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At least 613 records · Page 34

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NASA NTRS1974

A Computing Method for Sound Propagation Through a Nonuniform Jet Stream

Understanding the principles of jet noise propagation is an essential ingredient of systematic noise reduction research. High speed computer methods offer a unique potential for dealing with complex real life physical systems whereas analytical solutions are restricted to sophisticated idealized models. The classical formulation of sound propagation through a jet flow was found to be inadequate for computer solutions and a more suitable approach was needed. Previous investigations selected the phase and amplitude of the acoustic pressure as dependent variables requiring the solution of a system of nonlinear algebraic equations. The nonlinearities complicated both the analysis and the computation. A reformulation of the convective wave equation in terms of a new set of dependent variables is developed with a special emphasis on its suitability for numerical solutions on fast computers. The technique is very attractive because the resulting equations are linear in nonwaving variables. The computer solution to such a linear system of algebraic equations may be obtained by well-defined and direct means which are conservative of computer time and storage space. Typical examples are illustrated and computational results are compared with available numerical and experimental data.

Padula, S. L.↗

NASA NTRS1974

SPAR demonstration problems

A series of examples are presented to indicate some of the principal functions of the SPAR system and to illustrate SPAR's control card-data card structure. Information in the following categories is given: (1) a description of the problem and, in most cases, comparisons with analytical solutions; (2) a list of the input cards; (3) a printout of the table of contents of the direct access library into which all SPAR output was directed; and (4) a few representative plots.

Yen, C. L.↗

NASA NTRS1974

Solving multiple scattering problems in planetary atmospheres

Multiple scattering problems, radiative transfer problems in planetary atmospheres within extended visible portion of the spectrum, are examined. The direct and inverse problems and the extinction coefficient are defined, along with other scattering characteristics. Albedos in semi-infinite and finite atmospheres are considered, as well as surface illumination, energy deposition, and polarization. The Eddington approximation figures prominently in the calculations. Precise numerical methods and analytical solutions are included.

Irvine, W. M.↗

NASA NTRS1975

Evaluation of some control-volume techniques for analysis of shock-boundary layer interactions in supersonic inlets

Various control-volume models used to analyze the shock boundary layer bleed interaction were investigated. The bleed assumptions of the models and their influence on the analytical solutions are discussed. The results of the analysis using these models are compared with experimental boundary-layer data taken in a supersonic inlet. The experimental Mach number upstream of the interaction was 1.66, and the oblique-shock pressure ratio was 1.33. The boundary layer data included bleed flow rates up to approximately 0.6 of the upstream boundary layer mass flow rate. The first model assumed the bleed was removed from the control volume with a momentum that was characterized by a pressure intermediate between the upstream and downstream pressures. The second model assumed the control volume was bounded by a streamline dividing the bleed and residual flows and eliminated the need to specify the momentum of the bleed flow. Comparison of the results using the models showed that specifying the bleed pressure in one model was equivalent to specifying the pressure along the dividing streamline in the other.

Hingst, W. R.↗

NASA NTRS1975

The dynamics of spin stabilized spacecraft with movable appendages, part 1

The motion and stability of spin stabilized spacecraft with movable external appendages are treated both analytically and numerically. The two basic types of appendages considered are: (1) a telescoping type of varying length and (2) a hinged type of fixed length whose orientation with respect to the main part of the spacecraft can vary. Two classes of telescoping appendages are considered: (a) where an end mass is mounted at the end of an (assumed) massless boom; and (b) where the appendage is assumed to consist of a uniformly distributed homogeneous mass throughout its length. For the telescoping system Eulerian equations of motion are developed. During all deployment sequences it is assumed that the transverse component of angular momentum is much smaller than the component along the major spin axis. Closed form analytical solutions for the time response of the transverse components of angular velocities are obtained when the spacecraft hub has a nearly spherical mass distribution.

Bainum, P. M.↗

NASA NTRS1975

Analysis of transonic flow about lifting wing-body configurations

An analytical solution was obtained for the perturbation velocity potential for transonic flow about lifting wing-body configurations with order-one span-length ratios and small reduced-span-length ratios and equivalent-thickness-length ratios. The analysis is performed with the method of matched asymptotic expansions. The angles of attack which are considered are small but are large enough to insure that the effects of lift in the region far from the configuration are either dominant or comparable with the effects of thickness. The modification to the equivalence rule which accounts for these lift effects is determined. An analysis of transonic flow about lifting wings with large aspect ratios is also presented.

