Modeling two-dimensional ice shape based on fractal interpolation

Abstract

The ice accretion data obtained from ice wind tunnel tests reveal a multiscale structure and rough surface. In the follow-up aerodynamic evaluation of icing airfoils, simplified two-dimensional ice shapes are generally used as substitutes, but this simplification changes the aerodynamic effects of the original ice shape. Therefore, finding a simple and effective two-dimensional ice shape simulation method is urgent. Due to the self-similarity characteristics of ice shape surfaces, fractal interpolation is proposed for ice shape simulation. First, the geometric characteristics of the ice shapes are analyzed to determine interpolation points, and an iterative function system is constructed for interpolation simulation. Considering the influence of various characteristics of ice shapes on aerodynamics, interpolation parameters are limited to simulating more realistic ice shapes. High-order numerical simulation methods were utilized to numerically simulate and analyze the aerodynamic characteristics of icing airfoil while also verifying the feasibility of fractal interpolation for simulating ice shapes. The analysis revealed that this method could effectively simulate ice profiles of various feature scales with minimal ice shape data. These simulated shapes closely resemble real ice formations and maintain the original aerodynamic characteristics of the icing airfoil. This method can be used to improve the computational accuracy of ice accretion codes and provide improvement strategies for complex ice shape prediction; thus, this method has great application prospects in engineering.