Mohamed E. Eleshaky

Aerodynamic design optimization using sensitivity analysis and computational fluid dynamics

A new and efficient method is presented for aerodynamic design optimization, which is based on a computational fluid dynamics (CFD)-sensitivity analysis algorithm. The method is applied to design a simplified scramjet-afterbody configuration for an optimized axial thrust. The Euler equations are solved for the inviscid analysis of the flow, which provides the objective function and the constraints of the optimization problem. The CFD analysis is then coupled with the optimization procedure that used a constrained minimization method. The sensitivity coefficients, i.e., gradients of the objective function and the constraints, needed for the optimization are obtained using a quasi-analytic al method rather than the traditional finite difference approximations. During the one-dimensional search of the optimization procedure, an approximate flow analysis (predicted flow) based on a first-order Taylor series expansion is used to reduce the computational cost. Finally, the sensitivity of the optimum objective function to various flowfield problem parameters, such as the Mach number, which are kept constant during the optimization, is computed to predict new optimum solutions. The flow analysis of the demonstrative example are compared with the experimental data. It is shown that the method is more efficient than the traditional methods.

Aerodynamic Sensitivity Analysis Methods for the Compressible Euler Equations

This study presents a mathematical formulation developed for aerodynamic sensitivity coefficients based on a discretized form of the compressible 2D Euler equations. A brief motivating introduction to the aerodynamic sensitivity analysis and the reasons behind an integrated flow/sensitivity analysis for design algorithms are presented. The finite difference approach and the quasi-analytical approach are used to determine the aerodynamic sensitivity coefficients. A new flow prediction concept, which is an outcome of the direct method in the quasi-analytical approach, is developed and illustrated with an example. Surface pressure coefficient distributions of a nozzle-afterbody configuration obtained from the predicted flowfield solution are compared successfully with their corresponding values obtained from a flowfield analysis code and the experimental data.

Airfoil Shape Optimization Using Sensitivity Analysis on Viscous Flow Equations

An aerodynamic shape optimization method has previously been developed by the authors using the Euler equations and has been applied to supersonic-hypersonic nozzle designs. This method has also included a flowfield extrapolation (or flow prediction) method based on the Taylor series expansion of an existing CFD solution. The present paper reports on the extension of this method to the thin-layer Navier-Stokes equations in order to account for the viscous effects. Also, to test the method under highly nonlinear conditions, it has been applied to the transonic flows. Initially, the success of the flow prediction method is tested. Then, the overall method is demonstrated by optimizing the shapes of two supercritical transonic airfoils at zero angle of attack. The first one is shape optimized to achieve a minimum drag while obtaining a lift above a specified value. Whereas, the second one is shape optimized for a maximum lift while attaining a drag below a specified value. The results of these two cases indicate that the present method can produce successfully optimized aerodynamic shapes.

Improving the Efficiency of Aerodynamic Shape Optimization

The computational efficiency of an aerodynamic shape optimization procedure that is based on discrete sensitivity analysis is increased through the implementation of two improvements. The first improvement involves replacing a grid-point-based approach for surface representation with a Bezier-Bernstein polynomial parameterization of the surface. Explicit analytical expressions for the grid sensitivity terms are developed for both approaches. The second improvement proposes the use of Newtons method in lieu of an alternating direction implicit methodology to calculate the highly converged flow solutions that are required to compute the sensitivity coefficients

Aerodynamic Shape Optimization Using Sensitivity Analysis on Third-Order Euler Equations

Previously, the authors have shown an aerodynamic optimization method with two design variables using sensitivity analysis on the first-order-accurate discretization of the Euler equations. Two advancements of this method are reported in this article. First, nonlinear fluid dynamic phenomena including flow discontinuities are better predicted by an improved flow prediction method which uses the third-order accurate discretization of the Euler equations. Using this method, the flowfield of a modified shape which generates shocks and other large gradients is predicted based on the shock-free flowfield of the original shape and without solving the flowfield equations. Secondly, every surface grid point is used as a design variable, which virtually eliminates all geometrical restrictions on the shape as it is optimized for the specified objective. This improved algorithm is demonstrated by optimizing the ramp shape of a scramjet-afterbody configuration for maximum axial thrust. Starting with totally different initial designs, virtually identical shapes are obtained as the optimum. The method is more efficient than the traditional design methods for a few reasons, which include the use of flow predictions and the elimination of a priori guessing of possible shapes from which the optimum is to be selected.

