On the Scaling of Transient Laminar, Turbulent, and Spray Jets

Through numerical solutions of appropriate two-dimensional unsteady conservation equations, it is found that transient laminar incompressible jets, turbulent incompressible jets and non-vaporizing and vaporizing sprays reach steady state around the back of their head vortices. Thus, for many applications, the stems of such transient jets can be considered in steady state and steady state information can be applied to large fractions of transient jets. Equations are given for the penetration rate of such jets. In particular, an equation is obtained for the penetration rate of the tip of sprays that compares favorably with measured ones. Also, scaling laws are reported that are obeyed by each of the three families of jets. Since the laws are somewhat different, no precise similarity exists among the three types of jet. However, one type of jet can still be approximately simulated by another but only with respect to certain parameters and within definite time and space ranges, given the acceptable error.