closed-loop system with a prescribed degree of stability. This paper treats the extension of the alpha-shift to hereditary systems. As infinite dimensions, the shift can be accomplished by adding alpha times the identity to the open-loop semigroup generator and then solving an optimal regulator problem. However, this approach does not work with a new approximation scheme for hereditary control problems recently developed by Kappel and Salamon. Since this scheme is among the best to date for the numerical solution of the linear regulator problem for hereditary systems, an alternative method for shifting the closed-loop spectrum is needed. An alpha-shift technique that can be used with the Kappel-Salamon approximation scheme is developed. Both the continuous-time and discrete-time problems are considered. A numerical example which demonstrates the feasibility of the method is included.

Gibson, J. S.↗

NASA NTRS1987

Shifting the closed-loop spectrum in the optimal linear quadratic regulator problem for hereditary systems

Gibson, J. S.↗

NASA NTRS2017

Fast Optimization for Aircraft Descent and Approach Trajectory

We address problem of on-line scheduling of the aircraft descent and approach trajectory. We formulate a general multiphase optimal control problem for optimization of the descent trajectory and review available methods of its solution. We develop a fast algorithm for solution of this problem using two key components: (i) fast inference of the dynamical and control variables of the descending trajectory from the low dimensional flight profile data and (ii) efficient local search for the resulting reduced dimensionality non-linear optimization problem. We compare the performance of the proposed algorithm with numerical solution obtained using optimal control toolbox General Pseudospectral Optimal Control Software. We present results of the solution of the scheduling problem for aircraft descent using novel fast algorithm and discuss its future applications.

Luchinsky, Dmitry G.↗

NASA NTRS1977

Reynolds number effects on shock-wave turbulent boundary-layer interactions - A comparison of numerical and experimental results

An experiment is described that tests and guides computations of a shock-wave turbulent boundary-layer interaction flow over a 20-deg compression corner at Mach 2.85. Numerical solutions of the time-averaged Navier-Stokes equations for the entire flow field, employing various turbulence models, are compared with the data. Each model is critically evaluated by comparisons with the details of the experimental data. Experimental results for the extent of upstream pressure influence and separation location are compared with numerical predictions for a wide range of Reynolds numbers and shock-wave strengths.

Horstman, C. C.↗

NASA NTRS1983

Beam area determination for multiple-beam satellite communication applications

An exact analytical model and a simple numerical solution are presented for determining the surface area of the earth illuminated by a conical beam, with an elliptical cross section, emanating from a satellite. The model is used to generate sets of parametric curves for determination of the beam area as a function of the different satellite locations, beam locations, and beamwidths. Numerical results show that for a circular beam with a 0.25 deg beamwidth, the beam illuminating the northern Continental United States (CONUS) can cover an area about five times larger than the area covered by the same size beam illuminating the southern CONUS. Comparisons are also made with the available approximate methods.

Salmasi, A. B.↗

NASA NTRS1983

Optimal symmetric flight with an intermediate vehicle model

The present investigation is concerned with an examination of optimal symmetry flight on the basis of the intermediate vehicle model. The analysis is partly based upon an exploration of Euler solutions for the path-angle-as-control model carried out by Kelley (1958). The current analysis takes into account higher-order optimality conditions and 'chattering-control' phenomena. Attention is given to details regarding the intermediate vehicle model, the Legendre-Clebsch necessary condition, the conjugate-point test, and the numerical solution of the time-range problem. It is found that the flight path angle takes on the role of control variable in the model. From physical considerations, it can be seen that when a positive margin of thrust over drag exists, the maximum-range climb trajectory without time or fuel constraints has no proper maximum nor an upper bound.

Kelley, H. J.↗

NASA NTRS1983

Optimal symmetric flight with an intermediate vehicle model

The present investigation is concerned with an examination of optimal symmetry flight on the basis of the intermediate vehicle model. The analysis is partly based upon an exploration of Euler solutions for the path-angle-as-control model carried out by Kelley (1958). The current analysis takes into account higher-order optimality conditions and "chattering-control' phenomena. Attention is given to details regarding the intermediate vehicle model, the Legendre-Clebsch necessary condition, the conjugate-point test, and the numerical solution of the time-range problem. It is found that the flight path angle takes on the role of control variable in the model. From physical considerations, it can be seen that when a positive margin of thrust over drag exists, the maximum-range climb trajectory without time or fuel constraints has no proper maximum nor an upper bound.

