Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Numerical approximations”

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 325 records · Page 18

Flapping response characteristics of hingeless rotor blades by a gereralized harmonic balance method

Linearized equations of motion for the flapping response of flexible rotor blades in forward flight are derived in terms of generalized coordinates. The equations are solved using a matrix form of the method of linear harmonic balance, yielding response derivatives for each harmonic of the blade deformations and of the hub forces and moments. Numerical results and approximate closed-form expressions for rotor derivatives are used to illustrate the relationships between rotor parameters, modeling assumptions, and rotor response characteristics. Finally, basic hingeless rotor response derivatives are presented in tabular and graphical form for a wide range of configuration parameters and operating conditions.

Peters, D. A.↗

Detailed gravimetric geoid confirmation of short wavelength features of sea surface topography detected by the Skylab S-193 altimeter in the Atlantic Ocean

A detailed gravimetric geoid was computed for the Northwest Atlantic Ocean and Caribbean Sea area in support of the calibration and evaluation of the GEOS-C altimeter. This geoid, computed on a 15 ft. x 15 ft. grid was based upon a combination of surface gravity data with the GSFC GEM-6 satellite derived gravity data. A comparison of this gravimetric geoid with 10 passes of SKYLAB altimeter data is presented. The agreement of the two data types is quite good with the differences generally less than 2 meters. Sea surface manifestations of numerous short wavelength (approximately 100 km) oceanographic features are now indicated in the gravimetric geoid and are also confirmed by the altimetry data.

Marsh, J. G.↗

Magnetic attitude control system for dual-spin satellites

A closed-loop control law is developed for a dual-spin satellite control system which utilizes the interaction of the geomagnetic field with the satellite dipole parallel to the spin axis. The control law consists of the linear combination of the pitch axis component of the rate of change of the geomagnetic field and the product of the roll angle and roll axis component of the geomagnetic field. Application of the method of multiple time scales yields approximate solutions for the feedback gains in terms of the system parameters. Approximate solutions are also obtained for the response of the system to disturbance torques. A comparison of the approximate solutions and numerical solutions obtained by numerical integration of the exact equations of motion is then given.

Alfriend, K. T.↗

Three-dimensional turbulent boundary layer development and separation in V/STOL engine inlets at incidence with small-cross flow and curvature influences

The study concerns the influence of the three-dimensional cross flows on the compressible turbulent boundary layer development and flow separation prediction around V/STOL engine inlets at high incidence. The governing equations for the three-dimensional boundary layer flow with small-cross approximation are solved numerically on an intrinsic streamline coordinate system. Results are presented to illustrate the effects of small cross-flow, compressibility and streamline curvatures on the flow. Comparisons of the results with the wind tunnel data for scaled model and with data obtained from another existing compressible axisymmetric turbulent boundary layer scheme are included in the analysis.

Chou, D. C.↗

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.↗

Calculation and observation of thermal electrostatic noise in solar wind plasma

Calculations, both approximate algebraic and numerical, have been carried out for the noise due to electrostatic waves incident on a dipole antenna. The noise is calculated both for a thermal equilibrium plasma, and one having several components at different temperatures. The results are compared with measurements from the IMP-6 satellite. In various frequency ranges, the noise power is dominated by Langmuir oscillations, by electron acoustic waves and by ion acoustic waves. The measurements are consistent with all of these, although the ion waves are not definitely observed, due to interference from shot noise.

Kellogg, P. J.↗

Prediction of high speed propeller flow fields using a three-dimensional Euler analysis

To overcome the limitations of classical propeller theory, a computer program, NASPROP-E, was developed which solves for the flow field surrounding a multibladed propeller and axisymmetric nacelle combination using a finite difference method. The governing equations are the three dimensional unsteady Euler equations written in a cylindrical coordinate system. They are marched in time until a steady state solution is obtained. The Euler equations require no special treatment to model the blade work vorticity. The equations are solved using an implicit approximate factorization method. Numerical results are presented which have greatly increased the understanding of high speed propeller flow fields. Numerical results for swirl angle downstream of the propeller and propeller power coefficient are higher than experimental results. The radial variation of coefficient are higher than experimental results. The radial variation of swirl angle, however, is in reasonable agreement with the experimental results. The predicted variation of power coefficient with blade angle agrees very well with data.

Bober, L. J.↗

On the stellar rotation-activity connection

The relationship between rotation rates and surface activity in late-type dwarf stars is explored in a survey of recent theoretical and observational studies. Current theoretical models of stellar-magnetic-field production and coronal activity are examined, including linear kinematic dynamo theory, nonlinear dynamos using approximations, and full numerical simulations of the MHD equations; and some typical results are presented graphically. The limitations of the modeling procedures and the constraints imposed by the physics are indicated. The statistical techniques used in establishing correlations between various observational parameters are analyzed critically, and the methods developed for quasar luminosity functions by Avni et al. (1980) are used to evaluate the effects of upper detection bounds, incomplete samples, and missing data for the case of rotation and X-ray flux data.

