Abstract
Multi-scale fractal grids can be considered to mimic the fractal characteristic of objects of complex appearance in nature, such as branching pulmonary network and corals in biology, river network, trees, and cumulus clouds in geophysics, and the large-scale structure of the universe in astronomy. Understanding the role that multiple length scales have in momentum and energy transport is essential for effective utilization of fractal grids in a wide variety of engineering applications. Fractal square grids, consisted of the basic square pattern, have been used for enhancing fluid mixing as a passive flow control strategy. While previous studies have solidified the dominant effect of the largest scale, effects of the smaller scales and the interaction of the range of scales on the generated turbulent flow remain unclear. This research is to determine the relationship between the fractal scales (varying with the fractal iteration N), the turbulence statistics of the flow and the pressure drop across the fractal square grids using well-controlled water-tunnel experiments. Instantaneous and ensemble-averaged velocity fields are obtained by a planar Particle Image Velocimetry (PIV) method for a set of fractal square grids (N = 1, 2 and 4) at Reynolds number of 3400. The static pressure drop across the fractal square grid is measured by a differential pressure transducer. Flow fields indicate that the multiple jets, wakes and the shear layers produced by the multiple scales of bars are the fundamental flow physics that promote momentum transport in the fractal grid generated turbulence. The wake interaction length scale model is modified to incorporate the effects of smaller scales and thereof interaction, by the effective mesh size M e f f and an empirical coefficient β . Effectiveness of a fractal square grid is assessed using the gained turbulence intensity and Reynolds shear stress level at the cost of pressure loss, which varies with the distance downstream. In light of the promising capability of the fractal grids to enhance momentum and energy transport, this work can potentially benefit a wide variety of applications where energy efficient mixing or convective heat transfer is a key process.
Highlights
As an object composed of a hierarchy of length scales is partially or fully immersed in a fluid flow, various scales of turbulent flow motions are induced in response to the object0 s different scales
Fractal grids with more scales would be advantageous if a longer distance is required for turbulence enhancement
A set of fractal square grids are tested in water-tunnel experiments at Re = 3400, to determine the relationship between the fractal scales, the turbulence statistics of the generated turbulent flow and the pressure drop across the fractal grids
Summary
As an object composed of a hierarchy of length scales (or multi-scale) is partially or fully immersed in a fluid flow, various scales of turbulent flow motions are induced in response to the object0 s different scales. The results of this study, suggesting the additional fractal scales have an noticeable impact on the heat transfer enhancement, are aligned with the earlier research Another recent study compared the centerline streamwise turbulence intensity for fractal square grids (N = 1, 2, 3 and 4) having constant largest dimensions of t0 and L0 , focusing on the role of the fractal elements and what grid arrangement causes the elongated non-equilibrium region in the turbulent flow [22]. The present research aims to (1): understand how the multiple scales of a fractal square grid influence the flow structure, turbulence statistics and pressure drop; (2) revisit and modify the wake interaction length scale model to account for multiple scales’ effects This is conducted by comparing the turbulence statistics and the pressure drop induced by each of a set of fractal square grids (with iterations N = 1, 2, and 4). Please note that the blockage ratio σ increases as we add an additional scale, since they are coupled via Equation (6)
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