Research Papers

Fast Conjugate Heat Transfer Simulation of Long Transient Flexible Operations Using Adaptive Time Stepping

[+] Author and Article Information
R. Maffulli

Department of Engineering Science,
University of Oxford,
Oxford OX1 3PJ, UK
e-mail: roberto.maffulli@eng.ox.ac.uk

L. He

Department of Engineering Science,
University of Oxford,
Oxford OX1 3PJ, UK

P. Stein

GE Power,
Baden 5400, Switzerland

G. Marinescu

GE Power,
Baden 5400, Switzerland

1Corresponding author.

2Present address: Faculty of Mechanical Engineering, HTWG Konstanz, Alfred-Wachtel-Strasse 8, Konstanz 78315, Germany.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received July 10, 2018; final manuscript received July 25, 2018; published online August 28, 2018. Editor: Kenneth Hall.

J. Turbomach 140(9), 091005 (Aug 28, 2018) (10 pages) Paper No: TURBO-18-1151; doi: 10.1115/1.4040997 History: Received July 10, 2018; Revised July 25, 2018

The emerging renewable energy market calls for more advanced prediction tools for turbine transient operations in fast startup/shutdown cycles. Reliable numerical analysis of such transient cycles is complicated by the disparity in time scales of the thermal responses in fluid and solid domains. Obtaining fully coupled time-accurate unsteady conjugate heat transfer (CHT) results under these conditions would require to march in both domains using the time-step dictated by the fluid domain: typically, several orders of magnitude smaller than the one required by the solid. This requirement has strong impact on the computational cost of the simulation as well as being potentially detrimental to the accuracy of the solution due to accumulation of round-off errors in the solid. A novel loosely coupled CHT methodology has been recently proposed, and successfully applied to both natural and forced convection cases that remove these requirements through a source-term based modeling (STM) approach of the physical time derivative terms in the relevant equations. The method has been shown to be numerically stable for very large time steps with adequate accuracy. The present effort is aimed at further exploiting the potential of the methodology through a new adaptive time stepping approach. The proposed method allows for automatic time-step adjustment based on estimating the magnitude of the truncation error of the time discretization. The developed automatic time stepping strategy is applied to natural convection cases under long (2000 s) transients: relevant to the prediction of turbine thermal loads during fast startups/shutdowns. The results of the method are compared with fully coupled unsteady simulations showing comparable accuracy with a significant reduction of the computational costs.

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Fig. 1

Workflow of loosely coupled source-term based solver

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Fig. 2

Schematic representation of the geometry used for validation case with the used boundary conditions

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Fig. 3

Computational grid used for the validation case of Fig. 2

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Fig. 4

Grid sensitivity study. Temperature contours after 600 s using 30k (above) and 60k (below) nodes.

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Fig. 5

Temperature distribution (t = 600 s) along the central vertical section of the domain in Fig. 2

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Fig. 12

Evolution of time-step during the 2D calculations

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Fig. 7

Time discretization with variable time-step

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Fig. 13

Wall temperature distribution at different times for the laminar test case. Direct unsteady versus STM with adaptive time stepping.

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Fig. 8

Computational domain for the 2D test case. In Gray, the solid domain.

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Fig. 6

Modified workflow for adaptive time-stepping

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Fig. 9

Mesh dependency study for the 2D test case

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Fig. 10

Wall temperature distribution at different times. Direct unsteady versus STM with adaptive time stepping.

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Fig. 11

Temperature field at t = 1959.4 s. Direct unsteady versus STM with adaptive time stepping.

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Fig. 15

Computational domain for the 3D cylindrical cavity

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Fig. 16

Temperature field at initial conditions for the three analyzed grids

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Fig. 17

Temperature field cuts for t 2400.0 s. Source-term modeling versus direct unsteady.

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Fig. 14:

Temperature field at t = 2000s for the laminar case. Direct unsteady versus STM with adaptive time stepping.



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