Title: Thermal study of the internal flow in a circular tube with vibrational ball turbulators

Abstract

F low turbulators have promising heat transfer applications. Here, the novel design proposed in our previous study (vibrational ball turbulators, VBTs, mounted on an elastic wire inside a circular tube) is investigated experimentally from heat transfer and thermal performance standpoints. The effects of diameter (Y) and longitudinal distance (pitch, X) ratios of VBTs, the Reynolds number, and the axial tension of the wire (σ0) on the average Nusselt number (Nu), the average Nusselt number ratio (Nu divided by that of a plain tube, Nup), the friction factor ratio (f/fp) and a parameter called the thermal performance factor (η=(Nu/Nup)/(f/fp )1/3) are studied. Different ball diameter (Y=0.3, 0.38, and 0.46) and ball pitch ratios (X=1.53, 2.3, and 3.07) are utilized at Reynolds numbers between 10,000 and 15,000. VBTs are thermally advantageous, and for X=1.53 and Y=0.46, Nu/ Nup and f/fp peak at 2.3 and 18.06, respectively, averaged over all Re. However, η is maximum (1.2, Re-averaged) for the minimum X (=1.53) and, counterintuitively, the minimum Y (=0.3). Increasing σ0 also has an adverse effect on η. A correlation to predict η as a function of X, Y, and Re is proposed. Also, to bridge the gap between the thermal response and vibrational behavior of the system (which was studied in our earlier work), another correlation for η as a function of Re and dimensionless VBT amplitude and frequency is introduced and indicates that increasing the vibration amplitude (or reducing the frequency) slightly deteriorates η.