Direct numerical simulation of turbulent heat transfer in a square duct with transverse ribs mounted on one wall
Introduction
Turbulent heat and fluid flows in a rib-roughened duct feature interactions of four momentum and thermal boundary layers developed over the sidewalls of a square duct. Typical of a square duct flow, strong secondary flows occur, which facilitate turbulent transport of momentum and thermal energy in the cross-stream directions. Owing to the presence of the wall-mounted rib elements, the flow and temperature fields become highly disturbed, which further enhance heat transfer rate in heat exchangers (Yaglom and Kader, 1974). For the application to turbine blade cooling (Casarsa and Arts, 2005, Lohász et al., 2006), the aspect ratio (defined as , where H is the rib height and D is the duct width) can be as high as . In general, turbulent heat and fluid flows in a square duct with ribs mounted on one wall are intrinsically three dimensional (3-D), dominated by cross-stream secondary flows, and statistically inhomogeneous in all three directions. These interesting features make turbulent heat transfer in a ribbed duct flow qualitatively different from that over a two-dimensional (2-D) ribbed flat plate.
In the current literature, extensive experimental measurements and numerical simulations were conducted to investigate the effects of rib elements on heat transfer in 2-D plane-channel flows. For example, Hetsroni et al. (1999) measured temperature field in turbulent channel and pipe flows using a hot-foil infrared technique, and a significant increase of heat transfer was observed near the ribbed wall due to the destruction of the thermal streaky structures. Nagano et al. (2004) conducted DNS of a fully-developed turbulent channel flow to investigate the effects of transverse ribs on both the velocity and temperature fields. Their results showed that k-type roughness has optimal heat transfer performance due to the promotion of turbulent mixing in the downstream region of the ribs. Hattori and Nagano (2012) performed DNS to study the mechanism of heat transfer in turbulent boundary-layer flow developed over a plate roughened with rectangular ribs. They observed that the streamwise and spanwise fluctuating vorticities had significant impacts on the near-wall heat transfer rate, which further led to an enhancement of the wall-normal turbulent heat flux. Leonardi et al. (2015) studied the effects of pitch-to–height ratios () and rib shapes on heat transfer enhancement in a turbulent plane-channel flow. They found that turbulent heat flux reaches its maximum at for both square and circular ribs. Here, P and H denote the spacing between the ribs and the rib height, respectively. More recently, Li et al. (2018) investigated the effects of cube heights on turbulence modulation and heat transfer enhancement in a channel flow using DNS and observed a distinct correlation between enhancement of heat transfer and increase of drag.
As reviewed above, studies of 2-D turbulent flow and heat transfer in ribbed plane channels are relatively abundant, however, research on turbulent heat transfer within 3-D rib-roughened ducts is yet limited in the literature. Hirota et al. (1997) measured temperature variance and turbulent heat fluxes in a smooth square duct using multiple-wire probes. They observed that due to the confinement of the four sidewalls of the duct, secondary flows appear as four pairs of counter-rotating vortices in the cross-stream direction, which have a significant impact on the characteristics of both the velocity and temperature fields. Furthermore, in a transversely rib-roughened duct, the strength and appearance of the secondary flow motions are noticeably altered, as the rib elements impose significant disturbances to the flow field. Fujita et al. (1989) measured turbulent flows in a rectangular duct with perpendicular ribs mounted on one wall using hot-wire anemometry. They observed that secondary flows appeared as a pair of counter-rotating vortices, which exert a great influence on both momentum and heat transfer. Liou et al. (1993) conducted laser-Doppler velocimetry (LDV) measurements of a fully-developed duct flow with square ribs mounted on the top and bottom walls. They observed that the heat transfer rate enhances significantly due to the impingement of mean secondary flows onto the duct sidewalls. Their observations were later confirmed by Sewall et al. (2006) and Labbé (2013), who used large-eddy simulation (LES) to investigate the effects of secondary flow on heat transfer enhancement in a ribbed square duct.
Notwithstanding the aforementioned contributions, the number of detailed DNS studies of turbulent heat and fluid flows in a rib-roughened duct is scarce in the literature, and many questions regarding turbulent heat transfer remain open. In view of this, we aim at conducting a comparative DNS study of the effects of rib height on the first- and second-order statistical moments of the temperature field, the spectral characteristics of temperature fluctuations, and coherent structures that facilitate the turbulent transport of thermal energy. In order to examine the rib effects on the turbulent heat transfer, the results of the three ribbed duct cases are compared with those of a heated smooth square duct flow at the same bulk Reynolds number. The fluid dynamics of rib-roughened square duct flows of different blockage ratios have been thoroughly analyzed in Mahmoodi-Jezeh and Wang (2020). In this paper, we concentrate our attention on the analysis of the temperature field and turbulent heat fluxes. In regards to this topic, the remainder of this paper is organized as follows. In Section 2, the governing equations, numerical procedure, as well as test cases are described. In Section 3, detailed result analysis is presented. The impacts of rib aspect ratios on heat transfer and flow structures are investigated through vortex identifiers, joint probability density function (JPDF) of the velocity and temperature fluctuations, temporal auto-correlation functions, two-point cross-correlation functions, and pre-multiplied energy spectra. Finally, in Section 4, major findings of this research are summarized.
Section snippets
Test case and numerical algorithm
The length of the square duct is long and consists of eight rib periods, where D is the duct width. In the current study, three blockage ratios ( and 0.2) are compared, while the width and streamwise period of the bars are kept constant with and , respectively. The flow field is fully-developed, and periodic boundary conditions are applied to the streamwise direction. A no-slip boundary condition is imposed on all solid walls for the velocity field. The Reynolds
Mean flow and temperature fields
Fig. 3 compares the contours of the mean temperature field superimposed with in-plane streamlines in the central plane located at for the three blockage ratios studied. By comparing Fig. 3(a)–(c), it is observed that the size of the corner vortex (marked with “I”) immediately behind a rib increases monotonically as the rib height increases. The reason that the corner vortex I is the smallest for the case of (shown in Fig. 3(a)) is that the rib height is too small to cause
Conclusions
Direct numerical simulation is performed to study turbulent heat transfer in ribbed square duct flows of three different blockage ratios. In order to examine the effects of ribs on the turbulent heat transfer, the results of the three ribbed duct cases are compared with those of a smooth square duct flow case at the same bulk Reynolds number of . The effect of sidewalls and ribs on the statistical moments of the temperature field and coherent structures is investigated. In contrast to
CRediT authorship contribution statement
S.V. Mahmoodi-Jezeh: Conceptualization, Software, Methodology, Data curation, Writing - original draft, Formal analysis, Validation, Visualization. Bing-Chen Wang: Supervision, Funding acquisition, Conceptualization, Methodology, Writing - review & editing, Project administration.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
The authors would like to thank Western Canada Research Grid (WestGrid) for access to supercomputing and storage facilities. Research funding from Natural Sciences and Engineering Research Council (NSERC) of Canada to B.-C.W. is gratefully acknowledged.
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