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Transient mixed convection flow instabilities in a vertical pipe

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Abstract

The present paper investigates a numerical study of flow instabilities in transient mixed convection in a vertical pipe. At the entrance of the pipe, the flow is suddenly submitted to a temperature step. The convection heat transfer on the outer surface of the pipe is taken into account. The governing equations are solved using a finite difference explicit scheme. The numerical results show that the time development of streamlines and isotherms is strongly dependent on the inlet temperature steps. For positive temperature steps, the unsteady vortex is significant in the vicinity of the wall and the reversal flow appears below the wave instability. In the case of negative temperature steps and especially for the low Reynolds number, the reversal flow appears on top of the wave instability. During the transient, the apparition of the vortical structures along the wall leads to the wall boundary layer instability. This phenomenon is due to the transient mixed convection flows. The temperature step effects on the heat transfer of the flow are presented in our paper.

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Abbreviations

g :

acceleration of the gravity (m/s2)

h a :

convective exchange coefficient (W/m2.K)

Gr:

Grashoff number, gβΔTR3/ν2

r :

radial coordinate

R :

radius of the pipe (m)

Re:

Reynolds number, Vd R/ν

Ri:

Richardson number, Gr/Re2

t :

time (s)

T :

temperature (°C)

U :

velocity in the r-direction (m/s)

V :

velocity in the z-direction (m/s)

V d :

bulk velocity (m/s)

z :

axial coordinate

λ:

thermal conductivity (W/m K)

β:

coefficient of thermal expansion (1/K)

ΔT:

temperature step (°C)

ν:

kinematic viscosity (m2/s)

Ψ:

stream function (m3/s)

Ω:

vorticity (m2/s)

Φ:

heat flux (W)

a:

ambient reference quantity

e:

inlet

f:

fluid

w:

at the wall

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Acknowledgements

This work was carried out in the framework of the AMETH (Amélioration des Echanges Thermiques) programm.

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Authors and Affiliations

  1. Laboratoire de Thermomécanique, Faculté des Sciences, UTAP, EA 2061, BP 1039, 51687, Reims, France

    T. H. Mai, C. V. Popa & G. Polidori

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  1. T. H. Mai
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  2. C. V. Popa
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  3. G. Polidori
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Correspondence to T. H. Mai.

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Mai, T.H., Popa, C.V. & Polidori, G. Transient mixed convection flow instabilities in a vertical pipe. Heat Mass Transfer 41, 216–225 (2005). https://doi.org/10.1007/s00231-004-0528-2

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