# Abstr:Flow in pipes with sudden contraction

## Confined Flows

### Underlying Flow Regime 4-14

#### Abstract

Flow through ducts with sudden (sharp-edged) contractions occurs in many industrial applications. The flow separation in the vicinity of the contraction plane causes an increase in pressure loss, which affects erosion rates and heat and mass transfer rates at the separation and reattachment regions. In this work, the ESDU CFD predictions of the flow in a pipe sudden contraction were compared with the LDA measurements and numerical studies by Durst and Loy (1985) and Buckle and Durst (1993) for a contraction area ratio s=0.286, and Bullen et al. (1990; 1996) for a contraction area ratio s=0.332. The fluid was incompressible and Newtonian. The flow regimes were laminar, transitional, and turbulent (20 < Re < 10^{6}). The CFD predictions of the pressure loss coefficient for these geometries and flow conditions were compared with the ESDU correlation (ESDU, 2001) for laminar and turbulent flows, and Bullen et al. (1996) measurements for turbulent flow.

Pipe contractions exist in a variety of process and chemical plants. In order to determine the overall pumping power in a piping system, it is essential to have reliable design procedures to predict pressure losses. It is also important to know the flow details of the separations upstream and downstream of the contraction plane to avoid placing sensitive equipment in these regions. The pressure loss through the contraction is caused by two consecutive processes: (1) contraction of the flow to the vena contracta, and (2) expansion to the wall of the small pipe. The latter is an “uncontrolled” expansion against an adverse pressure gradient. The smaller the area ratio, the larger the pressure gradient and hence the loss.

A schematic of the flow through a pipe sudden contraction is shown in Fig.1. A notation of the terms used in this report can be found in the nomenclature section. In all flow regimes (laminar, transitional, and turbulent) the upstream fully developed flow conditions are not influenced by the contraction approximately 1-2 large tube diameters upstream of the contraction plane. Closer to the contraction plane the flow decelerates near the wall and accelerates in the central region. A separation occurs upstream of the contraction even at the low Re (the lowest considered here is ReD=23). See Fig. 2 for a sketch of the separation regions. With increase in Re, the upstream separation size (length and height) decreases slightly to reach a minimum value at about ReD=100. At around this flow condition the velocity profile immediately downstream of the contraction displays a velocity overshoot close to the wall with a magnitude higher than the centre line velocity. This flow feature is present at higher Re in the laminar, transitional and turbulent regimes. The upstream separation size increases with Re up to ReD=10^{4} and reduces slightly for ReD>10^{4}. At ReD > 300-400, a separation region develops immediately downstream of the contraction. The size of this separation increases with Re in the laminar and transitional regions. For Re> 10^{4} the length of the separation reduces slightly with the increase in Re while the height is nearly constant.

In order for CFD to predict reliably pressure losses in contractions, it is essential to capture the characteristic flow features for the whole range of geometries and flow conditions. The geometry range is defined by the contraction area ratio σ: 0 ≤ σ ≤ 1. The flow conditions are characterized by ReD (or Red): laminar, transition and turbulent. In this work, two geometries were analysed with s=0.286 and 0.332. ReD was varied from 23 to 10^{6}.

*Contributors: Francesca Iudicello - ESDU*

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