Analysis of Conductance Probes for Two-Phase Flow and Holdup Applications

[EN] In this paper we perform an analysis of the conductance probes used in two-phase flow applications especially for two-phase flow tomography of annular flow, to measure the waves produced in the interface with different boundary conditions without perturbing the flow, and in addition we examine the holdup applications as measuring the average void fraction in a given region. The method used to obtain the detector conductance between the electrodes is to solve analytically the generalized Laplace equation in 3D with the boundary conditions of the problem, and then to obtain the average potential difference between the detector electrodes. Then, dividing the current intensity circulating between the emitter and the receiver electrodes by the average potential difference yields the probe conductance, which depends on the geometric and physical characteristics of the measured system and the probe. This conductance is then non-dimensionalized by dividing by the conductance of the pipe full of water. In this way a set of analytical expression have been obtained for the conductance of two-plate sensors with different geometries and locations. We have performed an exhaustive comparison of the results obtained using the equations deduced in this paper with the experimental data from several authors in different cases with very good agreement. In some cases when the distribution of bubbles is not homogeneous, we have explored the different alternatives of the effective medium theory (EMT) in terms of the self-consistent EMT and the non-consistent EMT.This research was funded by Spain Ministry of Science and Technology previously dependent on MINECO (Ministry of Economy and Competitiveness), grant number ENE2016-79489-C2-1-P under Plan Nacional de I+D.Muñoz-Cobo González, JL.; Rivera-Durán, Y.; Berna Escriche, C.; Escrivá Castells, FA. (2020). Analysis of Conductance Probes for Two-Phase Flow and Holdup Applications. Sensors. 20(24):1-29. https://doi.org/10.3390/s20247042S129202

Feasibility Test of a Liquid Film Thickness Sensor on a Flexible Printed Circuit Board Using a Three-Electrode Conductance Method

Liquid film thickness measurements under temperature-varying conditions in a two-phase flow are of great importance to refining our understanding of two-phase flows. In order to overcome the limitations of the conventional electrical means of measuring the thickness of a liquid film, this study proposes a three-electrode conductance method, with the device fabricated on a flexible printed circuit board (FPCB). The three-electrode conductance method offers the advantage of applicability under conditions with varying temperatures in principle, while the FPCB has the advantage of usability on curved surfaces and in relatively high-temperature conditions in comparison with sensors based on a printed circuit board (PCB). Two types of prototype sensors were fabricated on an FPCB and the feasibility of both was confirmed in a calibration test conducted at different temperatures. With the calibrated sensor, liquid film thickness measurements were conducted via a falling liquid film flow experiment, and the working performance was tested

