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NASA NTRS1983

Vibration response of geometrically nonlinear elastic beams to pulse and impact loading

The governing equations for the geometrically nonlinear deformation of elastic beams subjected to dynamic bending loads are developed and solved for various initial conditions. Of primary interest is the response to pulse loading and simulated impact. Both transient and several cycle solutions are generated for the free vibration response to pulse loading. The results obtained are compared to a first mode analysis approximation. A model is developed to simulate impact loading by the distribution of additional mass to the elastic system and subjecting it to a velocity pulse. The governing equations are solved using second order finite differences in space and time. The solutions obtained are in reasonable agreement with experimental results.

Liebowitz, H.↗

NASA NTRS1983

A fully vectorized numerical solution of the incompressible Navier-Stokes equations

A vectorizable algorithm is presented for the implicit finite difference solution of the incompressible Navier-Stokes equations in general curvilinear coordinates. The unsteady Reynolds averaged Navier-Stokes equations solved are in two dimension and non-conservative primitive variable form. A two-layer algebraic eddy viscosity turbulence model is used to incorporate the effects of turbulence. Two momentum equations and a Poisson pressure equation, which is obtained by taking the divergence of the momentum equations and satisfying the continuity equation, are solved simultaneously at each time step. An elliptic grid generation approach is used to generate a boundary conforming coordinate system about an airfoil. The governing equations are expressed in terms of the curvilinear coordinates and are solved on a uniform rectangular computational domain. A checkerboard SOR, which can effectively utilize the computer architectural concept of vector processing, is used for iterative solution of the governing equations.

Patel, N.↗

NASA NTRS1983

Application of the method of lines for solutions of the Navier-Stokes equations using a nonuniform grid distribution

The feasibility of the method of lines for solutions of physical problems requiring nonuniform grid distributions is investigated. To attain this, it is also necessary to investigate the stiffness characteristics of the pertinent equations. For specific applications, the governing equations considered are those for viscous, incompressible, two dimensional and axisymmetric flows. These equations are transformed from the physical domain having a variable mesh to a computational domain with a uniform mesh. The two governing partial differential equations are the vorticity and stream function equations. The method of lines is used to solve the vorticity equation and the successive over relaxation technique is used to solve the stream function equation. The method is applied to three laminar flow problems: the flow in ducts, curved-wall diffusers, and a driven cavity. Results obtained for different flow conditions are in good agreement with available analytical and numerical solutions. The viability and validity of the method of lines are demonstrated by its application to Navier-Stokes equations in the physical domain having a variable mesh.

Abolhassani, J. S.↗

NASA NTRS1984

Theory and modeling of atmospheric turbulence, part 1

The cascade transfer which is the only function to describe the mode coupling as the result of the nonlinear hydrodynamic state of turbulence is discussed. A kinetic theory combined with a scaling procedure was developed. The transfer function governs the non-linear mode coupling in strong turbulence. The master equation is consistent with the hydrodynamical system that describes the microdynamic state of turbulence and has the advantages to be homogeneous and have fewer nonlinear terms. The modes are scaled into groups to decipher the governing transport processes and statistical characteristics. An equation of vorticity transport describes the microdynamic state of two dimensional, isotropic and homogeneous, geostrophic turbulence. The equation of evolution of the macrovorticity is derived from group scaling in the form of the Fokker-Planck equation with memory. The microdynamic state of turbulence is transformed into the Liouville equation to derive the kinetic equation of the singlet distribution in turbulence. The collision integral contains a memory, which is analyzed with pair collision and the multiple collision. Two other kinetic equations are developed in parallel for the propagator and the transition probability for the interaction among the groups.

