A computational method for the numerical integration of the Favre-Reynolds averaged, three-dimensional compressible Navier-Stokes equations in axial turbomachinery, using the Launder-Sharma near-wall k-epsilon turbulence closure, is developed, The mean how and turbulence transport equations are discretized using a finite volume method based on MUSCL Van Leer flux-vector splitting with Van Albada limiters and are integrated in time using a fully coupled, approximately factored, implicit backward Euler method. The resulting scheme is robust and was found stable for local time steps of Courant-Friedrichs-Lewy number (CFL)= 20. The computational domain is discretized using a basic H-O-H grid. The tip-clearance gap is discretized using a fine O-type grid, The radial distribution of nodes within the tip clearance gap is independent of the blade-row O grid, and a buffer overlap grid is used to convey information. Boundary conditions at periodicity boundaries and at domain interfaces are treated using five phantom nodes, This procedure ensures stability at high CFL. Results are presented for the NASA 37 rotor, at an operating point near surge. Computations are compared with measurements both for blade-to-blade Mach number contours and pitchwise distributions and for radial distributions downstream of the blades. Results are obtained using three grids of 10(6), 2 x 10(6), and 3 x 10(6) points, with 21, 31, and 41 radial stations within the tip-clearance gap, respectively, demonstrating that results are grid independent. Comparison with measurements is satisfactory, with the exception of pressure ratio overestimation due to unsatisfactory prediction of flow separation by the turbulence model.
