تشکیل یخ بر روی سطوح در معرض جریان حاوی قطرات فوق سرد با روش هیدرودینامیک ذرات هموار

نوع مقاله : مقاله پژوهشی

نویسنده

گروه مهندسی شیمی، دانشکده فنی و مهندسی، دانشگاه ولی عصر(عج)، رفسنجان، ایران

چکیده

برای شبیه­سازی پدیدۀ سه فازی تشکیل یخ روی یک جسم جامد که در معرض جریان هوای مرطوب قرار دارد، از روش هیدرودینامیک ذرات هموار با فرض قابلیت تراکم ضعیف با در نظر گرفتن معادلات در مختصات سه بعدی استفاده شد. فرض شد که هوا حامل قطرات آب فوق سرد است که در صورت برخورد به سطح جامد بخشی از این قطرات تغییر فاز داده، به یخ تبدیل می­شوند. برای توصیف این پدیده معادلات هیدرودینامیک سیال به همراه معادلات موازنۀ انرژی در نظرگرفته و حل شد. از آنجا که بازده جمع­آوری سطح به‌دست آمده از این روش برای جریان روی کره با آنچه که در منابع به‌دست آمده است، مطابقت خوبی داشت اعتبار روش تأیید شد. سپس از این روش برای پیش‌بینی فرایند تشکیل یخ در شرایط مختلف استفاده شد. از جمله اثر عدد بی بعد استوکس بر بازده محلی جمع­آوری و اثر شار حرارتی سطح بر بازده محلی و متوسط تشکیل یخ بررسی شد. مشاهده شد که بازده جمع­آوری در مرکز جسم بیشتر بوده و با افزایش عدد استوکس بیشتر می­شود. متعاقباً بازده متوسط تشکیل یخ با افزایش شار کاهش می­یابد، هم­چنین بازده کلی تشکیل یخ در مرکز جسم بیشتر و در کناره­ها کمتر است.

کلیدواژه‌ها


عنوان مقاله [English]

Predicting Ice Formation on the Surfaces Exposed to the Air Containing Supercooled Droplets Using Smooth Particle Hydrodynamics Method

نویسنده [English]

  • M. M. Kamyabi
Vali-e-Asr University of Rafsanjan
چکیده [English]

Weakly Compressible Smoothed Particle Hydrodynamics (WCSPH) was applied to simulate the three dimensional, three-phase phenomenon of ice formation on a solid surface exposed to the humid airflow. It was assumed that air contains supercooled droplets of that, upon collision with a solid surface, some of them undergo a phase change and turn to ice. To describe this phenomenon, fluid hydrodynamic equations along with energy balance equations were considered and solved. The validity of the method was confirmed because the collection efficiency obtained from this method for flow on spheres was in good agreement with the literature. Then this method was used to predict this process in different conditions. The effect of Stokes dimensionless number on local collection efficiency and the effect of surface heat flux on the local and average ice formation efficiency were investigated. It was observed that the collection efficiency is higher in the center of the body and increases with increasing Stokes number. Consequently, the average efficiency of ice formation decreases with increasing flux. Also, the overall efficiency of ice formation in the center of the body is higher and less at the sides.

کلیدواژه‌ها [English]

  • Smoothed Particle Hydrodynamics (SPH)
  • Phase change
  • Collection Efficiency
  • heat flux

 

[1]           Heinrich, A., Ross, R., Zumwalt, G., Provorse, J., Padmanabhan, V., Aircraft Icing Handbook. 1st edition ,Volume 2., Gates Learjet Corp Wichita KS , Lower Hutt, pp. 24-39 (1991).
[2]           Habashi, W. G., "Recent advances in CFD for in-flight icing simulations", Japan Society of Fluid Mechanics, 28(2), pp. 99-118 (2009).
[3]           Farzaneh, M., "Ice accretions on high–voltage conductors and insulators and related phenomena", Philosophical Transactions of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences,. 358(1776), pp. 2971-3005, (2000).
[4]           Hirata, T., Nagasaka, K., Ishikawa, M., "Crystal ice formation of solution and its removal phenomena at cooled horizontal solid surface: Part I: Ice removal phenomena", International journal of heat and mass transfer, 43(3), pp. 333-339, (2000)
 
 
 
 
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7/0
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4/0
3/0
2/0
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1/0                                         05/0                                            0                                           05/0-                                       1/0-
فاصله از مرکز (متر)
 
بازده جمع‌آوری
جزء جرمی یخ تشکیل شده
بازده تشکیل یخ
 
شکل 7. نرخ تشکیل یخ روی سطح در سرعت‌های نسبی مختلف بین هوا و مانع فیزیکی.
 
