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EFFECTIVE TREATMENT OF THE SINGULAR LINE BOUNDARY-PROBLEM FOR 3-DIMENSIONAL GRIDS

AIAA JOURNAL 1993年第10期31卷 1757-1758页

作者： PALMER, G VENKATAPATHY, E ELORET INST MT VIEWCA 94043

THREE-DIMENSIONAL grids of rotation contain a singular line where the radial grid planes meet. When the flow equations are transformed into generalized coordinates, a mathematical singularity is introduced into the governing equations. Specifically, the grid Jacobian J becomes infinite along the singular line. This can introduce nonphysical perturbations in the flow solution, particularly if a finite-difference solution algorithm is used. A number of recent publications1-5 have discussed problems associated with the singular line. This paper presents a method for eliminating the axis singularity. The governing equations are reformulated using a redefined grid Jacobian that can be evaluated at the singular line. This allows a finite-difference algorithm to compute a smooth, continuous solution in the region of the singular line.

关键词： solution algorithm Flow Equations Angle of Attack Blunt Bodies Navier Stokes Equations Stagnation Point Radial Velocity Aerospace Sciences Inviscid Flow Perfect Gas

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EFFICIENT SIMULATION OF INCOMPRESSIBLE VISCOUS-FLOW OVER SINGLE AND MULTIELEMENT AIRFOILS

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JOURNAL OF AIRCRAFT 1993年第5期30卷 736-743页

作者： ROGERS, SE WILTBERGER, NL KWAK, D NASA Ames Research Center Moffett Field California 94035

The incompressible, viscous, turbulent flow over single and multielement airfoils is numerically simulated in an efficient manner by solving the incompressible Navier-Stokes equations. The solution algorithm uses the method of pseudocompressibility with an upwind-differencing scheme for the convective fluxes, and an implicit line-relaxation scheme. The motivation for this work includes interest in studying high-lift takeoff and landing configurations of various aircraft. In particular, accurate computation of lift and drag at various angles of attack up to stall is desired. Two different turbulence models are tested in computing the flow over a NACA 4412 airfoil;an accurate prediction of stall is obtained. The approach used for multielement airfoils involves the use of multiple zones of structured grids fitted to each element. Two different approaches are compared: 1) a patched system of grids, and 2) an overlaid Chimera system of grids. Computational results are presented for two-element, three-element, and four-element airfoil configurations. Generally, good agreement with experimental surface pressure coefficients is seen. The code converges in less than 200 iterations, requiring on the order of 1 min of CPU time on a CRAY YMP per element in the airfoil configuration.

关键词： Incompressible Viscous Flow Lift Coefficient Supercritical Airfoils Reynolds Averaged Navier Stokes Baldwin Lomax Turbulence Model Navier Stokes Calculations Takeoff and Landing Computing solution algorithm Earth

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SPATIAL ADAPTATION OF UNSTRUCTURED MESHES FOR UNSTEADY AERODYNAMIC FLOW COMPUTATIONS

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AIAA JOURNAL 1992年第5期30卷 1243-1251页

作者： RAUSCH, RD BATINA, JT YANG, HTY NASA LANGLEY RES CTRUNSTEADY AERODYNAM BRANCHDIV STRUCT DYNAMHAMPTONVA 23665 PURDUE UNIV SCH ENGNW LAFAYETTEIN 47907

Spatial adaptation procedures for the accurate and efficient solution of steady and unsteady inviscid flow problems are described. The adaptation procedures were developed and implemented within a two-dimensional unstructured-grid upwind-type Euler code. These procedures involve mesh enrichment and mesh coarsening to either add points in high gradient regions of the flow or remove points where they are not needed, respectively, to produce solutions of high spatial accuracy at minimal computational cost. The paper describes a new approach to detect high gradient regions of the flow that uses the substantial derivative of density. Additionally, the paper gives a detailed description of the enrichment and coarsening procedures and further describes a new weighted averaging procedure and the interpolation of flow variables that improves the overall accuracy of the flow solver. Presented are comparisons with alternative results and experimental data to provide an assessment of the accuracy and efficiency of the capability. Steady and unsteady transonic results, obtained using spatial adaptation for the NACA 0012 airfoil, are shown to be of high spatial accuracy, primarily in that the shock waves are very sharply captured. The results were obtained with large computational savings when compared to results for a globally enriched mesh with cells subdivided as many times as the finest cells of the adapted grid.

