Document Type : Article

**Authors**

Department of Mechanical Engineering, Persian Gulf University, Bushehr, 75169, Iran

**Abstract**

The heat transfer from circular cylinders in turbulent cross flows plays a significant role in industrial operations. The objective of this paper is to evaluate the heat transfer from a cylinder with circular cross section and four flexible fins in turbulent flows numerically. The governing equations of thermal fluid are discretized by finite element method (FEM) while the equations of motion of deformable structure of fins are discretized by finite element method (FEM). The k-ω SST model is used to simulate the flow. The results are validated by comparing the heat transfer rate from the circular cylinder with that of other investigators’ experimental and numerical studies. In addition, the fluid-structure interaction (FSI) results are validated against a benchmark example. The flexible fins are glued to the circular cylinder by two different angles (θ=0° and θ=45°). In both cases, the thermal enhancement, as well as the flow-induced vibrations of the fins, are investigated for various non-dimensional flexural rigidity. It is found that attached fins in both angles and the flexural rigidity are significantly affect Nusselt number. Moreover, it is found that the very flexible fins can increase the Nusselt number by 26%.

**Keywords**

References:

1. Izadpanah, E., Ashouri, A., Liravi, M., et al. "Effect of vortex-induced vibration of ffnned cylinders on heat transfer enhancement", Physics of Fluids, 31(7), p. 073604 (2019).

2. Hadad, Y. and Jafarpur, K. "Laminar forced convection heat transfer from isothermal cylinders with active ends and different aspect ratios in axial air flows", Heat and Mass Transfer, 47(1), pp. 59-68 (2011).

3. Izadpanah, E., Amini, Y., and Ashouri, A. "A comprehensive investigation of vortex induced vibration effects on the heat transfer from a circular cylinder", International Journal of Thermal Sciences, 125, pp. 405-418 (2018).

4. Liu, J.-C., Wei, X.-T., Zhou, Z.-Y., and Wei, Z.-W. "Numerical analysis on interactions between fluid flow and structure deformation in plate-ffn heat exchanger by Galerkin method", Heat and Mass Transfer, 54(9), pp. 2835-2844 (2018).

5. Bergles, A.E. "Techniques to augment heat transfer", Handbook of Heat Transfer (A 74-17085 05-33), New York, McGraw-Hill Book Co., p. 10-1 (1973).

6. Amini, Y., Emdad, H., and Farid, M. "A new model to solve fluid-hypo-elastic solid interaction using the smoothed particle hydrodynamics (SPH) method", European Journal of Mechanics-B/Fluids, 30(2), p. 184-194 (2011).

7. Amini, Y., Emdad, H., and Farid, M. "An accurate model for numerical prediction of piezoelectric energy harvesting from fluid structure interaction problems", Smart Materials and Structures, 23(9), p. 095034 (2014).

8. Bazilevs, Y., Korobenko, A., Deng, X., and Yan, J. "Novel structural modeling and mesh moving techniques for advanced uid-structure interaction simulation of wind turbines", International Journal for Numerical Methods in Engineering, 102(3-4), pp. 766- 783 (2015).

9. Amini, Y., Emdad, H., and Farid, M. "Fluid-structure interaction analysis of a piezoelectric flexible plate in a cavity fflled with fluid", Scientia Iranica, Transactions B, Mechanical Engineering, 23(2), p. 559 (2016).

10. Muller, A., Favrel, A., Landry, C., et al. "Fluidstructure interaction mechanisms leading to dangerous power swings in Francis turbines at full load", Journal of Fluids and Structures, 69, pp. 56-71 (2017).

11. Amini, Y., Emdad, H., and Farid, M. "Piezoelectric energy harvesting from vertical piezoelectric beams in the horizontal fluid flows", Scientia Iranica, 24(5), pp. 2396-2405 (2017).

12. Amini, Y. and Zahed, I. "Flow-induced vibration of two tandemly arranged circular cylinders with attached splitter plates", Ocean Engineering, 237 p. 109604 (2021).

13. Joshi, R.U., Soti, A.K., and Bhardwaj, R. "Numerical study of heat transfer enhancement by deformable twin plates in laminar heated channel flow", Computational Thermal Sciences: An International Journal, 7(5-6), pp. 467-476 (2015).

