The flow and heat transfer characteristics in a rectangular channel with convergent and divergent slit ribs

Highlights

• The novel geometry of channel cooling was presented.

• The channel cooling with shaped slit ribs are further explored.

• The effect of the convergent and divergent angle on cooling performance are described.

Abstract

Described in this paper is a numerical investigation on the concept for improving thermal performance of internal cooling by placing the convergent and divergent slit ribs. Five different geometrical models are investigated, including the ribs of rectangular slits and trapezoidal slits with different convergent and divergent angles. The effects of slit shape and its convergent or divergent angles on thermal performance of internal cooling are evaluated with the Reynolds numbers ranging from 10,000 to 25,000. Results obtained show that the turbulence intensity in cases with the smallest angle trapezoidal slits are in the highest level, which produces the highest level of heat transfer enhancement and highest level of pressure loss. The thermal performance index, which comprehensively evaluates the thermal performance of internal cooling, shows that the thermal performance in cases with the smallest angle trapezoidal slits are in the highest level due to the increased heat transfer enhancement and limited increase of pressure loss.

Introduction

The internal cooling with turbulent ribs is widely used as an effective cooling method in many applications, such as the gas turbine blade cooling, the electrical component cooling, the solar air heater cooling and the nuclear reactor cooling. In recent years, more and more efforts have been focused on developing more efficient heat transfer technologies due to higher costs in energy sources and materials. A common way to enhance the heat transfer coefficient and reduce the pressure loss penalty is to modify the shapes of turbulent ribs. Thus, an insight into the internal cooling of a rectangular channel with shaped ribs, in terms of flow structures and heat transfer characteristics should be conducted.

Many researchers have presented highly effective results concerning the heat transfer enhancement by placing the turbulent ribs. Han et al. [1], [2], [3], [4] systematically investigated the effects of rib pitches, rib angles, channel aspect ratios and Reynolds numbers on heat transfer enhancement and found that the rectangular channels with angled ribs and narrow aspect ratios showed a superior to the transverse ribs and wide aspect ratios in heat transfer performance. Rau et al. [5] measured the local aerodynamic and heat transfer performance in a ribbed square channel. Their results illustrated that the flow structure was three-dimensional around the rib with significant lateral velocity components and a displacement of the maximum streamwise velocity towards the smooth side wall. In addition, the strong secondary flows resulted in a three-dimensional flow field with high gradients in the local heat transfer distributions on the smooth side walls. Casarsa et al. [6] used the methods of Particle Image Velocimetry (PIV) and Liquid Crystal Thermometry (LCT) to test the aero and thermal field of turbulent flow inside a rib roughed channel. Research conducted by Wright et al. in literature [7], Kamali et al. in literature[8] and Zhang et al. in literature [9] demonstrated that the features of the inter-rib distributions of the heat transfer coefficients were strongly affected by the rib shape. Viswanathan et al. [10] predicted the effect of rotation on the hydrodynamic and thermally developed turbulent flow in a rotating duct with square ribs by the method of detached eddy simulation. Their research indicated that the secondary flow impingement was observed stronger as rotation increases. Discussed by Schüler et al. in literature [11] showed that the turning vane configuration significantly influenced the pressure loss and the heat transfer in the bend region and the outlet pass. Then, Shevchuk et al. [12] numerically studied the effect of bend aspect ratios on the flow structure and corresponding heat transfer performance. The production of dean vortices and acceleration of the flow in the bend produced strongly increased heat transfer on both the ribbed and unribbed walls in the outlet channel.

