lagrange approach
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2021 ◽  
Vol 239 ◽  
pp. 116640
Author(s):  
Zhengzong Huang ◽  
Hongjie Yan ◽  
Liu Liu ◽  
Hao Gong ◽  
Ping Zhou

2021 ◽  
Author(s):  
Tim Wittmann ◽  
Christoph Bode ◽  
Jens Friedrichs
Keyword(s):  

2021 ◽  
Vol 143 (4) ◽  
Author(s):  
Tim Wittmann ◽  
Christoph Bode ◽  
Jens Friedrichs

Abstract This study investigates the applicability of an Euler–Lagrange approach for the calculation of nucleation and condensation of steam flows. Supersonic nozzles are used as generic validation cases, as their high expansion rates replicate the flow conditions in real turbines. Experimental and numerical validation data for these nozzles are provided by the International Wet Steam Modeling Project of Starzmann et al. (2018, “Results of the International Wet Steam Modeling Project,” Proc. Inst. Mech. Eng. A, 232(5), pp. 550–570). In contrast to most participants of that project, an Euler–Lagrange approach is utilized for this study. Therefore, the classical nucleation theory with corrections and different droplet growth laws is incorporated into the discrete phase model of ansysfluent. Suggestions for an efficient implementation are presented. The Euler–Lagrange results show a good agreement with the experimental and numerical validation data. The sensitivities of the Euler–Lagrange approach to modeling parameters are analyzed. Finally, an optimal parameter set for the calculation of nucleation and condensation is proposed.


Author(s):  
Tim Wittmann ◽  
Christoph Bode ◽  
Jens Friedrichs

Abstract This study investigates the applicability of an Euler-Lagrange approach for the calculation of nucleation and condensation of steam flows. Supersonic nozzles are used as generic validation cases, as their high expansion rates replicate the flow conditions in real turbines. Experimental and numerical validation data for these nozzles are provided by the International Wet Steam Modelling Project of Starzmann et al. (2018). In contrast to most participants of that project, an Euler-Lagrange approach is utilized for this study. Therefore, the classical nucleation theory with corrections and different droplet growth laws is incorporated into the Discrete Phase Model of ANSYS Fluent. Suggestions for an efficient implementation are presented. The Euler-Lagrange results show a good agreement with the experimental and numerical validation data. The sensitivities of the Euler-Lagrange approach to modelling parameters are analysed. Finally, an optimal parameter set for the calculation of nucleation and condensation is proposed.


Metals ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 1160
Author(s):  
Weidong Yang ◽  
Zhiguo Luo ◽  
Nannan Zhao ◽  
Zongshu Zou

A mathematic model considering the bubble coalescence and breakup using the Euler-Lagrange approach has been developed to study the effect of the initial bubble size on the distribution of bubbles captured by the solidification shell. A hard sphere model was applied for dealing with the bubble collision. Advanced bubble coalescence and breakup models suitable for the continuous casting system and an advanced bubble captured criteria have been identified established with the help of user-defined functions of FLUENT. The predictions of bubble behavior and captured bubble distribution agree with the water model and plant measurements well respectively. The results show that the number of small bubbles captured by solidification shell is much higher than that of large bubbles. What is more, the number of captured bubbles at the sidewalls decreases with the distance from the meniscus. For the case of large gas flow rate (gas flow fraction of 8.2%), the initial size of bubbles has little effect on bubble captured distribution under various casting speeds. When the gas flow rate is small (gas flow fraction of 4.1%), the number density of captured bubbles increases as the initial bubble size increases, and the effect of initial bubbles size on captured bubble number density is amplified when the casting speed decreases. The average captured bubble diameter is about 0.12–0.14 mm. Additionally, for all cases, the initial bubble size hardly affects the average size of captured bubbles.


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