CFD ANALYSIS OF A FLUID FLOWING PAST A PAIR OF MILDLY HEATED SIDE-BY-SIDE SQUARE CYLINDERS

Abstract

In this research work, a thorough analysis of qualitative and quantitative aspects of the dynamics of a Newtonian and non-Newtonian fluid has been carried out in a viscous dominant flow field. The domain is confined with horizontal walls and mildly heated isothermal square cylinders. The presence of temperature gradient creates cross-buoyancy in the flow field. The effect of thermal buoyancy creates a free convection current which interacts with the forced convective flow to create a mixed convective flow phenomenon. A substantial modification in the flow field is achieved due to the presence of a transverse gap zone between the side-by-side square cylinders. A further complication is encountered when the flow comprises of non-Newtonian fluids due to the effect of viscosity stratification. This is best realized for a shear-thinning fluid near the walls of the square cylinders. Based on these intriguing questions, the following studies have been carried out in the laminar regime: 1. Channel-confined, mixed-convective, and Newtonian-fluid flow past a pair of heated side-by-side cylinders: effect of buoyancy on wake interactions In this study, the phenomena of buoyancy-driven cross-flow impinging on a bulk flow from the inlet for a flow past a pair of side-by-side square cylinders in a confined channel walls (which are kept in an adiabatic condition), a special case of an “internal flow” type problem are investigated. The density difference in the flow was achieved through a subtle temperature difference between the ambient fluid and the solid walls present in the domain. The study has been carried out at Reynolds number Re = 1 to 40 for a transverse gap ratio s/d = 0.7 to 10 and Richardson number Ri = 0 to 1 at a constant value of Prandtl number Pr = 50. During a rigorous parametric study, it is found that the mixed convection not only brings an early unsteadiness in the flow but also fetches an early formation of different flow regimes at Re = 40. An effort has been made to identify the precise near-wake formations leading to the vortex shedding processes in a mixed convection flow for a various range of s/d values. Different flow regimes can be identified efficiently through a unique combination of occurrences for dominant frequencies in terms of the Strouhal number St of primary, secondary and harmonic frequencies in the flow. The time variant lift plots indicate that the unsteady periodicity in the flow varies from sinusoidal nature at s/d = 0.7 (single body type flow) to square wave (non-sinusoidal periodic waveform) for s/d = 1.5 (chaotic flow) and finally getting back to sinusoidal at s/d = 6 (non- ii interacting flow). Drastic pattern changes in the flow occurred due to the onset of recirculation followed by the transition of steady to unsteady periodic nature with Re = 1 to 40 for all the values of s/d. This case is analyzed in detail through the study of drag flow parameters. 2. Channel-confined, mixed-convective, and Newtonian-fluid flow past a pair of heated side-by-side cylinders: effect of buoyancy on vorticity production We have analyzed the effect of thermal stratification of shear layers due to mixed convection heat transfer past a pair of side-by-side square cylinders in a confined domain has been analyzed, an extended part of the previous study. Investigations from the studies of instantaneous and time-averaged isotherms revealed the actual stretches of the temperature gradient in streamwise and transverse extents at Re = 1 to 40, Ri = 0 to 1, s/d = 0.7 to 10 and Pr = 50. The effects of “baroclinic production”, embedded in the transport of vorticity, were rigorously analyzed through the determination of local period-averaged vorticity flux (LPAVF) at a certain cross-section in the near-field downstream. The study also revealed the underlying flow physics pertaining to the variations in period-averaged wall vorticity (PAWV) and local Nusselt number. The transport of vorticity has been explained in terms of the vortex structure formulations and because of the absence of any such similar studies for multiple bluff-body arrangements, the study has been thoroughly correlated from the cases of single bluff-body flow. In an attempt to control several flow regimes by slightly changing the flow and thermal parameters, it is found that chaotic flow cannot exist beyond a certain value of s/d. However, an abnormality was noted in terms of the flow bifurcations at s/d = 1.5 at the juncture of flow transition from unseparated to a separated steady flow for the first time and this is solely attributed to the effect of thermal buoyancy in the flow field. 3. Channel-confined, forced-convective, and pseudoplastic-fluid flow past a pair of heated side-by-side cylinders In this study, the dynamics of pseudoplastic fluids engulfing mildly heated side-by-side square cylinders in a restricted domain has been carried out. Investigation of vortex shedding patterns, near-wake streamlines and stretch of isotherms are carried out for steady unseparated flow, unsteady periodic flow, power-law index n ranging from 0.4 to 1 and traverse gap ratio ranging from 1 (pressure-driven flow regime) to 5 (momentum-driven flow regime). The study of time-averaged streamlines at Re = 100 depicted an iii early onset of leading edge flow separation when n is reduced from 0.8 to 0.4. Chaotic interactions are seen at Re = 100 and n = 0.4, which enhance time-averaged Nusselt number Nu. The vortex shedding in the downstream loses its symmetric nature when shear-thinning effects in the flow are enhanced. The shear-thinning property also enhances the dominance of the momentum-driven flow regime. The flow features of anti-phase vortex shedding revealed symmetrical structures of negative ζ (quantifies accumulation and propagation of vortices) contours in the downstream. Whereas, for an in-phase vortex shedding, the negative ζ contours die down very early in terms of streamwise distance in the downstream. Studies on the variation of space and time-averaged flow and thermal parameters are reported for various values of n and s/d. 4. Channel-confined, mixed-convective, and pseudoplastic-fluid flow past a pair of heated side-by-side cylinders In this study, the flow physics associated with a pseudoplastic fluid as it flows past a pair of side-by-side square cylinders. The flow encompasses a combined effect of flow diffusion, cross-buoyancy and viscosity stratification. The study involves mixed convection with Richardson number Ri varying from 0 to 1 and power-law index n ranging from 0.4 to 1 at Re = 1 (signifying steady flow) and 40 (signifying unsteady flow) for a constant value of Pr = 50 and transverse gap ratio ranging from 1 to 5. The time-averaged streamlines reveal that the leading edge flow separations play an important role in deciding the vortex shedding phenomenon at the downstream. The time-averaged isotherms turn from symmetric shape to asymmetric shape as effects of Ri and n come into play. The flow regimes, evolving with the side-by-side gap ratio at a constant value of Re = 40 and Ri = 1 for various values of n, are dependent on the transition from pressure-driven to momentum-driven regime. Such effects are also realized during the analysis of the variation of drag coefficients at various values of s/d and n.