Source record↗

NASA NTRS1984

Surface grid generation for wing-fuselage bodies

In the application of finite-difference methods to obtain numerical solutions of viscous compressible fluid flow about wing-fuselage bodies, it is advantageous to transform the governing equations to an idealized boundary-fitted coordinate system. The advantages are reduced computational complexity and added accuracy in the application of boundary conditions. The solution process requires that a grid be superimposed on the physical solution domain which corresponds to a uniform grid on a rectangular computational domain (uniform rectangular parallel-epiped). Grid generation is the determination of a one to one relationship between grid points in the physical domain and grid points in the computational domain. A technique for computing wing-fuselage surface grids using the Harris geometry and software for smooth-surface representation is described. Grid spacing control concepts which govern the relationship between the wing-fuselage surface and the computational grid are also presented.

Smith, R. E.↗

NASA NTRS1984

Large deflections of circular isotropic membranes subjected to arbitrary axisymmetric loading

Circular membranes with fixed peripheral edges, subjected to arbitrary axisymmetric loading are analyzed. A single governing differential equation in terms of radial stress is used. This nonlinear governing equation is solved using the finite difference method in conjunction with Newton-Raphson method. Three loading cases, namely (1) uniformly loaded membrane, (2) a membrane with uniform load over an inner portion, and (3) a membrane with ring load, are analyzed. Calculated central displacement and the central and edge radial stresses for uniformly loaded membrane, agree extremely well with the classical solution.

Kelkar, A.↗

NASA NTRS1983

An orthogonal coordinate grid following the three-dimensional viscous flow over a concave surface

Swept wings designed for laminar flow control exhibit both centrifugal and crossflow instabilities which produce streamwise vortices that can lead to early transition from laminar to turbulent flow in the presence of Tollmien-Schlichting waves. This paper outlines an iterative algorithm for generation of an orthogonal, curvilinear, coordinate grid following the streamlines of the three-dimensional viscous flow over a swept, concave surface. The governing equations for the metric tensor are derived from the Riemann-Christoffel tensor for an Euclidian geometry. Unit vectors along streamline, normal and binormal directions are determined. The governing equations are not solved directly, but are employed only as compatibility equations. The scale factor for the streamline coordinate is obtained by an iterative integration scheme on a 200 x 100 x 5 grid, while the other two scale factors are determined from definitions. Sample results are obtained which indicate that the compatibility equation error decreases linearly with grid step size. Grids smaller than 200 x 100 x 5 are found to be inadequate to resolve the grid curvature.

Dagenhart, J. R↗

NASA NTRS1983

Inlet flow distortion in turbomachinery - Comparison of theory and experiment in a transonic fan stage

Consideration is given to both velocity and temperature circumferential inlet distortions at upstream infinity (Seidel et al., 1980). The blade rows here are modeled as semiactuator disks, and losses and quasi-steady deviation angle correlations are included in the analysis. The governing equations are linearized, and the perturbations in stagnation pressure and stagnation temperature at upstream infinity are represented as Fourier series. The flow in the rotor is modeled as inviscid, one-dimensional, unsteady, and compressible. the flow is steady elsewhere. The deviation angles for the rotor and stator are taken to be functions of the relative inlet angle and Mach number, and use is made of the correlations contained in Johnson and Bullock (1965). It is assumed that the losses in relative stagnation pressure in the rotor and stator occur across the trailing edge. Boundary conditions applied at the various stations furnish the equations that make it possible to solve for the several quantities introduced in the linearization of the governing equations.

Seidel, B. S.↗

NASA NTRS1984

Embedded shear layer computations for increased drag reduction

One of the most promising methods of minimizing drag is the reduction of skin friction by injection of low momentum fluid into the near-wall region of turbulent boundary layer flows. This method could be made more effective by limiting the spread rate of the resulting mixing region. In order to achieve a better understanding of how this goal might be achieved, numerical investigations of the relevant fluid dynamic processes governing these regions have been conducted. A compact finite-difference algorithm has been applied to the complete form of the governing conservation equations for a two-dimensional laminar mixing layer. The ability of this computational approach to model successfully the formation and interaction of the large scale vortical structures which dominate such flow fields is verified in the present study. Parameters which affect the spread rate of the mixing region are also identified. In addition, the relative importance of viscous and momentum transport effects in the vortex interactions is determined.

