Estimation of critical heat flux in vertically downward two-phase flows

Abstract

Critical Heat Flux (CHF) is one of the important design considerations of two-phase flow equipment used in many industries including nuclear, chemical and power plants. If the CHF is not accounted for properly, it may lead to catastrophic failure of the equipment. The CHF of the two-phase flows, especially in the gas liquid flows, strongly depend on several parameters including individual phase mass flow rates, process conditions, fluid properties, geometric features, external factors like power/ heat input and the pipe orientation (or the flow direction). Most of the earlier CHF investigations gave due attention to the vertically upward two-phase flows, horizontal flows and inclined flows. Lot of CHF correlations covering wide range of process conditions were published in open literature for these flows. In the vertically upward two-phase flows, the buoyancy favors the steam/ vapor to flow in upward direction along with the water momentum, while gravity alone acts downwards, thereby making it a much simpler flow pattern. Flow in horizontal tubes is also a simple flow except for the stratification related issues. This is not true with the flows in a vertical tube with flow directed downwards. The fighting for the dominance between the buoyancy (acting upwards), the gravity and the momentum (acting downwards) between both the phases in the vertically downward flow makes the flow most complex and challenging. Further, the accumulation of the vapor in the top region due to the buoyancy of vapor would also bring in an additional risks of two-phase flow instabilities or the critical heat flux, resulting in the failure of the overall system much quicker. A critical review of literature was conducted in the field of vertically downward two-phase flows. Extensive literature search revealed that there was not much research work carried out to understand the CHF. The previous research work was mostly carried out at atmospheric pressure and by including CHF magnitude enhancing mechanisms like inlet plenum, and inlet throttling, which reduces the CHF risk significantly. Only a few CHF correlations were published and are mostly applicable at atmospheric pressure. On the other hand, absence of inlet throttling, inlet plenum or other CHF magnitude enhancing mechanisms increases the CHF risk tremendously. This constitutes the lower bound of CHF, below which the equipment should not be operated especially from safety perspective. However, literature search revealed that there was hardly any information available for such scenario. All these factors combined together gives an opportunity to explore this field further and is the motivation for the current investigations. The current research work focused on developing critical heat flux (CHF) correlation for vertically downward two-phase flows up to 5 bar pressure and in the absence of CHF magnitude enhancing mechanisms. An experimental test rig was developed and commissioned at the premises of one of the engineering colleges. All the safety checks were considered during the design, commissioning and the testing phases. Credibility checks were performed on the rig by conducting the tests based on the data published in open literature. Credibility checks revealed that the numbers were in good agreement at low mass fluxes but deviated at higher mass fluxes. The presence of inlet throttling and inlet plenum in the previous investigations enhanced the CHF magnitude significantly at higher mass flow rates, resulting in deviation with the current experimental results. Design of experiments (DOE) matrix was generated for current tests to develop CHF correlation. Experiments were performed based on DOE matrix. Additional tests were performed for intermediate points. A CHF correlation was developed as a function of inlet fluid temperature, pressure and mass flux using non linear regression analysis. The final CHF correlation is given below based on the current experimental investigations. The l/d was held constant for all these investigations. 𝑞𝐶𝐻𝐹,𝐷𝑟𝑒𝑓 = 93 ∗ 𝑃 0.0629 ∗ 𝑇𝑖𝑛 −0.03867 ∗ 𝐺 0.07982 The above equation holds good in the range of pressures 1 to 5 bar, mass fluxes up to 3000 kg/m2s and inlet fluid temperatures between 35 to 70oC. The proposed correlation shows a mean deviation of 13.87% and standard deviation of 18.71% when compared with the experimental data. A diameter correction factor for tube diameters less than 25 mm was also proposed to account for the diameter changes. Uncertainty analysis was carried out to determine the confidence levels on the predictions of CHF from current investigations. The results show a 91% confidence level on the predictions. A few trends were also drawn based on the experimental results, proposed correlation, and comparison with previous experimental data. Suitable conclusions were drawn based on the trends. Further, the same set of investigations were conducted numerically using the commercially available numerical software. Numerical simulations were carried out with the same geometric features and experimental test conditions using commercially available CFD software Fluent by ANSYS Inc., USA. Focus on numerical convergence at low pressures was given priority and a CHF correlation was developed using non linear regression analysis. The CHF correlation is given by the equation below. 𝑞𝐶𝐻𝐹,𝐷𝑟𝑒𝑓 = 17.05 ∗ 𝑃 0.5262 ∗ 𝑇𝑖𝑛 −0.2489 ∗ 𝐺 0.5922 The proposed correlation shows a mean deviation of 16% and standard deviation of 21%. The numerical results were compared with the experimental data. The trends from numerical simulations were in good agreement with current experimental data at low flow rates while the deviation tends to magnify with increase in flow rates. While preliminary investigations reveal the probable causes of deviation to be the absence of entry effects, more detailed investigations are required to understand the deviations to a greater extent. It is concluded that the current CHF investigations could be considered as the first successful step for the vertically downward two-phase flows. This in turn could lead to more active research in the field of vertically downward two-phase flows in the near future and to understand the CHF covering wide range of process conditions and the geometric conditions.