Effects of the Wall Temperature on Rarefied Gas Flows and Heat Transfer in a Micro-Nozzle
Abstract
:1. Introduction
2. Numerical Simulation
2.1. Direct Simulation Monte Carlo Method
2.2. Simulation Models
2.3. Validations of the Numerical Results
3. Results and Discussion
3.1. Flow Regime Spatial Distributions and Local Kn Distribution
3.2. Mach Number and Slip Velocity Distribution
3.3. Temperature and Wall Heat Flux Distribution
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
- Luo, J.; Chen, L.S.; Duan, H.Z.; Gong, Y.G.; Hu, S.; Ji, J.; Liu, Q.; Mei, J.; Milyukov, V.; Sazhin, M.; et al. TianQin: A space-borne gravitational wave detector. Class. Quantum Gravity 2016, 33, 035010. [Google Scholar] [CrossRef]
- Hu, W.R.; Wu, Y.L. The Taiji Program in Space for gravitational wave physics and the nature of gravity. Natl. Sci. Rev. 2017, 4, 685–686. [Google Scholar] [CrossRef]
- Schleicher, A.; Ziegler, T.; Schubert, R.; Brandt, N.; Bergner, P.; Johann, U.; Fichter, W.; Grzymisch, J. In-orbit performance of the LISA Pathfinder drag-free and attitude control system. CEAS Space J. 2018, 10, 471–485. [Google Scholar] [CrossRef]
- Köhler, J.; Bejhed, J.; Kratz, H.; Bruhn, F.; Lindberg, U.; Hjort, K.; Stenmark, L. A hybrid cold gas microthruster system for spacecraft. Sens. Actuators A Phys. 2002, 97, 587–598. [Google Scholar] [CrossRef]
- Gamero-Castano, M.; Hruby, V.; Spence, D.; Demmons, N.; McCormick, R.; Gasdaska, C. Micro Newton Colloid Thruster System Development for ST7-DRS Mission. In Proceedings of the 39th AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, Huntsville, AL, USA, 20–23 July 2003; p. 4543. [Google Scholar]
- Keller, A.; Köhler, P.; Hey, F.G.; Berger, M.; Braxmaier, C.; Feili, D.; Weise, D.; Johann, U. Parametric Study of HEMP-Thruster Downscaling to μN Thrust Levels. IEEE Trans. Plasma Sci. 2014, 43, 45–53. [Google Scholar] [CrossRef]
- Bird, G.A. Molecular Gas Dynamics and the Direct Simulation of Gas Flows; Oxford University Press: Oxford, UK, 1994. [Google Scholar]
- Li, D.; Yang, R.; Cao, H.; Yao, F.; Shen, C.; Zhang, C.; Wu, S. Experimental study on gas flow in a rough microchannel. Front. Energy Res. 2022, 10, 863733. [Google Scholar] [CrossRef]
- Sebastiao, I.B.; Santos, W.F.N. Impact of surface discontinuities on flowfield structure of a micro nozzle array. Nanoscale Microscale Thermophys. Eng. 2015, 18, 54–79. [Google Scholar] [CrossRef]
- Bird, G.A. Approach to translational equilibrium in a rigid sphere gas. Phys. Fluids 1963, 6, 1518–1519. [Google Scholar] [CrossRef]
- Le, N.T.; Roohi, E.; Tran, T.N. Comprehensive assessment of newly-developed slip-jump boundary conditions in high-speed rarefied gas flow simulations. Aerosp. Sci. Technol. 2019, 91, 656–668. [Google Scholar] [CrossRef]
- Michalis, V.K.; Kalarakis, A.N.; Skouras, E.D.; Burganos, V.N. Rarefaction effects on gas viscosity in the Knudsen transition regime. Microfluid. Nanofluidics 2010, 9, 847–853. [Google Scholar] [CrossRef]
- Darbandi, M.; Roohi, E. Study of subsonic–supersonic gas flow through micro/nanoscale nozzles using unstructured DSMC solver. Microfluid. Nanofluidics 2011, 10, 321–335. [Google Scholar] [CrossRef]
- Rosa, P.; Karayiannis, T.G.; Collins, M.W. Single-phase heat transfer in microchannels: The importance of scaling effects. Appl. Therm. Eng. 2009, 29, 3447–3468. [Google Scholar] [CrossRef]
- Akhlaghi, H.; Roohi, E.; Stefanov, S. A comprehensive review on micro-and nano-scale gas flow effects: Slip-jump phenomena, Knudsen paradox, thermally-driven flows, and Knudsen pumps. Phys. Rep. 2023, 997, 1–60. [Google Scholar] [CrossRef]
- Ji, Y.; Yuan, K.; Chung, J.N. Numerical simulation of wall roughness on gaseous flow and heat transfer in a microchannel. Int. J. Heat Mass Transf. 2006, 49, 1329–1339. [Google Scholar] [CrossRef]
- Kandlikar, S.G.; Joshi, S.; Tian, S. Effect of channel roughness on heat transfer and fluid flow characteristics at low Reynolds numbers in small diameter tubes. Atmosphere 2001, 4, 7. [Google Scholar]
- Shams, M.; Khadem, M.H.; Hossainpour, S. Direct simulation of roughness effects on rarefied and compressible flow at slip flow regime. Int. Commun. Heat Mass Transf. 2009, 36, 88–95. [Google Scholar] [CrossRef]
- Alexeenko, A.A.; Fedosov, D.A.; Gimelshein, S.F.; Levin, D.A.; Collins, R.J. Transient heat transfer and gas flow in a MEMS-based thruster. J. Microelectromechanical Syst. 2006, 15, 181–194. [Google Scholar] [CrossRef]
