Abstract
Direct contact condensation (DCC) is widely occurred in nuclear power systems and leads to undesired phenomena such as condensation-induced water hammer. For ocean nuclear power ships, DCC is inevitable in the passive heat removal system and influenced by sea conditions. In this paper, the characteristics of DCC under rolling conditions are analyzed. The numerical model of DCC is established based on computational fluid dynamics approach. The VOF model, SST k–ω turbulence model and the additional inertia force model are incorporated to describe the liquid-gas two-phase flow under the rolling motion. The condensation model based on surface renewal theory (SRT) is used to simulate steam-water DCC phenomenon. The simulation results are compared with the experimental data and show reasonable agreement. The effects of rolling motion on DCC for steam injection into a horizontal pipe filled with cold water are numerically investigated. The results show that the additional inertial forces and the average condensation rate increase with the increase of the rolling angle and frequency. The reverse flow of the seawater induced by rolling motion leads to the accumulation of the steam at the lower part of the pipe, resulting in a large pressure pulse. With the increase of rolling angle and frequency, the pressure pulse induced by DCC increases.
You have full access to this open access chapter, Download conference paper PDF
Similar content being viewed by others
Keywords
- Ocean nuclear power ships
- Direct contact condensation
- Rolling motion
- Average condensation rate
- Pressure pulse
1 Introduction
For the ocean nuclear power ships, the direct contact condensation (DCC) phenomenon is inevitably occurred due to the efficient heat transfer characteristics [1, 2]. In addition, when the nuclear power system is working in the marine environment, it will inevitably be affected by the ocean environment and produce a series of motions, such as heaving, pitching and rolling [3, 4]. These motions will affect the two-phase flow and heat transfer characteristics in the cooling systems [5]. Therefore, the research of the transient behaviors of the DCC phenomenon under ocean conditions is of great significance for the application of the ocean nuclear power ships.
At present, many experimental and numerical simulation researches have been conducted to focus on the DCC under static conditions [6]. Prasser et al. (2008) experimentally observed the DCC events induced by steam-water counterflow in the horizontal pipe, and focused on the number of pressure pulse and formation of steam slug [7]. Chong et al. (2020) experimentally studied the DCC phenomenon induced by steam discharged into a horizontal pipe and focused on the condensation induced water hammer induced phenomenon by the DCC [8]. Sun et al. (2020) experimentally observed the DCC phenomenon in the passive heat removal system for offshore application and analyzed the formation mechanism [9]. Wang et al. (2022) simulated the DCC phenomenon in the horizontal pipe by the ANSYS FLUENT software, and captured the formation process of DCC phenomenon by the VOF method [10].
The typical motion of the floating structures under ocean conditions, such as rolling motion, will generate various additional forces and further affect the coolant flow and heat and mass transfer. Peng et al. (2020) numerically studied the effect of rolling motion on the void distribution of subcooled flow boiling. The results indicated that the void fraction distribution is sensitive to the rolling period [11]. Wang et al. (2022) numerically investigated the flow characteristics of gas-liquid two-phase flow under rolling condition. They found that the void fraction presents periodical variation and will induce complex secondary-flow phenomenon [12]. Chen et al. (2022) numerically studied the dominant oscillation frequency of the unstable steam jet under rolling condition and indicated that the Coriolis force has a great influence on the dominant oscillation frequency [13]. Therefore, the effects of rolling motion on boiling two-phase flow and gas-liquid two-phase flow have attracted enough attention from relevant researchers.
Based on the literature review, the present study aims to study the transient behaviors of the direct contact condensation (DCC) phenomenon under rolling conditions. The DCC numerical model frame was established based on the volume of fluid (VOF) model, the condensation model and the rolling motion model. The additional inertial forces, formation process, average condensation rate, and pressure behaviors were obtained to study the effects of rolling motion on the DCC phenomenon.
2 Mathematic Model
2.1 Two-Phase Flow Mode
The direct contact condensation usually occurs at the steam-subcooled water interface, so obtaining a clear steam-subcooled water interface is the key to the numerical simulation. Previous studies indicated that the VOF model has significant advantages in tracking the gas-liquid interface [14]. Hence, the VOF model is used to describe the steam-subcooled water two-phase flow in the present study. The tracking of the steam-subcooled water interface is by solving the continuity equation for the volume fraction of each phase. The conservation of mass as follow:
There exists a closed equation for the volume fraction of gas phase and liquid phase:
In the VOF model, the gas and liquid phase share a set of momentum equations. The surface tension and the additional inertial forces are added to the momentum equation in the form of source terms. The momentum equation as follow:
Similarly, the gas and liquid phase share a set of momentum equation, as follow:
where: the \({Q}_{m}\) represents the energy source term and is modeled by the UDF, the specific form refers to the Sect. 2.2.
