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Numerical studies of heat transfer characteristics by using jet discharge at downstream of a backward-facing step

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Summary

This study presents the numerical predictions of the fluid flow and heat transfer characteristics for a backward-facing step by discharging a jet perpendicularly to the main flow. The turbulent governing equations are solved by a control-volume-based finite-difference method with power-law scheme and the well known K−ε model and its associate wall function to describe the turbulent behavior. The interesting parameters include entrance Reynolds number (Re h ), dimensionless jet location (X j/H) and the ratio of jet velocity (U j/U0) with channel expansion ratio ER=1.67. The predicted attachment point is in good agreement with the experiment. It is found that the optimum position is atX j/H=2.1 (X j: location of jet measured from the step position, H: the step height).

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Abbreviations

B:

nozzle width

C 1,C 2,C μ :

turbulent constant

D:

channel height

ER:

expansion ratio,\(\frac{{D + H}}{D}\)

G:

generation rate of turbulent kinetic energy

H:

step height

h x :

local heat transfer coefficient

J:

velocity ratio,U j/U 0

K:

turbulent kinetic energy

q″:

heat flux

Re h :

Reynolds number based on step height,U 0 H/ν

S ϕ :

source term

T:

temperature

U 0 :

inlet velocity

U j :

jet velocity

Uτ :

friction velocity

U, V:

x, y component velocity

X j :

position of discharging jet

X R :

reattachment length of the main flow

X jR :

reattachment length of the upper discharging jet flow

y + :

dimensionless distance from the wall

ϕ:

dependent variables

Γφ :

turbulent diffusion coefficient

μ e , μ l , μ T :

effective, laminar, turbulent viscosity

ϱ:

density

ϰ:

Von Kármán constant

σ:

turbulent Prandtl number

τ w :

wall shear stress

ε:

turbulent energy dissipation rate

References

  1. Abbot, D. E., Kline, S. J.: Experimental investigation of subsonic turbulent flow over single and double backward facing step. J. Basic Eng. Trans. ASME84, 317 (1962).

    Google Scholar 

  2. Seban, R. A.: Heat transfer to the turbulent separated flow of air downstream of a step in the surface of plate. J. Heat Transfer. Trans. ASME86, 259–262 (1964).

    Google Scholar 

  3. Aung, W., Goldstein, R. J.: Heat transfer in turbulent separated flow downstream of a rearward-facing step. Isr. J. Tech.10, 35–41 (1972).

    Google Scholar 

  4. Eaton, J., Johnston, J. P.: A review of research on subsonic turbulent flow reattachment. AIAA J.19, 1093–1100 (1981).

    Google Scholar 

  5. Armaly, B. F., Durst, F., Kottke, V.: Momentum heat and mass transfer in backward-facing step flow. Proceedings of 3rd Symposium on Turbulent Shear Flows, Davis, CA, 16.1–16.4 (1981).

  6. Armaly, B. F., Durst, F., Pereira, J. C. F., Schonung, B.: Experimental and theoretical investigation of backward facing step flow. J. Fluid Mech.127, 473–496 (1983).

    Google Scholar 

  7. Simpson, R. L.: A model for the backward mean velocity profile. AIAA J.21, 142–143 (1983).

    Google Scholar 

  8. Vogel, J. C., Eaton, J. K.: Combined heat transfer and fluid dynamic measurements downstream of a backward-facing step. J. Heat Transfer107, 922–929 (1985).

    Google Scholar 

  9. Sparrow, E. M., Kang, S. S., Chuck, W.: Relation between the points of flow reattachment and maximum heat transfer for regions of flow separation. Int. J. Heat Mass Transfer30, 1237–1246 (1987).

    Article  Google Scholar 

  10. Sparrow, E. M., Chuck, W.: PC solutions for heat transfer and fluid flow downstream of an abrupt, asymmetric enlargement in a channel. Numer. Heat Transfer12, 19–40 (1987).

    Google Scholar 

  11. Vradis, G., Nostrand, L. Van: Laminar flow and heat transfer downstream of a confined backward facing step including variable viscosity effects. Simul. Numer. Methods Heat Transfer, ASME, HTD,157, 1–8 (1990).

    Google Scholar 

  12. Hong, B., Armaly, B. F., Chen, T. S.: Mixed convection in a duct with a backward-facing step uniform heat flux case. Fundamentals of Mixed Convection, ASME HTD-213, 73–78 (1992).

    Google Scholar 

  13. Oyakawa, K., Koike, T., Mabuchi, I.: Studies of heat transfer control by using jet discharge at reattachment region downstream of a backward-facing step. JSME59, 543–549 (1993).

    Google Scholar 

  14. Jayatilleke, C. L. V.: The influence of Prandtl number and surface roughness on the resistance of the laminar sublayer to momentum and heat transfer. Prog. Heat Mass Transfer1, 193–329 (1969).

    Google Scholar 

  15. Patankar, S. V.: Numerical heat transfer and fluid flow. New York: Mc Graw-Hill 1980.

    Google Scholar 

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Author notes

  1. Y. T. Yang & M. L. Huang

    Present address: Department of Mechanical Engineering, National Cheng Kung University, 70101, Tainan, Taiwan Republic of China

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    1. Y. T. Yang
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    2. M. L. Huang
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    Yang, Y.T., Huang, M.L. Numerical studies of heat transfer characteristics by using jet discharge at downstream of a backward-facing step. Acta Mechanica 128, 29–37 (1998). https://doi.org/10.1007/BF01463157

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    • DOI: https://doi.org/10.1007/BF01463157

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