Aerodynamics of turbulent flow in rotating semi-closed cylinder

O. V. Matvienko   ; V. A. Arkhipov   ; N. N. Zolotorev

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 69 (2021), pp. 114-126

Résumé

The mathematical model and results of a numerical study of swirling turbulent air flow characteristics in a semi-closed cylinder rotating around a symmetry axis are presented. A physical and mathematical model is used to describe aerodynamics of the stationary isothermal axisymmetric swirling flow, which includes the Navier-Stokes equations in cylindrical coordinates. The study of turbulence characteristics is carried out using the composite model Menter SST (Shear Stress Transport). The numerical solution is obtained using a chess grid. Nodes for axial and radial velocity components are located in the middle of the control volume faces for scalar quantities. Calculations are performed on a grid with 2000 and 1700 nodes in the axial and radial directions, respectively. The grid refinement is performed near the walls and in the areas with large velocity gradients. The calculated results show that the main grid refinement by 2 times in the axial and radial coordinates leads to a change in the values of the main variables by less than 1%. It is shown that the flow structure is determined by the rotational speed and cylinder height. Analyzing the calculated results, the ratio of the cylinder height to the angular velocity of the cylinder rotation is obtained, which ensures the formation of a quasi-solid rotation zone in the near-edge region.

Détail

Keywords: semi-closed cylinder, swirling flow, rotational speed, turbulent flow structure, numerical study.

Bibliographie

[1] Gupta A., Lilli D., Saired N., Zakruchennye potoki, Mir, M., 1987, 588 pp.

[2] Khalatov A. A., Teoriya i praktika zakruchennykh potokov, Naukova dumka, Kiev, 1989, 190 pp.

[3] Gesheva E. S., Litvinov I. V., Shtork S. I., Alekseenko S. V., “Analiz aerodinamicheskoi struktury zakruchennogo techeniya v modelyakh vikhrevykh gorelochnykh ustroistv”, Teploenergetika, 2014, no. 9, 33–41

[4] Siddiquea H., Shafkat Bin Hoqueb Md., Mohammad A., “Effect of swirl flow on heat transfer characteristics in a circular pipe”, AIP Conference Proceedings, 1754 (2016), 050028 | DOI

[5] Ianiro A., Cardone G., “Heat transfer rate and uniformity in multichannel swirling impinging jets”, Applied Thermal Engineering, 49 (2012), 89–98 | DOI

[6] Nanan K., Wongcharee K., Nuntadusit C., Eiamsa-Ard S., “Forced convective heat transer by swirling impinging jets issuing from nozzles equipped with twisted tapes”, International Communications in Heat and Mass Transfer, 39 (2012), 844–852 | DOI

[7] Nuntadusit C., Wae-Hayee M., Bunyajitradulya A., Eiamsa-Ard S., “Heat transfer enhancement by multiple swirling impinging jets with twisted-tape swirl generators”, International Communications in Heat and Mass Transfer, 39 (2012), 102–107 | DOI

[8] Shevchuk I. V., Khalatov A. A., “Teploobmen i gidrodinamika v pryamykh kanalakh, vraschayuschikhsya otnositelno parallelnoi ili naklonnoi osi”, Teplofizika vysokikh temperatur, 34:3 (1996), 461–473

[9] Matvienko O. V., “Issledovanie teploobmena i formirovaniya turbulentnosti vo vnutrennem zakruchennom potoke zhidkosti pri nizkikh chislakh Reinoldsa”, Inzhenerno-fizicheskii zhurnal, 87:4 (2014), 908–918

[10] Arkhipov V. A., Matvienko O. V., “Nestatsionarnye protsessy goreniya v kanale pri zakrutke gazovogo potoka i ee prekraschenii”, Fizika goreniya i vzryva, 35:4 (1999), 33–40

[11] Matvienko O. V., Ushakov V. M., “Chislennoe issledovanie struktury zakruchennogo potoka v tsilindricheskoi kamere, chastichno zapolnennoi poristym materialom”, Vestnik Tomskogo gosudarstvennogo pedagogicheskogo universiteta, 2003, no. 4 (38), 14–24

[12] Menter F. R., Zonal two-equation $k$-$\omega$ turbulence models for aerodynamic flows, AIAA Paper. . Technical Report No 93-2906, 1993

[13] Menter F. R., Rumsey C. L., Assessment of two-equation turbulence models for transonic flows, AIAA Paper No 94-2343, 1994

[14] Piquet J., Turbulent flows: models and physics, Springer, Berlin, 1999, 762 pp. | MR | Zbl

[15] Jones W. P., Launder B. E., “The calculation of low Reynolds number phenomena with a two-equation model of turbulence”, Int. J. of Heat Mass Transfer, 16 (1973), 1119–1130 | DOI

[16] Arkhipov V. A., Matvienko O. V., Trofimov V. F., “Gorenie raspylennogo zhidkogo topliva v zakruchennom potoke”, Fizika goreniya i vzryva, 41:2 (2005), 26–37

[17] Matvienko O. V., Bubenchikov A. M., “Matematicheskoe modelirovanie teploobmena i khimicheskogo reagirovaniya zakruchennogo potoka dissotsiiruyuschego gaza”, Inzhenerno-fizicheskii zhurnal, 89:1 (2016), 118–126

[18] Wilcox D. C., A two-equation turbulence model for wall-bounded and free-shear flows, AIAA Paper No 93-2905, 1993

[19] Menter F. R., Kuntz M., Langtry R., “Ten years of industrial experience with the SST turbulence model”, Turbulence, Heat and Mass Transfer, v. 4, Begell House Inc, 2003, 625–632

[20] Spalart P. R., Shur M., “On the sensitization of turbulence models to rotation and curvature”, Aerospace Science and Technology, 1:5 (1997), 297–302 | DOI | Zbl

[21] Bradshaw P., Ferriss D. H., Atwell N. P., “Calculation of boundary layer development using the turbulent energy equation”, Journal of Fluid Mechanics, 28 (1967), 593–616 | DOI

[22] Patankar S., Chislennye metody resheniya zadach teploobmena i dinamiki zhidkosti, Energoatomizdat, M., 1984, 150 pp.

[23] Ferziger J. H., Peric M., Computational Methods for Fluid Dynamics, Springer, Berlin, 1996 | MR | Zbl

[24] Ushakov V. M., Matvienko O. V., “Chislennoe issledovanie teploobmena i zazhiganiya reaktsionnosposobnykh stenok kanala vysokotemperaturnym potokom zakruchennogo gaza”, Inzhenerno-fizicheskii zhurnal, 78:3 (2005), 123–128

[25] Egorov A. G., Tizilov A. S., Niyazov V. Ya., Arkhipov V. A., Matvienko O. V., “Issledovanie vliyaniya zakrutki sputnogo vysokoskorostnogo potoka vozdukha na geometricheskie parametry alyuminievo-vozdushnogo fakela”, Khimicheskaya fizika, 33:10 (2014), 58–61

[26] Van Leer B., “Towards the ultimate conservative differencing scheme. IV. A new approach to numerical convection”, Journal of Computational Physics, 23 (1977), 276–299 | DOI | MR | Zbl

[27] Harten A., “High resolution schemes for hyperbolic conservation laws”, Journal of Computational Physics, 49 (1983), 357–393 | DOI | MR | Zbl

[28] Van Doormal J. P., Raithby G. D., “Enhancements of the SIMPLE method for predicting incompressible fluid flows”, Numerical Heat Transfer, 7 (1984), 147–163 | Zbl