Near-Wall k-e Computation of Transonic Turbomachinery Flows with Tip Clearance

Abstract

Acomputational methodforthenumericalintegration oftheFavre ‐Reynolds averaged, three-dimensionalcompressible Navier ‐Stokes equations in axial turbomachinery, using the Launder ‐Sharma near-wall k‐ turbulence closure, is developed. The mean e ow and turbulence transport equations are discretized using a e nite volume method based on MUSCL Van Leere ux-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 e ne O-type grid. The radial distribution ofnodeswithin thetip-clearancegap is independent of theblade-rowO grid, and a bufferoverlap grid is used to convey information. Boundary conditions at periodicity boundaries and at domain interfaces are treated using e ve 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 ££ 10 6 , and 3 ££ 10 6 points, with 21, 31, and 41 radial stations within the tip-clearancegap,respectively,demonstratingthatresultsaregridindependent.Comparisonwithmeasurementsis satisfactory, with theexception of pressureratio overestimation due to unsatisfactory prediction ofe ow separation by the turbulence model.