A Continuous Adjoint Formulation for Hypersonic Flows in Thermochemical Nonequilibrium PDF Download

Author: Sean R. Copeland
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Languages : en
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Book Description
This thesis explores the formulation, derivation, and implementation of the continuous adjoint equations for hypersonic, nonequilibrium flow environments. The adjoint method is an efficient means for acquiring sensitivity information that can be used in a gradient-based framework to perform optimal shape design of aerospace systems. A solution to the adjoint system of equations carries a computational cost roughly equal to a single solution of the flow governing equations, regardless of the dimensionality of the design space. When compared to other gradient acquisition methods, where computational costs scale with design space dimensionality, the adjoint method is superior when the dimensionality is high and when solutions to the governing equations are expensive. Such conditions are often representative of most aerospace problems of practical interest. In addition to providing gradient information, solutions to the adjoint equations may be used as 'sensors' or 'weighting factors' to perform error estimation and adaptive mesh refinement. Hypersonic systems operate in unique flow environments that are dominated by chemical and thermodynamic phenomena not observed at lower Mach numbers. Accurate simulations of these environments require sophisticated thermochemical models to resolve atomic-scale physical processes that have first-order effects on integrated vehicle performance metrics, including lift, drag, stability, controllability, and heat transfer. Because of the computational expense demanded by these high-fidelity tools, the conceptual vehicle design process often relies heavily on low- to medium-fidelity, correlation-based tools that are confined to narrow regions of applicability. As a consequence, the hypersonic vehicle design process has remained relatively static for the past several decades. The adjoint method enables the use of high-fidelity tools early in the design cycle of hypersonic systems, and is a transformative technology for the hypersonic community. This work provides the first derivation, implementation, and verification of the continuous adjoint equations for hypersonic flow environments in thermochemical nonequilibrium. Appropriate boundary conditions and surface sensitivities are provided for both projected force and thermal objective functions for continuum, viscous, multi-component gas mixtures. The adjoint system is implemented in a second-order, unstructured, finite-volume-method (FVM) flow solver that is representative of the state-of-the-art in high-fidelity aerothermodynamic analysis for hypersonic entry systems. Gradients from the adjoint-derived surface sensitivities are verified against gradients calculated using a finite-difference methodology for several representative geometries relevant to ballistic and lifting-body entry vehicles.