Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “solve time”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 217 records · Page 12

Synthesis of data obtained at Jicamarca, Peru, during the September 11, 1969, eclipse.

Results of continuous measurements of electron temperatures, electron concentrations, and vertical plasma drift made at Jicamarca during the Sept. 11, 1969, solar eclipse and of control measurements made on Sept. 13, 1969. Synthesis of the observed electron concentrations was made, using a model that solved the time-dependent electron-ion continuity equations. Ions O(-), NO(+), O2(+), and N2(+) were treated. Physical and chemical processes pertinent to the F region were considered in a realistic way. At noon, 300 km above Jicamarca, the values q = 290 per cu cm per sec for the O(+) production rate, beta = 1.94 x 0.0001 per sec for the loss coefficient, and H = 59 km for the atomic oxygen scale height were obtained. All large-scale features observed in the F2 region were synthesized by the model. This synthesis was not sensitive to a simultaneous 30% reduction of q and beta.

Sterling, D. L.↗

Synthesis of Jicamarca data during the great storm of March 8, 1970.

Continuous measurement of electron temperature and electron concentration during the great magnetic storm of Mar. 8, 1970, when the F2 peak rose as high as 800 km. Continuous measurements of the vertical component of E x B drift were made from 1130 to 1730 LT. A synthesis of the observed electron concentrations was made using a model that solved the time-dependent electron-ion continuity equation for O(+) and the molecular ions; the latter chemistry was included to improve the solutions at lower heights. It was found, using the observed values of vertical drift, that most of the observed features of the F2-region ionosphere were synthesized by the model. An interpretation of the synthesis that emphasizes the importance of horizontal diffusion at the equator is given. Observations are presented for Mar. 7, 8, and 9, 1970, including the Huancayo magnetograms, which display a close correlation with the drift measurements.

Woodman, R. F.↗

Role of gas-surface interactions in the reduction of OGO 6 neutral-particle mass spectrometer data

Data obtained with the quadrupole mass spectrometer aboard the OGO 6 satellite show the effects of significant surface interaction processes, including nearly complete recombination of incoming atomic oxygen on the walls of the instrument antechamber plus absorption and desorption of oxygen and carbon monoxide. The observed data are fit by solving the time-dependent continuity equations accounting for production and loss of atomic oxygen, molecular oxygen, and (in the case of mass 28) carbon monoxide. The surface parameters that best fit the data are selected and applied to the determination of ambient densities and their estimated errors.

Hedin, A. E.↗

Role of gas-surface interactions in the reduction of Ogo 6 neutral particle mass spectrometer data.

Data obtained with the quadrupole mass spectrometer aboard the Ogo 6 satellite show the effects of significant surface interaction processes, including nearly complete recombination of incoming atomic oxygen on the walls of the instrument antechamber plus adsorption and desorption of oxygen and carbon monoxide. The observed data are fit by solving the time-dependent continuity equations accounting for production and loss of atomic oxygen, molecular oxygen, and (in the case of mass 28) carbon monoxide. The surface parameters that best fit the data are selected and applied to the determination of ambient densities and their estimated errors.

Hedin, A. E.↗

Theoretical model of vertical distributions of CO and CH4 in the mesosphere and upper stratosphere.

Carbon compounds (CO and CO2) and methane are added to an existing computer program (Shimazaki and Laird, 1970, 1972), which calculates diurnal variations in density distributions of pure oxygen compounds, hydrogen compounds, and nitrogen compounds. For the present model calculations, the original program was modified to calculate the steady-state profiles for all constituents, and then these solutions were used as the initial condition for solving the time-dependent equations. The effects of chemical reactions and vertical eddy diffusion transport on the CH4 and CO concentrations above 40 km, where one-dimensional treatment may not be too inappropriate, are discussed. Some of the 15 constituents included in the computer program interact with CO and CH4 chemically, and CH4 is more sensitive to the eddy diffusion coefficient than any other constituent. Therefore it is easier to determine the most appropriate profile of the eddy diffusion coefficient by comparing the model profile with the observations for CH4.

