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At least 811 records · Page 45

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NASA NTRS1977

Momentum and energy transport by waves in the solar atmosphere and solar wind

The fluid equations for the solar wind are presented in a form which includes the momentum and energy flux of waves in a general and consistent way. The concept of conservation of wave action is introduced and is used to derive expressions for the wave energy density as a function of heliocentric distance. The explicit form of the terms due to waves in both the momentum and energy equations are given for radially propagating acoustic, Alfven, and fast mode waves. The effect of waves as a source of momentum is explored by examining the critical points of the momentum equation for isothermal spherically symmetric flow. We find that the principal effect of waves on the solutions is to bring the critical point closer to the sun's surface and to increase the Mach number at the critical point. When a simple model of dissipation is included for acoustic waves, in some cases there are multiple critical points.

Jacques, S. A.↗

NASA NTRS1984

Spatial derivatives of flow quantities behind curved shocks of all strengths

Explicit formulas in terms of shock curvature are developed for spatial derivatives of flow quantities behind a curved shock for two-dimensional inviscid steady flow. Factors which yield the equations indeterminate as the shock strength approaches 0 have been cancelled analytically so that formulas are valid for shocks of any strength. An application for the method is shown in the solution of shock coalescence when nonaxisymmetric effects are felt through derivatives in the circumferential direction. The solution of this problem requires flow derivatives behind the shock in both the axial and radial direction.

Darden, C. M.↗

NASA NTRS1986

A second-order accurate kinetic-theory-based method for inviscid compressible flows

An upwind method for the numerical solution of the Euler equations is presented. This method, called the kinetic numerical method (KNM), is based on the fact that the Euler equations are moments of the Boltzmann equation of the kinetic theory of gases when the distribution function is Maxwellian. The KNM consists of two phases, the convection phase and the collision phase. The method is unconditionally stable and explicit. It is highly vectorizable and can be easily made total variation diminishing for the distribution function by a suitable choice of the interpolation strategy. The method is applied to a one-dimensional shock-propagation problem and to a two-dimensional shock-reflection problem.

Deshpande, Suresh M.↗

NASA NTRS1991

Computational study of three dimensional viscous flow through a turbine cascade using a multi-domain spectral technique

The three dimensional viscous flow through a planar turbine cascade is numerically simulated by direct solution of the incompressible Navier-Stokes equations. Flow dependence in the spanwise direction is represented by direct expansion in Chebyshev polynomials, while the discretization on planes parallel to the endwalls is accomplished using the spectral element method. Elemental mapping from the physical to the computational space uses an algebraic mapping technique. A fractional time stepping method that consists of an explicit nonlinear convective step, an implicit pressure correction step, and an implicit viscous step is used to advance the Navier-Stokes equations forward in time. Results computed at moderate Reynolds numbers show a three dimensional endwall flow separation, a midspan separation of the blade suction surface boundary layer, and other three-dimensional features such as the presence of a saddle point flow in the endwall region. In addition, the computed skin friction lines are shown to be orthogonal to the surface vorticity lines, demonstrating the accuracy achievable in the present method.

Renaud, Earl W.↗

NASA NTRS1992

Vortex breakdown incipience: Theoretical considerations

The sensitivity of the onset and the location of vortex breakdowns in concentrated vortex cores, and the pronounced tendency of the breakdowns to migrate upstream have been characteristic observations of experimental investigations; they have also been features of numerical simulations and led to questions about the validity of these simulations. This behavior seems to be inconsistent with the strong time-like axial evolution of the flow, as expressed explicitly, for example, by the quasi-cylindrical approximate equations for this flow. An order-of-magnitude analysis of the equations of motion near breakdown leads to a modified set of governing equations, analysis of which demonstrates that the interplay between radial inertial, pressure, and viscous forces gives an elliptic character to these concentrated swirling flows. Analytical, asymptotic, and numerical solutions of a simplified non-linear equation are presented; these qualitatively exhibit the features of vortex onset and location noted above.

Berger, Stanley A.↗

NASA NTRS1993

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 2: User's guide

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This is the User's Guide, and describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Towne, Charles E.↗

NASA NTRS1993

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 2: User's guide

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. This User's Guide describes the program's features, the input and output, the procedure for setting up initial conditions, the computer resource requirements, the diagnostic messages that may be generated, the job control language used to run the program, and several test cases.

