Journal of Applied and Computational Mechanics

Numerical Investigation on Flow Transition through a Curved ‎Square Duct with Negative Rotation

Document Type : Research Paper

Authors

1 Department of Mathematics, Bangabandhu Sheikh Mujibur Rahman Science and Technology University, Gopalganj-8100, Bangladesh‎

2 Department of Mathematics, Jagannath University, Dhaka-1100, Bangladesh‎

3 Department of Mathematics, Shahjalal University of Science and Technology, Sylet-3114, Bangladesh‎

4 Department of Mathematics, Jagannath University, Dhaka-1100, Bangladesh

5 Department of Engineering and Architecture, University of Parma, Parma 43124, Italy

Abstract

Application of the rotational phenomena in the curved ducts plays an important role in many engineering areas, so researchers are attracted to innovate something new in this area nowadays. In this regard, the current paper has performed the fluid flow through the curved duct for an extensive range of negative rotation (-10 ≤ Tr ≤ -1500). The other useful parameters such as Dean number (Dn), Curvature (d), Grashof number (Gr), and Prandtl number (Pr) are considered fixed. The investigations are divided into four parts. In the first portion, linear stability of the flows through the duct is discussed. Then time evolution calculations of the unsteady solutions for different Taylor numbers are demonstrated in the “time vs. heat flux” plane. This inquiry shows that the flow undergoes various instabilities for increasing the Taylor number. Thirdly, two types of flow velocity, axial flow and secondary flow and the temperature profiles are represented. It is obtained that two up to six vortex secondary flows are found for the regular and irregular oscillation and the flow patterns are different for a fixed period for regular oscillation. To show more clarity of the periodic and chaotic flow, power spectrum density is further examined. However, it is observed that the flows are mixed and enhanced heat transfer because of the acting of centrifugal force, Coriolis force, and heating induced buoyancy force on the duct. Finally, the numerical results are compared with the experimental data which shows that the numerical data fully matches with the experimental outcome.

