Turbulence Enhancement by Fractal Square Grids: Effects of Multiple Fractal Scales

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.

Partially-Covered Fractal Induced Turbulence On Fins Thermal Dissipation

“…The enhancement in Nu for PCSFG contrasting with PCRG may be due to the multi-length scale wake interactions via the multiplicity of fractal bar thickness. As reported earlier 9,16 , the interplay between accelerated airflow and wake structures through the variety of fractal bar thickness promotes generation of multi-length scale turbulent eddies. Small-scale eddies induced through thinner fractal bars are described to effectively facilitate plate-fin heat dissipation through flow dynamic energy cascading.…”

“…In the case of turbulent airflow, the effects of turbulence length scale L on the forced convective heat transfer should be considered as well, as it unveils critical thermo-fluid interplay upon heat exchanger thermal transfer 9,16 . L provides a representation of spatial dimension for turbulent vortices.…”