A method for calculating the turbulent isothermal flow in axisymmetric annular dump difluser geometries is described and appraised. The calculation method is based on the numerical solution of the time-averaged transport equations for momentum, continuity, turbulence kinetic energy and energy dissipation, using a jinite diyerence formulation. A boundary-jitted curvilinear orthogonal grid obtained from a solution of the inverse Laplace equations is used to represent the curved combustor head accurately and reduce numerical diffusion errors due to better alignment of the flow streamlines with the grid lines. Comparison between predicted results and measurements indicates that variations in ( a ) the overall pressure recovery and ( b ) the loss coeflcient performance of the dump diffuser system, with changes in diffuser design features (for example innerfouter annulus mass flow split or dump gap), can be predicted to within 7 per cent of the inlet dynamic head without adopting a more refined turbulence closure. The method is therefore demonstrated to be a usejiil design tool for dump diyuser geometries.
NOTATION
Roman charactersA cross-section area AR area ratio c,, c , , c2constants in k--E turbulence model k 11, 1, and 1, ui uj U U1 and U 2 *, Y static pressure coefficient dump gap annulus height turbulence kinetic energy metric coefficients relating to curvilinear system of coordinates mass flowrate total pressure static pressure radius mass flow split between outer and inner annulus source term in the transformed conservation equation Reynolds stress tensor mean axial velocity mean velocities in curvilinear coordinate directions 1 and 2 Cartesian coordinates dk, c~ constants in k-E turbulence model dependent variable ( = U , V , P, k, E ) in transformed conservation equation 4