In the present study, the SST k − ω turbulence model is used to compute the turbulence characteristics induced by the rolling motion [15]. The governing equations as follow:
The equation of turbulent kinetic energy:
The equation of specific dissipation rate:
where: the \({G}_{k}\) is the turbulent kinetic energy term due to velocity gradient, \({\varGamma }_{k}\) and \({\varGamma }_{\omega }\) represent the convective term of k and \(\omega\), \({Y}_{k}\) and \({Y}_{\omega }\) represent the effective diffusion term of k and \(\omega\) induced by turbulence, \({Y}_{k}\) represents the cross convective term. \({S}_{k}\) and \({S}_{\omega }\) represent the user-defined source terms.
2.2 Condensation Phase Change Model
During the process of condensation induced water hammer, only the condensation phenomenon occurs. It is assumed that condensation occurs only at the steam-subcooled water interface. The heat and mass transfer during the condensation is calculated by the UDF, and then added to the momentum and energy conservation equation [16]. The energy source term represents the heat transfer from the steam phase to the water phase at the interface, which is expressed as:
where: the \(HTC\) is the heat transfer coefficient, \({a}_{int}\) is the interfacial area density, \({T}_{sat}\) is the saturated temperature, \({T}_{l}\) is the subcooled water temperature.
For the VOF model, the absolute value of volume fraction gradient is defined as the interfacial area density [17], which is expressed as:
where: \({\alpha }_{l}\) is the liquid volume fraction, \(n\) is the unit vectors.
Mass transfer source can be obtained on the basis of the energy transfer source, which is expressed as:
where: \({h}_{lv}\) is the latent heat with a constant value of 1026 kJ/ kg
2.3 Rolling Motion Model
In the present study, the additional inertial force method is utilized to calculate the effects of rolling motion. Figure 1 shows the relationship between the non-inertial frame and inertial frame [18]. The additional inertial forces mainly include the centripetal force \(({F}_{ce})\), tangential force \(({F}_{ta})\), and Coriolis force \(({F}_{co})\).
The additional inertial force method involves two reference frames, an inertial frame and a non-inertial frame. The geometric model moves relative to the inertial frame, and we only considered the rolling motion in the YOZ plane. Hence, the equations of rolling motion are as follows [30]:
In conclusion, the additional inertial force can be calculated as follows:
2.4 Defined Geometry and Mesh Generation
For marine floating structures, the nuclear reactor is usually arranged in the reactor room. The DCC events mainly occurs in the upper horizontal pipe, as depicted in Fig. 2 (a). In addition, the length and inner diameter of the geometric model is 2.0 m and 0.1 m respectively [19]. In order to ensure the calculation convergence, the structured grid was generated in the ANSYS ICEM software, and the boundary layer was densified, as shown in Fig. 2 (b).
In this paper, the commercial CFD software Ansys Fluent 2020 has been utilized to conduct the numerical simulation. The numerical simulations adopt the pressure-based solver. The pressure- velocity coupling scheme adopts the pressure-implicit with splitting of operators (PISO). The QUICK discretization scheme is applied to the momentum and energy equations [20]. Geo-Reconstruct scheme is applied to the spatial discretization for volume fraction.
3 Results and Discussion
3.1 Mesh Independence Test
The mesh independence test was conducted with three different mesh sizes in the present study. The minimum size of the three meshes were selected 1 mm, 0.5 mm and 0.25 mm, respectively. Then, the temperature evolution and the variation of liquid volume fraction under different mesh sizes were analyzed. As depicted in Fig. 3 (a), with the decrease of the minimum size, the trend of the temperature evolution is gradually consistent. The mesh sizes also affect the variation of the liquid volume fraction. With the mesh size decreased from 0.5 mm to 0.25 mm, the variation trend of the liquid volume fraction is gradually consistent, as shown in Fig. 3 (b). Therefore, the subsequent numerical simulations are based on the mesh with the minimum size 0.5 mm.
3.2 Validation of DCC Numerical Model
We conducted the verification of the UDF by comparing the PMK-2 experimental results. The geometric model and boundary conditions of the PMK-2 experiment is shown in Fig. 4 (a). We selected the monitoring points T4 to compare the temperature evolution between the numerical simulation and experiment. Figure 4 (b) shows the comparison of the temperature evolution in T4 between the numerical simulation and experiment. The results indicated that the temperature step time obtained by the numerical simulation is basically consistent with the experiment. In summary, the present condensation model can effectively simulate the condensation behaviors and provide a guarantee for the subsequent numerical simulation of the DCC events.
