Determining the structure of a laminar detachable current in an open cavity
DOI:
https://doi.org/10.15587/1729-4061.2019.183811Keywords:
flow detachment, laminar mode, flow in a cavity, numerical modelling, vorticity formation structureAbstract
The paper reports a three-dimensional numerical solution to the test problem about a viscous incompressible liquid flow in the closed square-shaped cavity with a movable upper face. Disadvantages in a mathematical statement of the problem about a flow of fluid in a closed cavity have been identified. A finite element method was applied in order to investigate numerically the structure of a circulating detachable laminar movement of viscous incompressible fluid in an open cavity considering the external flow. The profiles of vorticity, the thickness of a boundary layer, the constituents of velocity components in different cross-sections of the cavity, in the boundary layer, as well as in the blending layer, have been given.
Typically, studying laminar currents in cavities employs a model of the cavity with a movable wall. However, such a statement of the problem imposes a restriction on the flow pattern in the form of a straight line of the flow that connects the upper corners of the cavity, which results in the distorted structure of vorticity formation in the cavity in general. Within the framework of the current study, the problem statement that overcomes the specified disadvantage has been proposed. The movement of fluid in a cavity occurs due to the shear stress of the external flow in a channel above the cavity, which rules out the straightness of the flow line, which connects the cavity's corner points. Reliability of the reported results has been confirmed by comparing certain parameters to known experimental data by other authors. The study's scientific result in the form of the vorticity structure of a viscous incompressible laminar flow in an open cavity with a channel is interesting from a theoretical point of view. As regards the practical point of view, the identified structure of the flow makes it possible to define the conditions to control a flow in the cavity and, therefore, allows determining the conditions for optimizing the aerodynamic forces acting on a cavity. The applied aspect of the obtained scientific result is the possibility to employ it for a flow over industrial facilities: buildings, inter-carriage space in a railroad train, etc.
References
- Chzhen, P. (1972). Otryvnye techeniya. Vol. 1. Moscow: Mir, 299.
- Krasnov, N. F., Koshevoy, V. N., Kalugin, V. P. (1988). Aerodinamika otryvnyh techeniy. Moscow: Vysshaya shkola, 351.
- Shlihting, G. (1969). Teoriya pogranichnogo sloya. Moscow: Nauka, 744.
- Simuni, L. M. (1965). Chislennoe reshenie zadachi dvizheniya zhidkosti v pryamougol'noy yame. PMTF, 6, 106–108.
- Charwat, A. F., Dewey, C. F., Roos, J. N., Hitz, J. A. (1961). An Investigation of Separated Flows- Part I I : Flow in the Cavity and Heat Transfer. Journal of the Aerospace Sciences, 28 (7), 513–527. doi: https://doi.org/10.2514/8.9099
- Kravets, E. V. (2005). Matematicheskoe modelirovanie turbulentnyh techeniy vyazkoy neszhimaemoy sredy v mezhvagonnom prostranstve s kryshnym obtekatelem. Visnyk DNU. Seriya: Mekhanika, 1 (10), 66–73.
- Kochubey, A. A., Kravets, E. V. (2012). Sravnitel'nyy analiz chislennyh i analiticheskih issledovaniy tsirkulyatsionnyh dvumernyh techeniy v kavernah. Tehnicheskaya mehanika, 1, 38–55.
- Kochubey, A. A., Kravets, E. V. (2013). Analiz eksperimental'nyh i chislennyh issledovaniy vihrevyh techeniy v trehmernyh kavernah. Visnyk Dnipropetrovskoho universytetu. Seriya: Mekhanika, 21 (17 (1)), 51–63.
- Terehov, V. I., Kalinina, S. V. (2002). Struktura techeniya i teploobmen pri obtekanii edinichnoy sfericheskoy kaverny. Sostoyanie voprosa i problemy (obzor). Teplofizika i aeromehanika, 4, 497–520.
- Terekhov, V. I., Kalinina, S. V., Mshvidobadze, Yu. M. (1994). Heat transfer from a spherical cavity located on a rectangular channel wall. Teplofizika vysokih temperatur, 32 (2), 249–254.
- Mironov, D. S. (2011). Eksperimental'noe issledovanie pul'satsiy davleniya, generiruemyh melkoy otkrytoy kavernoy, s primeneniem chastotno-vremennyh metodov obrabotki dannyh. Teplofizika i aeromehanika, 18 (3), 385–395.
