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Research Papers: Gas Turbines: Turbomachinery

Assessment of Unsteadiness Modeling for Transient Natural Convection

[+] Author and Article Information
M. Fadl

Department of Engineering Science,
University of Oxford,
Oxford OX1 3PJ, UK
e-mail: m.s.fadl@lboro.ac.uk

L. He

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

P. Stein, G. Marinescu

GE Power,
Baden 5400, Switzerland

1Present address: CREST, Loughborough University, Loughborough, UK, LE11 3TU.

2Corresponding author.

Contributed by the Turbomachinery Committee of ASME for publication in the JOURNAL OF ENGINEERING FOR GAS TURBINES AND POWER. Manuscript received July 6, 2017; final manuscript received July 11, 2017; published online September 26, 2017. Editor: David Wisler.

J. Eng. Gas Turbines Power 140(1), 012605 (Sep 26, 2017) (10 pages) Paper No: GTP-17-1306; doi: 10.1115/1.4037721 History: Received July 06, 2017; Revised July 11, 2017

Turbine flexible operations with faster startups/shutdowns are required to accommodate emerging renewable power generations. A major challenge in transient thermal design and analysis is the time scale disparity. For natural cooling, the physical process is typically in hours, but on the other hand, the time-step sizes typically usable tend to be very small (subseconds) due to the numerical stability requirement for natural convection as often observed. An issue of interest is: What time-step sizes can and should be used in terms of stability as well as accuracy? In this work, the impact of flow temporal gradient and its modeling is examined in relation to numerical stability and modeling accuracy for transient natural convection. A source term-based dual-timing formulation is adopted, which is shown to be numerically stable for very large time-steps. Furthermore, a loosely coupled procedure is developed to combine this enhanced flow solver with a solid conduction solver for solving unsteady conjugate heat transfer (CHT) problems for transient natural convection. This allows very large computational time-steps to be used without any stability issues, and thus enables to assess the impact of using different time-step sizes entirely in terms of a temporal accuracy requirement. Computational case studies demonstrate that the present method can be run stably with a markedly shortened computational time compared to the baseline solver. The method is also shown to be more accurate than the commonly adopted quasi-steady flow model when unsteady effects are non-negligible.

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References

Figures

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Fig. 1

Computational domain and mesh (fluid-domain only)

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Fig. 2

Residual histories for different time-step sizes (direct unsteady solver of fluent)

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Fig. 3

Residual histories for different time-step sizes (present source term-based unsteady solver)

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Fig. 4

Comparisons of wall heat fluxes (in W/m2) along circumference (in deg) between the present method with large time-steps (Δt = 10 s, 40 s, 160 s) and the direct method of fluent with a stability restricted small time-step (Δt = 0.2 s)

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Fig. 5

Instantaneous temperature fields for the present solutions ((a) Δt = 10 s and (b) 160 s, respectively) and the direct baseline solutions (Δt = 0.2 s for both cases)

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Fig. 6

Instantaneous velocity fields for the present solutions ((a) Δt = 10 s and (b) 160 s, respectively) and the direct baseline solutions (Δt = 0.2 s for both cases)

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Fig. 7

Wall heat fluxes (W/m2) along circumference (boundary temperature gradient of 20 K/0.2 s)

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Fig. 8

Wall heat fluxes (W/m2) along circumference (boundary temperature gradient of 5 K/0.2 s)

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Fig. 9

Fluid and solid domains and mesh

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Fig. 10

Comparison of fluid–solid interface temperatures (K) between the present loosely coupled CHT (“present”) and the direct fully coupled CHT (“direct”) solutions

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Fig. 11

Heat fluxes (W/m2) on both sides of interface

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Fig. 12

Convergence histories of the baseline direct coupled CHT solutions for different time-steps

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Fig. 13

Convergence histories of the present loosely coupled CHT solutions for different time-steps

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Fig. 14

Interface temperatures (in K) at t = 700 s by the direct CHT method with a small-time-step (Δt = 0.2 s) and the present loosely coupled CHT method with different time-steps

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Fig. 15

Time evolution of interface temperature profiles (K) (direct CHT: Δt = 0.2 s; loosely coupled CHT: Δt = 10 s): (a) 200–500 s and (b) 2500–5000 s

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Fig. 16

Comparison of temperature contours in solid and fluid domains between the direct solution (Δt = 0.2 s) and the present solution (Δt = 10 s) at t = 500 s and t = 1000 s, respectively: (a) t = 500 s and (b) t = 5000

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Fig. 17

Effect of the time-step sizes on the predicted interface wall temperature (K) distributions (t = 3000 s)

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Fig. 18

Effect of the time-step sizes on the predicted interface wall temperature (K) distributions (t = 4000 s)

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Fig. 19

Three-dimensional computational configuration

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Fig. 20

Comparison of instantaneous heat flux contours at fluid–solid interface (at t = 200 s), between the direct solution (Δt = 0.2 s) and the present loosely coupled solution (Δt = 10 s): (a) direct CHT and (b) loosely coupled CHT

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Fig. 21

Comparison of instantaneous temperatures on a mid-domain cut plane (at t = 200 s) between the direct solution (Δt = 0.2 s) and the present loosely coupled solution (Δt = 10 s): (a) direct CHT and (b) loosely coupled CHT

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