Abstract
Radial wall jet flows across flat smooth surfaces have been studied for decades. These studies show that the radial velocity of these jets decays inversely with distance from the nozzle with modest contribution from friction (Poreh, et al., 1967; Rajaratnam, 1976). However, the extent to which flat surface results apply to curved surfaces remains unclear. In this paper we explore the influence of settled particle bed slope on radial wall jet velocity profiles. Jet flows over particle beds often introduce curvature in the particle bed profile, but the influence of the developed curvature on the velocity profile has not been explored. We model the step change in thickness as a sigmoidal curve of variable steepness and use conservation of momentum to evaluate the velocity profile for steady fixed beds. We find that surface curvature has a significant influence on the velocity decay coefficients, provided there is a slip velocity in the vicinity of the particle bed interface, which is strictly true for particle surfaces. We show that the velocity profile attenuates because of curvature. Indeed, conservation of momentum predicts conditions where the forward momentum of the flow is directed completely upward. The solution identifies two new dimensionless groups that determine whether a curved surface is sufficient to block radial flow and force flow vertically.
