Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Boundary value problem”

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 901 records · Page 50
All sourcesNASA NTRSDOE OSTI
NASA NTRS1985

Parameterization in Grid Generation

The distribution of grid points for calculating the solution of partial differential equations is chosen so as to include consideration of truncation error, stability, and the resolution of the solution near boundary layers and shocks. It is important to specify the distribution of points along a grid line. The problem of distributing points along a curve is considered. It is assumed that the curve is defined parametrically. The objective is to select a set of parameter values so that the corresponding points on the curves are properly distributed. The distribution is based on some intrinsic property of the curve such as arc length or curvature.

Mastin, C. W.↗
NASA NTRS1975

Delta wing flutter based on doublet lattice method in NASTRAN

The subsonic doublet-lattice method (DLM) aeroelastic analysis in NASTRAN was successfully applied to produce subsonic flutter boundary data in parameter space for a large delta wing configuration. Computed flow velocity and flutter frequency values as functions of air density ratio, flow Mach number, and reduced frequency are tabulated. The relevance and the meaning of the calculated results are discussed. Several input-deck problems encountered and overcome are cited with the hope that they may be helpful to NASTRAN Rigid Format 45 users.

Jew, H.↗
NASA NTRS1977

The general solution to the classical problem of finite Euler Bernoulli beam

An analytical solution is obtained for the problem of free and forced vibrations of a finite Euler Bernoulli beam with arbitrary (partially fixed) boundary conditions. The effects of linear viscous damping, Winkler foundation, constant axial tension, a concentrated mass, and an arbitrary forcing function are included in the analysis. No restriction is placed on the values of the parameters involved, and the solution presented here contains all cited previous solutions as special cases.

Hussaini, M. Y.↗
NASA NTRS1980

Preliminary results of mapping urban land cover with Seasat SAR imagery

The detectability of urban land cover types is explored using digitally processed Seasat SAR imagery of the Denver, Colorado area. Test sites within the metropolitan area were selected to include a cross section of Anderson, et. al. Level II land cover classes and cover types representative of the urban area growth stages. Using the Image 100 interactive processing system each test site was level sliced in an attempt to define specific reflectance boundaries for each cover type and to determine the spectral and spatial characteristics of homogeneous response regions. The rural-urban fringe boundary was readily definable, but a precise Level I and Level II land cover classification was not possible. High density housing could be separated from low density housing and from parks, but reflectance values were often look angle dependent. Confusion between some water and vegetation responses also posed problems.

Henderson, F. M.↗
NASA NTRS1993

A study of eigenvalue sensitivity for hydrodynamic stability operators

The eigenvalue sensitivity for hydrodynamic stability operators is investigated. Classical matrix perturbation techniques as well as the concept of epsilon-pseudospectra are applied to show that parts of the spectrum are highly sensitive to small perturbations. Applications are drawn from incompressible plane Couette flow, trailing line vortex flow, and compressible Blasius boundary-layer flow. Parameter studies indicate a monotonically increasing effect of the Reynolds number on the sensitivity. The phenomenon of eigenvalue sensitivity is due to the nonnormality of the operators and their discrete matrix analogs and may be associated with large transient growth of the corresponding initial value problem.

Schmid, Peter J.↗
NASA NTRS1993

Equidistribution of energy and other quantities in oscillating systems

Energy of a high harmonic standing wave tends to be distributed equally over the whole wave even in a stratified medium where the wave's peak amplitude can be much larger near the upper boundary than the lower one. This fact is generalized to the many diverse physical problems which solve second-order differential equations of Sturm-Liouville type. For any such solution y(z) whose sign fluctuates along the z-axis, quantities are found which have the same value between any two neighboring zeros of y. One of the equidistributed quantities for an oscillating fluid sphere is similar to kinetic energy but is identical only in limiting cases. The acoustic midpoint of a cavity can be a unique place where some nonlinear perturbations have extra strength. This may apply to the puzzling solar phenomenon called supergranulation.