关键词： Aerodynamic Flows Shock Waves Pitching Airfoil Unstructured Grid Compressibility solution algorithm Conservation Equations Courant Friedrichs Lewy Lagrange Multipliers Stagnation Point

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HIGHER-ORDER EIGENPAIR PERTURBATIONS

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AIAA JOURNAL 1992年第7期30卷 1870-1876页

作者： ELDRED, MS LERNER, PB ANDERSON, WJ LOS ALAMOS NATL LAB LOS ALAMOSNM 87544

A matrix method is presented for the exact calculation of large eigenpair perturbations arising from design variable changes. The method is "forward analysis" in the sense that design variable changes are known and eigenpair perturbations are computed. Competing methods for forward analysis include reanalysis and first-order approximate methods. First-order methods are well known for their ability to calculate small eigenpair changes but are inadequate when large changes are required. In this paper, a new method of forward analysis is presented that takes into account all orders of the perturbation expansion. A benchmark cantilever beam will be analyzed with the new method for large perturbations in design variables. The method will be valuable for fast reanalysis and for identification and model correlation studies where sizeable differences exist between a baseline model and an objective model.

关键词： Cantilever Beam Finite Element Analysis Perturbation Method Structural Dynamics solution algorithm Iterative solution Bending Stiffness Nonlinear Systems Catalysts Nastran

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MULTIZONAL NAVIER-STOKES solutionS FOR THE MULTIBODY SPACE-SHUTTLE CONFIGURATION

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JOURNAL OF SPACECRAFT AND ROCKETS 1992年第1期29卷 129-137页

作者： CHEN, CL RAMAKRISHNAN, S SZEMA, KY DRESSER, HS RAJAGOPAL, K ROCKWELL INT CORP DIV SPACEDOWNEYCA 90241

Numerical simulation of flow past the multibody Shuttle configuration in ascent mode has been carried out using the USA (unified solution algorithms) code, which is a finite volume, unified time/space marching, zonal, Reynolds-averaged Navier-Stokes solver featuring an implicit, upwind-biased scheme and total variation diminishing discretization for high accuracy. Body conforming elliptic multizonal grids were used in the computation. The agreement between computed and experimental results is reasonable. The interference effects of various components on the surface pressure distribution are discussed. The results show the importance of ensuring simulation of proper blockages due to various components of the mated Space Shuttle vehicle to obtain a reliable prediction of aerodynamic forces. Agreement between computed and experimental results could be improved by refining the definition of various geometric features and by including all geometric complexities.

关键词： Space Shuttle Total Variation Diminishing Reynolds Averaged Navier Stokes Freestream Conditions solution algorithm Solid Rocket Boosters Roe Approximate Riemann Solver Flight Testing Wind Tunnel Walls Turbulent Boundary Layer

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HELICOPTER ROTOR BLADE AEROELASTICITY IN FORWARD FLIGHT WITH AN IMPLICIT STRUCTURAL FORMULATION

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AIAA JOURNAL 1992年第9期30卷 2274-2282页

作者： CELI, R University of Maryland College Park Maryland 20742

This paper describes an aeroelastic stability and response analysis in which the structural operator is formulated numerically, without expanding analytically the various algebraic expressions that make up the beam model. No ordering schemes need to be invoked to simplify the algebraic manipulations, and the various components of the mathematical model of the beam can be implemented and modified independently. The formulation is compatible with most solution algorithms. Two different implicit formulations are presented. The results of four illustrative examples are also presented. The first focuses on the effects of higher order kinematic nonlinearities on the aeroelastic stability and response of a hingeless rotor blade. The remaining three show how to introduce, using the implicit formulation, a nonlinear stress-strain relation in table look-up form, a composite cross section, and cross-sectional warping. Aeroelastic stability results are presented for all examples.

关键词： Aeroelastic Stability Helicopter Rotor Bernoulli Euler Beams Stress Strain Curve Hingeless Rotor Blade Composite Materials Mathematical Models Rotary Wing Elastic Deformation solution algorithm

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OPTIMAL OUTPUT-FEEDBACK FOR LINEAR TIME-PERIODIC SYSTEMS

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JOURNAL OF GUIDANCE CONTROL AND DYNAMICS 1992年第2期15卷 416-423页

作者： CALISE, AJ WASIKOWSKI, ME SCHRAGE, DP Georgia Institute of Technology Atlanta Georgia 30332

An approach is developed for applying optimal output feedback control theory to the design of fixed gain controllers for lime-periodic systems. Constant feedback gains based on plant outputs are calculated by minimizing a linear quadratic performance cost functional. A solution algorithm is developed using Floquet-Lyapunov theory and a generalized harmonic expansion technique. The theory is applied to the control of a helicopter rotor blade in forward flight through individual blade control. It is shown that constant gain output feedback can be used to augment the stability of the resulting time-periodic system, with the potential for greatly reducing the implementation complexity.