Rosner, R.↗

Atmospheric guidance law for planar skip trajectories

The applicability of an approximate, closed-form, analytical solution to the equations of motion, as a basis for a deterministic guidance law for controlling the in-plane motion during a skip trajectory, is investigated. The derivation of the solution by the method of matched asymptotic expansions is discussed. Specific issues that arise in the application of the solution to skip trajectories are addressed. Based on the solution, an explicit formula for the approximate energy loss due to an atmospheric pass is derived. A guidance strategy is proposed that illustrates the use of the approximate solution. A numerical example shows encouraging performance.

Mease, K. D.↗

Semiempirical methods for computing turbulent flows

Two semiempirical theories which provide a basis for determining the turbulent friction and heat exchange near a wall are presented: (1) the Prandtl-Karman theory, and (2) the theory utilizing an equation for the energy of turbulent pulsations. A comparison is made between exact numerical methods and approximate integral methods for computing the turbulent boundary layers in the presence of pressure, blowing, or suction gradients. Using the turbulent flow around a plate as an example, it is shown that, when computing turbulent flows with external turbulence, it is preferable to construct a turbulence model based on the equation for energy of turbulent pulsations.

Belov, I. A.↗

Effect of coulomb spline on rotor dynamic response

A rigid rotor system coupled by a coulomb spline is modelled and analyzed by approximate analytical and numerical analytical methods. Expressions are derived for the variables of the resulting limit cycle and are shown to be quite accurate for a small departure from isotropy.

Nataraj, C.↗

Incompressible Navier-Stokes computations of vortical flows over double-delta wings

An implicit flux-difference splitting scheme is used to compute incompressible laminar vortical flows about a thin round-edged double-delta wing with 80 deg and 60 deg leading-edged sweep for the strake and the main wing respectively. The numerical scheme combines approximate factorization in crossflow planes with a symmetric planar Gauss-Seidel relaxation in the remaining spatial direction. It is second-order accurate spatially by applying TVD-like upwind discretization to the inviscid fluxes and central differencing to the viscous shear fluxes. The interaction between the two primary vortices emanating from the apex and kink leading-edges is successfully simulated. The computed trajectories of vortical cores compare well with experimental data.

Hsu, Chung-Hao↗

Three-dimensional incompressible Navier-Stokes simulations of slender-wing vortices

The application of an implicit flux-difference splitting scheme to leading-edge vortex flows is described. The numerical scheme combines approximate factorization in crossflow planes with a symmetric planar Gauss-Seidel relaxation in the remaining spatial direction. Second-order spatial accuracy is achieved by applying TVD-like upwind discretization to the inviscid fluxes and central differencing to the viscous shear fluxes. Good agreement between computed results and experimental data has been obtained for three different low-aspect-ratio wings.

Hsu, Chung-Hao↗

Numerical simulation of a subsonic jet in a crossflow

The aerodynamic/propulsive interaction between a subsonic jet exhausting perpendicularly through a flat plate into a crossflow is investigated numerically using an approximately factored, partially flux-split, implicit solver for the three-dimensional, thin-layer Navier-Stokes equations. This algorithm is applied to flows with a range of jet-to-crossflow velocity ratios between 4 and 8. The computations model the jet trajectory, the contrarotating vortex pair and the wake region near the plate downstream of the jet orifice. Both qualitative and quantitative agreement with the existing experimental database are demonstrated. Flow visualization is instructive for understanding the physics of this flowfield.

Roth, Karlin R.↗

Capacity for patterns and sequences in Kanerva's SDM as compared to other associative memory models

The information capacity of Kanerva's Sparse Distributed Memory (SDM) and Hopfield-type neural networks is investigated. Under the approximations used here, it is shown that the total information stored in these systems is proportional to the number connections in the network. The proportionality constant is the same for the SDM and Hopfield-type models independent of the particular model, or the order of the model. The approximations are checked numerically. This same analysis can be used to show that the SDM can store sequences of spatiotemporal patterns, and the addition of time-delayed connections allows the retrieval of context dependent temporal patterns. A minor modification of the SDM can be used to store correlated patterns.

Keeler, James D.↗

Numerical simulation of flow over a hypersonic aircraft using an explicit upwind PNS solver

A hypersonic flow field over a generic airplane configuration is simulated by solving the Parabolized Navier-Stokes (PNS) equations. The finite difference solution of the PNS equations is calculated using a noniterative space marching, explicit, upwind scheme recently developed by the authors. Special gridding techniques are used which allowed the sharp changes in surface geometry of the airplane configuration to be modelled without smoothing of corners. Comparisons of the PNS results to a solution of the Navier-Stokes equations demonstrates a good agreement of the numerical results in approximately 1/6 of the cpu time. This paper demonstrates that the explicit upwind algorithm for solving the PNS equations is an efficient method for simulating hypersonic flow fields about complete airplane configurations and should be considered as an alternative to solving the Navier-Stokes equations for flow fields where the PNS equations are valid.

Korte, John J.↗

Radiation-driven winds of hot stars. VI - Analytical solutions for wind models including the finite cone angle effect

Analytical solutions for radiation-driven winds of hot stars including the important finite cone angle effect (see Pauldrach et al., 1986; Friend and Abbott, 1986) are derived which approximate the detailed numerical solutions of the exact wind equation of motion very well. They allow a detailed discussion of the finite cone angle effect and provide for given line force parameters k, alpha, delta definite formulas for mass-loss rate M and terminal velocity v-alpha as function of stellar parameters.

Kudritzki, R. P.↗