, 44:107 | Cite as

Analysis of heat and fluid flow around two co-rotating side-by-side cylinders

  • Rahim HassanzadehEmail author
  • Mohsen Darvishyadegari


Analysis of the heat and fluid flow around two co-rotating side-by-side cylinders is the subject of this numerical study which is done at constant Reynolds and Prandtl numbers of 200 and 7.0, respectively. Both cylinders rotate in the counterclockwise direction with an identical rotating speed (RS) in the range from 0 to 4. On the other hand, several gap spaces between the rotating cylinders such as G/D = 1.5, 2.0, and 3.0 are considered in the present study. The obtained results are validated against the available data in the open literature. Many different results have been reported in this investigation. It is observed that co-rotating the cylinders deforms the wake region downstream of both cylinders which the vortex strength of the lower cylinder against the rotation is stronger than that of the upper cylinder. On the other hand, co-rotating the cylinders develops a negative lift force on both cylinders. Finally, it was concluded that rotating the side-by-side cylinders reduces the heat transfer rate between the fluid flow and cylinders in general. At whole RS and G/D values, the heat transfer rate of the upper cylinder is realized to be less than that of the lower cylinder.


Forced convection co-rotating cylinders side-by-side cylinders fluid rotating zone 




\( A \)


\( C_{D} \)

drag coefficient

\( \bar{C}_{D} \)

mean drag coefficient

\( C_{L} \)

lift coefficient

\( \bar{C}_{L} \)

mean lift coefficient

\( C_{p} \)

pressure coefficient

\( c_{p} \)

specific pressure

\( D \)

cylinder diameter

\( F_{D} \)

drag force

\( F_{L} \)

lift force

\( G \)

gap space between the cylinders

\( k \)


\( n \)

surface vertical vector

\( Nu \)

Nusselt number

\( \overline{Nu} \)

mean Nusselt number

\( p \)


\( \Pr \)

Prandtl number (= \( \frac{{\mu c_{p} }}{k} \))

\( r \)

radial coordinate

\( R \)

cylinder radius

\( \text{Re} \)

Reynolds number (= \( \frac{\rho UD}{k} \))

\( RS \)

non-dimensional rotating speed (= \( \frac{{\omega_{o} D}}{2U} \))

\( t \)


\( T \)


\( u \)

streamwise velocity

\( \bar{u} \)

time-averaged streamwise velocity

\( U \)

free-stream velocity

\( u_{rms} \)

root mean square of the streamwise velocity

\( \overrightarrow {V} \)

velocity vector

\( v \)

vertical velocity

\( \bar{v} \)

time-averaged vertical velocity

\( v_{rms} \)

root mean square of the vertical velocity

\( x \)

streamwise dimension of coordinates

\( y \)

vertical dimension of coordinates

Greek symbols

\( \mu \)

dynamic viscosity of the fluid

\( \upsilon \)

kinematic viscosity of the fluid

\( \rho \)

density of the fluid

\( \alpha \)

angular location

\( \omega_{o} \)

rotating speed

\( \omega \)


\( \tau \)

cyclic period of vortex shedding


\( 1 \)

upper cylinder

\( 2 \)

lower cylinder

\( s \)

surface of the cylinder

\( \infty \)



