Home Numerical investigation of inlet pressure effects on condensation flow regime in a supersonic nozzle
Article
Licensed
Unlicensed Requires Authentication

Numerical investigation of inlet pressure effects on condensation flow regime in a supersonic nozzle

  • Yu Qian EMAIL logo
Published/Copyright: February 19, 2025
Become an author with De Gruyter Brill
Submit Manuscript Author Information
Chemical Product and Process Modeling
From the journal Chemical Product and Process Modeling Volume 20 Issue 3

Abstract

Non-equilibrium condensation (NEC) is a prevalent phenomenon in various industrial equipment, and it can substantially affect their operational efficiency and overall performance. Droplet nucleation and growth is one of the important aspects of NEC and needs to be investigated and studied, whatever affects these parameters. On the other hand, NEC has a considerable impact on the flow pattern and condensation shock causes a sudden change in flow parameters. This study has been conducted with the aim of investigating the impact of inlet pressure (IP) on the flow pattern and two-phase flow parameters. The values of 90 kPa, 95 kPa, 99.98 kPa, 105 kPa, and 110 kPa are considered as the nozzle IP for this investigation, and its impact on the parameters of pressure, temperature, speed, density, droplet radius, liquid mass fraction (LMF), nucleation rate, Number of drops and condensed mass rate. According to the results, as the IP increases, the condensation shock occurs earlier and the LMF in the nozzle increases. As the pressure increases from 90 kPa to 110 kPa, the amount of LMF increases by about 5.7 %, and more LMF is produced in the nozzle. This study provides a good understanding of the impact of IP on NEC.

Keywords: non-equilibrium condensation; supersonic nozzle; inlet pressure; liquid phase; nucleation rate
Corresponding author: Yu Qian, Fushun Vocational Technology Institute, Fushun 113122, Liaoning, China, E-mail:

Funding source: the National Natural Science Foundation of China

Award Identifier / Grant number: 52106208

Funding source: the Natural Science Foundation of Sichuan Province

Award Identifier / Grant number: 2023NSFSC0924

Acknowledgments

I would like to take this opportunity to acknowledge that there are no individuals or organizations that require acknowledgment for their contributions to this work.

  1. Research ethics: Research involving Human Participants and Animals: The observational study conducted on medical staff needs no ethical code. Therefore, the above study was not required to acquire ethical code.

  2. Informed consent: This option is not necessary due to that the data were collected from the references.

  3. Author contributions: All authors contributed to the study’s conception and design. Data collection, simulation and analysis were performed by “Yu Qian”. The first draft of the manuscript was written by “Yu Qian”.

  4. Use of Large Language Models, AI and Machine Learning Tools: To ensure the integrity of my research, I affirm that this study does not utilize any large language models, AI, or machine learning tools in its methodology or analysis.

  5. Conflict of interest: The authors declare no competing of interests.

  6. Research funding: This work was supported by the National Natural Science Foundation of China (grant number 52106208), and the Natural Science Foundation of Sichuan Province (2023NSFSC0924).

  7. Data availability: The authors do not have permissions to share data.

Appendix A

NEC in supersonic nozzle

As illustrated in Figure A1, a typical CD nozzle experiences expansion of the working fluid. This expansion process is accompanied by a phase change, starting with superheated dry steam and progressing towards a state containing both vapor and liquid (wet steam). As depicted in Figure A1, at Point 1, the stream enters the channel or nozzle as superheated dry vapor. The vapor expands towards sonic conditions at the throat due to the divergent shape of the channel. Between Points 1 and 2, the steam maintains its superheated dry state, signifying that it has not yet reached the conditions where condensation begins. The saturation line, marking the onset of liquid phase formation, is crossed at Point 3. The precise place of this transition (after of before the throat) is influenced by the particular geometry of the channel and the extent to which the steam is expanded. In this region, liquid droplets begin to form and dissipate within the vapor, but their nucleation rate is initially quite low. Consequently, the vapor continues to expand as a dry stream in a metastable condition. A significant increase in the nucleation rate occurs, culminating at spot 4. Beyond this spot, the rate of droplet formation becomes constant, leading to a stable number of droplets within the flow. These droplets subsequently experience rapid growth between Points 4 and 5, facilitating the progression towards a state where the flow is in thermodynamic balance. The expansion of the stream between spots 5 and 6 happens close to equilibrium states. As the system reaches thermodynamic stability through a condensation, latent heat is released from the liquid state to the steam state. This heat emission results in a shock of pressure between spots 5 and 4, revealing the taking place of the condensation process within the expanding flow [54].

