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Computation of Three-Dimensional Turbulent Jets in Cross Flow

  • A. O. Demuren

Abstract

Two finite-difference numerical procedures have been employed in calculating the flow of a row of jets issuing normally into a nearly uniform cross flow at a jet to cross flow velocity ratio of 1.96. Calculations with different grids have shown that grid independent results could be obtained within the limits of current medium-sized computers if a higher-order scheme like the QUICK scheme of Leonard is employed in estimating the convection terms in the momentum equations. It may not be possible to obtain grid-independent results, even with the currently available very large computers, if the widely-used Hybrid scheme is employed. The fine grid calculation employing the QUICK scheme agrees fairly well with the measurement of the total pressures within the jet, but the extent of the wake zone below the jet is over-predicted by about 17 %, beyond about 3 jet diameters from the discharge port. The k-ε turbulence model does not adequately reflect the high complexity of the turbulence in the wake region and may be the cause of the discrepancy. The need for an improved turbulence model exists.

Keywords

Turbulence Model Cross Flow Hybrid Scheme Wake Region Grid Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Nomenclature

Cp

(PT - pTIN) / (PTj - PTIN)

c1, c2, cµ

constants in turbulence model

D

diameter of jet

G

generation rate of k

H

Hybrid (Central/Upwind) difference scheme

k

kinetic energy of turbulenc

P

static pressure

Pe

cell face Peclet number

PT

total pressure

Q

QUICK (Quadratic Upstream Interpolation for Convective Kinematics) difference scheme

R

Jet to Crossflow velocity ratio

Sø

Source of dependent variable Φ

s

Jet spacing

T

Temperature

U

x-direction velocity

V

y-direction velocity

W

z-direction velocity

x, x1

lateral coordinate

y, x2

vertical coordinate

z, x3

streamwise coordinate

| |

modulus

A

cell width

δij

Kronecker delta

ɛ

dissipation rate of k

Γø

transport property of Φ

vt

turbulent viscosity

ρ

density

σΦ

PrandtI/Schmidt number for Φ

Φ,φ

dependent variable and its fluctuation

Subscripts

IN

Initial value

(i,j,k)

x,y,z directions

j

Jet value

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References

  1. Abramovich, G.N. (1963) The Theory of Turbulent Jets. M.I.T. Press.Google Scholar
  2. Andreopoulos, J. (1980) Measurements in a pipe flow issuing perpendicular into a cross stream. ASME, Winter annual meeting, Chicago, Illinois.Google Scholar
  3. Andreopoulos, J. (1981) Measurements in a low momentum jet into a cross flow. 3rd Turbulent Shear Flows Conference, Davis, California.Google Scholar
  4. BergeIes, G., Gosman, A.D., and Launder, B.E. (1978) The turbulent jet in a cross-stream at low injection rates. Rep. TF/ 78/3, Mech. Eng. Dept., Univ. California, Davis.Google Scholar
  5. Crabb, D., Durao, D.F.G., and Whitelaw, J.H. (1980) A round jet normal to a cross-flow. ASME, Winter annual meeting, Chicago, Illinois.Google Scholar
  6. De Vahl Davis, G., and Mallinson, G.D. (1967) An evaluation of upwind and central difference approximations by a study of recirculating flow. Computers and Fluids 4, 29.CrossRefGoogle Scholar
  7. Kamotani, Y., and Greber, I. (1974) Experiments on confined turbulent jets in cross flow. NASA, CR-2392.Google Scholar
  8. Launder, B.E., and Spalding, D.B. (1974) The numerical computation of turbulent flows. Comp. Meths. Appl. Mech. Eng. 3, 269.MATHCrossRefGoogle Scholar
  9. Leonard, B.P. (1979) A stable and accurate convective modelling procedure based on quadratic upstream interpolation. Comp. Meths. Appl. Mech. Eng. 19, 59.MATHCrossRefGoogle Scholar
  10. Leschziner, M.A. (1980) Practical evaluation of three finite-difference schemes for the computation of steady-state recirculating flows, Comp. Meths. Appl. Mech. Eng. 23, 293.MATHCrossRefGoogle Scholar
  11. Moussa, Z.M., Trischka, J.W., and Eskinazi, S. (1977) The near field in the mixing of a round jet with a cross-stream. J. Fluid Mech. 15, 243.Google Scholar
  12. Patankar, S.V., and Spalding, D.B. (1972) A calculation procedure for heat, mass and momentum transfer in three-dimensional parabolic flows. IJHMT 15, 1787.MATHCrossRefGoogle Scholar
  13. Patankar, S.V., Basu, D.K., and Alpay, S.A. (1977) Prediction of the three-dimensional velocity field of a deflected turbulent jet. J. Fluids Eng. 99, 758.CrossRefGoogle Scholar
  14. Ramsey, J.W., and Goldstein, R.J., (1972) Interaction of a heated jet in a deflecting stream. NASA CR 72613.Google Scholar
  15. Rodi, W., and Srivatsa, S.K. (1980) A locally elliptic calculation procedure for three-dimensional flows and its application to a jet in a cross-flow. Comp. Meths. Appl. Mech. Eng. 23, 67.CrossRefGoogle Scholar
  16. Spalding, D.B. (1972) A novel finite difference formulation for differential expressions involving both first and second derivatives. Int. J. Num. Meths. Eng. 4, 551.CrossRefGoogle Scholar
  17. Sugiyma, Y., and Usami, Y. (1979) Experiments on the flow in and around jets directed normal to a cross flow. Bulletin JSME 22, 1736.CrossRefGoogle Scholar
  18. White, A.J. (1980) The prediction of the flow and heat transfer in the vicinity of a jet in cross flow. ASME Winter annual meeting, Chicago, Illinois.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • A. O. Demuren
    • 1
  1. 1.Sonderforschungsbereich 80Universität KarlsruheGermany

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