Wolff, Charles L.↗
NASA NTRSDate not supplied

TPSAS-NF1676L-33433-DND

Reducing aircraft noise is a major objective in the field of computational aeroacoustics. When designing next generation quiet aircraft, it is important to be able to accurately and efficiently predict the acoustic scattering by an aircraft body from a given noise source. Acoustic liners are an effective tool for aircraft noise reduction, and are characterized by a complex valued frequency-dependent impedance. Converted into the time-domain using Fourier transforms, an impedance boundary condition can be used to simulate the acoustic scattering of geometric bodies treated with acoustic liners. This work considers using either an impedance boundary condition or admittance boundary condition to allow acoustic scattering problems to be modeled with geometries consisting of both un-lined and lined surfaces; admittance is defined to be the inverse of impedance. Three different acoustic liner models will be discussed: the Extended Helmholtz Resonator Model, the Three-Parameter Impedance Model, and a Broadband Model. In the Extended Helmholtz Resonator Model and Three-Parameter Impedance Model, the liner impedance is specified at a single frequency; the Broadband Model allows for the investigation of multiple frequencies simultaneously. The impedance and admittance boundary conditions for each model will be derived and coupled with a time-domain boundary integral equation. The scattering solution will be obtained iteratively using spatial and temporal basis functions. Stability will be demonstrated through eigenvalue analysis. Moreover, fast algorithms and high performance computing are considered to both assess and reduce the computational cost of the simulation.

Michelle E Rodio↗
NASA NTRS1978

The general solution to the classical problem of the finite Euler-Bernoulli beam

An analytical solution is obtained for the problem of free and forced vibrations of a finite Euler-Bernoulli beam with arbitrary (partially fixed) boundary conditions. The effects of linear viscous damping, Winkler foundation, constant axial tension, a concentrated mass, and an arbitrary forcing function are included in the analysis. No restriction is placed on the values of the parameters involved, and the solution presented here contains all cited previous solutions as special cases.

Hussaini, M. Y.↗
NASA NTRS1988

Stochastic time-optimal control problems

Two types of stochastic time-optimal controls in a one-dimensional setting are considered. Multidimensional problems, in the case of complete state information available and the system modeled by stochastic differential equations, are studied under the formulation of minimizing the expected transient-response time. The necessary condition of optimality is the satisfaction for the value function of a parabolic partial differential equation with boundary conditions. The sufficient condition of optimality is also provided, based on Dynkin's formula. Finally, three examples are given.

Zhang, W.↗
NASA NTRS1990

Scattering by an impedance sphere coated with a chiral layer

The scattering of a plane, linearly polarized electromagnetic wave by a sphere on whose surface an impedance boundary condition holds, and that is covered with a concentric layer of chiral material, is considered. Exact, explicit expressions are derived for the scattered field coefficients. The co-polarized and cross-polarized components of the far backscattered field are determined and discussed. The value of this canonical problem as a benchmark for computer codes is pointed out.

Uslenghi, Piergiorgio L. E.↗
NASA NTRS1989

Singular trajectories for time-optimal half-loop maneuvers of a high alpha fighter aircraft

Consideration is given to the problem of deriving a time-optimal open-loop control for the half-loop maneuver of a high-alpha aircraft, with initial conditions Mach 0.6 and 15,000 feet. Pontriagin's maximum principle is used to derive candidate optimal solutions. Using the two-point boundary-value algorithm, the flight path angle is maximized for various increasing specified final times until a final time of 13.6 sec yields a 180-deg flight-path angle. As the final time increased from 0.0 to 13.6 sec, the optimization process revealed 13 distinct switching structures of the control law, of which 11 contained singular arcs, and two had double singular arcs.

Hoffman, Eric↗
NASA NTRS1992

Sensitivity analysis of hydrodynamic stability operators

The eigenvalue sensitivity for hydrodynamic stability operators is investigated. Classical matrix perturbation techniques as well as the concept of epsilon-pseudoeigenvalues are applied to show that parts of the spectrum are highly sensitive to small perturbations. Applications are drawn from incompressible plane Couette, trailing line vortex flow and compressible Blasius boundary layer flow. Parametric studies indicate a monotonically increasing effect of the Reynolds number on the sensitivity. The phenomenon of eigenvalue sensitivity is due to the non-normality of the operators and their discrete matrix analogs and may be associated with large transient growth of the corresponding initial value problem.