Figure A1: NEC in supersonic nozzle [54].
Figure A1:

NEC in supersonic nozzle [54].

References

1. Xu, Y, Zhang, X, Bai, Y, Li, X. Numerical investigation of liquid mass fraction and condensation shock of wet-steam flow through convergence-divergence nozzle using strategic water droplets injection. Chem Prod Process Model 2024;19:315–27. https://doi.org/10.1515/cppm-2023-0043.Search in Google Scholar

2. Wu, Z, Gang, J. Numerical investigation of exit pressure on flow structure in steam ejector by considering condensation and evaporation process. In: Proceedings of the Indian National Science Academy 2024;90:113–23.10.1007/s43538-023-00227-0Search in Google Scholar

3. Lin, Y, Xie, Z, Guan, W, Gan, L. Numerical investigation of discharge pressure effect on steam ejector performance in renewable refrigeration cycle by considering wet steam model and dry gas model. Chem Prod Process Model 2024;19:535–50. https://doi.org/10.1515/cppm-2023-0092.Search in Google Scholar

4. Cong, H, Zhang, J. Numerical investigation of the effects of dry gas model and wet steam model in solar-driven refrigeration ejector system. Chem Prod Process Model 2023;16.10.1515/cppm-2023-0042Search in Google Scholar

5. zhang Wang, H. Energy and exergy analysis of primary steam superheating effects on the steam ejector applied in the solar renewable refrigeration cycle in the presence of spontaneous nucleation. Chem Prod Process Model 2023;1.10.1515/cppm-2023-0038Search in Google Scholar

6. Fu, M, Ding, Y. Investigating the effects of outlet pressure from steam turbine blade on wetness and entropy generation with consideration of non-equilibrium condensation. Computational Thermal Sciences. Int J 2023;15. https://doi.org/10.1615/computthermalscien.2023048626.Search in Google Scholar

7. Zhang, G, Wang, X, Dykas, S, Aliabadi, MA. Reduction entropy generation and condensation by NaCl particle injection in wet steam supersonic nozzle. Int J Therm Sci 2022;171:107207. https://doi.org/10.1016/j.ijthermalsci.2021.107207.Search in Google Scholar

8. Kouchaksaraei, SJ, Akrami, M. Numerical investigation of non-equilibrium condensation in a supersonic nozzle based on spontaneous nucleation. Aerospace 2024;11:1032. https://doi.org/10.3390/aerospace11121032.Search in Google Scholar

9. Aliabadi, MA, Jahangiri, A, Khazaee, I, Lakzian, E. Investigating the effect of water nano-droplets injection into the convergent-divergent nozzle inlet on the wet steam flow using entropy generation analysis. Int J Therm Sci 2020;149:106181. https://doi.org/10.1016/j.ijthermalsci.2019.106181.Search in Google Scholar

10. Jahangiri, A, Aliabadi, MA, Pourranjbar, D, Mottahedi, HR, Gharebaei, H, Ghamati, E. A comprehensive investigation of non-condensable gas and condenser temperature effects on power plant ejector performance by considering condensation flow regime. Therm Sci Eng Prog 2023;45:102128. https://doi.org/10.1016/j.tsep.2023.102128.Search in Google Scholar