- Louisos, W.; Hitt, D. Heat transfer & viscous effects in 2D & 3D supersonic micro-nozzle flows. In Proceedings of the 37th AIAA Fluid Dynamics Conference and Exhibit, Miami, FL, USA, 25–28 June 2007; p. 3987. [Google Scholar]
- Hameed, A.H.; Kafafy, R.; Asrar, W.; Idres, M. Two-dimensional flow properties of micronozzle under varied isothermal wall conditions. Int. J. Eng. Syst. Model. Simul. 2013, 5, 174–180. [Google Scholar] [CrossRef]
- Sukesan, M.K.; Shine, S.R. Thermal effects on flow through micronozzles with various geometries. In Proceedings of the 26th National and 4th International ISHMT-ASTFE Heat and Mass Transfer Conference, IIT Madras, Chennai-600036, Tamil Nadu, India, 17–20 December 2021; Begel House Inc.: Danbury, CT, USA, 2021. [Google Scholar]
- Rafi KM, M.; Deepu, M.; Rajesh, G. Effect of heat transfer and geometry on micro-thruster performance. Int. J. Therm. Sci. 2019, 146, 106063. [Google Scholar] [CrossRef]
- Pulvirenti, M.; Wagner, W.; Zavelani Rossi, M.B. Convergence of particle schemes for the Boltzmann equation. Eur. J. Mech. B Fluids 1994, 13, 339–351. [Google Scholar]
- He, X.; He, B.; Cai, G. Simulation of rocket plume and lunar dust using DSMC method. Acta Astronaut. 2012, 70, 100–111. [Google Scholar] [CrossRef]
- Lee, K.H. Plume simulation of liquid apogee engine for GEO satellite using parallel DSMC method. Comput. Fluids 2020, 208, 104612. [Google Scholar] [CrossRef]
- Oblapenko, G.; Goldstein, D.B.; Varghese, P.; Moore, C. Velocity-space Hybridization of DSMC and a Boltzmann Solver. In Proceedings of the AIAA Scitech 2020 Forum, Orlando, FL, USA, 6–10 January 2020; p. 1063. [Google Scholar]
- Saadati, S.A.; Roohi, E. Detailed investigation of flow and thermal field in micro/nano nozzles using Simplified Bernoulli Trial (SBT) collision scheme in DSMC. Aerosp. Sci. Technol. 2015, 46, 236–255. [Google Scholar] [CrossRef]
- Bird, G.A. Perception of numerical methods in rarefied gasdynamics. Prog. Astronaut. Aeronaut. 1989, 117, 211–226. [Google Scholar]
- Bird, G.A. Molecular gas dynamics. NASA STI/Recon Tech. Rep. A 1976, 76, 40225. [Google Scholar]
- Bird, G.A. Monte-Carlo simulation in an engineering context. Prog. Astronaut. Aeronaut. 1981, 74, 239–255. [Google Scholar]
- Koura, K.; Matsumoto, H. Variable soft sphere molecular model for inverse-power-law or Lennard-Jones potential. Phys. Fluids A Fluid Dyn. 1991, 3, 2459–2465. [Google Scholar] [CrossRef]
- Hassan, H.A.; Hash, D.B. A generalized hard-sphere model for Monte Carlo simulation. Phys. Fluids A Fluid Dyn. 1993, 5, 738–744. [Google Scholar] [CrossRef]
- Fan, J. A generalized soft-sphere model for Monte Carlo simulation. Phys. Fluids 2002, 14, 4399–4405. [Google Scholar] [CrossRef]
- Cercignani, C.; Lampis, M. Kinetic models for gas-surface interactions. Transp. Theory Stat. Phys. 1971, 1, 101–114. [Google Scholar] [CrossRef]
- Mohammadzadeh, A.; Roohi, E.; Niazmand, H.; Stefanov, S.; Myong, R.S. Detailed investigation of thermal and hydrodynamic behaviour in micro/nano cavity using DSMC. Phys. Rev. E 2012, 85, 056305. [Google Scholar]
- Liu, X.; Li, D.; Fu, X.; Gao, Y.; Wang, X. MODELING of Rarefied Gas Flows Inside a Micro-Nozzle Based on the DSMC Method Coupled with a Modified Gas–Surface Interaction Model. Energies 2023, 16, 505. [Google Scholar] [CrossRef]
Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |
© 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
Share and Cite
Zhang, S.; Li, Y.; Wang, X.; Lu, S.; Yu, Y.; Yang, J. Effects of the Wall Temperature on Rarefied Gas Flows and Heat Transfer in a Micro-Nozzle. Micromachines 2024, 15, 22. https://doi.org/10.3390/mi15010022
Zhang S, Li Y, Wang X, Lu S, Yu Y, Yang J. Effects of the Wall Temperature on Rarefied Gas Flows and Heat Transfer in a Micro-Nozzle. Micromachines. 2024; 15(1):22. https://doi.org/10.3390/mi15010022
Chicago/Turabian StyleZhang, Shurui, Yong Li, Xudong Wang, Songcai Lu, Yusong Yu, and Jun Yang. 2024. "Effects of the Wall Temperature on Rarefied Gas Flows and Heat Transfer in a Micro-Nozzle" Micromachines 15, no. 1: 22. https://doi.org/10.3390/mi15010022
APA StyleZhang, S., Li, Y., Wang, X., Lu, S., Yu, Y., & Yang, J. (2024). Effects of the Wall Temperature on Rarefied Gas Flows and Heat Transfer in a Micro-Nozzle. Micromachines, 15(1), 22. https://doi.org/10.3390/mi15010022