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Research Papers

Two-Scale Methodology for URANS/Large Eddy Simulation Solutions of Unsteady Turbomachinery Flows

L. He and J. Yi
[+] Author and Article Information
L. He

Department of Engineering Science,
University of Oxford,
Oxford OX2 0ES, UK
e-mail: Li.He@eng.ox.ac.uk

J. Yi

Department of Engineering Science,
University of Oxford,
Oxford OX2 0ES, UK
e-mail: Junsok.Yi@eng.ox.ac.uk

1Present address: Rolls-Royce Plc., P.O. Box 31, Derby DE24 8BJ, UK.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received January 3, 2017; final manuscript received April 28, 2017; published online June 13, 2017. Assoc. Editor: Rakesh Srivastava.

J. Turbomach 139(10), 101012 (Jun 13, 2017) (14 pages) Paper No: TURBO-17-1001; doi: 10.1115/1.4036765 History: Received January 03, 2017; Revised April 28, 2017

A general issue in turbomachinery flow computations is how to capture and resolve two kinds of unsteadiness efficiently and accurately: (a) deterministic disturbances with temporal and spatial periodicities linked to blade count and rotational speed and (b) nondeterministic disturbances including turbulence and self-excited coherent patterns (e.g., vortex shedding, shear layer instabilities, etc.) with temporal and spatial wave lengths unrelated to blade count and rotational speed. In particular, the high cost of large eddy simulations (LES) is further compounded by the need to capture the deterministic unsteadiness of bladerow interactions in computational domains with large number of blade passages. This work addresses this challenge by developing a multiscale solution approach. The framework is based on an ensemble-averaging to split deterministic and nondeterministic disturbances. The two types of disturbances can be solved in suitably selected computational domains and solvers, respectively. The local fine mesh is used for nondeterministic turbulence eddies and vortex shedding, while the global coarse mesh is for deterministic unsteadiness. A key enabler is that the unsteady stress terms (UST) of the nondeterministic disturbances are obtained only in a small set of blade passages and propagated to the whole domain with many more passages by a block spectral mapping. This distinctive multiscale treatment makes it possible to achieve a high-resolution unsteady Reynolds-averaged Navier–Stokes (URANS)/LES solution in a multipassage/whole annulus domain very efficiently. The method description will be followed by test cases demonstrating the validity and potential of the proposed methodology.

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References

Figures

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Fig. 1

Decomposition of unsteady flow disturbance

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Fig. 2

Clocking dependence of periodic flow [32]

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Fig. 3

Spectra of unsteady flow disturbances: (a) full spectrum (composite disturbances), (b) deterministic disturbances, and (c) nondeterministic disturbances

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Fig. 4

Dual computational meshes: (a) base mesh (for deterministic disturbances), (b) embedded mesh (nondeterministic disturbances), and (c) composite mesh

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Fig. 5

Base and embedded meshes in near-wall and wake regions

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Fig. 6

3 × 3 fine mesh cells embedded in a coarse base mesh cell (bold dash line)

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Fig. 7

Coupled two-scale solution process

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Fig. 8

Base domain and embedded domain for cylinder

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Fig. 9

Comparison of Mach number contours: (a) steady solution (no stress term), (b) instantaneous unsteady solution, (c) base mesh solution of two-scale method (with stress term), and (d) time-averaged solution of direct unsteady method

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Fig. 10

Contrasting convergence histories, steady solution (without stress term) versus two-scale solution (with stress term)

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Fig. 11

Trailing-edge vortex shedding of a turbine blade (in terms of Q criterion): (a) direct solution and (b) embedded solution

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Fig. 12

Time-averaged static pressure contours (lines indicate the embedded region): (a) steady solution, (b) direct URANS, (c) two-scale URANS, (d) direct LES, and (e) two-scale LES

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Fig. 13

Two-passage domain for flow with inlet distortion

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Fig. 14

Instantaneous entropy contours of the direct unsteady solution: (a) overall domain and (b) close-up for trailing-edge vortex shedding

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Fig. 15

Comparison of unsteady entropy contours (at a given phase) among three solutions: (a) STG solution without unsteady stresses, (b) ensemble-averaged direct unsteady solution, and (c) two-scale solution with unsteady stresses

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Fig. 16

Embedded domains for baseline solution (a) and block-spectral mapping ((b) and (c)): (a) all passages (baseline), (b) two harmonics, and (c) one harmonic

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Fig. 17

Comparison of entropy contours (ensemble-averaged): (a) STG (without stress), (b) all passages embedded (baseline), (c) two harmonics, and (d) one harmonic

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Fig. 18

Comparison of local static pressures (ensemble-averaged): (a) STG (without stresses), (b) all passages embedded (baseline), (c) two harmonics, and (d) one harmonic

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Fig. 19

Comparison of surface pressures around blade trailing edge

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Fig. 20

Instantaneous vorticity contours: (a) laminar solution on coarse mesh, (b) direct unsteady solution using embedded fine mesh, and (c) two-scale solution on embedded fine mesh

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Fig. 21

Mach number contours of time-averaged flow: (a) coarse mesh laminar solution, (b) direct unsteady solution using embedded fine mesh, and (c) two-scale solution with unsteady stresses

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Fig. 22

Calculated surface pressures compared to experiment [45] for compressor cascade

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