Barnwell, R. W.↗

NASA NTRS1975

Analytical simulation of the far-field jet noise and the unsteady jet flow-field by a model of periodic shedding of vortex ring from the jet exit

The construction of a theoretical flow field due to shedding of vortex rings, the identification of the controlling parameters, and the determination of whether the theoretical model successfully simulated the unsteady pressure field near jet (and consequently the far field noise) was studied. The basic parameters contained in the analytic solutions were the epoch at which a vortex ring was shed near the jet exit and the eddy viscosity coefficient. These parameters were identified from the experimental data for the real-time pressure and from the spread of the mixing layer of the jet. Results of the theoretical analysis show good qualitative agreement with the experimental data.

Liu, C. H.↗

NASA NTRS1975

A cubic spline approximation for problems in fluid mechanics

A cubic spline approximation is presented which is suited for many fluid-mechanics problems. This procedure provides a high degree of accuracy, even with a nonuniform mesh, and leads to an accurate treatment of derivative boundary conditions. The truncation errors and stability limitations of several implicit and explicit integration schemes are presented. For two-dimensional flows, a spline-alternating-direction-implicit method is evaluated. The spline procedure is assessed, and results are presented for the one-dimensional nonlinear Burgers' equation, as well as the two-dimensional diffusion equation and the vorticity-stream function system describing the viscous flow in a driven cavity. Comparisons are made with analytic solutions for the first two problems and with finite-difference calculations for the cavity flow.

Rubin, S. G.↗

NASA NTRS1975

Reduced backscattering cross section (Sigma degree) data from the Skylab S-193 radar altimeter

Backscattering cross section per unit scattering area data, reduced from measurements made by the Skylab S-193 radar altimeter over the ocean surface are presented. Descriptions of the altimeter are given where applicable to the measurement process. Analytical solutions are obtained for the flat surface impulse response for the case of a nonsymmetrical antenna pattern. Formulations are developed for converting altimeter AGC outputs into values for the backscattering cross section. Reduced data are presented for Missions SL-2, 3 and 4 for all modes of the altimeter where sufficient calibration existed. The problem of interpreting land scatter data is also discussed. Finally, a comprehensive error analysis of the measurement is presented and worst case random and bias errors are estimated.

Brown, G. S.↗

NASA NTRS1974

An optimal control of a rigid spinning satellite

An analytical solution is provided of a simple control problem. A rigid symmetric spinning satellite is considered and the optimal control torque vector is obtained. It is pointed out that optimal control can be obtained even with unequal torque magnitudes.

Das, A.↗

NASA NTRS1975

Simulation by vortex rings of the unsteady pressure field near a jet

A coordinated theoretical and experimental program has been undertaken to construct a model for the shedding of vortex rings in order to simulate the real-time pressure variation in the acoustic region near the jet. The basic parameters in the analytic solutions are the eddy viscosity coefficient and the time intervals between successive shedding of vortex rings from the nozzle lip. The experimental and theoretical results show good qualitative agreement.

Liu, C. H.↗

NASA NTRS1974

On the design of optimal input signals in system identification

The problem of designing optimal inputs in the identification of multi-input multi-output linear systems with unknown time-varying parameters is considered using a Bayesian approach. A sensitivity index gives a measure of performance for the closed-loop system inputs. The computation of the optimal closed-loop mappings is shown to be a nontrivial exercise in stochastic control with no analytic solution, but optimal open-loop and affine laws yield much more tractable problems. For time-invariant systems, the sensitivity index considered is shown to be equivalent to the trace of the (strictly positive definite) information matrix associated with the system. Numerical examples are given. A Kalman filter is used to estimate the parameters. A necessary condition for the Kalman filter not to diverge when applying linear feedback is also given.

