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Leakage effects in laminar duct flow: a numerical study

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Abstract

The influence of transverse leakage into a pressure-driven laminar flow in an infinitely long square duct is investigated. By a simple decomposition of the resulting three-dimensional pressure field, the leakage-induced secondary flow problem decouples from the primary flow problem. The numerical study reveals that two qualitatively different secondary flow patterns may occur, depending on the leakage flow rate. For a given streamwise pressure gradient it is observed that the axial mass flow rate may reduce by about 30 percent under certain leakage conditions, accompanied by a corresponding 50 percent increase in the Darcy-Weisbach friction factor.

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Abbreviations

D :

duct height and width

D h :

hydraulic diameter

D i,j :

cell divergence

F :

dimensionless pressure force

h :

dimensionless slit height,H/D

H :

slit height

i,j :

indices

K :

streamwise kinematic pressure gradient

n :

summation index, time level

p :

dimensionless pressure

δp :

pressure increment

P :

pressure

\(\tilde P\) :

cross-sectional pressure variation

q :

dimensionless volumetric axial flow rate

Q :

leakage flow rate in m2/s

Re:

leakage Reynolds number,U 0 D/v

Re q :

primary flow Reynolds number

δt :

time increment

x, y :

dimensionless cross-sectional coordinates

δx, δy :

cell widths

X, Y :

cross-sectional coordinates

z :

dimensionless axial coordinate

Z :

axial coordinate

u, v, w :

dimensionless velocity components

U, V, W :

velocity components

U 0 :

leakage velocity,Q/H

V :

cross-sectional average velocity

W 0 :

dummy velocity scale

ρ :

density

ν :

kinematic viscosity

ω :

overrelaxation factor

References

  1. Andersson, H. I. and Kristoffersen, R., Numerical simulation of unsteady viscous flow.Arch. Mech. 41 (1989) 207–223.

    Google Scholar 

  2. Andersson, H. I. and Kristoffersen, R., Start-up of laminar pipe flow.Proc. AIAA/ASME/SIAM/APS 1st National Fluid Dynamics Congress, Cincinnati. Washington: AIAA (1988) pp. 1356–1363.

    Google Scholar 

  3. Anwar, I., Evaluation of seal concepts for advanced flywheel systems.Energy Conservation Through Fluid Film Lubrication Technology: Frontiers in Research and Design. New York: ASME (1979) pp. 147–167.

    Google Scholar 

  4. Bayada, G. and Chambat, M., Asymptotic behaviour of a thin film flow in junction with a cavity. In: R. Gruber, J. Periaux and R. P. Shaw (eds),Proc. 5th International Symposium on Numerical Methods in Engineering, Vol. 1. Berlin/Heidelberg: Springer Verlag (1989) pp. 737–742.

    Google Scholar 

  5. Brekke, H., The influence from the guide vane clearance gap on efficiency and scale effect for Francis turbines.Proc. 14th IAHR Symposium on Progress within Large and High-Specific Energy Units. Trondheim: Tapir Publishers (1988) pp. 825–837.

    Google Scholar 

  6. Brekke, H., Schanke, P. and Haugen, J. O., The influence of the guide vane clearance gap on efficiency and scale effect.Proc. 15th IAHR Symposium on Modern Technology in Hydraulic Energy Production, Paper B3. Belgrade (1990).

  7. Cheremisinoff, N. P., Principles of polymer mixing and extrusion. In: N. P. Cheremisinoff (ed.),Encyclopedia of Fluid Mechanics, Vol. 7, Rheology and Non-Newtonian Flows. Houston: Gulf Publishing Company (1988) pp. 761–865.

    Google Scholar 

  8. Demko, J. A., Morrison, G. L. and Rhode, D. L., Effect of shaft rotation on the incompressible flow in a labyrinth seal. In: C. Taylor, W. G. Habashi and M. M. Hafez (eds),Proc. 5th International Conference on Numerical Methods in Laminar and Turbulent Flow. Swansea: Pineridge Press (1987) pp. 509–520.

    Google Scholar 

  9. Hirt, C. W., Heuristic stability theory for finite-difference equations.J. Comp. Phys. 2 (1968) 339–355.

    Article  MATH  ADS  Google Scholar 

  10. Hirt, C. W., Nichols, B. D. and Romero, N. C., SOLA-A numerical solution algorithm for transient fluid flows. Los Alamos Scientific Laboratory Report LA-5852 (1975).

  11. Kalyon, D. M., Mixing in continuous processors. In: N. P. Cheremisinoff (ed.),Encyclopedia of Fluid Mechanics, Vol. 7, Rheology and Non-Newtonian Flows. Houston: Gulf Publishing Company (1988) pp. 887–926.

    Google Scholar 

  12. Kristoffersen, R., Billdal, J. T. and Andersson, H. I., The three-dimensional lid-driven cavity flow as test case for numerical solution algorithms. In: C. Taylor, P. M. Gresho and R. L. Sani (eds),Proc. 6th International Conference on Numerical Methods in Laminar and Turbulent Flow. Swansea: Pineridge Press (1989) pp. 133–143.

    Google Scholar 

  13. Press, W. H., Flannery, B. P., Teukolsky, S. A. and Vetterling, W. T.,Numerical Recipes. Cambridge: Cambridge University Press (1986).

    Google Scholar 

  14. Rauwendaal, C.,Polymer Extrusion. Munich: Hanser Publishers (1986).

    Google Scholar 

  15. Rhode, D. L., Demko, J. A., Traegner, U. K., Morrison, G. L. and Sobolik, S. R., Prediction of incompressible flow in labyrinth seals.ASME J. Fluids Engrg. 108 (1986) 19–25.

    Article  Google Scholar 

  16. Shah, R. K. and London, A. L.,Laminar Flow Forced Convection in Ducts. New York: Academic Press (1978).

    Google Scholar 

  17. Stoff, H., Incompressible flow in a labyrinth seal.J. Fluid Mech. 100 (1980) 817–829.

    Article  ADS  Google Scholar 

  18. Timin, T. and Esmail, M. N., A comparative study of central and upwind difference schemes using the primitive variables.Int. J. Num. Meth. Fluids 3 (1983) 295–305.

    Article  MATH  Google Scholar 

  19. White, F. M.,Viscous Fluid Flow. New York: McGraw-Hill (1974).

    MATH  Google Scholar 

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Author notes

  1. Knut L. Tiseth

    Present address: OECD Halden Reactor Project, P.O. Box 173, N-1751, Halden, Norway

Authors and Affiliations

  1. Division of Applied Mechanics, The Norwegian Institute of Technology, N-7034, Trondheim, Norway

    Helge I. Andersson & Knut L. Tiseth

Authors
  1. Helge I. Andersson
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Andersson, H.I., Tiseth, K.L. Leakage effects in laminar duct flow: a numerical study. Appl. Sci. Res. 49, 117–134 (1992). https://doi.org/10.1007/BF02984173

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