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All sourcesNASA NTRSDOE OSTI
NASA NTRS1989

Rarefied gas flow through two-dimensional nozzles

A kinetic theory analysis is made of the flow of a rarefied gas from one reservoir to another through two-dimensional nozzles with arbitrary curvature. The Boltzmann equation simplified by a model collision integral is solved by means of finite-difference approximations with the discrete ordinate method. The physical space is transformed by a general grid generation technique and the velocity space is transformed to a polar coordinate system. A numerical code is developed which can be applied to any two-dimensional passage of complicated geometry for the flow regimes from free-molecular to slip. Numerical values of flow quantities can be calculated for the entire physical space including both inside the nozzle and in the outside plume. Predictions are made for the case of parallel slots and compared with existing literature data. Also, results for the cases of convergent or divergent slots and two-dimensional nozzles with arbitrary curvature at arbitrary knudsen number are presented.

De Witt, Kenneth J.↗
NASA NTRS1989

Development of an integrated BEM for hot fluid-structure interaction

The Boundary Element Method (BEM) is chosen as a basic analysis tool principally because the definition of quantities like fluxes, temperature, displacements, and velocities is very precise on a boundary base discretization scheme. One fundamental difficulty is, of course, that the entire analysis requires a very considerable amount of analytical work which is not present in other numerical methods. During the last 18 months all of this analytical work was completed and a two-dimensional, general purpose code was written. Some of the early results are described. It is anticipated that within the next two to three months almost all two-dimensional idealizations will be examined. It should be noted that the analytical work for the three-dimensional case has also been done and numerical implementation will begin next year.

Banerjee, P. K.↗
NASA NTRS1998

Measurements of Heat Transfer, Flow, and Pressures in a Simulated Turbine Blade Internal Cooling Passage

An experimental study was made to obtain quantitative information on heat transfer, flow, and pressure distribution in a branched duct test section that had several significant features of an internal cooling passage of a turbine blade. The objective of this study was to generate a set of experimental data that could be used for validation of computer codes that would be used to model internal cooling. Surface heat transfer coefficients and entrance flow conditions were measured at nominal entrance Reynolds numbers of 45,000, 335,000, and 726,000. Heat transfer data were obtained by using a steady-state technique in which an Inconel heater sheet is attached to the surface and coated with liquid crystals. Visual and quantitative flow-field data from particle image velocimetry measurements for a plane at midchannel height for a Reynolds number of 45,000 were also obtained. The flow was seeded with polystyrene particles and illuminated by a laser light sheet. Pressure distribution measurements were made both on the surface with discrete holes and in the flow field with a total pressure probe. The flow-field measurements yielded flow-field velocities at selected locations. A relatively new method, pressure sensitive paint, was also used to measure surface pressure distribution. The pressure paint data obtained at Reynolds numbers of 335,000 and 726,000 compared well with the more standard method of measuring pressures by using discrete holes.

Russell, Louis M.↗
NASA NTRS1976

A subvortex technique for the close approach to a discretized vortex sheet

The close-approach problem associated with vortex-lattice methods was examined numerically with the objective of calculating velocities at arbitrary points, not just at midpoints, between the vortices. The objective was achieved using a subvortex technique in which a vortex splits into an increasing number of subvortices as it is approached. The technique, incorporated in a two-dimensional potential flow method using "submerged" vortices and sources, was evaluated for a cambered Joukowski airfoil. The method could be extended to three dimensions, and should improve non-linear methods, which calculate interference effects between multiple wings and vortex wakes, and which include procedures for force-free wakes.

Maskew, B.↗
NASA NTRS1979

A vector-continuous loading concept for aerodynamic panel methods

An approach to the reduction of discretization errors in aerodynamic panel methods is presented. The approach is based on preventing the occurence of induced velocity singularities at panel slope discontinuities by maintaining continuity of the velocity jump vector across the panels. The approach was implemented in a two-dimensional incompressible panel method formulation and evaluated by application to several external and internal flow problems. The method is shown to exhibit a second order accuracy trend and to produce smaller errors with velocity component boundary conditions imposed on the real flow than with equipotential boundary conditions imposed on the imaginary flow behind the panels. For flows around airfoil sections with either sharp or blunt trailing edges, the method gives excellent agreement with results from a well developed finite difference method. The method is well behaved and is insensitive to irregularities in panel size distribution.

Kemp, W. B., Jr.↗
NASA NTRS1993

Accuracy of least-squares methods for the Navier-Stokes equations

Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations.

