Spectral Techniques for Solving PDE Stability Model of Vortex Rope

TL;DR

This paper applies spectral methods to analyze the hydrodynamic instability in swirling flows of hydraulic turbines, demonstrating their accuracy and efficiency in modeling vortex stability and flow control.

Contribution

It introduces spectral methods for PDE stability analysis of vortex flows, comparing L2-projection and collocation techniques with validation against existing results.

Findings

Spectral methods accurately model vortex instability.

Both methods show high efficiency and precision.

Results align well with previous studies.

Abstract

In this paper spectral methods are applied to investigate the hydrodynamic instability of swirling flow with application to Francis hydraulic turbine. Spectral methods imply representing the problem solution as truncated series of smooth global functions. An L2 - projection and the collocation methods are developed assessing both analytically methodology and computational techniques using symbolic and numerical conversions. Remarks concerning the efficiency and the accuracy of each method in this case are presented. The model of the trailing vortex is used to validate the numerical algorithms with existing results in the literature. All the results are compared to existing ones and they prove to agree quite well. The advantages of using this methods in flow control problems are pointed out.