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NASA NTRS1985

Three dimensional flow phenomena in fluid machinery; Proceedings of the Winter Annual Meeting, Miami Beach, FL, November 17-22, 1985

For papers presented in this volume provide an overview of the latest developments in experimental measurements and analytical and numerical predictions of three-dimensional flows in fluid machinery. Topics discussed include three-dimensional cascade testing of turbine nozzles at high exit Mach number; the use of a secondary flow computation in the compressor design process; an experimental investigation of static propeller flow field; and calculation of three-dimensional boundary layers on rotating turbine blades. Papers are also presented on a three-dimensional solution method for turbomachinery analysis; analysis of rotational inviscid flows in curved passages; and a mathematical model for the analysis of fluid flow in a scroll.

Hamed, A.↗

NASA NTRS1986

Mach reflection and aerodynamic choking in two-dimensional ducted flow

Flow through a two-dimensional duct with supersonic inflow is numerically investigated, from the viewpoint of the formation of Mach reflection, aerodynamic choking, and the possibility of constructing a curve similar to that for the quasi-one-dimensional flow in a converging-diverging duct. Such a curve can be used to determine whether a duct with a certain area ratio will or will not choke for a given inflow Mach number. Plots of pressure and mass flux contours are obtained for a given duct configuration. It is found that the two-dimensional flow always chokes at a higher Mach number than the corresponding quasi-one-dimensional flow for a given throat/inlet flow area ratio.

Kumar, A.↗

NASA NTRS1984

Calculation of two- and three-dimensional transonic cascade flow field using the Navier-Stokes equations

A Navier-Stokes analysis employing the time-dependent Linearized Block Implicit scheme (LBI) was applied to two-dimensional and three-dimensional transonic turbulent cascade flows. In general, the geometrical configuration of the turbine blade impacts both the grid construction procedure and the implementation of the numerical algorithm. Since modern turbine blades of interest are characterized by very blunt leading edges, rounded trailing edges and high stacking angles, a robust grid construction procedure is required that can accommodate the severe body shape while resolving regions of large flow gradients. A constructive O-type grid generation technique, suitable for cascades with rounded trailing edges, was developed and used to construct the C3X turbine cascade coordinate grid. Two-dimensional calculations were performed employing the Navier-Stokes procedure for the C3X turbine cascade, and the predicted pressure coefficients and heat transfer rates were compared with the experimental data. Three-dimensional Navier-Stokes calculations were also performed.

Weinberg, B. C.↗

NASA NTRS1987

Two- and three-dimensional viscous computations of a hypersonic inlet flow

The three-dimensional parabolized Navier-Stokes code has been used to investigate the flow through a Mach 7.4 inlet. A two-dimensional parametric study of grid resolution, turbulence modeling and effect of gamma has been done and compared with experimental results. The results show that mesh resolution of the shock waves, real gas effects and turbulence length scaling are very important to get accurate results for hypersonic inlet flows. In addition a three-dimensional calculation of the Mach 7.4 inlet has been done on a straight sideplate configuration. The results show that the glancing shock/boundary layer interaction phenomena causes significant three-dimensional flow in the inlet.

Kunik, William G.↗

NASA NTRS1987

Two-dimensional nozzle plume characteristics

Future high performance aircraft will likely feature asymmetric or two-dimensional nozzles with or without ejectors. In order to design two-dimensional nozzle/ejector systems of minimum size and weight, the plume decay and spreading characteristics of basic two-dimensional nozzles must first be established. The present work deals with the experimental analyses of these plume characteristics and includes the effects of nozzle aspect ratio and flow conditions (jet Mach number and temperature) on the plume decay and spreading of two-dimensional nozzles. Correlations including these variables are developed in a manner similar to those previously developed successfully for conic and dual-flow plumes.

Vonglahn, Uwe H.↗

NASA NTRS1987

A three-dimensional dual potential procedure with applications to wind tunnel inlets and interacting boundary layers

A dual potential decomposition of the velocity field into a scalar and a vector potential function is extended to three dimensions and used in the finite-difference simulation of steady three-dimensional inviscid rotational flows and viscous flow. The finite-difference procedure was used to simulate the flow through the 80 by 120 ft wind tunnel at NASA Ames Research Center. Rotational flow produced by the stagnation pressure drop across vanes and screens which are located at the entrance of the inlet is modeled using actuator disk theory. Results are presented for two different inlet vane and screen configurations. The numerical predictions are in good agreement with experimental data. The dual potential procedure was also applied to calculate the viscous flow along two and three dimensional troughs. Viscous effects are simulated by injecting vorticity which is computed from a boundary layer algorithm. For attached flow over a three dimensional trough, the present calculations are in good agreement with other numerical predictions. For separated flow, it is shown from a two dimensional analysis that the boundary layer approximation provides an accurate measure of the vorticity in regions close to the wall; whereas further away from the wall, caution has to be exercised in using the boundary-layer equations to supply vorticity to the dual potential formulation.