14. Ghalambaz, M., Jamesahar, E., Ismael, M.A., et al. "Fluid-structure interaction study of natural convection heat transfer over a flexible oscillating ffn in a square cavity", International Journal of Thermal Sciences, 111, pp. 256-273 (2017).

15. Park, S.G., Chang, C.B., Kim, B., et al. "Simulation of fluid-flexible body interaction with heat transfer", International Journal of Heat and Mass Transfer, 110, pp. 20-33 (2017).

16. Khanafer, K. and Vafai, K. "Effect of a circular cylinder and flexible wall on natural convective heat transfer characteristics in a cavity fflled with a porous medium", Applied Thermal Engineering, 181, p. 115989 (2020).

17. Mehryan, S.A.M., Alsabery, A., Modir, A., et al. "Fluid-structure interaction of a hot flexible thin plate inside an enclosure", International Journal of Thermal Sciences, 153, p. 106340 (2020).

18. Liu, B. "A Nitsche stabilized ffnite element method: Application for heat and mass transfer and fluidstructure interaction", Computer Methods in Applied Mechanics and Engineering, 386, p. 114101 (2021).

19. Amini, Y., Akhavan, S., and Izadpanah, E. "A numerical investigation on the heat transfer characteristics of nanofluid flow in a three-dimensional microchannel with harmonic rotating vortex generators", Journal of Thermal Analysis and Calorimetry, 139(1), pp. 755- 764 (2020).

20. Li, Z., Xu, X., Li, K., et al. "A apping vortex generator for heat transfer enhancement in a rectangular airside ffn", International Journal of Heat and Mass Transfer, 118, pp. 1340-1356 (2018).

21. Ali, S., Habchi, C., Menanteau, S., et al. "Heat transfer and mixing enhancement by free elastic flaps oscillation", International Journal of Heat and Mass Transfer, 85, pp. 250-264 (2015).

22. Ali, S., Menanteau, S., Habchi, C., et al. "Heat transfer and mixing enhancement by using multiple freely oscillating flexible vortex generators", Applied Thermal Engineering, 105, pp. 276-289 (2016).

23. Lee, J.B., Park, S.G., Kim, B., et al. "Heat transfer enhancement by flexible flags clamped vertically in a Poiseuille channel flow", International Journal of Heat and Mass Transfer, 107, pp. 391-402 (2017).

24. Lee, J.B., Park, S.G., and Sung, H.J. "Heat transfer enhancement by asymmetrically clamped flexible flags in a channel flow", International Journal of Heat and Mass Transfer, 116 pp. 1003-1015 (2018).

25. Chen, Y., Yu, Y., Zhou, W., et al. "Heat transfer enhancement of turbulent channel flow using tandem self-oscillating inverted flags", Physics of Fluids, 30(7), p. 075108 (2018).

26. Gallegos, R.K.B. and Sharma, R.N. "Heat transfer performance of flag vortex generators in rectangular channels", International Journal of Thermal Sciences, 137, pp. 26-44 (2019).

27. Mohammadshahi, S., Nili-Ahmadabadi, M., Samsam- Khayani, H., et al. "Numerical study of a vortexinduced vibration technique for passive heat transfer enhancement in internal turbulent flow", European Journal of Mechanics-B/Fluids, 72, pp. 103-113(2018).

28. Soti, A.K., Bhardwaj, R., and Sheridan, J. "Flowinduced deformation of a flexible thin structure as manifestation of heat transfer enhancement", International Journal of Heat and Mass Transfer, 84, pp. 1070-1081 (2015).

29. Sun, X., Ye, Z., Li, J., et al. "Forced convection heat transfer from a circular cylinder with a flexible ffn", International Journal of Heat and Mass Transfer, 128, pp. 319-334 (2019).

30. Sun, X., Li, S., Lin, G.-G., et al. "Effects of flowinduced vibration on forced convection heat transfer from two tandem circular cylinders in laminar flow", International Journal of Mechanical Sciences, 195, p. 106238 (2021).

31. Duan, D., Cheng, Y., Ge, M., et al. "Experimental and numerical study on heat transfer enhancement by Flow-induced vibration in pulsating flow", Applied Thermal Engineering, 207, p. 118171 (2022).

