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Report presents computational study of unsteady transonic flow about airplanelike body as body pitches upward in increasing angle of attack.

Longitudinal dynamic stability derivatives required for design of aircraft are computed by using the state-of-the-art numerical methods for wing-body configurations. The flow is modeled using the Euler/Navier-Stokes equations with turbulence models and solved using an efficient finite-difference scheme suitable for patched structured grids. Computations are made at a flow regime that is beyond the limits of the current linear methods mostly used for computing stability derivatives. Flow conditions include shockwaves and viscous dominated vortical flows. Effect of Mach number and angle-of-attack on stability derivatives are demonstrated for a typical wing-body configuration. For the same configuration the effects of wing flexibility on the magnitude and phase angles of stability derivatives are also demonstrated.

New capabilities have been added to a Navier-Stokes solver to perform steady-state simulations more efficiently. The flow solver for solving the Navier-Stokes equations is completely rewritten with a combination of the LU-SGS (Lower-Upper factored Symmetric Gauss-Seidel) implicit method and the modified HLLE (Harten-Lax-van Leer-Einfeldt) upwind scheme. A pseudo-time marching method is used for the directly coupled structural equations to improve overall convergence rates for static aeroelastic analysis. Results are demonstrated for transonic flows over rigid and flexible wings.

The development of a streamwise upwind algorithm is presented. Applications of this algorithm to steady flow over a delta wing and unsteady flow over an oscillating wing, respectively, are covered. An extension to higher order accuracy for upwind methods is discussed. This scheme will use the compatibility relations for the extension. The use of multiple zones in the calculation of unsteady flows is considered. Multiple zones are one way to treat complex configurations, such as complete aircraft. Aeroelastic calculations are discussed. A procedure for aeroelastic calculations is described that simultaneously solves the aerodynamic and structural equations of motion. Sample calculations are given to illustrate the above.

A computational procedure is developed that uses a moving zonal grid concept to model complex flexible aerospace vehicles. The Euler/Navier-Stokes equations are used to model the flow, and computations are made using efficient methods based on both central and upwind schemes. The structure is represented by a finite element method which can model general aerospace vehicles. Provisions are made to accommodate other disciplines such as controls and thermal loads. The code is capable of computing unsteady flows on flexible wings with vortical flows. Adaptation of this procedure for parallel processing and validation for complete aerospace configurations is in progress.

The flow over the B-1 wing is studied computationally, including the aeroelastic response of the wing. Computed results are compared with results from wind tunnel and flight tests for both low- and high-sweep cases, at 25.0 and 67.5 deg, respectively, for selected transonic Mach numbers. The aerodynamic and aeroelastic computations are made by using the transonic unsteady code ATRAN3S. Steady aerodynamic computations compare well with wind tunnel results for the 25.0 deg sweep case and also for small angles of attack at 67.5 deg sweep case. The aeroelastic response results show that the wing is stable at the low-sweep angle for the calculation at the Mach number at which there is a shock wave. In the higher-sweep case, for the higher angle of attack at which oscillations were observed in the flight and wind tunnel tests, the calculations do not show any shock waves. Their absence lends support to the hypothesis that the observed oscillations are due to the presence of leading-edge separation vortices and not to shock wave motion, as was previously proposed.

The development and applications of the unsteady transonic code ATRAN3S for clean wings are discussed. Explanations of the unsteady, transonic small-disturbance aerodynamic equations that are used and their solution procedures are discussed. A detailed user's guide, along with input and output for a sample case, is given.

The presence of tip stores influences both aerodynamic and aeroelastic performances of wings. Such effects are more pronounced in the transonic regime. In this study, transonic aeroelasticity of wings with tip stores is studied for the first time by a theoretical method using the unsteady-small disturbance transonic aerodynamic equations coupled with modal structural equations of motion. The aerodynamic and structural equations of motion are simultaneously integrated by a time-accurate numerical scheme. To validate the tip store simulation, aeroelastic computations are made for a typical rectangular wing with a tip store and results are correlated with available wind tunnel data for the corresponding wing without a tip store at various flight conditions. Aeroelastic computations are also made for a typical fighter wing with a tip store. Present computations show that it is important to account for the aerodynamics of the tip store, particularly in the transonic regime where the tip store can make the wing aeroelastically unstable.

The flow over the B-1 wing is studied computationally, including the aeroelastic response of the wing. Computed results are compared with results from wind tunnel and flight tests for both low-sweep and high-sweep cases, at 25.0 and 67.5 deg., respectively, for selected transonic Mach numbers. The aerodynamic and aeroelastic computations are made by using the transonic unsteady code ATRAN3S. Steady aerodynamic computations compare well with wind tunnel results for the 25.0 deg sweep case and also for small angles of attack at the 67.5 deg sweep case. The aeroelastic response results show that the wing is stable at the low sweep angle for the calculation at the Mach number at which there is a shock wave. In the higher sweep case, for the higher angle of attack at which oscillations were observed in the flight and wind tunnel tests, the calculations do not show any shock waves. Their absence lends support to the hypothesis that the observed oscillations are due to the presence of leading edge separation vortices and are not due to shock wave motion as was previously proposed.

The development and application of transonic small disturbance codes for computing two dimensional flows, using the code ATRAN2, and for computing three dimensional flows, using the code ATRAN3S, are described. Calculated and experimental results are compared for unsteady flows about airfoils and wings, including several of the cases from the AGARD Standard Aeroelastic Configurations. In two dimensions, the results include AGARD priority cases for the NACA 54A006, NACA 64A010, NACA 0012, and MBB-A3 airfoils. In three dimensions, the results include flow about the F-5 wing, a typical wing, and the AGARD rectangular wings. Viscous corrections are included in some calculations, including those for the AGARD rectangular wing. For several cases, the aerodynamic and aeroelastic calculations are compared with experimental results.

The development and application of transonic small disturbance codes for computing two dimensional flows, using the code ATRAN2, and for computing three dimensional flows, using the code ATRAN3S, are described. Calculated and experimental results are compared for unsteady flows about airfoils and wings, including several of the cases from the AGARD Standard Aeroelastic Configurations. In two dimensions, the results include AGARD priority cases for the NACA 64A006, NACA 64A010, NACA 0012, and MBB-A3 airfoils. In three dimensions, the results include flows about the F-5 wing, a typical wing, and the AGARD rectangular wings. Viscous corrections are included in some calculations, including those for the AGARD rectangular wing. For several cases, the aerodynamic and aeroelastic calculations are compared with experimental results.

The unsteady transonic aerodynamic and aeroelastic behavior of a rectangular wing with a NACA 64A010 profile and a swept-back wing with a supercritical MBB-A3 profile is investigated analytically, applying 2D analysis of viscous effects to the 3D case. The results are presented in graphs and tables and discussed. It is found that the inclusion of viscous effects increases the flutter speed of the wings.

An efficient coordinate transformation technique is presented for constructing grids for unsteady, transonic aerodynamic computations for delta-type wings. The original shearing transformation yielded computations that were numerically unstable and this paper discusses the sources of those instabilities. The new shearing transformation yields computations that are stable, fast, and accurate. Comparisons of those two methods are shown for the flow over the F5 wing that demonstrate the new stability. Also, comparisons are made with experimental data that demonstrate the accuracy of the new method. The computations were made by using a time-accurate, finite-difference, alternating-direction-implicit (ADI) algorithm for the transonic small-disturbance potential equation.