Flow field characteristic and heat transfer performance in a channel with miniature square filament

https://doi.org/10.1016/j.ijheatmasstransfer.2020.120433Get rights and content

Highlights

  • A single miniature square filament (MSF or MCVG) is located in the viscous sub-layer, the buffer layer and the logarithmic law region of turbulent boundary layer, respectively.

  • By setting MCVG in boundary layer, most of velocity profiles in viscous sub-layer are suppressed; most of velocity and temperature profiles are promoted in logarithmic law region.

  • MCVG immersed in three typical regions of boundary layer can reduce the bottom wall shear stress, which results in the drag reduction.

  • The highest heat transfer effect and synthesis performance coefficient are achieved in the case that setting MCVG in the buffer layer.

Abstract

The miniature square filament (MSF) is a kind of miniature cuboid vortex generator (MCVG). The effects of a single MCVG (MSF) immersed in various turbulent regions on the original flow and heat transfer performance in a rectangular channel are studied with large eddy simulation. The results show that the synthesis performance coefficients of the cases that setting MCVG in the buffer layer or the logarithmic law region are greater than 1. However, the synthesis performance coefficient of the case that setting MCVG in the viscous sublayer is lower than 1. Moreover, by setting MCVG in the channel, the friction coefficient reduces up to 8.67%, the Nusselt number increases up to 7.04%. The synthesis performance coefficient increases up to 7.39%, and the maximum synthesis performance coefficient is achieved in the case that setting MCVG in the buffer layer.

Introduction

Flow field characteristic and heat transfer performance in near-wall region is frequently encountered in many engineering applications, like chemistry industry and aerospace industry. Kline et al. [1] and Praturi et al. [2] found that the near-wall turbulence structures involved speed streak structures and various vortices. And burst motion, ejection motion as well as sweep motion were observed in the flow field.

It is well-known that turbulence control methods can influence the original flow field [3,4]. The active control method usually need additional energy and intricate devices [5]. However, the passive control method has many advantages, like no external energy consumption, easier control, better economy and better practicability. The passive control methods (such as vortex generators, roughness elements and deformed surface) usually strengthen the disturbance of the turbulent flow field to facilitate the fluid mixing, thus achieving heat transfer enhancement. For instance, Wang et al. [6] adopted delta winglet to strengthen jet penetration and increase the impingement heat transfer performance. Wu et al. [7] investigated fluid flow past delta winglet vortex generator (DWVG) and found that the heat transfer effects of the inflow region was better. Gallegos et al. [8] found that setting a flapping flag in the channel could increase the turbulent unsteadiness and Nusselt number increased 1.34 to 1.62 times that of channel having nothing. Khanjian et al. [9] studied the effects of the rectangular winglet pair vortex generators’ roll-angle on the flow performance and heat transfer characteristics. And in order to achieve the best values, the roll-angle is not necessarily 90. Zhai et al. [10] obtained the maximum Nusselt number of the tube with the DWVG pairs, and this number was 73% bigger than that of the tube without DWVG pairs, while the maximum friction factor of the tube with the DWVG pairs was 2.5 times greater than that of the tube without DWVG pairs. Oneissi et al. [11] studied the DWVG and found that convective heat transfer was enhanced by inducing more vortices. Oneissi et al. [12] conducted the simulation of parallel plate-fin heat exchanger with longitudinal VG having protrusions. It was found that the inclined projected winglet pair (IPWP) with protrusions achieved 7.1% heat transfer increasement compared to the delta winglet pair (DWP). Luo et al. [13] investigated the flow past dimples, and the best flow mixing behaviors as well as heat transfer characteristics were achieved with the dimples arranged in inline. In addition, Luo et al. [14] investigated flow field characteristic and heat transfer behavior of the surface equipped with diverse dimples and DWVGs. It revealed that the heat transfer coefficient was largely augmented by the use of heterogeneous surface, and the greatest heat transfer effect was increased by 72%. Li et al. [15] conducted the channel flow simulation with dimples and protrusions. It was found that the inline dimple-protrusion arrangements could obtain higher thermal effect. Liu et al. [16] found that the total heat transfer effects of the dimpled swirl cooling tubes could increase by as much as 7.2%, which was derived from the increase of heat transfer area as well as the interaction between the wall and the swirling flow. Soleimani et al. [17] found that the transverse rectangular micro-fin with a pitch-to-height ratio of 3.5 could increase the performance factor by about 40% compared to a smooth surface. Sadeghianjahromi et al. [18] found that punching slits on the top of wavy fin could reduce the thermal resistance by about 7%. Song et al. [19] found that the concave curved DWVG was good to heat transfer increasement compared to the normal plane VG, and the highest Nusselt number of the case with concave curved VG was greater (19.7%) than that of the case with convex curved DWVG. Tong et al. [20] numerically studied the multiple impingement jet system, and found that the cambered rib surface achieved the optimal increasement of the impingement cooling performance among different surface devices. Ranjana et al. [21] found that both the pressure drop decline and heat transfer enhancement were achieved because of the addition of inserts, and a much greater heat transfer augmentation effect was achieved.

