In real application, once the pattern of fin is determined, fin spacing of tube bank fin heat exchanger can be adjusted in a small region, and air flow velocity in the front of the heat exchanger is not all the same. Therefore, the effects of fin spacing on heat transfer performance of such heat exchanger are needed. This paper numerically studied the optimal fin spacing regarding the different front flow velocities of a circular tube bank fin heat exchanger with vortex generators. To screen the optimal fin spacing, an appropriate evaluation criterion JF was used. The results show that when front velocity is 1.75 m/s, the optimal fin spacing is 2.25 mm, when front velocity is 2.5 m/s, the optimal fin spacing is 2 mm, and when front velocity is higher than 2.5 m/s, the optimal fin spacing is 1.75 mm.
List of symbolsA Cross section area of flow passage (m 2 ) A front Cross section area of flow passage at front inlet (m 2 ) c p Specific heat capacity (J/kg K) D Diameter of the tube (m) d e Characteristic length of flow channel (m) F Total surface involved in heat transfer in the computational domain (m 2 ) f Friction factor, f = Dpd e /(L x qu max 2 /2) h Convective heat transfer coefficient (W/m 2 K) H Height of winglet type vortex generator (m) J n ABS Absolute vorticity flux along the normal direction of cross section (1/s) J n ABS;S Cross section average absolute vorticity flux (1/s) J n ABS;V Volume average absolute vorticity flux (1/s) L Base length of vortex generator (m) L x Stream wise length of fin (m) n Direction normal to the cross section or wall surface N 2 Number of the tubes Nu Nusselt number, Nu = hd e /k p Pressure (Pa) Re Reynolds number, Re = qu max d e /l S 1 Transversal pitch between the tubes (m) S 2 Longitudinal pitch between the tubes (m) T p Net fin spacing (m) T Temperature (K) u front Velocity of air at front inlet (m/s) u in Velocity of air at fin passage inlet (m/s) u max Maximum average velocity of air (m/s) u i , u, v, w Components of velocity vector (m/s) x, y, z CoordinatesGreek variables k Thermal conductivity (W/m K) lViscosity (kg/m s) qDensity (kg/m 3 )
Fish have appeared since Precambrian more than 500 million years ago. Yet, there are still much untamed areas for fish propulsion research. The swordfish has evolved a light thin/high crescent tail fin for pushing a large amount of water backward with a small velocity difference. Together with a streamlined forward-enlarged thin/high body and forwardbiased dorsal fin enclosing sizable muscles as the power source, the swordfish can thus achieve unimaginably high propulsion efficiency and an awesome maximum speed of 130 km/h as the speed champion at sea. This paper presents the innovative concepts of ''kidnapped airfoils'' and ''circulating horsepower'' using a vivid neat-digit model to illustrate the swordfish's superior swimming strategy. The body and tail work like two nimble deformable airfoils tightly linked to use their lift forces in a mutually beneficial manner. Moreover, they use sensitive rostrum/lateral-line sensors to detect upcoming/ambient water pressure and attain the best attack angle to capture the body lift power aided by the forwardbiased dorsal fin to compensate for most of the water resistance power. This strategy can thus enhance the propulsion efficiency greatly to easily exceed an astonishing 500%. Meanwhile, this amazing synergy of force/beauty also solves the perplexity of dolphin's Gray paradox lasting for more than 70 years and gives revelations for panoramic fascinating future studies.
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