3.3 DCC Process Under Rolling Conditions
Figure 5 shows the formation process of the CIWH phenomenon under rolling condition. Similarly, the stratified-wave flow is formed in the horizontal pipe at the early stage. From 0 to T/4, the additional inertial force accelerates the reverse flow of the subcooled water. During the process of the reverse flow, the saturated steam is continuously squeezed down the pipe until the isolated steam bubble is formed. From T/4 to T/2, the isolated steam bubble is surrounded by the subcooled water, and the steam bubble collapse quickly due to the DCC. At T/2, the condensation induced water hammer occurs. After the CIWH event, the horizontal pipe is filled with water and has a larger subcooling. Hence, from T/2 to T, the saturated steam flowing into the pipe is rapidly condensed, and the formation mechanism of the CIWH disappears. With the temperature field in the horizontal pipe increases, the saturated steam can flow into again, which in turn triggers a new CIWH event. In summary, the formation mechanism of the CIWH under static and rolling condition is basically the same. While, it is worth noting that the rolling motion complicates the reverse flow of the subcooled water and the DCC phenomenon.
3.4 Effect of Rolling Motion on Condensation Rate
The condensation rate is a key parameter to describe the DCC phenomenon. Thus, the effects of rolling motion on the condensation rate are numerically studied. The condensation rate is calculated by the UDF and recorded by the UDM function in the present study. As depicted in Fig. 6 (a) and (b), compared to the static condition, the average condensation rate under rolling conditions has a remarkable increase. The average condensation rate has a tendency to decrease as the rolling period increased, and has a tendency to increase with the rolling angle increased. This is mainly due to the larger rolling angle and high rolling frequency enhanced the contact area between the steam and subcooled water, which in turn improved the capacity of heat and mass transfer at the steam- subcooled water interface. In addition, the average condensation rate is proportional to the steam inlet velocity, as depicted in Fig. 6 (c) and (d). This is mainly due to the increase of the steam inlet velocity increased the amount of steam in the pipe, and then increased the average condensation rate.
3.5 Effect of Rolling Motion on Pressure Behaviors
Figure 7 shows the comparison of the pressure behaviors induced by the DCC events under static condition and rolling conditions. The main pressure behaviors observed in the time domain signals are as flows: (1) the pressure peak under rolling conditions is obviously greater than that under static condition. This is mainly due to the larger condensation rate and reverse flow of subcooled water under rolling condition aggravated the pressure peak. (2) the pressure behaviors under rolling conditions are more complex, which present periodic fluctuations after generating the violent pressure peak. This is mainly due to the rapid formation and collapse of the isolated steam bubbles in the early stage of the rolling motion. Then the subcooled water filled with the pipe, and the saturated steam is completely condensed at the pipe inlet due to the larger subcooling. Therefore, the periodic fluctuation is mainly induced by the subcooled water flow under the rolling motion. (3) the pressure peak decreased with the rolling period increase and increased with the rolling angle increase. This is mainly due to the high-frequency and large-angle rolling motions have aggravated the reverse flow of the subcooled water and increased the average condensation rate. In addition, we also found that as the steam inlet velocity is constant, the occurrence positions of the pressure peaks under different rolling parameters are consistent.
4 Conclusions
In this paper, the direct contact condensation (DCC) numerical model under rolling conditions is established based on the CFD code combined with UDFs. The effects of rolling motion on the transient behaviors of the DCC are investigated, including transient formation process, average condensation rate and pressure behaviors. The main conclusions are summarized as follows:
-
(1)
The rolling motion intensifies the reverse flow of subcooled water and causes the gas phase to be continuously squeezed moved down the pipe until an isolated steam slug is formed. The volume of the steam slug is significantly larger than that in the static condition, and the steam-subcooled water contact area is significantly increased.
-
(2)
The average condensation rate under rolling conditions is always larger than that in the static condition. This is mainly due to the large volume of isolated steam bubbles increasing the steam-subcooled water contact area. With the increase of the rolling angle and decrease of the rolling period, the average condensation rate increased.
-
(3)
Under rolling condition, the pressure behaviors are more complex and the pressure peak induced by the DCC is increased significantly. This is largely because the rolling motion intensifies the subcooled water reverse flow and enhances the condensation rate. Similar, the pressure peak by the DCC increases with the increasing rolling angle and rolling frequency. In addition, the location where the pressure peak occurred gradually moves towards the pipe outlet with the steam inlet velocity increased.