32. Xie, P. and Zhang, X. "Study of laminar convection heat transfer in single-side-heating small-scale cooling channel with vibration cylinder", International Communications in Heat and Mass Transfer, 120, p. 105030 (2021).

33. Amini, Y. and Habibi, S.E. "Effects of multiple flexible vortex generators on the hydrothermal characteristics of a rectangular channel", International Journal of Thermal Sciences, 175, p. 107454 (2022).

34. Shahrestani, A.B., Alshuraiaan, B., and Izadi, M. "Combined natural convection-FSI inside a circular enclosure divided by a movable barrier", International Communications in Heat and Mass Transfer, 126, p. 105426 (2021).

35. Zhong, X., Fu, S., Chan, K., Wang, et al. "Experimental and numerical study of heat transfer performance of a channel flow with an inverted flag", International Journal of Heat and Mass Transfer, 193, p. 122969 (2022).

36. Hakim, M.A., Ahad, A.I., Karim, A.U., et al. "Fluid structure interaction and heat transfer enhancement with dynamic flexible flow modulator", International Communications in Heat and Mass Transfer, 134, p. 105983 (2022).

37. Mehryan, S., Alsabery, A., Modir, A., et al. "Fluidstructure interaction of a hot flexible thin plate inside an enclosure", International Journal of Thermal Sciences, 153, p. 106340 (2020).

38. Dey, P. "Fluid flow and heat transfer around square cylinder with dual splitter plates arranged at novel positions", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 236(9), pp. 5060-5077 (2022).

39. Menter, F.R. "Two-equation eddy-viscosity turbulence models for engineering applications", AIAA Journal, 32(8), pp. 1598-1605 (1994).

40. Churchill, S. and Bernstein, M. "A correlating equation for forced convection from gases and liquids to a circular cylinder in cross flow", Journal of Heat Transfer, 99(2), pp. 300-306 (1977).

41. Knudsen, J.G., Katz, D.L., and Street, R.E. "Fluid dynamics and heat transfer", Physics Today, 12, p. 40 (1959).

42. Giedt, W. "Investigation of variation of point unit heat transfer coefficient around a cylinder normal to an air stream", Trans. ASME, 71, pp. 375-381 (1949).

43. Turek, S. and Hron, J. Proposal for Numerical Benchmarking of Fluid-Structure Interaction between an Elastic Object and Laminar Incompressible Flow, Fluid-Structure Interaction, (2006), Springer, p. 371- 385.

44. Mahir, N. and Altac, Z. "Numerical investigation of convective heat transfer in unsteady flow past two cylinders in tandem arrangements", International Journal of Heat and Fluid Flow, 29(5), p. 1309-1318 (2008).

45. Kravchenko, A.G. and Moin, P. "Numerical studies of flow over a circular cylinder at Re D= 3900", Physics of Fluids, 12(2), pp. 403-417 (2000).

2. Hadad, Y. and Jafarpur, K. "Laminar forced convection heat transfer from isothermal cylinders with active ends and different aspect ratios in axial air flows", Heat and Mass Transfer, 47(1), pp. 59-68 (2011).

3. Izadpanah, E., Amini, Y., and Ashouri, A. "A comprehensive investigation of vortex induced vibration effects on the heat transfer from a circular cylinder", International Journal of Thermal Sciences, 125, pp. 405-418 (2018).

4. Liu, J.-C., Wei, X.-T., Zhou, Z.-Y., and Wei, Z.-W. "Numerical analysis on interactions between fluid flow and structure deformation in plate-ffn heat exchanger by Galerkin method", Heat and Mass Transfer, 54(9), pp. 2835-2844 (2018).

5. Bergles, A.E. "Techniques to augment heat transfer", Handbook of Heat Transfer (A 74-17085 05-33), New York, McGraw-Hill Book Co., p. 10-1 (1973).

6. Amini, Y., Emdad, H., and Farid, M. "A new model to solve fluid-hypo-elastic solid interaction using the smoothed particle hydrodynamics (SPH) method", European Journal of Mechanics-B/Fluids, 30(2), p. 184-194 (2011).

7. Amini, Y., Emdad, H., and Farid, M. "An accurate model for numerical prediction of piezoelectric energy harvesting from fluid structure interaction problems", Smart Materials and Structures, 23(9), p. 095034 (2014).

