Resolution Requirements for DNS of Turbulent Heat Transfer Near the Heated Wall at Prandtl Number 5.4

2001 ◽  
Author(s):  
Robert Bergant ◽  
Iztok Tiselj ◽  
Gad Hetsroni
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Normal Direction ◽  
Heated Wall ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Grid Refinement ◽  
Grid Spacing ◽  
Prandtl Numbers ◽  
Refined Grid

Abstract Theoretically, the grid spacing for Direct Numerical Simulations of heat transfer at Prandtl numbers higher than one should be inversely proportional to the square root of Prandtl number (Tennekes, H., Lumley, J.L [1]). The grid refinement study of Na and Hanratty (2000) [2] at Pr = 10 showed that finer grid is not required in streamwise and spanwise directions, but is necessary in the wall-normal direction. In the present work three different DNS studies were performed with different resolutions at Pr = 5.4 and friction Reynolds number Re = 171. The first DNS was performed using the resolution, which is known to be sufficient for the velocity field simulation, the second simulation was performed with the refined grid in the wall-normal direction and the third DNS was using finer grid in all three directions. Results have shown that there are no significant differences in the first-order statistics and spectra for all three cases.

Direct Numerical Simulation of the Flow in a Bare Rod Bundle at Different Prandtl Numbers

2019 ◽  
Vol 141 (12) ◽  
Author(s):  
Jonathan K. Lai ◽  
Giacomo Busco ◽  
Elia Merzari ◽  
Yassin A. Hassan
Keyword(s):  
Heat Transfer ◽  
Numerical Simulation ◽  
Reynolds Number ◽  
Prandtl Number ◽  
Direct Numerical Simulation ◽  
Frequency Analysis ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Rod Bundle ◽  
Prandtl Numbers

Abstract A direct numerical simulation (DNS) of bare rod bundles with a low pitch-to-diameter ratio is performed with heat transfer at different Prandtl numbers. Turbulence statistics for temperature and velocity as well as the turbulent budgets have been collected. High-fidelity simulations are performed with the spectral element method (SEM) using Nek5000, a highly scalable code. To pertain to industrial-related flows, a rod bundle model is based on Hooper and Wood's (Hooper, J. D., and Wood, D., 1984, “Fully Developed Rod Bundle Flow Over a Large Range of Reynolds Number,” Nucl. Eng. Des., 83(1), pp. 31–46) experimental setup. Both wall normalized velocity profile and turbulent kinetic energy are validated with a Reynolds number of 22,600. Kolmogorov length scales and time scales are calculated to be within the simulation's spatial–temporal resolution. Moreover, gap vortices and coherent structures are quantified by using Lambda2 vortex criterion, frequency analysis, and two-point correlation. Heat transfer statistics are discussed with a constant heat flux for six different Prandtl numbers ranging from 2 to 0.002. This range shows significantly different characteristics in temperature for both mean and variance. Mean temperature profiles in the subchannel center are very sensitive to the Prandtl number when it becomes small. It is also found that the location of the local maxima for the variance of temperature fluctuations becomes very sensitive at larger Prandtl numbers. The temperature frequency analysis reveals a shift to lower frequencies for low Prandtl numbers. The DNS results provided in this work will contribute as benchmark for the improvement and development of existing and new turbulent heat transfer models at different Prandtl number regimes.

scholarly journals Nusselt number correlation for turbulent heat transfer of helium–xenon gas mixtures

2021 ◽  
Vol 32 (11) ◽  
Author(s):  
Biao Zhou ◽  
Yu Ji ◽  
Jun Sun ◽  
Yu-Liang Sun
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Prandtl Number ◽  
Liquid Metals ◽  
Turbulent Heat Transfer ◽  
Working Fluid ◽  
Turbulent Heat ◽  
Heat Transfer Correlation ◽  
Heat Transfer Correlations ◽  
Prandtl Numbers

AbstractA gas-cooled nuclear reactor combined with a Brayton cycle shows promise as a technology for high-power space nuclear power systems. Generally, a helium–xenon gas mixture with a molecular weight of 14.5–40.0 g/mol is adopted as the working fluid to reduce the mass and volume of the turbomachinery. The Prandtl number for helium–xenon mixtures with this recommended mixing ratio may be as low as 0.2. As the convective heat transfer is closely related to the Prandtl number, different heat transfer correlations are often needed for fluids with various Prandtl numbers. Previous studies have established heat transfer correlations for fluids with medium–high Prandtl numbers (such as air and water) and extremely low-Prandtl fluids (such as liquid metals); however, these correlations cannot be directly recommended for such helium–xenon mixtures without verification. This study initially assessed the applicability of existing Nusselt number correlations, finding that the selected correlations are unsuitable for helium–xenon mixtures. To establish a more general heat transfer correlation, a theoretical derivation was conducted using the turbulent boundary layer theory. Numerical simulations of turbulent heat transfer for helium–xenon mixtures were carried out using Ansys Fluent. Based on simulated results, the parameters in the derived heat transfer correlation are determined. It is found that calculations using the new correlation were in good agreement with the experimental data, verifying its applicability to the turbulent heat transfer for helium–xenon mixtures. The effect of variable gas properties on turbulent heat transfer was also analyzed, and a modified heat transfer correlation with the temperature ratio was established. Based on the working conditions adopted in this study, the numerical error of the property-variable heat transfer correlation was almost within 10%.

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