Research Papers: Natural and Mixed Convection

Large Eddy Simulation of Liquid Metal Turbulent Mixed Convection in a Vertical Concentric Annulus

[+] Author and Article Information
Luca Marocco

Department of Energy,
Politecnico di Milano,
Milan 20156, Italy
e-mail: luca.marocco@polimi.it

Francesco Garita

Department of Energy,
Politecnico di Milano,
Milan 20156, Italy

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received June 6, 2017; final manuscript received September 8, 2017; published online April 6, 2018. Editor: Portonovo S. Ayyaswamy.

J. Heat Transfer 140(7), 072504 (Apr 06, 2018) (10 pages) Paper No: HT-17-1330; doi: 10.1115/1.4038858 History: Received June 06, 2017; Revised September 08, 2017

In the present study, turbulent forced and mixed convection heat transfer to a liquid metal flowing upwards in a concentric annulus is numerically investigated by means of large eddy simulation (LES). The inner-to-outer radius ratio is 0.5. The Reynolds number based on bulk velocity and hydraulic diameter is 8900, while the Prandtl number is set to a value of 0.026. A uniform and equal heat flux is applied on both walls. LES has been chosen to provide sufficiently accurate results for validating Reynolds-averaged turbulence models. Moreover, with the thermal sublayer thickness of liquid metals being much larger than the viscous hydrodynamic one, liquid metals present a separation between the turbulent thermal and hydrodynamic scales. Thus, with the same grid resolution, it is possible to perform a LES for the flow field and a “thermal” direct numerical simulation (DNS) for the temperature field. Comparison of the forced convection results with available DNS simulations shows satisfying agreement. Results for mixed convection are analyzed and the differences with respect to forced convection at the same Reynolds number are thoroughly discussed. Moreover, where possible, a comparison with air is made.

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Pacio, J. , Daubner, M. , Fellmoser, F. , Litfin, K. , Marocco, L. , Stieglitz, R. , Taufall, S. , and Wetzel, T. , 2014, “ Heavy-Liquid Metal Heat Transfer Experiment in a 19-Rod Bundle With Grid Spacers,” Nucl. Eng. Des., 273, pp. 33–46. [CrossRef]
Litfin, K. , Batta, A. , Class, A. , Wetzel, T. , and Stieglitz, R. , 2011, “ Investigation on Heavy Liquid Metal Cooling of ADS Fuel Pin Assemblies,” J. Nucl. Mater., 415(3), pp. 425–432. [CrossRef]
Flesch, J. , Fritsch, A. , Cammi, G. , Marocco, L. , Fellmoser, F. , Pacio, J. , and Wetzel, T. , 2015, “ Construction of a Test Facility for Demonstration of a Liquid Lead-Bismuth-Cooled 10 kW Thermal Receiver in a Solar Furnace Arrangement—SOMMER,” Energy Procedia, 69, pp. 1259–1268. [CrossRef]
Marocco, L. , Cammi, G. , Flesch, J. , and Wetzel, T. , 2016, “ Numerical Analysis of a Solar Tower Receiver Tube Operated With Liquid Metals,” Int. J. Therm. Sci., 105, pp. 22–35. [CrossRef]
Pacio, J. , Marocco, L. , and Wetzel, T. , 2015, “ Review of Data and Correlations for Turbulent Forced Convective Heat Transfer of Liquid Metals in Pipes,” Heat Mass Transfer, 51(2), pp. 153–164. [CrossRef]
Jackson, J. , Cotton, M. , and Axcell, B. P. , 1989, “ Studies of Mixed Convection in Vertical Tubes,” Int. J. Heat Fluid Flow, 10(1), pp. 2–15. [CrossRef]
Marocco, L. , Alberti di Valmontana, A. , and Wetzel, T. , 2017, “ Numerical Investigation of Turbulent Aided Mixed Convection of Liquid Metal Flow Through a Concentric Annulus,” Int. J. Heat Mass Transfer, 105, pp. 479–494. [CrossRef]
Buhr, H. O. , Horsten, E. A. , and Carr, A. D. , 1974, “ The Distortion of Turbulent Velocity and Temperature Profiles on Heating, for Mercury in a Vertical Pipe,” ASME J. Heat Transfer, 96(2), pp. 152–158. [CrossRef]
Jackson, J. , Axcell, B. , and Walton, A. , 1994, “ Mixed Convection Heat Transfer to Sodium in a Vertical Pipe,” Exp. Heat Transfer, 7(1), pp. 71–90. [CrossRef]
Marocco, L. , Loges, A. , Wetzel, T. , and Stieglitz, R. , 2012, “ Experimental Investigation of the Turbulent Heavy Liquid Metal Heat Transfer in the Thermal Entry Region of a Vertical Annulus With Constant Heat Flux on the Inner Surface,” Int. J. Heat Mass Transfer, 55(23–24), pp. 6435–6445. [CrossRef]
Grötzbach, G. , 2013, “ Challenges in Low-Prandtl Number Heat Transfer Simulation and Modelling,” Nucl. Eng. Des., 264, pp. 41–55. [CrossRef]
Duponcheel, M. , Bricteux, L. , Manconi, M. , Winckelmans, G. , and Bartosiewicz, Y. , 2014, “ Assessment of RANS and Improved Near-Wall Modeling for Forced Convection at Low Prandtl Numbers Based on LES Up to Reτ = 2000,” Int. J. Heat Mass Transfer, 75, pp. 470–482. [CrossRef]
Lilly, D. , 1992, “ A Proposed Modification of the Germano Subgrid-Scale Closure Method,” Phys. Fluids A, 4(3), pp. 633–635. [CrossRef]
Greenshields, C. , 2016, “OpenFOAM User Guide Version 4.0,” OpenFOAM Foundation Ltd., London.
Chung, S. Y. , Rhee, G. H. , and Sung, H. J. , 2002, “ Direct Numerical Simulation of Turbulent Concentric Annular Pipe Flow—Part 1: Flow Field,” Int. J. Heat Fluid Flow, 23(4), pp. 426–440. [CrossRef]
Ould-Rouiss, M. , Redjem-Saad, L. , Lauriat, G. , and Mazouz, A. , 2010, “ Effect of Prandtl Number on the Turbulent Thermal Field in Annular Pipe Flow,” Int. Commun. Heat Mass, 37(8), pp. 958–963. [CrossRef]
Liu, N. , and Lu, X. , 2004, “ Large Eddy Simulation of Turbulent Concentric Annular Channel Flows,” Int. J. Numer. Methods Fluids, 45(1), pp. 1317–1338. [CrossRef]
Kays, W. , and Leung, E. , 1963, “ Heat Transfer in Annular Passages—Hydrodynamically Developed Turbulent Flow With Arbitrarily Prescribed Heat Flux,” Int. J. Heat Mass Transfer, 6(7), pp. 537–557. [CrossRef]
Kader, B. , 1981, “ Temperature and Concentration Profiles in Fully Turbulent Boundary Layers,” Int. J. Heat Mass Transfer, 24(9), pp. 1541–1544. [CrossRef]
Kim, W. , He, S. , and Jackson, J. , 2008, “ Assessment by Comparison With DNS Data of Turbulence Models Used in Simulations of Mixed Convection,” Int. J. Heat Mass Transfer, 51(5–6), pp. 1293–1312. [CrossRef]
Kays, W. , 1994, “ Turbulent Prandtl Number—Where Are We?,” ASME J. Heat Transfer, 116(2), pp. 284–295. [CrossRef]
Tiselj, I. , 2014, “ Tracking of Large-Scale Structures in Turbulent Channel With Direct Numerical Simulation of Low Prandtl Number Passive Scalar,” Phys. Fluids, 26(12), p. 125111. [CrossRef]
Garita, F. , 2017, “ Large Eddy Simulation of Turbulent Forced and Mixed Convection to a Liquid Metal Flowing in an Annulus,” Master's thesis, Politecnico di Milano, Milan, Italy.


