Numerical investigation of wall temperature effects on non-equilibrium condensation in supersonic nozzle using Eulerian-Eulerian model
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Xueyao Zhang
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Guodong Ma
Abstract
Non-equilibrium condensation (NEC) commonly arises in various industrial applications, including steam turbines, supersonic nozzles, and aerospace propulsion systems. This phenomenon can significantly impair system efficiency and reliability by introducing abrupt phase transitions and associated energy losses. To mitigate its effects, several control methods have been proposed, among which surface heating stands out as a widely studied technique. In most existing research, surface heating has been implemented by applying a heat flux to the nozzle walls. In contrast, the present study investigates a different approach, wherein a constant-temperature wall is employed to introduce surface heating directly into the supersonic flow. The objective is to evaluate how this thermal boundary condition affects key two-phase flow parameters, including droplet size, condensed mass, nucleation rate, droplet growth rate, and liquid mass fraction (LMF). The numerical framework is validated using experimental data from the International Wet Steam Experimental Project (IWSEP) nozzle, ensuring the reliability of the predictions. Following validation, the study examines the influence of two wall temperatures – 400 °C and 800 °C – on nozzle performance and condensation behavior. Results indicate that heating the wall to 800 °C induces substantial changes in the internal flow structure and condensation characteristics. Specifically, the condensation shock shifts noticeably downstream, and both the peak nucleation rate and maximum LMF decrease sharply – by approximately 91 % and 6 %, respectively – compared to an adiabatic baseline. Additionally, the analysis reveals a clear relationship between wall temperature and mass flow rate. As the wall temperature increases, the mass flow rate decreases, with a reduction of about 3.86 % observed at 800 °C. Overall, these findings demonstrate that surface heating through wall temperature control offers an effective mechanism to influence and manage the behavior of NEC, with important implications for improving the efficiency and control of high-speed flow systems.
Funding source: Science and Technology Research Project of Jilin Provincial Department of Education
Award Identifier / Grant number: JJKH20241761KJ
Funding source: Changchun Technical University of Automobile Scientific Research Project《Research on Abrasive Flow Machining Effect Prediction Model Based on BP Neural Network
Award Identifier / Grant number: XJKY202514
Acknowledgment
We would like to take this opportunity to acknowledge that there are no individuals or organizations that require acknowledgment for their contributions to this work.
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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.
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Informed consent: This option is not neccessary due to that the data were collected from the references.
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Author contributions: All authors contributed to the study’s conception and design. Data collection, simulation and analysis were performed by “ Xueyao Zhang, Guodong Ma and Jiamei Sun”. The first draft of the manuscript was written by ” Xueyao Zhang “and all authors commented on previous versions of the manuscript. All authors have read and approved the manuscript.
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Use of Large Language Models, AI and Machine Learning Tools: During the preparation of this work, the authors used Large Language Models, AI, and Machine Learning tools for tasks such as language refinement, data analysis, or figure generation, with all outputs being reviewed and validated by the authors to ensure accuracy and originality. After using these tools/services, the authors reviewed and edited the content and take full responsibility for the content of the published article.
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Conflict of interest: The authors declare no competing of interests.
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Research funding: This work was supported by Science and Technology Research Project of Jilin Provincial Department of Education, Project Number: JJKH20241761KJ. Changchun Technical University of Automobile Scientific Research Project《Research on Abrasive Flow Machining Effect Prediction Model Based on BP Neural Network》, Project Number: XJKY202514.
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Data availability: The authors do not have permissions to share data.
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