Coefficient of discharge and spray cone angle of a pressure nozzle with combined axial and tangential entry of power-law fluids

Abstract

Flows of incompressible, time-independent purely viscous power-law fluids through pressure nozzle with combined axial and tangential entry are analysed. Theoretical predictions of coefficient of discharge and spray cone angle are made through an approximate analytical solution of hydrodynamics of flow inside the nozzle. In the converging section of the nozzle, the boundary layer equations have been derived with modified order approximation [O(δ/R)≈1, O(δ²/R²)«1] of Navier-Stokes equations for a better accuracy. Smoother attainment of the free-stream condition at the edge of the boundary layer is ensured by requiring the appropriate shear rate terms, compatible with the above order analysis, to be zero. The pertinent independent input parameters which govern the flow field are the generalized Reynolds number at inlet to the nozzle based on the tangential velocity of injection Re_Gi, the ratio of the axial-to-tangential velocity at the inlet to the nozzle V_R, the flow behaviour index of the fluid n, the length-to-diameter ratio of the swirl chamber L₁/D₁, the spin chamber angle 2α and the orifice-to-swirl-chamber-diameter ratio D₂/D₁. Experiments reported in the paper corroborate the qualitative trends of analytical results.