Investigation on energy distribution in steady and unsteady flow instabilities through a bend square pipe
DOI:
https://doi.org/10.31181/rme200102086hKeywords:
Curved pipe, Steady solution, Unsteady solution, Energy Distribution, Experimental validation.Abstract
Fluid flow analysis through a bend pipe is extensively conducted in practical and cell separation operations. It is observed that flow behaviors in the bend pipe are influenced by some parameters such as curvature, aspect ratio, etc. As a result, various phenomena, steady solution branches, unsteady solutions, energy transfer are changed. In this paper, the acts of flows are performed together for fixed curvature, δ = 0.2, and Prandtl number, Pr = 7.0 (water). Here, for a wide variety of Dean numbers (100 ≤ Dn ≤ 1000) and three fixed Grashof numbers, Gr = 100, 500, and 1000; time-independent solutions with linear stabilities are investigated first where only the first steady branch exhibits linear stability out of two steady solution branches obtained. Then, different flow transitions between the required range of Dean numbers (Dn) and several Grashof numbers (Gr) are investigated using time-dependent solutions. Power spectrum density (PSD) is further revealed in order to gain a deeper understanding of periodic and multi-periodic flows. Flow velocity contours including axial flow (AF) and secondary flow (SF) and their temperature profiles (TP) are also exposed. The SFs reveal that two- to four-vortex flows are produced due to the turning of steady branch and the flow instabilities. Furthermore, the energy transfer between the cooled and heated sidewalls of the pipe is calculated. Finally, a link between centrifugal and body force with the energy transfer has been shown in this research which reveals that the fluid has merged that certainly rises the overall energy transfer.
References
Alam, M.M., Ota, M., Ferdows, M., Islamv, M.N., Wahiduzzaman, M., & Yamamoto, K. (2007). Flow through a rotating helical pipe with a wide range of the Dean number. Arch. Mech., 59(6), 501–517.
Anand, R.B., & Sandeep, R. (2010). Effect of Angle of Turn on Flow Characteristics of Y-Shaped Diffusing Duct Using CFD. IEEE conference proceedings, Frontiers in Automobile and Mechanical Engineering, 295-300. https://doi.org/10.1109/FAME.2010.5714819
Arpino, F., Cortellessa, G., & Mauro, A. (2015). Transient Thermal Analysis of Natural Convection in Porous and Partially Porous Cavities. Numerical Heat Transfer, Part A, 67, 605–631. https://doi.org/10.1080/10407782.2014.949133
Arvanitisa, K.D., Bourisa, D., & Papanicolaou, D. (2018). Laminar flow and heat transfer in U-bends: The effect of secondary flows in ducts with partial and full curvature. International Journal of Thermal Sciences, 130, 70-93. https://doi.org/10.1016/j.ijthermalsci.2018.03.027
Bhuyan, D., & Giri, A. (2021). Heat transfer and second law analysis of turbulent flow mixed convection condensation inside a vertical channel. International Journal of Heat and Mass Transfer, 165, 120658. https://doi.org/10.1016/j.ijheatmasstransfer.2020.120658
Bu, H.X., Tan, H.J., Chen, H., & He, X.M. (2015). Investigation on Secondary Flow Characteristics in a Curved Annular Duct with Struts. Flow Turbulence Combust, 97(1), 27-41. https://doi.org/10.1007/s10494-015-9674-5
Canton, J., Örlü, R., Chin, C., Hutchins, N., Monty, J., & Schlatter, P. (2016). On Large-Scale Friction Control in Turbulent Wall Flow in Low Reynolds Number Channels. Flow Turbulence Combust, 97, 811–827. https://doi.org/10.1007/s10494-016-9723-8
Chanda, R.K., Hasan, M.S., Alam, M.M., & Mondal, R.N. (2020). Hydrothermal behavior of transient fluid flow and heat transfer through a rotating curved rectangular duct with natural and forced convection. Mathematical Modelling of Engineering Problems, 7(4), 501-514. https://doi.org/10.18280/mmep.070401
