scholarly journals Discussion: “On Turbulent Flow Between Parallel Plates” (Pai, S. I., 1953, ASME J. Appl. Mech., 20, pp. 109–114)

1953 ◽  
Vol 20 (3) ◽  
pp. 445
Author(s):  
A. M. Kuethe
Keyword(s):  
Turbulent Flow ◽  
Parallel Plates

On Turbulent Flow Between Parallel Plates

1953 ◽  
Vol 20 (1) ◽  
pp. 109-114
Author(s):  
S. I. Pai
Keyword(s):  
Turbulent Flow ◽  
Velocity Distribution ◽  
Poiseuille Flow ◽  
The Other ◽  
Turbulent Velocity ◽  
Parallel Plates ◽  
Mean Velocity ◽  
Reynolds Equations ◽  
Mean Pressure ◽  
The Mean

Abstract The Reynolds equations of motion of turbulent flow of incompressible fluid have been studied for turbulent flow between parallel plates. The number of these equations is finally reduced to two. One of these consists of mean velocity and correlation between transverse and longitudinal turbulent-velocity fluctuations u 1 ′ u 2 ′ ¯ only. The other consists of the mean pressure and transverse turbulent-velocity intensity. Some conclusions about the mean pressure distribution and turbulent fluctuations are drawn. These equations are applied to two special cases: One is Poiseuille flow in which both plates are at rest and the other is Couette flow in which one plate is at rest and the other is moving with constant velocity. The mean velocity distribution and the correlation u 1 ′ u 2 ′ ¯ can be expressed in a form of polynomial of the co-ordinate in the direction perpendicular to the plates, with the ratio of shearing stress on the plate to that of the corresponding laminar flow of the same maximum velocity as a parameter. These expressions hold true all the way across the plates, i.e., both the turbulent region and viscous layer including the laminar sublayer. These expressions for Poiseuille flow have been checked with experimental data of Laufer fairly well. It also shows that the logarithmic mean velocity distribution is not a rigorous solution of Reynolds equations.

Radial Turbulent Flow Between Parallel Plates

1985 ◽  
Vol 111 (4) ◽  
pp. 695-712 ◽  
Author(s):  
Girdhari L. Asawa ◽  
Pramod K. Pande ◽  
Pramod N. Godbole
Keyword(s):  
Turbulent Flow ◽  
Parallel Plates

scholarly journals Flow in a pipe of rectangular cross-section

1928 ◽  
Vol 120 (786) ◽  
pp. 691-700 ◽  
Keyword(s):  
Laminar Flow ◽  
Turbulent Flow ◽  
Cross Section ◽  
Rectangular Cross Section ◽  
Stream Line ◽  
Parallel Plates ◽  
Rectangular Section ◽  
Circular Section ◽  
Line Flow ◽  
Minimum Ratio

The object of the research was to investigate the flow of water in a pipe of rectangular cross-section. Much work has been done on similar problems with pipes of circular section, and pipes of rectangular section have been investigated by Fromm and Davies and White. Fromm avoided with pipes in which the ratio of the sides was never less than 6 to 1; his report deals only with turbulent flow. In the case of Davies and White's research, the minimum ratio of the sides was 40 to 1, so that the laminar flow could be calculated from the formula for flow between infinitely wide parallel plates. The present writer used a pipe of section 1·178 cms. by 0·404 cms, (ratio of sides = 2·92); this presents a fresh problem were stream line flow is concerned, and shows interesting results in the region of the critical velocity.

A Theory of Transitional and Turbulent Flow of Non-Newtonian Slurries Between Flat Parallel Plates

1971 ◽  
Vol 11 (01) ◽  
pp. 52-56 ◽  
Author(s):  
Richard W. Hanks ◽  
Maheshkumar P. Valia
Keyword(s):  
Reynolds Number ◽  
Turbulent Flow ◽  
Critical Reynolds Number ◽  
Frictional Resistance ◽  
Newtonian Fluids ◽  
Transitional Flow ◽  
Parallel Plates ◽  
Bingham Plastic ◽  
Turbulent Transition ◽  
Large Width

Abstract A theoretical model is developed which Permits prediction of velocity profiles and frictional prediction of velocity profiles and frictional resistance factors for the isothermal flow of Bingham plastic non-Newtonian slurries in laminar, transitional, and turbulent flow between that parallel walls, in rectangular ducts of large width-to-height ratios, or in concentric annuli with radius ratios approaching unity. The theory is tested with available frictional resistance data for a range of Hedstrom numbers from 10(4) to 10(8) and a set of theoretical design curves of friction factor vs Reynolds number is developed. The model indices that for certain ranges of Hedstrom number (the non-Newtonian index) turbulence is suppressed relative to Newtonian flow behavior, whereas for other ranges of Hedstrom number, the converse is true. Introduction The handling of non-Newtonian fluids in turbulent motion is an important operation in many modern technological processes. Despite this fact, however, little has been done to develop models which are comparable to those available for Newtonian turbulent flow. In particular, a model of the transitional flow regime is notably lacking. Recently, a theory of laminar-turbulent transition for non-Newtonian slurries flowing in pipes and parallel plates was presented. A theory of parallel plates was presented. A theory of transitional and turbulent flow of Newtonian fluids in pipes and parallel plate ducts has also recently been developed. This theory permits the analytic calculation of the friction factor-Reynolds number curves as a continuous function of Reynolds number from the critical Reynolds number of laminar turbulent transition to any condition of turbulent flow. In this paper these two theories will be combined in order to develop a theory for the transitional and turbulent flow of non-Newtonian slurries in parallel plate ducts, rectangular ducts of large width-to-height ratio, or concentric annuli with radius ratios approaching unity. THEORETICAL ANALYSIS The rheological model which will be used to represent the non-Newtonian slurry behavior is the linear Bingham plastic model, ..............(1) ............(2) For this model the laminar flow curve is given by ..............(3) where q = 2v/b, b is one-half the distance between the plates, w = b(−dp/dz) is the wall shear stress, and D = o/ w. The end of the laminax flow, region is determined by the equations ........(4) .........(5) where N Rec = 4bp vc/ p is the critical Reynolds number, Dc is the critical transitional value of D and N He -16bp o/ p is the Hedstrom number expressed in terms of the hydraulic diameter for parallel plates. parallel plates. The calculation of the transitional flow field for this type of fluid will be based upon the model developed by Hanks for Newtonian fluids. SPEJ P. 52

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