11. Dykas, S, Majkut, M, Smołka, K, Strozik, M. Experimental research on wet steam flow with shock wave. Exp Heat Transf 2015;28:417–29. https://doi.org/10.1080/08916152.2014.913090.Search in Google Scholar

12. Dykas, S, Majkut, M, Smołka, K, Strozik, M. An attempt to make a reliable assessment of the wet steam flow field in the de Laval nozzle. Heat Mass Tran 2018;54:2675–81. https://doi.org/10.1007/s00231-018-2313-7.Search in Google Scholar

13. Faghih Aliabadi, MA, Mahpeykar, MR. Comparison between polydispersed and monodispersed models on condensing water-vapor flow in a supersonic convergent-divergent nozzle. Modares Mech Eng 2017;17:19–30.Search in Google Scholar

14. Amiri Rad, E, Mahpeykar, MR, Teymourtash, AR. Analytic investigation of the effects of condensation shock on turbulent boundary layer parameters of nucleating flow in a supersonic convergent-divergent nozzle. Sci Iran 2014;21:1709–18.Search in Google Scholar

15. Dolatabadi, AM, Pour, MS, Rezaee, K, Ajarostaghi, SS. Applying machine learning for optimization of dehumidification strategy on the modified model for the non-equilibrium condensation in steam turbines. Eng Anal Bound Elem 2022;145:13–24. https://doi.org/10.1016/j.enganabound.2022.09.013.Search in Google Scholar

16. Dolatabadi, AM, Eghbali, MJ, Florin-Emilian, Ț, Mohamadpour, E, Amini, R. Performance evaluation of condensing flow behavior considering magneto hydrodynamics field effects. Appl Therm Eng 2023;219:119472. https://doi.org/10.1016/j.applthermaleng.2022.119472.Search in Google Scholar

17. Dolatabadi, AM, Moslehi, J, Pour, MS, Ajarostaghi, SS, Poncet, S, Arıcı, M. Modified model of reduction condensing losses strategy into the wet steam flow considering efficient energy of steam turbine based on injection of nano-droplets. Energy 2022;242:122951. https://doi.org/10.1016/j.energy.2021.122951.Search in Google Scholar

18. Aliabadi, MA, Zhang, G, Dykas, S, Li, H. Control of two-phase heat transfer and condensation loss in turbine blade cascade by injection water droplets. Appl Therm Eng 2021;186:116541. https://doi.org/10.1016/j.applthermaleng.2020.116541.Search in Google Scholar

19. Aliabadi, MA, Bahiraei, M. Effect of water nano-droplet injection on steam ejector performance based on non-equilibrium spontaneous condensation: a droplet number study. Appl Therm Eng 2021;184:116236. https://doi.org/10.1016/j.applthermaleng.2020.116236.Search in Google Scholar

20. Li, H, Wang, X, Huang, H, Ning, J, Li, A, Tu, J. Numerical study on the effect of superheat on the steam ejector internal flow and entropy generation for MED-TVC desalination system. Desalination 2022;537:115874. https://doi.org/10.1016/j.desal.2022.115874.Search in Google Scholar

21. Yousefi Rad, E, Mahpeykar, MR. A novel hybrid approach for numerical modeling of the nucleating flow in Laval nozzle and transonic steam turbine blades. Energies 2017;10:1285. https://doi.org/10.3390/en10091285.Search in Google Scholar

22. Rad, EY, Mahpeykar, MR. Studying the effect of convergence parameter of CUSP’s scheme in 2D modeling of the novel combination of two schemes in nucleating steam flow in cascade blades. Numer Heat Tran, Part B: Fundam 2017;72:325–47. https://doi.org/10.1080/10407790.2017.1400319.Search in Google Scholar

23. Mahpeykar, MR, Mohammadi, AR. Effect of important thermophysical properties on condensation shock in a steam flow. J thermos-phys heat tran 2013;27:286–97. https://doi.org/10.2514/1.t3999.Search in Google Scholar

