Numerical simulation on performances of plane and curved winglet – Pair vortex generators in a rectangular channel and field synergy analysis

Highlights

• Curved vortex generators show better thermo-hydraulic performance than plane ones.

• The optimum attack angle to enhance heat transfer for curved vortex generators is 45°.

• The field synergy principle is used to clarify the mechanism of heat transfer.

• The volume-average synergy angle θ_m increases with the increasing of Re.

• θ_m decreases with the increasing of inclination angle.

Abstract

Thermal and flow characteristics of plane and curved longitudinal vortex generators (LVGs) are investigated and the corresponding mechanism is analyzed based on field synergy principle (FSP). 3 – D numerical simulations are carried out in a channel flow (Re = 700–26500) embedded with a pair of plane and curved delta, trapezoidal and rectangular winglet – type LVGs, respectively. The effects of the these LVGs are examined and compared using the dimensionless parameters Nu_m/Nu_m0, f/f₀ and R = (Nu_m/Nu_m0)/(f/f₀). The results show that the curved trapezoidal winglet pair (CTWP) provides the best thermo – hydraulic performance with the value of R ranging from 0.68 to 1.14 under the present conditions. Parametric study on CTWP reveals that the attack angle of β = 45° and inclination angle of α = 20° perform better than other conditions. The heat transfer characteristics and flow structure are explored with the help of secondary velocity vectors, streamlines and isotherms. The volume – average synergy angle θ_m between velocity vector and temperature gradient first decreases with β, reaches the minimum value for β = 45°, and then rises back to the maximum value for β = 90°. Correspondingly, the Nu_m/Nu_m0 shows the opposite trend to θ_m while varying with β. It is confirmed that the maximum value of heat transfer augmentation is achieved at the minimum synergy angle, which indicates that the mechanism of heat transfer enhancement can be well explained by FSP.

Introduction

Heat transfer enhancement is of significant importance in such fields as power systems, automobile industry, heating, ventilation, air conditioning systems and aerospace, etc. However, as the heat transfer performance improves, the corresponding pressure drop also becomes tremendous for conventional passive methods such as adding fins or baffles.