Bochev, Pavel B.↗
NASA NTRS1993

Accuracy of least-squares methods for the Navier-Stokes equations

Recently there has been substantial interest in least-squares finite element methods for velocity-vorticity-pressure formulations of the incompressible Navier-Stokes equations. The main cause for this interest is the fact that algorithms for the resulting discrete equations can be devised which require the solution of only symmetric, positive definite systems of algebraic equations. On the other hand, it is well-documented that methods using the vorticity as a primary variable often yield very poor approximations. Thus, here we study the accuracy of these methods through a series of computational experiments, and also comment on theoretical error estimates. It is found, despite the failure of standard methods for deriving error estimates, that computational evidence suggests that these methods are, at the least, nearly optimally accurate. Thus, in addition to the desirable matrix properties yielded by least-squares methods, one also obtains accurate approximations.

Bochev, Pavel B.↗
NASA NTRS1974

Computer programs for pressurization (RAMP) and pressurized expulsion from a cryogenic liquid propellant tank

An analysis to predict the pressurant gas requirements for the discharge of cryogenic liquid propellants from storage tanks is presented, along with an algorithm and two computer programs. One program deals with the pressurization (ramp) phase of bringing the propellant tank up to its operating pressure. The method of analysis involves a numerical solution of the temperature and velocity functions for the tank ullage at a discrete set of points in time and space. The input requirements of the program are the initial ullage conditions, the initial temperature and pressure of the pressurant gas, and the time for the expulsion or the ramp. Computations are performed which determine the heat transfer between the ullage gas and the tank wall. Heat transfer to the liquid interface and to the hardware components may be included in the analysis. The program output includes predictions of mass of pressurant required, total energy transfer, and wall and ullage temperatures. The analysis, the algorithm, a complete description of input and output, and the FORTRAN 4 program listings are presented. Sample cases are included to illustrate use of the programs.

Masters, P. A.↗
NASA NTRS1978

A computer program for calculating aerodynamic characteristics of low aspect-ratio wings with partial leading-edge separation

The necessary information for using a computer program to predict distributed and total aerodynamic characteristics for low aspect ratio wings with partial leading-edge separation is presented. The flow is assumed to be steady and inviscid. The wing boundary condition is formulated by the Quasi-Vortex-Lattice method. The leading edge separated vortices are represented by discrete free vortex elements which are aligned with the local velocity vector at midpoints to satisfy the force free condition. The wake behind the trailing edge is also force free. The flow tangency boundary condition is satisfied on the wing, including the leading and trailing edges. The program is restricted to delta wings with zero thickness and no camber. It is written in FORTRAN language and runs on CDC 6600 computer.

Mehrotra, S. C.↗
NASA NTRS2007

Proximity Navigation of Highly Constrained Spacecraft

Bandit is a 3-kg automated spacecraft in development at Washington University in St. Louis. Bandit's primary mission is to demonstrate proximity navigation, including docking, around a 25-kg student-built host spacecraft. However, because of extreme constraints in mass, power and volume, traditional sensing and actuation methods are not available. In particular, Bandit carries only 8 fixed-magnitude cold-gas thrusters to control its 6 DOF motion. Bandit lacks true inertial sensing, and the ability to sense position relative to the host has error bounds that approach the size of the Bandit itself. Some of the navigation problems are addressed through an extremely robust, error-tolerant soft dock. In addition, we have identified a control methodology that performs well in this constrained environment: behavior-based velocity potential functions, which use a minimum-seeking method similar to Lyapunov functions. We have also adapted the discrete Kalman filter for use on Bandit for position estimation and have developed a similar measurement vs. propagation weighting algorithm for attitude estimation. This paper provides an overview of Bandit and describes the control and estimation approach. Results using our 6DOF flight simulator are provided, demonstrating that these methods show promise for flight use.

Scarritt, S.↗
NASA NTRS1978

A theoretical investigation of the aerodynamics of low-aspect-ratio wings with partial leading-edge separation

A numerical method is developed to predict distributed and total aerodynamic characteristics for low aspect-ratio wings with partial leading-edge separation. The flow is assumed to be steady and inviscid. The wing boundary condition is formulated by the quasi-vortex-lattice method. The leading-edge separated vortices are represented by discrete free vortex elements which are aligned with the local velocity vector at mid-points to satisfy the force free condition. The wake behind the trailing-edge is also force free. The flow tangency boundary condition is satisfied on the wing, including the leading- and trailing-edges. Comparison of the predicted results with complete leading-edge separation has shown reasonably good agreement. For cases with partial leading-edge separation, the lift is found to be highly nonlinear with angle of attack.