关键词： Full State Feedback Helicopter Blade solution algorithm Linear Time Invariant System Linear Quadratic Gaussian Numerical Integration Aeroelastic Stability Damping Ratio Angle of Attack Rotor Blades

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EXTENSION OF THE LAMBDA-FORMULATION TO IMPERFECT GAS-FLOWS

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AIAA JOURNAL 1992年第11期30卷 2785-2788页

作者： LENTINI, D Universita degli Studi di Roma "La Sapienza " 1-00184 Rome Italy

The λ formulation has proven to be a powerful tool for the numerical solution of compressible flows of a perfect gas. In this note we extend the λ formulation to (inert) flows of thermally perfect gas with cp varying as a function of the temperature T. Such gases are sometimes referred to as 'imperfect gases'. The resulting formulation is extremely simple and involves a minimum computational overhead in comparison to the perfect gas case. Indeed, existing algorithms for a perfect gas can easily be upgraded with a minimum coding effort, without fundamentally altering their structure. The proposed formulation is applied to the computation of flow in a quasi-one-dimensional nozzle to prove the workability of this approach and to demonstrate the differences with respect to a perfect gas computation. It is apparent, however, that the range of application of the present formulation is completely general.

关键词： Perfect Gas One Dimensional Flow Chemical Equilibrium Shock Tunnels Stagnation Temperature Chemically Reacting Flow Continuity Equation Stagnation Enthalpy Vibrational Energy solution algorithm

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FAR-FIELD COMPUTATIONAL BOUNDARY-CONDITIONS FOR 2-DIMENSIONAL EXTERNAL FLOW PROBLEMS

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AIAA JOURNAL 1992年第11期30卷 2585-2594页

作者： VERHOFF, A STOOKESBERRY, D AGRAWAL, S McDonnell Aircraft Company St. Louis Missouri 63166

Far-field computational boundary conditions for external flow problems have been developed from analytic solutions of the linearized steady-state Euler equations. These boundary conditions have improved accuracy compared with commonly used characteristic boundary conditions. The Euler equations are linearized about a constant pressure, rectilinear flow condition that truly represents conditions at infinity. Because the Euler equations are used to develop the boundary conditions, the now crossing the boundary can be rotational. The boundary conditions can be used with any numerical Euler solution method and allow computational boundaries to be located very close to the nonlinear region of interest. This leads to a significant reduction in the number of grid points required for numerical solution. Numerical results are presented that show that the boundary conditions and far-field analytic solutions provide a smooth transition across a computational boundary to the true far-field conditions at infinity. They also demonstrate the synergism that can be realized from coupling analytic and computational methods. Computational efficiency gains are shown to be substantial.

关键词： External Flows Euler Equations Computational Methods Freestream Mach Number Lift Coefficient solution algorithm Stagnation Temperature Integral Transform Unstructured Grid NACA 0012

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IMPROVED CALCULATION OF TRANSONIC POTENTIAL FLOW PAST SWEPT WINGS

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JOURNAL OF AIRCRAFT 1992年第5期29卷 961-964页

作者： WANG, LX CAUGHEY, DA Cornell University Ithaca New York 14853

In spite of recent advances in numerical methods to solve the Euler and Navier-Stokes equations for transonic flow problems, the transonic potential equation is still widely used in design work. Among the algorithms for solving three-dimensional transonic potential flows, the computer program Flo-22 developed by A. Jameson and D.A. Caughley has proved to be economical and robust for many practical applications. The purpose of this paper is to describe some recent improvements in Flo-22, that include a chordwise scaling to render the trailing edge a grid line, and a modification to the symmetry plane boundary condition to better enforce the noflux condition there. Results are presented for the transonic flow past a supercritical wing, using the original and modified versions of Flo-ww, as well as the fully-conservative Euler code developed by Y. Yadlin and D.A. Caughey.

关键词： Potential Flow Swept Wing Freestream Mach Number Lift Coefficient Wing Root solution algorithm Supercritical Wings Tapered Wings Finite Difference Method Navier Stokes Equations

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