As is known that the air side thermal resistance is inherently higher than that on the liquid side for air – to – liquid and phase – change heat exchangers (HXs). A passive strategy for air – side heat transfer enhancement is to use longitudinal vortex generators (LVGs), which can be stamped on or punched out from the surface of HXs. The earlier work using LVGs for heat transfer enhancement was reported by Johnson and Joubert in 1969 [1]. They found that the local Nu (Nusselt number) was increased at the position of LVGs, while the overall Nu was not much increased due to the decrease elsewhere on the cylinder. Tiggelbeck et al. [2] experimentally investigated the heat transfer enhancement and drag in transitional channel flow containing double rows of delta winglets. They reported that the critical angle of attack for the formation of longitudinal vortices behind the second row was smaller than that behind the first one, and heat transfer coefficient and drag were increased by 80% and 160%, respectively. Tiggelbeck et al. [3] compared several wing – type LVGs for heat transfer enhancement using liquid crystal thermograph method. They found the drag induced by LVGs was nearly proportional to the projected area and independent of Re and the shape of LVGs. Fiebig et al. [4], [5] studied the thermal – hydraulic characteristics of LVGs in the form of delta wing, delta winglet pair, rectangular wing and rectangular winglet pair in the rectangular channel flow. They quantitatively discussed the heat transfer enhancement mechanism in three ways: (1) developing boundary layers on the LVGs surface; (2) swirling; and (3) flow destabilization. The followed results were also presented: (1) winglets brought about higher heat transfer enhancement than wings for otherwise identical parameters; (2) the heat transfer enhancement was higher in laminar flow than that in turbulent flow; (3) for single vortex generators, heat transfer enhancement increased with the angle of attack and peaked at around 45°. Biswas et al. [6] studied the flow structures of LVGs in channel flow in numerical and experimental methods. They found the vortices were complex and consisted of a main vortex, a corner vortex and induced vortices. The combined effect of these vortices distorted the temperature field in the channel and ultimately brought about the heat transfer enhancement between the fluid and its neighboring surface. Torii and Kwak [7], [8] proposed a common – flow – up configuration of winglets, which could augment heat transfer but nevertheless reduce pressure loss in a fin – tube heat exchanger. The results showed that heat transfer was increased by 10–30% and meanwhile the pressure loss was reduced by 34–55% for a single row of winglets placed in staggered arrangement compared with the situation without winglets. Kim and Yang [9] studied the flow and heat transfer characteristics of a pair of embedded counter – rotating vortices using thermo – chromatic liquid crystal method and they found that the common – flow – down cases showed better heat transfer characteristics than the common – flow – up cases. Different arrangements of LVGs to optimize the heat transfer enhancement and flow loss have been experimentally studied in Refs. [10], [11], [12] and the results showed that specially designed configuration could optimize the heat transfer coefficient. In addition to the study on configurations of LVGs, the development of new shape of LVGs attracts many researchers in recent years. Min et al. [13] experimentally investigated the modified LVGs by cutting off the four corners of a rectangular wing and the heat transfer performance was reported to be improved. Zhou et al. [14], [15] proposed a kind of LVG called curved trapezoidal winglet and experimentally investigated its performance of heat transfer enhancement and flow resistance by comparison with those of traditional vortex generators – rectangular winglet, trapezoidal winglet and delta winglet. The results indicated that curved trapezoidal winglet pair performed better in fully turbulent region with higher heat transfer enhancement and lower pressure loss. Caliskan [16] studied the heat transfer enhancement of punched LVGs using the infrared thermal image technique. He reported 23–55% increase in heat transfer performance and correlations for Nu were developed for corresponding LVGs.

Wang et al. [17] numerically studied the hydrodynamic performances from a rectangular channel fitted with LVGs and found the heat and mass transfer were intensified for a transient – state flow. Wu and Tao [18] investigated four horizontally placed plates with a pair of delta winglets punched directly from the plates at an attack angle of 15°, 30°, 45°, 60°, respectively. And the results revealed that the average Nu on the plate increased with the increase of attack angle. Du et al. [19] numerically studied the flow structure and heat transfer enhancement of LVGs applied in direct air – cooled condenser using RNG k–ε model and found that the delta winglet pair with attack angle of 25° could reach the optimum thermal and flow performances. Gong et al. [20] fitted curved rectangular vortex generators in the wake regions of a fin – tube exchanger and found that the heat transfer performance was significantly improved.

The inherent mechanism of heat transfer enhancement by LVGs can be explained in two folds from the above literature: (1) the secondary flow induced by LVGs swirls and disturbs the fluid flow; (2) the boundary layer is distorted and thinned, which are mainly from the point of qualitative description. Guo et al. [21] firstly proposed a quantitative analysis method named field synergy principle (FSP) concerning both velocity field and gradient of temperature field for the boundary – layer flow in 1997. Wu et al. [22], [23] verified that the theory could be applied to explain the mechanism of heat transfer for a channel flow with LVGs. Tian et al. [24] and Saha et al. [25] numerically analyzed the thermal – hydraulic performance with FSP of rectangular winglet pair and delta winglet pair, respectively. Both of them concluded that better heat transfer enhancement was achieved with smaller synergy angle. Mohammed et al. [26] reported that desired swirls of flow could be generated under the guidance of FSP.

The present study aims at a numerical investigation of thermal performances of a rectangular channel flow embedded with plane and curved LVGs, respectively. Additionally, the FSP is applied to demonstrate the inherent mechanism of heat transfer enhancement, and the velocity vectors of secondary flow, streamlines and temperature fields are also analyzed. Parametric studies of LVGs with the best overall performance are further examined.