A Novel Approach to Modeling of Compressor Characteristics

This paper presents a novel approach to modeling a turbojet engine compressor through the approximation and interpolation of performance characteristics. A hybrid method is proposed, fitting each speed line individually with the most suitable function from a predefined library of candidate functions. To address the ill-conditioning issue, a modified <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\beta$</tex> interpolation method is introduced. The <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\beta$</tex> curves are carefully defined to ensure that the <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\beta$</tex> grid remains entirely within the map, avoiding extrapolation. Each <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\beta$</tex> curve is defined by a set of control points given by its intersections with speed lines, and an optimization problem is formulated to evenly distribute these points along the speed line. The resulting control points are parametrized for each <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\beta$</tex> curve, allowing for a coordinate transform that facilitates well-behaved nonlinear interpolation.