Numerical Investigation of Power-law Fluid Flow and Heat Transfer over a Rotating Elliptic Cylinder in Laminar Flow Regime

Abstract

A two-dimensional laminar flow of non-Newtonian fluid over a heated rotating elliptic cylinder is numerically studied in the present work. The flow field around the cylinder is computed by solving non-linear partial differential governing equations using ANSYS FLUENT (2015). The computational domain and mesh are generated and implemented using ANSYS Workbench. The sliding mesh method (SMM) is implemented to capture the transient flow behaviour around the rotating elliptic cylinder. The non-Newtonian shear-thinning and shear-thickening fluid behaviour is modelled by power-law model. The aim of the work is to study the effect of cylinder rotation, fluid behaviour and cylinder’s aspect ratio along with Reynolds and Prandtl number on fluid flow and heat transfer phenomena. The range of dimensionless parameters considered are aspect ratio of the cylinder 𝑒 = 0.1, 0.4, 0.7 and 1.0, power-law index 0.4 ≤ 𝑛 ≤ 1.8, rotational speed 0.5 ≤ 𝛼 ≤ 2.0, Reynolds number 5 ≤ 𝑅𝑒 ≤ 100 and Prandtl number 1 ≤ 𝑃𝑟 ≤ 100. The engineering parameters, like drag and lift coefficient (𝐶𝐷 and 𝐶𝐿), stream function and vorticity contours, local and average Nusselt number (𝑁𝑢) are reported to demonstrate the effect. Streamline and vorticity patterns in the vicinity of the cylinder illustrate the wake formation and vortex shedding phenomenon in the rear part of the cylinder. Due to the cylinder rotation, vortices attached to it either merge and/or detach to/from the cylinder, and are termed as enveloping and detached vortex, respectively. Their size and characteristics largely depend upon 𝑅𝑒, 𝑒, 𝛼, and 𝑛. The power-law index (𝑛), aspect ratio (𝑒), and rotational speed (𝛼) encourage the formation of enveloping vortex; however, they have a negative impact on detached vortex. The average values of the drag coefficient are seen to decrease with 𝑅𝑒 and 𝛼. And, a non-monotonous trend is observed with the power-law index (𝑛) and aspect ratio (𝑒). The negative lift coefficient is observed due to the anticlockwise rotation of the cylinder for all parameters considered here. At a higher Reynolds number, 𝑅𝑒 = 100, the flow around the rotating elliptic cylinder exhibit the Von-Karman vortex shedding phenomenon. However, the high rotation of the cylinder (𝛼 > 1.0) obstructs the shedding of the vortices significantly. For shear-thinning and Newtonian fluids, the vortex at the top edge starts hovering in the vicinity of the cylinder. The vortex is named as Hovering vortex (HV). The shearthinning behaviour of the fluid encourages the formation of HV; however, HV is not observed for shear-thickening fluids. The HV causes a long shedding period. The variation of the local Nusselt number on the surface of the cylinder is seen to be maximum at the edges of the cylinder for all 𝑅𝑒, 𝑒, 𝛼, and 𝑛 considered here. As expected, the Prandtl number (𝑃𝑟) and shear-thinning behaviour (𝑛 < 1.0) encourage the heat transfer from the cylinder. In addition, the Nusselt number is more at higher rotational speed of the cylinder. A correlation is presented for the time average surface Nusselt number (𝑁𝑢𝑎𝑣𝑔) as the function of Prandtl number (𝑃𝑟), fluid behaviour (𝑛), and rotational speed (𝛼), i.e. 𝑁𝑢𝑎𝑣𝑔 = 𝑓(𝑅𝑒, 𝑃𝑟, 𝑛, and 𝛼) to find the Nu at intermediate values of 𝑒, 𝑃𝑟, 𝑛, and 𝛼.