Parabolic transport measurement of hydrodynamic forces for flow around circular/triangular distance dependent obstructions: Finite element analysis

Khalil Ur Rehman; Wasfi Shatanawi; Kamal Abodayeh; Taqi A.M. Shatnawi; Khalil Ur Rehman; Wasfi Shatanawi; Kamal Abodayeh; Taqi A.M. Shatnawi

doi:10.3934/math.2023444

AIMS Mathematics

2023, Volume 8, Issue 4: 8847-8866. doi: 10.3934/math.2023444

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Parabolic transport measurement of hydrodynamic forces for flow around circular/triangular distance dependent obstructions: Finite element analysis

1.
Department of Mathematics and Sciences, College of Humanities and Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia
2.
Department of Mathematics, Air University, PAF Complex E-9, Islamabad 44000, Pakistan
3.
Department of Mathematics, Faculty of Science, The Hashemite University, P.O. Box 330127, Zarqa 13133, Jordan

Received: 14 September 2022 Revised: 31 December 2022 Accepted: 18 January 2023 Published: 08 February 2023
MSC : 35A25, 65MO6, 76D05

The present effort is the low Reynolds finite element hybrid meshed solution to apprehend the flow field properties in a convergent-divergent (CD) domain having engineering standpoints applications. To be more specific, we have considered the CD domain rooted with two types of obstructions in three various arrangements namely triangular/triangular, circular/triangular, and triangular/circular in CD throat. The viscous fluid is introduced from the inlet and interacts with installed obstacles. The moving stream in the channel is modelled mathematically in terms of the two-dimensional time-independent equations. The finite element approach is used to disclose numerical solutions by means of a hybrid meshing scheme. Optimized drag and lift force values encountered by an obstruction are offered through line integration across the external obstruction surfaces. In comparison to obstruction in left vicinity, the lift force faced by the triangle obstacle on the right side of the CD throat is larger. Furthermore, as compared to the drag force faced by the triangular obstruction in the same proximity, the circular obstacle experienced greater values as a drag. The lifting force sensed by the triangular cylinder is larger than circular cylinders. The assessment of marine hydrodynamic forces and stability individualities for fully or partially submerged objects in ocean engineering will benefit from the results of this study.
- fractional distance,
- hydrodynamic forces,
- nonlinear PDEs,
- newtonian model,
- triangular/circular obstructions,
- CD domain,
- hybrid meshing
Citation: Khalil Ur Rehman, Wasfi Shatanawi, Kamal Abodayeh, Taqi A.M. Shatnawi. Parabolic transport measurement of hydrodynamic forces for flow around circular/triangular distance dependent obstructions: Finite element analysis[J]. AIMS Mathematics, 2023, 8(4): 8847-8866. doi: 10.3934/math.2023444

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Abstract

The present effort is the low Reynolds finite element hybrid meshed solution to apprehend the flow field properties in a convergent-divergent (CD) domain having engineering standpoints applications. To be more specific, we have considered the CD domain rooted with two types of obstructions in three various arrangements namely triangular/triangular, circular/triangular, and triangular/circular in CD throat. The viscous fluid is introduced from the inlet and interacts with installed obstacles. The moving stream in the channel is modelled mathematically in terms of the two-dimensional time-independent equations. The finite element approach is used to disclose numerical solutions by means of a hybrid meshing scheme. Optimized drag and lift force values encountered by an obstruction are offered through line integration across the external obstruction surfaces. In comparison to obstruction in left vicinity, the lift force faced by the triangle obstacle on the right side of the CD throat is larger. Furthermore, as compared to the drag force faced by the triangular obstruction in the same proximity, the circular obstacle experienced greater values as a drag. The lifting force sensed by the triangular cylinder is larger than circular cylinders. The assessment of marine hydrodynamic forces and stability individualities for fully or partially submerged objects in ocean engineering will benefit from the results of this study.

