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At least 145 records · Page 8

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NASA NTRS1983

A method for solving the transonic full-potential equation for general configurations

A method is developed for solving the full-potential equation for two-dimensional and axisymmetric flow which retains the grid and boundary condition simplicity of the transonic small-disturbance codes. The method is based on a finite-volume formulation of the mass conservation equation in a Cartesian coordinate system, and is an extension of the method of Purvis and Burkhalter (1979). This finite-volume approach, combined with the simple boundary treatment, is shown to result in a highly robust method applicable to a wide range of geometries and flow conditions. The accuracy of the method is demonstrated for general geometries in two-dimensional and axisymmetric flows. The use of this method results in significant gains in convergence rate over the vertical-line over-relaxation scheme by incorporating an AF2-type algorithm (Ballhaus et al., 1978). It is suggested that the simplicity of this method shold allow a relatively easy extension to complex geometries in three-dimensional flows, and complex two-dimensional configurations such as multielement airfoils should be amenable to this method.

Wedan, B.↗

NASA NTRS1984

Tortuosity of lightning return stroke channels

Data obtained from photographs of lightning are presented on the tortuosity of return stroke channels. The data were obtained by making piecewise linear fits to the channels, and recording the cartesian coordinates of the ends of each linear segment. The mean change between ends of the segments was nearly zero in the horizontal direction and was about eight meters in the vertical direction. Histograms of these changes are presented. These data were used to create model lightning channels and to predict the electric fields radiated during return strokes. This was done using a computer generated random walk in which linear segments were placed end-to-end to form a piecewise linear representation of the channel. The computer selected random numbers for the ends of the segments assuming a normal distribution with the measured statistics. Once the channels were simulated, the electric fields radiated during a return stroke were predicted using a transmission line model on each segment. It was found that realistic channels are obtained with this procedure, but only if the model includes two scales of tortuosity: fine scale irregularities corresponding to the local channel tortuosity which are superimposed on large scale horizontal drifts. The two scales of tortuosity are also necessary to obtain agreement between the electric fields computed mathematically from the simulated channels and the electric fields radiated from real return strokes. Without large scale drifts, the computed electric fields do not have the undulations characteristics of the data.

Levine, D. M.↗

NASA NTRS1984

Three-dimensional transonic potential flow about complex 3-dimensional configurations

An analysis has been developed and a computer code written to predict three-dimensional subsonic or transonic potential flow fields about lifting or nonlifting configurations. Possible condfigurations include inlets, nacelles, nacelles with ground planes, S-ducts, turboprop nacelles, wings, and wing-pylon-nacelle combinations. The solution of the full partial differential equation for compressible potential flow written in terms of a velocity potential is obtained using finite differences, line relaxation, and multigrid. The analysis uses either a cylindrical or Cartesian coordinate system. The computational mesh is not body fitted. The analysis has been programmed in FORTRAN for both the CDC CYBER 203 and the CRAY-1 computers. Comparisons of computed results with experimental measurement are presented. Descriptions of the program input and output formats are included.

Reyhner, T. A.↗

NASA NTRS1984

Observable in the reversible reaction gamma + d yields n + p

Calculations are presented on the effect of the two-body charge and current density effects on the observables in the photodisintegration of a deuteron. The computations are performed in a cartesian coordinate system, initially for gamma rays plane-polarized in the x-direction. Unpolarized photons are treated with an incoherent superposition of transition amplitudes for gamma rays polarized in the x- and y- directions. Account is taken of recoil and interaction energies after an initial state is defined. Consideration is focused on the cross section, polarization, and asymmetry of the reaction at low and medium energy incident gamma rays.

Rustgi, M. L.↗

NASA NTRS1984

Finite-amplitude models of convection in the early mantle

Models of finite-amplitude, time-dependent mantle convection at Reynolds number ten million are calculated. The models are based on the Boussinesq approximation for convection at infinite Prandtl number and treat convection in a two-dimensional, Cartesian coordinate box with an aspect ratio of 1.4. The initial conditions consist of a static fluid with a purely conductive temperature profile, while the boundary conditions are taken to be free slip, with impenetrable insulating side walls. The initial conditions are found to result in an initial burst of convection that reverses the horizontally averaged temperature gradient, making the middle layers stable with respect to convection. With bottom heating and cooling of the top, two distinct layers of convective cells occur; with top cooling only, the upper layer alone convects.

Boss, A. P.↗

NASA NTRS1985

A direct-inverse method for transonic and separated flows about airfoils

A direct-inverse technique and computer program called TAMSEP that can be sued for the analysis of the flow about airfoils at subsonic and low transonic freestream velocities is presented. The method is based upon a direct-inverse nonconservative full potential inviscid method, a Thwaites laminar boundary layer technique, and the Barnwell turbulent momentum integral scheme; and it is formulated using Cartesian coordinates. Since the method utilizes inverse boundary conditions in regions of separated flow, it is suitable for predicing the flowfield about airfoils having trailing edge separated flow under high lift conditions. Comparisons with experimental data indicate that the method should be a useful tool for applied aerodynamic analyses.