고정밀 실험 및 해석에 기반한 원자로 강수부 상부에서의 액막 견인 모델링

학위논문(박사) -- 서울대학교대학원 : 공과대학 원자핵공학과, 2021.8. 조형규.본 연구의 목적은 고정밀 실험과 CFD 해석으로부터 얻은 국소 유동 변수들을 기반으로 원자로 강수부 상부에서 발생할 수 있는 액막 견인 현상을 모델링하는 것이다. 먼저 안전주입수 우회 현상에서의 액막 거동에 대한 이해를 제고하고, CFD 해석 검증에 적합한 고정밀 실험 데이터를 확보하기 위해 1/10 스케일로 축소된 강수부에서 실험 연구가 수행되었다. 실험에서의 주요 측정 변수는 액막 두께였으며, 액막 두께 분포를 효율적으로 측정할 수 있는 전기적 기법의 액막 센서가 본 연구에서 개발되었다. 개발 센서는 폴리이미드(polyimide) 필름 기반의 연성회로기판을 이용하여 제작되었기 때문에 강수부와 같은 곡면부에도 쉽게 부착될 수 있었다. 공기 유동에 따라서 변하는 액막 거동에 대해서 시간 평균 액막 두께를 센서로 측정하고 이를 관측 결과와 비교하였다. 공기 유속이 증가할수록 액막이 퍼지는 폭은 파단부 중심으로 좁아졌으며, 두꺼운 액막 경계에서 액적 이탈이 발생하는 것이 관측되었다. 또한 공기 유속이 큰 경우에 파단부 주위에서의 두꺼운 액막으로부터 wisp가 생성되어 파단부로 견인되는 것이 확인되었다. 이와 같은 관측을 통해 액막 센서 측정에 대한 양적, 질적 평가를 수행할 수 있었다. CFD 해석은 3차원 형상 효과가 수반되는 이상유동의 거동을 정확히 예측하고자 할 때 유용하게 활용될 수 있다. 그러나 전통적인 이상유동 모델은 분산상과 연속상이 혼재해 있는 이상유동의 거동을 적절하게 다룰 수 없기 때문에 CFD 해석의 활용에 제한이 있었다. 본 연구에서는 VOF 모델과 Mixture 모델이 결합된 형태의 VOF-slip 모델을 활용하여 강수부에서의 액막견인 현상을 상용 CFD 코드인 STAR-CCM+로 해석하였다. VOF-slip 기법에서는 액막과 wisp와 같은 large-scale interface는 VOF로 해석하고, 액적과 같은 subgrid-scale interface는 Mixture 모델로 해석하는 것이 가능하다. 본 연구에서는 VOF-slip 모델을 활용할 때, 액적 직경값과 계면난류댐핑 계수가 해석 결과에 주요한 영향을 주는 파라미터임을 확인할 수 있었다. 민감도 분석을 통해 합리적인 액막 폭 및 우회율을 도출할 수 있는 액적 직경과 계면난류댐핑 계수를 결정하였다. 고정밀 실험 및 해석연구로부터 액막 견인 현상은 기상 및 액상의 유량과 액막 경계의 위치에 의해 결정된다는 것을 확인할 수 있었다. 따라서 이들의 특성을 대변할 수 있는 파라미터들을 Re_la, We, 그리고 R_fb와 같이 정의하고 정규화된 액막견인률을 예측할 수 있는 상관식을 개발했다. 개발 모델에서는 파단 저온관을 중심으로 off-take 볼륨이 두 섹션(LEFT, RIGHT)으로 구분된다. 그리고 각 섹션에서 예측된 우회율을 합산하여 전체 우회율이 도출된다. 개발된 액막견인률 모델은 MARS-multiD 코드에 삽입되었으며, SNU 실험과 KAERI에서 수행된 DIVA 실험 (1/5 스케일) 해석을 통해 검증되었다. 검증 결과, 개발 모델이 기존 MARS 해석보다 전체적으로 개선된 우회율 예측 성능을 보였다. 추가적으로 개발 모델의 활용이 증기-물 조건으로 확장될 수 있는지 확인해보기 위해 MIDAS 실험에 대한 해석을 수행하였다. 증기-물 조건에서는 모델이 개선될 여지가 있음이 확인되었으며, 모델 개선을 위해서는 응축 현상이 수반된 실험 연구가 추후에 수행되어야 할 것이다. 본 연구에서 수행된 원자로 강수부에서의 액막 견인 현상에 대한 고정밀 실험 및 해석, 그리고 상관식 개발 및 MARS-multiD 코드 적용은 향후 원자로 냉각재상실사고 조건 시, 안전주입수 우회량 예측에 유용하게 사용될 수 있다. 특히, 개발 모델은 재관수 기간 동안 우회율에 따른 노심의 재가열을 예측하는데 중요한 역할을 할 것으로 기대된다.This study focuses on the modelling of the film off-take phenomenon in a reactor vessel downcomer based on local flow parameters obtained from experiment and computational fluid dynamics (CFD) analysis. Experiments are conducted in the reduced-scale downcomer annulus of a nuclear reactor pressure vessel to investigate the liquid film behaviors under emergency core coolant (ECC) bypass conditions and to obtain high-fidelity data for the validation of two-phase flow CFD codes. The main instrumentation is an electrical conductance sensor for measuring the local liquid film thickness, which is developed in this study. The fabrication of the electrodes on a flexible printed circuit board enabled the installation of the sensor on the curved surface. The developed sensor is used to measure the time-averaged liquid film thickness, which shows the influence of the lateral air flow on the liquid film flow, and the results are compared with visual observations. As the air velocity increased, a droplet that was created in the thick part of the liquid film appeared, and the wisps generated near the broken cold leg could be observed. In the experiment, qualitative and quantitative analyses of the measurement results showed the reliability of the developed sensor, and helped to understand the liquid film behavior in the ECC bypass phenomenon. Furthermore, the measured film thickness could contribute to film off-take modelling and to validating the CFD codes, which have not been validated sufficiently because of the absence of local measurement data. Recent advances in computational power have resulted in the application of CFD to nuclear reactor safety analyses, which require accurate predictability for two-phase flow with three-dimensional (3D) geometrical effects. Even though the different flow regimes can exist simultaneously in the real flow, the traditional two-phase CFD models have a disadvantage with respect to regime dependency. Therefore, the