Numerical simulations of three‐dimensional transitional compressible flows in turbomachinery cascades

P. De Palma (Dipartimento di Ingegneria Meccanica e Gestionale (DIMeG), Centro di Eccellenza in Meccanica Computazionale (CEMeC), Politecnico di Bari, Bari, Italy)

International Journal of Numerical Methods for Heat & Fluid Flow

ISSN: 0961-5539

Publication date: 1 June 2006



This paper aims to provide a validation of a state‐of‐the‐art methodology for computing three‐dimensional transitional flows in turbomachinery.


The Reynolds‐averaged Navier‐Stokes equations for compressible flows are solved. Turbulence is modeled using an explicit algebraic stress model and kω turbulence closure. A numerical method has been developed, based on a cell‐centered finite volume approach with Roe's approximate Riemann solver and formally second‐order‐accurate MUSCL extrapolation. The method is validated versus two severe test cases, namely, the subsonic flow through a turbine cascade with separated‐flow transition; and the transonic flow through a compressor cascade with transitional boundary layers, shock‐induced separation and corner stall. For the first test case, the transition model of Mayle for separated flow has been employed, whereas, for the second one, the transition has been modeled employing the Abu‐Ghannam and Shaw correlation.


The comparison of numerical results with the experimental data available in the literature shows that, for such complex flow configurations, an improved numerical solution could be achieved by employing transition models. Unfortunately, the available models are case‐dependent, each of them being suitable for specific applications.


A state‐of‐the‐art numerical methodology has been developed and applied to compute very complex flows in turbomachinery. Through an original analysis of the results, the merits and limits of the considered approach have been assessed. The paper points up the fundamental role of transition modeling for turbomachinery flow simulations.



De Palma, P. (2006), "Numerical simulations of three‐dimensional transitional compressible flows in turbomachinery cascades", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 16 No. 4, pp. 509-529.

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