Carlson, K. D.↗

NASA NTRS1985

Formulation and application of Russell's method

It is shown that the numerical technique of Russell's momentum approach can be derived by using Hamilton's principle and Vance's numerical scheme. It results in a set of first order differnce equations for solving the angular velocities. The numerical examples show that the method is reliable. The algorithm is modified next to perform the analysis of N-body systems with closed loop topology. To increase the formulation flexibility, the equations of motion are represented by using Cartesian coordinates and Lagrange multipliers. The algorithm consists of two parts, Vance's scheme and an unconstrained minimization. The Vance's scheme is used to find the angular velocities, and the unconstrained minimization is applied to provide the correct angular displacements. The proposed scheme is further extended to find the design sensitivity of an N-body system with closed loop configuration, and to carry out the design optimization as well. The numerical example of a small-scaled mechanical system is presented to verify the proposed formulation.

Hou, J. W.↗

NASA NTRS1986

Analytical investigation of the dynamics of tethered constellations in Earth orbit, phase 2

The development of a two dimensional analytical model that describes the dynamics of an n-mass vertical tethered system is reported. Two different approaches are described: in the first one the control quantities are the independent variables while in the second one the Cartesian coordinates of each mass expressed in the orbiting reference frame are the independent variables. The latter model was used in the 3-mass version to simulate the dynamics of the tethered system in applications involving the displacement of the middle mass along the tether. In particular, issues related to reproducing predetermined acceleration profiles and g-tuning are reported.

Lorenzini, E.↗

NASA NTRS1986

Aeolian processes aboard a space station: Saltation and particle trajectory analysis

The Carousel wind tunnel (CWT) proposed to study aeolian processes aboard a space station consists of two concentric rotating drums. The space between the two drums comprises the wind tunnel test section. Differential rates of rotation of the two drums would provide a wind velocity with respect to either drum surface. Preliminary results of measured velocity profiles made in a CWT prototype indicate that the wall bounded boundary layer profiles are suitable to simulate flat plate turbulent boundary layer flow. The two dimensional flat plate Cartesian coordinate equations of motion of a particle moving through the air are explained. In order to assess the suitability of CWT in the analysis of the trajectories of windblown particles, a series of calculations were conducted comparing cases for gravity with those of zero gravity. Results from the calculations demonstrate that a wind tunnel of the carousel design could be fabricted to operate in a space station environment and that experiments could be conducted which would yield significant results contributing to the understanding of the physics of particle dynamics.

White, B. R.↗

NASA NTRS1986

A direct-inverse method for the prediction of transonic and separated flows about airfoils at high angles of attack

A direct-inverse technique and computer program called TAMSEP that can be used for the analysis of the flow about airfoils at subsonic and low transonic freestream velocities is presented. The method is based upon a direct-inverse nonconservative full potential inviscid method, a Thwaites laminar boundary layer technique, and the Barnwell turbulent momentum integral scheme; and it is formulated using Cartesian coordinates. Since the method utilizes inverse boundary conditions in regions of separated flow, it is suitable for predicting the flowfield about airfoils having trailing edge separated flow under high lift conditions. Comparisons with experimental data indicate that the method should be a useful tool for applied aerodynamic analyses.

Carlson, L. A.↗

NASA NTRS1985

Implicit finite-difference methods for the Euler equations

The present paper is concerned with two-dimensional Euler equations and with schemes which are in use of the time of this writing. Most of the development presented carries over directly to three dimensions. The characteristics of the two-dimensional Euler equations in Cartesian coordinates are considered along with generalized curvilinear coordinate transformations, metric relations, invariants of the transformation, flux Jacobian matrices and eigensystems, numerical algorithms, flux split algorithms, implicit and explicit nonlinear control (smoothing), upwind differencing in supersonic regions, unsteady and steady-state computation, the diagonal form of implicit algorithm, metric differencing and invariants, boundary conditions, geometry and mesh generation, and sample solutions.

Pulliam, T. H.↗

NASA NTRS1986

Static current-sheet models of quiescent prominences

A particular class of theoretical models idealize the prominence to be a discrete flat electric-current sheet suspended vertically in a potential magnetic field. The weight of the prominence is supported by the Lorentz force in the current sheet. These models can be extended to have curved electric-current sheets and to vary three-dimensionally. The equation for force balance is 1 over 4 pi (del times B) times Bdel p- p9 z=zero. Using Cartesian coordinates we take, for simplicity, a uniform gravity with constant acceleration g in the direction -z. If we are interested not in the detailed internal structure of the prominence, but in the global magnetic configuration around the prominence, we may take prominence plasma to be cold. Consideration is given to how such equilibrium states can be constructed. To simplify the mathematical problem, suppose there is no electric current in the atmosphere except for the discrete currents in the cold prominence sheet. Let us take the plane z =0 to be the base of the atmosphere and restrict our attention to the domain z greater than 0. The task we have is to solve for a magnetic field which is everywhere potential except on some free surface S, subject to suit able to boundary conditions. The surface S is determined by requiring that it possesses a discrete electric current density such that the Lorentz force on it is everywhere vertically upward to balance the weight of the material m(S). Since the magnetic field is potential in the external atmosphere, the latter is decoupled from the magnetic field and its plane parallel hydrostatic pressure and density can be prescribed.

