Drag coefficient of a solid sphere under non-isothermal conditions

V. A. Arkhipov   ; S. A. Basalaev   ; K. G. Perfilieva   ; A. S. Usanina

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 71 (2021), pp. 13-24

Résumé

The results of an experimental study of the gravitational settling of single solid spherical particles under non-isothermal conditions (with the inequality of the temperature of the particle and the carrier medium) in a viscous fluid in the range of Reynolds numbers $\mathrm{Re} < 1$. The influence of the inequality of the temperature of the particle and the carrier medium on the drag coefficient of the hard sphere is analyzed. A comparison is made of experimental data on cooling and heating of a particle at the stationary rate of its deposition. Empirical dependences are obtained for the drag coefficient of a single hard sphere under non-isothermal conditions.

Détail

Keywords: solid sphere, gravitational settling, cooled particle, heated particle, temperature difference, experimental study.
Mots-clés : hydrodynamic drag coefficient

Bibliographie

[1] Nigmatulin R. I., Dinamika mnogofaznykh sred, v. 1, Nauka, M., 1987

[2] Asovskii V. P., “Osobennosti tusheniya lesnykh pozharov vertoletami s ispolzovaniem podvesnykh vodoslivnykh ustroistv”, Nauchnyi vestnik MGTU GA: Aeromekhanika i prochnost, 2009, no. 138, 142–149

[3] Piskunov M. V., Strizhak P. A., “Rost ploschadi poverkhnosti otdelivshikhsya fragmentov zhidkosti pri vysokotemperaturnom droblenii neodnorodnoi kapli vody”, Pisma v ZhTF, 43:12 (2017), 34–41 | DOI

[4] Pfender E., Lee Y. C., “Particle dynamics and particle heat and mass transfer in thermal plasmas. Part 1. The motion of a single particle without thermal effects”, Plasma Chemistry and Plasma Processing, 5:3 (1985), 211–237 | DOI

[5] Eisenklam P., Arunachalam S. A., “The drag resistance of burning drops”, Combustion and Flame, 10:2 (1966), 171–181 | DOI

[6] Boronenko M. P., Gulyaev I. P., Seregin A. E., “Model dvizheniya i nagreva chastits v plazmennoi strue”, Vestnik Yugorskogo gosudarstvennogo universiteta, 2012, no. 2 (25), 7–15

[7] Gulyaev I. P., Solonenko O. P., “Modelirovanie povedeniya polykh chastits ZrO$_2$ v plazmennoi strue s uchetom ikh termicheskogo rasshireniya”, Teplofizika i aeromekhanika, 20:6 (2013), 789–802

[8] Trapeznikov S. Yu., Lushkin K. A., “Issledovanie koeffitsienta gidravlicheskogo soprotivleniya pri neizotermicheskom dvizhenii vysokovyazkoi nefti po truboprovodu”, Setevoe izdanie «Neftegazovoe delo», 2011, no. 2, 304–312

[9] Bar-Ziv E., Zhao B., Mograbi E., Katoshevski D., Ziskind G., “Experimental validation of the Stokes law at nonisothermal conditions”, Physics of Fluids, 14:6 (2002), 20152018 | DOI

[10] Malai N. V., Glushak A. V., Limanskaya A. V., “Reshenie kraevoi zadachi medlennogo obtekaniya sfery vyazkim neizotermicheskim gazom”, Izv. vuzov. Matematika, 2016, no. 12, 54–65 | Zbl

[11] Aleksandrov V. Yu., Fridlender O. G., “Medlennye techeniya gaza i effekt otritsatelnogo soprotivleniya silno nagretoi sfericheskoi chastitsy”, Izvestiya Rossiiskoi akademii nauk. Mekhanika zhidkosti i gaza, 2008, no. 3, 168–177 | Zbl

[12] Zavershinskii I. P., Kogan E. Ya., “Vliyanie geterogennykh protsessov na poverkhnosti, obtekaemoi potokami neravnovesnykh gazov na gidrodinamicheskoe soprotivlenie”, Pisma v ZhTF, 25:5 (2000), 76–79

[13] Kassoy D. R., Adamson T. C., Messiter A. F., “Compressible low Reynolds number flow around a sphere”, The Physics of Fluids, 9:4 (1966), 671–681 | DOI | Zbl

[14] Galkin V. S., Kogan M. N., Fridlender O. G., “Obtekanie silno nagretoi sfery potokom gaza pri malykh chislakh Reinoldsa”, Prikladnaya matematika i mekhanika, 36:5 (1972), 880–885 | Zbl

[15] Fridlender O. G., “Techenie gaza okolo neravnomerno nagretoi sfery”, Uchenye zapiski TsAGI, 6:5 (1975), 55–57

[16] Boris A. Yu., “Dvizhenie ostyvayuschei ili nagrevayuscheisya v gaze sfericheskoi chastitsy”, Uchenye zapiski TsAGI, 15:6 (1984), 43–50

[17] Dong-Yan X., Xin-Can W., Xi C., “Motion and heating of non-spherical particles in a plasma jet”, Surface and Coatings Technology, 171 (2003), 149–156 | DOI

[18] Malai N. V., Limanskaya A. V., Shchukin E. R., “Solution of a boundary value problem for the Navier-Stokes equations linearized with respect to velocity: non isothermal flow of a gaseous medium past a uniformly heated sphere”, Differential Equations, 51:10 (2015), 1319–1329 | DOI | Zbl

[19] Malai N. V., Schukin E. R., Stukalov A. A., Ryazanov K. S., “Gravitatsionnoe dvizhenie ravnomerno nagretoi tverdoi chastitsy v gazovoi srede”, Prikladnaya mekhanika i tekhnicheskaya fizika, 49:1 (2008), 74–80

[20] Malai N. V., Schukin E. R., Stukalov A. A., Ryazanov K. S., “K voprosu o gravitatsionnom dvizhenii neravnomerno nagretoi tverdoi chastitsy v gazoobraznoi srede”, Zhurnal tekhnicheskoi fiziki, 80:3 (2010), 49–54

[21] Ziskind G., Zhao B., Katoshevski D., Bar-Ziv E., “Experimental study of the forces associated with mixed convection from a heated sphere at small Reynolds and Grashof numbers. Part I: Cross-flow”, International Journal of Heat and Mass Transfer, 44:23 (2001), 43814389 | DOI

[22] Mograbi E., Ziskind G., Katoshevski D., Bar-Ziv E., “Experimental study of the forces associated with mixed convection from a heated sphere at small Reynolds and Grashof numbers. Part II: Assisting and opposing flows”, International journal of heat and mass transfer, 45:12 (2002), 2423–2430 | DOI

[23] Matvienko O. V., Andropova A. O., “Issledovanie dvizheniya chastitsy v potoke zhidkosti vblizi podvizhnoi stenki”, Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mekhanika, 2015, no. 36, 85–92 | DOI

[24] Vasenin I. M., Arkhipov V. A., Butov V. G., Glazunov A. A., Trofimov V. F., Gazovaya dinamika dvukhfaznykh techenii v soplakh, Izd-vo Tomskogo un-ta, Tomsk, 1986