Rao, K. V.↗

NASA NTRS1987

Two-component LDV investigation of 3-dimensional shock/turbulent boundary layer interactions

Mean-velocity and turbulence measurements obtained by two-component laser Doppler velocimetry are presented, together with numerical predictions, for the shock-related separation of a turbulent boundary layer at Mach 2.85. The basic geometry, a 30 deg half-angle flare mounted on a long cylinder, is made three-dimensional by tipping the flare at an angle of attack, alpha. The separation length and general upstream influence increase with alpha. A recirculating vortex in the separated zone becomes stronger as three-dimensionality increases. A large-scale unsteadiness of the separation shock wave and surrounding flowfields grows in amplitude with alpha, and appears to strongly influence the amplification of turbulence correlations ahead of detachment. Scaling of the streamwise coordinate by separation length causes two-dimensional and three-dimensional data profiles on the cylinder to collapse for most measured quantities.

Brown, J. D.↗

NASA NTRS1987

Two- and three-dimensional viscous computations of a hypersonic inlet flow

Kunik, William G.↗

NASA NTRS1987

On the 3-dimensional structure of plasmoids

The hypothesis that the IMF penetrates plasmoids causing them to be three- rather than two-dimensional is tested by comparing observations of By within plasmoids and related tail structures to upstream IMF By data. The magnetic topologies that result from the mergings of closed plasma sheet flux tubes and open tail lobe flux tubes at a near-earth neutral line, and merging near the tail flanks are described and studied. The particle signals and isotropic electron distributions are examined. It is observed that the IMF By penetrates plasmoids and that their structure is three-dimensional. In the three-dimensional model of plasmoids the reconnected plasma sheet field lines form a magnetic flux-ropelike structure. The three-dimensional model is utilized to analyze stagnant, slowly moving and earthward moving structures.

Hughes, W. J.↗

NASA NTRS1987

Two-dimensional nozzle plume characteristics

Von Glahn, Uwe H.↗

NASA NTRS1987

Variational four-dimensional analysis using quasi-geostrophic constraints

A variational four-dimensional analysis technique using quasi-geostrophic models as constraints is examined using gridded fields as data. The analysis method uses a standard iterative nonlinear minimization technique to find the solution to the constraining forecast model which best fits the data as measured by a predefined functional. The minimization algorithm uses the derivative of the functional with respect to each of the initial condition values. This derivative vector is found by inserting the weighted differences between the model solution and the inserted data into a backwards integrating adjoint model. The four-dimensional analysis system was examined by applying it to fields created from a primitive equations model forecast and to fields created from satellite retrievals. The results show that the technique has several interesting characteristics not found in more traditional four-dimensional assimilation techniques. These features include a close fit of the model solution to the observations throughout the analysis interval and an insensitivity to the frequency of data insertion or the amount of data. The four-dimensional analysis technique is very versatile and can be extended to more complex problems with little theoretical difficulty.

Derber, John C.↗

NASA NTRS1988

Three-Dimensional Complex Variables

Report presents new theory of analytic functions of three-dimensional complex variables. While three-dimensional system subject to more limitations and more difficult to use than the two-dimensional system, useful in analysis of three-dimensional fluid flows, electrostatic potentials, and other phenomena involving harmonic functions.

Martin, E. Dale↗

NASA NTRS1987

Vectorizable implicit algorithms for the flux-difference split, three-dimensional Navier-Stokes equations

The computational efficiency of four vectorizable implicit algorithms is assessed when applied to calculate steady-state solutions to the three-dimensional, incompressible Navier-Stokes equations in general coordinates. Two of these algorithms are characterized as hybrid schemes; that is, they combine some approximate factorization in two coordinate directions with relaxation in the remaining spatial direction. The other two algorithms utilize an approximate factorization approach which yields two-factor algorithms for three-dimensional systems. All four algorithms are implemented in identical high-resolution upwind schemes for the flux-difference split Navier-Stokes equations. These highly nonlinear schemes are obtained by extending an implicit Total Variation Diminishing (TVD) scheme recently developed for linear one-dimensional systems of hyperbolic conservation laws to the three-dimensional Navier-Stokes equations. The computation of vortical flow over a sharp-edged, thin delta wing has been chosen as a common numerical test case. The convergence of the algorithms is discussed and the accuracy of the computed flow-field results is assessed. The validity of the present results are demonstrated by a comparison with experimental data.

