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Research Papers: Techniques and Procedures

Theoretical Analysis of Computational Fluid Dynamics–Discrete Element Method Mathematical Model Solution Change With Varying Computational Cell Size

[+] Author and Article Information
Annette Volk

Department of Mechanical and
Materials Engineering,
University of Cincinnati,
Cincinnati, OH 45241
e-mail: volkam@mail.uc.edu

Urmila Ghia

Department of Mechanical and
Materials Engineering,
University of Cincinnati,
Cincinnati, OH 45241
e-mail: ghiau@ucmail.uc.edu

1Corresponding author.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received July 24, 2018; final manuscript received February 14, 2019; published online April 1, 2019. Assoc. Editor: Wayne Strasser.

J. Fluids Eng 141(9), 091402 (Apr 01, 2019) (10 pages) Paper No: FE-18-1498; doi: 10.1115/1.4042956 History: Received July 24, 2018; Revised February 14, 2019

Successful verification and validation is crucial to build confidence in the application of coupled computational fluid dynamics–discrete element method (CFD–DEM). Model verification includes ensuring a mesh-independent solution, which poses a major difficulty in CFD–DEM due to the complicated relationship between solution and computational cell size. In this paper, we investigate the production of numerical error in the CFD–DEM coupling procedure with computational grid refinement. The porosity distribution output from simulations of fixed-particle beds is determined to be Gaussian, and the average and standard deviation of the representative distribution are reported against cell size. We find that the standard deviation of bed porosity increases exponentially as the cell size is reduced. The average drag calculated from each drag law is very sensitive to changes in the porosity standard deviation. When combined together, these effects result in an exponential change in expected drag force when the cell size is small relative to the particle diameter. The divided volume fraction method of porosity calculation is shown to be superior to the centered volume fraction (CVF) method. The sensitivity of five popular drag laws to changes in the porosity distribution is presented, and the Ergun and Beetstra drag laws are shown to be the least sensitive to changes in the cell size. A cell size greater than three average particle diameters is recommended to prevent errors in the simulation results. A grid refinement study (GRS) is used to quantify numerical error.

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References

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Figures

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Fig. 1

Porosity distribution represented as a Gaussian distribution

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Fig. 2

Standard deviation of porosity distribution with cell size, divided volume fraction method

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Fig. 3

Standard deviation of porosity distribution with cell size, CVF method

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Fig. 4

Changes in average porosity as percent of overall average

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Fig. 5

Average drag response to changes in standard deviation, binary fixed-bed conditions

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Fig. 6

Average drag response to changes in standard deviation, monosized fixed-bed conditions

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Fig. 7

Drag calculation amplifies change in porosity, binary fixed-bed conditions

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Fig. 8

Drag calculation amplifies change in porosity, monosized fixed-bed conditions

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Fig. 9

Nonlinear relationship of drag with change in porosity, binary fixed-bed conditions

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Fig. 10

Average drag law response to changes in cell size based on DVF porosity calculation for binary fixed-bed

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Fig. 11

Average drag law response to changes in cell size based on CVF porosity calculation for binary fixed-bed

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Fig. 12

Average drag law response to changes in cell size based on DVF porosity calculation for monosized fixed-bed

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Fig. 13

Average drag law response to changes in cell size based on CVF porosity calculation for monosized fixed-bed

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Fig. 14

Expected numerical error (GCI) with computational grid refinement for binary-size particle fixed bed: (a) CVF and (b) DVF

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Fig. 15

Expected numerical error (GCI) with computational grid refinement for monosize particle fixed bed: (a) CVF and (b) DVF

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Fig. 16

Determining cell size at which simulation will predict dead zones based on velocity and porosity distributions

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Fig. 17

Time-averaged porosity distribution in fluidized bed representation as a combination of gaussian and uniform distributions

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Fig. 18

Gaussian representation standard deviation of dense phase and frequency of voids increase as computational cell size is reduced

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