In this research, unsteady three-dimensional incompressible Navier–Stokes equations are solved to simulate experiments with the Boussinesq approximation and validate the proposed numerical model for the design of a circular fin-tube heat exchanger. Unsteady time marching is proposed for a time sweeping analysis of various Rayleigh numbers. The accuracy of the natural convection data of a single horizontal circular tube with the proposed numerical method can be guaranteed when the Rayleigh number based on the tube diameter exceeds 400, which is regarded as the limitation of numerical errors due to instability. Moreover, the effective limit for a circular fin-tube heat exchanger is reached when the Rayleigh number based on the fin gap size ( Ra s ) is equal to or exceeds 100. This is because at low Rayleigh numbers, the air gap between the fins is isolated and rarely affected by natural convection of the outer air, where the fluid provides heat resistance. Thus, the fin acts favorably when Ra s exceeds 100.
This research focused on the correlations associated with the physics of natural convection in circular fin-tube models. The limiting conditions are defined by two conditions. The lower limit ( D o / D → 1, s/D = finite value) corresponds to a horizontal circular tube, while the upper limit ( D o / D → ∞, s/D << 1) corresponds to vertical flat plates. In this paper, we proposed a corrected correlation based on empirical result. The circular fin-tube heat exchanger was divided into the A and B types, the categorizing criteria being D o / D = 1.2 , where D and D o refer to the diameter of the circular tube and the diameter of the circular fin, respectively. Moreover, with the computational fluid dynamics technique used to investigate the limiting conditions, the parametric range was extended substantially in this research for type B, namely 1.2 < D o / D ≤ 10. The complex correlation was also simplified to the form Nu L = C Ra s n , where C and n are the functions of the diameter ratio D o / D .
The purpose of the present study is to investigate the flow resistances and heat transfer characteristics of V-bent circular fin-tube heat exchangers. Two types of V-bent fin, in which the fin areas are identical but the type of bend is different (uni- and bi-directional), have been tested numerically. The heat transfer, pressure drop, fin temperature, and fin efficiency are discussed. The uni-directional bent fin showed higher flow resistance and better heat transfer performance than the bi-directional fin. With a 37% V-bent design, the heat transfer coefficient of the uni-directional fin was up to 33% higher than that of the plain circular fin in the present test range.
In the manufacturing process of hard-board poly-urethane foams, the uniformity is a very important issue for the raw compound of the liquid poly-urethane system flow for the quality control of such products. One of the universal methods to generate more uniform flow is that some obstacles are located inside the diffuser at the end of injector. For the regime of non-Newtonian laminar flow, better flow uniformity can be achieved with the enhancement of mixing in the wake after the resistive obstacles. In this research, the parametric study is made for the gap interval between adjacent obstacle components as well as the cross-sectional shape with a computational fluid dynamics (CFD) technique. The flow fields around circular and elliptic cylinders are visualized for flow velocity and vorticity with the comparison of root-mean-square (RMS) error for the deviation of velocity at the outlet as a lumped parameter to estimate flow uniformity and mixing. When the blockage ratio is fixed 0.3 for the pipe of Reynolds number 58.5 based on its diameter, eliminating the effect of wall boundary ratio with the classical Blasius velocity profile, the RMS error is reduced 77% to 92% from the baseline case in the case of 60%-diameter gaps for the figure of circles and 2:1 longitudinal ellipse, respectively. The flow is visualized around obstacle components with vorticity as well as flow velocity where the three-dimensional components of vorticity vector are also elucidated in physics for the evolution of complex multi-dimensional flow wake.
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