Gatski, T. B.↗

NASA NTRS1983

High frequency green function for aerodynamic noise in moving media. I - General theory. II - Noise from a spreading jet

It is shown how a high frequency analysis can be made for general problems involving flow-generated noise. In the parallel shear flow problem treated by Balsa (1976) and Goldstein (1982), the equation governing sound propagation in the moving medium could be transformed into a wave equation for a stationary medium with an inhomogeneous index of refraction. It is noted that the procedure of Avila and Keller (1963) was then used to construct a high frequency Green function. This procedure involves matching a solution valid in an inner region around the point source to an outer, ray-acoustics solution. This same procedure is used here to construct the Green function for a source in an arbitrary mean flow. In view of the fact that there is no restriction to parallel flow, the governing equations cannot be transformed into a wave equation; the analysis therefore proceeds from the equations of motion themselves.

Durbin, P. A.↗

NASA NTRS1984

Numerical simulation of turbulent flows

Computational models of turbulence in incompressible Newtonian fluids governed by the Navier-Stokes equations are reviewed. The governing equations are presented, and both direct and large-eddy-simulations are examined. Resolution requirements and numerical techniques of spatial representation, definition of initial and boundary conditions, and time advancement are considered. Results of simulations of homogeneous turbulence in uniform shear, the evolution of a turbulent mixing layer, and turbulent channel flow are presented graphically and discussed.

Rogallo, R. S.↗

NASA NTRS1984

Formation and dynamics of large-scale magnetic structures in the ionosphere of Venus

The formation and dynamics of large-scale magnetic structures in the ionosphere of Venus are examined. It is shown that such structures must be the result of steady state convection of interplanetary field lines into the ionosphere by the small amount of solar wind plasma (less than or approximately equal to 1-5 percent) absorbed by the planetary atmosphere below the ionopause, rather than isolated remnants of large fields persisting for long periods without connection to the solar wind induced current and convection pattern. In particular, it is demonstrated that the magnetic diffusion of such structures would result in their dissipation with time scales of 1-10 min, if they were not steady state structures in convective and diffusive equilibriuim. It is shown that the equations governing the diffusion of these magnetic structures are similar to those governing diffusion of a gas out of an enclosed chamber with a porous wall, and a simple analog is illustrated. The application of these results to magnetic fields of astrophysical plasmas is discussed.

Cloutier, P. A.↗

NASA NTRS1984

An analytical model for the vorticity associated with a transverse jet

A two dimensional model is developed for a turbulent jet injected normally into a uniform crossflow, in which particular emphasis is placed on the contra-rotating vortex pair associated with the jet. By approximating the forces acting on each of the viscous vortices, equations governing the vortex spacing and downstream jet velocity are evolved. No empirical information is incorporated into this model. A description of the variation in total vortex strength is utilized in which vorticity generated by the jet's impulse dominates the farfield. Numerical solution of the governing equations yields results for the vortex trajectory, half spacing, varying circulation, and viscous core size that correlate quite well with experimental data and asymptotic relations. Based on these findings, we conclude that vortex separation and other important characteristics of the jet cross-section are two dimensional and viscous in nature. Hence it becomes possible to predict, on purely theoretical grounds, the behavior of the vortex pair and of the jet itself.

Karagozian, A. R.↗

NASA NTRS1984

The future of satellite remote sensing: A worldwide assessment and prediction

A frame-work in which to assess and predict the future prospects for satellite remote sensing markets is provided. The scope of the analysis is the satellite-related market for data, equipment, and services. It encompasses both domestic and international markets and contains an examination of the various market characteristics by market segment (e.g., Federal Government, State and Local Governments, Academic Organizations, Industrial Companies, and Individuals) and primary applications areas (e.g., Geology, Forestry, Land Resource Management, Agriculture and Cartography). The forecasts are derived from an analysis of both U.S. and foreign market data. The evolution and current status of U.S. and Foreign markets to arrive at market growth rates is evaluated. Circumstances and events which are likely to affect the future market development are examined. A market growth scenario is presented that is consistent with past data sales trends and takes into account the dynamic nature of the future satellite remote sensing market. Several areas of current and future business opportunities available in this market are discussed. Specific worldwide forecasts are presented in three market sectors for the period 1980 to 1990.