  1. 1.
    Lloyd T P and James M 2016 Large eddy simulations of a circular cylinder at Reynolds numbers surrounding the drag crisis. Applied Ocean Research 59: 676–686CrossRefGoogle Scholar
  2. 2.
    Yeon S M, Yang J and Stern F 2016 Large-eddy simulation of the flow past a circular cylinder at sub-to super-critical Reynolds numbers. Applied Ocean Research 59: 663–675CrossRefGoogle Scholar
  3. 3.
    Gao D L, Chen W L, Li H and Hu H 2017 Flow around a circular cylinder with slit. Experimental Thermal and Fluid Science 82: 287–301CrossRefGoogle Scholar
  4. 4.
    Gonçalves R T, Franzini G R, Rosetti G F, Meneghini J R and Fujarra A L C 2015 Flow around circular cylinders with very low aspect ratio. Journal of Fluids and Structures 54: 122–141CrossRefGoogle Scholar
  5. 5.
    Nguyen V T and Nguyen H H 2016 Detached eddy simulations of flow induced vibrations of circular cylinders at high Reynolds numbers. Journal of Fluids and Structures 63: 103–119CrossRefGoogle Scholar
  6. 6.
    Hsieh S C, Low Y M and Chiew Y M 2016 Flow characteristics around a circular cylinder subjected to vortex-induced vibration near a plane boundary. Journal of Fluids and Structures 65: 257–277CrossRefGoogle Scholar
  7. 7.
    Zhang K, Katsuchi H, Zhou D, Yamada H and Han Z 2016 Numerical study on the effect of shape modification to the flow around circular cylinders. Journal of Wind Engineering and Industrial Aerodynamics 152: 23–40CrossRefGoogle Scholar
  8. 8.
    Kim S, Alam M M and Maiti D K 2018 Wake and suppression of flow-induced vibration of a circular cylinder. Ocean Engineering 151: 298–307CrossRefGoogle Scholar
  9. 9.
    Aljure D E, Lehmkhul O, Rodríguez I and Oliva A 2017 Three dimensionality in the wake of the flow around a circular cylinder at Reynolds number 5000. Computers and Fluids 147: 102–118MathSciNetCrossRefGoogle Scholar
  10. 10.
    Chung M H 2016 Transverse vortex-induced vibration of spring-supported circular cylinder translating near a plane wall. European Journal of Mechanics-B/Fluids 55: 88–103MathSciNetCrossRefGoogle Scholar
  11. 11.
    Deylami H M, Amanifard N, Hosseininezhad S S and Dolati F 2017 Numerical investigation of the wake flow control past a circular cylinder with Electrohydrodynamic actuator. European Journal of Mechanics-B/Fluids 66: 71–80MathSciNetCrossRefGoogle Scholar
  12. 12.
    Wang C, Tang H, Duan F and Simon C M 2016 Control of wakes and vortex-induced vibrations of a single circular cylinder using synthetic jets. Journal of Fluids and Structures 60: 160–179CrossRefGoogle Scholar
  13. 13.
    Xu W, Ma Y, Cheng A and Yuan H 2018 Experimental investigation on multi-mode flow-induced vibrations of two long flexible cylinders in a tandem arrangement. International Journal of Mechanical Sciences 135: 261–278CrossRefGoogle Scholar
  14. 14.
    Li Z, Prsic M A, Ong M C and Khoo B C 2018 Large Eddy Simulations of flow around two circular cylinders in tandem in the vicinity of a plane wall at small gap ratios. Journal of Fluids and Structures 76: 251–271CrossRefGoogle Scholar
  15. 15.
    Huertas-Cerdeira C, Fan B and Gharib M 2018 Coupled motion of two side-by-side inverted flags. Journal of Fluids and Structures 76: 527–535CrossRefGoogle Scholar
  16. 16.
    Xu W, Cheng A, Ma Y and Gao X 2018 Multi-mode flow-induced vibrations of two side-by-side slender flexible cylinders in a uniform flow. Marine Structures 57: 219–236CrossRefGoogle Scholar
  17. 17.
    Shaaban M and Mohany A 2018 Flow-induced vibration of three unevenly spaced in-line cylinders in cross-flow. Journal of Fluids and Structures 76: 367–383CrossRefGoogle Scholar
  18. 18.
    Alam M M, Zheng Q, Derakhshandeh J F, Rehman S, Ji C and Zafar F 2018 On forces and phase lags between vortex sheddings from three tandem cylinders. International Journal of Heat and Fluid Flow 69: 117–135CrossRefGoogle Scholar
  19. 19.
    Chen W, Ji C, Williams J, Xu D, Yang L and Cui Y 2018 Vortex-induced vibrations of three tandem cylinders in laminar cross-flow: Vibration response and galloping mechanism. Journal of Fluids and Structures 78: 215–238CrossRefGoogle Scholar
  20. 20.
    da Silva B L, Luciano R D, Utzig J and Meier H F 2018 Flow patterns and turbulence effects in large cylinder arrays. International Journal of Heat and Fluid Flow 69: 136–149CrossRefGoogle Scholar
  21. 21.
    Alam M M, Zheng Q and Hourigan K 2017 The wake and thrust by four side-by-side cylinders at a low Re. Journal of Fluids and Structures 70: 131–144CrossRefGoogle Scholar
  22. 22.
    Shaafi K, Naik S N and Vengadesan S 2017 Effect of rotating cylinder on the wake-wall interactions. Ocean Engineering 139: 275–286CrossRefGoogle Scholar
