Analysis of heat transfer and flow characteristics in typical cambered ducts

https://doi.org/10.1016/j.ijthermalsci.2019.106226Get rights and content

Highlights

  • Performance in divergent cambered ducts are better than that of equal cross section duct.

  • The cambered ducts have uniform temperature difference distribution.

  • The smaller the amplitude is, the better overall heat transfer performance is.

  • Temperature gradient in the peak region is bigger than that in the trough region.

Abstract

The heat transfer and flow characteristics of the air-water cross flow over cambered ducts were experimental and numerical investigated. The sequence of their Core Volume Goodness Factor (CVGF) is cosinoidal, parabolic, circular, trapezoidal and rectangular ducts successively from superior to inferior. Cambered ducts have more uniform temperature difference distribution than the equal cross section duct, and it has the minimum temperature difference in inlet and outlet of the cosinoidal duct. With the optimal overall heat transfer performance, the cosinoidal duct is superior to that of the rectangular duct by 7.3%–28.1%. In the cosinoidal duct, the smaller the amplitude is, the better the heat transfer performance is. The thickness of the thermal and velocity boundary layers adjacent to the wall surface decreases constantly with increased Reynolds number. In the near wall region, n = 5um, the main heat transfer area is the peak and middle areas, but with weaker heat transfer performance in the trough region. Although gradually expanding cambered duct slows down the flow velocity, the structure form decreases the pressure drop loss during the flow process. While improving the convective heat exchange capability of the upstream, the heat transfer area of the downstream is also improved to boost the overall heat transfer performance.

Introduction

Due to its simple structure, lower cost, superior heat transfer performance and other advantages, the uniform cross section duct is applied widely to the plate-fin heat exchangers [[1], [2], [3]], with its structure sketch shown in Fig. 1(a). The flow pattern of the plate-fin heat exchangers is usually cross flow between two parallel plates with different constructions. This traditional duct structure has many defects: (1) Bigger temperature difference at the inlet but smaller one at the outlet. During cooling medium flowing, the temperature difference at the outlet decreases, which confines the convective heat exchange capability in the outlet area; (2) Accelerated flow velocity of the cooling medium increases the pressure drop loss. With accelerated flow velocity, the pressure drop rises in the form of parabola. To improve the two main defects in uniform cross section ducts, this paper proposes the cambered duct structure, i.e. the transverse section area changes along the direction of cooling medium flow and the duct between the inlet and the outlet has the gradually expanding structure, with its sketch shown in Fig. 1(b).

In our previous research investigation [4], relevant discussions have been conducted for the heat transfer performance of the trapezoidal duct which was a type of the cambered duct in a special shape. The results indicated when the slope angle (β) in the trapezoidal duct ranges from 0 to 40°, the overall heat transfer performance of the trapezoidal duct was superior to that of the rectangular duct. Core Volume Goodness Factor (CVGF), which is proposed by Shah and Sekulić [5], is adopted to evaluate the overall heat transfer performance of five different ducts. The significance of adopting the CVGF is that it can compare the overall heat transfer performance of different duct structures under various heat transfer areas. The CVGF of trapezoidal duct was superior by 5–20% than that of rectangular duct. Meanwhile, the change of temperature difference between the inlet and outlet in the trapezoidal duct showed a linear distribution, which improved the heat transfer performance in the outlet area, with the schematic diagram of temperature difference shown in Fig. 1(c).

Some analysis investigations were made in the theory, numerical and experiment for the analysis of the trapezoidal duct. During the application, Cur and Anselmino [6] proposed an Accelerated Flow Evaporator (AFE) for the first time, which was a trapezoidal duct structure with a big inlet and a small outlet. During its flow in the evaporator, the flow velocity of air at the downstream accelerated and improved the local convection heat transfer performance of the downstream. However, the accelerated flow evaporator increased more pressure drop loss. Waltrich et al. [7,8] conducted the experimental analysis of nine accelerated evaporator samples with different structural parameters. The results indicated that the accelerated evaporator, at a low heat transfer capability, required less pump power when comparing it with a reference evaporator (a straight evaporator). Therefore, in this practical application, the accelerated evaporator had a smaller volume and consumes less material than the straight evaporator. However, with a high heat transfer capability, the accelerated evaporator showed exponential growth of power consumption, which confined practical applications of the accelerated evaporator. The reason behind it was that a reducing evaporator had more pressure drop loss at high Reynolds number. Therefore, the gradually expanding cambered duct structure in the paper can overcome the practical application better when the reducing duct structure cannot be applied to the high heat transfer capability.

