Forced convection heat transfer from an asymmetric wavy cylinder at a subcritical Reynolds number
Introduction
The forced convection and fluid flow around bluff bodies have been investigated extensively by numerous researchers. This topic is associated with diverse applications, such as heat exchangers, offshore structures (including pipelines and risers), nuclear reactors, overhead cables, power generators, and thermal apparatuses [1], [2], [3], [4], [5], [6], [7], [8], [9], [10], [11], [12], [13], [14], [15], [16], [17], [18], [19], [20]. Hence, it is essential to understand the improvement or suppression of heat transfer from a structure. To achieve this, control of the forced convection is required, which is dominated by the fluid flow.
One approach in direct wake control methods is introducing some form of three-dimensional (3-D) geometric disturbances to the base form of a nominally two-dimensional (2-D) bluff body. One example is waviness on a cylinder with a sinusoidal variation in the cross sectional area along the spanwise direction, which has been investigated for its effect on flow characteristics such as wake vortices and body forces. The main purposes of flow control are drag reduction, reduction of the lift fluctuation, enhancement of the lift force, suppression of the vortex-shedding, reduction of flow-induced noise and vibration, and improvement or suppression of mixing or heat transfer in systems exposed to the fluid flow. Thus, many studies have been performed [21], [22], [23], [24], [25], [26], [27], [28], [29], [30], [31], [32]. Also, the comprehensive reviews have been done by several researches [24], [29].
Recently, several researches evaluated the effect of the various geometric perturbations on the forced convection heat transfer.
Kim and Yoon [15] numerically investigated the forced-convection heat transfer around a biomimetic elliptic cylinder inspired by a harbor seal vibrissa (HSV) at a Reynolds number of 500 and Prandtl number of 0.7. The HSV provided stable heat transfer behavior by significantly suppressing the Nusselt number fluctuation. The HSV formed spanwise sinusoidal variation of the Nusselt number, resulting in sinusoidal profiles with a maximum and a minimum at the saddle and node, respectively. This spanwise variation of the Nusselt number was identified by the flow structures. The node where the local mean Nusselt number is the minimum, since the HSV reveals the stream-like body. Hence, the streamlines do not clearly present the separation and subsequently vortices in the wake, resulting in the non-existence of the secondary heat transfer by the recirculation in the near-wake.
Kim and Yoon [16] extended their previous work [15] to research the effect of the Reynolds number (Re) on the characteristics of the fluid flow and heat transfer from a biomimetic elliptic cylinder inspired by a HSV. They considered the range of 50 ≤ Re ≤ 500 and Pr = 0.7. They confirmed the effectiveness of the unique geometry of the HSV on the low Reynolds number regime to achieve the drag reduction and the suppression of the lift fluctuation. They reported that the existence of the the onset of the unsteady flow for the HSV within the present range of Re. The spanwise dependency of the local surface-averaged Nusselt number becomes stronger as Reynolds number increases. In the unsteady flow regime for the HSV, the periodic thermal plume appears at the nodes. This periodical thermal plume was induced by the non-reverse flow region expending the isotherms to the downstream.
Yoon et al. [33] considered a helically twisted elliptical (HTE) cylinder inspired by a daffodil stem. They carried out numerical simulations to investigate the flow and heat transfer around the cylinder in the range of with a Prandtl number of 0.7. The 3D geometry of the HTE cylinder resulted in spanwise variation of the Nusselt number (Nu) and sinusoidal profiles. This spanwise variation was identified by the flow structures and the isotherm distribution. The time- and total surface- averaged Nusselt number of the HTE cylinder decreases from about 1.2% to 2.8% compared to a smooth cylinder. Consequently, the heat transfer characteristics strongly correlate with the flow modification by the unique HSV and HTE geometries.
