Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “numerical computation”

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 361 records · Page 20
All sourcesNASA NTRSDOE OSTI
NASA NTRS1979

Boundary conditions for exterior acoustic problems

Problems of acoustics are generally posed in unbounded regions. Numerical computations require that the infinite regions be truncated with artificial finite boundaries. Boundary conditions must be developed at these artificial boundaries which approximate the conditions for outgoing waves. These conditions should be asymptotic in the distance of the boundaries from the source terms and should give rise to well posed problems interior to fairly arbitrary regions, which can be chosen on the basis of computational efficiency rather than for mathematical (i.e., well posedness) reasons. A family of such conditions is presented and their properties are discussed. These conditions can be thought of as extensions of the Sommerfeld radiation condition for outgoing waves.

Bayliss, A.↗
NASA NTRS1980

Interaction between a normal shock wave and a turbulent boundary layer at high transonic speeds. II - Wall shear stress

Asymptotic methods are used to calculate the shear stress at the wall for the interaction between a normal shock wave and a turbulent boundary layer on a flat plate. A mixing length model is used for the eddy viscosity. The shock wave is taken to be strong enough that the sonic line is deep in the boundary layer and the upstream influence is thus very small. It is shown that unlike the result found for laminar flow an asymptotic criterion for separation is not found; however, conditions for incipient separation are computed numerically using the derived solution for the shear stress at the wall. Results are compared with available experimental measurements.

Liou, M. S.↗
NASA NTRS1979

A kinetic approach to compressible turbulence

A kinetic theory of strong turbulence is developed by decomposing fluctuation of distribution function into scaled components, or ranks, to represent three transport processes: macroscopic evolution, transport property and relaxation. Closure is obtained by formulating a relaxation process for the approach of eddy diffusivity to equilibrium. The kinetic equation is solved and three transport functions of turbulence in adiabatic gas are derived: two transfer functions describe turbulent mode transfer, and a coupling function describes the build-up of kinetic energy at the expense of internal energy. The energy balance in the inertial subrange of homogeneous and isotropic turbulence in an adiabatic gas yields a k to the -3rd law, in agreement with numerical computations from one dimensional model of compressible turbulence.

Tchen, C. M.↗
NASA NTRS1981

Impulsive phase of solar flares. 1: Characteristics of high energy electrons

The variation along a magnetic field line of the energy and pitch angle distribution of high energy electrons injected into a cold hydrogen plasma containing either an open or closed magnetic field structure was investigated. The problem is formulated as a time independent Fokker-Planck Equation for the electron number distribution as a function of the electron energy, electron pitch angle, and the structure of the global magnetic field. Simple analytic solution valid in the small pitch angle regime and for slowly varying magnetic field is presented. For the more general situation a numerical code for solving the Fokker-Planck Equation was used and it was found that the analytic expression agrees well with the numerical results to values of the pitch angle much larger than expected. For most practical applications, one many confidently use the analytic expression instead of having to resort to lengthy numerical computations. These results are useful in the study of the nonthermal models of the impulsive phase of solar flares.

Leach, J.↗
NASA NTRS1981

Compressible turbulent boundary layer interaction experiments

Four phases of research results are reported: (1) experiments on the compressible turbulent boundary layer flow in a streamwise corner; (2) the two dimensional (2D) interaction of incident shock waves with a compressible turbulent boundary layer; (3) three dimensional (3D) shock/boundary layer interactions; and (4) cooperative experiments at Princeton and numerical computations at NASA-Ames.

Settles, G. S.↗
NASA NTRS1981

Simple approximations for the asymptotic description of the interaction between a normal shock wave and a turbulent boundary layer at transonic speeds

The asymptotic description of the interaction between a normal shock wave and a turbulent boundary layer is reviewed. The layers necessary in a rational analysis of the interaction are discussed with emphasis on the differences from an interaction with a laminar boundary layer, the uncoupling of solutions for the distribution of pressure and skin friction at the wall, and the role of the Reynolds shear stress in these solutions. The accuracy of asymptotic solutions in flows at Reynolds numbers of technical interest is discussed. Solutions for the distribution of pressure and skin friction at the wall and the shape of the shock are considered for the case where the flow is near separation. For the pressure and skin friction, it is possible to write two simplified partial solutions, one valid at the beginning of the interaction and one valid somewhat downstream of the shock wave. A solution composed of these two parts and a linear interpolation between them appears to give good comparison with experiment; one unknown constant, independent of the parameters of the interaction, must be found from experiment. The simplified relations are presented. Comparison of numerical computations with experimental data indicates a possible value for the constant and shows quite satisfactory results.

