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Research Papers: Fundamental Issues and Canonical Flows

Calculation of Friction Factors and Nusselt Numbers for Twisted Elliptical Tube Heat Exchangers Using Nek5000

[+] Author and Article Information
Dillon R. Shaver

Argonne National Laboratory,
Lemont, IL 60439
e-mail: dshaver@anl.gov

Lane B. Carasik

Kairos Power LLC,
Oakland, CA 94501
e-mail: lane.carasik@gmail.com

Elia Merzari

Argonne National Laboratory,
Lemont, IL 60439
e-mail: emerzari@anl.gov

Nate Salpeter

Kairos Power LLC,
Oakland, CA 94501
e-mail: salpeter@kairospower.com

Edward Blandford

Kairos Power LLC,
Oakland, CA 94501
e-mail: blandford@kairospower.com

1Corresponding author.

2Present address: Virginia Commonwealth University, Richmond, VA 23284.

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received October 16, 2018; final manuscript received February 9, 2019; published online April 4, 2019. Assoc. Editor: Riccardo Mereu.

J. Fluids Eng 141(7), 071205 (Apr 04, 2019) (11 pages) Paper No: FE-18-1691; doi: 10.1115/1.4042889 History: Received October 16, 2018; Revised February 09, 2019

Twisted elliptical tube geometries for heat exchanger design are expected to offer significant enhancement in heat transfer with a marginal increase in frictional losses. The presented work focuses on computational fluid dynamics (CFD) simulations of heated molten salt flows through twisted elliptical tube geometries at low modified Froude numbers. The objectives of this work are to evaluate the available correlations at low Froude numbers and to determine the impact of using a small gap to resolve contact points. The spectral element CFD code Nek5000 was used for all simulations, which were performed in periodic domains of triangular and square unit cells surrounding a single tube through a complete twist using an explicit filtering large eddy simulation (LES) method. The simulation methodology was validated by comparing to the experimental data of Tan et al. Excellent agreement was observed for this comparison. The Dzyubenko correlation for transitional flow was evaluated for a range of Froude numbers. This correlation demonstrated good agreement with LES results at high modified Froude number. As Froude number was decreased toward the bounds of the correlation, the agreement worsened. Cases were then simulated at low Froude number, testing the effects of tube spacing. It was determined that the laminar case for the square unit cell is the most affected by increasing gap size, which should be minimized to mitigate the effect. In the triangular unit cell, the laminar flow regime is also more significantly impacted by increasing gap size compared to the turbulent flow regime which was only marginally impacted.

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References

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Figures

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Fig. 1

Twisted-elliptical-tube bundles showing (top) a square array and (bottom) a triangular array

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Fig. 2

Square and triangular unit cells of twisted-elliptical-tubes

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Fig. 3

Cross section view of the 9th-order meshes used for (a) the square array and (b) the triangular array, both show the distribution of the Gauss–Lobatto–Legendre quadrature points: (a) square array and (b) triangular array

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Fig. 4

Percent difference compared to 11th-order solution in friction factor with changing polynomial approximation order

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Fig. 5

Instantaneous results for (a) the velocity magnitude and (b) temperature defect in the seven tube domain

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Fig. 6

Comparison of nek5000 simulations with the experimental data of Tan et al. [6], indicates ±10%

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Fig. 7

Predicted Nusselt numbers at various modified Froude numbers compared to the transitional flow correlation of Dzyubenko, Eq. (11) … … indicates ±10%, - - - - indicates lower range of Eq. (11)

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Fig. 8

CFD results for Re = 12,200 and ST/dmax = 1.02 in the square array showing the (left) instantaneous and (right) averaged velocity fields with a quarter of the domain removed

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Fig. 9

Effect of ST/dmax on friction factor for the square unit cell

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Fig. 10

Effect of ST/dmax on Nusselt number for the square unit cell

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Fig. 11

CFD results for Re = 9000 and ST/dmax = 1.02 in the triangular array showing the (left) instantaneous and (right) averaged velocity fields with a quarter of the domain removed

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Fig. 12

Effect of ST/dmax on friction factor for the triangular unit cell

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Fig. 13

Effect of ST/dmax on Nusselt number for the triangular unit cell

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