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  • 1
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    A procedure for analyzing transonic flow over harmonically oscillating airfoils (1978)
    In:  CASI
    Details
    Publication Date: 2006-02-22
    Description: Finite difference procedures were successfully used to solve the steady transonic flow about airfoils and appear to provide a practical means for calculating the corresponding unsteady flow. The purpose of the paper is to describe a finite difference procedure derived from the equations for the potential flow by assuming small perturbations and harmonic motion. The velocity potential is divided into steady and unsteady parts, and the resulting unsteady equation is linearized on the basis of small amplitudes of oscillation. The steady velocity potential, which must be calculated first, is described by the classical nonlinear transonic differential equation.
    Keywords: AERODYNAMICS
    Type: NASA. Langley Res. Center Advanced Technol. Airfoil Res., Vol. 1, Pt. 2; p 657-670
    Format: text
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  • 2
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    Further investigation of a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings (1980)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. The steady velocity potential is obtained first from the well-known nonlinear equation for steady transonic flow. The unsteady velocity potential is then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. An out-of-core direct solution procedure was developed and applied to two-dimensional sections. Results are presented for a section of vanishing thickness in subsonic flow and an NACA 64A006 airfoil in supersonic flow. Good correlation is obtained in the first case at values of Mach number and reduced frequency of direct interest in flutter analyses. Reasonable results are obtained in the second case. Comparisons of two-dimensional finite difference solutions with exact analytic solutions indicate that the accuracy of the difference solution is dependent on the boundary conditions used on the outer boundaries. Homogeneous boundary conditions on the mesh edges that yield complex eigenvalues give the most accurate finite difference solutions. The plane outgoing wave boundary conditions meet these requirements.
    Keywords: AERODYNAMICS
    Type: NASA-CR-3195 , D-48851
    Format: application/pdf
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  • 3
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    An investigation of several factors involved in a finite difference procedure for analyzing the transonic flow about harmonically oscillating airfoils and wings (1979)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: Analytical and empirical studies of a finite difference method for the solution of the transonic flow about harmonically oscillating wings and airfoils are presented. The procedure is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances. Since sinusoidal motion is assumed, the unsteady equation is independent of time. Three finite difference investigations are discussed including a new operator for mesh points with supersonic flow, the effects on relaxation solution convergence of adding a viscosity term to the original differential equation, and an alternate and relatively simple downstream boundary condition. A method is developed which uses a finite difference procedure over a limited inner region and an approximate analytical procedure for the remaining outer region. Two investigations concerned with three-dimensional flow are presented. The first is the development of an oblique coordinate system for swept and tapered wings. The second derives the additional terms required to make row relaxation solutions converge when mixed flow is present. A finite span flutter analysis procedure is described using the two-dimensional unsteady transonic program with a full three-dimensional steady velocity potential.
    Keywords: AERODYNAMICS
    Type: NASA-CR-159143 , D6-48852
    Format: application/pdf
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  • 4
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    The practical application of a finite difference method for analyzing transonic flow over oscillating airfoils and wings (1978)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: Separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady equations for small disturbances was performed. The steady velocity potential was obtained first from the well known nonlinear equation for steady transonic flow. The unsteady velocity potential was then obtained from a linear differential equation in complex form with spatially varying coefficients. Since sinusoidal motion is assumed, the unsteady equation is independent of time. The results of an investigation into the relaxation-solution-instability problem was discussed. Concepts examined include variations in outer boundary conditions, a coordinate transformation so that the boundary condition at infinity may be applied to the outer boundaries of the finite difference region, and overlapping subregions. The general conclusion was that only a full direct solution in which all unknowns are obtained at the same time will avoid the solution instabilities of relaxation. An analysis of the one-dimensional form of the unsteady transonic equation was studied to evaluate errors between exact and finite difference solutions. Pressure distributions were presented for a low-aspect-ratio clipped delta wing at Mach number of 0.9 and for a moderate-aspect-ratio rectangular wing at a Mach number of 0.875.
    Keywords: AERODYNAMICS
    Type: NASA-CR-2933 , D6-44419
    Format: application/pdf
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  • 5
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    A user's guide for V174, a program using a finite difference method to analyze transonic flow over oscillating wings (1977)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: The design and usage of a pilot program using a finite difference method for calculating the pressure distributions over harmonically oscillating wings in transonic flow are discussed. The procedure used is based on separating the velocity potential into steady and unsteady parts and linearizing the resulting unsteady differential equation for small disturbances. The steady velocity potential which must be obtained from some other program, is required for input. The unsteady differential equation is linear, complex in form with spatially varying coefficients. Because sinusoidal motion is assumed, time is not a variable. The numerical solution is obtained through a finite difference formulation and a line relaxation solution method.