Keywords

Main Subjects

[1] Elsamni, O.A., Elsamni, A.A., El-Masry, O.A., Developing laminar flow in curved semi-circular ducts, Alexandria Engineering Journal, 58(1), 2019, 1-8. https://doi.org/10.1016/j.aej.2018.03.013
[2] Du, W., Luo, L., Wang, S., Liu, J., Sunden, B., Heat transfer and flow structure in a rotating duct with detached pin fins, Numerical Heat Transfer, Part A: Applications, 75(4), 2019, 217–241. https://doi.org/10.1080/10407782.2019.1580957
[3] Chandratilleke, T.T., Nadim, N., Forced Convective Heat Transfer and Fluid Flow Characteristics in Curved Ducts, An overview of heat transfer phenomena, Intech open sciences, 2012. https://doi.org/125-150. 10.5772/53064
[4] Mondal, R.N., Islam, M.S., Uddin, M.K., Hossain, M.A., Effects of Aspect Ratio on Unsteady Solutions through a Curved Duct Flow, Applied Mathematics and Mechanics, 34(9), 2013, 1-16. https://doi.org/10.1007/s10483-013-1731-8
[5] Anand, R.B., Sandeep, R., Effect of Angle of Turn on Flow Characteristics of Y- Shaped Diffusing Duct Using CFD, Frontiers in Automobile and mechanical Engineering, IEEE, 2010. https://doi.org/10.1109/FAME.2010.5714819
[6] Fiola, C., Agarwal, R.K., Simulation of Secondary and Separated Flow in Diffusing S Ducts, Journal of Propulsion and Power, 31(1), 2015, 180-191. https://doi.org/10.2514/1.B35275
[7] Rumsey, C.L., Gatski, T.B., Morrison, J.H., Turbulence Model Predictions of Strongly Curved Flow in a U-Duct, AIAA Journal, 38(8), 2000, 1394-1402. https://doi.org/10.2514/2.1115
[8] Chamkha, A., Ismael, M., Kasaeipoor, A., Armaghani, T., Entropy Generation and Natural Convection of CuO-Water Nanofluid in C-Shaped Cavity under Magnetic Field, Entropy, 18(2), 2016, 1-18. https://doi.org/10.3390/e18020050
[9] Nowruzi, H., Ghassemi, H., Nourazar, S.S., Study of the effects of aspect ratio on hydrodynamic stability in curved rectangular ducts using energy gradient method, Engineering Science and Technology, an International Journal, 23(2), 2019, 334-344. https://doi.org/10.1016/j.jestch.2019.05.004
[10] Watanabe, T., Yanase, S., Bifurcation Study of Three-Dimensional Solutions of the Curved Square-Duct Flow, Journal of the Physical Society of Japan, 82(074402), 2013, 1-9. https://doi.org/10.7566/JPSJ.82.074402
[11] Mondal, R.N., Kaga, Y., Hyakutake, T., Yanase, S., Bifurcation Diagram for Two-dimensional Steady Flow and Unsteady Solutions in a Curved Square Duct, Fluid Dynamics Research, 39, 2007, 413-446. https://doi.org/10.1016/j.fluiddyn.2006.10.001
[12] Nazeer, G., Shams-ul-Islam, Shigri, S.H., Saeed, S., Numerical investigation of different flow regimes for multiple staggered rows, AIP Advances, 9 (035247), 2019. https://doi.org/10.1063/1.5091668
[13] Krishna, C.V., Gundiah, N., Arakeri, J.H., Separation and secondary structures due to unsteady flow in a curved pipe, Journal of Fluid Mechanics, 815, 2017, 25-59. https://doi.org/10.1017/jfm.2017.7
[14] Islam, M.Z., Mondal, R.N., Rashidi, M.M., Dean-Taylor Flow with Convective Heat Transfer through a Coiled Duct, Computers & Fluids, 149, 2017, 41-55. https://doi.org/10.1016/j.compfluid.2017.03.001
[15] Sultana, M.N., Hasan, M.S., Mondal, R.N., A numerical study of unsteady heat and fluid flow through a rotating curved channel with variable curvature, AIP Conference Proceedings, 2121 (030009), 2019. https://doi.org/10.1063/1.5115854
[16] Hasan, M.S., Islam, M.M., Ray, S.C., Mondal, R.N., Bifurcation structure and unsteady solutions through a curved square duct with bottom wall heating and cooling from the ceiling, AIP Conference Proceedings, 2121 (050003), 2019. https://doi.org/10.1063/1.5115890.
[17] Wang, L., Pang, O., Cheng, L., Bifurcation and stability of forced convection in tightly coiled ducts: stability, Chaos, Solitons and Fractals, 27, 2006, 991-1005. https://doi.org/10.1016/j.chaos.2005.04.066
[18] Chamkha, A.J., Al-Mudhaf, A., Unsteady heat and mass transfer from a rotating vertical cone with a magnetic field and heat generation or absorption effects, International Journal of Thermal Sciences, 44, 2005, 267–276. https://doi.org/10.1016/j.ijthermalsci.2004.06.005
[19] Yanase, S., Mondal, R.N., Kaga, Y., Numerical study of non-isothermal flow with convective heat transfer in a curved rectangular duct. International Journal of Thermal Science, 44, 2005, 1047-60. https://doi.org/10.1016/j.ijthermalsci.2005.03.013
[20] Islam, M.N., Ray, S.C., Hasan, M.S., Mondal, R.N., Pressure-driven flow instability with convective heat transfer through a rotating curved rectangular duct with differentially heated top and bottom walls, AIP Conference Proceedings, 2121 (030011), 2019. https://doi.org/10.1063/1.5115856