Though the turbulent ribs prove to be greatly effective on heat transfer enhancement, the limitation, which adversely influences the wide application, is the hot spot area occurring in the region just behind a solid type rib [13]. To reduce the hot spot area, the perforated ribs and slit ribs are proposed to replace the solid type ribs. According to Huang [14] and Kukreja et al. in literature [15], the slit-ribbed geometry displayed higher floor heat transfer than the solid-ribbed geometry resulting from the greater turbulence mixing effects. Besides, the perforated ribs caused lower pressure drop and thus, lower required pumping power. Sara et al. [16] investigated the thermal performance of solid and perforated rectangular blocks attached on the flat surface. Their research demonstrated that for the perforated blocks, the higher the perforation diameter, perforated area open area ratio and inclination of the perforation hole towards the surface of the plate, the better their heat transfer enhancement performance. Then, they completed their research in literature [17]. Liou et al. [18] took the numerical method of a Reynolds stress model with the wall function and a modified wall-related pressure-strain model to examine the effect of rib open area ratio on spatially periodic turbulent fluid flow and heat transfer in a channel with slit rectangular ribs mounted on one wall. They pointed out that the larger rib open area ratio led to smaller negative pressure behind the rib and, in turn, the smaller recirculation zone behind the rib. Additionally, the hole-type perforated ribs provided the highest thermal performance under the same pumping power, followed by the vertical slit-type perforated ribs, and then the horizontal slit-type perforated ribs. Moon et al. [19] carried out an experiment to study the effect of the hole diameter on steady heat transfer between two blockages with holes and pressure drop across the blockages for turbulent flow in a rectangular channel. Their research showed that smaller holes caused higher heat transfer enhancement, but also significantly larger increase of the pressure drop than larger holes. Yang et al. [20] numerically investigated the heat transfer and fluid flow characteristics in rectangular ducts with slit and solid ribs mounted on one wall. They found that the slit rib had a lower friction factor owing to less duct blockage. With greater turbulence mixing effect, the slit-ribbed geometry provided a better heat transfer than the solid-ribbed geometry. Panigrahi et al. [21] used the flow visualization and PIV (2-C and 3-C) technique to measure the flow behind surface mounted permeable rib geometrical models. Their research illustrated that the permeable ribs had shorter reattachment length compared to impermeable ribs. Shorter reattachment length resulted in higher heat transfer enhancement of inclined split-slit ribs. Then, they completed their research on the flow structure in detail in literature [22]. Liu et al. [23] proposed a novel design of the rib called the semi-attached rib. The ribs are perforated at the rib corners to form two rectangular holes for the fluid passing through the holes. As discussed in their research, the semi-attached rib could significantly improve local heat transfer and fluid flow performances and eliminate the low heat transfer area behind the solid rib. Nuntadusit et al. [24] reported the heat transfer and flow characteristics in a channel with different types of transverse perforated ribs, including the solid rib, straight perforated ribs with different heights and inclined perforated ribs with different inclinations. Revealed by their results was that the inclined perforated rib considerably improved the heat transfer just downstream the ribs, compared to straight perforated and solid ones, resulting in superior overall heat transfer performance due to jet-like flows impinging on the surface. Sharma et al. [25] studied the heat transfer and frictional characteristics in rectangular ducts with solid ribs, converging slit ribs and alternate solid slit ribs mounted transversely on the bottom wall. As expected, the converging slit rib considerably enhanced the heat transfer rate in the downstream vicinity and obviated the local hot spot formation. Qayoum et al. [26] analyzed the thermal performance of repeated permeable ribs mounted on the bottom surface of a two-pass square channel and found that split-slit configuration showed a dramatic heat transfer improvement in comparison to the solid rib and slit rib, without any commensurate increase in the pressure penalty.

These works above were all focused on the flow structure and heat transfer enhancement in a ribbed channel with minimizing the pressure loss. Most focuses paid attention to the modification of the rib in terms of geometry, aiming at the improvement of thermal performance by eliminating the hot spot just behind the solid ribs. Above investigations on eliminating the hot spot were to incline the slit ribs or split the slit ribs and the shape of convergent and divergent slit ribs were rarely considered. In this paper, the internal cooling with ribbed channel is further explored. The convergent and divergent slit ribs are applied to enhance the thermal performance. The purpose is to examine the efficacy of modified slit rib and the mechanism of it. The effects of convergent and divergent level of the slit rib are numerical simulated to facilitate the study.