  23. 23.
    Rana K, Manzoor S, Sheikh N A, Ali M and Ali H M 2017 Gust response of a rotating circular cylinder in the vortex suppression regime. International Journal of Heat and Mass Transfer 115: 763–776CrossRefGoogle Scholar
  24. 24.
    Bayat R and Rahimi A B 2017 Numerical solution of three-dimensional NS equations and energy in the case of unsteady stagnation-point flow on a rotating vertical cylinder. International Journal of Thermal Sciences 118: 386–396CrossRefGoogle Scholar
  25. 25.
    Thakur P, Tiwari N and Chhabra R P 2018 Flow of a power-law fluid across a rotating cylinder in a confinement. Journal of Non-Newtonian Fluid Mechanics 251: 145–161.MathSciNetCrossRefGoogle Scholar
  26. 26.
    Naik S N, Vengadesan S and Prakash K A 2017 Numerical study of fluid flow past a rotating elliptic cylinder. Journal of Fluids and Structures 68: 15–31CrossRefGoogle Scholar
  27. 27.
    Hassanzadeh R 2018 Effects of Unsteady Flow Generation Over a Hot Plate on the Cooling Mechanism Using a Rotating Cylinder. Arabian Journal for Science and Engineering 1–11Google Scholar
  28. 28.
    Darvishyadegari M and Hassanzadeh R 2018 Convective heat transfer and fluid flow of two counter-rotating cylinders in tandem arrangement. Acta Mechanica 229(4): 1783–1802MathSciNetCrossRefGoogle Scholar
  29. 29.
    Darvishyadegari M and Hassanzadeh R 2019 Heat and fluid flow around two co-rotating cylinders in tandem arrangement. International Journal of Thermal Sciences 135: 206–220CrossRefGoogle Scholar
  30. 30.
    Darvishyadegari M and Hassanzadeh R 2018 Analysis of the convective heat transfer and flow behavior around two counter‐rotating side‐by‐side cylinders. Heat Transfer—Asian Research 47(6): 835–854CrossRefGoogle Scholar
  31. 31.
    Selimefendigil F, Ismael M A and Chamkha A J 2017 Mixed convection in superposed nanofluid and porous layers in square enclosure with inner rotating cylinder. International Journal of Mechanical Sciences 124: 95–108CrossRefGoogle Scholar
  32. 32.
    Kareem A K and Gao S 2017 Mixed convection heat transfer of turbulent flow in a three-dimensional lid-driven cavity with a rotating cylinder. International Journal of Heat and Mass Transfer. 112: 185–200CrossRefGoogle Scholar
  33. 33.
    Khanafer K and Aithal S M 2017 Mixed convection heat transfer in a lid-driven cavity with a rotating circular cylinder. International Communications in Heat and Mass Transfer 86: 131–142CrossRefGoogle Scholar
  34. 34.
    Selimefendigil F and Öztop H F 2018 Mixed convection of nanofluids in a three dimensional cavity with two adiabatic inner rotating cylinders. International Journal of Heat and Mass Transfer 117: 331–343CrossRefGoogle Scholar
  35. 35.
    Patankar S V 1980 Numerical Heat transfer and Fluid Flow, New York: Taylor & FranciszbMATHGoogle Scholar
  36. 36.
    Ding H, Shu C, Yeo K S and Xu D 2007 Numerical simulation of flows around two circular cylinders by mesh‐free least square‐based finite difference methods. International Journal for Numerical Methods in Fluids 53(2): 305–332CrossRefGoogle Scholar
  37. 37.
    Sarvghad-Moghaddam H, Nooredin N and Ghadiri-Dehkordi B 2011 Numerical simulation of flow over two side-by-side circular cylinders. Journal of Hydrodynamics, Ser. B 23(6): 792–805CrossRefGoogle Scholar
  38. 38.
    Meneghini J R, Saltara F, Siqueira C L R and Ferrari Jr J A 2001 Numerical simulation of flow interference between two circular cylinders in tandem and side-by-side arrangements. Journal of Fluids and Structures 15(2): 327–350CrossRefGoogle Scholar
  39. 39.
    Hilpert R 1933 Heat transfer from cylinders. Forsch. Geb. Ingenieurwes 4: 215CrossRefGoogle Scholar
  40. 40.
    Churchill S W and Bernstein M 1977 A correlating equation for forced convection from gases and liquids to a circular cylinder in crossflow. Journal of Heat Transfer 99(2): 300–306CrossRefGoogle Scholar
  41. 41.
    Harimi I and Saghafian M 2012 Numerical simulation of fluid flow and forced convection heat transfer from tandem circular cylinders using overset grid method. Journal of Fluids and Structures 28: 309–327CrossRefGoogle Scholar
  42. 42.
    Hassanzadeh R, Sahin B and Ozgoren M 2013 Large eddy simulation of flow around two side-by-side spheres. Journal of Mechanical Science and Technology 27(7): 1971–1979CrossRefGoogle Scholar

Copyright information

© Indian Academy of Sciences 2019

Authors and Affiliations

  1. 1.Faculty of the Mechanical EngineeringUrmia University of TechnologyUrmiaIran

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