Research Papers: Multiphase Flows

Direct Numerical Simulation of Pebble Bed Flows: Database Development and Investigation of Low-Frequency Temporal Instabilities

[+] Author and Article Information
Lambert H. Fick

Department of Nuclear Engineering,
Texas A&M University,
College Station, TX 77845
e-mail: Lambert.Fick@tamu.edu

Elia Merzari

Nuclear Engineering Division,
Argonne National Laboratory,
Lemont, IL 60439

Yassin A. Hassan

Department of Nuclear Engineering,
Texas A&M University,
College Station, TX 77845

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received June 1, 2016; final manuscript received November 14, 2016; published online February 20, 2017. Assoc. Editor: Francine Battaglia.The United States Government retains, and by accepting the article for publication, the publisher acknowledges that the United States Government retains, a nonexclusive, paid-up, irrevocable, worldwide license to publish or reproduce the published form of this work, or allow others to do so, for United States Government purposes.

J. Fluids Eng 139(5), 051301 (Feb 20, 2017) (12 pages) Paper No: FE-16-1337; doi: 10.1115/1.4035300 History: Received June 01, 2016; Revised November 14, 2016

Computational analyses of fluid flow through packed pebble bed domains using the Reynolds-averaged Navier–Stokes (RANS) framework have had limited success in the past. Because of a lack of high-fidelity experimental or computational data, optimization of Reynolds-averaged closure models for these geometries has not been extensively developed. In the present study, direct numerical simulation (DNS) was employed to develop a high-fidelity database that can be used for optimizing Reynolds-averaged closure models for pebble bed flows. A face-centered cubic (FCC) domain with periodic boundaries was used. Flow was simulated at a Reynolds number of 9308 and cross-verified by using available quasi-DNS data. During the simulations, low-frequency instability modes were observed that affected the stationary solution. These instabilities were investigated by using the method of proper orthogonal decomposition, and a correlation was found between the time-dependent asymmetry of the averaged velocity profile data and the behavior of the highest-energy eigenmodes. Finally, the effects of the domain size and the method of averaging were investigated to determine how these parameters influenced the stationary solution. A violation of the ergodicity assumption was observed.

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Fig. 3

Section of the spectral-element mesh after subdiscretization, illustrating the area of minimum interpebble spacing

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Fig. 1

Computational domain comprising an extended, single-FCC unit cell geometry with a porosity of 0.42. (a) Volume rendering of the instantaneous velocity magnitude illustrating the fluid domain with sectioned cutaway of −1 ≤ y ≤ 0 and 0 ≤ z ≤ 1. Flow is in the positive z-direction. (b) Position of the [x, 0, z] and [0, y, z] lateral planes in the domain.

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Fig. 5

Normalized power spectrum for the velocity time history at the C (top) and TRX (bottom) probe point

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Fig. 4

Planar view of the Pyy component of the TKE production tensor for the [0, y, z] plane

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Fig. 10

Line profiles of the z-velocity component plotted for different lengths of time-integration: (a) velocity component 〈Uz〉, for line CX1 and (b) velocity component 〈Uz〉, for line CY1

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Fig. 2

Interpolation line and point probe locations and naming convention

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Fig. 8

Profiles of the z-component of the velocity for the 7th-, 9th-, and 13th-degree cases: (a) TLX and TRX interpolation lines and (b) BLX and BRX interpolation lines

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Fig. 6

Temporal autocorrelation function for the fluctuating velocity time history at the TRX probe point

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Fig. 7

Velocity (top) and covariance (bottom) profiles extracted at times f(t) = 294 FTT and f(t + τ) = 300 FTT for the 9th-degree data set

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Fig. 9

Profiles of the z-component of the covariance tensor for the 7th-, 9th-, and 13th-degree cases: (a) TLX and TRX interpolation lines and (b) BLX and BRX interpolation lines

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Fig. 11

Line profiles of the in-plane covariance components plotted for different lengths of time-integration: (a) covariance component 〈uxuz〉, for line CX1 and (b) covariance component 〈uyuz〉, for line CY1

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Fig. 12

Evolution of the z-velocity (streamwise) components, averaged per 64 (top) and 128 (bottom) FTT, respectively, at four time probe locations

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Fig. 13

Vector fields of the most energetic eigenmode in the domain for two time sequences separated by a long time-integration period. (a) and (b) Transverse and lateral views of the central pebble gap area for sequence one, respectively. (c) and (d) The same for sequence 2. Black lines are overlaid to highlight relevant behavior. (a) POD sequence 1, [x, y, 0] transverse plane, (b) POD sequence 1, [x, 0, z] lateral plane, (c) POD sequence 2, [x, y, 0] transverse plane, and (d) POD sequence 2, [0, y, z] lateral plane.

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Fig. 14

Pseudocolor rendering of the ensemble-averaged velocity magnitude in the [x, 0, z] plane for the expanded domain

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Fig. 15

Line profiles of ensemble-averaged data in the expanded computational domain. Line locations are shown in Fig. 14. (a) Velocity component 〈Uz〉 and (b) covariance component 〈uxuz〉.




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