Research Papers

Direct Numerical Simulation of Heated Turbulent Pipe Flow at Supercritical Pressure

[+] Author and Article Information
Xu Chu

Institute of Nuclear Technology and Energy Systems, University of Stuttgart,
Pfaffenwaldring 31, Stuttgart 70569, Germany
e-mail: xu.chu@ike.uni-stuttgart.de

Eckart Laurien

Institute of Nuclear Technology and Energy Systems, University of Stuttgart,
Pfaffenwaldring 31, Stuttgart 70569, Germany
e-mail: Laurien@ike.uni-stuttgart.de

1Corresponding author.

Manuscript received April 30, 2015; final manuscript received January 5, 2016; published online June 17, 2016. Assoc. Editor: Thomas Schulenberg.

ASME J of Nuclear Rad Sci 2(3), 031019 (Jun 17, 2016) (11 pages) Paper No: NERS-15-1065; doi: 10.1115/1.4032479 History: Received April 30, 2015; Accepted January 05, 2016

For fluids at supercritical pressure, the phase change from liquid to gas does not exist. Meanwhile, the fluid properties change drastically in a narrow temperature range. With supercritical fluid as working fluid in a heated pipe, heat-transfer deterioration and recovery have been observed, which corresponds to the turbulent flow relaminarization and recovery. Direct numerical simulation (DNS) of supercritical carbon dioxide flow in a heated vertical circular pipe is developed with the open-source code OpenFOAM in this study. Forced-convection and mixed-convection cases including upward and downward flow have been considered in the simulation. In the forced convection, flow turbulence is attenuated due to acceleration from thermal expansion, which leads to a peak of the wall temperature. However, buoyancy shows a stronger impact on the flow. In the upward flow, the average streamwise velocity distribution turns into an M-shaped profile because of the external effect of buoyancy. Besides that, negative buoyancy production caused by the density variation reduces the Reynolds shear stress to almost zero, which means that the flow is relaminarized. Further downstream, turbulence is recovered. This behavior of flow turbulence is confirmed by visualization of turbulent streaks and vortex structures.

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The National Institute of Standards and Technology, 2015, “Nist Chemistry Webbook,” , http://webbook.nist.gov/chemistry/.
Brunner, G., 2010, “Applications of Supercritical Fluids,” Ann. Rev. Chem. Biomol. Eng., 1(1), pp. 321–342. 10.1146/annurev-chembioeng-073009-101311
Dostal, V., Driscoll, M. J., and Hejzlar, P., 2004, “A Supercritical Carbon Dioxide Cycle for Next Generation Nuclear Reactors,” PhD thesis, Massachusetts Institute of Technology, Cambridge, MA.
Shiralkar, B. S., and Griffith, P., 1968, “The deterioration in heat transfer to fluids at supercritical pressure and high heat fluxes,” , Department of Mechanical Engineering, Engineering Projects Laboratory, MIT, Cambridge, MA.
Bae, Y.-Y., and Kim, H.-Y., 2009, “Convective Heat Transfer to co2 at a Supercritical Pressure Flowing Vertically Upward in Tubes and an Annular Channel,” Exp. Therm. Fluid Sci., 33(2), pp. 329–339. 10.1016/j.expthermflusci.2008.10.002
Licht, J., Anderson, M., and Corradini, M., 2008, “Heat Transfer to Water at Supercritical Pressures in a Circular and Square Annular Flow Geometry,” Int. J. Heat Fluid Flow, 29(1), pp. 156–166. 10.1016/j.ijheatfluidflow.2007.09.007
Li, Z.-H., Jiang, P.-X., Zhao, C.-R., and Zhang, Y., 2010, “Experimental Investigation of Convection Heat Transfer of CO2 at Supercritical Pressures in a Vertical Circular Tube,” Exp. Therm. Fluid Sci., 34(8), pp. 1162–1171. 10.1016/j.expthermflusci.2010.04.005
Duffey, R. B., and Pioro, I. L., 2005, “Experimental Heat Transfer of Supercritical Carbon Dioxide Flowing Inside Channels (Survey),” Nucl. Eng. Des., 235(8), pp. 913–924. 10.1016/j.nucengdes.2004.11.011
Yoo, J. Y., 2013. “The Turbulent Flows of Supercritical Fluids With Heat Transfer,” Ann. Rev. Fluid Mech., 45(1), pp. 495–525. 10.1146/annurev-fluid-120710-101234
He, S., Kim, W. S., and Bae, J. H., 2008, “Assessment of Performance of Turbulence Models in Predicting Supercritical Pressure Heat Transfer in a Vertical Tube,” Int. J. Heat Mass Transfer, 51(19–20), pp. 4659–4675. 10.1016/j.ijheatmasstransfer.2007.12.028
Cheng, X., Kuang, B., and Yang, Y. H., 2007, “Numerical Analysis of Heat Transfer in Supercritical Water Cooled Flow Channels,” Nucl. Eng. Des., 237(3), pp. 240–252. 10.1016/j.nucengdes.2006.06.011
Yang, J., Oka, Y., Ishiwatari, Y., Liu, J., and Yoo, J., 2007, “Numerical Investigation of Heat Transfer in Upward Flows of Supercritical Water in Circular Tubes and Tight Fuel Rod Bundles,” Nucl. Eng. Des., 237(4), pp. 420–430. 10.1016/j.nucengdes.2006.08.003
Bae, J. H., Yoo, J. Y., and Choi, H., 2005, “Direct Numerical Simulation of Turbulent Supercritical Flows With Heat Transfer,” Phys. Fluids, 17(10), p. 105104. 10.1063/1.2047588
Bae, J. H., Yoo, J. Y., and McEligot, D. M., 2008, “Direct Numerical Simulation of Heated CO2 Flows at Supercritical Pressure in a Vertical Annulus at Re=8900,” Phys. Fluids, 20(5), p. 055108. 10.1063/1.2927488
Nemati, H., Patel, A., Boersma, B. J., and Pecnik, R., 2015, “Mean Statistics of a Heated Turbulent Pipe Flow at Supercritical Pressure,” Int. J. Heat Mass Transfer, 83, pp. 741–752. 10.1016/j.ijheatmasstransfer.2014.12.039
Ničeno, B., and Sharabi, M., 2013, “Large Eddy Simulation of Turbulent Heat Transfer at Supercritical Pressures,” Nucl. Eng. Des., 261, pp. 44–55. 10.1016/j.nucengdes.2013.03.042
OpenFOAM Foundation, 2013, “Openfoam User Guide,” No. Version 2.2.2, http://foam.sourceforge.net/docs/Guides-a4/UserGuide.pdf.
Leonard, B. P., 1979, “A Stable and Accurate Convective Modelling Procedure Based on Quadratic Upstream Interpolation,” Comput. Methods Appl. Mech. Eng., 19(1), pp. 59–98. 10.1016/0045-7825(79)90034-3
Orlanski, I., 1976, “A Simple Boundary Condition for Unbounded Hyperbolic Flows,” J. Comput. Phys., 21(3), pp. 251–269. 10.1016/0021-9991(76)90023-1
Tabor, G. R., and Baba-Ahmadi, M. H., 2010, “Inlet Conditions for Large Eddy Simulation: A Review,” Comput. Fluids, 39(4), pp. 553–567. 10.1016/j.compfluid.2009.10.007
Eggels, J., Unger, F., Weiss, M. H., Westerweel, J., Adrian, R. J., Friedrich, R., and Nieuwstadt, F., 1994, “Fully Developed Turbulent Pipe Flow: A Comparison Between Direct Numerical Simulation and Experiment,” J. Fluid Mech., 268, pp. 175–210. 10.1017/S002211209400131X
Komen, E., Shams, A., Camilo, L., and Koren, B., 2014. “Quasi-dns Capabilities of Openfoam for Different Mesh Types,” Comput. Fluids, 96, pp. 87–104. 10.1016/j.compfluid.2014.02.013
Shehata, A. M., and McEligot, D. M., 1995, “Turbulence Structure in the Viscous Layer of Strongly Heated Gas Flows,” , Lockheed Idaho Technologies Co., Idaho Falls, ID.
Pope, S. B., 2000, Turbulent Flows, Cambridge University Press, Cambridge.