24. Amiri Rad, E, Naeemi, S, Davoodi, B. Examining the curvature dependency of surface tension in a nucleating steam flow. Heat Mass Tran 2020;56:207–17. https://doi.org/10.1007/s00231-019-02709-8.Search in Google Scholar

25. Mahpeykar, MR. On the theoretical treatment of two-dimensional nucleating flows of steam and comparison with measurements [Doctoral dissertation]. University of Birmingham; 1991.Search in Google Scholar

26. Aliabadi, MA, Lakzian, E, Khazaei, I, Jahangiri, A. A comprehensive investigation of finding the best location for hot steam injection into the wet steam turbine blade cascade. Energy 2020;190:116397. https://doi.org/10.1016/j.energy.2019.116397.Search in Google Scholar

27. Starzmann, J, Hughes, FR, White, AJ, Grübel, M, Vogt, DM. Numerical investigation of boundary layers in wet steam nozzles. J Eng Gas Turbines Power 2017;139:012606. https://doi.org/10.1115/1.4034213.Search in Google Scholar

28. Senguttuvan, S, Lee, JC. Numerical study of wet-steam flow in Moore nozzles. J Mech Sci Technol 2019;33:4823–30. https://doi.org/10.1007/s12206-019-0923-8.Search in Google Scholar

29. Wittmann, T, Bode, C, Friedrichs, J. The feasibility of an euler–Lagrange approach for the modeling of wet steam. J Eng Gas Turbines Power 2021;143:041004. https://doi.org/10.1115/1.4049859.Search in Google Scholar

30. Han, X, Guan, J, Zhu, Q, Han, Z. Application of quadratic regression orthogonal design to optimization surface heating for control wet steam condensation flow in nozzle. Case Stud Therm Eng 2022;34:101987. https://doi.org/10.1016/j.csite.2022.101987.Search in Google Scholar

31. Post, P, Winhart, B, di Mare, F. Large eddy simulation of a condensing wet steam turbine cascade. J Eng Gas Turbines Power 2021;143:021016. https://doi.org/10.1115/1.4049348.Search in Google Scholar

32. Deng, Q, Jiang, Y, Hu, Z, Li, J, Feng, Z. Condensation and expansion characteristics of water steam and carbon dioxide in a Laval nozzle. Energy 2019;175:694–703. https://doi.org/10.1016/j.energy.2019.03.108.Search in Google Scholar

33. Dolatabadi, AM, Pour, MS, Ajarostaghi, SS, Poncet, S, Hulme-Smith, C. Last stage stator blade profile improvement for a steam turbine under a non-equilibrium condensation condition: a CFD and cost-saving approach. Alex Eng J 2023;73:27–46. https://doi.org/10.1016/j.aej.2023.04.011.Search in Google Scholar

34. Aliabadi, MA, Lakzian, E, Jahangiri, A, Khazaei, I. Numerical investigation of effects polydispersed droplets on the erosion rate and condensation loss in the wet steam flow in the turbine blade cascade. Appl Therm Eng 2020;164:114478. https://doi.org/10.1016/j.applthermaleng.2019.114478.Search in Google Scholar

35. Hosseinizadeh, SE, Ghamati, E, Jahangiri, A, Majidi, S, Khazaee, I, Aliabadi, MA. Reduction of water droplets effects in steam turbine blade using multi-objective optimization of hot steam injection. Int J Therm Sci 2023;187:108155. https://doi.org/10.1016/j.ijthermalsci.2023.108155.Search in Google Scholar

36. Edalatpour, A, Hassanvand, A, Gerdroodbary, MB, Moradi, R, Amini, Y. Injection of multi hydrogen jets within cavity flameholder at supersonic flow. Int J Hydrogen Energy 2019;44:13923–31. https://doi.org/10.1016/j.ijhydene.2019.03.117.Search in Google Scholar

