# Development of a blade to blade solver for axial turbomachinery

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2015
Bilgiç, Mustafa
In this thesis, a blade to blade solver for axial turbomachinery is developed. Actual blade to blade surface is three dimensional but it is reduced to two dimensions. This simplification is valid only for the turbomachinery having high solidity. Two different approaches are used for the solution of the two dimensional Euler equations through blade to blade streamsurface. The first one includes the solution of the steady form of the two dimensional Euler equations. The characteristics of the steady Euler equations depend on the local Mach number. Normally, the steady solver does not have capability of the solving transonic flows but implementation of the artificial compressibility to the solver provides the capability of the solving transonic flow. The flow equations are discretized on the intrinsic streamline grid so that there is no mass flux across the streamline grid. Since the grid is an actual streamline, the grid nodal displacement becomes an additional unknown to the thermodynamic variables. After discretization, Newton-Raphson linearization is applied to momentum equations which reduces the number of unknowns to two. Since the characteristic of the equation is elliptic, physical boundary conditions are applied to the inlet and outlet of the domain. The nodal displacement at the wall is set to zero as the wall boundary condition. At the stagnation streamlines, periodicity is given as the pressure equivalence, that is, the pressure values on the upper and lower stagnation streamlines are forced to be identical. The resulting linear system is solved with modified tridiagonal matrix algorithm. The second method includes the solution of the unsteady from of the governing Euler equations. The characteristic of the flow equation for all speed regimes is hyperbolic in time so transonic flow is covered without any additional procedure. The flow equations are discretized on a fixed structured polyhedral grid. The fluxes through the faces of the computational cells are calculated using flux difference splitting schemes. The right and left state of the cell faces, which are used in the flux calculation, are calculated using MUSCL (Monotonic Upstream-Centered Scheme for Conservation Laws) approach. Modified Van Albada limiter function is used to prevent the oscillations at the shocks for second order calculations. Characteristic inlet and outlet boundary conditions are applied at the inlet and outlet of the domain. The slip conditions are applied on the wall and ghost cell concept is used for the calculation of the fluxes at the periodic boundaries. The conservative variables at the new time level is evaluated using multistage Runge-Kutta time integration scheme. The same source terms for rotor case are implemented to both solvers. Both time marching solver and Newton solver are validated comparing with the analytical and/or experimental test case. The subsonic and transonic flow over the bump, flow inside the converging diverging nozzle, flow through turbine and compressor cascades and flow through R030 rotor blade are the test cases for the validation of the codes.
Citation Formats
M. Bilgiç, “Development of a blade to blade solver for axial turbomachinery,” M.S. - Master of Science, Middle East Technical University, 2015. 