A phase change model for simulation of vapor-liquid phase change process

doi:10.11949/0438-1157.20200663

Abstract

Abstract:

A new phase change model based on VOF (volume of fluid) method is proposed to calculate the energy and mass source terms in the equations describing the vapor-liquid phase change process. The heat transfer occurring near the interface is considered as a transient thermal diffusion process. The phase change model calculates the energy and mass source terms in terms of the temperature of the interfacial cell, thermal physical properties of gas and liquid phases, and the time step. One-dimension Stefan problem and two-dimension horizontal film boiling were adopted to verify this new phase change model. Simulation results of the interface position and temperature distribution agree well with analytical solutions. The effect of the time step on the simulation accuracy is discussed. The results show that the deviations between the simulation results and the theoretical results decrease with the decreasing time step.

Key words: phase change, VOF, source, simulation, multiphase flow

摘要：

提出了一种基于VOF（volume of fluid）方法的相变模型，用于计算气液相变过程的控制方程中的传热传质源项。在单位时间步长上相界面附近发生的传热以瞬态热扩散来考虑，并假设该传热导致了相变的发生。相变模型能够通过相界面单元的温度、流体热物性以及时间步长来计算传热传质源项。通过一维Stefan问题和二维水平膜沸腾问题对该相变模型进行验证，对比了相界面位置以及温度分布，结果与理论解吻合良好。进一步探讨了相变模型中的时间步长对计算精度的影响。结果表明时间步长越小，本相变模型模拟得到的结果与理论解的偏差越小。

关键词: 相变, VOF, 源相, 模拟, 多相流

CLC Number:

TQ 021

Guang CHEN, Xiaohong YAN. A phase change model for simulation of vapor-liquid phase change process[J]. CIESC Journal, 2020, 71(S2): 62-69.

陈光, 闫孝红. 一种模拟气液相变过程的相变模型[J]. 化工学报, 2020, 71(S2): 62-69.

Figures/Tables 12

Fig.1 Interfacial cell and near superheating cell during one-dimension phase change process

Fig.2 One-dimension Stefan phase change problem diagram and boundary conditions

Table 1 Physical properties of water and steam at 101.3 kPa

表面张力系数

σ_l_v/(N/m)

Table 2 Calculation cases of Stefan problem

编号	网格尺寸/μm	时间步长/s
1	5	2×10^-5
2	5	5×10^-5
3	5	1×10^-4
4	10	2×10^-5

Fig.3 Interface position varying with time of Stefan problem under different grid sizes

Fig.4 Interface position varying with time of Stefan problem from 0.4 s to 0.5 s under different time steps

Fig.5 Deviation between interfacial cell temperature and saturation temperature with time under different time steps

Fig.6 Schematic diagram of two-dimensional axisymmetric horizontal film boiling

Table 3 Properties of vapor and liquid in two-dimensional horizontal film boiling problem

项目

密度ρ/

(kg/m³)

黏度μ/

(Pa·s)

比热容c_p/

(J/(kg·K))

热导率k/

(W/(m·K))

Fig.7 Total vapor volume varying with time of two-dimensional film boiling under different grid sizes

Fig.8 Contours of interface, velocity vector and temperature of two-dimensional film boiling at different times

