Investigating Circumferential Non-Uniformities in Throughflow Calculations Using an Harmonic Reconstruction

Thomas, Jean-Philippe; ́onard, O. Le

doi:10.1115/gt2008-50328

Cited by 2 publications

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References 17 publications

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“…A project studying the feasibility of a circumferential closure by a method inspired from the non linear harmonic method is currently undertaken by Thomas [23]. Some modifications of the original method will be necessary concerning the function chosen to represent the fluctuations.…”

Section: Discussionmentioning

confidence: 99%

On the Role of the Deterministic and Circumferential Stresses in Throughflow Calculations

Simon

Thomas

Léonard

2009

Journal of Turbomachinery

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This paper presents a throughflow analysis tool developed in the context of the average-passage flow model elaborated by Adamczyk. The Adamczyk's flow model describes the 3-D timeaveraged flow field within a blade row passage. The set of equations that governs this flow field is obtained by performing a Reynolds averaging, a time averaging and a passage-to-passage averaging on the Navier-Stokes equations. The throughflow level of approximation is obtained by performing an additional circumferential averaging on the 3-D average-passage flow.The resulting set of equations is similar to the 2-D axisymmetric Navier-Stokes equations but additional terms resulting from the averages show up : blade forces, blade blockage factor, Reynolds stresses, deterministic stresses, passage-to-passage stresses and circumferential stresses. This set of equations represents the ultimate throughflow model provided that all stresses and blade forces can be modeled. The relative importance of these additional terms is studied in the present contribution.The stresses and the blade forces are determined from 3-D steady and unsteady databases (a low speed compressor stage and a transonic turbine stage) and incorporated in a throughflow model based on the axisymmetric Navier-Stokes equations. A good agreement between the throughflow solution and the averaged 3-D results is obtained. These results are also compared to those obtained with a more "classical" throughflow approach based on a Navier-Stokes formulation for the endwall losses, correlations for profile losses and a simple radial mixing model assuming turbulent diffusion. INTRODUCTIONThe throughflow level of approximation still remains an important tool for designing turbomachines [10] even though 3-D calculations are used more and more early in the design process. Throughflow codes are mainly used at the preliminary design stage for specifying the target aerodynamic performances to be achieved by the blading. They can be used either in the design mode, where the angular momentum and/or the total conditions are prescribed and the flow angles are sought, either in the analysis mode, where a known machine geometry is analyzed for its performance. The throughflow models are also used to exploit experimental results or to couple single blade row calculations in order to compute the flow field inside a multistage machine [4].Unfortunately, these models heavily rely on empirical inputs, such as profile losses correlations or end-wall loss models. They can accurately predict the flow field inside a turbomachine provided that the design parameters are not too far from those of the reference machines that were used to calibrate the throughflow model. This approach has shown to be efficient but lacks of generality.The most widespread throughflow method is certainly the streamline curvature method (SLC). In 1980, Spuur has proposed another approach based on the Euler equations. This approach has only started to retain attention in the 1990. Recent works using this approach can be foun...

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Section: Discussionmentioning

confidence: 99%

On the Role of the Deterministic and Circumferential Stresses in Throughflow Calculations

Simon

Thomas

Léonard

2009

Journal of Turbomachinery

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Toward a High Order Throughflow––Investigation of the Nonlinear Harmonic Method Coupled With an Immersed Boundary Method for the Modeling of the Circumferential Stresses

Thomas

Léonard

2011

Journal of Turbomachinery

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Capturing a level of modeling of the flow inside a multistage turbomachine, such as unsteadiness for example, can be done at different levels of detail, either by capturing all deterministic features of the flow with a pure unsteady method or by settling for an approximated solution at a lower computational cost. The harmonic methods stand in this second category. Among them, the “nonlinear harmonic method” (NLHM) from He and Ning [1998, “Efficient Approach for Analysis of Unsteady Viscous Flows in Turbomachines,” AIAA J., 36, pp. 2005–2012] revealed the most efficient. This method consists of solving the fully nonlinear 3D steady problem and a linearized perturbation system in the frequency domain. As it has been shown by the authors that the circumferential variations exhibit a harmonic behavior, it is proposed here to adapt the NLHM to the throughflow model, where the main nonlinear system would be the common throughflow equations and the auxiliary system would give access to the circumferential stresses. As the numerical local explicit impermeability conditions are unsupported by Fourier series, the adaptation of this technique to the throughflow model relies on a reformulation of the blade effect by a smooth force field as in the “immersed boundary method” from Peskin [2002, “The Immersed Boundary Method,” Acta Numerica, 11, pp. 1–39]. A simple example of an inviscid flow around a cylinder will illustrate the preceding developments, bringing back the mean effect of the circumferential nonuniformities into the meridional flow.

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Investigating Circumferential Non-Uniformities in Throughflow Calculations Using an Harmonic Reconstruction

Cited by 2 publications

References 17 publications

On the Role of the Deterministic and Circumferential Stresses in Throughflow Calculations

On the Role of the Deterministic and Circumferential Stresses in Throughflow Calculations

Toward a High Order Throughflow––Investigation of the Nonlinear Harmonic Method Coupled With an Immersed Boundary Method for the Modeling of the Circumferential Stresses

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