From the results of many experiments carried out in the past, it is clear that the transition between laminar and turbulent flows occurs in the entrance region, and that the critical Reynolds number (Rc) is governed by the shape of the bellmouth entrance. To date, it has not been considered how a bellmouth-shaped entrance affects the flow in pipes. If it governs the transition, the turbulence can be controlled. These findings are verified by reproducing Reynolds color-dye experiments, in particular, varying the ratio of the bellmouth diameter to pipe diameter (BD/D). CASE I through IV are devised for natural disturbance conditions. We found that (i) there were two types of Rc, namely, Rc1 for the laminar to turbulent flow transition and Rc2 for the turbulent to laminar flow transition, (ii) each bellmouth-shaped entrance had a minimum value, Rc2(min, ent), which increased as BD/D increased, and (iii) when using a straight pipe, the Rc value of 2050 was obtained as a minimum value in CASE II and IV, and the Rc2(min) value was approximately 1750 in CASE III.

Volume Subject Area:
Fluids Engineering
Topics:
Pipe flow, Reynolds number, Turbulence, Pipes, Entrance region, Flow (Dynamics), Laminar flow, Shapes
1.
Reynolds
O.
,
1883
, “
An Experimental Investigation of the Circumstances Which Determine Whether the Motion of Water Shall be Direct or Sinuous, and of the Law of Resistance in Parallel Channels
,”
Trans. Roy. Soc. Lond.
,
174
, pp.
935
–
982
.
2.
Lamb, H., 1975, Hydrodynamics (6th ed.), pp. 664–665.
3.
Schlichting, H., 1979, Boundary-Layer Theory (7th ed.), p. 451.
4.
White, F. M., 1991, Viscous Fluid Flow, McGraw-Hill, p. 369.
5.
Prandtl, L., and Tietjens, O.G., 1957, Applied Hydro- and Aeromechanics, Dover.
6.
Kanda, H., and Oshima, K., 1998, “Pressure Distribution on a Cross Section in the Entrance Flow Region of a Circular Pipe,” Proc. of 1998 ASME Fluids Engineering Division - Summer Meeting, FED-Vol. 245, FEDSM 98-5005.
7.
Kanda, H., 1998, “Numerical Study of Effects of a Bellmouth on the Entrance Flow in a Circular Pipe,” Proc. of ASME Fluids Engineering Division - 1998, FED-Vol. 247, pp. 181–188.
8.
Kanda, H., 1999a, “Computerized Model of Transition in Circular Pipe Flows. Part 1. Experimental Definition of the Problem,” Proc. of ASME Fluids Engineering Division - 1999, FED-Vol. 250, pp. 189–196.
9.
Kanda, H., 1999b, “Computerized Model of Transition in Circular Pipe Flows. Part 2. Calculation of the Minimum Critical Reynolds Number,” Proc. of ASME Fluids Engineering Division - 1999, FED-Vol. 250, pp. 197–204.
10.
Kanda, H., 2000a, “Simulation of Reynolds’ Color-Dye Experiments on Instability of Circular Pipe Flows. Part 1. Discussion of the Problem,” Proc. of ASME Fluids Engineering Division - 2000, ASME FED-Vol. 253, pp. 611–618.
11.
Kanda, H., 2000b, “Simulation of Reynolds’ Color-Dye Experiments on Instability of Circular Pipe Flows. Part 2. Definition of the Problem,” Proc. of ASME Fluids Engineering Division - 2000, ASME FED-Vol. 253, pp. 619–626.
12.
Kanda, H., 2001, “Difference in Critical Reynolds Number between Hagen-Poiseuille and Plane Poiseuille Flows,” Proc. of ASME Fluids Engineering Division - 2001, ASME FED-Vol. 256, pp. 189–196.
13.
Kanda, H., 2002, “Calculation of a Minimum Critical Reynolds Number for Flow between Parallel Plates,” Proc. of ASME Fluids Engineering Division - 2002, ASME IMECE2002-33273.
14.
Rivas, Jr., M. A., and Shapiro, A. H., 1956, “On the Theory of Discharge Coefficients for Rounded-Entrance Flowmeters and Venturis,” Transactions of ASME, April, 1956, pp. 489–497.
15.
Wygnanski
I. J.
and
Champagne
F. H.
,
1973
, “
On Transition in a Pipe. Part 1. The Origin of Puffs and Slugs and the Flow in a Turbulent Slug
,”
Journal of Fluid Mechanics
, Vol.
59
, part
2
, pp.
281
–
335
.
16.
Kestin
J.
, and
Wakeham
W. A.
,
1988
,
Transport Properties of Fluids: Thermal Conductivity, Viscosity, and Diffusion Coefficient
,
Center for Information and Numerical Data Analysis and Synthesis, Data Series
, Vol.
I-1
, Hemisphere, p.
142
142
.
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