NON-NEWTONIAN FLOW AND HEAT TRANSFER AROUND TRIANGULAR BLUFF BODIES

Abstract

A bluff body is characterized by an early boundary layer separation from its surface along with the formation of wakes at its rear. Also, the pressure drag for the bluff bodies is much higher than the viscous/friction drag. The flow around the bluff body not only depends on the its shape, but also on its orientation with respect to the incoming flow direction. However, depending on the location of the boundary layer separation points, bluff bodies can be categorized into two groups. Firstly, are the bluff bodies with rounded corners, such as circular, elliptical, etc. for which the point of separation can take arbitrary positions. Secondly, are the sharp edged bluff bodies such as triangular, square, trapezoidal, etc., for which the flow separation is usually fixed by the sharp edges. Among these, triangular bluff bodies are one of the important configurations for engineering point of view. Further, the non-Newtonian fluids such as dilute polymer solutions with smaller molecules, foams, syrups, starch solutions, polymeric systems with higher molecular weight (i.e., blends, melts, solutions), emulsions and pulp and paper suspensions, which come across in chemical and related process industries exhibit either shear-thinning (or pseudo-plastic fluids, n < 1) and/or shear-thickening (or dilatant fluids, n > 1) behavior under suitable flow conditions. A very few facts are known on the flow and heat transfer of these non-Newtonian fluids past a triangular bluff body, in spite of their widespread importance in various engineering applications for instance, electronic cooling, natural circulation boilers, flow dividers in polymer processing, heat exchange systems, nuclear reactors, polymer and food industries, etc. Thus, the present dissertation numerically analyzes the characteristics of the flow and the convective heat transfer of Newtonian and non-Newtonian (power-law) fluids around a long horizontal triangular shaped bluff body/s over a wide scope of settings, namely Reynolds number (Re), Prandtl number (Pr), power-law index (n) and blockage ratio (β). In the present dissertation, the results are represented for the following five sets of problems. ii Case Domain Triangular bluff body arrangement Reynolds number (Re) Prandtl number (Pr) Power-law index (n) Blockage ratio (β) Gap ratio (S/b) I Confined Tandem 1 - 40 0.71 - 50 1 25% 1 - 4 II Confined Tandem 1 - 40 50 0.2 - 1 25% 1 - 4 III Confined Single 1 - 40 1 - 50 0.4 - 1.8 12.5% - 50% - IV Unconfined Single 50 - 150 - 0.4 - 1.8 - - V Unconfined Single 50 - 150 1 - 50 0.4 - 1.8 - - The finite volume method based computational fluid dynamics solver ANSYS FLUENT (2009) is used to numerically examine the above cases. The detailed momentum and thermal characteristics are interpreted by the terminology of streamlines and isotherms, respectively. Further, substantial consequences on total drag coefficient and its components, Nusselt number, the Colburn heat transfer factor and local Nusselt number alteration over the surfaces of a single triangular bluff body and the pair of the triangular bluff bodies are reported to explain the integrated effects of Re, Pr, n, β and S/b, as per the problem in consideration. In Case I, flow and thermal fields change from symmetric to time-periodic for 30 ≤ Re ≤ 40 at S/b = 4. As expected, the individual and overall drag coefficients decrease with the increase in Re at all gap ratios for both the triangular bluff bodies. Whereas, the average Nusselt number of both the bluff bodies increase with increasing Re, gap ratio and Pr. The average Nusselt number of the first triangular bluff body is found to be larger than the corresponding value for the second triangular cylinder in the tandem configuration. Lastly, a correlation for steady heat transfer has been established for each of the triangular bluff bodies. Additionally, the local Nusselt number alteration on the duo of tandemly arranged triangular cylinders surfaces is presented to illuminate the role of Re and Pr and gap ratios. For the shear-thinning fluid flow around the tandem pair of bluff bodies in Case II, an increment in the two individual drag coefficients and the total drag coefficient with the enhancement in n for all Re is observed for a fixed value of gap ratio in the steady regime. The first triangular cylinder is not affected by the gap ratio much and behaves similar to a single triangular bluff body. Thus, for the first triangular obstacle, the rate of heat transfer is iii seen to be greater for the shear-thinning fluids than that for Newtonian fluids (n = 1) as the average Nusselt number enhances with the increase in shear-thinning behavior, at all Re for all the gap ratios studied in steady as well as time-periodic regimes. Whereas, different trends of the Nusselt number variation with n are observed at the three gap ratios for the second triangular bluff body in steady and time-periodic regimes. Also, critical Reynolds numbers for the transition from a steady to a time-periodic are analyzed, separately for both tandem triangular bluff bodies, at each gap ratio for all n. Finally, the augmentation in the heat transfer with respect to gap ratio as well as power-law index is calculated and the maximum increment in heat transfer for the first and the second triangular bluff bodies is found approximately 72% and 215%, respectively, with respect to gap ratio, and is found approximately 110% and 102%, respectively, with respect to power-law index. In Case III, for the constant Re, Pr and n, an enhancement in the average and the local Nusselt numbers is observed with the growing β, but the opposite trends are observed at Re = 1 and Pr = 1. For the unchanged Re, Pr and β, the average Nusselt number grows as the nature of the fluid alters from shear-thickening to shear-thinning. For the constant Re, Pr and n, the Colburn jh factor enhances with increase in β. The maximum percent enhancements in the average Nusselt numbers are observed to be approximately 80% for β = 12.5% and 25%, and approximately 89% for β = 50%. Finally, a simple Colburn heat transfer factor correlation is entrenched for the preceding range of settings such that all of the results collapse into a single expression. In Case IV, the engineering parameters, for instance time-averaged drag and lift coefficients and their root-mean-square values and Strouhal number, are calculated for the power-law flow around an unbounded equilateral triangular bluff body. The flow is found to be periodic with time for the entire scope of control parameters studied. The time-averaged drag coefficient rises with the increase in Re for shear-thinning and Newtonian natures. On the other hand, a mixed trend of time-averaged drag coefficient is observed with respect to the power-law index, for shear-thickening fluids. There is an increase in Strouhal number with the increase in Re for fluids with shear-thickening nature, whereas a mixed trend of Strouhal number with Re is observed for the fluids with shear-thinning nature. Further, on studying the heat transfer for quiescent non-Newtonian power-law fluids across a heated triangular bluff body in an unconfined time-periodic regime in Case V, for the constant Pr, the values of the local Nusselt number and the time-averaged Nusselt number are iv seen to enhance with the rise in Re irrespective of n. Whereas, the local Nusselt number and the time-averaged Nusselt number decrease as the nature of the fluid alters from shear-thinning to shear-thickening for the unchanged Re and Pr. The maximum enhancements in the values of average Nusselt numbers for Pr = 10, 20 and 50 with respect to Pr = 1 are observed to be approximately 180%, 273% and 438% respectively. It is also observed that for the constant Pr and n, the Colburn heat transfer factor decreases with rising Re. Finally, the various values of the Colburn heat transfer factor at different Re, n and Pr have been correlated via a simple expression thereby enabling its estimation in a new application.