Wu, F.↗

NASA NTRS1987

JAWS multiple Doppler derived winds

An elementary working knowledge is given of the advantages and limitations of the multiple Doppler radar analyses that have recently become available from the Joint Airport Weather Studies (JAWS) project. What Doppler radar is and what it does is addressed and the way Doppler radars were used in the JAWS project to gather wind shear data is described. The working definition of wind shear used is winds that affect aircraft flight over a span of 15 to 45 seconds and turbulence is defined as air motion that cause abrupt aircraft motions. The JAWS data current available contain no turbulence data. The concept of multiple Doppler analysis and the geometry of how it works are described, followed by an explanation of how data gathered in radar space are interpolated to a common Cartesian coordinate system and the limitations involved. A discussion is also presented of the analysis grid and how it was constructed. What the user actually gets is discussed, followed by a discussion of the expected errors in the three orthogonal wind components. Finally, a discussion is presented of why JAWS data are significant.

Elmore, Kimberly L.↗

NASA NTRS1987

Nonlinear beam kinematics for small strains and finite rotations

A simple matrix expression is obtained for the strain components of a beam in which the magnitudes of neither beam displacements nor rotations are explicitly restricted. The only kinematical restrictions are that: (1) strains are small compared to unity and (2) components of local rotation, a newly identified kinematical quantity, are of the order of the strains to a fractional power equal to at least one half. Local rotations are defined as the change of orientation of material elements off the beam reference axis relative to those on the beam reference axis. Local rotations appear explicitly in the resulting strain expressions, facilitating the treatment of both open- and closed-section beams in applications of the theory. The resulting strain components are expressed in a local Cartesian coordinate system and can be calculated directly in that way. Thus, one can use a curvilinear coordinate system that is natural to the beam problem without the complications that usually surround such an approach. Examples show the simplicity and the generality of the present approach as well as why previously published results differ among themselves concerning tension-torsion coupling.

Hodges, Dewey H.↗

NASA NTRS1988

Numerical analysis of three-dimensional viscous internal flows

A 3-D Navier-Stokes code has been developed for analysis of turbomachinery blade rows and other internal flows. The Navier-Stokes equations are written in a Cartesian coordinate system rotating about the x-axis, and then mapped to a general body-fitted coordinate system. Streamwise viscous terms are neglected using the thin-layer assumption, and turbulence effects are modeled using the Baldwin-Lomax turbulence model. The equations are discretized using finite differences on stacked C-type grids and are solved using a multistage Runge-Kutta algorithm with a spatially-varying time step and implicit residual smoothing. Calculations have been made of a horseshoe vortex formed in front of a flat plate with a round leading edge standing in a turbulent endwall boundary layer. Comparisons are made with experimental data taken by Eckerle and Langston for a circular cylinder under similar conditions. Computer and measured results are compared in terms of endwall flow visualization pictures and total pressure loss contours and vector plots on the symmetry plane. Calculated details of the primary vortex show excellent agreement with the experimental data. The calculations also show a small secondary vortex not seen experimentally.

Chima, Rodrick V.↗

NASA NTRS1988

Numerical analysis of three-dimensional viscous internal flows

Chima, Rodrick V.↗

NASA NTRS1989

Algorithm For Hypersonic Flow In Chemical Equilibrium

Implicit, finite-difference, shock-capturing algorithm calculates inviscid, hypersonic flows in chemical equilibrium. Implicit formulation chosen because overcomes limitation on mathematical stability encountered in explicit formulations. For dynamical portion of problem, Euler equations written in conservation-law form in Cartesian coordinate system for two-dimensional or axisymmetric flow. For chemical portion of problem, equilibrium state of gas at each point in computational grid determined by minimizing local Gibbs free energy, subject to local conservation of molecules, atoms, ions, and total enthalpy. Major advantage: resulting algorithm naturally stable and captures strong shocks without help of artificial-dissipation terms to damp out spurious numerical oscillations.

Palmer, Grant↗

NASA NTRS1988

Discretization formulas for unstructured grids

The Galerkin weighted residual technique using linear triangular weight functions is employed to develop finite difference formula in cartesian coordinates for the Laplacian operator, first derivative operators and the function for unstructured triangular grids. The weighted residual coefficients associated with the weak formulation of the Laplacian operator are shown to agree with the Taylor series approach on a global average. In addition, a simple algorithm is presented to determine the Voronoi (finite difference) area of an unstructured grid.

Baumeister, Kenneth J.↗