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Research Papers

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

[+] Author and Article Information
J.-F. Simon

Techspace Aero, Safran Group, Route de Liers 121, B-4041 Milmort, Belgiumjsimon@techspace-aero.be

J. P. Thomas

Turbomachinery Group, University of Liège, Chemin des Chevreuils 1, B-4000 Liège, Belgiumjp.thomas@ulg.ac.be

O. Léonard

Turbomachinery Group, University of Liège, Chemin des Chevreuils 1, B-4000 Liège, Belgiumo.leonard@ulg.ac.be

J. Turbomach 131(3), 031019 (Apr 20, 2009) (12 pages) doi:10.1115/1.2992514 History: Received June 30, 2008; Revised July 30, 2008; Published April 20, 2009

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 3D time-averaged 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 3D average-passage flow. The resulting set of equations is similar to the 2D 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 3D 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 3D 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.

Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Flat plate definition and mesh

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Figure 3

Mass-averaged versus density-averaged entropy

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Figure 4

Wake mixing problem

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Figure 5

Contributions to entropy production in the wake

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Figure 6

Entropy evolution in the wake

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Figure 2

Impact of the additional terms on entropy along the flat plate

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Figure 8

Absolute flow angle from 3D averaged solution (top) and throughflow solution (bottom)

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Figure 9

Comparison between the throughflow solution (plain lines) and the 3D solution circumferentially averaged (symbols) at three locations inside the rotor domain

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Figure 10

Comparison between the throughflow solution (plain lines) and the 3D solution circumferentially averaged (symbols) at three locations inside the stator domain

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Figure 11

Impact of the blade forces and of the circumferential stresses on the entropy field

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Figure 12

Impact of the blade forces and of the circumferential stresses on the radial distribution of entropy

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Figure 13

Contributions to the axial momentum balance

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Figure 14

Classical versus high-order throughflows: axial velocity

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Figure 15

Classical versus high-order throughflows: radial velocity

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Figure 16

Classical versus high-order throughflows: flow angle

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Figure 17

Classical versus high-order throughflows: total temperature

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Figure 20

Axial velocity from 3D averaged solution (top) and throughflow solution (bottom)

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Figure 21

Comparison between the throughflow solution (plain lines) and the averaged unsteady 3D solution (symbols) at three locations inside the stator domain

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Figure 22

Comparison of the throughflow simulations with and without deterministic stresses (rotor outlet)

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Figure 23

Comparison of the throughflow simulations with and without deterministic stresses (rotor outlet)

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Figure 18

Prerotation in the leading edge region of the rotor

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Figure 19

Time-averaged radial velocity downstream of the stator

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Figure 7

Meridional mesh of the CME2 compressor

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