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A Preconditioned solution scheme for the computation of compressible flow in turbomachinery at arbitrary mach numbers

Anker J. E., Mayer J. F., Stetter H.

TASK Quarterly : scientific bulletin of Academic Computer Centre in Gdansk

2002

Vol. 6, No 1

143-176

A preconditioned solution scheme for the computation of compressible flow in turbomachinery at arbitrary Mach numbers is presented. The preconditioning technique used is applied to a state-of-the-art explicit, time-marching Navier-Stokes code which originally was developed for compressible, high-speed turbomachinery applications. It combines the ideas of low Mach number preconditioning and artificial compressibility method into a unified approach where principally fluids with arbitrary equations of state can be simulated. As shown by the test cases presented, it allows the code to simulate flows efficiently and accurately independent of the Mach number. A description of the Navier-Stokes equations for rotating coordinate systems, along with the solution scheme and the details of the preconditioning method is given. Since turbomachinery computations are often performed on truncated domains, the solution scheme should be used in conjunction with non-reflecting boundary conditions. A change in the time-dependency of the equations due to preconditioning necessitates a modification of the boundary conditions. Thus, a derivation of the appropriate boundary conditions for the presented preconditioned scheme was performed and the resultant equations are given in this paper. The effectiveness of the new boundary conditions is demonstrated by comparing them with both boundary conditions that use the standard one-dimensional characteristic approach and the original boundary conditions for the non-preconditioned case.

Unsteady blade loads caused by stator / rotor interaction in an axial turbine stage

Jung A.R., Mayer J.F., Stetter H.

Transactions of the Institute of Fluid-Flow Machinery

1998

nr 104

45-58

The results of a simulation of the three-dimansional unsteady viscous flow in a highly loaded last stage of an axial flow low pressure turbine are presented. The focus in the flow analysis is on the temporal fluctuations of the rotor lift and the resulting unsteady forces and torques acting on the rotor blading. In the lower 50% of the rotor span the stator exit flow is transonic and strong interaction effects between the stator and the rotor potentials can be observed. The resulting temporal fluctuations of the static pressure on the rotor blades amount to maximum of more than 40% of the time-mean value. In the region between 20 and 40 % of the span where the unsteady interaction effects are maximal, complex shock motion patterns are found. The unsteady static pressure is integrated along the chord and over the surface of the rotor blade to yield the unsteady distributed loads, forces, and torques, respectively. These quantities are analysed both in time and the frequency domain. It is found that the first harmonic of the blade passing frequency of the driving torque amounts to 6,3% of the time-mean value. The second harmonic still amounts to 3,4%.

Przedstawiono wyniki symulacji nieustalonego trójwymiarowego przepływu lepkiego w wysoce obciążonym niskociśnieniowym stopniu turbiny osiowej. W analizie przepływu uwagę skupiono na fluktuacjach chwilowych siły nośnej wirnika oraz wynikających stąd nieustalonych siłach i momentach działających na ułopatkowienie wirnika.