    Keywords: AERODYNAMICS
    Type: NASA-CR-145214
    Format: application/pdf
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  • 6
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    Computation of the transonic perturbation flow fields around two- and three-dimensional oscillating wings (1975)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: Analytical and empirical studies of a finite difference method for the solution of the transonic flow about an harmonically oscillating wing are presented along with a discussion of the development of a pilot program for three-dimensional flow. In addition, some two- and three-dimensional examples are presented.
    Keywords: AERODYNAMICS
    Type: NASA-CR-2599 , D6-42536
    Format: application/pdf
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  • 7
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    Prediction of unsteady aerodynamic loadings caused by leading edge and trailing edge control surface motions in subsonic compressible flow: Analysis and results (1975)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: A theoretical analysis and computer program was developed for the prediction of unsteady lifting surface loadings caused by motions of leading edge and trailing edge control surfaces having sealed gaps. The final form of the downwash integral equation was formulated by isolating the singularities from the nonsingular terms and using a preferred solution process to remove and evaluate the downwash discontinuities in a systematic manner. Comparisons of theoretical and experimental pressure data are made for several control surface configurations. The comparisons indicate that reasonably accurate theoretical pressure distributions and generalized forces may be obtained for a wide variety of control surface configurations. Spanwise symmetry or antisymmetry of motion, and up to six control surfaces on each half span can be accommodated.
    Keywords: AERODYNAMICS
    Type: NASA-CR-2543
    Format: application/pdf
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  • 8
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    Some recent developments in predicting unsteady loadings caused by control surface motions (1975)
    In:  Other Sources
    Details
    Publication Date: 2019-07-13
    Description: Solution instabilities are identified within the procedures used to predict unsteady loadings due to motions of swept hingeline control surfaces. A preferred solution process that demonstrates the need of calculating smooth residual downwash distributions is described. Numerical results displaying erratic solution behavior when use is made of various forms of pressure expressions currently employed in control surface analyses are presented. A new expression of the asymptotic pressure function is derived, which exactly satisfies the change in boundary conditions around the boundary of the control surface. Results of applying the new pressure function are presented and indicate that stable converged solutions may be achieved for predicting the unsteady loadings caused by motions of swept hingeline control surfaces.
    Keywords: AERODYNAMICS
    Type: AIAA PAPER 75-101 , American Institute of Aeronautics and Astronautics, Aerospace Sciences Meeting; Jan 20, 1975 - Jan 22, 1975; Pasadena, CA
    Format: text
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  • 9
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    Reduction of computer usage costs in predicting unsteady aerodynamic loadings caused by control surface motions: Analysis and results (1979)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: Results of theoretical and numerical investigations conducted to develop economical computing procedures were applied to an existing computer program that predicts unsteady aerodynamic loadings caused by leading and trailing edge control surface motions in subsonic compressible flow. Large reductions in computing costs were achieved by removing the spanwise singularity of the downwash integrand and evaluating its effect separately in closed form. Additional reductions were obtained by modifying the incremental pressure term that account for downwash singularities at control surface edges. Accuracy of theoretical predictions of unsteady loading at high reduced frequencies was increased by applying new pressure expressions that exactly satisified the high frequency boundary conditions of an oscillating control surface. Comparative computer result indicated that the revised procedures provide more accurate predictions of unsteady loadings as well as providing reduction of 50 to 80 percent in computer usage costs.
    Keywords: AERODYNAMICS
    Type: NASA-CR-3009
    Format: application/pdf
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  • 10
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    Application of a finite difference method to the analysis of transonic flow over oscillating airfoils and wings (1977)
    In:  CASI
    Details
    Publication Date: 2019-06-27
    Description: A finite difference method for solving the unsteady flow about harmonically oscillating wings is investigated. The procedure is based on separating the velocity potential into steady and unsteady parts and linearing the resulting unsteady differential equation for small disturbances. Solutions are obtained using relaxation procedures. The means for improving the solution stability characteristics of the relaxation process are explored. A direct procedure is formulated which permits obtaining solutions for combinations of Mach number and reduced frequency for which the relaxation process has proved unstable. The pressure distribution for an aspect ratio 5 rectangular wing oscillating in pitch is presented.
    Keywords: AERODYNAMICS
    Type: AGARD Unsteady Airloads in Separated and Transonic Flow; 13 p
    Format: text
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