Accuracy and efficiency improvements in synthetic eddy methods.

Abstract

With performance in mind, we propose two general improvements to the popular class of turbulent inlet boundary conditions known as the ‘synthetic eddy method’, originally proposed 10 years ago by Jarrin 2006. Our updated version offers improvement in both statistical accuracy and computational efficiency. We first demonstrate that the original approach led to inaccuracies where eddy length-scale prescription was inhomogeneous. We then describe a correction to the normalisation procedure to ensure that prescribed statistics can be correctly recovered. A second improvement focusses on the computational efficiency of the method; by generalising the method to allow for arbitrary eddy placement, the required number of eddies whilst conserving the target ‘eddy density’ is reduced. The former enhancement is observed to deliver a consistent and measurable improvement over the standard formulation, whilst the latter provides efficiency savings of around 1–2 orders of magnitude. The original SEM has spawned a number of derivatives over the past decade, many of which would be expected to benefit from the improvements reported herein (whether they are used as boundary conditions, volume source terms or as part of a dynamic forcing algorithm). We apply the improved formulation to the case of a turbulent channel flow at two Reynolds numbers as well as to the case of an asymmetric planar diffuser, which is set up to exhibit a pressure-induced separation expected to be highly sensitive to upstream flow conditions. It is demonstrated that even apparently small errors in the imposed flow field can persist in such cases, adversely affecting the downstream flow prediction.