CFD study used VOF-slip, which is a hybrid model combining volume of fluid (VOF) and mixture model offered by STAR-CCM+ 15.04 was used. This approach enables the large-scale interface to be treated using the VOF method and the subgrid-scale interface to be treated with a mixture model that accounts for a phase slip via the drag law. The key parameters of the VOF-slip model for the film off-take phenomenon were the droplet diameter and the interface turbulence damping coefficient. Therefore, the sensitivity analyses are conducted by varying droplet diameter and damping coefficient and a suitable value was determined based on the film spreading width and ECC bypass fraction. The droplet diameter was determined to be 150 μm for all simulation cases. The interface turbulence damping coefficients ranged from 0 to 30 and mesh-independent damping term ranged from 2.7×10-5m to 5.7×10-5m. From experiment and CFD analysis studies, it was confirmed that the liquid film off-take phenomenon is governed by the air flow rate, water flow rate, and the film boundary position. Considering these three parameters, the normalized film off take rate was correlated with Rela, We, Rfb, and Bo. The concept of the model was to divide the off-take volume into two sections (LEFT and RIGHT) through a virtual boundary so that the model could evaluate the film off-take rate in each section differently. The developed film off-take model was implemented in MARS-multiD, and it was validated with the SNU experiment (1/10 scale) and DIVA test (1/5 scale). The validation results showed that the newly developed film off-take model could improve the predictability of the bypass fraction. In addition, the MIDAS test with steam-water flow was simulated using the developed model, and the results was confirmed that the phenomenon accompanied by condensation should be experimentally investigated in future study to accurately predict the film off-take in the steam-water condition.Chapter 1 Introduction 1 1.1 Background and Motivation 1 1.1.1 Liquid film off-take in reactor vessel downcomer 1 1.1.2 Challenges with multi-dimensional system code simulation 3 1.2 Literature Review 5 1.2.1 ECC bypass experiment 5 1.2.2 Liquid film thickness sensor 7 1.2.3 CFD analysis 9 1.2.4 Modelling 11 1.3 Objectives and Scopes 12 Chapter 2 Liquid Film Thickness Sensor 18 2.1 Sensor Design 18 2.1.1 Features with flush-mounted electrode 18 2.1.2 Electrode design 19 2.1.3 Circuitry design 22 2.2 Sensor Calibration 23 2.2.1 Calibration method 23 2.2.2 Calibration result 24 Chapter 3 Experiment for Two-phase Film Flow 40 3.1 Scaling for ECC bypass phenomenon 40 3.2 Experimental Setup and Conditions 42 3.2.1 Experiment facility 42 3.2.2 Test matrix 43 3.3 Experimental Results 45 3.3.1 Time-averaged film thickness 45 3.3.2 Fluctuation of film thickness 51 3.3.3 ECC bypass fraction 53 Chapter 4 CFD Analysis 71 4.1 Two-phase CFD Models 71 4.1.1 VOF model 71 4.1.2 Mixture model 73 4.1.3 Two-fluid model 74 4.2 CFD Modelling 75 4.2.1 VOF-slip model 75 4.2.2 Interface turbulence damping 77 4.2.3 Computational domain and simulation cases 79 4.3 Simulation Results 79 4.3.1 No air flow conditions 79 4.3.2 Determination of droplet diameter 80 4.3.3 Effect of interface turbulence damping 83 Chapter 5 Modelling of Film Off-take 104 5.1 Difficulties Associated with Simulating Film Off-take Phenomenon 104 5.2 Development of Film Off-take Model 106 5.2.1 Strategy for model development 106 5.2.2 Definition of modelling parameters 108 5.2.3 Development of film off-take model 114 5.3 Validation of Developed Film Off-take Model 115 5.3.1 SNU experiment 115 5.3.2 DIVA experiment 116 5.3.3 MIDAS experiment 119 5.4 Applicability of Developed Film Off-take Model 121 Chapter 6 Conclusions 147 6.1 Summary 147 6.2 Recommendations 149 Nomenclature 150 References 154 Appendix A Uncertainty Analysis 162 Appendix B Implementation of Model in MARS 166 국문 초록 169박