# UFR 4-14 References

# Flow in pipes with sudden contraction

Underlying Flow Regime 4-14 © copyright ERCOFTAC 2004

## References

Astarita, G. and Greco, G. (1968) “Excess pressure drop in laminar flow through sudden contraction”, *Ind. Engng Chem. Fundam*., Vol. 7 (1), pp. 27-31

Benedict, R.P., Carlucci, N.A., Swetz, S.D. (1966) “Flow losses in abrupt enlargements and contractions”. *J. Engineering Power*, Vol. 88 (1), pp 73-81

Boger, D. (1982) “Circular entry flows of inelastic and visco-elastic 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*. FED-Vol. 146, pp. 61-78.

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.431-433

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*, Springer-Verlag, pp.567-576

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

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Christiansen, E.B., Kelsey, S.J., Carter, T.R. (1972) “Laminar tube flow through an abrupt contraction”, *American Institute of Chemical Engineers Journal*, Vol. 18 (2), pp.372-380

Durst F., and Loy T. (1985) “Investigation of laminar flow in a pipe with sudden contraction of cross sectional area”, *Computers & Fluids*, Vol. 13(1), pp15-36.

ESDU (2001) “Pressure Losses in flow through a sudden contraction of duct area”,* Data Item 01016*, ESDU International, London.

Idel’chik, I.E. (1986) “Handbook of hydraulic resistance”, 2^{nd} edition, Hemisphere Publishing Corporation

Jones, W.P. and Launder, B.E. (1973) “Calculation of Low-Reynolds-Number phenomena with a two-equation model of turbulence”, *Int. J. of Heat and Mass Transfer*, Vol. 16 (6), pp. 1119-1130

Kaye, S.E. and Rosen, S.L. (1971) “The dependence of laminar entrance loss coefficients on contraction ratio for Newtonian fluids”, *Am. Inst. Chem. Engrs J.*, Vol. 17 (5), pp. 1269-1270

Kays, W. M. (1950) “Loss coefficients for abrupt changes in flow cross section with low Reynolds number flow in single and multiple tube systems”, *Trans. ASME*, Vol. 72, pp. 1067-1074

Kelsey S. (1971) “Isothermal and non-isothermal, laminar, Newtonian and non-Newtonian entrance region flow”. PhD Thesis, University of Utah, Salt Lake City

Levin, L., Clermont, F. (1970) “Etude des pertes de charge singulieres dans les convergents coniques”, *Le Genie Civil, *T. 147, No.10, pp. 463-470

Menter, F.R. (1994) “Two-equation eddy-viscosity turbulence models for engineering applications”, *AIAA Journal*, vol. 32 (8), pp. 1598-1605

Miller, D.S. (1971) “Internal flow — a guide to losses in pipe and duct systems”. British Hydromechanics research Association, Cranfield, UK

Sylvester, N. D. and Rosen, S. L. (1970) “Laminar flow in the entrance region of a cylindrical tube: Part I. Newtonian Fluids”, *Am. Institute of Chemical Engineers Journal*, Vol. 16 (6), pp. 964-966

Vrentas, J.S. and Duda, J.L. (1973) “Flow of a Newtonian fluid through a sudden contraction”, *Applied Scientific Research*, Vol. 28, pp. 241-260

Wilcox, D.C. (1998) “Turbulence modeling for CFD”, 2^{nd} ed., DCW Industries, Inc., La Canada, CA, pp.103-217.

Zhang, Z. and Kleinstreuer, C. (2003) “Low-Reynolds-Number turbulent flows in locally constricted conduits: a comparison study”, *AIAA Journal*, Vol. 41 (5), pp. 831-840.

**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 |
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 |
Centre-line 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