Three-dimensional Integral Boundary Layer Method for Viscous Aerodynamic Analysis

Abstract

Viscous aerodynamic analysis is crucial for aircraft design in terms of understanding key performance metrics such as drag. However, despite advances in computational fluid dynamics (CFD) in the past few decades, a physics-based three-dimensional (3D) viscous analysis suitable for aircraft preliminary design remains a challenge. To that end, the integral boundary layer (IBL) method is a promising candidate primarily for its superior computational efficiency and aerodynamic design insights, evidenced from its success in existing two-dimensional (2D) applications. This thesis aims to develop a reliable off-the-shelf three-dimensional (3D) IBL method through contributions in both the physical and numerical modeling aspects.

First, this thesis presents novel closure modeling strategies for 3D IBL and develops a new set of closure models, which were lacking in previous 3D IBL methods. Original 3D boundary layer data sets have been generated and form the basis for data-driven closure modeling in this work. New neural network regression models with embedded constraints are proposed for constructing 3D IBL closure and to help identify important parameters. Moreover, a model inversion formulation is devised for automated data-driven calibration of the turbulence shear stress transport model in the IBL context. Numerical studies demonstrate the effective boundary layer modeling by the proposed closure models through comparison against higher-fidelity reference solution and previous 3D IBL formulations.

Second, the proper stabilization scheme is explored for the numerical discretization of the 3D IBL equations. On the one hand, difficulties have been identified for a rigorous stabilization formulation guided by conventional characteristic analysis. On the other hand, heuristically-defined numerical stabilization schemes are revealed to be ill-posed based on the numerical examples of this work. Instead, an intermediate fix to the numerical discretization is tailored for 3D IBL based on its underlying conservation principles. This fix is observed to produce well-behaved solution as in the numerical results throughout this thesis.

Finally, this work develops the capability of flow transition prediction that is missing from existing 3D IBL methods. Two ways of numerical treatment for free transition are proposed and compared in detail, namely, transition fitting versus transition capturing. With its advantageous implementation convenience, solution robustness and interface resolution, the transition capturing approach is demonstrated to be effective based on both 2D and 3D test cases, and hence is recommended for 3D IBL transition modeling.