References

[1]	J. H. Gerrard, An experimental investigation of the oscillating lift and drag of a circular cylinder shedding turbulent vortices, J. Fluid Mech., 11 (1961), 244–256. https://doi.org/10.1017/S0022112061000494 doi: 10.1017/S0022112061000494
[2]	S. C. Kacker, B. Pennington, R. S. Hill, Fluctuating lift coefficient for a circular cylinder in cross flows, J. Mech. Eng. Sci., 16 (1974), 215–224. https://doi.org/10.1243/JMES_JOUR_1974_016_040_02 doi: 10.1243/JMES_JOUR_1974_016_040_02
[3]	J. H. Gerrard, The wakes of cylindrical bluff bodies at low Reynolds number, Philos. Trans. R. Soc. Lond. Ser. A Math. Phys. Sci., 288 (1978), 351–382.
[4]	C. Norberg, Flow around a circular cylinder: Aspects of fluctuating lift, J. Fluides Struct., 15 (2001), 459–469. https://doi.org/10.1006/jfls.2000.0367 doi: 10.1006/jfls.2000.0367
[5]	P. Catalano, M. Wang, G. Iaccarino, P. Moin, Numerical simulation of the flow around a circular cylinder at high Reynolds numbers, Int. J. Heat Fluid Fl., 24 (2003), 463–469. https://doi.org/10.1016/S0142-727X(03)00061-4 doi: 10.1016/S0142-727X(03)00061-4
[6]	M. Zhao, L. Cheng, B. Teng, D. F. Liang, Numerical simulation of viscous flow past two circular cylinders of different diameters, Appl. Ocean Rese., 27 (2005), 39–55. http://doi.org/10.1016/j.apor.2004.10.002 doi: 10.1016/j.apor.2004.10.002
[7]	J. Deng, A. -L. Ren, J. -F. Zou, X. -M. Shao, Three-dimensional flow around two circular cylinders in tandem arrangement, Fluid Dynam. Res., 38 (2006), 386. http://doi.org/10.1016/j.fluiddyn.2006.02.003 doi: 10.1016/j.fluiddyn.2006.02.003
[8]	M. M. Alam, Y. Zhou, Flow around two side-by-side closely spaced circular cylinders, J. Fluids Struct., 23 (2007), 799–805. https://doi.org/10.1016/j.jfluidstructs.2006.12.002 doi: 10.1016/j.jfluidstructs.2006.12.002
[9]	T. Kitagawa, H. Ohta, Numerical investigation on flow around circular cylinders in tandem arrangement at a subcritical Reynolds number, J. Fluids Struct., 24 (2008), 680–699. http://doi.org/10.1016/j.jfluidstructs.2007.10.010 doi: 10.1016/j.jfluidstructs.2007.10.010
[10]	M. C. Ong, T. Utnes, L. E. Holmedal, D. Myrhaug, B. Pettersen, Numerical simulation of flow around a smooth circular cylinder at very high Reynolds numbers, Mar. Struct., 22 (2009), 142–153. https://doi.org/10.1016/j.marstruc.2008.09.001 doi: 10.1016/j.marstruc.2008.09.001
[11]	S. Y. Cao, S. Ozono, Y. Tamura, Y. J. Ge, H. Kikugawa, Numerical simulation of Reynolds number effects on velocity shear flow around a circular cylinder, J. Fluids Struct., 26 (2010), 685–702. https://doi.org/10.1016/j.jfluidstructs.2010.03.003 doi: 10.1016/j.jfluidstructs.2010.03.003
[12]	M. Zhao, L. Cheng, T. M. Zhou, Three-dimensional numerical simulation of oscillatory flow around a circular cylinder at right and oblique attacks, Ocean Eng., 38 (2011), 2056–2069. https://doi.org/10.1016/j.oceaneng.2011.09.007 doi: 10.1016/j.oceaneng.2011.09.007
[13]	M. S. Akoz, Investigation of vortical flow characteristics around a partially buried circular cylinder, Ocean Eng., 52 (2012), 35–51. https://doi.org/10.1016/j.oceaneng.2012.06.011 doi: 10.1016/j.oceaneng.2012.06.011
[14]	L. -H. Yu, J. -M. Zhan, Y.-S. Li, Numerical investigation of drag force on flow through circular array of cylinders, J. Hydrodyn., 25 (2013), 330–338. https://doi.org/10.1016/S1001-6058(11)60371-6 doi: 10.1016/S1001-6058(11)60371-6
[15]	O. Lehmkuhl, I. Rodríguez, R. Borrell, J. Chiva, A. Oliva, Unsteady forces on a circular cylinder at critical Reynolds numbers, Phys. Fluids, 26 (2014), 125110. https://doi.org/10.1063/1.4904415 doi: 10.1063/1.4904415
[16]	H. Mehdi, V. Namdev, P. Kumar, A. Tyagi, Numerical analysis of fluid flow around a circular cylinder at low Reynolds number, IOSR J. Mech. Civil Eng., 3 (2016), 94–101. http://doi.org/10.9790/1684-13030294101 doi: 10.9790/1684-13030294101