[21] Ray, S.C., Hasan, M.S., Mondal, R.N., On the Onset of Hydrodynamic Instability with Convective Heat Transfer Through a Rotating Curved Rectangular Duct, Mathematical Modelling of Engineering Problems, 7(1), 2020, 31-44. https://doi.org/10.18280/mmep.070105
[22] Dean, W.R., Note on the motion of fluid in a curved pipe, Philos Mag, 4, 1927, 208-23. https://doi.org/10.1080/14786440708564324
[23] Harding, B., Stokes, Y.M., Bertozzi, A.L., Effect of inertial lift on a spherical particle suspended in flow through a curved duct, Journal of Fluid Mechanics, 25, 2019, 1-43. https://doi.org/10.1017/jfm.2019.323
[24] Nowruzi, H., Ghassemi, H., Nourazar, S.S., Hydrodynamic stability study in a curved square duct by using the energy gradient method, Journal of the Brazilian Society of Mechanical Sciences and Engineering, 41, 2019, 1-20. https://doi.org/10.1007/s40430-019-1790-z
[25] Kabanemi, K.K., Marcotte, J.P., Numerical Simulation of Suction Blow Molding Process for Producing Curved Ducts, Polymer engineering and science, Wiley online library, 59(2), 2020, 1-17. https://doi.org/10.1002/pen.24939
[26] Parvin, S., Nasrin, R., Alim, M.A., Hossain, N.F., Chamkha, A.J., Thermal conductivity variation on natural convection flow of water–alumina nanofluid in an annulus, International Journal of Heat and Mass Transfer, 55(19-20), 2012, 5268-5274. https://doi.org/10.1016/j.ijheatmasstransfer.2012.05.035
[27] Mondal, R.N., Watanabe, T., Hossain, M.A., Yanase, S., Vortex-Structure and Unsteady Solutions with Convective Heat Transfer Through a Curved Duct, Journal of Thermophysics and Heat Transfer, 31(1), 2017, 243-254. https://doi.org/10.2514/1.T4913
[28] Dolon, S.N., Hasan, M.S., Ray, S.C., Mondal, R.N., Vortex-structure of secondary flows with effects of strong curvature on unsteady solutions through a curved rectangular duct of large aspect ratio, AIP Conference Proceedings, 2121(050004), 2019. https://doi.org/10.1063/1.5115891
[29] Arifuzzaman, M., Islam, M.M., Paul, S.K.,  Mondal, R.N. Pressure-driven Flow Instability with Convective Heat Transfer through a Rotating Curved Square Duct with Strong Curvature, Current Journal of Applied Science and Technology, 23(2), 2017, 1-18.https://doi.org/10.9734/CJAST/2017/31612
[30] Yanase, S., Watanabe, T., Hyakutake, T., Traveling-wave solutions of the flow in a curved-square duct, Physics of Fluids, 20, 2008, 124101. https://doi.org/10.1063/1.3029703
[31] Yamamoto, K., Wu, X., Nozaki K., Hayamizu, Y., Visualization of Taylor–Dean flow in a curved duct of square cross-section, Fluid Dynamics Research, 38, 2006, 1-18. https://doi.org/10.1016/j.fluiddyn.2005.09.002
[32] Nivedita, N., Ligrani, P., Papautsky, I., Dean Flow Dynamics in Low-Aspect Ratio Spiral Microchannels, Scientific Reports, 7, 2017, 44072. https://doi.org/10.1038/srep44072
[33] Mondal, R.N., Kaga, Y., Hyakutake, T., Yanase, S., Effects of curvature and convective heat transfer in curved square duct flows, Trans. ASME, Journal of Fluids Engineering, 128 (9), 2006, 1013-1022. https://doi.org/10.1115/1.2236131
[34] Hasan, M.S., Mondal, R.N., Kouchi, T., Yanase, S. Hydrodynamic instability with convective heat transfer through a curved channel with strong rotational speed, AIP Conference Proceedings, 2121 (030006), 2019. https://doi.org/10.1063/1.5115851
[35] Umavathi, J.C., Chamkha, A.J., Mateen, A., Al-Mudhaf, A., Unsteady two-fluid flow and heat transfer in a horizontal channel, Heat Mass Transfer, 42, 2005, 81–90 https://doi.org/10.1007/s00231-004-0565-x
[36] Chandratilleke, T.T., Nadim, N., Narayanaswamy, R., Vortex structure-based analysis of laminar flow behaviour and thermal characteristics in curved ducts, International Journal of Thermal Sciences, 59, 2012, 75-86. https://doi.org/10.1016/j.ijthermalsci.2012.04.014
[37] Hasan, M.S., Mondal, R.N., Lorenzini, G., Numerical Prediction of Non-isothermal Flow with Convective Heat Transfer Through a Rotating Curved Square Channel with Bottom Wall Heating and Cooling from the Ceiling, International Journal of Heat and Technology, 37 (3), 2019, 710-726. https://doi.org/10.18280/ijht.370307
[38] Hasan, M.S., Mondal, R.N., Lorenzini, G., Centrifugal Instability with Convective Heat Transfer Through a Tightly Coiled Square Duct, Mathematical Modelling of Engineering Problems, 6 (3), 2019, 397-408. https://doi.org/10.18280/mmep.060311
Journal of Applied and Computational Mechanics
Volume 7, Issue 3
July 2021
Pages 1435-1447