Prediction of secondary vortex flowfields generated by an interacting multiple free-jet configuration

Abstract

APENALTY finite element algorithm for solution of the three-dimensional parabolic Navier-Stokes equations for subsonic turbulent flows is applied to the prediction of secondary vortex flowfields induced by a multiple free-jet configuration. The combined action of rapid decay of the initial high-speed parallel jets, turbulence level, induced entrainment from the far field, and geometric discreteness of a four-jet configuration, is predicted to produce a persistent system of eight counterrotating vortex pairs in the plane normal to the initial jet axis. Numerical predictions are interpreted and compared with available experimental data. Contents As detailed in the complete paper,1 a penalty finite element numerical algorithm is well suited to the solution of subsonic, three-dimensional multiple free-jet problem definitions. The abiding predominance of a preferred (axial) flow direction permits an order-of-magn itude analysis confirming that associated diffusion effects are insignificant. Discarding these terms yields the thin-layer Navier-Stokes (TLNS) approximation; provided a suitable pressure interaction procedure exists, solution of the TLNS system can be cast into the efficient space-marching, initial-value, parabolic NavierStokes (PNS) equation set. The ordering analysis also confirms that the transverse plane momentum equations govern pressure modifications to first order, while the continuity equation is the principal (divergence-free) momentum constraint statement. The key features of the PNS penalty finite element algorithm, as applied to the free-jet problem class, directly address these fundamental issues by 1) establishment of a quasilinear pressure Poisson equation, with complementary and particular solutions that readily admit interaction and far-field boundary condition requirements; and 2) a specific continuity equation constraint yielding efficient and accurate global communication of the local momentum defect relaxa