Previous studies mainly focused on the effect of the wavelength on the fluid flow regarding flow control for force reduction. However, few studies have dealt with heat transfer around a wavy cylinder and the effect of the wavelength on the heat transfer. Only Ahn et al. [12] dealt with the forced heat transfer around a wavy cylinder for three different wavelengths of , , and with a fixed wavy amplitude of 0.1 at a Reynolds number of 300 and a Prandtl number of 0.71. They considered shorter wavelengths than the optimal wavelength of [22]. They showed that the variation of time- and local surface-averaged Nusselt numbers for a wavy cylinder along the spanwise direction have a strong dependence on the location in the spanwise direction with a larger value at the node than at the saddle of the wavy cylinder. The time- and total surface-averaged Nusselt numbers at are higher than that of a smooth cylinder, whereas the values at and are lower.
Recently, Yoon et al. [26] proposed an asymmetric wavy disturbance as the passive control. The optimum [29] for the wavy cylinder for the drag reduction was adopted to form the asymmetric wavy disturbance which is designed by joining two half sinusoidal waves with different wave lengths. The ASW cylinder provides additional reduction of and of which is obtained by the SW cylinder with long optimum wavy length where the maximum reduction of and is achieved [29]. They considered the effect of the asymmetric ratio for s of 0.25, 0.5 and 0.75 on the force coefficients. As a result, gives a larger drag reduction and suppression of lift fluctuation.
The asymmetric wavy cylinder gives apparently the drag reduction and the suppression of the lift fluctuation. However, there is no information for the characteristics of the heat transfer around the asymmetric wavy cylinder. Therefore, this study aims to provide the information of the heat transfer around the asymmetric wavy cylinder. Eventually, we can provide the effectiveness of the asymmetric cylinders with different wavelengths on the forced convection heat transfer, in terms of the enhancement or suppression of heat transfer.
The purpose of the present study is to evaluate the effect of the asymmetric wavy disturbance on the forced convection heat transfer. For the purpose of the comparison, the smooth and symmetric wavy cylinders are considered. Finally, the LES is carried out to solve the momentum and energy equations governing the flow and thermal fields at the subcritical Reynolds number of 3000. The SW cylinder has a wavelength of which is the optimum where the maximum force reduction is achieved [29]. For the ASW cylinder, asymmetric ratio of = 0.5 is considered in this study. Eventually, we will compare the overall heat transfer performances for the CY, SW and ASW cylinders. In order to support the variation of the mean Nusselt number, the the local distribution of the Nusselt number along the surface of the cylinder. Also, the distributions of the temperature and vorticities are considered to give a physical interpretation at several cross sections where the Nusselt number changes.
Section snippets
Governing equations and numerical methods
The Navier-Stokes, continuity, and energy equations are considered to simulate the unsteady three-dimensional incompressible flow and thermal fields around the wavy cylinder. The governing equations are used in the large eddy simulation (LES):where t is time; is the Cartesian coordinates; is a corresponding velocity component; is the pressure; Re is the Reynolds number; and is a subgrid
Total surface-averaged Nusselt number
Fig. 5(a) and (b) shows the time histories of total surface-averaged drag and lift coefficients ( & ), respectively, for different cylinders. The ASW cylinder provide smaller and the fluctuation of than the SW cylinder which has the optimal wavelength where the drag and the lift fluctuation are minimum Lin et al., [29]. The present results of & for the ASW are the same tendency with those of Yoon et al. [26].
This capability of the ASW cylinder to reduce the forces can be
Conclusions
The present study considered the asymmetric wavy disturbance which has been confirmed as the passive control to modify the force coefficients [26]. We evaluated the effect of the asymmetric wavy disturbance on the forced convection heat transfer. For the purpose of the comparison, the smooth and symmetric wavy cylinders are considered. Finally, the LES has been carried out to solve the momentum and energy equations governing the flow and thermal fields at the subcritical Reynolds number of
Conflict of interest
The authors declare that there is no conflict of interest.
Acknowledgments
This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) through GCRC-SOP (No. 2011-0030013).
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