37. Salimi, H, Hashemipour, N, Karimi-Sabet, J, Amini, Y. Appling the computational fluid dynamics studies of the thermogravitational column for N2-CO2 and He-Ar gas mixtures separation. Chem Prod Process Model 2023;18:33–50. https://doi.org/10.1515/cppm-2021-0036.Search in Google Scholar

38. Lin, L, Cheng, W, Luo, X, Qin, F. On nitrogen condensation in hypersonic nozzle flows: numerical method and parametric study. Shock Waves 2014;24:179–89. https://doi.org/10.1007/s00193-013-0490-3.Search in Google Scholar

39. Mottahedi, HR, Aliabadi, MA, Gharehbaei, H, Iraj, L, Bouzari, S, Akrami, M, et al.. Effects of motive flow temperature on holding steam ejector performance under condenser temperature change by considering entropy generation and non-equilibrium condensation. Appl Therm Eng 2024;257:124268. https://doi.org/10.1016/j.applthermaleng.2024.124268.Search in Google Scholar

40. Man, Y. Prediction of surface heating effect on non-equilibrium homogeneous condensation in supersonic nozzle using CFD method. Chem Prod Process Model 2024;23.10.1515/cppm-2024-0061Search in Google Scholar

41. Ding, H, Zhang, Y, Sun, C, Lakzian, E, Wen, C, Wang, C. Unsteady non-equilibrium condensation flow of 3-D wet steam stage of the steam turbine with roughness using sliding mesh method. Int J Therm Sci 2022;179:107674. https://doi.org/10.1016/j.ijthermalsci.2022.107674.Search in Google Scholar

42. Zhang, G, Wang, X, Pourranjbar, D, Dykas, S, Li, H, Chen, J. The comprehensive analysis of the relationship between the latent heat, entrainment ratio, and ejector performance under different superheating degree conditions considering the non-equilibrium condensation. Appl Therm Eng 2022;200:117701. https://doi.org/10.1016/j.applthermaleng.2021.117701.Search in Google Scholar

43. Zhang, G, Wang, F, Wang, D, Wu, T, Qin, X, Jin, Z. Numerical study of the dehumidification structure optimization based on the modified model. Energy Convers Manag 2019;181:159–77. https://doi.org/10.1016/j.enconman.2018.12.001.Search in Google Scholar

44. Dolatabadi, AM, Mottahedi, HR, Aliabadi, MA, Pour, MS, Wen, C, Akrami, M. Evaluating and optimizing of steam ejector performance considering heterogeneous condensation using machine learning framework. Energy 2024;305:132240. https://doi.org/10.1016/j.energy.2024.132240.Search in Google Scholar

45. Lai, S, Wang, W. A comprehensive investigation of two-phase flow in off-design operating condition of ejector performance by using entropy generation analysis. In: Proceedings of the Indian National Science Academy 2024;23:1–3.10.1007/s43538-024-00301-1Search in Google Scholar

46. Zhang, G, Wang, X, Jin, Z, Dykas, S, Smołka, K. Numerical study of the loss and power prediction based on a modified non-equilibrium condensation model in a 200 MW industrial-scale steam turbine under different operation conditions. Energy 2023;275:127530. https://doi.org/10.1016/j.energy.2023.127530.Search in Google Scholar

47. Dolatabadi, AM, Aliabadi, MA. Evaluating sustainability power plant efficiency: unveiling the impact of power plant load ratio on holding steam ejector performance. Energy 2024;305:132315. https://doi.org/10.1016/j.energy.2024.132315.Search in Google Scholar

48. Zhang, G, Li, Y, Jin, Z, Dykas, S. Prediction of the non-equilibrium condensation characteristic of CO2 based on a Laval nozzle to improve carbon capture efficiency. Fuel 2025;381:133303. https://doi.org/10.1016/j.fuel.2024.133303.Search in Google Scholar

