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  • 1985-1989  (9)
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  • 1
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    An embedded mesh procedure for leading-edge vortex flows (1989)
    In:  CASI
    Details
    Publication Date: 2013-08-31
    Description: A cell-vertex scheme is outlined for solving the flow about a delta wing with M (sub infinity) is greater than 1. Embedded regions of mesh refinement allow solutions to be obtained which have much higher resolution than those achieved to date. Effects of mesh refinement and artificial viscosity on the solutions are studied, to determine at what point leading-edge vortex solutions are grid-converged. A macroscale and a microscale for the size of the vortex are defined, and it is shown that the macroscale (which includes the wing surface properties) is converged on a moderately refined grid, while the microscale is very sensitive to grid spacing. The level of numerical diffusion in the core of the vortex is found to be substantial. Comparisons with the experiment are made for two cases which have transonic cross-flow velocities.
    Keywords: AERODYNAMICS
    Type: NASA, Langley Research Center, Transonic Symposium: Theory, Application, and Experiment, Volume 1, Part 1; p 231-259
    Format: application/pdf
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  • 2
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    An adaptive embedded mesh procedure for leading-edge vortex flows (1989)
    In:  Other Sources
    Details
    Publication Date: 2019-06-28
    Description: A procedure for solving the conical Euler equations on an adaptively refined mesh is presented, along with a method for determining which cells to refine. The solution procedure is a central-difference cell-vertex scheme. The adaptation procedure is made up of a parameter on which the refinement decision is based, and a method for choosing a threshold value of the parameter. The refinement parameter is a measure of mesh-convergence, constructed by comparison of locally coarse- and fine-grid solutions. The threshold for the refinement parameter is based on the curvature of the curve relating the number of cells flagged for refinement to the value of the refinement threshold. Results for three test cases are presented. The test problem is that of a delta wing at angle of attack in a supersonic free-stream. The resulting vortices and shocks are captured efficiently by the adaptive code.
    Keywords: AERODYNAMICS
    Type: AIAA PAPER 89-0080
    Format: text
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  • 3
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    Comparison of measured and computed pitot pressures in a leading edge vortex from a delta wing (1987)
    In:  Other Sources
    Details
    Publication Date: 2019-06-28
    Description: Calculations are presented for a 75-deg swept flat plate wing tested at a freestream Mach number of 1.95 and 10 degrees angle of attack. Good agreement is found between computational data and previous experimental pitot pressure measurements in the core of the vortex, suggesting that the total pressure losses predicted by the Euler equation solvers are not errors, but realistic predictions. Data suggest that the magnitude of the total pressure loss is related to the circumferential velocity field through the vortex, and that it increases with angle of attack and varies with Mach number and sweep angle.
    Keywords: AERODYNAMICS
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  • 4
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    Leading-edge vortex solutions with large total pressure losses (1987)
    In:  Other Sources
    Details
    Publication Date: 2019-06-28
    Description: Computations are presented for a Lambda = 75 deg delta wing in a supersonic freestream under two conditions which lead to leading-edge vortices. For one condition, analysis of the computed vortical flow reveals a closed streamline in the core. From varying computational parameters, it appears that this is due to truncation error of the convective derivatives. For the other condition, comparisons are made with wind-tunnel data, and good agreement is noted for pitot pressure distributions, flow angles on the symmetry plane, and the position of an embedded shock. Many of the aerodynamic parameters are shown to be insensitive to grid spacing.
    Keywords: AERODYNAMICS
    Type: AIAA PAPER 87-0039
    Format: text
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  • 5
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    A genuinely multi-dimensional upwind cell-vertex scheme for the Euler equations (1989)
    In:  Other Sources
    Details
    Publication Date: 2019-06-28
    Description: A scheme of solving the two-dimensional Euler equations is developed. The scheme is genuinely two-dimensional. At each iteration, the data are locally decomposed into four variables, allowing convection in appropriate directions. This is done via a cell-vertex scheme with a downwind-weighted distribution step. The scheme is conservative and third-order accurate in space. The derivation and stability analysis of the scheme for the convection equation, and the derivation of the extension to the Euler equations are given. Preconditioning techniques based on local values of the convection speeds are discussed. The scheme for the Euler equations is applied to two channel-flow problems. It is shown to converge rapidly to a solution that agrees well with that of a third-order upwind solver.