Spann, G. W.↗

NASA NTRS1984

Bulk composition of the Moon in the context of models for condensation in the solar nebula

The FeO content of the Moon is substantially higher than the present FeO content of the Earth's mantle. If the Moon formed by fission from the Earth's mantle, then the conclusion that the Earth's mantle must have been much richer in FeO at the time of fission appears firm. If the Moon formed independently in geocentric orbit, then the FeO contents of the two bodies should be similar, because both would be accreting from the same source of silicate material. Therefore, Earth's mantle at the time of lunar formation probably had an FeO content quite similar to the present FeO content of the Moon. This conclusion, if valid, has profound implications in two areas: (1) the differentiation history of the Earth's mantle and core; and (2) the processes responsible for governing the bulk compositions of the terrestrial planets. If Earth had more FeO than previously thought, then the composition differences between Earth and Mars are less than previously believed. This suggests that condensation temperature and heliocentric distance may have been less important in governing planetary compositions and other mechanisms, including iron/silicate fractionation may have been more important. The implication of this model for the compositions of the Moon and the other terrestrial planets are discussed.

Goettel, K. A.↗

NASA NTRS1984

Thermal-stress analysis for a wood composite blade

A thermal-stress analysis of a wind turbine blade made of wood composite material is reported. First, the governing partial differential equation on heat conduction is derived, then, a finite element procedure using variational approach is developed for the solution of the governing equation. Thus, the temperature distribution throughout the blade is determined. Next, based on the temperature distribution, a finite element procedure using potential energy approach is applied to determine the thermal-stress distribution. A set of results is obtained through the use of a computer, which is considered to be satisfactory. All computer programs are contained in the report.

Fu, K. C.↗

NASA NTRS1985

Numerical solutions of 3-dimensional Navier-Stokes equations for closed bluff-bodies

The Navier-Stokes equations are solved numerically. These equations are unsteady, compressible, viscous, and three-dimensional without neglecting any terms. The time dependency of the governing equations allows the solution to progress naturally for an arbitrary initial guess to an asymptotic steady state, if one exists. The equations are transformed from physical coordinates to the computational coordinates, allowing the solution of the governing equations in a rectangular parallelepiped domain. The equations are solved by the MacCormack time-split technique which is vectorized and programmed to run on the CDc VPS 32 computer. The codes are written in 32-bit (half word) FORTRAN, which provides an approximate factor of two decreasing in computational time and doubles the memory size compared to the 54-bit word size.

Abolhassani, J. S.↗

NASA NTRS1984

An integrated voice and data multiple-access scheme for a land-mobile satellite system

An analytical study is performed of the satellite requirements for a land mobile satellite system (LMSS). The spacecraft (MSAT-X) would be in GEO and would be compatible with multiple access by mobile radios and antennas and fixed stations. The FCC has received a petition from NASA to reserve the 821-825 and 866-870 MHz frequencies for the LMSS, while communications with fixed earth stations would be in the Ku band. MSAT-X transponders would alter the frequencies of signal and do no processing in the original configuration considered. Channel use would be governed by an integrated demand-assigned, multiple access protocol, which would divide channels into reservation and information channels, governed by a network management center. Further analyses will cover tradeoffs between data and voice users, probability of blocking, and the performance impacts of on-board switching and variable bandwidth assignment. Initial calculations indicate that a large traffic volume can be handled with acceptable delays and voice blocking probabilities.

Li, V. O. K.↗