Shimazaki, T.↗

On the shock-on-shock interaction problem

The unsteady, inviscid flowfield that results when a supersonic vehicle strikes a planar oblique shock wave, though difficult to simulate experimentally, is quite easy to model and compute numerically. The complicated flowfield, which contains multiple shock wave interactions, is determined using a second-order, shock-capturing, finite-difference approach which solves the time-dependent Euler equations under a self-similar transformation. A series of numerical results for a simple two-dimensional wedge is presented which describes the entire disturbed region, including the wave structure, and shows good agreement with the available two- and three-dimensional experimental data.-

Kutler, P.↗

Recent computation of viscous effects in transonic flow

The paper describes some improvements to a method of solving the time-dependent Reynolds-averaged Navier-Stokes equations for two-dimensional compressible flows for describing the coupling between viscous and inviscid regions in transonic flows. Mesh patching is implemented at the sublayer-boundary layer interfaces and the boundary layer-inviscid flow interface. Mesh stretching is geometric and is small in regions of large gradients and large in regions of small gradients, thus preserving second-order accuracy. Mesh lines are arranged so as to accommodate MacCormack's rapid solver for hyperbolic systems and a wider class of turbulent transport models. Results of computations of transonic flows over lifting airfoils are compared with experimental data and other solutions.

Deiwert, G. S.↗

Nitramine smokeless propellant research

A transient ballistics and combustion model is derived to represent the closed vessel experiment that is widely used to characterize propellants. A computer program is developed to solve the time-dependent equations, and is applied to explain aspects of closed vessel behavior. In the case of nitramine propellants the cratering of the burning surface associated with combustion above break-point pressures augments the effective burning rate as deduced from the closed vessel experiment. Low pressure combustion is significantly affected by the ignition process and, in the case of nitramine propellants, by the developing and changing surface structure. Thus, burning rates deduced from the closed vessel experiment may or may not agree with those measured in the equilibrium strand burner. Series of T burner experiments are performed to compare the combustion instability characteristics of nitramine (HMX) containing propellants and ammonium perchlorate (AP)propellants. Although ash produced by more fuel rich propellants could have provided mechanical suppression, results from clean-burning propellants permit the conclusion that HMX reduces the acoustic driving.

Cohen, N. S.↗

Steady and unsteady transonic flow

An investigation of the transonic flow over a circular arc airfoil was conducted to obtain basic information for turbulence modeling of shock-induced separated flows and to verify numerical computer codes which are being developed to simulate such flows. The investigation included the employment of a laser velocimeter to obtain data concerning the mean velocity, the shear stress, and the turbulent kinetic energy profiles in the flowfield downstream of the airfoil midchord where the flow features are more complex. Depending on the free-stream Mach number, the flowfield developed was either steady with shock-wave-induced separation extending from the foot of the shock wave to beyond the trailing edge or unsteady with a periodic motion also undergoing shock-induced separation. The experimental data were compared with the results of numerical simulations in which a computer code was employed that solved the time-dependent Reynolds' averaged compressible Navier-Stokes equations.

Seegmiller, H. L.↗

Numerical solution of supersonic laminar flow over an inclined body of revolution

A mixed explicit-implicit scheme is used to solve the time-dependent thin-layer approximation of the Navier-Stokes equations for a supersonic laminar flow over an inclined body of revolution. Test cases for Mach 2.8 flow over a cylinder with 15 deg flare angle at angles of attack of 0, 1, and 4 deg are calculated. Good agreement is obtained between the present computed results and experimental measurements of surface pressure. A pair of vortices on the leeward and a peak in the normal force distribution near the flared juncture are predicted; the role of circumferential communication is discussed.

Hung, C. M.↗

Documentation of the Fourth Order Band Model

A general circulation model is presented which uses quadratically conservative, fourth order horizontal space differences on an unstaggered grid and second order vertical space differences with a forward-backward or a smooth leap frog time scheme to solve the primitive equations of motion. The dynamic equations for motion, finite difference equations, a discussion of the structure and flow chart of the program code, a program listing, and three relevent papers are given.

