# Abstr:Pipe expansion (with heat transfer)

## Semi-Confined Flows

### Underlying Flow Regime 3-11

#### Abstract

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.

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:

- The shape and size of the recirculation zone, including the secondary recirculation bubble, and the location of the reattachment point.
- The skin friction coefficient distribution downstream of the expansion.
- 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.

*Contributors: Jeremy Noyce - Magnox Electric*

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