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Fig. 1

Variation of thermophysical properties of CO2: dynamic viscosity μ ((a), –); thermal conductivity κ ((a), – –); density ρ ((b), –); and specific heat capacity Cp ((b), – –) of CO2 as a function of the temperature at a supercritical pressure of P0=8  MPa. Data from NIST database [1]

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Fig. 2

Schematic diagram of geometry and velocity inlet boundary conditions: upper, library method; down, mapping method

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Fig. 3

Validation of the mapping inlet boundary condition. (a) Dimensionless velocity fluctuation, from top to bottom: Uz,rms+, Uθ,rms+, Ur,rms+; lines: current DNS; symbols: DNS results from Eggels et al. [21]. (b) Averaged wall temperature in one of the simulation case 22U with two different boundary conditions. Mapping inlet (–), library inlet (– –), results from Bae et. al. [13] (°).

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Fig. 4

Average wall temperature Tw of case Run 635 from Shehata and McEligot [23] (°) and current DNS results (–).

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Fig. 5

Average velocity profile U¯z/U0 (a) and average flow temperature profile T¯/T0 (b) from case Run635 of Shehata and McEligot [23], DNS results in line, experiments in symbol, and from bottom to top are profiles on z=3.2D, z=8.7D, z=14.2D, z=19.9D, z=24.5D.

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Fig. 6

Average wall temperature Tw of the present DNS (–) with results by Bae et al. (°) and Nemati et al. (□). (a) Case 1U and (b) case 22U.

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Fig. 7

Average wall temperature Tw of cases 2F (–), 2U (– –), and 2D (⋯).

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Fig. 8

Mean velocity profiles U˜z (m/s) of 2F (a), 2U (b), and 2D (c) on z=0D (–), z=20D (∗), z=30D (□), z=40D (°).

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Fig. 9

Turbulent kinetic energy: (1/2)ρUiUi¯(kg/m s2) of cases 2F (a), 2U (b), and 2D (c) on z=0D (−), z=20D (∗), z=30D (□), z=40D (°).

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Fig. 10

Reynolds shear stress: ρUz′′Ur′′¯ (kg/m s2) of cases 2F (a), 2U (b), and 2D (c) on z=0D (−), z=20D (∗), z=30D (□), z=40D (°).

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Fig. 11

Turbulent heat flux: ρUz′′h′′¯ (J/m2 s) of cases 2F (a), 2U (b), and 2D (c) on z=0D (−), z=20D (∗), z=30D (□), z=40D (°).

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Fig. 12

Turbulent heat flux: ρUr′′h′′¯ (J/m2 s) of cases 2F (a), 2U (b), and 2D (c) on z=0D (−), z=20D (∗), z=30D (□), z=40D (°).

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Fig. 13

Turbulent streaks of upward flow of case 2U, at different wall distance y+, at the position of inlet (z=0D−3D), flow relaminarized (z=25D−28D), and flow recovered (z=40D−43D).

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Fig. 14

Vortex structure according to lambda-2 criterium of 2F (left) and 2U (right). Pipe sections from left to right are z=0D−8D, 8D−16D, 16D−24D, 24D−32D, 32D−40D,  and 40D−45D.




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