Chandratilleke, T.T., Nadim, N., & Narayanaswamy, R. (2013). Analysis of Secondary Flow Instability and Forced Convection in Fluid Flow through Rectangular and Elliptical Curved Ducts. Heat Transfer Engineering, 34(14), 1237-1248. https://doi.org/10.1080/01457632.2013.777249
Chen, L. Cai, J., Lv, K., Yang, X., Chen, S., & Houa. Y. (2020). Distributed Joule-Thomson effects and convective heat transfer of high-pressure argon gas flow in helically coiled mini-tubes. Applied Thermal Engineering, 181, 115955. https://doi.org/10.1016/j.applthermaleng.2020.115955
Czajkowski, C., Nowak, A.I., & Pietrowicz, S. (2020). Flower Shape Oscillating Heat Pipe – A novel type of oscillating heat pipe in a rotary system of coordinates – An experimental investigation. Applied Thermal Engineering, 179, 115702. https://doi.org/10.1016/j.applthermaleng.2020.115702
Dean, W.R. (1927). Note on the motion of fluid in a curved pipe. Philos Mag., 4(20), 208-223. https://doi.org/10.1080/14786440708564324
Dolon, S.N., Hasan, M.S., Lorenzini, G., & Mondal, R.N. (2021). A computational modeling on transient heat and fluid flow through a curved duct of large aspect ratio with centrifugal instability. The European Physical Journal Plus, 136, 382. https://doi.org/10.1140/epjp/s13360-021-01331-0
Dolon, S.N., Hasan, M.S., Ray, S.C., & Mondal, R.N. (2019). 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. https://doi.org/10.1063/1.5115891
Fiola, C., & Agarwal, R.K. (2015). Simulation of Secondary and Separated Flow in Diffusing S Ducts. Journal of Propulsion and Power, 31(1), 180-191. https://doi.org/10.2514/1.B35275
Fomicheva, M., Müller, W.H., Vilchevskaya, E.N., & Bessonov, N. (2019). Funnel flow of a navier-stokes-fluid with potential applications to micropolar media. facta universitatis Series: Mechanical Engineering, 17(2): 255 – 267. https://doi.org/10.22190/FUME190401029F
Gao, Y., Feng, Y., Tanga, K., & Hrnjaka, P. (2020). Experimental study on forced convection hydraulic and thermal characteristics in a dimpled flat duct. Applied Thermal Engineering,181, 115921. https://doi.org/10.1016/j.applthermaleng.2020.115921
Gelfgat, A. (2020), Instability of steady flows in helical pipes. Physical Review Fluids, 5, 103904. https://doi.org/10.1103/PhysRevFluids.5.103904
Ghobadi, M., & Muzychka, Y.S. (2015). A Review of Heat Transfer and Pressure Drop Correlations for Laminar Flow in Curved Circular Ducts. Heat Transfer Engineering, 37(10), 815-839. https://doi.org/10.1080/01457632.2015.1089735
Hasan, M.S., & Dolon, S.N., Chakraborty, H.S., Mondal, R.N., Lorenzini, G. (2021). Numerical Investigation on Flow Transition through a Curved Square Duct with Negative Rotation. Journal of Applied and Computational Mechanics (in press), 1–13. https://doi.org/10.22055/JACM.2020.33606.2253
Hasan, M.S., Mondal, R.N., & Lorenzini, G. (2020). Physics of bifurcation of the flow and heat transfer through a curved duct with natural and forced convection. Chinese Journal of Physics, 67: 428-457. https://doi.org/10.1016/j.cjph.2020.07.004
Hasan, M.S., Islam, M.S., Badsha, M.F., Mondal, R.N., & Lorenzini G. (2020). Numerical Investigation on the Transition of Fluid Flow Characteristics Through a Rotating Curved Duct. International Journal of Applied Mechanics and Engineering, 25(3), 45-63. https://doi.org/10.2478/ijame-2020-0034
Hasan, M.S., Mondal, R.N., & Lorenzini, G. (2020). Coriolis force effect in steady and unsteady flow characteristics with convective heat transfer through a curved square duct. International Journal of Mechanical Engineering, 5(1), 1-39.