Furthermore, the dimensions of the following small-scale passive control devices are rather smaller than the devices as mentioned above. Fernández-Gámiz et al. [22] investigated the fluid flowing past a vane-type VG, and the dimension of VG was similar as the thickness of boundary layer. The results showed that vortices were self-similar at axial velocity component (uz) and azimuthal velocity component (uθ). Wang et al. [23] researched the fluid flowing past micro-ramp and found that the streamwise vortices derived from micro-ramp made the near-wall layer fluid gathered toward the micro-ramp's wake. Mallor et al. [24] studied the fluid flowing past a cube with diverse perforation structures. And the highest heat transfer effect was achieved in the case that the jet-to-surface distance was small and this jet was perpendicular to surface.

In short, the passive control devices [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20], [21], [22], [23], [24] usually improve heat transfer effect by augmenting turbulent flow instabilities and particularly affecting near-wall flow structures, which often lead to an unavoidable increase in flow drag or pressure drop. However, the frictional features of these devices were always ignored in previous studies, which should be further explored.

On the other hand, in previous investigations [25], [26], [27], the passive control devices like roughness elements added perturbations to expedite the transition process (the laminar to turbulence), which inevitably increased the skin friction. However, it should be noted that in some investigations [28], [29], [30], [31], [32], by using passive control devices, transition could be delayed remarkably and friction could be decreased. Shahinfar et al. [28] found that the miniature VG (MVG) effectively achieved the delay of transition, and skin resistance could be reduced. Besides, it was worth noting that the dimensions of MVGs used in those cases [29,30] were (at most) half of the boundary layer thickness. Fransson et al. [31] found that MVGs could be used to suppress turbulence in flow control. And the results showed that net drag reduced by at least 65% with the second array of MVGs put at the downstream of the first array of MVGs. Fransson et al. [30] and Shahinfar et al. [32] probed transient growth or boundary layer streaks, but the descriptions about the influences of MVGs on turbulence structures had not been clarified.

As mentioned above, the reduction of skin-friction can be achieved by the proper control method. The effects of MVG on heat transfer are seldom attentioned and even ignored in most investigations. It is suggested that for the better practicability, both skin friction and heat transfer should be considered in the further investigation of MVG. Wang et al. [33] (our previous work) found that the turbulent movement can be restricted by MVGs, and the Nusselt number increased by 5.17%. But the influences of MVG located in various regions of turbulence boundary layer on flow field have not been probed.

Besides, the flow field characteristic and the heat transfer behavior of the channel with a single VG in near-wall region are related to factors such as the dimension and shape of VG, the gap between VG and the wall, etc. Price et al. [34], Wang and Tan et al. [35] investigated fluid flowing past a circular cylinder set in near-wall region. And it was found that the gap ratios made a big difference in affecting the flow characteristics. Cheraghi et al. [36] investigated the influence of near-wall cylinder on enhancement of heat transfer. It revealed that if the gap between bottom surface and cylinder got smaller, the velocity and temperature distributions became more stable, and the heat transfer became smaller. Wang et al. [37] studied the fluid flowing past a small circular cylinder, the vortices shedding from VG interacted with boundary layer and improved the synthesis performance coefficient. Derakhshandeh et al. [38] studied heat transfer augmentation with a rectangular cylinder located parallel with the heated wall. The maximum heat transfer effect was obtained at the single-row vortex street flow. Specifically, an increase of 8% was achieved at C/W=2, G/W=0.75-1.25 (C/W refereed to the cylinder chord-to-height ratio, G refereed to the gap distance). Zafar et al. [39] numerically studied the influence of corner modification (cylinders modified from square to circular) on flow feature and heat transfer performance. In brief, only a few investigations have been conducted on the fluid flowing past a single MVG because of the complexity interactions between near-wall flow structures and the MVG. The effects of a single MCVG in various boundary layer regions on near-wall flow and heat transfer behaviors have not been fully explored. It deserves to find a layout method of MCVG to obtain optimal performance combining the drag reduction and the heat transfer improvement.