- Terekhov, V. I., Kalinina, S. V., Sharov, K. A. (2012). Features of flow and heat transfer for the jet interaction with a spherical cavity-shaped obstacle with a round edge. High Temperature, 50 (2), 295–297. doi: https://doi.org/10.1134/s0018151x12020198
- Burtsev, S., Vinogradov, Y., Kiselev, N., Strongin, M. (2016). Selection of Rational Heat Transfer Intensifiers in the Heat Exchanger. Science and Education of the Bauman MSTU, 12, 35–56. doi: https://doi.org/10.7463/1216.0852444
- Pavan Kumar Reddy, M., Ramana Murthy, J. V. (2019). Entropy analysis for heat transfer in a rectangular channel with suction. Heat Transfer-Asian Research, 48 (7), 2773–2798. doi: https://doi.org/10.1002/htj.21513
- Biswas, N., Manna, N. K. (2017). Transport phenomena in a sidewall-moving bottom-heated cavity using heatlines. Sādhanā, 42 (2), 193–211. doi: https://doi.org/10.1007/s12046-016-0586-4
- Curi, M., De Sampaio, P. A. B., Gonçalves Junior, M. A. (2017). Study of natural convection with a stabilized finite element formulation. Computational Thermal Sciences: An International Journal, 9 (6), 513–527. doi: https://doi.org/10.1615/computthermalscien.2017018186
- Purusothaman, A., Baïri, A., Nithyadevi, N. (2016). 3D natural convection on a horizontal and vertical thermally active plate in a closed cubical cavity. International Journal of Numerical Methods for Heat & Fluid Flow, 26 (8), 2528–2542. doi: https://doi.org/10.1108/hff-08-2015-0341
- Roy, M., Basak, T., Roy, S. (2015). Analysis of Entropy Generation During Mixed Convection in Porous Square Cavities: Effect of Thermal Boundary Conditions. Numerical Heat Transfer, Part A: Applications, 68 (9), 925–957. doi: https://doi.org/10.1080/10407782.2015.1023134
- Umavathi, J. C., Ojjela, O., Vajravelu, K. (2017). Numerical analysis of natural convective flow and heat transfer of nanofluids in a vertical rectangular duct using Darcy-Forchheimer-Brinkman model. International Journal of Thermal Sciences, 111, 511–524. doi: https://doi.org/10.1016/j.ijthermalsci.2016.10.002
- Ternik, P., Buchmeister, J. (2015). Buoyancy-Induced Flow and Heat Transfer of Power Law Fluids in a Side Heated Square Cavity. International Journal of Simulation Modelling, 14 (2), 238–249. doi: https://doi.org/10.2507/ijsimm14(2)5.293
- Rashad, A., Mansour, M., Gorla, R. S. R. (2016). Mixed convection from a discrete heater in lid-driven enclosures filled with non-Newtonian nanofluids. Proceedings of the Institution of Mechanical Engineers, Part N: Journal of Nanomaterials, Nanoengineering and Nanosystems, 231 (1), 3–16. doi: https://doi.org/10.1177/1740349916634749
- Polyakov, A. F. (2014). A steady viscous-thermogravitational flow of capillary liquid and heat transfer in a vertical cavity under asymmetric heat conditions. High Temperature, 52 (1), 72–77. doi: https://doi.org/10.1134/s0018151x14010179
- Aksouh, A., Mataoui, A., Seghouani, N. (2012). Low Reynolds-number effect on the turbulent natural convection in an enclosed 3D tall cavity. Progress in Computational Fluid Dynamics, An International Journal, 12 (6), 389. doi: https://doi.org/10.1504/pcfd.2012.049811
- Noori Rahim Abadi, S. M. A., Jafari, A. (2012). Investigating the natural convection heat transfer from two elliptic cylinders in a closed cavity at different cylinder spacings. Heat Transfer Research, 43 (3), 259–284. doi: https://doi.org/10.1615/heattransres.2012002036
- Kaluri, R. S., Basak, T. (2011). Role of entropy generation on thermal management during natural convection in porous square cavities with distributed heat sources. Chemical Engineering Science, 66 (10), 2124–2140. doi: https://doi.org/10.1016/j.ces.2011.02.009
- Bouabid, M., Magherbi, M., Hidouri, N., Brahim, A. B. (2011). Entropy Generation at Natural Convection in an Inclined Rectangular Cavity. Entropy, 13 (5), 1020–1033. doi: https://doi.org/10.3390/e13051020
- Boger, A. A., Ryabov, S. V., Ryazhskikh, V. I., Slyusarev, M. I. (2010). Calculation of a conductive-laminar thermo-convection regime of a Newtonian fluid in a rectangular cavity with isothermal vertical boundaries. Fluid Dynamics, 45 (3), 355–358. doi: https://doi.org/10.1134/s0015462810030026
- Bulat, A., Blyuss, B., Dreus, A., Liu, B., Dziuba, S. (2019). Modelling of deep wells thermal modes. Mining of Mineral Deposits, 13 (1), 58–65. doi: https://doi.org/10.33271/mining13.01.058
- Asadi, H., Javaherdeh, K., Ramezani, S. (2013). Finite element simulation of micropolar fluid flow in the lid-driven square cavity. International Journal of Applied Mechanics, 05 (04), 1350045. doi: https://doi.org/10.1142/s1758825113500452
- Yamouni, S., Mettot, C., Sipp, D., Jacquin, L. (2013). Passive Control of Cavity Flows. Journal AerospaceLab, 6, 1–7.
