Methods for determining the drag coefficient at gas injection from the surface of spherical particle

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

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 76 (2022), pp. 56-69

Résumé

New methods for studying the effect of gas injection from the surface of a solid spherical particle on its drag coefficient in the transient and self-similar regimes of flow around the particle have been presented. An advantage of the proposed methods is the ability to isolate in a pure form the effect of the mass flux from the particle surface (without the effect of other factors, for example, particle acceleration) on the drag coefficient. New results of an experimental study of the effect of air flow blowing on the drag coefficient of a solid perforated sphere in the Reynolds number range $\mathrm{Re} = 133\div9900$ have been presented. It has been shown that the drag coefficient decreases when air is blown from the particle surface. As the Reynolds number $\mathrm{Re}$ increases, the drag coefficient $C_{D}$ upon gas injection in the transient flow regime decreases to a certain critical value corresponding to the onset of the self-similar regime. At the onset of the selfsimilar regime (reaching the critical value of $C_{D}$), the drag coefficient increases with an increase in the Reynolds number and asymptotically tends to a constant value $C_{D} = 0.44$. However, the opposite effect has been found for a small diameter of the particle ($D = 1$ cm) at a blowing velocity $u_{e} \ge 1.3$ m/s: an increase in the drag coefficient of the particle $C_{D}$ at air efflux from the particle surface in comparison with the drag coefficient value in the absence of gas flow injection ($u_{e} = 0$ m/s). This is apparently associated with a change in the characteristics of the boundary layer of the particle due to the rearrangement of the flow profile near the spherical particle surface caused by a decrease in its size. An empirical dependence of the drag coefficient of a solid sphere on the ratio of the velocity of injection from the surface of the particle to the velocity of blowing $C_{D} = 0.15 + (0.44 - 0.15)/ (1 + (9\overline{u}/5)^{3.8}$) (with the coefficient of determination $R^{2} = 0.89$) has been obtained for a self-similar particle regime flow.

Détail

Keywords: solid sphere, Reynolds number, transient flow regime, self-similar flow regime, experimental study.
Mots-clés : gas injection, drag coefficient

Bibliographie

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

[2] Arkhipov V.A., Vasenin I.M., Usanina A.S., Shrager G.R., Dinamicheskoe vzaimodeistvie chastits dispersnoi fazy v geterogennykh potokakh, Izd. Dom Tom. gos. un-ta, Tomsk, 2019

[3] Pomerantsev V.V., Arefev K.M., Akhmedov D.B., Konovich M.N., Korchunov Yu.N., Rundygin Yu.A., Shagalova S.L., Shestakov S.M., Osnovy prakticheskoi teorii goreniya, Energotomizdat, L., 1986

[4] Raushenbakh B.V., Belyi S.A., Bespalov I.V., Borodachev V.Ya., Volynskii M.S., Prudnikov A.G., Fizicheskie osnovy rabochego protsessa v kamerakh sgoraniya vozdushno-reaktivnykh dvigatelei, Mashinostroenie, M., 1964

[5] 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

[6] Sternin L.E., Shraiber A.A., Mnogofaznye techeniya gaza s chastitsami, Mashinostroenie, M., 1994

[7] Shraiber A.A., “Mnogofaznye polidispersnye techeniya s peremennym fraktsionnym sostavom diskretnykh vklyuchenii”, Itogi nauki i tekhniki. Kompleksnye i spetsialnye razdely mekhaniki, 3, VINITI, M., 1988, 3–80

[8] Nikolskii Yu.V., Khlopkov Yu.I., “Teoreticheskoe i eksperimentalnoe issledovanie obtekaniya sfery sverkhzvukovym potokom maloi plotnosti s uchetom kondensatsii i ispareniya s poverkhnosti”, Uchenye zapiski TsAGI, 20:5 (1989), 118–122

[9] Koval M.A., Stulov V.P., Shvets A.I., “Eksperimentalnoe issledovanie sverkhzvukovogo obtekaniya zatuplennykh tel s silnym raspredelennym vduvom”, Izvestiya AN SSSR. Mekhanika zhidkosti i gaza, 1978, no. 3, 84–95

[10] Glotov O.G., “Gorenie sfericheskikh titanovykh aglomeratov v vozdukhe. I. Eksperimentalnyi podkhod”, Fizika goreniya i vzryva, 49:3 (2013), 50–57

[11] Glotov O.G., “Gorenie sfericheskikh titanovykh aglomeratov v vozdukhe. II. Rezultaty eksperimentov”, Fizika goreniya i vzryva, 49:3 (2013), 58–71

[12] Arkhipov V.A., Basalaev S.A., Polenchuk S.N., Perfileva K.G., Yusupov R.A., Maslov E.A., Sposob opredeleniya koeffitsienta soprotivleniya sfericheskoi chastitsy pri vduve gaza s ee poverkhnosti, Patent 2700728 RF. G01N 15/10, Opubl. 19.09.2019. Byul. No 26, 13

[13] Petunin A.N., Metody i tekhnika izmerenii parametrov gazovogo potoka, Mashinostroenie, M., 1996

[14] Arkhipov V.A., Binfet R.G., Rozhin Yu.K., Sobolevskii V.I., Schetchik gaza «SG-6», Patent RF No 43023 na promyshlennyi obrazets. MKPO 10-04, Opubl. 16.12.1996. Byul. No 12

[15] Goronovskii I.T., Kratkii spravochnik po khimii, Naukova dumka, Kiev, 1987