 
 
[5]           Hayashi, R., Yamamoto, M., "Numerical Simulation on Ice Shedding Phenomena in Turbomachinery." International Journal of Energy and Power Engineering, pp. 45-53, (2015).
[6]           Silva, G. A. L. d., Silvares, O. D. M., Zerbini, E. J. D. G. J., "Numerical simulation of airfoil thermal anti-ice operation, part 2: implementation and results", Journal of aircraft, 44(2), pp. 634-641, (2007).
[7]           Politovich, M. K., "Aircraft icing caused by large supercooled droplets", Journal of Applied Meteorology, 28(9), pp. 856-868, (1989).
[8]           Flemming, R. J., Britton, R. K., Bond. T. H., "Model rotor icing tests in the NASA" Lewis Icing Research Tunnel. (1991).
[9]           Fortin, G., Perron J., "Spinning rotor blade tests in icing wind tunnel", in 1st AIAA Atmospheric and Space Environments Conference, p. 4260, (2009).
[10]         Cui, X., Bakkar, A., Habashi, W. G., "A multiphase SPH framework for supercooled large droplets dynamics", International Journal of Numerical Methods for Heat & Fluid Flow, pp. 101-115, (2019).
[11]         Pulley, R., Walters, J., "The effect of interception on particle collection by spheres and cylinders", Journal of aerosol science, 21(6), pp. 733-743, (1990).
[12]         Da Silveira, R. A., Maliska, C. R., Estivam, D. A., Mendes, R., "Evaluation of collection efficiency methods for icing analysis", in Proceedings of 17th International Congress of Mechanical Engineering. (2003).
[13]         Abdollahi, V., Habashi, W. G., Fossati, M.,
"Multi-phase smoothed particle hydrodynamics modeling of supercooled large droplet dynamics for in-flight icing conditions", Aerospace Science and Technology, 82, pp. 252-261, (2018).
[14]         Liu, G. R., Liu M. B., Smoothed particle hydrodynamics: a meshfree particle method. World scientific. Singapore, pp. 110-140, (2003)
[15]         Tezduyar, T. "Interface-tracking and interface-capturing techniques for computation of moving boundaries and interfaces", in Proceedings of the Fifth World Congress on Computational Mechanics, (2002).
[16]         Lucy, L. B., "A numerical approach to the testing of the fission hypothesis", The astronomical journal, 82, pp. 1013-1024, (1977).
[17]         Gingold, R. A., Monaghan J. J., "Smoothed particle hydrodynamics: theory and application to non-spherical stars", Monthly notices of the royal astronomical society, 181(3), pp. 375-389, (1977).
 
[18]         Marrone, S., Antuono, M. A. G. D., Colagrossi, A., Colicchio, G., Le Touzé, D., Graziani, G., "δ-SPH model for simulating violent impact flows", Computer Methods in Applied Mechanics and Engineering, 200(13-16), pp. 1526-1542, (2011).
[19]         Kamyabi, M., Ramazani, A., Kamyabi, A., "Transient Analysis of Falling Cylinder in Non-Newtonian Fluids: Further Opportunity to Employ the Benefits of SPH Method in Fluid–Structure Problems", Chemical Product and Process Modeling, 12(1), pp. 29-39 )2017).
[20]         Farrokhpanah, A., Bussmann M., Mostaghimi, J., "New smoothed particle hydrodynamics (SPH) formulation for modeling heat conduction with solidification and melting", Numerical Heat Transfer, Part B: Fundamentals, 71(4), pp. 299-312, (2017).
[21]         Monaghan, J. J., Huppert, H. E., Worster M. G., "Solidification using smoothed particle hydrodynamics", Journal of Computational Physics, 206(2), pp. 684-705, (2005).
[22]         Cleary, P. W., "Extension of SPH to predict feeding, freezing and defect creation in low pressure die casting", Applied Mathematical Modelling, 34(11), pp. 3189-3201, (2010).
[23]         Alexiadis, A., Ghraybeh, S., Qiao, G., "Natural convection and solidification of phase-change materials in circular pipes: A SPH approach", Computational Materials Science, 150,
pp. 475-483, (2018).
[24]         Zhang, M., Zhang, H., Zheng, L., "Numerical investigation of substrate melting and deformation during thermal spray coating by SPH method", Plasma Chemistry and Plasma Processing, 29(1), pp. 55-68, (2009).
[25]         Abdollahi, V., Habashi, W. G., Fossati, M., "Hybrid quasi molecular-continuum modeling of supercooled large droplet dynamics for in-flight icing conditions", in 54th AIAA Aerospace Sciences Meeting, p. 0061, (2016).
[26]         Messinger, B. L., "Equilibrium temperature of an unheated icing surface as a function of air speed", Journal of the aeronautical sciences, 20(1),
pp. 29-42, (1953).
[27]         Müller, M., Charypar, D., Gross, M., "Particle-based fluid simulation for interactive applications", in Proceedings of the symposium on Computer animation, pp. 154-159, (2003).
[28] Kelager, M., Lagrangian fluid dynamics using smoothed particle hydrodynamics. University of Copenhagen: Department of Computer Science, (2006).