Surrogate Representation for the Aerodynamic Coefficients of Supersonic Airfoils

Abstract

Generally, physical phenomena are represented in the form of explicit mathematical expressions that stem from basic governing equations. However, in many cases, having these expressions may not be achieved and a considerable part of our knowledge relies on abstract numbers produced via lab experiments or computer simulations. In the absence of explicit relations for the variables of the physical phenomena, surrogates emerge as a reliable alternative. Surrogates have evolved in the recent years and gained the attention of researchers and, in the field of aerodynamics; surrogates have been widely used in multiple applications. In the present paper, surrogates are implemented in a new application namely, the relation between the design of a 10% diamond airfoil and its aerodynamic coefficients. Kriging interpolation and polynomial regression surrogates are constructed based on data taken from CFD simulations of the turbulent, Mach 2, zero-incidence flow about 104 airfoil samples representing almost all possible designs of that airfoil. The constructed surrogates are proved to incorporate the CFD data with a high accuracy. They also yield useful visual representations of the physical phenomena in hand and generate simple mathematical expressions for these phenomena as well.