Fig.9 Nu varying with time of two-dimensional film boiling

References 27

1	Kharangate C R, Mudawar I. Review of computational studies on boiling and condensation [J]. Int. J. Heat Mass Transfer, 2017, 108(A): 1164-1196.
2	Gibou F, Chen L G, Nguyen D, et al. A level set based sharp interface method for the multiphase incompressible Navier-Stokes equations with phase change [J]. J. Comput. Phys., 2007, 222(2): 536-555.
3	Sun D L, Xu J L, Wang L. Development of a vapor-liquid phase change model for volume-of-fluid method in Fluent [J]. Int. Commun. Heat Mass Transfer, 2012, 39(8): 1101-1106.
4	孙东亮, 徐进良, 王丽. 求解两相蒸发和冷凝问题的气液相变模型 [J]. 西安交通大学学报, 2012, 46(7): 7-11.
	Sun D L, Xu J L, Wang L. A vapor-liquid phase change model for two-phase boiling and condensation [J]. Journal of Xi􀆳an Jiaotong University, 2012, 46(7): 7-11.
5	Sun D L, Xu J L, Chen Q C. Modeling of the evaporation and condensation phase-change problems with Fluent [J]. Numer. Heat Transfer Part B - Fundam., 2014, 66(4): 326-342.
6	Perez-Raya I, Kandlikar S G. Numerical modeling of interfacial heat and mass transport phenomena during a phase change using ANSYS-Fluent [J]. Numer. Heat Transfer Part B-Fundam., 2016, 70(4): 322-339.
7	Sato Y, Ničeno B. A sharp-interface phase change model for a mass-conservative interface tracking method [J]. J. Comput. Phys., 2013, 249: 127-161.
8	Tsui Y Y, Lin S W, Lai Y N, et al. Phase change calculations for film boiling flows [J]. Int. J. Heat Mass Transfer, 2014, 7: 745-757.
9	Perez-Raya I, Kandlikar S G. Discretization and implementation of a sharp interface model for interfacial heat and mass transfer during bubble growth [J]. Int. J. Heat Mass Transfer, 2018, 116: 30-49.
10	Schrage R W. A Theoretical Study of Interphase Mass Transfer [M]. New York: Columbia University Press, 1953.
11	Tanasawa I. Advances in condensation heat transfer [J]. Advances in Heat Transfer, 1991, 21: 55-139.
12	Lee W H. A Pressure Iteration Scheme for Two-Phase Flow Modeling [M]// Multi-phase Transport: Fundamentals, Reactor Safety, Applications. Washington, DC: Hemisphere Publishing, 1980.
13	Yang Z, Peng X F, Ye P. Numerical and experimental investigation of two phase flow during boiling in a coiled tube [J]. Int. J. Heat Mass Transfer, 2008, 51(5/6): 1003-1016.
14	Kim D G, Jeon C H, Park I S. Comparison of numerical phase-change models through Stefan vaporizing problem [J]. Int. Commun. Heat Mass Transfer, 2017, 87: 228-236.
15	Gorlé C, Lee H, Houshmand F, et al. Validation study for VOF simulations of boiling in a microchannel [C]//ASME International Technical Conference & Exhibition on Packaging & Integration of Electronic & Photonic Microsystems Collocated with the ASME International Conference on Nanochannels. 2015.
16	de Schepper S C K, Heynderickx G J, Marin G B. Modeling the evaporation of a hydrocarbon feedstock in the convection section of a steam cracker [J]. Comput. Chem. Eng., 2009, 33(1): 122-132.
17	Hirt C W, Nichols B D. Volume of fluid (VOF) method for the dynamics of free boundaries [J]. J. Comput. Phys., 1981, 39(1): 201-225.
18	Brackbill J U, Kothe D B, Zemach C. A continuum method for modeling surface tension [J]. J. Comput. Phys., 1992, 100(2): 335-354.
19	Deen W M. Analysis of Transport Phenomena [M]. New York/Oxford: Oxford University Press, 1998.
20	Welch S W J, Wilson J. A volume of fluid based method for fluid flows with phase change [J]. J. Comput. Phys., 2000, 160(2): 662-682.
21	Alexiades V, Solomon A D. Mathematical modeling of melting and freezing processes [J]. Journal of Solar Energy Engineering, 1993, 115(2): 121.
22	Agarwal D K, Welch S W J, Biswas G, et al. Planar simulation of bubble growth in film boiling in near-critical water using a variant of the VOF method [J]. J. Heat Transfer, 2004, 126(3): 329-338.
23	Ding S T, Luo B, Li G. A volume of fluid based method for vapor-liquid phase change simulation with numerical oscillation suppression [J]. Int. J. Heat Mass Transfer, 2017, 110: 348-359.
24	Akhtar M W, Kleis S J. Boiling flow simulations on adaptive octree grids [J]. Int. J. Multiphase Flow, 2013, 53: 88-99.
25	曹志柱, 孙东亮, 魏进家, 等. 基于非结构化VOSET方法的沸腾传热[J]. 科学通报, 2020, 65(17): 1723-1733.
	Cao Z Z, Sun D L, Wei J J, et al. Boiling heat transfer by using the VOSET method based on unstructured grids [J]. Chinese Science Bulletin, 2020, 65(17): 1723-1733.
26	Klimenko V V. Film boiling on a horizontal plate — new correlation [J]. Int. J. Heat Mass Transfer, 1981, 24: 69-79.
27	Berenson P J. Film-boiling heat transfer from a horizontal surface [J]. J. Heat Transfer, 1961, 83(3): 351-356.