    Keywords: FLUID MECHANICS AND HEAT TRANSFER
    Type: AIAA PAPER 89-0095
    Format: text
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  • 6
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    Comparison of experimental and numerical results for delta wings with vortex flaps (1988)
    In:  Other Sources
    Details
    Publication Date: 2019-07-12
    Keywords: AERODYNAMICS
    Type: Journal of Aircraft (ISSN 0021-8669); 25; 405-412
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  • 7
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    Sonic-point capturing (1989)
    In:  Other Sources
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    Publication Date: 2019-07-13
    Description: A prototype scheme that produces perfectly smooth transonic solutions to nozzle-flow problems is derived and tested. The basic upwind scheme is described as well as satisfying the entropy condition, treatment of the source term, and numerical verification. The analysis yielded a numerical flux function for use near a sonic point, which is based on a full model of a transonic expansion wave, and a matched treatment for the source term.
    Keywords: AERODYNAMICS
    Type: AIAA PAPER 89-1945 , AIAA Computational Fluid Dynamics Conference; Jun 13, 1989 - Jun 15, 1989; Buffalo, NY; United States
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  • 8
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    A genuinely multi-dimensional upwind cell-vertex scheme for the Euler equations (1989)
    In:  CASI
    Details
    Publication Date: 2019-07-13
    Description: The solution of the two-dimensional Euler equations is based on the two-dimensional linear convection equation and the Euler-equation decomposition developed by Hirsch et al. The scheme is genuinely two-dimensional. At each iteration, the data are locally decomposed into four variables, allowing convection in appropriate directions. This is done via a cell-vertex scheme with a downwind-weighted distribution step. The scheme is conservative, and third-order accurate in space. The derivation and stability analysis of the scheme for the convection equation, and the derivation of the extension to the Euler equations are given. Preconditioning techniques based on local values of the convection speeds are discussed. The scheme for the Euler equations is applied to two channel-flow problems. It is shown to converge rapidly to a solution that agrees well with that of a third-order upwind solver.
    Keywords: NUMERICAL ANALYSIS
    Type: NASA-TM-102029 , E-4772 , NAS 1.15:102029 , ICOMP-89-13 , AIAA PAPER 89-0095 , Aerospace Sciences Meeting; Jan 09, 1989 - Jan 12, 1989; Reno, NV; United States
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  • 9
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    Design of optimally smoothing multi-stage schemes for the Euler equations (1989)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: In this paper, a method is developed for designing multi-stage schemes that give optimal damping of high-frequencies for a given spatial-differencing operator. The objective of the method is to design schemes that combine well with multi-grid acceleration. The schemes are tested on a nonlinear scalar equation, and compared to Runge-Kutta schemes with the maximum stable time-step. The optimally smoothing schemes perform better than the Runge-Kutta schemes, even on a single grid. The analysis is extended to the Euler equations in one space-dimension by use of 'characteristic time-stepping', which preconditions the equations, removing stiffness due to variations among characteristic speeds. Convergence rates independent of the number of cells in the finest grid are achieved for transonic flow with and without a shock. Characteristic time-stepping is shown to be preferable to local time-stepping, although use of the optimally damping schemes appears to enhance the performance of local time-stepping. The extension of the analysis to the two-dimensional Euler equations is hampered by the lack of a model for characteristic time-stepping in two dimensions. Some results for local time-stepping are presented.
    Keywords: AERODYNAMICS
    Type: AIAA PAPER 89-1933 , AIAA Computational Fluid Dynamics Conference; Jun 13, 1989 - Jun 15, 1989; Buffalo, NY; United States
    Format: text
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