Wall effects on the cross-buoyancy around a square cylinder in the steady regime

Abstract

-The effects of blockage ratio on the combined free and forced convection from a long heated square obstacle confined in a horizontal channel are investigated in this work. The numerical computations are performed in the steady regime for Reynolds number = 1 -30, Richardson number = 0 -1 for blockage ratios of 0.125 and 0.25 for the fixed Prandtl number of 0.7 (air). The governing equations, along with appropriate boundary conditions, are solved by using a semi-explicit finite volume method implemented on the collocated grid arrangement. The total drag and lift coefficients, local and average Nusselt numbers and the representative streamline, vorticity and isotherm patterns are presented to elucidate the role of blockage ratio on the cross-buoyancy across a confined square cylinder. The asymmetry in the flow and temperature fields decreases with increasing value of the blockage ratio. Similar to forced convection, the total drag coefficient increases with increasing value of the blockage ratio for the fixed values of the Reynolds and Richardson numbers.

Transition to periodic unsteady and effects of Prandtl and Richardson numbers on the flow across a confined heated trapezoidal prism

“…It has been observed that for a fixed value of the blockage ratio, the size of recirculation region increases with an increase in the Re. This nature is found similar to that of the confined flow across the square [14,15,23], triangular [12] and circular [19][20][21] bluff bodies. For the fixed value of the Re, the size of recirculation region decreases with an increase in the blockage ratio from 12.5 to 50 %.…”

“…The wake region around the trapezoidal prism diminishes with increasing Richardson number due to higher mass flow rate passing underneath the prism than above it. The similar behavior of the flow patterns with respect to Richardson number is observed for the confined flow around a square prism [15,23].…”

“…Table 7 shows the corner/peak values of the local Nusselt numbers for different Prandtl number, blockage ratio and Reynolds number at Ri = 0. The local Nusselt number increases toward the corners (A or B) on the front surface of the tapered trapezoidal prism as there is the highest crowding of isotherms at this surface thereby resulting in high heat transfer from the front surface similar to what has been observed in a confined square prism [14,15,23]. The value of the local Nusselt number decreases on top (B to C) and bottom (A to D) surfaces and then increases piercingly toward the rear corners (C or D) of trapezoidal prism.…”

“…It is also observed that for the blockage ratio of 12.5 %, the wavering effect increases with the increase in Prandtl number because of the time-periodic nature found at Re = 40. Similar to the confined square [14,15,23], triangular [12] and circular [22] obstacles in a channel, the highest crowding of isotherms is observed on the front surface of the tapered trapezoidal prism which is quite apparent from the thermal patterns. It therefore results in high heat transfer from the front surface of the tapered trapezoidal prism as compared to the other surfaces of the tapered prism.…”

“…With the influence of cross buoyancy, the asymmetry increases with the increase in Richardson number for the temperature field. The clustering of isotherms near the surfaces of the trapezoidal prism also increases with the increase in Richardson number [15,23]. Table 7 shows the corner/peak values of the local Nusselt numbers for different Prandtl number, blockage ratio and Reynolds number at Ri = 0.…”