There are relatively fewer analyses of the cambered duct. Poskas et al. [9] experimentally studied heat transfer performance for both convex and concave surfaces of helical ducts with curvature D/H = 5–9 and width b/H = 2–20. D (D = 0.5(d1+d2)/sin2ϕ), b and H are mean curvature diameter, mean channel width and channel height respectively, which is shown in Fig. 2. With both convex and concave surfaces heated, they found that the heat transfer from convex and concave walls increases by 20% than that of one sided heating. Bahaidarah et al. [10] analyzed the volume entropy generation rate in the sharp edge wavy duct. The results indicated that the total entropy rises gradually with the increased Re. However, the total entropy production along the duct direction decreased gradually when Reynolds number ranged from 25 to 400. Sarkar et al. [11] and others analyzed the two-dimensional flow characteristics in the wavy duct under different Reynolds numbers (100 < Re < 2123). At the states of laminar and transient flows, the Nusselt number, friction factor and Area Goodness Factor were adopted to compare and analyze the heat transfer and flow performance in ducts of six structures under different amplitudes (0.05 mm, 0.075 mm and 0.1 mm) and wavelength (0.5 mm and 1 mm). In the research of Baik et al. [12], the thermal performance of the corrugated channel in a printed circuit heat exchanger (PCHE) and the effects of amplitude and periodic equivalence factors were numerically studied. The results indicated that the recirculating flow caused by the waviness can be ignored while the mass flow of CO2 was in the typical range. Matsubara et al. [13] numerically analyzed the heat transfer and flow characteristics in a curved duct with a radius ratio are 0.92. They concluded that the convection heat transfer performance on the outer wall of the curved duct was the strongest by the evaluation of the local Nusselt number. In addition, this enhanced heat transfer came from large-scale organized vortex, which exacerbated the lateral convection of the secondary flow, thereby increased the turbulent heat flux value. Direct Numerical Simulation (DNS) is a common and effective method in the various flow ducts, such as Vinuesa et al. [14], Marin et al. [15] and Vidal et al. [16] conducted numerical studies for rectangular, hexagonal and sinusoidal ducts respectively.

As for cambered ducts studied in this paper, basically no relevant literature has been published. However, the cambered ducts are similar to a diffuser, which has been studied for years. Ghosh et al. [17] optimized the shapes of diffusers with different lengths, and used a genetic algorithm for the optimum design of plane symmetric diffusers. They found that not much difference has been noted in the optimum C values (pressure recovery factor) obtained by using different methods. The expression of the C is C=Δp/(12ρfvinl2), where Δp is the gain in static pressure, ρf is the density of the fluid and υinl is the inlet velocity of the fluid flow. Chen et al. [18] used CFD method to study the effects of injectors with different structures and obtained optimal geometrical factors to maximize entrainment ratio. They concluded that the optimum inclination of the mixing chamber is 14°; the optimum diameter ratio between the mixing tube and the primary nozzle is 1.7. In fact, studies involving heat transfer in such diffusers are still limited.

The meaning of analyzing the cambered duct is that the cambered duct can improve the distribution of temperature difference, raise the efficiency of heat transfer, reduce the pressure drop and accelerate the drainage of condensate liquid. Taking five different duct structures as an instance, this paper conducts experimental and numerical analysis of cambered ducts.

Section snippets

Physical model

Experimental analysis has been carried out for five ducts including rectangular, trapezoidal, circular, parabolic and cosinoidal ducts respectively. Processed from 6061 aluminum alloy, the five heat exchange units do not have the same overall heat transfer area but have the same volume. Fig. 3 and Fig. 4 are physical and parameter drawings of five different duct structures respectively. Table 1, Table 2, Table 3, Table 4 and Table 5 are specific parameters of five different duct structures. A

Computational domain

Taking the parabolic duct as an instance for analysis, the boundary conditions in the calculation region is shown in Fig. 6. In the figure, “Mass flow inlet” condition is applied to the inlet surface of the calculation region and the initial temperature of the flow is 293.15 K which remains constant. “Mass flow inlet” boundary conditions provided mass flow rate distribution at an inlet, which is used when it is more important to match a prescribed mass flow rate. And “Pressure outlet” condition

Comparison of overall heat transfer performance of different cambered duct structures

The Core Volume Goodness Factor (CVGF) is adopted to evaluate the overall heat transfer performance, which can be described as:η0hstdα=cpμPr2/3η04σDh2jReEstdα=μ32gcρ24σDh4fRe3

In the formula, ηohstdα is the heat transfer power of the unit heat exchanger volume per unit temperature change; Estdα is the consumed friction power per unit heat exchanger volume. The subscript “std” is the comparison benchmark and follows the ARI standard [26]. For the same “Estdα”, a bigger ηohstdα value means only a

Conclusions

This paper analyzes the flow and heat transfer characteristics in five different cambered ducts through the experimental and numerical method. The Core Volume Goodness Factor (CVGF) is adopted for the comparative analysis of rectangular, trapezoidal, circular, parabolic and cosinoidal ducts. And the following conclusions can be reached:

  • (1)

    The Core Volume Goodness Factor is adopted to compare five ducts. It is concluded that the sequence of their overall heat transfer performance is cosinoidal,

Acknowledgements

Financial support is provided by the National Natural Science Foundation of China (51806114, 51874187) and China Postdoctoral Fund.

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