49. Zhang, G, Yang, Y, Chen, J, Jin, Z, Dykas, S. Numerical study of heterogeneous condensation in the de Laval nozzle to guide the compressor performance optimization in a compressed air energy storage system. Appl Energy 2024;356:122361. https://doi.org/10.1016/j.apenergy.2023.122361.Search in Google Scholar

50. Hui, X, Ma, Y, Deng, X. Numerical simulation on effects of augmentation in temperature of inlet steam on wet steam flow in supersonic nozzle: energy and exergy analysis. Multiscale Multidiscip Model Exp Des 2023;6:723–32. https://doi.org/10.1007/s41939-023-00164-x.Search in Google Scholar

51. Hu, P, Zhao, P, Li, Q, Hou, T, Wang, S, Cao, L, et al.. Performance of non-equilibrium condensation flows in a wet steam zone of the steam turbine based on modified model. Energy 2023;267:126571. https://doi.org/10.1016/j.energy.2022.126571.Search in Google Scholar

52. Xia, R, Li, D, Faghih Aliabadi, MA. A comprehensive investigation and optimization of superheat degree on performance of supersonic nozzle by considering non-equilibrium condensation and entropy generation analysis. Phys Fluids 2024;36. https://doi.org/10.1063/5.0224884.Search in Google Scholar

53. Zhang, G, Dykas, S, Majkut, M, Smołka, K, Cai, X. Experimental and numerical research on the effect of the inlet steam superheat degree on the spontaneous condensation in the IWSEP nozzle. Int J Heat Mass Tran 2021;165:120654. https://doi.org/10.1016/j.ijheatmasstransfer.2020.120654.Search in Google Scholar

54. Lakzian, E, Yazdani, S, Salmani, F, Mahian, O, Kim, HD, Ghalambaz, M, et al.. Supersonic separation towards sustainable gas removal and carbon capture. Prog Energy Combust Sci 2024;103:101158. https://doi.org/10.1016/j.pecs.2024.101158.Search in Google Scholar
Received: 2024-03-30
Accepted: 2025-02-02
Published Online: 2025-02-19

© 2025 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. An improvement of level control of non-linear horizontal tank process using sliding mode controller
  4. Numerical investigation of inlet pressure effects on condensation flow regime in a supersonic nozzle
  5. Effects of tapered helical obstacles on heat transfer in tubes
  6. Gasification process prediction using a novel and reliable metaheuristic algorithm coupled with the K-nearest neighbors
  7. Evaluating the ionic liquids, commercial solvents, and pressure-swing for efficient azeotropic separation
  8. A synergistic approach to CO2 sequestration: evaluating trapping mechanisms in saline aquifers
  9. Diffusion modeling and optimization of drying dynamics of ogbono seed (Irvingea gabonensis): empirical insights into energy indices and process conditions
  10. Production of polyphenol extracts with antioxidant activity from olive pomace: process modeling and optimization
https://doi.org/10.1515/cppm-2024-0022
Keywords for this article
non-equilibrium condensation; supersonic nozzle; inlet pressure; liquid phase; nucleation rate

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. An improvement of level control of non-linear horizontal tank process using sliding mode controller
  4. Numerical investigation of inlet pressure effects on condensation flow regime in a supersonic nozzle
  5. Effects of tapered helical obstacles on heat transfer in tubes
  6. Gasification process prediction using a novel and reliable metaheuristic algorithm coupled with the K-nearest neighbors
  7. Evaluating the ionic liquids, commercial solvents, and pressure-swing for efficient azeotropic separation
  8. A synergistic approach to CO2 sequestration: evaluating trapping mechanisms in saline aquifers
  9. Diffusion modeling and optimization of drying dynamics of ogbono seed (Irvingea gabonensis): empirical insights into energy indices and process conditions
  10. Production of polyphenol extracts with antioxidant activity from olive pomace: process modeling and optimization
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 19.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/cppm-2024-0022/html
Scroll to top button