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Fig. 2

Mean velocity profiles

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Fig. 3

Turbulent and total shear stress; open symbols refer to DNS of Ref. [15]. Values nondimensionalized with uτ,o.

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Fig. 4

Root-mean-square profiles (rms) of velocity fluctuations: (a) inner and (b) outer walls; open symbols refer to DNS of Ref. [15]

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Fig. 1

Schematic of computational domain

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Fig. 8

Mixed and forced convection Reynolds shear stress. Values nondimensionalized with uτ,o.

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Fig. 5

Profiles of molecular (Pr−1dΘ¯/dr)+, turbulent (v′Θ′)¯+, and total ((Pr−1dΘ¯/dr)−(v′Θ′)¯)+ wall-normal heat flux: (a) Pr = 0.026 and (b) Pr = 0.71

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Fig. 6

Mixed and forced convection mean streamwise velocity profiles in global coordinates

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Fig. 7

Mean velocity profile: (a) inner wall and (b) outer wall

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Fig. 9

Profiles of (a) turbulent kinetic energy, k and (b) shear production of k, Pk

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Fig. 10

Mean temperature (a) wall coordinates together with correlation of Ref. [19] for forced convection (b) global coordinates

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Fig. 11

Profiles of (a) root-mean-square of temperature fluctuations and (b) production of temperature variance, PΘ (note that the values of PΘ for air are plotted on the right axis)

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Fig. 12

Near-wall behavior of (a) turbulent viscosity and (b) turbulent thermal diffusivity

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Fig. 13

Turbulent Prandtl number from LES2 and calculated with Eq. (6)

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Fig. 14

Two-point correlation coefficients at y+ = 5 from inner and outer walls: (a) u′ streamwise, (b) Θ′ streamwise, (c) u′ circumferential, and (d) Θ′ circumferential

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Fig. 15

Kolmogorov scale, Corrsin scale and Δ nondimensionalized with corresponding mean friction velocity

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Fig. 16

Visualization of instantaneous (a) velocity field and (b) temperature field



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