Flow in pipes with sudden contraction

Underlying Flow Regime 4-14 © copyright ERCOFTAC 2004

Description

Preface

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 < 10⁶). 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=10⁴ and reduces slightly for ReD>10⁴. 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> 10⁴ 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 10⁶.

Figure 1. Schematic of the flow through a pipe with a sudden contraction.

Figure 2. Sketch of the upstream and downstream separations in the vicinity of the contraction.

Review of UFR studies and choice of test case

Extensive experimental and numerical studies have been carried out to investigate the flow in pipes with sudden contraction. A literature survey can be found in (Boger, 1982). A number of publications provide experimental data on wall static pressure drop, flow redevelopment length downstream the contraction plane and flow patterns using flow visualization techniques. However, reliable experimental data for comparison with CFD predictions are scarce. For example, the wall pressure measurements published by Astarita and Greco (1968), and Sylvester and Rosen (1970) differ by more than 100% in some ranges of Re. Velocity measurements using Laser Doppler Anemometry (LDA) are generally very reliable as the flow field is undisturbed and the temporal and spatial resolution is high. A summary of the published experimental and numerical data for CFD validation is given in Tables 1 to 3.

**Table 1. Experimental and numerical velocity data for CFD validation in the literature**
Reference	Type of data	ReD	σ
Christianen et al. (1972)	Exp. and numerical	65, 108	0.047
Vrentas and Duda (1973)	Numerical	200	0.063, 0.444
Durst and Loy (1985)	Exp. and numerical	23-1213	0.286
Xia et al. (1992)	Exp. and numerical	12	0.19, 0.31
Buckle and Durst (1993)	Exp. and numerical	23 968	0.286
Bullen et al. (1996)	Exp. and numerical	1.538×10⁵	0.332

**Table 2. Experimental and numerical pressure data for CFD validation in the literature**
Reference	Type of data	ReD	σ
Kays (1950)	Semi-empirical (*)	2000-3000	0.1 - 0.95
Astarita and Greco (1968)	Experimental	20-2000	0.162
Sylvester and Rosen (1970)	Experimental	4-1100	0.0156
Levin and Clermont (1970)	Experimental	10⁵- 10⁶	0.223, 0.476, 0.885
Kaye and Rosen (1971)	Experimental	4-1100	0.041-0.636
Durst and Loy (1985)	Numerical	563	0.286
Durst and Loy (1985)	Experimental	20-1200	0.0156
Bullen et al. (1996)	Experimental	4×10⁴-2×10⁵	0.13-0.67

(*) based on analyticalmethods that use empirical coefficients for free discharge flow '

**Table 3. Experimental and numerical separation size data for CFD validation in the literature**
Reference	Type of data	ReD	σ
Durst and Loy (1985)	Exp. and numerical	23-1213	0.286
Buckle and Durst (1993)	Numerical	23 - 968	0.286
Bullen et al. (1996)	Exp. and numerical	1.538×10⁵	0.332

Among these available data, those published by Durst and co-workers (Durst and Loy, 1985; Buckle and Durst, 1993), and by Bullen and co-workers (Bullen et al., 1990, 1996) are probably the most relevant.

Durst and Loy (1985) and Buckle and Durst (1993) carried out experimental and numerical investigations of laminar flow (23 ≤ ReD ≤ 1213) for a contraction ratio σ=0.286. Reliable LDA measurements data are provided, and compared with their numerical predictions obtained using a finite volume computer code. Good agreement was achieved over most parts of the flow field. Small discrepancies were found downstream the contraction plane. Pressure profile predictions at ReD=563 are provided, and comparisons of the CFD pressure loss coefficient K_L (see Appendix A for definition) are displayed for σ=0.0156 against the experimental predictions of Sylvester and Rosen (1970). Differences up to 50% can be estimated from the graphs. CFD predictions of the upstream separation size are published in Durst and Loy (1985). Estimated measurements and CFD predictions of the downstream separation size are compared in Durst and Loy (1985) and Buckle and Durst (1993) for different mesh sizes.

Bullen and his co-workers have published a number of papers on pipe contractions (Bullen et al., 1984; 1987; 1988; 1990; 1996). The flow regime is turbulent with Re in the range of 4×10⁴ to 2×10⁵. The geometry is characterized by contraction area ratios σ between 0.13 and 0.67. The effect of the contraction edge sharpness is also reported. Measurements of the pressure loss coefficients are provided for the above geometry and flow conditions ranges. LDA measurements of mean velocity and turbulence intensities, and downstream separation size estimation, are provided for σ=0.332 and ReD=1.54×10⁵ (Bullen et al., 1990, 1996). CFD predictions were obtained using FLUENT and the standard k-ε turbulent model. The general trends of the flow are predicted by CFD, but significant differences in the flow field are seen in the vicinity of the contraction.

Prediction of the contraction pressure loss coefficient has relied on experimental measurements of the static pressure drop across the contraction. Correlations provided by Miller (1971) and Idelchik (1986) are not based on experimental data. Although a large number of papers have been published on this subject, some inconsistencies are present which can be attributed to ill-defined geometry and flow conditions. A summary can be found in (Bullen et al., 1987). The ESDU correlations data for the pressure loss coefficient in sudden contractions (ESDU, 2001) are based on the most reliable sources. Correlations are provided by ESDU (2001) for laminar flow, based on Kaye and Rosen (1971), and turbulent flow based on Benedict et al. (1966), Levin and Clermont (1970), Bullen et al. (1987, 1988). In the transitional region (2000 ≤ Re ≤ 4000), the flow condition is considered uncertain and no data are provided. The error of the correlation data depends on the experimental data on which the data are based, plus any curve fitting operated on those, and varies with Re and contraction area ratio σ. The ESDU method of prediction of the pressure loss coefficient K_L in turbulent flow is a function of σ, and is independent of Re. While this assumption is supported by Benedict et al. (1966) and Levin and Clermont (1970) for example, Bullen et al. (1987; 1996) have reported that K_L is slightly dependent on Re. This variation is small and falls within the experimental uncertainty, but it is consistently apparent at all contraction area ratios for 4×10⁴ < ReD < 2×10⁵.

Contributors: Francesca Iudicello - ESDU