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Research Papers: Gas Turbines: Structures and Dynamics

Differential Equation-Based Specification of Turbulence Integral Length Scales for Cavity Flows

[+] Author and Article Information
Richard J. Jefferson-Loveday

Gas Turbine and Transmissions Research Centre,
Faculty of Engineering,
The University of Nottingham,
Nottingham NG7 2RD, UK
e-mail: Richard.Jefferson-Loveday@nottingham.ac.uk

Contributed by the Structures and Dynamics Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received October 11, 2016; final manuscript received November 23, 2016; published online February 7, 2017. Editor: David Wisler.

J. Eng. Gas Turbines Power 139(6), 062508 (Feb 07, 2017) (12 pages) Paper No: GTP-16-1497; doi: 10.1115/1.4035602 History: Received October 11, 2016; Revised November 23, 2016

A new modeling approach has been developed that explicitly accounts for expected turbulent eddy length scales in cavity zones. It uses a hybrid approach with Poisson and Hamilton–Jacobi differential equations. These are used to set turbulent length scales to sensible expected values. For complex rim-seal and shroud cavity designs, the method sets an expected length scale based on local cavity width which accurately accounts for the large-scale wakelike flow structures that have been observed in these zones. The method is used to generate length scale fields for three complex rim-seal geometries. Good convergence properties are found, and a smooth transition of length scale between zones is observed. The approach is integrated with the popular Menter shear stress transport (SST) Reynolds-averaged Navier–Stokes (RANS) turbulence model and reduces to the standard Menter model in the mainstream flow. For validation of the model, a transonic deep cavity simulation is performed. Overall, the Poisson–Hamilton–Jacobi model shows significant quantitative and qualitative improvement over the standard Menter and k–ε two-equation turbulence models. In some instances, it is comparable or more accurate than high-fidelity large eddy simulation (LES). In its current development, the approach has been extended through the use of an initial stage of length scale estimation using a Poisson equation. This essentially reduces the need for user objectivity. A key aspect of the approach is that the length scale is automatically set by the model. Notably, the current method is readily implementable in an unstructured, parallel processing computational framework.

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Figures

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Fig. 1

Process chain for the Poisson–Hamilton–Jacobi length scale method

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Fig. 2

Computational meshes for (a) a simple axial seal, (b) a seal with a single radial clearance, and (c) a seal with two radial clearances

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Fig. 3

Contours of standard wall distance y (m) (left) and contours of Poisson–Hamilton–Jacobi length scale L̃PHJ (m) (right) for (a) a simple axial seal, (b) a seal with a single radial clearance, and (c) a seal with two radial clearances

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Fig. 4

Schematic of the cavity simulation domain

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Fig. 5

Mesh sensitivity for (a) horizontal velocity profile, (b) vertical velocity profile, and (c) cross Reynolds stress at the cavity midpoint (x/L = 0.5)

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Fig. 6

Experimental vorticity contour plot [23] with the standard Menter, k–ε, Poisson–Hamilton–Jacobi, and LES [25] integral length scales superimposed. The centers C1 and C2 of the structures are indicated.

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Fig. 7

Cross Reynolds stress sensitivity to inlet turbulent intensity for the standard Menter model Ti = 1.5% and Ti = 5.0%; Poisson–Hamilton–Jacobi Menter model Ti = 1.5% and Ti = 5.0%, at location x/D = 0.8

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Fig. 8

Comparison of horizontal velocity profiles, experimental measurements: ○, standard Menter model: solid curve; k–ε model: dotted curve; Poisson–Hamilton–Jacobi Menter model: dashed curve; and LES [25]: dashed-dotted curve

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Fig. 9

Flow streamline plots at cavity leading edge: (a) standard Menter model, (b) Poisson–Hamilton–Jacobi Menter model, and (c) k–ϵ model

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Fig. 10

Comparison of vertical velocity profiles, experimental measurements: ○, standard Menter model: solid curve; k–ε model: dotted curve; Poisson–Hamilton–Jacobi Menter model: dashed curve; and LES [25]: dashed-dotted curve

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Fig. 11

Comparison of horizontal Reynolds stress profiles, experimental measurements: ○, standard Menter model: solid curve; k–ε model: dotted curve; Poisson–Hamilton–Jacobi Menter model: dashed curve; and LES [25]: dashed-dotted curve

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Fig. 12

Comparison of vertical Reynolds stress profiles, experimental measurements: ○, standard Menter model: solid curve; k–ε model: dotted curve; Poisson–Hamilton–Jacobi Menter model: dashed curve; and LES [25]: dashed-dotted curve

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Fig. 13

Comparison of cross Reynolds stress profiles, experimental measurements: ○, standard Menter model: solid curve; k–ε model: dotted curve; Poisson–Hamilton–Jacobi Menter model: dashed curve; and LES [25]: dashed-dotted curve

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