Adamson, T. C., Jr.↗
NASA NTRS1981

Flight experiments with a slender cone at angle of attack

The three-dimensional leeward separation about a 5 deg semi-angle cone at an 11 deg angle of attack was investigated in flight, in the wind tunnel, and by numerical computations. The test conditions were Mach numbers of 0.6, 1.5, and 1.8 at Reynolds numbers between 7 and 10 million based on free-stream conditions and a 30-inch wetted length or surface. The surface conditions measured included mean static and fluctuating pressures; skin friction magnitudes and separation line positions were obtained using obstacle blocks. The mean static pressures from flight and wind tunnel were in good agreement. The computed results gave the same distributions, but were slightly more positive in magnitude. The experimentally measured primary and secondary separation line locations compared closely with computed results. There were substantial differences in level and in trend between the surface root-mean-square pressure fluctuations obtained in flight and in the wind tunnel, due, it is thought, to a relatively high acoustic disturbance level in the tunnel compared with the quiescent conditions in flight.

Peake, D. J.↗
NASA NTRS1981

Closed coronal structures. II - Generalized hydrostatic model

Numerical computations of stationary solar coronal loop atmospheres are used to extend earlier analytical work. Two classes of loops are examined, namely symmetric loops with a temperature maximum at the top but now having a length greater than the pressure scale height and loops which have a local temperature minimum at the top. For the first class, new scaling laws are found which relate the base pressure and loop length to the base heating, the heating deposition scale height, and the pressure scale height. It is found that loops for which the length is greater than about two to three times the pressure scale height do not have stable solutions unless they have a temperature minimum at the top. Computed models with a temperature inversion at the top are permitted in a wider range of heating deposition scale height values than are loops with a temperature maximum at the top. These results are discussed in relation to observations showing a dependence of prominence formation and stability on the state of evolution of magnetic structures, and a general scenario is suggested for the understanding of loop evolution from emergence in active regions through the large-scale structure phase to opening in coronal holes.

Serio, S.↗
NASA NTRS1980

Sound field near the edge of a liner in uniform flow

The classical concept of energy flux in sound propagation in a uniform medium without flow was extended to sound propagation with mean flow. A simple case of constant velocity mean flow is discussed for a two-dimensional duct with constant cross-section and a liner of finite length. Results do not show acoustic energy conservation and it is concluded that the liner converts flow energy into acoustic energy. It is important that results do not take into consideration nonlinear terms which are usually considered responsible for sound generation. Numerical computations estimated orders of magnitude and confirm the conclusions.

Moehring, W.↗
NASA NTRS1981

Prediction of swirling reacting flow in ramjet combustors

Numerical computations have been undertaken for a basic two-dimensional axisymmetric flowfield which is similar to that found in conventional gas turbine and ramjet combustors. A swirling flow enters a larger chamber via a sudden or gradual expansion. The calculation method involves a staggered grid system for axial and radial velocities, a line relaxation procedure for efficient solution of the equations, a two-equation turbulence energy-turbulence dissipation rate turbulence model, a stairstep boundary representation of the expansion flow, and realistic accommodation of swirl effects. The results include recirculation zone characterization and predicted mean streamline patterns. Predictions with and without chemical reaction are obtained. An associated isothermal experimental flow study is providing a useful data base. Successful outcomes of the work can be incorporated into the more combustion- and hardware-oriented activities of industrial concerns.

Lilley, D. G.↗
NASA NTRS1951

An Empirical Method Permitting Rapid Determination of the Area, Rate and Distribution of Water-Drop Impingement on an Airfoil of Arbitrary Section at Subsonic Speeds

An empirical method for the determination of the area, rate, and distribution of water-drop impingement on airfoils of arbitrary section is presented. The procedure represents an initial step toward the development of a method which is generally applicable in the design of thermal ice-prevention equipment for airplane wing and tail surfaces. Results given by the proposed empirical method are expected to be sufficiently accurate for the purpose of heated-wing design, and can be obtained from a few numerical computations once the velocity distribution over the airfoil has been determined. The empirical method presented for incompressible flow is based on results of extensive water-drop. trajectory computations for five airfoil cases which consisted of 15-percent-thick airfoils encompassing a moderate lift-coefficient range. The differential equations pertaining to the paths of the drops were solved by a differential analyzer. The method developed for incompressible flow is extended to the calculation of area and rate of impingement on straight wings in subsonic compressible flow to indicate the probable effects of compressibility for airfoils at low subsonic Mach numbers.