Hartwich, P. M.↗

NASA NTRS1987

Three-dimensional test requirement for random vibration testing

An approach to defining and evaluating three-dimensional vibration test requirements is discussed. The approach is used to develop the three-dimensional space random-vibration test requirements for missile components subjected to truck transportation environments. One-dimensional testing parameters such as power spectral density and overall g rms values for three mutually perpendicular directions represent the test requirements. The coherence characteristics between each input axis were established and adjusted empirically in an attempt to simulate the cross-correlation in three-dimensional random vibration excitation.

Chang, Kurng↗

NASA NTRS1988

Adaptive wall research with two- and three-dimensional models in low speed and transonic tunnels

This paper summarises recent research at the University of Southampton into adaptive wall technology and outlines the direction of current efforts. The work is aimed at developing techniques for use in test sections where the top and bottom walls may be adjusted in single curvature. Wall streamlining eliminates, as far as experimentally possible, the top and bottom wall interference in low speed and transonic aerofoil testing. A streamlining technique has been developed for low speeds which allows the testing of swept wing panels in low interference environments. At higher speeds, a comparison of several two-dimensional transonic streamlining algorithms has been made and a technique for streamlining with a choked test section has also been developed. Three-dimensional work has mainly concentrated on tests of sidewall mounted half-wings and the development of the software packages required to assess interference and to adjust the flexible walls. It has been demonstrated that two-dimensional wall adaptation can significantly modify the level of wall interference around relatively large three-dimensional models. The residual interferences are small and are probably amenable to standard post-test correction methods. Tests on a calibrated wing-body model are planned in the near future to further validate the proposed streamlining technique.

Lewis, M. C.↗

NASA NTRS1988

Embedding of attitude determination in n-dimensional spaces

The problem of attitude determination in n-dimensional spaces is addressed. The proper parameters are found, and it is shown that not all three-dimensional methods have useful extensions to higher dimensions. It is demonstrated that Rodriguez parameters are conveniently extendable to other dimensions. An algorithm for using these parameters in the general n-dimensional case is developed and tested with a four-dimensional example. The correct mathematical description of angular velocities is addressed, showing that angular velocity in n dimensions cannot be represented by a vector but rather by a tensor of the second rank. Only in three dimensions can the angular velocity be described by a vector.

Bar-Itzhack, Itzhack Y.↗

NASA NTRS1989

Multigrid calculation of three-dimensional turbomachinery flows

Research was performed in the general area of computational aerodynamics, with particular emphasis on the development of efficient techniques for the solution of the Euler and Navier-Stokes equations for transonic flows through the complex blade passages associated with turbomachines. In particular, multigrid methods were developed, using both explicit and implicit time-stepping schemes as smoothing algorithms. The specific accomplishments of the research have included: (1) the development of an explicit multigrid method to solve the Euler equations for three-dimensional turbomachinery flows based upon the multigrid implementation of Jameson's explicit Runge-Kutta scheme (Jameson 1983); (2) the development of an implicit multigrid scheme for the three-dimensional Euler equations based upon lower-upper factorization; (3) the development of a multigrid scheme using a diagonalized alternating direction implicit (ADI) algorithm; (4) the extension of the diagonalized ADI multigrid method to solve the Euler equations of inviscid flow for three-dimensional turbomachinery flows; and also (5) the extension of the diagonalized ADI multigrid scheme to solve the Reynolds-averaged Navier-Stokes equations for two-dimensional turbomachinery flows.

Caughey, David A.↗

NASA NTRS1988

An approximation technique for computing optimal fixed-order controllers for infinite-dimensional systems

The finite-dimensional approximation of the infinite-dimensional Bernstein/Hyland optimal projection theory is investigated analytically. The approach yields fixed-finite-order controllers which are optimal with respect to high-order approximating finite-dimensional plant models. The technique is illustrated by computing a sequence of first-order controllers for a one-dimensional SISO parabolic (heat/diffusion) system using a spline-based Ritz-Galerkin finite-element approximation. The numerical studies indicate convergence of the feedback gains with less than 2-percent performance degradation over full-order LQG controllers.

Bernstein, Dennis S.↗