Towne, Charles E.↗

NASA NTRS1993

Proteus three-dimensional Navier-Stokes computer code, version 1.0. Volume 3: Programmer's reference

A computer code called Proteus 3D was developed to solve the three-dimensional, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Towne, Charles E.↗

NASA NTRS1993

Proteus two-dimensional Navier-Stokes computer code, version 2.0. Volume 3: Programmer's reference

A computer code called Proteus 2D was developed to solve the two-dimensional planar or axisymmetric, Reynolds-averaged, unsteady compressible Navier-Stokes equations in strong conservation law form. The objective in this effort was to develop a code for aerospace propulsion applications that is easy to use and easy to modify. Code readability, modularity, and documentation were emphasized. The governing equations are solved in generalized nonorthogonal body-fitted coordinates, by marching in time using a fully-coupled ADI solution procedure. The boundary conditions are treated implicitly. All terms, including the diffusion terms, are linearized using second-order Taylor series expansions. Turbulence is modeled using either an algebraic or two-equation eddy viscosity model. The thin-layer or Euler equations may also be solved. The energy equation may be eliminated by the assumption of constant total enthalpy. Explicit and implicit artificial viscosity may be used. Several time step options are available for convergence acceleration. The documentation is divided into three volumes. The Programmer's Reference contains detailed information useful when modifying the program. The program structure, the Fortran variables stored in common blocks, and the details of each subprogram are described.

Towne, Charles E.↗

NASA NTRS1993

Application of high precision two-way S-band ranging to the navigation of the Galileo Earth encounters

The application of high-accuracy S/S-band (2.1 GHz uplink/2.3 GHz downlink) ranging to orbit determination with relatively short data arcs is investigated for the approach phase of each of the Galileo spacecraft's two Earth encounters (8 December 1990 and 8 December 1992). Analysis of S-band ranging data from Galileo indicated that under favorable signal levels, meter-level precision was attainable. It is shown that ranginging data of sufficient accuracy, when acquired from multiple stations, can sense the geocentric angular position of a distant spacecraft. Explicit modeling of ranging bias parameters for each station pass is used to largely remove systematic ground system calibration errors and transmission media effects from the Galileo range measurements, which would otherwise corrupt the angle finding capabilities of the data. The accuracy achieved using the precision range filtering strategy proved markedly better when compared to post-flyby reconstructions than did solutions utilizing a traditional Doppler/range filter strategy. In addition, the navigation accuracy achieved with precision ranging was comparable to that obtained using delta-Differenced One-Way Range, an interferometric measurement of spacecraft angular position relative to a natural radio source, which was also used operationally.

Pollmeier, Vincent M.↗

NASA NTRS1997

Parallel Computation of Unsteady Flows on a Network of Workstations

Parallel computation of unsteady flows requires significant computational resources. The utilization of a network of workstations seems an efficient solution to the problem where large problems can be treated at a reasonable cost. This approach requires the solution of several problems: 1) the partitioning and distribution of the problem over a network of workstation, 2) efficient communication tools, 3) managing the system efficiently for a given problem. Of course, there is the question of the efficiency of any given numerical algorithm to such a computing system. NPARC code was chosen as a sample for the application. For the explicit version of the NPARC code both two- and three-dimensional problems were studied. Again both steady and unsteady problems were investigated. The issues studied as a part of the research program were: 1) how to distribute the data between the workstations, 2) how to compute and how to communicate at each node efficiently, 3) how to balance the load distribution. In the following, a summary of these activities is presented. Details of the work have been presented and published as referenced.

Source record↗

NASA NTRS1986

A spectral multidomain method for the solution of hyperbolic systems

A multidomain Chebyshev spectral collocation method for solving hyperbolic partial differential equations were developed. Though spectral methods are global methods, an attractive idea is to break a computational domain into several domains, and a way to handle the interfaces is described. The multidomain approach offers advantages over the use of a single Chebyshev grid. It allows complex geometries to be covered, and local refinement can be used to resolve important features. For steady state problems it reduces the stiffness associated with the use of explicit time integration as a relaxation scheme. Furthermore, the proposed method remains spectrally accurate. Results showing performance of the method on one dimensional linear models and one and two dimensional nonlinear gas dynamics problems are presented.

Kopriva, D.↗

NASA NTRS1973

A finite element tensor approach to plate buckling and postbuckling.

A practical finite element method is presented for geometrically nonlinear (von Karman) plate problems. Symmetric strain energy tensors provide an efficient formulation and solution, and allow the effects of initial imperfections to be considered. An unbalanced force iteration is employed, with the advantage that the time consuming Gauss decomposition needs to be performed only once. The convergence is controlled by an automatically computed relaxation factor, and this makes the method applicable in advanced stages of non-linearity. Several different triangular elements are used in explicitly deriving the required tensors.