Menon, P. K. A.↗

NASA NTRS1988

A forward method for optimal stochastic nonlinear and adaptive control

A computational approach is taken to solve the optimal nonlinear stochastic control problem. The approach is to systematically solve the stochastic dynamic programming equations forward in time, using a nested stochastic approximation technique. Although computationally intensive, this provides a straightforward numerical solution for this class of problems and provides an alternative to the usual dimensionality problem associated with solving the dynamic programming equations backward in time. It is shown that the cost degrades monotonically as the complexity of the algorithm is reduced. This provides a strategy for suboptimal control with clear performance/computation tradeoffs. A numerical study focusing on a generic optimal stochastic adaptive control example is included to demonstrate the feasibility of the method.

Bayard, David S.↗

NASA NTRS1991

A two-dimensional Euler solution for an unbladed jet engine configuration

A two dimensional nonaxisymmetric Euler solution in a geometric representation of a jet engine configuration without blades is presented. The domain, including internal and external flow, is covered with a multiblock grid. To construct the grid, a domain decomposition technique is used to subdivide the domain and smooth grids are dimensioned and placed in each block. The grid contains 44 blocks which cover the external field, the inlet, bypass duct, core duct and nozzle of the nonaxisymmetric engine configuration. The geometry is symmetric about the meanline of the hub, but the grid is not since there is no symmetry condition applied to the grid between the two halves. With a symmetric grid at zero angle of attack, the measures of the solution would cancel exactly. With an asymmetric grid, the solution will not necessarily be symmetric and the lift coefficient will not necessarily be zero. Thus, grid asymmetry can be exploited to verify the resolution of the solution. The solution may be verified on the basis of five theoretical quantities: conservation of mass and energy, deviation of the lift coefficient from zero, deviation of the drag coefficient from zero, deviations from constant entropy, and deviations in the pressure distributions over the symmetric surfaces of the components. This technique is suitable for obtaining numerical solutions in complex geometries and provides a foundation for complete engine throughflow calculations.

Stewart, Mark E. M.↗

NASA NTRS2000

Conditioning of the Stable, Discrete-time Lyapunov Operator

The Schatten p-norm condition of the discrete-time Lyapunov operator L(sub A) defined on matrices P is identical with R(sup n X n) by L(sub A) P is identical with P - APA(sup T) is studied for stable matrices A is a member of R(sup n X n). Bounds are obtained for the norm of L(sub A) and its inverse that depend on the spectrum, singular values and radius of stability of A. Since the solution P of the the discrete-time algebraic Lyapunov equation (DALE) L(sub A)P = Q can be ill-conditioned only when either L(sub A) or Q is ill-conditioned, these bounds are useful in determining whether P admits a low-rank approximation, which is important in the numerical solution of the DALE for large n.

Tippett, Michael K.↗

DOE OSTI2021

Machine Learning for Conservative-to-Primitive in Relativistic Hydrodynamics

The numerical solution of relativistic hydrodynamics equations in conservative form requires root-finding algorithms that invert the conservative-to-primitive variables map. These algorithms employ the equation of state of the fluid and can be computationally demanding for applications involving sophisticated microphysics models, such as those required to calculate accurate gravitational wave signals in numerical relativity simulations of binary neutron stars. This work explores the use of machine learning methods to speed up the recovery of primitives in relativistic hydrodynamics. Artificial neural networks are trained to replace either the interpolations of a tabulated equation of state or directly the conservative-to-primitive map. The application of these neural networks to simple benchmark problems shows that both approaches improve over traditional root finders with tabular equation-of-state and multi-dimensional interpolations. In particular, the neural networks for the conservative-to-primitive map accelerate the variable recovery by more than an order of magnitude over standard methods while maintaining accuracy. Neural networks are thus an interesting option to improve the speed and robustness of relativistic hydrodynamics algorithms.

79 ASTRONOMY AND ASTROPHYSICS↗