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Pulsatile entrance flow in curved pipes: effect of various parameters

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Abstract

This paper presents the results of an experimental study on the developing pulsatile flow in curved pipes with a long, straight pipe upstream. In order to examine the dependence of flow-field development on the governing parameters, LDV measurements were conducted systematically for six cases of flow, where the Womersley number α was varied from 5.5 to 18, the mean Dean number D m was 200 and 300, the flow rate ratio η was 0.5 and 1, and the curvature radius ratio Rc was 10 and 30. Peculiar flow phenomena, such as flow reversal for all values of α and a depression in the axial velocity profile for α = 10, were analyzed by decomposing the axial velocity into a time-mean and a varying component, as well as by obtaining the bias of their profiles. The velocity distributions abruptly change with the phase at turn angles Ω of 15–30°, corresponding to the nondimensional axial length z′ ≅ 1–2 from the bend entrance, and their development along the pipe axis is the most complicated for the flow at a moderate α of 10 and large η of 1. The entrance length in the case of pulsatile flow is shorter than that for steady flow with the same flow rate as the maximum pulsatile flow rate.

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Abbreviations

a :

radius of pipe, a = d/2

C p :

pressure coefficient, C p  = (P − P ref)/(ρW 2 m /2)

D :

Dean number, D = Re Rc −1/2

P :

static pressure at pipe wall

P ref :

reference value of P, i.e., P at z/d = −2

R :

curvature radius of pipe

R c :

curvature radius ratio, R c  = R/a

Re :

Reynolds number, Re = W m d/ν

u, w :

velocities in x and z directions, respectively

W :

axial velocity averaged over cross section

x, y, z :

coordinate system, see Fig. 2

z′:

nondimensional axial length, z′ = z/(aR)1/2

α :

Womersley number, α = a(ω/ν)1/2

β :

deflection of axial flow, see Eqs. (3) and (4)

ϕ :

phase difference, see Eq. (2)

η :

flow rate ratio, η = W o /W m

Θ :

phase angle, Θ = ωt (t: time, ω: angular frequency)

ν :

kinematic viscosity of fluid

ρ :

density of fluid

Ω :

turn angle, see Fig. 2

m, o :

time-mean and amplitude values, respectively

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Acknowledgment

The author would like to thank Professor Emeritus K. Sudo of Hiroshima University for his useful and helpful suggestions.

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Authors and Affiliations

  1. School of Engineering, Kinki University, 1 Takaya Umenobe, Higashi-Hiroshima, 739-2116, Japan

    Masaru Sumida

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  1. Masaru Sumida
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Correspondence to Masaru Sumida.

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Sumida, M. Pulsatile entrance flow in curved pipes: effect of various parameters. Exp Fluids 43, 949–958 (2007). https://doi.org/10.1007/s00348-007-0365-4

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  • DOI: https://doi.org/10.1007/s00348-007-0365-4

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