Vos, R. G.↗

NASA NTRS1977

Departures of the electron energy distribution from a Maxwellian in hydrogen. I - Formulation and solution of the electron kinetic equation. II - Consequences

The problem of calculating the steady-state free-electron energy distribution in a hydrogen gas is considered in order to study departures of that distribution from a Maxwellian at sufficiently low degrees of ionization. A model kinetic equation is formulated and solved analytically for the one-particle electron distribution function in a steady-state partially ionized hydrogen gas, and it is shown that the formal solution can be accurately approximated by using the WKB method. The solutions obtained indicate that the high-energy tail of the distribution is susceptible to distortion by imbalanced inelastic collisions for ionization fractions not exceeding about 0.1 and that such departures from a Maxwellian can lead to significant changes in the collisional excitation and ionization rates of ground-state hydrogen atoms. Expressions for the electron-hydrogen collision rates are derived which explicitly display their dependence on the hydrogen departure coefficients. The results are applied in order to compare self-consistent predictions with those based on the a priori assumption of a Maxwellian distribution for models of the thermal ionization equilibrium of hydrogen in the optically thin limit, spectral-line formation by a gas consisting of two-level atoms, and radiative transfer in finite slabs by a gas of four-level hydrogen atoms.

Shoub, E. C.↗

NASA NTRS1982

Fracture and crack growth in orthotropic laminates. Part 1: Analysis of a hybrid, unidirectional laminate with damage

The fracture behavior of unifirectional hybrid (buffer strip) composite laminates is studied. Three particular solutions are discussed: (1) broken fibers in a unidirectional half plane; (2) adjoined half planes of different fiber and matrix properties and (3) the solution of two half planes bounding a third distinct region of finite width. This finite width region represents a buffer strip and the potential of this strip to arrest a crack that originates in one of the half planes is investigated. The analysis is based on a materials modeling approach using the classical shear lag assumption to described the stress transfer between fibers. Explicit fiber and matrix properties of the three regions are retained and changes in the laminate behavior as a function of the relative material properties, buffer strip width and initial crack length are discussed.

Goree, J. G.↗

NASA NTRS1983

Shear-lag analysis of a hybrid, unidirectional composite with fiber damage

Development of a method of analysis capable of predicting accurately the fracture behavior of unidirectional hybrid (buffer strip) composite laminates was studied. Three particular solutions are discussed in detail: broken fibers in a unidirectional half-plane; adjoined half planes of different fiber and matrix properties; and the solution of two half planes bounding a third distinct region of finite width. This finite width region represents a buffer strip and primary attention is given to the potential of this strip to arrest a crack that originates in one of the half planes. A materials modeling approach using the classical shear lag assumption to describe the stress transfer between fibers was analyzed. Explicit fiber and matrix properties of the three regions are retained, and changes in the laminate behavior as a function of the relative material properties, buffer strip width, and initial crack length are discussed.

Goree, J. G.↗

NASA NTRS1988

Supersonic combusting flow - A comparison of numerical and experimental results

The flow field of an unconfined coaxial supersonic burner (SSB) was obtained numerically, using a CFD code. The explicit MacCormack algorithm, with point implicit treatment of chemistry source terms, was employed in the CFD code. Combustion of hydrogen and air was simulated by a two-step finite-rate combustion model whereas turbulence was accounted for by a Prandtl mixing length scheme. Boundary conditions and some important features of the numerical scheme were discussed. The qualitative features of the numerical solution were compared with those obtained by regular as well as schlieren photographs. General agreements of the CFD solution and the experimental photographs were observed.

Chitsomboon, T.↗

NASA NTRS1991

Synchrotron radiation with radiation reaction

A rigorous discussion is presented of the classical motion of a relativistic electron in a magnetic field and the resulting electromagnetic radiation when radiation reaction is important. In particular, for an electron injected with initial energy gamma(0), a systematic perturbative solution to the Lorentz-Dirac equation of motion is developed for field strengths satisfying gamma(0) B much less than 6 x 10 to the 15th G. A particularly accurate solution to the electron orbital motion in this regime is found and it is demonstrated how lowest-order corrections can be calculated. It is shown that the total energy-loss rate corresponds to what would be found using the exact Larmor power formula without including radiation reaction. Provided that the particle energy and field strength satisfy the same contraint, it is explicitly demonstrated that the intuitive prescription for calculating the time-integrated radiation spectrum described above is correct.

Nelson, Robert W.↗