Terry L. Holst

Viscous Transonic Airfoil Workshop Compendium of Results

Results from the Viscous Transonic Airfoil Workshop held at the AIAA 25th Aerospace Sciences Meeting at Reno, NV in January 1987, are compared with each other and with experimental data. Test cases used in this workshop include attached and separated transonic flows for three different airfoils: the NACA 0012 airfoil, the RAE 2822 airfoil, and the Jones airfoil. A total of 23 sets of numerical results from 15 different author groups are included. The numerical methods used vary widely and include: 16 Navier-Stokes methods, 2 Euler/boundary-layer methods, and 5 full-potential/boundary-layer methods. The results indicate a high degree of sophistication among the numerical methods with generally good agreement between the various computed and experimental results for attached or moderately-separated cases. The agreement for cases with larger separation is only fair and suggests additional work is required in this area.

Aerodynamic Shape Optimization Using A Real-Number-Encoded Genetic Algorithm

A new method for aerodynamic shape optimization using a genetic algorithm with real number encoding is presented. The algorithm is used to optimize three different problems, a simple hill climbing problem, a quasi-one-dimensional nozzle problem using an Euler equation solver and a three-dimensional transonic wing problem using a nonlinear potential solver. Results indicate that the genetic algorithm is easy to implement and extremely reliable, being relatively insensitive to design space noise.

Transonic Flow Computations Using Nonlinear Potential Methods

Abstract This presentation describes the state of transonic flow simulation using nonlinear potential methods for external-aerodynamic applications. The presentation begins with a review of the various potential equation forms (with emphasis on the full potential equation) and includes a discussion of pertinent mathematical characteristics and all derivation assumptions. Impact of the derivation assumptions on simulation accuracy, especially with respect to shock wave capture, is discussed. Key characteristics of all numerical algorithm types used for solving nonlinear potential equations, including steady, unsteady, space marching, and design methods, are described. Both spatial discretization and iteration scheme characteristics are examined. Numerical results for various aerodynamic applications are included throughout the presentation to highlight key discussion points. The presentation ends with concluding remarks and recommendations for future work. Overall, nonlinear potential solvers are efficient, highly developed and routinely used in the aerodynamic design environment for cruise conditions.

Overset Solution Adaptive Grid Approach Applied to Hovering Rotorcraft Flows

Numerical simulation of hovering rotorcraft flow fields with emphasis on the accurate capture of the vortical wake is examined. The present approach utilizes the OVERFLOW Navier-Stokes flow solver, which has been enhanced with a solution adaptive grid capability. Regions of the flow within the off-body Cartesian grid that contain concentrated levels of vorticity are systematically refined within the constraints of the overset zonal grid approach. The resulting vortical flow field is captured more accurately relative to solutions that do not use any form of refinement and with significantly fewer grid points relative to solutions that utilize uniform refinement.

Numerical simulation of transonic flow over porous airfoils

A numerical study was made to examine the effect of a porous surface on the aerodynamic performance of a transonic airfoil. The pressure jump across the normal shock wave on the upper surface of the airfoil was reduced by making the surface below the shock porous. The weakened shock is preceded by an oblique shock at the upstream end of the porous surface where air is blown out of the cavity. The lambda shock structure shown in the numerical result qualitatively agrees with that observed in the wind tunnel. According to the present analysis, the porous airfoil has a smaller drag and a higher lift than the solid airfoil.

Multizone Chimera Algorithm for Solving the Full-Potential Equation

A numerical scheme utilizing a chimera zonal grid approach for solving the three-dimensional fullpotential equation is described. Within each grid zone a new approximate factorization scheme based on the approximation factorization scheme 2 algorithm is utilized to advance the solution one iteration. This is followed by the explicit advance of all common zonal grid boundaries using trilinear interpolation of the velocity potential. Two spatial discretization variations are presented; one using a hybrid e rst-order/ second-order-accurate scheme and the second using a fully second-order-accurate scheme. The presentation is highlighted with a grid ree nement study and a number of transonic wing e owe eld computations.

Transonic Wing Shape Optimization Using a Genetic Algorithm

A method for aerodynamic shape optimization based on a genetic algorithm approach is demonstrated. The algorithm is coupled with a transonic full potential flow solver and is used to optimize the flow about transonic wings including multi-objective solutions that lead to the generation of pareto fronts. The results indicate that the genetic algorithm is easy to implement, flexible in application and extremely reliable.

Comparison of the full-potential and Euler formulations for computing transonic airfoil flows

A study involving four transonic airfoil computer codes, two FP and two Euler, has been performed. The major conclusions of the study are as follows: (1) the FP codes are faster than the Euler codes by about an order of magnitude based on CPU time on the Cray XMP; (2) the FP formulation loses accuracy as transonic flow develops, but entropy corrections yield FP solutions comparable to those of the Euler; (3) grid coarseness and type can be significant in affecting both accuracy and convergence characteristics; (4) the FP formulation must be more tightly converged than the Euler formulation for comparable levels of accuracy in the lift coefficient; and (5) in general, good accuracy for adequate meshes can be obtained with both formulations, irrespective of the solution method.

Chimera Donor Cell Search Algorithm Suitable for Solving the Full Potential Equation

An approximate iterative search algorithm for finding donor cells associated with the chimera zonal grid approach is presented. This new algorithm is both fast and simple. It is used in conjunction with a chimera-based full potential solver for computing transonic flow solutions about wing and wing/fuselage configurations. Within each grid zone a fully implicit approximate factorization scheme is used to advance the solution one iteration. This is followed by the explicit advance of all common intergrid boundaries using a trilinear interpolation of the velocity potential. The presentation is highlighted with numerical result comparisons, a grid refinement study, and parametric variation of pertinent algorithm parameters. The new search algorithm produces donor cells for the two-zone wing problem at a rate in excess of 60,000 cells/s (single processor Cray C90). The approximate nature of the search algorithm, which causes some of the donor cells to be approximated by nearest neighbor cells, does not cause any impact on solution accuracy. Overall the results indicate that the present chimera zonal grid approach is a viable technique for solving the full potential equation for aerodynamic applications

Visualization and Analysis of Vortex Features in Helicopter Rotor Wakes

Vortex interactions in helicopter rotor wakes are visualized using enhanced flow visualization techniques, which in turn play a crucial role in understanding the dynamics of these complex flows. Iso-surfaces are clipped in a 3D volume to reduce visual clutter. Flow textures are improved to highlight vortical flow structure and vortex-wake interactions. These visualization techniques are applied to three Computational Fluid Dynamics (CFD) simulations of helicopter flow fields. The presented techniques provide a good depiction of rotor tip vortices in these flows.