228 JOURNAL OF AIRCRAFT Vol. 34, No. 2, March – April 1997 Automated Design Optimization for the P2 and P8 Hypersonic Inlets Vijay Shukla,* Andrew Gelsey,† Mark Schwabacher,‡ Donald Smith,§ and Doyle D. Knight} Rutgers University, New Brunswick, New Jersey 08903 An automated design methodology incorporating industry-standard Navier – Stokes codes and a gra- dient-based optimizer has been developed. This system is used to redesign the well-known NASA P2 and P8 hypersonic inlets. First, the Navier – Stokes simulations of the original P2 and P8 inlet designs are validated using numerical convergence studies and comparison with wind-tunnel experimental data for the original inlets published by NASA in the early 1970s. Second, the P2 and P8 inlets are redesigned with the objective of canceling the cowl shock (and, in the case of the P8 inlet, the additional cowl- generated compression) at the centerbody by appropriate contouring of the centerbody boundary. The original inlets were intended to achieve these same objectives, but detailed experimental measurements indicated that a substantial reected shock system was present. The choice of the objective function, which is used to drive the optimization, has a signicant impact on the nal design. Several different formulations for the objective function have been employed, and improvements of 60 – 90% in the objec- tive function have been achieved. This automated design system represents one of the rst successful combinations of numerical optimization methods with Reynolds-averaged Navier – Stokes uid dynamics simulation for high-speed inlets, and demonstrates a new area in which high-performance computing may have considerable impact on problems of military and industrial signicance. Nomenclature N BL = number of points in incoming centerbody boundary layer N cent BL = number of points in centerbody boundary layer at throat N cowl BL = number of points in cowl boundary layer at throat Dy u max = height of grid cell with greatest y extent 1 Dy 2 = nondimensional estimate of resolution of viscous sublayer on centerbody = Dy 2 u * /nw, where u * = and t w = local shear at the t /r Ï w w wall = mw (-u/-n ) d 0 = thickness of incoming centerbody boundary layer, ’1.1 cm at inlet entrance, x = 81.28 cm s p , s sh s , ¯ p = objective functions s , r , r p p p t t = measures used in optimization I. Introduction R ECENTLY there has been work on integrating design and computational uid dynamics (CFD). Compared to wind- tunnel testing of designs, this process is lower in cost and can be completed in a relatively short period of time. For exam- ple, experimentally validated Navier – Stokes codes have been developed and used for turbomachinery design. 1 Typically, these codes are used by expert designers, who guide the selec- tion of designs and shape modications. Improvements are achieved by a manual, labor-intensive process. The complex Received Dec. 30, 1995; revision received Oct. 22, 1996; accepted for publication Dec. 30, 1996. Copyright Q 1997 by the authors. Published by the American Institute of Aeronautics and Astronautics, Inc., with permission. *Postdoctoral Research Associate, Department of Mechanical and Aerospace Engineering. Member AIAA. †Assistant Professor, Computer Science Department. Member AIAA. ‡Graduate Student, Computer Science Department. §Assistant Professor, Computer Science Department. }Professor, Department of Mechanical and Aerospace Engineering. Associate Fellow AIAA. ows in aerodynamic applications make it unlikely to attain optimum designs manually. Automatic design optimization techniques are thus essential to exploit the potential gains of using CFD in the design process. Recently there has been work to automate the design pro- cess. This involves a description of the shape by a set of pa- rameters and an objective function that describes the desired design goal. Aerodynamic shape optimization of inlets has been performed to minimize the peak inlet Mach number. 2 Nonlinear optimization has also been used in inlet design by coupling optimization with an inviscid ow solver to minimize total pressure loss. 3 Optimum shape design for minimization of drag for high-speed civil transport has been investigated using a simulated annealing algorithm. 4 Genetic algorithm- based optimization has been used for drag minimization over aerofoils. 5 A simplied scramjet-afterbody conguration has been optimized for axial thrust, using sensitivity analysis and analytical expressions for derivatives used in the optimization. 6 Optimization techniques based on control theory, which use adjoint equations for gradient calculation, are used for aerofoil and wing design. 7,8 We have developed a prototype software system that com- bines Navier – Stokes simulations and numerical optimization methods. This system has been tested by redesigning the P2 and P8 inlets. The P2 and P8 inlets 9 were designed in the 1970s for a proposed hypersonic cruise vehicle for Mach 10 to 12. Models were built at approximately one-third scale and tested in the NASA Ames Research Center’s 3.5-ft hypersonic wind tunnel. There was a forebody wedge of 6.5 deg, intended to match a design Mach number of 6 at the inlet entrance under the test conditions of a freestream Mach number of 7.4 (see Fig. 1). The freestream conditions at the entrance to the inlet were M = 5.8, = 2.69 3 10 6 Pa, = 770 K, and the p T t t 0 0 incoming centerbody boundary layer was turbulent and had a thickness of d0 = 1.1 cm. The cowl was designed with a lead- ing-edge diameter of 0.114 cm and both centerbody and cowl were cooled to maintain a temperature of 302 K. The P2 inlet cowl boundary layer was laminar. In the case of the P8 inlet, the cowl boundary layer transitioned from laminar to turbulent halfway between the cowl leading edge and the throat station. In the P2 inlet, a pressure rise by a factor of 2 (thus the name