Abstract
The turbulent flow characteristics in the inlet regions of circular pipes and parallel plates are considered separately in this paper. The momentum integral equation of the boundary layer near the wall and the overall continuity equation for the flow are solved. The variation of the shape factor is taken into consideration in the solution by supplementing the two basic equations by an entrainment equation. Numerical solutions and available experimental results show that the present theory is in good agreement with experimental data for flow in both pipe and parallel plates.
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Abbreviations
- a 11...a 34 :
-
defined in (30)
- A 1...A 14 :
-
defined in (17)
- b 11...b 23 :
-
defined in (30)
- H :
-
the shape factor, δ*/ϑ
- L :
-
half width between parallel plates
- n :
-
constant in velocity distribution
- r :
-
radial coordinate
- R :
-
radius of pipe
- Re:
-
Reynolds number, \(2RU_{{\text{p}}_{\text{0}} } /v\) for pipe flow, and \(2LU_{{\text{p}}_{\text{0}} } /v\) for flow between parallel plates
- u :
-
velocity component in x-direction
- U p :
-
center line velocity
- v :
-
velocity component in r- or y-direction
- x :
-
flow direction coordinate
- y :
-
coordinate perpendicular to x
- ρ :
-
density
- τ :
-
shearing stress
- δ :
-
boundary layer thickness
- δ*:
-
displacement thickness
- ϑ :
-
momentum thickness
- ν :
-
dynamic viscosity
- η :
-
y/δ
- Δ :
-
defined in (31)
- o:
-
inlet to channel
- w:
-
condition at wall
- fd:
-
fully developed condition
- f:
-
condition at location where the boundary layers join
- -:
-
dimensionless quantities
References
Latzko, H., Heat Transfer in a Turbulent Liquid or Gas Stream, NACA TM 1068, 1944.
Holdhusen, J. S., The Turbulent Boundary Layer in the Inlet Region of Smooth Pipes, Ph.D. thesis, University of Minnesota, 1952.
Deissler, R. G., Trans. ASME 77 (1955) 1221.
Filippov, G. V., Soviet Physics — Tech. Phys. 32 (1958) 1681.
Bowlus, D. A. and J. A. Brighton, J. Basic Eng. Trans. ASME 90, Ser. D (1968) 431.
Barbin, A. R. and J. B. Jones, J. Nasic Eng. Trans. ASME (1963) 29.
Byrne, J., A. P. Hatton and P. G. Marriott, Proc. Inst. of Mech. Engrs. 184 (1969–1970) 697.
Schlichting, H., Boundary Layer Theory, McGraw-Hill Book Company, Inc., 1968, chaps. 20 and 22.
Rotta, J. C., Progress in Aeronautical Sciences 2 (1962) 1–220.
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All opinions or assertions made in this paper are those of the authors and are not to be construed as official or necessarily reflecting the views of the Navy or the naval service at large.
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Na, T.Y., Lu, Y.P. Turbulent flow development characteristics in channel inlets. Appl. Sci. Res. 27, 425–439 (1973). https://doi.org/10.1007/BF00382505
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DOI: https://doi.org/10.1007/BF00382505