[1]	Zhanyu YE, He SHAN, Zhenyuan XU. Performance simulation of paper folding-like evaporator for solar evaporation systems [J]. CIESC Journal, 2023, 74(S1): 132-140.
[2]	Shuangxing ZHANG, Fangchen LIU, Yifei ZHANG, Wenjing DU. Experimental study on phase change heat storage and release performance of R-134a pulsating heat pipe [J]. CIESC Journal, 2023, 74(S1): 165-171.
[3]	Long ZHANG, Mengjie SONG, Keke SHAO, Xuan ZHANG, Jun SHEN, Runmiao GAO, Zekang ZHEN, Zhengyong JIANG. Simulation study on frosting at windward fin end of heat exchanger [J]. CIESC Journal, 2023, 74(S1): 179-182.
[4]	Yifei ZHANG, Fangchen LIU, Shuangxing ZHANG, Wenjing DU. Performance analysis of printed circuit heat exchanger for supercritical carbon dioxide [J]. CIESC Journal, 2023, 74(S1): 183-190.
[5]	Zhiguo WANG, Meng XUE, Yushuang DONG, Tianzhen ZHANG, Xiaokai QIN, Qiang HAN. Numerical simulation and analysis of geothermal rock mass heat flow coupling based on fracture roughness characterization method [J]. CIESC Journal, 2023, 74(S1): 223-234.
[6]	He JIANG, Junfei YUAN, Lin WANG, Guyu XING. Experimental study on the effect of flow sharing cavity structure on phase change flow characteristics in microchannels [J]. CIESC Journal, 2023, 74(S1): 235-244.
[7]	Yanpeng WU, Qianlong LIU, Dongmin TIAN, Fengjun CHEN. A review of coupling PCM modules with heat pipes for electronic thermal management [J]. CIESC Journal, 2023, 74(S1): 25-31.
[8]	Xin YANG, Wen WANG, Kai XU, Fanhua MA. Simulation analysis of temperature characteristics of the high-pressure hydrogen refueling process [J]. CIESC Journal, 2023, 74(S1): 280-286.
[9]	Jiahao SONG, Wen WANG. Study on coupling operation characteristics of Stirling engine and high temperature heat pipe [J]. CIESC Journal, 2023, 74(S1): 287-294.
[10]	Siyu ZHANG, Yonggao YIN, Pengqi JIA, Wei YE. Study on seasonal thermal energy storage characteristics of double U-shaped buried pipe group [J]. CIESC Journal, 2023, 74(S1): 295-301.
[11]	Congqi HUANG, Yimei WU, Jianye CHEN, Shuangquan SHAO. Simulation study of thermal management system of alkaline water electrolysis device for hydrogen production [J]. CIESC Journal, 2023, 74(S1): 320-328.
[12]	Ruitao SONG, Pai WANG, Yunpeng WANG, Minxia LI, Chaobin DANG, Zhenguo CHEN, Huan TONG, Jiaqi ZHOU. Numerical simulation of flow boiling heat transfer in pipe arrays of carbon dioxide direct evaporation ice field [J]. CIESC Journal, 2023, 74(S1): 96-103.
[13]	Song HE, Qiaomai LIU, Guangshuo XIE, Simin WANG, Juan XIAO. Two-phase flow simulation and surrogate-assisted optimization of gas film drag reduction in high-concentration coal-water slurry pipeline [J]. CIESC Journal, 2023, 74(9): 3766-3774.
[14]	Yuanchao LIU, Bin GUAN, Jianbin ZHONG, Yifan XU, Xuhao JIANG, Duan LI. Investigation of thermoelectric transport properties of single-layer XSe₂(X=Zr/Hf) [J]. CIESC Journal, 2023, 74(9): 3968-3978.
[15]	Zhewen CHEN, Junjie WEI, Yuming ZHANG. System integration and energy conversion mechanism of the power technology with integrated supercritical water gasification of coal and SOFC [J]. CIESC Journal, 2023, 74(9): 3888-3902.