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Flow in pipes with sudden contraction
Underlying Flow Regime 414 © copyright ERCOFTAC 2004
References
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Benedict, R.P., Carlucci, N.A., Swetz, S.D. (1966) “Flow losses in abrupt enlargements and contractions”. J. Engineering Power, Vol. 88 (1), pp 7381
Boger, D. (1982) “Circular entry flows of inelastic and viscoelastic fluids”, Advances in Transport Processes, vol.2
Buckle, U. and Durst, F. (1993) “Investigation of laminar flow in a pipe with sudden contraction of cross sectional area”, Trans. ASME Data for Validation of CFD codes. FEDVol. 146, pp. 6178.
Bullen, P.R. and Cheeseman, D.J. (1984) “The definition of pipe contraction pressure loss coefficients for incompressible flow”, Report No. TFAR/1/84, Kingston Polytechnic
Bullen, P.R., Cheeseman, D.J., Hussain, L.A., Ruffell, A.E. (1987) “The determination of pipe contraction pressure loss coefficients for incompressible turbulent flow”, Int. Journal of Heat and Fluid Flow, Vol. 8 (2), pp. 111 – 118
Bullen, P.R., Cheeseman, D.J., Hussain, L.A. (1988) “The effects of inlet sharpness on the pipe contraction pressure loss coefficient”, Int. Journal of Heat and Fluid Flow, Vol. 9 (4), pp.431433
Bullen, P.R., Hussain, L.A., Cheeseman, D.J. (1990) “Laser Doppler Anemometry measurements of flow through a sudden pipe contraction and comparison with computer predictions”, 3^{rd} International Conf. on Laser Anemometry, Advances and Applications, SpringerVerlag, pp.567576
Bullen, P.R., Cheeseman, D.J., Hussain, L.A. (1996) “A study of turbulent flow in pipe contractions”, Proc. of IMechE Part E: Journal of Process Mechanical Engineering, Vol. 210 (E3), pp. 171–180
CFX5 Version 5.6 (2003) “CFX5 Solver and Solver Manager Manual”
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Menter, F.R. (1994) “Twoequation eddyviscosity turbulence models for engineering applications”, AIAA Journal, vol. 32 (8), pp. 15981605
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Nomenclature
d 
Small tube diameter 
Re 
Reynolds Number 
D 
Large tube diameter 
Red 
Small tube outlet Re 
K 
Kinetic turbulent energy 
ReD 
Large tube inlet Re 
K_{L} 
Pressure loss coefficient 
u 
Axial fluid velocity 
l 
Small tube length 
U1 
Inlet average velocity 
L 
Large tube length 
U2 
Outlet average velocity 
Ls1x 
Upstream separation length 
ucl 
Centreline fluid velocity 
Ls1r 
Upstream separation height 
v 
Radial fluid velocity 
Ls2x 
Downstream separation length 
x 
Axial distance from contraction plane 
Ls2r 
Downstream separation height 
y 
Radial distance 
Lx,th 
Throat axial location of downstream sep. 
b 
Contraction ratio (d/D) 
p 
Static Pressure 
m 
Fluid dynamic viscosity 
ptot 
Total Pressure 
r 
Fluid density 
R 
Pipe radius 
s 
Contraction area ratio 
APPENDIX A
Pressure Loss Coefficient
The pressure loss coefficient for a sudden contraction is defined as
where Δp_{t12 }is the total pressure loss due to the contraction, and 1/2 ρ U_{2}^{2 }is the kinetic pressure at Station 2 (see Fig.1). Δp_{t12 }is defined as the total pressure drop between Station 1 in the large pipe and Station 2 in the small pipe minus the losses due to friction for fully developed flow in the large and small pipes extrapolated to the contraction plane. Station 1 and 2 are located in the fully developed regions upstream and downstream of the contraction respectively, outside the region of influence of the contraction. The total pressure loss Δp_{t12 }is derived from measurements of static pressure loss Δp_{12}.
© copyright ERCOFTAC 2004
Contributors: Francesca Iudicello  ESDU