[17]	D. -L. Gao, W. -L. Chen, H. Li, H. Hu, Flow around a circular cylinder with slit, Exp. Therm. Fluid Sci., 82 (2017), 287–301. https://doi.org/10.1016/j.expthermflusci.2016.11.025 doi: 10.1016/j.expthermflusci.2016.11.025
[18]	Z. Z. Bao, G. L. Qin, W. Q. He, Y. Z. Wang, Numerical investigation of flow around a slotted circular cylinder at low Reynolds number, J. Wind Eng. Ind. Aerod., 183 (2018), 273–282. https://doi.org/10.1016/j.jweia.2018.11.010 doi: 10.1016/j.jweia.2018.11.010
[19]	A. Escobar, V. Negro, J. S. López-Gutiérrez, M. D. Esteban, Influence of temperature and salinity on hydrodynamic forces, J. Ocean Eng. Sci., 1 (2016), 325–336. https://doi.org/10.1016/j.joes.2016.09.004 doi: 10.1016/j.joes.2016.09.004
[20]	H. X. Zheng, J. S. Wang, Efficient three-dimensional high-resolution simulations of flow fields around cylinders, J. Ocean Eng. Sci., 3 (2018), 205–217. https://doi.org/10.1016/j.joes.2018.08.001 doi: 10.1016/j.joes.2018.08.001
[21]	A. Najafi, H. Nowruzi, On hydrodynamic analysis of stepped planing crafts, J. Ocean Eng. Sci., 4 (2019), 238–251. https://doi.org/10.1016/j.joes.2019.04.007 doi: 10.1016/j.joes.2019.04.007
[22]	M. Schäfer, S. Turek, F. Durst, E. Krause, R. Rannacher, Benchmark computations of laminar flow around a cylinder, In: Flow Simulation with High-Performance Computers Ⅱ, 1996,547–566. https://doi.org/10.1007/978-3-322-89849-4_39
[23]	R. Mahmood, N. Kousar, K. Usman, A. Mehmood, Finite element simulations for stationary Bingham fluid flow past a circular cylinder, J. Braz. Soc. Mech. Sci. Eng., 40 (2018), 459. http://doi.org/10.1007/s40430-018-1383-2( doi: 10.1007/s40430-018-1383-2
[24]	K. U. Rehman, M. S. Alqarni, R. Mahmood, N. Kousar, M. Y. Malik, A classical remark on the compatibility of inlet velocity and pressure singularities: Finite-element visualization, Eur. Phys. J. Plus, 134 (2019), 230. http://doi.org/10.1140/epjp/i2019-12628-8 doi: 10.1140/epjp/i2019-12628-8
[25]	Y. -M. Chu, M. S. Hashmi, N. Khan, S. U. Khan, M. I. Khan, S. Kadry, et al., Thermophoretic particles deposition features in thermally developed flow of Maxwell fluid between two infinite stretched disks, J. Mater. Res. Technol., 9 (2020), 12889–12898. https://doi.org/10.1016/j.jmrt.2020.09.011 doi: 10.1016/j.jmrt.2020.09.011
[26]	M. Nazeer, F. Hussain, M. I. Khan, A. -U. Reham, E. R. El-Zahar, Y. -M. Chu, et al., Theoretical study of MHD electro-osmotically flow of third-grade fluid in micro channel, Appl. Math. Comput., 420 (2022), 126868. http://doi.org/10.1016/j.amc.2021.126868 doi: 10.1016/j.amc.2021.126868
[27]	K. U. Rehman, E. A. Algehyne, F. Shahzad, E. -S. M. Sherif, Y. -M. Chu, On thermally corrugated porous enclosure (TCPE) equipped with casson liquid suspension: Finite element thermal analysis, Case Stud. Therm. Eng., 25 (2021), 100873. https://doi.org/10.1016/j.csite.2021.100873 doi: 10.1016/j.csite.2021.100873
[28]	Introduction to COMSOL multiphysicsⓇ, In: COMSOL Multiphysics, Available from: https://cdn.comsol.com/doc/6.1.0.282/IntroductionToCOMSOLMultiphysics.zh_CN.pd
[29]	A. Pishkoo, M. Darus, Using fractal calculus to solve fractal Navier-Stokes equations, and simulation of laminar static mixing in COMSOL Multiphysics, Fractal Fract., 5 (2021), 16. https://doi.org/10.3390/fractalfract5010016 doi: 10.3390/fractalfract5010016
[30]	A. A. Memon, M. A. Memon, K. Bhatti, K. Jacob, T. Sitthiwirattham, C. Promsakon, et al., Modelling and simulation of fluid flow through a circular cylinder with high Reynolds number: A COMSOL multiphysics study, J. Math., 2022 (2022), 5282980. https://doi.org/10.1155/2022/5282980 doi: 10.1155/2022/5282980

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