Computers & Fluids Vol. 17, No. 3, pp. 453-465, 1989 0045-7930/89 $3.00+0.00 Printed in Great Britain Pergamon Preu pk MODELLING THE EFFECTS OF LATERAL DIVERGENCE ON RADIALLY SPREADING TURBULENT JETS M. R. MALIN CHAM Limited, Bakery House, 40 High Street, Wimbledon, London SWI9 5AU, U.K. (Received 21 June 1988; /n revisedform 26 July 1988) Abstract--The two-equation turbulence models of Harlow and Nakayama (k-f) and Spalding (k-W) are used to predict the spreading rates of the radial free jet and the radial wall jet. Spalding's model appears to fare best for these flows, but both models tend to underestimate the measured spreading rates, especially for the wall-jet configuration. It is shown that improved predictions can be obtained by making the length-scale-determining equation much more sensitive to the generation rates of turbulence energy associated with the turbulent normal stresses. Calculations obtained with the modified scale equation are also presented for the plane and round free jet. The plane-jet growth rate is still predicted reasonably well, and the round-jet predictions show some improvement over those obtained with the unmodified turbulence models. NOTATION b jet width measured from the wall or flow axis; value of y at which U is equal to Um/lO0. C's coefficients in the turbulence models } - u/u. f~ turbulence-model function defined by eqn (11) f2 mean-flow retardation function defined by eqn (13) k turbulent kinetic energy per unit mass £ = klVl L length scale of the large-seale turbulent motion Pk stress production of k S z secondary source term in the Z-equation U streamwise mean velocity u 2 kinematic streamwise normal stress kinematic turbulent shear stress v 2 kinematic normal stress in the y-direction W time-mean square of the vorticity fluctuations w: kinematic normal stress in the z-direction x streamwise coordinate y cross-stream coordinate Z dependent variable of the length-seale-determining equation z transverse coordinate Greek symbols -- ~ - v_Dlk b - (v 2 - w:)/k 6u jet half-width; value of y at which U is equal to U®I2 rate of dissipation of k ~, dynamic turbulent viscosity v, kinematic turbulent viscosity v molecular kinematic viscosity p fluid density ~'s empirical diffusion coefficients in the turbulence models t~ time-mean vorticity regardless of direction empirical constant in eqn (12) • ylrv Subscripts m maximum value 1. INTRODUCTION Radial jets find applications in many industrial processes concerned with cooling and heating, and they are also of interest in connection with the design of vertical-take-off aircraft. Although a number of authors have used two-equation turbulence models, such as the k--¢ [l], k-W [2] and k-kL [3] models, for the prediction of various jet flows [4-10], a systematic assessment of their 453