# UFR 3-15 Description

# 2D flow over backward facing step

Underlying Flow Regime 3-15 © copyright ERCOFTAC 2004

# Description

## Preface

The underlying flow regime (UFR) documented here, the 2D backward facing step (BFS) flow is a well-known case. Since it is a simple geometry containing complex fluid dynamic features such as separation, reattachment and recovery of a boundary layer, a shear layer interacting with a wall and recirculation zones, it is revisited every time a new turbulence model is proposed and it is commonly used to test numerical formulations. This is also due to the availability of experimental results and recently of direct numerical simulations (DNS).

Although this UFR has been mentioned in only two application challenges, is a very important regime that is found in many problems. Every problem possessing a complex geometry will probably have an abrupt expansion.

## Introduction

The flow over a BFS is determined by an abrupt expansion in the geometry, which give rise to a fixed separation of the boundary layer at the corner. Then it generates a curved shear layer with a bifurcation at the reattachment point whose position depends on the Reynolds number as well as the expansion ratio. A main recirculation zone appears at the bottom wall downstream of the step. In the laminar case there is also a second bubble at the top wall. In the turbulent case the main recirculation zone is smaller and a secondary bubble appears inside this region. Following the reattachment point there is a region where the wall boundary layer recovers.

The main features to be compared in this test case are the general pattern of the streamlines, the length of the recirculation zone, the skin friction coefficient distribution along the bottom wall, the profiles of mean velocities as well as turbulence quantities and also, if the temperature prediction is of interest, the Nusselt number distribution along the bottom wall. The last one takes into account the heat exchange between the flow and the wall and depends entirely on the prediction of turbulence variables in absence of buoyancy coupling.

The reattachment length shows the overall predictive capability of the model, as it is a global parameter. The skin friction coefficient distribution includes the reattachment length but also some other information on the performance of the model. It is related to how steep velocity gradients are near the wall. It can also provide some insight on the wall treatment accuracy.

The BFS flow can be examined (Hanjalic and Jakirlic (1998) in three major regions in order to study the predictive capability of a given turbulence model:

- recirculation zone: the shape of the main bubble and the curvature of the dividing streamline, the prediction of the secondary eddy and the turbulent quantities profiles. This is particularly important, as will be shown below, because of the absence of kinetic energy production-dissipation balance in this separated region.

- reattachment region: its location and turbulent structure.

- downwards the reattachment: the boundary layer recovery.

These zones and the associated phenomena are not independent but the dominant mechanisms are different.

## Review of UFR studies and choice of test case

Many experimental studies have been performed on this problem: Kim (1978), Kim et al. (1980), Driver and Seegmiller (1985), Durst and Schmitt (1985), Vogel and Eaton (1985), Armaly et al. (1983), Lekakis et al. (1994), Kasagi and Matsunaga (1995) and Jovic and Driver (1995). They cover a wide range of expansion ratios. The expansion ratio is defined as R=(h+d)/d where h is the step height and d is the width of the flow before the expansion, that is half of the channel width or pipe diameter. As mentioned, the sudden expansion generates a curvature in the streamline pattern and a pressure gradient appears. A higher expansion ratio causes a bigger curvature of streamlines, a stronger perturbation of the pressure field and a slower boundary layer recovery after the reattachment, which is also located further from the step, as mentioned in Hanhalic and Jakirlic(1998). The experimental results also cover a wide range of Reynolds numbers. Some of them are available in public databases.

Here we will consider two different test cases as they provide comparisons for different regimes (Re number) of the flow.

The first one is the BFS at Re_{h}=5000 and expansion ratio of 1.2. The experimental data of Jovic and Driver (1995) (JD) are available in the AGARD public database and are widely used. AGARD has since been subsumed into the NATO RTO. Apart from the low expansion ratio another interesting feature is that the most commonly used DNS simulation of Le et al. (1997) is based on these experiments, and can also be found in the same database.

The second one is the BFS at Re_{h}=37500 and expansion ratio of 1.125. The experimental data of Driver and Seegmiller (1985) (DS) are also available in the Ercoftac Classic database here and in the AGARD databases. Although there is no DNS available for this case, it has been used to test many turbulence models.

© copyright ERCOFTAC 2004

Contributors: Arnau Duran - CIMNE