Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Approximation methods”

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 1,387 records · Page 77

Simulation of charge exchange plasma propagation near an ion thruster propelled spacecraft

A model describing the charge exchange plasma and its propagation is discussed, along with a computer code based on the model. The geometry of an idealized spacecraft having an ion thruster is outlined, with attention given to the assumptions used in modeling the ion beam. Also presented is the distribution function describing charge exchange production. The barometric equation is used in relating the variation in plasma potential to the variation in plasma density. The numerical methods and approximations employed in the calculations are discussed, and comparisons are made between the computer simulation and experimental data. An analytical solution of a simple configuration is also used in verifying the model.

Robinson, R. S.↗

Numerical simulation of one-dimensional heat transfer in composite bodies with phase change

A numerical simulation was developed to investigate the one dimensional heat transfer occurring in a system composed of a layered aircraft blade having an ice deposit on its surface. The finite difference representation of the heat conduction equations was done using the Crank-Nicolson implicit finite difference formulation. The simulation considers uniform or time dependent heat sources, from heaters which can be either point sources or of finite thickness. For the ice water phase change, a numerical method which approximates the latent heat effect by a large heat capacity over a small temperature interval was applied. The simulation describes the temperature profiles within the various layers of the de-icer pad, as well as the movement of the ice water interface. The simulation could also be used to predict the one dimensional temperature profiles in any composite slab having different boundary conditions.

Dewitt, K. J.↗

Development of a locally mass flux conservative computer code for calculating 3-D viscous flow in turbomachines

The VANS successive approximation numerical method was extended to the computation of three dimensional, viscous, transonic flows in turbomachines. A cross-sectional computer code, which conserves mass flux at each point of the cross-sectional surface of computation was developed. In the VANS numerical method, the cross-sectional computation follows a blade-to-blade calculation. Numerical calculations were made for an axial annular turbine cascade and a transonic, centrifugal impeller with splitter vanes. The subsonic turbine cascade computation was generated in blade-to-blade surface to evaluate the accuracy of the blade-to-blade mode of marching. Calculated blade pressures at the hub, mid, and tip radii of the cascade agreed with corresponding measurements. The transonic impeller computation was conducted to test the newly developed locally mass flux conservative cross-sectional computer code. Both blade-to-blade and cross sectional modes of calculation were implemented for this problem. A triplet point shock structure was computed in the inducer region of the impeller. In addition, time-averaged shroud static pressures generally agreed with measured shroud pressures. It is concluded that the blade-to-blade computation produces a useful engineering flow field in regions of subsonic relative flow; and cross-sectional computation, with a locally mass flux conservative continuity equation, is required to compute the shock waves in regions of supersonic relative flow.

Walitt, L.↗

Scattering by ensembles of small particles experiment, theory and application

A hypothetical self consistent picture of evolution of prestellar intertellar dust through a comet phase leads to predictions about the composition of the circum-solar dust cloud. Scattering properties of thus resulting conglomerates with a bird's-nest type of structure are investigated using a micro-wave analogue technique. Approximate theoretical methods of general interest are developed which compared favorably with the experimental results. The principal features of scattering of visible radiation by zodiacal light particles are reasonably reproduced. A component which is suggestive of (ALPHA)-meteoroids is also predicted.

Gustafson, B. A. S.↗

Experimental and numerical studies of the incompressible viscous flow over a two-dimensional airfoil

Physical and numerical experiments for the low Reynolds number flow over a two-dimensional NACA 66(3)-018 airfoil have been performed. Pressure distributions and smoke flow photographs have been obtained for a Reynolds number based on airfoil chord and free-stream conditions of approximately 40,000 at angles of attack of 0 and 6 deg, and for a Reynolds number based on airfoil chord and free-stream conditions of approximately 400,000 at angles of attack of 0 and 12 deg in a low turbulence wind tunnel. Finite difference numerical experiments, using an approximate factorization method, have been obtained for a Reynolds number of 40,000 at angles of attack of 0 and 6 deg. Although the comparison of the wind tunnel and computer results is encouraging, further studies of this type are clearly necessary.

Mueller, T. J.↗

Discrete-time stability of continuous-time controller designs for large space structures

In most of the stable control designs for flexible structures, continuous time is assumed. However, in view of the implementation of the controllers by on-line digital computers, the discrete-time stability of such controllers is an important consideration. In the case of direct-velocity feedback (DVFB), involving negative feedback from collocated force actuators and velocity sensors, it is not immediately apparent how much delay due to digital implementation of DVFB can be tolerated without loss of stability. The present investigation is concerned with such questions. A study is conducted of the discrete-time stability of DVFB, taking into account an employment of Euler's method of approximation of the time derivative. The obtained result gives an indication of the acceptable time-step size for stable digital implementation of DVFB. A result derived in connection with the consideration of the discrete-time stability of stable continuous-time systems provides a general condition under which digital implementation of such a system will remain stable.