8. Bazilevs, Y., Korobenko, A., Deng, X., and Yan, J. "Novel structural modeling and mesh moving techniques for advanced uid-structure interaction simulation of wind turbines", International Journal for Numerical Methods in Engineering, 102(3-4), pp. 766- 783 (2015).

9. Amini, Y., Emdad, H., and Farid, M. "Fluid-structure interaction analysis of a piezoelectric flexible plate in a cavity fflled with fluid", Scientia Iranica, Transactions B, Mechanical Engineering, 23(2), p. 559 (2016).

10. Muller, A., Favrel, A., Landry, C., et al. "Fluidstructure interaction mechanisms leading to dangerous power swings in Francis turbines at full load", Journal of Fluids and Structures, 69, pp. 56-71 (2017).

11. Amini, Y., Emdad, H., and Farid, M. "Piezoelectric energy harvesting from vertical piezoelectric beams in the horizontal fluid flows", Scientia Iranica, 24(5), pp. 2396-2405 (2017).

12. Amini, Y. and Zahed, I. "Flow-induced vibration of two tandemly arranged circular cylinders with attached splitter plates", Ocean Engineering, 237 p. 109604 (2021).

13. Joshi, R.U., Soti, A.K., and Bhardwaj, R. "Numerical study of heat transfer enhancement by deformable twin plates in laminar heated channel flow", Computational Thermal Sciences: An International Journal, 7(5-6), pp. 467-476 (2015).

14. Ghalambaz, M., Jamesahar, E., Ismael, M.A., et al. "Fluid-structure interaction study of natural convection heat transfer over a flexible oscillating ffn in a square cavity", International Journal of Thermal Sciences, 111, pp. 256-273 (2017).

15. Park, S.G., Chang, C.B., Kim, B., et al. "Simulation of fluid-flexible body interaction with heat transfer", International Journal of Heat and Mass Transfer, 110, pp. 20-33 (2017).

16. Khanafer, K. and Vafai, K. "Effect of a circular cylinder and flexible wall on natural convective heat transfer characteristics in a cavity fflled with a porous medium", Applied Thermal Engineering, 181, p. 115989 (2020).

17. Mehryan, S.A.M., Alsabery, A., Modir, A., et al. "Fluid-structure interaction of a hot flexible thin plate inside an enclosure", International Journal of Thermal Sciences, 153, p. 106340 (2020).

18. Liu, B. "A Nitsche stabilized ffnite element method: Application for heat and mass transfer and fluidstructure interaction", Computer Methods in Applied Mechanics and Engineering, 386, p. 114101 (2021).

19. Amini, Y., Akhavan, S., and Izadpanah, E. "A numerical investigation on the heat transfer characteristics of nanofluid flow in a three-dimensional microchannel with harmonic rotating vortex generators", Journal of Thermal Analysis and Calorimetry, 139(1), pp. 755- 764 (2020).

20. Li, Z., Xu, X., Li, K., et al. "A apping vortex generator for heat transfer enhancement in a rectangular airside ffn", International Journal of Heat and Mass Transfer, 118, pp. 1340-1356 (2018).

21. Ali, S., Habchi, C., Menanteau, S., et al. "Heat transfer and mixing enhancement by free elastic flaps oscillation", International Journal of Heat and Mass Transfer, 85, pp. 250-264 (2015).

22. Ali, S., Menanteau, S., Habchi, C., et al. "Heat transfer and mixing enhancement by using multiple freely oscillating flexible vortex generators", Applied Thermal Engineering, 105, pp. 276-289 (2016).

23. Lee, J.B., Park, S.G., Kim, B., et al. "Heat transfer enhancement by flexible flags clamped vertically in a Poiseuille channel flow", International Journal of Heat and Mass Transfer, 107, pp. 391-402 (2017).

24. Lee, J.B., Park, S.G., and Sung, H.J. "Heat transfer enhancement by asymmetrically clamped flexible flags in a channel flow", International Journal of Heat and Mass Transfer, 116 pp. 1003-1015 (2018).

25. Chen, Y., Yu, Y., Zhou, W., et al. "Heat transfer enhancement of turbulent channel flow using tandem self-oscillating inverted flags", Physics of Fluids, 30(7), p. 075108 (2018).

