Parameter Extension Simulation of Turbulent Flows

TL;DR

This paper introduces a parameter extension simulation (PES) method combined with a controlled eddy simulation (CES) approach to efficiently simulate various turbulent flows with comparable accuracy to traditional methods but at lower computational costs.

Contribution

The paper proposes a novel PES/CES method that extends reference solutions to desired parameters, reducing computational costs while maintaining accuracy in turbulent flow simulations.

Findings

PES/CES achieves similar accuracy to traditional LES.

Higher order PES improves model accuracy.

Method successfully applied to multiple turbulent flow types.

Abstract

Parameter extension simulation (PES) as a mathematical method for simulating turbulent flows has been proposed in the study. It is defined as a calculation of the turbulent flow for the desired parameter values with the help of a reference solution. A typical PES calculation is composed of three consecutive steps: Set up the asymptotic relationship between the desired solution and the reference solution; Calculate the reference solution and the necessary asymptotic coefficients; Extend the reference solution to the desired parameter values. A controlled eddy simulation (CES) method has been developed to calculate the reference solution and the asymptotic coefficients. The CES method is a special type of large eddy simulation (LES) method in which a weight coefficient and an artificial force distribution are used to model part of the turbulent motions. The artificial force distribution is modeled based on the eddy viscosity assumption. The reference weight coefficient and the asymptotic coefficients can be determined through a weight coefficient convergence study. The proposed PES/CES method has been used to simulate four types of turbulent flows. They are decaying homogeneous and isotropic turbulence, smooth wall channel flows, rough wall channel flows, and compressor blade cascade flows. The numerical results show that the 0-order PES solution (or the reference CES solution) has a similar accuracy as a traditional LES solution, while its computational cost is much lower. A higher order PES method has an even higher model accuracy.