Experimental study on a single-phase natural circulation loop and its steady-state solution
Introduction
A closed-loop system driven by natural circulation (NC) is operated passively by a thermally generated buoyancy force without active pumps [1]. Hence, the principle of the NC loop (NCL) is widely employed as an energy-transfer mechanism in many thermosyphon applications [2], [3], including solar power [4], [5], geothermal systems [6], and cooling systems [7], [8]. In the nuclear industry, NC is actively studied for the development of pumpless reactors [9], [10], [11] and passive safety systems [12], [13].
A number of remarkable studies on single-phase NC (SPNC) have been reported. Vijayan et al. [14] suggested a nondimensional formula for an SPNC loop to simulate steady-state operation, where the entire loop follows a single friction law. Swapnalee and Vijayan [15] extended their work by proposing a generalized flow equation where multiple friction laws are applicable, and the equation exhibited good prediction capability against experimental data obtained from a uniform-diameter rectangular loop. Srivastava et al. [16] performed steady-state and transient tests using a molten salt NCL at a high temperature above 400 °C. Then, the test results were used to validate both the Swapnalee’s nondimensional correlation and a one-dimensional (1D) code (LeBENC). Moreover, significant studies by utilizing experimental and analytical approaches have recently been carried out on specific types of SPNC loops [17], [18], [19].
Most theoretical studies have focused on the flow resistance, assumed that flow paths are adiabatic, and utilized a simple rectangular loop for validation. In practical applications with a complex configuration, the governing factors in buoyancy force and flow resistance should be simultaneously treated with the energy transfer over the system to achieve a reliable solution.
In addition to the steady NC flowrate prediction, the stability analysis is an important topic that should be carefully treated for SPNC loops adopting horizontal heater and horizontal cooler (HHHC). Misale [20] carried out an experimental investigation on the effect of power steps on the thermo-hydraulic behavior of a rectangular SPNC loop. Luzzi et al. [21] assessed the analytical and CFD models to study the dynamic behavior of NC against the experimental data. They verified the influences of thermal inertia of piping materials on NCL behavior. Cammi et al. [22] proposed a method utilizing the information entropy to assess the equilibrium stability of a SPNC loop.
In small modular reactors (SMRs), the configuration of vertical heater and vertical cooler (VHVC) are generally employed to design the primary system. SPNC in the primary system is used as the core heat-removal mechanism under nominal and accident conditions. Park et al. [23] performed a set of NC tests using the VISTA facility to investigate the thermal–hydraulic characteristics in SMART design. Additionally, a mathematical model of an integrated reactor plant IP200 was developed, and its operation characteristics in the NC state were studied using the model. The study revealed that the primary coolant can form stable NC under low-load conditions, and determined the operating boundary for stable NC [24].
In this study, the practical case of an SPNC loop having a considerable length of the flow path and non-uniform structures is investigated via experimental and analytical approaches. This target facility is the NCL type of VHVC which corresponds to general configuration for SMRs, and the maximum height and total circulation length are 12.2 and 34.5 m, respectively. A steady-state solution that reflects both heat-loss and heat-sink effects is proposed using the lumped-component method and moving-boundary algorithm. The appropriateness of the methodology and the correlation used in the NCL model is assessed by comparing the results with experimental data.
Section snippets
Description of test facility
The Facility to Investigate Natural Circulation in SMART (FINCLS), as shown in Fig. 1, was established for a comprehensive understanding of the NC phenomena occurring at SMART [25], which is a small modular reactor developed by the Korea Atomic Energy Research Institute. The loop configuration was derived from the SMART design with simplified geometrical features and commercial pipe components. In this study, the FINCLS is treated as a specified NCL characterized by a non-uniform diameter and a
Modeling of NCL
According to the 1D governing equations for the conditions around a closed loop, the integrated form of the momentum equation for the steady state can be expressed as [1]The energy equation for the steady state with neglecting the diffusion term isEqs. (1), (2) must be treated simultaneously to obtain a reliable solution reflecting practical influences. The left-hand side of Eq. (1) represents the buoyancy-force term with the loop
Model validation
This chapter describes the assessment of the correlations and parameters employed in the sub-models, including the pipe and SG, via experimental verification. Then, the performance of the present NCL model is evaluated via comparison with the results of the SPNC test.
Effects of primary loop models
Fig. 18 shows the evolutions of predicted NC flow rate in the cases of SPNC-P60 and SPNC-P150. In the first calculation (purple line), only the friction loss is considered. Thereafter, step-by-step, the form loss, heat loss, and SG model are additionally considered. Before the SG model is employed, the temperature profile inside the SG is approximated to be linear. The results clearly indicate that practical considerations improve the predictability of the NC flow rate, making the predicted
Conclusions
The natural circulation characteristics in FINCLS—a VHVC-type NCL characterized by a considerable circulation length and non-uniform structures—were investigated via experimental and analytical approaches.
A series of SPNC tests consisting of 29 steady-state conditions was performed with five test groups under a wide range of working pressures and temperatures. The trends of the NC flow rate for all the test groups were proportional to the core power input but not to the working temperature.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgements
This work was supported by a National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT): (No. 2016M2C6A1004894).
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