Balas, M. J.↗

An experimental heat-transfer investigation of an advanced winged entry vehicle at Mach 10

Heat-transfer measurements have been made at Mach 10 in air on an instrumented 0.006-scale model of an advanced winged entry vehicle. Data were obtained at 83 thermocouple stations which include locations on the lower and upper surface centerlines, spanwise positions along the lower and upper surfaces of the wing, the lower surface of the body flap, and radial locations on the fuselage. Data were obtained for angles of attack ranging from 0 to 45 deg, sideslip angles of + or - 2 deg, Reynolds numbers of 0.5, 1.0 and 2.0 million per foot, and body-flap deflections of 0, 10, and 20 deg. The data generally indicate increased windward heating and decreased leeside heating with increased angle of attack, significantly increased body-flap heating with deflection angle, and minor variations in heating with sideslip, increasing in magnitude with angle of attack. Windward centerline data are shown to be in fair agreement with results of predictions based on an approximate engineering method.

Wurster, K. E.↗

Kinematics of velocity and vorticity correlations in turbulent flow

The kinematic problem of calculating second-order velocity moments from given values of the vorticity covariance is examined. Integral representation formulas for second-order velocity moments in terms of the two-point vorticity correlation tensor are derived. The special relationships existing between velocity moments in isotropic turbulence are expressed in terms of the integral formulas yielding several kinematic constraints on the two-point vorticity correlation tensor in isotropic turbulence. Numerical evaluation of these constraints suggests that a Gaussian curve may be the only form of the longitudinal velocity correlation coefficient which is consistent with the requirement of isotropy. It is shown that if this is the case, then a family of exact solutions to the decay of isotropic turbulence may be obtained which contains Batchelor's final period solution as a special case. In addition, the computed results suggest a method of approximating the integral representation formulas in general turbulent shear flows.

Bernard, P. S.↗

Homogeneous crystal nucleation in binary metallic melts

A method for calculating the homogeneous crystal nucleation frequency in binary metallic melts is developed. The free energy of crystallization is derived from regular solution models for the liquid and solid and is used, together with model-based estimates of the interfacial tension, to calculate the nucleation frequency from the classical theory. The method can account for the composition dependence of the maximum undercooling observed in a number of experiments on small droplet dispersions. It can also be used to calculate the driving force for crystal growth and to obtain more precise estimates of the homogeneous crystal nucleation frequency in glass-forming alloys. This method, although approximate, is simple to apply, and requires only knowledge of the phase diagram and a few readily available thermodynamic quantities as input data.

Thompson, C. V.↗

An experimental investigation of surface pressure measurements on an advanced winged entry vehicle at Mach 10

Surface pressure measurements have been made at Mach 10 in air on an instrumented 0.006-scale model of an advanced (control configured) winged entry vehicle. The tests were conducted in the Langley Continuous Flow Hypersonic Tunnel. Data were obtained at 83 surface pressure stations, which include locations on the lower and upper surface centerlines, spanwise positions along the lower and upper surfaces of the wing, the lower surface of the body flap, and radial locations on the fuselage. Data were obtained for angles of attack ranging from zero to 40 deg, sideslip angles of -2 deg to +5 deg, Reynolds numbers of 0.5, 1.0, and 2.0 million per foot, and body-flap deflections of zero, 10, and 20 deg. Test conditions and orifice locations were chosen to correspond directly with those for the heat transfer measurements previously reported on the same configuration. Comparison of windward symmetry plane data with predictions based upon an approximate engineering method was found to yield reasonable agreement for angles of attack from 20 to 40 deg. The leeward surface pressure data were observed to be roughly an order of magnitude lower than the corresponding windward data. At low angles of attack, regions of high pressure were noted on the windward wing surface. The result is attributed to vortical action or shock impingement. High pressures were also measured on the deflected body flap, a critical region for this type of vehicle. Reynolds number effects were found to be insignificant.

Wurster, K. E.↗

Spatial variation of cosmic rays near the heliospheric current sheet

A quantitative comparison between theoretical predictions and observations of the intensity of galactic cosmic rays near the interplanetary current sheet is reported. Comparison of model calculations is made with a statistical analysis of observations of galactic cosmic rays at Earth and the simultaneous position of the current sheet. An ensemble of different current sheet inclinations is used, in order to make the analysis of the computations approximate the method used to analyses the data.

