# UFR 3-11 Description

# Pipe expansion (with heat transfer)

Underlying Flow Regime 3-11 © copyright ERCOFTAC 2004

# Description

## Preface

The underlying flow regime (UFR) documented here, flow and heat transfer in a pipe expansion, relates to a flow geometry which is often encountered in industrial applications. Although this UFR has only been associated with two application challenges (AC3-08 and 3-10), for a simple geometry it results in relatively complex fluid dynamics features such as separation and reattachment, recirculation zones and enhanced heat transfer due to impingement effects. It is therefore commonly used as a test of turbulence models and numerical formulations and has consequently been studied in some detail over the years.

It should be noted at the outset that this UFR has features in common with both the 2D backward-facing step (UFR3-15) and the impinging jet (UFR3-09), so that the documentation on these should also be consulted for relevant advice.

## Introduction

As well as having industrial relevance, the pipe expansion has become a routine test case for CFD calculations due to the simple geometry but relative complexity of the flow phenomena that take place, particularly when heat transfer is also occurring. These include a fixed separation of the boundary layer at the inlet, and a curved shear layer with a bifurcation at the reattachment point. The location of the reattachment point is dependent on the Reynolds number, and a recirculating region of flow is contained between the expansion step, the larger pipe wall and the shear layer. A secondary recirculation bubble is also present at the corner between the outer pipe wall and the expansion step. At the reattachment point, there is strong streamline curvature as the shear layer is deflected by the wall. Further downstream, there is a region where the wall boundary layer recovers, with fully-developed pipe flow eventually being achieved if the length of pipe downstream of the expansion is long enough.

Depending on the Reynolds number, laminar or turbulent flow regimes may be present. However, for many industrial applications and for other purposes, such as testing various types of turbulence models, the Reynolds number of the inlet pipe flow is usually set to be high enough for fully turbulent flow conditions to be achieved. The flow is generally assumed to be steady and, in cases where heat transfer is also present, buoyancy effects are taken to be negligible.

The main features of the flow which must be captured by the CFD modelling are:

i) The shape and size of the recirculation zone, including the secondary recirculation bubble, and the location of the reattachment point.

ii) The skin friction coefficient distribution downstream of the expansion.

iii) The Nusselt number distribution downstream of the expansion.

Since, as described in more detail below, measured mean velocity and turbulence profiles are available for this geometry, agreement of model predictions with measurements throughout the flow domain should also be sought.

As noted in the Preface, this UFR has features in common with both the 2D backward-facing step and the impinging jet. In recent years, the latter has tended to receive more attention as a test case for turbulence and wall heat transfer models as it provides more challenging conditions due to stronger streamline curvature.

## Review of UFR studies and choice of test case

This UFR, both with and without heat transfer, received considerable attention in the 1980's as it was used for early comparisons of CFD codes and turbulence models. It was developed as a test case by the International Association for Hydraulic Research (IAHR), the results of which are documented by Hutton and Szczepura (1987). The comparisons were based on experimental measurements of mean velocities and turbulence quantities made in a test rig using water as the working fluid (Szczepura (1985)). These experiments were intended to provide improved quantity and quality of data for this geometry relative to previous work by Chaturvedi (1963), Zemanick and Dougall (1970), Moon and Rudinger (1977) and Freeman (1982). The data from Szczepura (1985) are available on the ERCOFTAC Classic Database Collection, currently maintained by UMIST ( http://cfd.me.umist.ac.uk/ercoftac ). Spectral measurements were also made by Szczepura (1986) using the same rig. Heat transfer measurements for this UFR were made at about the same time in an airflow rig with a constant heat flux from the larger pipe wall by Baughn et al. (1984). Subsequently, measurements were made with a constant wall temperature (Yap (1987), Baughn et al. (1989)); flow velocity and temperature measurements were also taken in these experiments. Rather more recently, flow measurements in this geometry have also been made by Stieglmeier et al. (1989), Gould et al. (1990) and Devenport and Sutton (1993). Results from Gould et al. (1990) are also available in the ERCOFTAC Classic Database Collection.

As they were specifically designed for code and model comparisons, the results of Szczepura (1985), Baughn et al. (1984, 1989) and Yap (1987) are detailed and comprehensive. For example, the experiments proved sufficiently accurate and detailed to reveal the presence of the small secondary recirculation bubble in the corner between the step and the larger pipe wall. The quality of these results and the more recent focus on the impinging jet may be reasons why there appears to have been relatively little further experimental work on this UFR in recent years.

The focus for the documentation of this UFR has been on the heat transfer measurements of Baughn et al. (1984, 1989) and Yap (1987) since:

- The isothermal flow in this geometry is largely covered by the 2D backward-facing step UFR.
- Most recent work to address the known deficiencies in standard turbulence modelling approaches for this geometry has been aimed at improving the predicted heat transfer distribution on the larger pipe wall.

© copyright ERCOFTAC 2004

Contributors: Jeremy Noyce - Magnox Electric