Schmid, Peter J.↗
NASA NTRS1991

Magnetic field draping at the low-latitude magnetopause

Magnetohydrodynamic simulations are used to investigate the structure of the low-latitude magnetopause for interplanetary magnetic field conditions with a dominant southward component. The structure is self-consistently calculated as an initial-value problem in which the system is allowed to evolve into a quasi-steady state. All components of the 3D velocity and magnetic field as well as compressibility, resistivity, and viscosity are included in the 2D calculation. The simulation model shows that magnetic field draping can occur at the magnetopause boundary when magnetic merging takes place in the presence of a tangential shear flow. For 'normal' (positive Bx) draping, the higher-latitude portion of the field lines are curved toward the sun on the magnetospheric side of the magnetopause and away from the sun on the magnetosheath side. The thickness of the normal draping structure scales with the viscosity. The field-aligned current system that accompanies normal magnetic draping is consistent with the sense of the region 1 currents that flow into the dayside ionosphere.

Richard, R. L.↗
NASA NTRS2005

Laminar Heating Validation of the OVERFLOW Code

OVERFLOW, a structured finite difference code, was applied to the solution of hypersonic laminar flow over several configurations assuming perfect gas chemistry. By testing OVERFLOW's capabilities over several configurations encompassing a variety of flow physics a validated laminar heating was produced. Configurations tested were a flat plate at 0 degrees incidence, a sphere, a compression ramp, and the X-38 re-entry vehicle. This variety of test cases shows the ability of the code to predict boundary layer flow, stagnation heating, laminar separation with re-attachment heating, and complex flow over a three-dimensional body. In addition, grid resolutions studies were done to give recommendations for the correct number of off-body points to be applied to generic problems and for wall-spacing values to capture heat transfer and skin friction. Numerical results show good comparison to the test data for all the configurations.

Lillard, Randolph P.↗
NASA NTRS1982

Optimality criteria design and stress constraint processing

Methods for pre-screening stress constraints into either primary or side-constraint categories are reviewed; a projection method, which is developed from prior cycle stress resultant history, is introduced as an additional screening parameter. Stress resultant projections are also employed to modify the traditional stress-ratio, side-constraint boundary. A special application of structural modification reanalysis is applied to the critical stress constraints to provide feasible designs that are preferable to those obtained by conventional scaling. Sample problem executions show relatively short run times and fewer design cycle iterations to achieve low structural weights; those attained are comparable to the minimum values developed elsewhere.

Levy, R.↗
NASA NTRS1984

Progress in wind tunnel wall interference assessment/correction procedures at the NAE

Wall corrections as a function of wall porosity in the transonic wall interference problem was assessed. Effective porosities primarily for the two dimensional case were established as follows: (1) comparison of experimental data for two geometrically similar models of different chord/height ratio, an overall value of wall porosity could be deduced; (2) theoretical development which allows for unequal porosity for the floor and ceiling and wall boundary pressure measurements, porosities for floor and ceiling could be deduced; (3) a scheme was developed which allowed unequal porosity of floor and ceiling and streamwise varying porosity. The boundary layer development along the perforated floor and ceiling under the influence of the model pressure field, variations in boundary layer thickness underlining the difficulties in deducing meaningful values of wall porosity were determined. Wall boundary pressure measurement, in combination with singularity modelling of the airfoil, was sufficient to yield required information on the wall interference flow without having to establish some value for wall porosity. The singularity modelling of the airfoil initially covered only lift and volume but was extended to include drag and pitching moment, and second order volume term. It is shown by asymptotic transonic small disturbance analysis, that the derived corrections to angle of attack and free stream Mach number are correct to the first order.

Ohman, L. H.↗
NASA NTRS1990

Boundary element analysis of sound scattered by a moving surface

A solution for the acoustic field scattered from a uniformly moving rigid body in the presence of a harmonic incident source has been obtained using a boundary integral method. A derivation of the Kirchhoff formula given by Farassat and Myers (1988) for moving surfaces forms the basis for the analysis, and the development of a boundary integral method for the solution of scattering problems from moving rigid bodies is described. Finite elements are used in conjunction with the Galerkin method in order to solve the integral equation that results from the Kirchhoff formula when the observer point is placed on the moving body surface. Once appropriate surface field values are known they are inserted back into the formula in order to predict the field scattered off the body. Tests, including the so called superposition method, are carried out in order to validate the technique and to establish some confidence in its accuracy. Application of the superposition method to moving bodies is presented, and results of the two approaches are discussed. Sample calculations of scattering from a simple body are presented to illustrate the effects of variations in relevant parameters.

Myers, M. K.↗