Lopez-Toledo, A. A.↗

NASA NTRS1975

Theoretical performance of cross-wind axis turbines with results for a catenary vertical axis configuration

A general analysis capable of predicting performance characteristics of cross-wind axis turbines was developed, including the effects of airfoil geometry, support struts, blade aspect ratio, windmill solidity, blade interference and curved flow. The results were compared with available wind tunnel results for a catenary blade shape. A theoretical performance curve for an aerodynamically efficient straight blade configuration was also presented. In addition, a linearized analytical solution applicable for straight configurations was developed. A listing of the computer program developed for numerical solutions of the general performance equations is included in the appendix.

Muraca, R. J.↗

NASA NTRS1975

Development of a three dimensional numerical water quality model for continental shelf applications

A model to predict the distribution of water quality parameters in three dimensions was developed. The mass transport equation was solved using a non-dimensional vertical axis and an alternating-direction-implicit finite difference technique. The reaction kinetics of the constituents were incorporated into a matrix method which permits computation of the interactions of multiple constituents. Methods for the computation of dispersion coefficients and coliform bacteria decay rates were determined. Numerical investigations of dispersive and dissipative effects showed that the three-dimensional model performs as predicted by analysis of simpler cases. The model was then applied to a two dimensional vertically averaged tidal dynamics model for the Providence River. It was also extended to a steady state application by replacing the time step with an iteration sequence. This modification was verified by comparison to analytical solutions and applied to a river confluence situation.

Spaulding, M.↗

NASA NTRS1975

The role of multiple scattering in one-dimensional radiative transfer

The usual methods of solving the radiative transfer equation yield answers which embrace all orders of scattering and thus shed little light on the underlying physical process. The present analysis examines the contributions of the various orders of scattering to the one dimensional transfer of radiation. In the one dimensional case an exact analytical solution exists and the problem reduces to that of expanding these exact solutions in powers of the albedo for single scattering. Formulas are given which permit the calculation of any order of scattering in an atmosphere of arbitrary optical thickness, particle albedo, and asymmetry parameter. The results should aid in identifying those physical situations where only the lowest orders of scattering play a significant role and where appropriate approximate methods might provide results of acceptable accuracy.

Adamson, D.↗

NASA NTRS1975

Earth-moon system: Dynamics and parameter estimation

A theoretical development of the equations of motion governing the earth-moon system is presented. The earth and moon were treated as finite rigid bodies and a mutual potential was utilized. The sun and remaining planets were treated as particles. Relativistic, non-rigid, and dissipative effects were not included. The translational and rotational motion of the earth and moon were derived in a fully coupled set of equations. Euler parameters were used to model the rotational motions. The mathematical model is intended for use with data analysis software to estimate physical parameters of the earth-moon system using primarily LURE type data. Two program listings are included. Program ANEAMO computes the translational/rotational motion of the earth and moon from analytical solutions. Program RIGEM numerically integrates the fully coupled motions as described above.

Breedlove, W. J., Jr.↗

NASA NTRS1976

Performance analysis of a laser propelled interorbital tansfer vehicle

Performance capabilities of a laser-propelled interorbital transfer vehicle receiving propulsive power from one ground-based transmitter was investigated. The laser transmits propulsive energy to the vehicle during successive station fly-overs. By applying a series of these propulsive maneuvers, large payloads can be economically transferred between low earth orbits and synchronous orbits. Operations involving the injection of large payloads onto escape trajectories are also studied. The duration of each successive engine burn must be carefully timed so that the vehicle reappears over the laser station to receive additional propulsive power within the shortest possible time. The analytical solution for determining these time intervals is presented, as is a solution to the problem of determining maximum injection payloads. Parameteric computer analysis based on these optimization studies is presented. The results show that relatively low beam powers, on the order of 50 MW to 60 MW, produce significant performance capabilities.

Minovitch, M. A.↗

NASA NTRS1975

Studies on the dynamic characteristics of gas film bearings and dampers

The dynamic characteristics of inherently compensated gas film bearings have been investigated for small excursion ratios. Both circular and rectangular cases have been solved for the stiffness and damping as a function of supply pressure, restrictor coefficient, and squeeze number. The effect of disturbance amplitude has been studied for the inherently compensated strip. Analytical solutions for the simple gas film damper problem have established the effect of disturbance amplitude at low squeeze numbers. These results are applicable to pressurized bearings as limiting case of the restrictor coefficient.

Stiffler, A. K.↗