Analysis and Adjoint Design Optimization of Hypersonic Blunt Bodies

Abstract

The main purpose of this study is to analyze hypersonic flow field around the blunt bodies and to design of that bodies in order to obtain minimum pressure drag. Modeling of non-equilibrium must be done properly. In this study, non-equilibriums of thermal and chemical modes are considered. Translational and rotational energy modes are assumed that energy exchange between these modes is so fast. Vibrational and electronic energy terms are neglected. Therefore, one temperature is used to model thermo-chemical non-equilibrium. Flow field is assumed as inviscid and continuum region. Moreover, there is not diffusion. Thus, to model chemical non-equilibrium, finite rate chemistry can be used. For the thermal-nonequilibrium, enthalpy, entropy and specific heat constants are obtained from curve fitting methods. The coupled flow field equations are solved by using Newton's methods. To solve Newton's method, Jacobian matrices evaluation is required. In terms of convergence, Jacobian matrices are obtained by using analytical methods. At the design part, sensitivities are obtained by using adjoint design methods. The aim of design part is finding a hypersonic blunt geometry with minimum pressure drag while keeping the maximum temperature smaller than the baseline value. Nomenclature w flow variable vector in computational domain F, G flux vectors H, S source vector R residual in computational domain P static pressure of mixture P e electron pressure E total energy per unit mass H total enthalpy per unit mass h s mixture enthalpy per unit mass E v mixture vibrational-electronic energy per unit mass J coordinate transformation Jacobian e v vibrational-electronic mass e sf source term of electron  , curvilinear coordinates s  species density s  mass production rate of chemical reactions , ij  viscous shear stress 1 Graduated Students, Aeronautical and Astronatical Engineering, tugba.piskin@metu.edu.tr , AIAA Member 2 Associated Professor, Aeronautical and Astronatical Engineering, seyi@metu.edu.tr, AIAA Member Downloaded by UNIVERSITY OF NEW SOUTH WALES on August 13, 2015 | http://arc.aiaa.org |

Adjoint-based aerodynamic design optimisation in hypersonic flow

“…The objective was to minimise pressure drag on the blunt-body. This work has most recently been extended to include thermal non-equilibrium [78].…”