Hasan, M.S., Mondal, R.N., & Lorenzini, G. (2019). Centrifugal Instability with Convective Heat Transfer through a Tightly Coiled Square Duct. Mathematical Modelling of Engineering Problems, 6(3), 397-408. https://doi.org/10.18280/mmep.060311
Hasan, M.S., Islam, M.M., Ray, S.C., & Mondal, R.N. (2019). Bifurcation structure and unsteady solutions through a curved square duct with bottom wall heating and cooling from the ceiling. AIP Conference Proceedings, 2121, 050003. https://doi.org/10.1063/1.5115890
Hasan, M.S., Mondal, R.N., & Lorenzini, G. (2019). 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), 710-726. https://doi.org/10.18280/ijht.370307
Hasan, M.S., Mondal, R.N., Kouchi, T., & Yanase, S. (2019). Hydrodynamic instability with convective heat transfer through a curved channel with strong rotational speed. AIP Conference Proceedings, 2121, 030006. https://doi.org/10.1063/1.5115851
Hashemi, A., Fischer, P.F., & Loth, F. (2018). Direct numerical simulation of transitional flow in a finite length curved pipe. Journal of Turbulence, 19(8), 664-682. https://doi.org/10.1080/14685248.2018.1497293
Islam, M.N., Ray, S.C., Hasan, M.S., & Mondal, R.N. (2019). 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. https://doi.org/10.1063/1.5115856
Kim, Y.I., Kim, S.H., Hwang, Y.D., & Park, J.H. (2011). Numerical investigation on the similarity of developing laminar flows in helical pipes. Nuclear Engineering and Design, 241, 5211–5224. https://doi.org/10.1016/j.nucengdes.2011.09.020
Li, Y., Wang, X., Yuan, S., & Tan, S.K. (2016). Flow development in curved rectangular ducts with continuously varying curvature. Experimental Thermal and Fluid Science, 75, 1–15. https://doi.org/10.1016/j.expthermflusci.2016.01.012
Li, Y., Wang, X., Zhou, B., Yuan, S., & Tan, S.K. (2017). Dean instability and secondary flow structure in curved rectangular ducts. International Journal of Heat and Fluid Flow, 68, 189-202. https://doi.org/10.1016/j.ijheatfluidflow.2017.10.011
Lin, T.S., Rogers, S., Tseluiko, D., & Thiele, U. (2016). Bifurcation analysis of the behavior of partially wetting liquids on a rotating cylinder. Physics of Fluids, 28, 082102. https://doi.org/10.1063/1.4959890
Lin, Z., Zhu, Y., & Wang, Z. (2017). Local bifurcation of electrohydrodynamic waves on a conducting fluid. Physics of Fluids, 29, 032107. https://doi.org/10.1063/1.4979064
Leong, F.Y., Smith, K.A., & Wang, C.H. (2009). Secondary flow behavior in a double bifurcation. Physics of Fluids, 21, 043601. https://doi.org/10.1063/1.3100211
Liu, F., & Wang, L. (2009). Analysis on multiplicity and stability of convective heat transfer in tightly curved rectangular ducts. International Journal of Heat and Mass Transfer, 52, 5849–5866. https://doi.org/10.1016/j.ijheatmasstransfer.2009.07.019
Mechane, W. (2010). Bifurcation and stability analysis of laminar flow in curved ducts. International Journal for Numerical Methods in Fluids, 64(4), 355–375. https://doi.org/10.1002/fld.2147
Mokeddem, M., Laidoudi, H., Makinde, O.D., & Bouzit, M. (2019). 3D Simulation of Incompressible Poiseuille Flow through 180° Curved Duct of Square Cross-section under Effect of Thermal Buoyancy. Periodica Polytechnica, Mechanical Engineering, 63(4), 257–269. https://doi.org/10.3311/PPme.12773
Mondal, R.N., Watanabe, T., Hossain, M.A., & Yanase, S. (2017). Vortex-Structure and Unsteady Solutions with Convective Heat Transfer Trough a Curved Duct. Journal of Thermophysics And Heat Transfer, 31(1), 243-254. https://doi.org/10.2514/1.T4913
Mondal, R.N., Islam, M.Z., Islam, M.M., & Yanase, S. (2015). Numerical Study of Unsteady Heat and Fluid Flow through a Curved Rectangular Duct of Small Aspect Ratio. Science and Technology Asia, 20(4), 1-20.
