# Description

## Introduction

This test case focuses on the incipient separation occuring on a curved backward facing step, illustrated by visualization of the LES results in Fig. 1. The results were obtained using highly-resoved LES. The primary focus of this case is on the details of the separation process and the properties of the separated region, including reattachment. Results are reported and analysed in two journal papers [‌13,3] and only the main elements of those papers, pertinent to use and analyse the data provided, are reported here. This geometry shows particular features of separation from gently-curved surfaces: the separation process is highly unsteady in time and space; turbulence is highly non-local in character; the mean reverse-flow region is thin and highly elongated; no part of the flow is reversed at all times; the level of production is extremely high following separation, resulting in massive departures from turbulence-energy equilibrium, very high anisotropy and a trend towards one-component turbulence in the separated shear layer. The LES results constitute a valuable data set for benchmarking model solutions and investigating statistical turbulence-closure proposals.

## Review of UFR studies and choice of test case

Separation from a gently curving surface is considerably more complicated than that from a sharp step, because its details depend sensitively on the properties of the boundary layer approaching the separation region. In confined geometries, in particular, there is a pronounced two-way interaction between the outer-flow pressure field acting on the boundary layer and the separation process. In such circumstances, the separation process is highly unsteady, being affected by the turbulent structures within the boundary layer, including the near-wall streaks, and it features intermittently separated and attached patches over a streamwise band around the time-averaged separation line. From a statistical point of view, one recurring observation is that the turbulence-energy and shear-stress levels are extremely high in the vicinity of the nominal separation point and in the initial stretch of the separated shear layer, this being consistent with the highly unsteady nature of the separation process. Another observation is that the separation region is extremely thin, tapering knife-like towards the separation line. This implies the importance of the near-wall processes to the separation behaviour.

In recent years, there have been several simulation studies focusing on separation from curved surfaces. On the one hand, this trend has been encouraged by the rapidly increasing availability, and declining costs, of high-performance computing, allowing highly wall-resolving LES to be performed on separated flows at elevated Reynolds numbers. On the other hand, there has been an increasing realisation that the performance of RANS models in predicting separation from curved surfaces was especially variable -- indeed, often very poor -- so that high-fidelity DNS and LES for carefully controlled conditions have been deemed essential for assessing alternative RANS models and for identifying the origins of defects of specific closure approximations. Specifically in relation to the last driver, an outstanding advantage of simulations is that these can be exploited, if conducted with great care, to generate benchmark data that are, arguably, more extensive and accurate than experimental data, especially if statistical two-dimensionality is desired. A case in point is the flow in a channel with streamwise-periodic hills on one wall, investigated by [‌8] and, for a higher Reynolds numbers and finer grids, by [‌4]. This geometry has served as a basis for several studies and workshops in which the performance of various RANS and RANS-LES hybrid models have been examined (e.g. [‌28,1,12]) and the test case is included as UFR3-30 in the Knowledge Base Wiki. An important disadvantage of this geometry is, however, that it is rather unrepresentative of the large majority of real flows. Specifically, the structure of flow approaching separation from any one hill is extremely complex, due to separation, reattachment and acceleration of the flow in the preceding periodic segment. This makes the results derived from RANS models difficult to interpret, because even small modelling errors can translate to large differences in predictive performance as a consequence of periodicity-induced feedback and modelling-error amplification.

Flows that are more amenable to a physical interpretation that has greater general applicability entail the separation of a (close to) canonical turbulent boundary layer and subsequent reattachment and recovery. Computational studies of such flows have been reported by [‌29,5,6,20,22] and [‌9], the last one being the most elaborate of a number of studies focusing on a boundary layer separating from a 3D hill. Several of the above efforts relate to the experimental investigation of [‌27] in which an equilibrium boundary layer at ${\displaystyle {Re=9100}}$ was made to separate from a rounded step. While all studies report a range of flow properties and discuss flow-physical features, the scope of the results presented is rather limited, partly because the main emphasis was on assessing approximate modelling schemes [‌29,21], or because the simulations were done in the context of flow-control with pulsed jets ([‌20,5]). In all cases, but the DNS by [‌5] and [‌18], grid resolution was relatively modest, in the range ${\displaystyle {1.5-7}}$ million nodes. This prevented results beyond second moments and flow-structure information being extracted at acceptable accuracy.

The present test case was devised jointly between Imperial College London (for the simulation part) and University of Manchester (for the experimental work) to allow an accurate characterization of different separation control mechanisms (like pulsed jets), and exactly the same operating conditions for the LES and the experiments. The present test case corresponds to the baseline flow configuration, ie. without any applied control.

Contributed by: Sylvain Lardeau — CD-adapco, London, UK