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Research Papers

Space–Time Gradient Method for Unsteady Bladerow Interaction—Part II: Further Validation, Clocking, and Multidisturbance Effect

[+] Author and Article Information
L. He

Fellow ASME
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

P. Adami

ET-Design System Engineering – CFD Methods,
Rolls-Royce Deutschland,
Blankenfelde-Mahlow 15827, Germany
e-mail: Paolo.Adami@rolls-royce.com

L. Capone

CFD Methods,
Rolls-Royce plc,
Derby DE24 8BJ, UK
e-mail: Luigi.Capone@rolls-royce.com

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received July 4, 2015; final manuscript received August 13, 2015; published online September 23, 2015. Editor: Kenneth C. Hall.

J. Turbomach 137(12), 121004 (Sep 23, 2015) (12 pages) Paper No: TURBO-15-1134; doi: 10.1115/1.4031464 History: Received July 04, 2015; Revised August 13, 2015

For efficient and accurate unsteady flow analysis of blade row interactions, a space–time gradient (STG) method has been proposed. The development is aimed at maintaining as many modeling fidelities (the interface treatment in particular) of a direct unsteady time-domain method as possible while still having a significant speed-up. The basic modeling considerations, main method ingredients and some preliminary verification have been presented in Part I of the paper. Here in Part II, further case studies are presented to examine the capability and applicability of the method. Having tested a turbine stage in Part I, here we first consider the applicability and robustness of the method for a three-dimensional (3D) transonic compressor stage under a highly loaded condition with separating boundary layers. The results of the STG solution compare well with the direct unsteady solution while showing a speed up of 25 times. The method is also used to analyze rotor–rotor/stator–stator interferences in a two-stage turbine configuration. Remarkably, for stator–stator and rotor–rotor clocking analyses, the STG method demonstrates a significant further speed-up. Also interestingly, the two-stage case studies suggest clearly measurable clocking dependence of blade surface time-mean temperatures for both stator–stator clocking and rotor–rotor clocking, though only small efficiency variations are shown. Also validated and illustrated is the capacity of the STG method to efficiently evaluate unsteady blade forcing due to the rotor–rotor clocking. Considerable efforts are directed to extending the method to more complex situations with multiple disturbances. Several techniques are adopted to decouple the disturbances in the temporal terms. The developed capabilities have been examined for turbine stage configurations with inlet temperature distortions (hot streaks), and for three blade-row turbine configurations with nonequal blade counts. The results compare well with the corresponding direct unsteady solutions.

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References

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Figures

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Fig. 1

Instantaneous entropy contours at midspan: (a) mixing plane, (b) frozen rotor, (c) direct unsteady, and (d) present (STG)

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Fig. 2

Axial velocity contours at 90% span: (a) direct unsteady, and (b) present (STG)

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Fig. 3

Instantaneous entropy contours: (a) direct unsteady, and (b) present (STG)

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Fig. 4

Time-averaged entropy contours (for 2 statorstator clocking positions): (a) reference clocking and (b) second stator clocked by 50% pitch

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Fig. 5

Exit time-averaged total temperature profiles for different statorstator clocking positions

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Fig. 6

Time-averaged blade surface temperatures for different statorstator clocking positions (second stator)

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Fig. 7

Time-averaged blade surface temperatures for different statorstator clocking positions (second rotor)

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Fig. 8

Total-to-total efficiencies for different statorstator clocking positions

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Fig. 9

Time-averaged temperatures on second rotor surface for different rotorrotor clocking positions

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Fig. 10

Time-averaged exit total temperature profiles for different rotorrotor clocking positions

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Fig. 11

Total-to-total efficiencies for different rotorrotor clocking positions

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Fig. 12

Time traces of unsteady tangential forces for various rotorrotor clocking (comparisons between direct and STG solutions are made for two clocking positions)

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Fig. 13

Time traces of unsteady axial forces for various rotorrotor clocking (comparisons between direct and STG solutions are made for two clocking positions)

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Fig. 14

Instantaneous entropy contours for hot streaks (hot streak/NGV counts: 1/2): (a) mixing plane, (b) frozen rotor, (c) direct unsteady, and (d) present (STG)

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Fig. 15

Circumferential distributions of time-averaged total temperatures at exit (hot streak/NGV counts: 1/2)

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Fig. 16

Circumferential distributions of instantaneous total temperatures at exit (hot streak/NGV counts: 1/8)

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Fig. 17

Instantaneous entropy contours for long scale hot streak (hot streak/NGV counts: 1/8): (a) mixing plane, (b) frozen rotor, (c) direct unsteady, and (d) present (STG)

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Fig. 18

Instantaneous temperatures at 90% span

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Fig. 19

Time-averaged entropy contours at exit

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Fig. 20

Comparison of instantaneous entropy contours (statorrotorstator counts: 326139): (a) mixing plane, (b) frozen rotor, (c) direct unsteady, and (d) present (STG)

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Fig. 21

Circumferential distributions of time-averaged total temperatures (statorrotorstator counts: 326139)

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Fig. 22

Time-averaged entropy contours (statorrotorstator counts: 326139): (a) mixing plane and (b) present (STG)

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Fig. 23

Time-averaged surface temperatures (first stator) (statorrotorstator counts: 326139)

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Fig. 24

Time-averaged surface temperatures (rotor) (statorrotorstator counts: 326139)

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Fig. 25

Time-averaged surface temperatures (second stator) (statorrotorstator counts: 326139)

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