Bergrun, N. R.↗
NASA NTRS1982

On the application and extension of Harten's high resolution scheme

Extensions of a second order high resolution explicit method for the numerical computation of weak solutions of one dimensonal hyperbolic conservation laws are discussed. The main objectives were (1) to examine the shock resoluton of Harten's method for a two dimensional shock reflection problem, (2) to study the use of a high resolution scheme as a post-processor to an approximate steady state solution, and (3) to construct an implicit in the delta-form using Harten's scheme for the explicit operator and a simplified iteration matrix for the implicit operator.

Yee, H. C.↗
NASA NTRS1982

Turbine endwall single cylinder program

Detailed measurement of the flow field in front of a large-scale single cylinder, mounted in a wind tunnel is discussed. A better understanding of the three dimensional separation occuring in front of the cylinder on the endwall, and of the vortex system that is formed is sought. A data base with which to check analytical and numerical computer models of three dimensional flows is also anticipated.

Langston, L. S.↗
NASA NTRS1981

On the prediction of swirling flowfields found in axisymmetric combustor geometries

The paper reports research restricted to steady turbulence flow in axisymmetric geometries under low speed and nonreacting conditions. Numerical computations are performed for a basic two-dimensional axisymmetrical flow field similar to that found in a conventional gas turbine combustor. Calculations include a stairstep boundary representation of the expansion flow, a conventional k-epsilon turbulence model and realistic accomodation of swirl effects. A preliminary evaluation of the accuracy of computed flowfields is accomplished by comparisons with flow visualizations using neutrally-buoyant helium-filled soap bubbles as tracer particles. Comparisons of calculated results show good agreement, and it is found that a problem in swirling flows is the accuracy with which the sizes and shapes of the recirculation zones may be predicted, which may be attributed to the quality of the turbulence model.

Rhode, D. L.↗
NASA NTRS1981

Absorption and emission of extraordinary-mode electromagnetic waves near cyclotron frequency in nonequilibrium plasmas

An investigation is presented of two cases: (1) weakly relativistic electrons with a loss-cone type distribution, and (2) electrons with a drift velocity parallel to the ambient magnetic field. Numerical computations are given for physical parameters close to those in the polar region of the earth magnetosphere and laboratory experiments, with attention to the fast extraordinary-mode radiation whose frequency is near that of the electron cyclotron frequency. The fast extraordinary mode can escape from a strong field region to the weaker field region and may therefore be measured outside the plasma. It is found that the X mode radiation can be amplified by means of a cyclotron maser effect when the electrons have a loss-cone distribution, and it is concluded that, when the electron energy is sufficiently high, the X mode cutoff frequency may be lower than the cyclotron frequency.

Wu, C. S.↗
NASA NTRS1981

Thermonuclear processes on accreting neutron stars

Theoretical models for X-ray burst sources that invoke thermonuclear flashes on the surface layers of an accreting neutron star are discussed. The historical development of X-ray burst observation is summarized, and a physical picture of a neutron star undergoing accretion is drawn. Detailed numerical computations of the evolution of the surface layers of such a star are reviewed. The need for general relativistic corrections to the model is pointed out. Finally, comparisons are made with observations of X-ray bursts, the rapid burster, fast X-ray transients, X-ray pulsars, and gamma-ray burst sources.

Joss, P. C.↗
NASA NTRS1982

Manufacturing in space: Fluid dynamics numerical analysis

Numerical computations were performed for natural convection in circular enclosures under various conditions of acceleration. It was found that subcritical acceleration vectors applied in the direction of the temperature gradient will lead to an eventual state of rest regardless of the initial state of motion. Supercritical acceleration vectors will lead to the same steady state condition of motion regardless of the initial state of motion. Convection velocities were computed for acceleration vectors at various angles of the initial temperature gradient. The results for Rayleigh numbers of 1000 or less were found to closely follow Weinbaum's first order theory. Higher Rayleigh number results were shown to depart significantly from the first order theory. Supercritical behavior was confirmed for Rayleigh numbers greater than the known supercritical value of 9216. Response times were determined to provide an indication of the time required to change states of motion for the various cases considered.

Robertson, S. J.↗
NASA NTRS1982

Excited waves in shear layers

The generation of instability waves in free shear layers is investigated. The model assumes an infinitesimally thin shear layer shed from a semi-infinite plate which is exposed to sound excitation. The acoustical shear layer excitation by a source further away from the plate edge in the downstream direction is very weak while upstream from the plate edge the excitation is relatively efficient. A special solution is given for the source at the plate edge. The theory is then extended to two streams on both sides of the shear layer having different velocities and densities. Furthermore, the excitation of a shear layer in a channel is calculated. A reference quantity is found for the magnitude of the excited instability waves. For a comparison with measurements, numerical computations of the velocity field outside the shear layer were carried out.

Bechert, D. W.↗