Aerodynamic shape optimization via sensitivity analysis on decomposed computational domains

Direct and iterative method considered to be most applicable to large systems of linear equations arising in discrete sensitivity analysis are assessed. Based on a single-domain grid, computations are performed using a banded matrix solver and an iterative solver, the generalized minimum residual (GMRES) method. The banded matrix solver is found to be generally the most economical method for those applications where the number of right-hand sides is large (i.e., a large number of design variables or a large number of adjoint vectors). For systems of equations that are too large to be solved by direct methods, an approach is proposed whereby the computational domain is divided into small subdomains, and each subdomain is solved separately.

Improving the efficiency of aerodynamic shape optimization procedures

The computational efficiency of an aerodynamic shape optimization procedure which is based on discrete sensitivity analysis is increased through the implementation of two improvements. The first improvement involves replacing a grid point-based approach for surface representation with a Bezier-Bernstein polynomial parameterization of the surface. Explicit analytical expressions for the grid sensitivity terms are developed for both approaches. The second improvement proposes the use of Newtons method in lieu of an alternating direction implicit (ADI) methodology to calculate the highly converged flow solutions which are required to compute the sensitivity coefficients. The modified design procedure is demonstrated by optimizing the shape of an internal-external nozzle configuration. A substantial factor of 8 decrease in computational time for the optimization process was achieved by implementing both of the design improvements.

Discrete aerodynamic sensitivity analysis on decomposed computational domains

Abstract A new scheme is presented for solving the large sparse unsymmetric systems of linear equations which arise from the application of the aerodynamic sensitivity equation to large two-dimensional as well as three-dimensional design optimization problems. Performance comparisons between a generalized minimum residual (GMRES) method and a direct solution method are performed on a single computational domain. Results show that, due to the use of preconditioning, the GMRES method requires almost the same memory allocation as that required by the direct method. Moreover, it is found that for many right-hand sides of the above systems, the GMRES method is significantly less efficient than the direct method. Since large systems cannot be solved by direct methods on a single domain, due to the computer memory limitations, the computational domain in the new scheme is divided into small manageable ones and each one is solved separately. In addition to the savings in memory requirements, this scheme can be applied easily to complex-geometry problems which cannot be represented by single computational grids. The computational performance of this scheme is assessed by considering the flow over a transonic airfoil. The sensitivity equation is solved for three cases where the computational domains are represented by different numbers of subdomains. Identical results are obtained in all cases without any visible effect due to the subdivisions of the computational grids. This indicates the schemes high accuracy in solving the above system on decomposed computational domains.

Design of 3-D Nacelle near Flat-Plate Wing Using Multiblock Sensitivity Analysis (ADOS)

One of the major design tasks involved in reducing aircraft drag is the integration of the engine nacelles and airframe. With this impetus, nacelle shapes with and without the presence of a flat-plate wing nearby were optimized. This also served as a demonstration of the 3-D version of the recently developed aerodynamic design optimization methodology using sensitivity analysis, ADOS. The required flow analyses were obtained by solving the three-dimensional, compressible, thin-layer Navier-Stokes equations using an implicit, upwind-biased, finite volume scheme. The sensitivity analyses were performed using the preconditioned version of the SADD scheme (sensitivity analysis on domain decomposition). In addition to demonstrating the present methods capability for automatic optimization, the results offered some insight into two important issues related to optimizing the shapes of multicomponent configurations in close proximity. First, inclusion of the mutual interference between the components resulted in a different shape as opposed to shaping an isolated component. Secondly, exclusion of the viscous effects compromised not only the flow physics but also the optimized shapes even for isolated components.

Shape Optimizing Nacelle near Flat-Plate Wing Using Multiblock Sensitivity Analysis

A major design task in reducing the overall aircraft drag is the integration of the engine nacelles and the airframe. With this impetus, a methodology was demonstrated to optimize nacelle shapes with and without the presence of a e at-plate nearby to account for the wing interference. Overly simplie ed shapes notwithstanding, this process requires multiblock grids not only for its aerodynamic analysis, but also for its optimization. Although the former is a standard practice, the latter has only recently been possible for the gradient-based optimizations with the development of the sensitivity analysis with domain decomposition scheme. The analyses were obtained by solving the three-dimensional, compressible, thin-layer Navier ‐ Stokes equations using an implicit, upwind-biased, e nite volume scheme. In addition to demonstrating the present method’ s suitability for automated shape optimization of interfering aircraft components, such as a nacelle and a wing, the results verie ed two important issues. First, accounting for the aerodynamic mutual interference between components in close proximity manifested itself in a shape different than that obtained when a component was assumed to be isolated. Secondly, even for isolatedcomponent designs, neglecting the viscous effects compromised not only the e ow physics but also the optimized shapes.