No abstract

An analytical model for the behavior of normally injected jets in a cross flow is developed and applied to fluids of differing densities. Central to the model are the dynamics of the vortex pair structure associated with the local jet cross section and the entrairiment of cross flow by jet fluid. Two specific cases are modeled: one involving a single (hot or cold) jet in a cross flow, in which trajectories are found to scale primarily with jet-to-cross flow momentum ratio, and the other involving a series of spanwise jets injected into a cross flow, which indicates scaling with momentum ratio and with the spacing-to-orifice-diameter ratio. In the case of multiple jet penetration, however, merging of the jets into an approximately two-dimensional jet downstream of injection is observed for low spacing-to-diameter ratios. PyOPoo v Nomenclature = radius of viscous core = orifice diameter = local entrainment parameter = "lift" force acting to separate vortices = half-spacing of vortices = virtual mass coefficient for motion of vortex cores = spanwise spacing of multiple injected jets = characteristic length for transverse jet* = Rd --impulse per unit depth of transverse jet = square root of jet-to-cross flow momentum ratio, T c (t) = U(t) U,(t) MO = v r (r,t) = characteristic Reynolds number, (U w L/v) flow time parameterizing location of vortex pair along trajectory temperature of fluid in viscous core temperature of jet at orifice temperature of cross flow cross flow velocity in reference frame of vortices induced velocity of infinite row of vortex pairs cross flow velocity (absolute frame) jet velocity at the orifice mass-averaged velocity of fluid in jet along trajectory radial velocity field exterior to viscous core complex potential in vortex pair reference frame downstream location of vortex pair transverse location of vortex pair total (integrated) circulation of each vortex average eddy viscosity density of fluid in vortex cores density of fluid in recirculation cell (except in cores) density of jet at the orifice density of cross flow angle describing orientation of vortex pair