26. Gallegos, R.K.B. and Sharma, R.N. "Heat transfer performance of flag vortex generators in rectangular channels", International Journal of Thermal Sciences, 137, pp. 26-44 (2019).

27. Mohammadshahi, S., Nili-Ahmadabadi, M., Samsam- Khayani, H., et al. "Numerical study of a vortexinduced vibration technique for passive heat transfer enhancement in internal turbulent flow", European Journal of Mechanics-B/Fluids, 72, pp. 103-113(2018).

28. Soti, A.K., Bhardwaj, R., and Sheridan, J. "Flowinduced deformation of a flexible thin structure as manifestation of heat transfer enhancement", International Journal of Heat and Mass Transfer, 84, pp. 1070-1081 (2015).

29. Sun, X., Ye, Z., Li, J., et al. "Forced convection heat transfer from a circular cylinder with a flexible ffn", International Journal of Heat and Mass Transfer, 128, pp. 319-334 (2019).

30. Sun, X., Li, S., Lin, G.-G., et al. "Effects of flowinduced vibration on forced convection heat transfer from two tandem circular cylinders in laminar flow", International Journal of Mechanical Sciences, 195, p. 106238 (2021).

31. Duan, D., Cheng, Y., Ge, M., et al. "Experimental and numerical study on heat transfer enhancement by Flow-induced vibration in pulsating flow", Applied Thermal Engineering, 207, p. 118171 (2022).

32. Xie, P. and Zhang, X. "Study of laminar convection heat transfer in single-side-heating small-scale cooling channel with vibration cylinder", International Communications in Heat and Mass Transfer, 120, p. 105030 (2021).

33. Amini, Y. and Habibi, S.E. "Effects of multiple flexible vortex generators on the hydrothermal characteristics of a rectangular channel", International Journal of Thermal Sciences, 175, p. 107454 (2022).

34. Shahrestani, A.B., Alshuraiaan, B., and Izadi, M. "Combined natural convection-FSI inside a circular enclosure divided by a movable barrier", International Communications in Heat and Mass Transfer, 126, p. 105426 (2021).

35. Zhong, X., Fu, S., Chan, K., Wang, et al. "Experimental and numerical study of heat transfer performance of a channel flow with an inverted flag", International Journal of Heat and Mass Transfer, 193, p. 122969 (2022).

36. Hakim, M.A., Ahad, A.I., Karim, A.U., et al. "Fluid structure interaction and heat transfer enhancement with dynamic flexible flow modulator", International Communications in Heat and Mass Transfer, 134, p. 105983 (2022).

37. Mehryan, S., Alsabery, A., Modir, A., et al. "Fluidstructure interaction of a hot flexible thin plate inside an enclosure", International Journal of Thermal Sciences, 153, p. 106340 (2020).

38. Dey, P. "Fluid flow and heat transfer around square cylinder with dual splitter plates arranged at novel positions", Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science, 236(9), pp. 5060-5077 (2022).

39. Menter, F.R. "Two-equation eddy-viscosity turbulence models for engineering applications", AIAA Journal, 32(8), pp. 1598-1605 (1994).

40. Churchill, S. and Bernstein, M. "A correlating equation for forced convection from gases and liquids to a circular cylinder in cross flow", Journal of Heat Transfer, 99(2), pp. 300-306 (1977).

41. Knudsen, J.G., Katz, D.L., and Street, R.E. "Fluid dynamics and heat transfer", Physics Today, 12, p. 40 (1959).

42. Giedt, W. "Investigation of variation of point unit heat transfer coefficient around a cylinder normal to an air stream", Trans. ASME, 71, pp. 375-381 (1949).

43. Turek, S. and Hron, J. Proposal for Numerical Benchmarking of Fluid-Structure Interaction between an Elastic Object and Laminar Incompressible Flow, Fluid-Structure Interaction, (2006), Springer, p. 371- 385.

44. Mahir, N. and Altac, Z. "Numerical investigation of convective heat transfer in unsteady flow past two cylinders in tandem arrangements", International Journal of Heat and Fluid Flow, 29(5), p. 1309-1318 (2008).

45. Kravchenko, A.G. and Moin, P. "Numerical studies of flow over a circular cylinder at Re D= 3900", Physics of Fluids, 12(2), pp. 403-417 (2000).

Transactions on Mechanical Engineering (B)

January and February 2023Pages 64-76