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The role of cross thermal buoyancy on flow transition around side-by-side cylinders at low Reynolds numbers

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Abstract

We investigate the influence of cross thermal buoyancy to initiate the vortex shedding process around two side-by-side circular cylinders kept in a free stream flow. The critical buoyancy parameter is assessed for the Reynolds number in the range 10–40. In the stated range, a steady separated flow evolves under the pure forced convective condition. However, with the introduction of thermal buoyancy, instability grows and at a specific value of the buoyancy parameter, the flow turns into unsteady periodic with the formation of vortex shedding. The above phenomena have been examined numerically by a two dimensional simulation based on a finite volume method for a fixed gap spacing between the cylinders and considering air as the working medium. It is observed that the strength of the buoyancy could be a decisive factor in demarcating various flow regimes. The critical strengths of buoyancy where the flow transforms into unsteady periodic from the steady pattern are estimated for the Reynolds number range. It shows a decreasing pattern with increasing Reynolds number. The flow transition is visualized through the vorticity, isotherm contours, lift signals and phase diagrams. Furthermore, a regime diagram is constructed to clearly depict various zones of hydrodynamic behavior.

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Abbreviations

C D :

Drag coefficient

C L :

Lift coefficient

D :

Diameter of cylinder (m)

F D :

Force due to drag (N)

F L :

Force due to lift (N)

G :

Gap spacing (m)

g* :

Gap spacing (dimensionless)

\(\hat{g}\) :

Acceleration due to gravity (m2 s–1)

Gr :

Grashoff number

H :

Convective heat transfer coefficient (W m–1 K–1)

K :

Thermal conductivity (W m–2 K–1)

Nu :

Nusselt number

P :

Pressure (dimensionless)

Pr :

Prandtl number

Re :

Reynolds number

Ri :

Richardson number

T :

Dimensionless time

T :

Temperature (K)

T w :

Wall temperature (K)

T ∞ :

Temperature of free stream fluid (K)

u ∞ :

Velocity of free stream fluid (m s–1)

u, v :

Velocities (m s–1)

x, y :

Coordinates (m)

\(\alpha\) :

Thermal diffusivity (m2 s–1)

\(\beta\) :

Coefficient of thermal expansion (K–1)

\(\eta\) :

Kinematic viscosity (m2 s–1)

\(\Theta\) :

Temperature (dimensionless)

\(\rho\) :

Density of fluid (kg m–3)

Cr :

Critical

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Acknowledgments

N. V. V. Krishna Chaitanya gratefully acknowledges financial support from Council of Scientific and Industrial Research (CSIR-HRDG), India through CSIR – Senior Research Fellowship with award no. 31/0019(11395)/2021-EMR-I.

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Authors and Affiliations

  1. CSIR - Central Mechanical Engineering Research Institute, Durgapur, 713209, India

    N. V. V. Krishna Chaitanya, Dipankar Chatterjee & Bittagopal Mondal

  2. Academy of Scientific and Innovative Research, Ghaziabad, 201002, India

    N. V. V. Krishna Chaitanya, Dipankar Chatterjee & Bittagopal Mondal

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  1. N. V. V. Krishna Chaitanya
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Contributions

NVVKC: Methodology, Software, Writing- Original draft preparation. DC: Conceptualization, Writing- Reviewing and Editing, Supervision. BM: Software, Validation.

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Correspondence to Dipankar Chatterjee.

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Chaitanya, N.V.V.K., Chatterjee, D. & Mondal, B. The role of cross thermal buoyancy on flow transition around side-by-side cylinders at low Reynolds numbers. J Therm Anal Calorim 148, 2921–2931 (2023). https://doi.org/10.1007/s10973-022-11620-0

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