The miniature square filament (MSF) is a kind of miniature cuboid vortex generator (MCVG). And MCVG is used to represent MSF in the following sections. In present work, a single MCVG is immersed in the logarithmic law region, the buffer layer as well as the viscous sublayer, respectively. Compared with our previous work [37], the shape of MCVG changes from cylinder to cuboid, and the dimension of VG become smaller, which makes the Reynolds number (based on the dimension of VG) not big enough to occur vortex shedding, thus the flow behavior and heat transfer feature would be worth further probing.

Section snippets

Physical models

In present work, the rectangular channel without MCVG (also called the empty rectangular channel) is defined as Case0. The single MCVG in various arrangement are defined as Case1, Case2 and Case3.

As illustrated in Fig. 1(a), the computational domain dimension is 4πH × 2H × 2πH in x-direction (i.e. streamwise direction), y-direction (i.e. normal direction) and z-direction (i.e. spanwise direction), respectively, which has the same dimension as that of Case0. The corresponding velocity components

Conservation equations and boundary conditions

A channel flow is simulated by the large eddy simulation (LES) that has been used in many turbulence studies [40,41]. The conservation equations solved by LES are listed as following:ui¯xi=0ui¯t+(ui¯uj¯)xj=1ρp¯xi+ν2ui¯xjxj+τij¯xjT¯t+(uj¯T¯)xj=νPr2T¯xjxjqj¯xj

Where ui¯ and uj¯ (i=1,2,3; j=1,2,3) signify components of velocity, p is pressure, τij¯=(uiuj¯ui¯·uj¯) signifies the subgrid-scale stress tensor, qj¯=ujT¯uj¯·T¯ signifies the subgrid-scale heat flux.

The

Mesh independence test and numerical method validation

The mesh independence test and numerical method validation of Case0~Case3 are consistent with our previous work [33,37]. The finite volume method (FVM) and the Semi-Implicit Method for Pressure Linked Equations (SIMPLE) algorithm are adopted to solve the Eqs. (5)–(7). The continuity, momentum and energy equations are respectively discretized by the bounded central difference scheme and a second-order upwind scheme. The standard scheme is adopted to discretize the pressure item. In selecting the

Results and discussions

Flow and heat transfer characteristics of present cases as well as the synthesis performance are analysed. The simulation of every case last for 16100 time steps. In other words, it takes 35 flow periods (35T) for every case to run. Here flow period is the time of fluid flows from the inlet to outlet of the computational domain. And the data between 26T and 35T are selected to be summed and averaged. In fact, the relevant flow parameters before 26T have reached the statistical convergence state.

Conclusion

The flow field characteristics and heat transfer effects in a rectangular channel with a single MCVG are numerically investigated. By setting MCVG (MSF) in a certain region of boundary layer, drag reduction and heat transfer enhancement can be obtained synchronously. The conclusions are drawn as follows:

  • (1)

    When MCVG is located in the viscous sublayer, the influence of MCVG on flow field is within limits. However, MCVG can steady the turbulence and reduce the flow drag as well as locally obstruct

CRediT authorship contribution statement

Yu Jiao: Investigation, Methodology, Conceptualization, Formal analysis, Validation, Visualization, Writing - original draft, Writing - review & editing, Software. Jiansheng Wang: Supervision, Funding acquisition, Resources, Project administration. Xueling Liu: Supervision, Project administration.

Declaration of Competing Interest

None.

Acknowledgement

The authors gratefully acknowledge the financial support by the Key Natural Science Foundation of Tianjin (No. 17JCZDJC31200).

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