Kalnay-Rivas, E.↗

Program of research in severe storms

Two modeling areas, the development of a mesoscale chemistry-meteorology interaction model, and the development of a combined urban chemical kinetics-transport model are examined. The problems associated with developing a three dimensional combined meteorological-chemical kinetics computer program package are defined. A similar three dimensional hydrostatic real time model which solves the fundamental Navier-Stokes equations for nonviscous flow is described. An urban air quality simulation model, developed to predict the temporal and spatial distribution of reactive and nonreactive gases in and around an urban area and to support a remote sensor evaluation program is reported.

Source record↗

Application of a Galerkin finite element method to atmospheric transport problems

Numerical simulation of the movement of a contaminant within the atmosphere presents difficulties due to the multidimensionality of the problem and the fact that the horizontal transport is usually convection dominated, that the boundary conditions are mixed, and that both slow and fast atmospheric chemical reactions can be important. In this study, numerical experiments using a Crank-Nicolson Galerkin finite element method to solve the time-dependent partial differential equations demonstrate the applicability and accuracy of this method for the variety of conditions encountered in atmospheric pollutant modeling. The Crank-Nicolson Galerkin method using piecewise linear, piecewise cubic Hermite polynomials, and upwind finite elements is shown to accurately model the pure convection of initial wave forms. Numerical results studying the interactions of convection, diffusion, chemical reaction, pollutant removal, and the effects of contaminant emission source strength, source location and multiple sources are also presented.

Carmichael, G. R.↗

Feedback laws for fuel minimization for transport aircraft

The Theoretical Mechanics Branch has as one of its long-range goals to work toward solving real-time trajectory optimization problems on board an aircraft. This is a generic problem that has application to all aspects of aviation from general aviation through commercial to military. Overall interest is in the generic problem, but specific problems to achieve concrete results are examined. The problem is to develop control laws that generate approximately optimal trajectories with respect to some criteria such as minimum time, minimum fuel, or some combination of the two. These laws must be simple enough to be implemented on a computer that is flown on board an aircraft, which implies a major simplification from the two point boundary value problem generated by a standard trajectory optimization problem. In addition, the control laws allow for changes in end conditions during the flight, and changes in weather along a planned flight path. Therefore, a feedback control law that generates commands based on the current state rather than a precomputed open-loop control law is desired. This requirement, along with the need for order reduction, argues for the application of singular perturbation techniques.

Price, D. B.↗

Theoretcial studies of solar-pumped lasers

A method of pumping a COhZ laser by a hot cavity was demonstrated. The cavity, heated by solar radiation, should increase the efficiency of solar pumped lasers used for energy conversion. Kinetic modeling is used to examine the behavior of such a COhZ laser. The kinetic equations are solved numerically vs. time and, in addition, steady state solutions are obtained analytically. The effect of gas heating filling the lower laser level is included. The output power and laser efficiency are obtained as functions of black body temperature and gas ratios (COhZ-He-Ar) and pressures. The values are compared with experimental results.

Harries, W. L.↗

A spectral numerical method for the Navier-Stokes equations with applications to Taylor-Couette flow

A new spectral method for solving the incompressible Navier-Stokes equations in a plane channel and between concentric cylinders is presented. The method uses spectral expansions which inherently satisfy the boundary conditions and the continuity equation and yield banded matrices which are efficiently solved at each time step. In addition, the number of dependent variables is reduced, resulting in a reduction in computer memory requirements. Several test problems have been computed for the channel flow and for flow between concentric cylinders, including Taylor-Couette flow with axisymmetric Taylor vortices and wavy vortices. In all cases, agreement with available experimental and theoretical results is very good.

Moser, R. D.↗

Resonant absorption of phase-mixed Alfven surface waves in ideal and resistive magnetohydrodynamics - Initial-value problem

An initial-value approach to the study of Alfven surface waves, in which the linearized MHD equations are solved numerically in time and space, is considered. A disturbance of a particular wavelength is excited in a nonuniform plasma and its temporal evolution is simulated with numerical solutions of the ideal and resistive MHD equations in slab geometry. This procedure generates a continuous spectrum and therefore simulates phase-mixing and subsequent resonant absorption. Energy in the phase-mixed surface waves resistively dissipates with the absorption time and width scaling as resistivity to the -1/3 and 1/6 powers, respectively.

Steinolfson, R. S.↗