Triple Hill’s Vortex Synthetic Eddy Method

• Published in: Flow, turbulence and combustion Vol. 108; no. 3; pp. 627 - 659
• Main Authors: Haywood, John S., Sescu, Adrian, Bhushan, Shanti, Kees, Christopher E.
• Format: Journal Article
• Language: English
• Published: Dordrecht Springer Netherlands 01.03.2022; Springer Nature B.V
• Subjects: Automotive Engineering; Channel flow; Engineering; Engineering Fluid Dynamics; Engineering Thermodynamics; Fluid flow; Fluid- and Aerodynamics; Heat and Mass Transfer; Incompressibility; Inflow; Large eddy simulation; Mathematical analysis; Reynolds stress; Scalars; Tensors; Turbulence; Turbulent flow; Velocity; Velocity distribution; Vortices; Synthetic eddy method; Turbulent inflow; Synthetic turbulence
• ISSN: 1386-6184; 1573-1987
• DOI: 10.1007/s10494-021-00289-4

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.