The inviscid impingement of a jet with arbitrary velocity profile

Abstract

Accurate determination of wall shear stress and heat and mass transfer rates under an impinging jet requires careful analysis of the boundary layer at the impingement surface due to the large pressure gradients near the stagnation point. Modeling the inviscid flow just outside the boundary layer provides the boundary conditions necessary for such an analysis. Previous inviscid models have considered only a small subset of possible jet velocity profiles and with limited spatial resolution. In the present work, analytical solutions to the stream-vorticity equation for two-dimensional and axisymmetric impingement flow with arbitrary velocity profile are found in terms of a surface integral involving the vorticity function, allowing an iterative determination of the stream function throughout the impingement region. Surface pressure distributions and streamline plots are calculated for various impinging jet configurations, including plane, round, and annular jet nozzles. The calculations show excellent agreement with previous experimental and numerical results, while requiring relatively short computation times. Flow predictions are also made for impinging jet configurations for which no previous data or calculations exist.

Coating Weight Model for the Continuous Hot-Dip Galvanizing Process

“…Because the jet velocity profile is no longer self-similar due to the uniform velocity of the potential core, the surface pressure assumes a top-hat profile in the near-field region (i.e., Z/d £ 8) of the air knife. [10] IV. PRESSURE CORRELATIONS…”

“…[10]. Equation [11] is a modified form of the formula that was used by Brenhorst and Harch [15] to initialize the computational domain for near-field measurements in a fully pulsed subsonic air jet.…”

The wall shear stress produced by the normal impingement of a jet on a flat surface

“…For the purpose of calculating wall shear stress, the significant quantity needed from the inviscid analysis is the velocity, U, at the surface y = 0, which is assumed to be the velocity at the top of the boundary layer. It follows from the development of Phares et al (2000b) that this velocity distribution is the converging infinite series:…”

“…Therefore, treatment of the inviscid impingement region must not be limited to a single velocity profile. Phares, Smedley & Flagan (2000b) solved (2.13) and (2.14) for an arbitrary influx stream function profile, Ψ , in terms of a surface integral involving the vorticity function, Ω. By assuming an appropriate stream function distribution, the vorticity function and, thus, the surface integral could be calculated, yielding a corrected stream function distribution.…”

On the non-parallel instability of the rotating-sphere boundary layer

“…The boundary conditions of U I = 0 along the sphere surface and ∂V I /∂β = ∂W I /∂β = ω I = 0 in the equatorial plane cannot be fulfilled by (2.20) and should be satisfied through the presence of local boundary layers. The solution of (2.20) has been discussed in the literature (Rubel 1983;Phares et al 2000), but here it is further complicated by the presence of a recirculation region where the value of the vorticity is unknown, so that equation (2.20) cannot be solved directly, but we need to solve (2.13)-(2.16) instead. Nevertheless the solution as η → ∞ must approach the inflow, so that the outflow asymptotes to…”