Mehrotra, S. C.↗
NASA NTRS1986

Two-phase flow

An experimental program to characterize the spray from candidate nozzles for icing-cloud simulation is discussed. One canidate nozzle, which is currently used for icing research, has been characterized for flow and drop size. The median-volume diameter (MVD) from this air-assist nozzle is compared with correlations in the literature. The new experimental spray facility is discussed, and the drop-size instruments are discussed in detail. Since there is no absolute standard for drop-size measurements and there are other limitations, such as drop -size range and velocity range, several instruments are used and results are compared. A two-phase model was developed at Pennsylvania State University. The model uses the k-epsilon model of turbulence in the continous phase. Three methods for treating the discrete phase are used: (1) a locally homogeneous flow (LHF) model, (2) a deterministic separated flow (DSF) model, and (3) a stochastic separated flow (SSF) model. In the LHF model both phases have the same velocity and temperature at each point. The DSF model provides interphase transport but ignores the effects of turbulent fluctuations. In the SSF model the drops interact with turbulent eddies whose properties are determined by the k-epsilon turbulence model. The two-phase flow model has been extended to include the effects of evaporation and combustion.

Tacina, Robert R.↗
NASA NTRS1990

Application of the TRANAIR rectangular grid approach to the aerodynamic analysis of complex configurations

A numerical method is described which uses a rectangular grid to solve the nonlinear full potential equation about complex configurations. The grid is locally refined to resolve high velocity gradients arising from leading edge expansions or shock waves. The grid penetrates the boundary (described by networks of quadrilateral panels) and is generated automatically. Discrete operators are constructed using the finite element method. The system of nonlinear discrete equations is solved iteratively using a Krylov subspace method preconditioned by an exterior Poisson solver and a direct sparse solver. The primary emphasis is to provide design engineers with an aerodynamic analysis tool (the TRANAIR code) which is accurate, reliable, economical, and flexible to use. Computational results for many interesting configurations are presented.

Johnson, Forrester T.↗
NASA NTRS1992

Calculation of fully three-dimensional separated flow with an unsteady viscous-inviscid interaction method

Three previous papers have shown that the viscous inviscid numerical methods were capable of calculating separated turbulent flows. The 'Semi-inverse method' and the models of the first author allow the computation of massive separations, stalled flows, and shock wave-boundary layer interactions, in two-dimensional or quasi-three-dimensional conditions, from low speeds to supersonic speeds. The 'Semi-implicit' method for time-consistent coupling allows for the computation of time-accurate transonic separated flow and buffer computations in two-dimensions. The present paper shows that the viscous-inviscid interaction approach is also able to compute the fully three-dimensional flow separation phenomena. The method is based on a thin-layer approximation of the theory of 'Defect-Formulation' that provides the viscous-inviscid splitting of the Navier-Stokes equations. A parametric analytical modelling of the 3D-turbulent velocity profiles is involved. Numerically, the 3D-velocity profiles are discretized in the normal z-direction and driven by parametric integral 3D-equations in direct or inverse modes in the x-direction. The viscous-inviscid coupling is fully 3D and solved the time-consistency problem with an extension of the 'Semi-implicit' method previously suggested in two-dimensions. A 3D inviscid subroutine with TSP approximation is used. Results are obtained for transonic steady flows over wings with shock-induced transonic separation. The method provides results for highly three-dimensional flow separations, such as induced by a three-dimensional through at the wall of a flat plate. The 3D viscous-inviscid coupling and the 3D model of the velocity field provide three-dimensional instantaneous skin-friction lines whose patterns exhibit the same complex topology as Navier-Stokes solvers, with foci, nodes, and saddle-points.

Leballeur, J. C.↗
NASA NTRS1976

Extended applications of the vortex lattice method

The application of the vortex lattice method to problems not usually dealt with by this technique is considered. It is shown that if the discrete vortex lattice is considered as an approximation to surface-distributed vorticity, then the concept of the generalized principal part of an integral yields a residual term to the vortex-induced velocity that renders the vortex lattice method valid for supersonic flow. Special schemes for simulating non-zero thickness lifting surfaces and fusiform bodies with vortex lattice elements are presented. Thickness effects of wing-like components are simulated by a double vortex lattice layer, and fusiform bodies are represented by a vortex grid arranged on a series of concentric cylindrical surfaces. Numerical considerations peculiar to the application of these techniques are briefly discussed.

Miranda, L. R.↗
NASA NTRS1989

A multidomain spectral collocation method for the Stokes problem

A multidomain spectral collocation scheme is proposed for the approximation of the two-dimensional Stokes problem. It is shown that the discrete velocity vector field is exactly divergence-free and we prove error estimates both for the velocity and the pressure.

Landriani, G. Sacchi↗
NASA NTRS1981

Velocity-space synthesis of ISEE-1 measurements of the three dimensional electron distribution function

A computer package which produces contour plots of the three dimensional electron distribution function measured by an electron spectrometer aboard ISEE-1 is described. Examples of the contour plots and an explanation of how to use the program, including the necessary computer code for running the program on the GSFC 360/91 computer is presented. The method by which the discrete measurements of the distribution function, given by points on the four dimensional surface are synthesized into a smooth surface in a three dimensional space which can be contoured is described. The velocity components are parallel and perpendicular to the magnetic field, respectively, in the proper frame of the electrons.

Fitzenreiter, R. J.↗