References
Zhang, Y.L., Buongiorno, J.: Safety analysis of a 300-MW (electric) offshore floating nuclear power plant in marine environment. Nucl. Tech. 203, 129–145 (2018)
Sun, J.C., Ding, M.: Experimental research on reverse flow phenomenon in an equal-height-difference natural circulation system at low pressure. Nucl. Eng. Des. 370, 110–121 (2021)
Chun, M.H., Yu, S.O.: A parametric study and a guide chart to avoid condensation induced water hammer in a horizontal pipe. Nucl. Eng. Des. 201, 239–257 (2000)
Wang, C.Y., Peng, M.J., Xia, G.L.: Sensitivity analysis based on Morri’s method of passive system performance under ocean conditions. Ann. Nucl. Energy. 137, 107067 (2020)
Kim, G., Yoo, J., Lee, C.: Critical heat flux characteristics of flow boiling on a heater rod under inclined and rolling conditions. Int. J. Heat Mass Transf. 189, 662–670 (2022)
Datta, P., Chakravarty, A., Ghosh, K.: Modeling and analysis of condensation induced water hammer. Num. Heat. Transf. Part A Appl. 74, 975–982 (2018)
Prasser, H., Baranyai, G.: Water Hammer Tests, Condensation caused by Cold water Injection into Main Steam-Line of VVER-440-type PWR-Quick-Look Report (QLR), Technical report. 236–248 (2004)
Chong, D.T., Wang, L.T.: Characteristics of entrapped bubbles of periodic condensation-induced water hammer in a horizontal pipe. Int. J. Heat Mass Transf. 152, 119–134 (2020)
Sun, J.C., Ding, M.: Experimental research on characteristics of condensation induced water hammer in natural circulation systems. J. Int. Commun. Heat Mass Transf. 114, 104–112 (2020)
Wang, Z.W., He, Y.P., Duan, Z.D.: Numerical investigation on direct contact condensation-induced water hammer in passive natural circulation system for offshore applications. Num. Heat. Transf. Part A Appl. 63(3), 974–985 (2022)
Peng, J., Chen, D.Q., Xu, J.J.: CFD simulation focusing on void distribution of subcooled flow boiling in circular tube under rolling condition. Int. J. Heat Mass Transf. 156, 380–390 (2020)
Wang, Z.W., He, Y.P., Duan, Z.D.: Effects of rolling motion on transient flow behaviors of gas-liquid two-phase flow in horizontal pipes. Ocean Eng. 255, 111–122 (2022)
Chen, W.X., Mo, Y.L., Wei, P.B.: Numerical study on dominant oscillation frequency of unstable steam jet under rolling condition. Ann. Nucl. Energy. 171, 109–116 (2022)
Li, S.Q., Wang, P.: CFD based approach for modeling steam-water direct contact condensation in subcooled water flow in a tee junction. Prog. Nucl. Energy. 85, 729–746 (2015)
Tan, H.B., Wen, N., Ding, Z.: Numerical study on heat and mass transfer characteristics in a randomly packed air-cooling tower for large-scale air separation systems. Int. J. Heat Mass Transf. 178, 121–129 (2021)
Szijártó, R., Badillo, A., Prasser, H.: Condensation models for the water–steam interface and the volume of fluid method. Int. J. Multiphase Flow. 93, 63–70 (2017)
Antham, R.: Condensation induced water hammer, Ph. D thesis, Chalmers University of Technology Gothenburg, Sweden (2016)
Liu, Z.P., Huang, D.S., Wang, C.L.: Flow and heat transfer analysis of lead–bismuth eutectic flowing in a tube under rolling conditions. Nucl. Eng. Des. 382, 111–128 (2021)
Adumene, S., Islam, R., Amin, M.: Advances in nuclear power system design and fault-based condition monitoring towards safety of nuclear-powered ships. Ocean Eng. 251, 111–126 (2022)
Li, M.Z., He, Y.P., Liu, Y.D.: Hydrodynamic simulation of multi-sized high concentration slurry transport in pipelines. Ocean. Eng. 163, 691–705 (2018)
Acknowledgments
This work was sponsored by Young Talent Project of China National Nuclear Corporation and LingChuang Research Project of China National Nuclear Corporation.
Author information
Authors and Affiliations
Corresponding authors
Editor information
Editors and Affiliations
Rights and permissions
Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.
The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Copyright information
© 2023 The Author(s)
About this paper
Cite this paper
Wang, Z., He, Y., Duan, Z., Huang, C., Liu, S. (2023). Direct Contact Condensation Characteristics of Steam Injection into Cold-Water Pipe Under Rolling Condition. In: Liu, C. (eds) Proceedings of the 23rd Pacific Basin Nuclear Conference, Volume 1. PBNC 2022. Springer Proceedings in Physics, vol 283. Springer, Singapore. https://doi.org/10.1007/978-981-99-1023-6_65
Download citation
DOI: https://doi.org/10.1007/978-981-99-1023-6_65
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-99-1022-9
Online ISBN: 978-981-99-1023-6
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)