- Nagarajan, K. K., Singha, S., Cordier, L., Airiau, C. (2018). Open-loop control of cavity noise using Proper Orthogonal Decomposition reduced-order model. Computers & Fluids, 160, 1–13. doi: https://doi.org/10.1016/j.compfluid.2017.10.019
- Iorio, C. S., Goncharova, O., Kabov, O. (2011). Influence of Boundaries on Shear-driven Flow of Liquids in Open Cavities. Microgravity Science and Technology, 23 (4), 373–379. doi: https://doi.org/10.1007/s12217-011-9257-6
- González, L. M., Ahmed, M., Kühnen, J., Kuhlmann, H. C., Theofilis, V. (2011). Three-dimensional flow instability in a lid-driven isosceles triangular cavity. Journal of Fluid Mechanics, 675, 369–396. doi: https://doi.org/10.1017/s002211201100022x
- Senel, P., Tezer-Sezgin, M. (2018). Convective Flow of Blood in Square and Circular Cavities. Analele Universitatii “Ovidius” Constanta - Seria Matematica, 26 (2), 209–230. doi: https://doi.org/10.2478/auom-2018-0026
- Senel, P., Tezer-Sezgin, M. (2016). DRBEM solution of biomagnetic fluid flow and heat transfer in cavities-CMMSE2016. Journal of Mathematical Chemistry, 55 (7), 1407–1426. doi: https://doi.org/10.1007/s10910-016-0721-9
- Senel, P., Tezer-Sezgin, M. (2016). DRBEM solutions of Stokes and Navier–Stokes equations in cavities under point source magnetic field. Engineering Analysis with Boundary Elements, 64, 158–175. doi: https://doi.org/10.1016/j.enganabound.2015.12.007
- Jin, K., Vanka, S. P., Thomas, B. G. (2015). Three-Dimensional Flow in a Driven Cavity Subjected to an External Magnetic Field. Journal of Fluids Engineering, 137 (7). doi: https://doi.org/10.1115/1.4029731
- Ahmed, S. E., Hussein, A. K., Mohammed, H. A., Adegun, I. K., Zhang, X., Kolsi, L. et. al. (2014). Viscous dissipation and radiation effects on MHD natural convection in a square enclosure filled with a porous medium. Nuclear Engineering and Design, 266, 34–42. doi: https://doi.org/10.1016/j.nucengdes.2013.10.016
- Brès, G. A., Colonius, T. (2008). Three-dimensional instabilities in compressible flow over open cavities. Journal of Fluid Mechanics, 599, 309–339. doi: https://doi.org/10.1017/s0022112007009925
- Sinha, J. (2013). Studies on the Transition of the Flow Oscillations over an Axisymmetric Open Cavity Model. Advanced in Aerospace Science and Applications, 3 (2), 83–90.
- Sinha, J., Arora, K. (2017). Review of the flow-field analysis over cavities. 2017 International Conference on Infocom Technologies and Unmanned Systems (Trends and Future Directions) (ICTUS). doi: https://doi.org/10.1109/ictus.2017.8286128
- Yang, G., Sun, J., Liang, Y., Chen, Y. (2014). Effect of Geometry Parameters on Low-speed Cavity Flow by Wind Tunnel Experiment. AASRI Procedia, 9, 44–50. doi: https://doi.org/10.1016/j.aasri.2014.09.009
- Isaev, S. A., Sudakov, A. G., Luchko, N. N., Sidorovich, T. V., Harchenko, V. B. (2002). Chislennoe modelirovanie laminarnogo tsirkulyatsionnogo techeniya v kubicheskoy kaverne s podvizhnoy gran'yu. Inzhenerno-fizicheskiy zhurnal, 75 (1), 49–53.
- Bogatyrev, V. Ya., Dubnishchev, Yu. N., Muhin, V. A., Nakoryakov, V. E., Sobolev, V. S., Utkin, E. N., SHmoylov, N. F. (1976). Eksperimental'noe issledovanie techeniya v transhee. PMTF, 2, 76–86.
- Bogatyrev, V. Ya., Gorin, A. V. (1976). O tortsevyh effektah v transheyah pryamougol'nogo poperechnogo secheniya. Gradientnye i otryvnye techeniya. Novosibirsk, 132–139.
- Kármán, T. V. (1921). Über laminare und turbulente Reibung. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift Für Angewandte Mathematik Und Mechanik, 1 (4), 233–252. doi: https://doi.org/10.1002/zamm.19210010401
- Pohlhausen, K. (1921). Zur näherungsweisen Integration der Differentialgleichung der Iaminaren Grenzschicht. ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift Für Angewandte Mathematik Und Mechanik, 1 (4), 252–290. doi: https://doi.org/10.1002/zamm.19210010402
- Loytsyanskiy, L. G. (1970). Mehanika zhidkosti i gaza. Moscow: Nauka, 904.
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