Mondal, R.N., Islam, M.S., Uddin, K., & Hossain, M.A. (2013). Effects of aspect ratio on unsteady solutions through curved duct flow. Applied Mathematics and Mechanics, 34(9), 1107-1122. https://doi.org/10.1007/s10483-013-1731-8
Mondal, R.N., Kaga, Y., Hyakutake, T., & Yanase, S. (2007). Bifurcation diagram for two-dimensional steady flow and unsteady solutions in a curved square duct. Fluid Dynamics Research, 39(5), 413–446. https://doi.org/10.1016/j.fluiddyn.2006.10.001
Mondal, R.N., Kaga, Y., Hyakutake, T., & Yanase, S. (2006). Effects of curvature and convective heat transfer in curved square duct flows. Trans. ASME, Journal of Fluids Engineering, 128(9), 1013-1022. https://doi.org/10.1115/1.2236131
Manesh, B.E., Shahmardan, M.M., Rahmani, H., & Norouzi, M. (2019). Heterogeneous anisotropic conductive heat transfer in composite conical shells: An exact analysis. International Journal of Heat and Mass Transfer, 144, 118614. https://doi.org/10.1016/j.ijheatmasstransfer.2019.118614
Nazeer, G., Islam, S., Shigri, S.H., & Saeed, S. (2019). Numerical investigation of different flow regimes for multiple staggered rows. AIP Advances, 9, 035247. https://doi.org/10.1063/1.5091668
Nobari, M.R.H., Ahrabi, B.R., & Akbari, G. (2009). A numerical analysis of developing flow and heat transfer in a curved annular pipe. International Journal of Thermal Sciences, 48, 1542–1551. https://doi.org/10.1016/j.ijthermalsci.2008.12.004
Norouzi, M., Kayhani, M.H., Nobari, M.R.H., & Talebi, F. (2011). Analytical Investigation of Viscoelastic Creeping Flow and Heat Transfer Inside a Curved Rectangular Duct. Theoretical Foundations of Chemical Engineering, 45(1), 53–67. https://doi.org/10.1134/S0040579511010052
Rahmani, H., Norouzi, M., Birjandi, A.K., & Birjandi, A.K. (2019). An exact solution for transient anisotropic heat conduction in composite cylindrical shells. Journal of Heat Transfer, 141(10), 101301. https://doi.org/10.1115/1.4044157
Razavi, S.E., Soltanipour, H., & Choupani, P. (2015). Second Law Analysis of Laminar Forced Convection in a Rotating Curved Duct. Thermal Science, 19(1), 95-107. https://doi.org/10.2298/TSCI120606034R
Sultana, M.N., Hasan, M.S., & Mondal, R.N. (2019). A numerical study of unsteady heat and fluid flow through a rotating curved channel with variable curvature. AIP Conference Proceedings, 2121, 030009. https://doi.org/10.1063/1.5115854
Soltanipour, H., Gharegöz, A. & & Oskooee, M.B. (2020). Numerical study of magnetic field effect on the ferrofluid forced convection and entropy generation in a curved pipe. Journal of the Brazilian Society of Mechanical Science and Engineering, 42, 135. https://doi.org/10.1007/s40430-020-2218-5
Wang, L., & Yang, T. (2005). Periodic oscillation in curved duct flows. Physica D, 200, 296-302. https://doi.org/10.1016/j.physd.2004.11.003
Wang, X.K., Li, Y.L., Yuan, S.Q., & Tan, S.K. (2018). Flow past a near-wall retrograde rotating cylinder at varying rotation and gap ratios. Ocean Engineering, 156, 240–251. https://doi.org/10.1016/j.oceaneng.2018.03.015
Watanabe, T., & Yanase, S. (2013). Bifurcation Study of Three-Dimensional Solutions of the Curved Square-Duct Flow. Journal of the Physical Society of Japan, 82, 074402, 1-9. https://doi.org/10.7566/JPSJ.82.074402
Yanase, S., Mondal, R.N., & Kaga, Y. (2005). Numerical Study of Non-Isothermal Flow with Convective Heat Transfer in a Curved Rectangular Duct. International Journal of Thermal Science, 44(11), 1047-1060. https://doi.org/10.1016/j.ijthermalsci.2005.03.013
Yanase, S., Kaga, Y., & Daikai, R. (2002). Laminar flows through a curved rectangular duct over a wide range of the aspect ratio. Fluid Dynamics Research, 31, 151–183. https://doi.org/10.1016/S0169-5983(02)00103-X
Yang, T., & Wang, L. (2001). Solution Structure and Stability of Viscous Flow in Curved Square Ducts. Journal of Fluids Engineering, 123(4), 863-868. https://doi.org/10.1115/1.1412457
Zhang, J., Chen, H., Zhou, B., & Wang, X. (2019). Flow around an array of four equispaced square cylinders. Applied Ocean Research, 89, 237-250. https://doi.org/10.1016/j.apor.2019.05.019.
