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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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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