N. Pagaldipti

A multidisciplinary optimization using semi-analytical sensitivity analysis procedure and multilevel decomposition

Abstract This paper addresses the development of a multidisciplinary optimization procedure using an efficient semi-analytical sensitivity analysis technique and multilevel decomposition for the design of aerospace vehicles. A semi-analytical sensitivity analysis procedure is developed for aerodynamic design sensitivities. Accuracy and efficiency of the sensitivity analysis procedure is established through comparison of the results with those obtained using a finite difference technique. The optimization problem, with the integration of aerodynamics and structures, is decomposed into two levels. Optimization is performed for improved aerodynamic performance at the first level and improved structural performance at the second level. Aerodynamic analysis is performed by solving the three-dimensional parabolized Navier Stokes equations. A nonlinear programming technique and an approximate analysis procedure are used for optimization. The procedure developed is applied to design the wing of a high speed aircraft. Results obtained show significant improvements in the wing aerodynamic and structural performance when compared to a reference or baseline wing configuration. The use of the semi-analytical sensitivity technique provides significant computational savings.

Multilevel Decomposition Procedure for Efficient Design Optimization of Helicopter Rotor Blades

This paper addresses a multilevel decomposition procedure, for efficient design optimization of helicopter blades, with the coupling of aerodynamics, blade dynamics, aeroelasticity, and structures. The multidisciplinary optimization problem is decomposed into three levels. The rotor is optimized for improved aerodynamic performance at the first level. At the second level, the objective is to improve the dynamic and aeroelastic characteristics of the rotor. A structural optimization is performed at the third level. Interdisciplinary coupling is established through the use of optimal sensitivity derivatives. The Kreisselmeier-Steinhauser function approach is used to formulate the optimization problem when multiple design objectives are involved. A nonlinear programming technique and an approximate analysis procedure are used for optimization. Results obtained show significant improvements in the rotor aerodynamic, dynamic, and structural characteristics, when compared with a reference or baseline rotor.

A discrete semianalytical procedure for aerodynamic sensitivity analysis including grid sensitivity

Abstract A discrete semianalytical sensitivity analysis procedure has been developed for calculating aerodynamic design sensitivities. The sensitivities are numerically calculated using direct differentiation of the discretized flow equations. A new approach has been developed and employed to calculate the sensitivities of the discretized grid, which are integral to the calculation of the aerodynamic sensitivities. Representative results from the grid sensitivity analysis and semianalytical sensitivity analysis procedures are compared with those obtained from the finite difference approach to establish their efficiency and accuracy. The developed procedures offer significant savings in computing time over the finite difference approach, thus allowing the use of comprehensive analysis procedures in design optimization.

A Design Optimization Procedure for Efficient Turbine Airfoil Design

Abstract An optimization procedure has been developed for the efficient design of turbine blade airfoil sections. A shape sensitivity study of the airfoils has been performed considering two leading edge shapes, circular and elliptic. Pressure and suction surfaces are approximated by polynomials. A two-level, nonlinear constrained optimization problem is formulated and is solved using the method of feasible directions. The aerodynamic analysis is performed using a two-dimensional panel code. Since several evaluations of the objective functions and the constraints are required within the optimizer, and exact aerodynamic analysis at each step is computationally prohibitive, a two-point exponential approximation technique has been used. The procedure developed successfully eliminates the sharp leading edge velocity spikes, characteristic of typical blade sections, without compromising blade performance. Circular leading edge airfoils appear to be more effective in eliminating the spikes than elliptic leading edge airfoils. However, the elliptic leading edge sections are more slender than the circular leading edge sections. Optimum results are compared with a reference design.

MULTIDISCIPLINARY OPTIMIZATION PROCEDURE FOR HIGH SPEED AIRCRAFT USING A SEMI-ANALYTICAL SENSITIVITY ANALYSIS PROCEDURE AND MULTILEVEL DECOMPOSITION

Abstract A multidisciplinary design optimization procedure is developed for the simultaneous improvement of sonic boom, aerodynamic and structural performance of high speed aircraft. The coupled problem is decomposed into two levels of optimization. At the first level, optimization is performed for simultaneous reduction in sonic boom and improvements in aerodynamic performance using a nonlinear programming technique. An advanced CFD solver is used to evaluate the supersonic flow field about high speed aircraft configurations. Sonic boom analysis is performed using an extrapolation procedure. The wing structural performance is improved at the second level using a hybrid optimization technique that solves the problem with both continuous and discrete design variables. The wing load carrying member, modelled as a composite box beam, is analyzed using a quasi-one-dimensional, finite element model. A discrete semi-analytical sensitivity analysis technique is employed for evaluating the aerodynamic and sonic b...

Shape optimization of turbine blades with the integration of aerodynamics and heat transfer

A multidisciplinary optimization procedure, with the integration of aerodynamic and heat transfer criteria, has been developed for the design of gas turbine blades. Two different optimization formulations have been used. In the first formulation, the maximum temperature in the blade section is chosen as the objective function to be minimized. An upper bound constraint is imposed on the blade average temperature and a lower bound constraint is imposed on the blade tangential force coefficient. In the second formulation, the blade average and maximum temperatures are chosen as objective functions. In both formulations, bounds are imposed on the velocity gradients at several points along the surface of the airfoil to eliminate leading edge velocity spikes which deteriorate aerodynamic performance. Shape optimization is performed using the blade external and coolant path geometric parameters as design variables. Aerodynamic analysis is performed using a panel code. Heat transfer analysis is performed using the finite element method. A gradient based procedure in conjunction with an approximate analysis technique is used for optimization. The results obtained using both optimization techniques are compared with a reference geometry. Both techniques yield significant improvements with the multiobjective formulation resulting in slightly superior design.

Optimization procedure with analytical aerodynamic sensitivity for reduced sonic boom design

A design optimization procedure for improved sonic boom and aerodynamic performance of highspeed aircraft has been developed. The multiobjective optimization procedure simultaneously minimizes the primary sonic boom and the drag-to-lift ratio of the aircraft. Constraints are imposed on the secondary sonic boom and lift coefficient. The flow equations are solved using the three-dimensional parabolized Navier-Stokes solver, and sonic boom analysis is performed using an extrapolation procedure. A nonlinear programming technique and an approximate analysis procedure are used in the optimization. An efficient, semianalytical sensitivity analysis technique is used to calculate the aerodynamic and sonic boom design sensitivities. The optimization procedure and sensitivity analysis technique are applied to two high-speed wing body configurations (delta wing and doubly swept wing). Results obtained in both cases show improvements in the sonic boom pressure peaks and aerodynamic performance of the aircraft. The tradeoff between the sonic boom and aerodynamic performance of the aircraft is brought out by the reductions in the lift of the optimum configurations associated with the reductions in the second pressure peak of their sonic boom signatures.