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%.

Turbulent Heat Transfer Downstream of an Unsymmetric Blockage in a Tube

1978 ◽  
Vol 100 (4) ◽  
pp. 588-594 ◽  
Author(s):  
K. K. Koram ◽  
E. M. Sparrow
Keyword(s):  
Heat Transfer ◽  
Nusselt Number ◽  
Turbulent Heat Transfer ◽  
Working Fluid ◽  
Initial Increase ◽  
Turbulent Heat ◽  
Transfer Coefficients ◽  
Tube Cross Section ◽  
Nusselt Numbers ◽  
Prandtl Numbers

Pipe flow experiments were performed to study the heat transfer in the separation, reattachment, and redevelopment regions downstream of a wall-attached blockage in the form of a segmental orifice plate. Water was the working fluid, and the Reynolds number encompassed the range from about 10,000–60,000. The extent of the flow blockage was varied from one-fourth to three-fourths of the tube cross section. Heat transfer coefficients were determined both around the circumference of the uniformly heated tube and along its length. The axial distributions of the circumferential average Nusselt numbers show an initial increase, then attain a maximum, and subsequently decrease toward the fully developed regime. These Nusselt numbers are much higher than those for a conventional thermal entrance region. The unsymmetric blockage induces variations of the Nusselt number around the circumference of the tube. Axial distributions of the Nusselt number at various fixed angular positions reveal the presence of two types of maxima. One of these is associated with the reattachment of the flow and the other occurs due to the impingement of flow deflected by the blockage onto the tube wall. The circumferential variations decay with increasing downstream distance, but the rate of decay for the case of the smallest blockage is remarkably slow. Although most of the tests were performed for Pr = 4, supplementary experiments for Pr = 8 showed that the results are valid for a range of Prandtl numbers.

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.

Turbulent Heat Transfer to Heavy Liquid Metals in Circular Tubes

Volume 4 ◽  
2004 ◽  
Author(s):  
X. Cheng ◽  
A. Batta ◽  
H. Y. Chen ◽  
N. I. Tak
Keyword(s):  
Heat Transfer ◽  
Prandtl Number ◽  
Liquid Metals ◽  
Turbulence Models ◽  
Numerical Results ◽  
Heavy Liquid ◽  
Turbulent Heat Transfer ◽  
Turbulent Heat ◽  
Turbulent Prandtl Number ◽  
Mesh Structure

The present paper gives a brief literature review on turbulent heat transfer in heavy liquid metals (HLM), especially liquid lead-bismuth eutectic (LBE). Some models available in the open literature on heat transfer and turbulent Prandtl number are assessed. In addition, CFD analysis is carried out for circular tube geometries. The effect of turbulence models, mesh structure and turbulent Prandtl number on the numerical results is studied. Application of ε-type turbulence models with scalable wall function shows less dependence of the numerical results on mesh structure than the ω-type turbulence models with automatic wall treatment. The turbulent Prandtl number affects strongly the heat transfer performance. Comparison between the CFD results, heat transfer correlations and heat transfer test data reveals a decrease in turbulent Prandtl number by increasing Reynolds number. Based on the results achieved, recommendations are made on correlations of heat transfer and turbulent Prandtl number for LBE flows.

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.

Validation and Development of DNS Database for Low Prandtl Numbers in Rod Bundle

2019 ◽  
Author(s):  
Jonathan K. Lai ◽  
Elia Merzari ◽  
Yassin A. Hassan ◽  
Aleksandr Obabko
Keyword(s):  
Heat Transfer ◽  
Thermal Diffusivity ◽  
Prandtl Number ◽  
Liquid Metals ◽  
Heat Transfer Characteristics ◽  
Reynolds Analogy ◽  
Transfer Characteristics ◽  
Rod Bundle ◽  
High Thermal Diffusivity ◽  
Prandtl Numbers

Abstract Difficulty in capturing heat transfer characteristics for liquid metals is commonplace because of their low molecular Prandtl number (Pr). Since these fluids have very high thermal diffusivity, the Reynolds analogy is not valid and creates modeling difficulties when assuming a turbulent Prandtl number (Prt) of near unity. Baseline problems have used direct numerical simulations (DNS) for the channel flow and backward facing step to aid in developing a correlation for Prt. More complex physics need to be considered, however, since correlation accuracy is limited. A tight lattice square rod bundle has been chosen for DNS benchmarking because of its presence of flow oscillations and coherent structures even with a relatively simple geometry. Calculations of the Kolmogorov length and time scales have been made to ensure that the spatial-temporal discretization is sufficient for DNS. In order to validate the results, Hooper and Wood’s 1984 experiment has been modeled with a pitch-to-diameter (P/D) ratio of 1.107. The present work aims at validating first- and second-order statistics for the velocity field, and then analyzing the heat transfer behavior at different molecular Pr. The effects of low Pr flow are presented to demonstrate how the normalized mean and fluctuating heat transfer characteristics vary with different thermal diffusivity. Progress and future work toward creating a full DNS database for liquid metals are discussed.

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