Novel, Unified, Curvature-Based Airfoil Parameterization Model for Turbomachinery Blades and Wings

The predictable effect of surface curvature on the contiguous streamtube allows for the use of geometric curvature as a direct and aerodynamically meaningful parametric model to generate airfoil geometry. A novel and parsimonious parameterization technique driven by specifications of normalized meanline second derivatives, which is related to curvature, and a superimposed thickness distribution which explicitly eliminates or minimizes unintentional oscillations in curvature, is resented. The focus on smooth curvature control is inherently relevant to both internal and external flow geometries, enabling a unified method for generating both isolated airfoils and cascade sections. This technique is implemented and included in T-Blade3 which is an existing in-house open-source code. The underlying methodology for construction of camber-line is entirely analytical ensuring speed of execution. Two different thickness distributions are presented, one based on specifications of thickness B-spline control points, and another based on specifications of exact thickness. The B-spline thickness method requires a simple implementation and executes faster, but cannot impose an exact value of thickness at a specified location. The exact thickness method is capable of imposing specified thickness values both chord-wise and span-wise, while quantifying and optimizing the quality of the thickness curve based on curvature. Consequently, unintentional bumps on the airfoil and oscillations in curvature are eliminated or minimized. The parameterization ensures curvature and slope of curvature continuity on the airfoil surface which are critical for smooth surface pressure distributions. Consequently, losses due to unintentional pressure spikes are minimized and likelihood of separation reduced, resulting in a class of high-performance airfoils. The direct relationship between the parameterization and surface aerodynamics is demonstrated for both isolated and cascade airfoils. A framework for 2D airfoil shape optimization is developed which uses a parallelized Genetic Algorithm implementation from the US Department of Energy optimization system, DAKOTA. As a demonstration of the parameterization capability, optimization is performed to maximize lift-to-drag ratios of an isolated airfoil over a range of angles of attack at two Reynolds numbers using Genetic Algorithm. The tool-chain uses XFOIL to evaluate drag polars. Two different cases are presented, each using a different thickness parameterization. The maximum thickness to chord ratio is fixed at 21%, enabling direct comparison of the optimized shapes with the S809 airfoil, which is used as a comparison benchmark. Drag improvements ranging from 17% to 55% for Cl between 0.3 and 1, for Reynolds numbers of 7*10^5 and 9.5*10^5 were achieved by the optimized airfoil using the B-spline based thickness parameterization, while improvements ranging from 11% to 52% were achieved by the optimized airfoil using exact thickness parameterization for the same range of Reynolds numbers and Cl .