Counterflow laminar gas jets issuing from aligned planar nozzles

The laminar flow resulting from the impingement of two gaseous jets issuing from aligned planar nozzles of semi-width $R$ separated a distance $2H$ is investigated by numerical and analytical methods, with specific consideration given to the high-Reynolds and low-Mach number conditions typically present in counterflow-flame experiments. The resulting flow, nearly inviscid and effectively incompressible, can be described by using a density-weighted stream-function/vorticity formulation that removes the need to consider specifically the boundary separating the two jet streams. Besides the geometric parameter $H/R$, the solution depends only on the shape of the velocity profiles in the feed streams and on the jet momentum-flux ratio $\Lambda$. While conformal mapping can be used to determine the potential solution corresponding to uniform feed-stream velocity profiles, numerical integration is required in general to compute vortical flows, including those arising with Poiseuille velocity profiles, with simplified solutions found in the limits $H/R \ll 1$ and $H/R \gg 1$.