Improved closure relations for the two fluid-model in flashing flows
The two-fluid model is a widely used approach for the modeling of two-phase flows, consisted of two separate sets of mass, momentum, and energy conservation equations for the liquid and gas phases. In the two-fluid model, the interaction between the phases is determined by the mass, momentum, and energy transfer terms, which in turn are a function of the interfacial area concentration and the driving flux. Hence, it is important that the closure models for the interfacial area concentration and the driving fluxes are validated and benchmarked extensively for a wide range of flow conditions. Different approaches to predict the interfacial area concentration are available such as the static correlations and the Interfacial Area Transport Equation (IATE). In this work, the closure models of the two-fluid model, particularly those of the mass conservation equation, are studied and validated under flashing conditions with additional modifications proposed to improve the accuracy of the models. Three sets of experiments are performed in this work with a closed-loop test facility. Two-phase parameters are measured with four-sensor conductivity probes at five axial locations along the test section, consisted of 3 m of heated length, followed by 2 m of unheated length. Two-phase measurements such as void fraction, interfacial area concentration, and gas velocity, as well as flow parameters such as flow rate, fluid temperature, and pressure are measured in the experiments. The first set is a natural circulation experiment carried out with an annulus test section, while the second and third sets are forced convective flashing experiments carried out with an annulus and an annulus-to-pipe test section. In the natural circulation experiment, measurements are taken at three locations in the heated length and two in the unheated length to observe the change of two-phase parameters across the entire test section. On the other hand, for the forced convection experiments, all five measurements are taken at the unheated length to increase the axial resolution of the data. The data are useful for the validation of one-dimensional thermal-hydraulic systems codes and multi-dimensional Computational Fluid Dynamics (CFD) tools. The forced convection flashing data are used to benchmark the systems code, RELAP5/MOD3.3 where the void fraction is slightly underpredicted. The benchmarking of the static correlations used by RELAP5/MOD3.3 and TRACE to calculate the interfacial area concentration shows inaccuracy, suggesting that the existing model is underpredicting the interfacial mass generation rate. The data is also used for benchmarking the decoupled one-group IATE where the result suggests the need for separate treatments of small and large bubbles. The analysis is extended for the coupled two-group model with IATE using the interfacial mass generation models from RELAP5/MOD3.3 and TRACE where the results indicate the need for an improved interfacial mass generation model to match the drastic growth of bubbles under flashing conditions. Interfacial mass generation models are derived from the mass-energy balance equation for group-2 bubbles with the spherical and cylindrical growth assumptions. A different Nusselt number correlation is also suggested for the one-group interfacial mass generation model. The models are implemented to the coupled two-group model with IATE for benchmarking and favorable predictions are obtained, especially for the model based on the cylindrical growth assumption. Sensitivity studies are performed to investigate the effects of heat transfer characteristic length scale, initial superheat, group-2 shape coefficient, and relative velocities. Furthermore, the coupled two-group model with IATE is benchmarked against flashing flows with near-zero initial void fraction and flows with an initial condensation phase followed by a flashing phase. Various approaches to model the nucleation of bubbles from surface discontinuities are explored and benchmarked. Lastly, modifications are proposed to the interfacial area concentration correlation. The modified correlation is coupled to the one-group void transport equation and benchmarked with the newly acquire dataset where improved predictions are obtained. This work has paved the way for several opportunities for future work. Future experimental works should include the expansion of the current experimental dataset to cover a wider range of flow conditions in different flow geometries. Further validation of the proposed interfacial mass generation model and the modified interfacial area concentration correlation under different flashing conditions is also necessary. The proposed closure models should be implemented to simulation tools such as system analysis codes and CFD codes and validated extensively. Lastly, improvements to the bubble interaction mechanism models and the bubble shape factors of the IATE are recommended.
Interfacial Area Transport Equation, Interfacial Mass Generation Rate, System Analysis Codes, Flashing, Two-Fluid Model
University of Illinois - Urbana-Champaign
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University of Illinois at Urbana-Champaign