# Computation of Three-Dimensional Turbulent Jets in Cross Flow

## 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## Nomenclature

- C
_{p} (P

_{T}- p_{TIN}) / (P_{Tj}- P_{TIN})- c
_{1}, c_{2}, c_{µ} 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

- P
_{e} cell face Peclet number

- P
_{T} total pressure

- Q
QUICK (Quadratic Upstream Interpolation for Convective Kinematics) difference scheme

- R
Jet to Crossflow velocity ratio

- S
_{ø} Source of dependent variable Φ

- s
Jet spacing

- T
Temperature

- U
x-direction velocity

- V
y-direction velocity

- W
z-direction velocity

- x, x
_{1} lateral coordinate

- y, x
_{2} vertical coordinate

- z, x
_{3} streamwise coordinate

- | |
modulus

- A
cell width

- δ
_{ij} Kronecker delta

- ɛ
dissipation rate of k

- Γ
_{ø} transport property of Φ

*v*_{t}turbulent viscosity

- ρ
density

- σ
_{Φ} 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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