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In this paper, we present the results from Direct Numerical Simulations of turbulent, incompressible flow through a square duct, with an imposed temperature difference between two opposite walls, while the other two walls are assumed perfectly insulated. The mean flow is sustained by an imposed, mean pressure gradient. The most interesting feature, characterizing this geometry, consists in the presence of turbulence-sustained mean secondary motions in the cross-flow plane. In this study, we focus on weak turbulence, in that the Reynolds number, based on bulk velocity and hydraulic diameter, is about 4450. Our results indicate that secondary motions do not affect dramatically the global parameters, like friction factor and Nusselt number, in comparison with the plane-channel flow. This issue is investigated by looking at the distribution of the various contributions to the total heat flux, with particular attention to the mean convective term, which does not appear in the plane channel flow.
This integrated thesis documents a series of complementary numerical investigations aimed at an improved understanding of turbulent flows and heat transfer in a square duct with ribs of different shapes mounted on one wall. Direct numerical simulation (DNS) is used to accurately resolve the spatial and temporal scales of the simulated flows. The first DNS investigates the turbulent flow in a ribbed square duct of different blockage ratios. The results are compared with those of a smooth duct flow. It is observed that an augmentation of the blockage ratio concurrently generates stronger turbulent secondary flow motions, which drastically alter the turbulent transport processes between the sidewall and duct center, giving rise to high-degrees of non-equilibrium states. The dynamics of coherent structures are studied by examining characteristics of the instantaneous velocity field, swirling strength, spatial two-point auto-correlations, and velocity spectra. The impact of the blockage ratio on the turbulent heat transfer is investigated in the second numerical study. The results show that owing to the existence of the ribs and confinement of the duct, organized secondary flows appear as large streamwise-elongated vortices, which have profound influences on the transport of momentum and thermal energy. This study also shows that the spatial distribution and magnitude of the drag and heat transfer coefficients are highly sensitive to the rib height. The final study focuses on a comparison of highly-disturbed turbulent flows in a square duct with inclined and V-shaped ribs mounted on one wall. The turbulence field is highly sensitive to not only the rib geometry but also the boundary layers developed over the side and top walls. Owing to the difference in the pattern of the cross-stream secondary flow motions of these two ribbed duct cases, the flow physics in the inclined rib case is significantly different from the V-shaped rib case. It is found that near the leeward and windward faces of the ribs, the mean inclination angle of turbulence structures in the V-shaped rib case is greater than that of the inclined rib case, which subsequently enhances momentum transport between the ribbed bottom wall and the smooth top wall.
Heat transfer and fluid flow issues are of great significance and this state-of-the-art edited book with reference to new and innovative numerical methods will make a contribution for researchers in academia and research organizations, as well as industrial scientists and college students. The book provides comprehensive chapters on research and developments in emerging topics in computational methods, e.g., the finite volume method, finite element method as well as turbulent flow computational methods. Fundamentals of the numerical methods, comparison of various higher-order schemes for convection-diffusion terms, turbulence modeling, the pressure-velocity coupling, mesh generation and the handling of arbitrary geometries are presented. Results from engineering applications are provided. Chapters have been co-authored by eminent researchers.
Direct numerical simulations are performed to investigate turbulent flows in a rectangular duct of aspect ratio varying from 1.0 to 3.0 at a fixed low Reynolds number 150. Persistent secondary flows of Prandtl's second kind are observed in the corners of the ducts. As the aspect ratio increases, streamwise vortices near the top and bottom walls extend towards to the central vertical plane of ducts. Particularly, the displacement of vortex cores near the top/bottom wall can be described as a function of the distance to the sidewall. Detailed analyses of turbulence statistics including the mean flow, turbulent kinetic energy, turbulent intensities, Reynolds stress budgets, and pre-multiplied one-dimensional energy spectrum are conducted to understand the aspect ratio effects on the flow physics. In the duct of aspect ratio 3.0, hairpin flow structures are present in the central regions of the duct, and their characteristics are similar to those exhibited in the plane channel flows. Furthermore, as indicated by the energy spectra, a spanwise quasi-homogeneous region spans over approximately 270 wall units in the central region of the rectangular duct.