This paper studies different acceleration techniques for unsteady flow calculations. The results are compared with a non-accelerated, fully-explicit solution in terms of time-averaged pressure distributions, the unsteady pressure and entropy in the frequency domain and the skin friction factor. The numerical method solves the unsteady three-dimensional Navier-Stokes equations via an explicit time-stepping procedure. The flow in the first stage of a modern industrial gas turbine is chosen as a test case. After a description of the numerical method used for the simulation, the test case is introduced. The comparison of the different numerical algorithms for explicit schemes is intended to ease the decision about which acceleration technique to use for calculations as far as accuracy and computational time are concerned. The convergence acceleration methods under consideration are, respectively, explicit time-stepping with implicit residual averaging, explicit time-consistent multigrid and implicit dual time stepping. The investigation and comparison of the different acceleration techniques are applicable to all explicit unsteady flow solvers.
As another point of interest, the influence of the stage blade count ratio on the flow field is investigated. For this purpose, a simulation with a stage pitch ratio of unity is compared with a calculation using the real ratio of 78:80, which requires a more sophisticated method for periodic boundary condition treatment. This paper should help to decide whether it is vital from the turbine designer’s point of view to model the real pitch ratio in unsteady flow simulations in turbine stages.
Semi-analytic numerical method for unsteady flow in leaky confined aquifers
