Triple Hill's Vortex Synthetic Eddy Method

TL;DR

This paper introduces a novel synthetic eddy method using superposed Hill's vortices to generate divergence-free anisotropic turbulent velocity fields that match specified Reynolds stress tensors, improving inflow turbulence modeling.

Contribution

A new synthetic eddy method based on superposing three orthogonal Hill's vortices to produce realistic, anisotropic turbulence fields that satisfy incompressibility and Reynolds stress constraints.

Findings

Successfully reproduces isotropic and anisotropic turbulence.

Minimal artificial transition near inflow boundaries.

Applicable to grid turbulence decay and channel flow.

Abstract

The generation of initial or inflow synthetic turbulent velocity or scalar fields reproducing statistical characteristics of realistic turbulence is still a challenge. The synthetic eddy method, previously introduced in the context of inflow conditions for large eddy simulations, is based on the assumption that turbulence can be regarded as a superposition of coherent structures. In this paper, a new type of synthetic eddy method is proposed, where the fundamental eddy is constructed by superposing three Hill's vortices, with their axes orthogonal to each other. A distribution of Hill's vortices is used to synthesize an anisotropic turbulent velocity field that satisfies the incompressibility condition and match a given Reynolds stress tensor. The amplitudes of the three vortices that form the fundamental eddy are calculated from known Reynolds stress profiles through a transformation from the physical reference frame to the principal-axis reference frame. In this way, divergence-free anisotropic turbulent velocity fields are obtained that can reproduce a given Reynolds stress tensor. The model was tested on both isotropic and anisotropic turbulent velocity fields, in the framework of grid turbulence decay and turbulent channel flow, respectively. The transition from artificial to realistic turbulence in the proximity to the inflow boundary was found to be small in all test cases that were considered.