On the Scaling of Impulsively Started Incompressible Turbulent Round Jets

Abstract

A scaling law for transient, turbulent, incompressible, round jets is reported. Numerical solutions of the Navier-Stokes equations were obtained using a k-ε model for turbulence. The constants of the k-ε model were optimized by comparing computed centerline velocity, mean radial velocity distribution, longitudinal kinetic energy distributions with those measured by other authors in steady round jets. The resulting constants are those also used in computations of steady planar jets except for the one that multiplies the source term in the ε-equation. After optimization, the agreement is satisfactory for all mean quantities but is still rather poor for the kinetic energy distribution. Parameteric studies of the transient were performed for 9•103 ≤ ReD ≤ 105. Then the definition was adopted that a jet reaches steady state between the nozzle and an axial location when, at that location, the centerline velocity achieves 70 percent of its steady state value, and characteristic steadying length and time scales (D•ReD0.053 and D•ReD0.053/u cL,0 respectively) were determined as well as a unique function that relates dimensionless steadying time to dimensionless steadying length. This function changes in a predictable way if a percent other than 70 is selected but the characteristic length and time scales do not. It is found that the 70 percent threshold is reached within the head vortex of the transient jet. Thus a transient jet, practically, is a steady jet except within its head vortex. This, in part, justifies our use of steady state k-ε constants in our transient computations. The computed jet tip arrival times are shown to compare favorably with measured ones.