Jokipii, J. R.↗

An improved computational approach for multilevel optimum design

A penalty-function algorithm employing Newton's method with approximate second derivatives (Haftka and Starnes, 1980) is developed for two-level hierarchical design optimization problems. The difficulties posed by discontinuous behavior in typical multilevel problems are explained and illustrated for the case of a three-bar truss; the algorithm is formulated; and its advantages are demonstrated in the problem of a portal framework having three beams (described by six cross-section parameters), subjected to two loading conditions, and to be constructed in six different materials for comparison. The final design parameters are listed in a table.

Haftka, R. T.↗

Nonlinear Dynamics of a Helicopter Model in Ground Resonance

An approximate theoretical method is presented which determined the limit cycle behavior of a helicopter model which has one or two nonlinear dampers. The relationship during unstable ground resonance oscillations between lagging motion of the blades and fuselage motion is discussed. An experiment was carried out on using a helicopter scale model. The experimental results agree with those of the theoretical analysis.

Tang, D. M.↗

Investigation of solid plume simulation criteria to produce flight plume effects on multibody configuration in wind tunnel tests

An investigation to determine the sensitivity of the space shuttle base and forebody aerodynamics to the size and shape of various solid plume simulators was conducted. Families of cones of varying angle and base diameter, at various axial positions behind a Space Shuttle launch vehicle model, were wind tunnel tested. This parametric evaluation yielded base pressure and force coefficient data which indicated that solid plume simulators are an inexpensive, quick method of approximating the effect of engine exhaust plumes on the base and forebody aerodynamics of future, complex multibody launch vehicles.

Frost, A. L.↗

An optimization model for the US Air-Traffic System

A systematic approach for monitoring U.S. air traffic was developed in the context of system-wide planning and control. Towards this end, a network optimization model with nonlinear objectives was chosen as the central element in the planning/control system. The network representation was selected because: (1) it provides a comprehensive structure for depicting essential aspects of the air traffic system, (2) it can be solved efficiently for large scale problems, and (3) the design can be easily communicated to non-technical users through computer graphics. Briefly, the network planning models consider the flow of traffic through a graph as the basic structure. Nodes depict locations and time periods for either individual planes or for aggregated groups of airplanes. Arcs define variables as actual airplanes flying through space or as delays across time periods. As such, a special case of the network can be used to model the so called flow control problem. Due to the large number of interacting variables and the difficulty in subdividing the problem into relatively independent subproblems, an integrated model was designed which will depict the entire high level (above 29000 feet) jet route system for the 48 contiguous states in the U.S. As a first step in demonstrating the concept's feasibility a nonlinear risk/cost model was developed for the Indianapolis Airspace. The nonlinear network program --NLPNETG-- was employed in solving the resulting test cases. This optimization program uses the Truncated-Newton method (quadratic approximation) for determining the search direction at each iteration in the nonlinear algorithm. It was shown that aircraft could be re-routed in an optimal fashion whenever traffic congestion increased beyond an acceptable level, as measured by the nonlinear risk function.

Mulvey, J. M.↗

Multigrid acceleration of the flux split Euler equations

Multigrid acceleration is applied to a flux-split algorithm for solving the Euler equations in two and three dimensions. The basic algorithm is an implicit spatially-split approximate factorization method. The stability of the scheme in comparison to other factorization is examined. Results are presented for two-dimensional airfoil flows and three-dimensional wing flows which demonstrate substantially improved convergence with the multigrid algorithm. An asymptotic spectral radius of 0.89 and 0.93 is attained for a 97 x 17 x 17 wing solution at subcritical and supercritical conditions, respectively.

Anderson, W. K.↗

Cosmic rays near the heliospheric current sheet. II - An ensemble approach to comparing theory and observation

A quantitative comparison is carried out between theoretical predictions and observations of the intensity of galactic cosmic rays near the interplanetary current sheet. Model calculations are compared with a statistical analysis of observations of galactic cosmic rays at the earth and the simultaneous position of the current sheet. Since the observations were made over a period of several years, the inclination of the current sheet varied considerably, and comparison with any one model calculation referring to a given inclination would not be appropriate. An ensemble of different current sheet inclinations are used to generate expected values with the model in order to make the analysis of the computations approximate the method used to analyze the data. Agreement is found between theory and observation at energies of the order of a few GeV.

Jokipii, J. R.↗

Finite element analysis of flexible, rotating blades

A reference guide that can be used when using the finite element method to approximate the static and dynamic behavior of flexible, rotating blades is given. Important parameters such as twist, sweep, camber, co-planar shell elements, centrifugal loads, and inertia properties are studied. Comparisons are made between NASTRAN elements through published benchmark tests. The main purpose is to summarize blade modeling strategies and to document capabilities and limitations (for flexible, rotating blades) of various NASTRAN elements.

Mcgee, Oliver G.↗