# 扭曲矩形管管内传热与压降特性的数值研究Numerical Study of Heat Transfer and Pressure Drop Characteristics in Twisted Rectangular Tube

DOI: 10.12677/APP.2021.112012, PDF, HTML, XML, 下载: 91  浏览: 572  科研立项经费支持

Abstract: The characteristics of heat transfer and pressure drop in the twisted rectangular tubes are numerically studied by CFD method. Some sets of data about heat transfer and pressure drop characteristics of twisted rectangular tube with different geometric parameters under the Reynolds number 5000~40,000 are obtained. In addition, the mechanism heat transfer enhancement was analyzed by data comparison. The results show that: in turbulent flow, the friction coefficient decreased with the increase of the aspect ratio, and the Nusselt number first increased and then decreased with the increase of the aspect ratio. The Nusselt number reached the maximum when the twist ratio was 0.4. In turbulent flow, the friction coefficient decreased with the increase of the torque, and reached the maximum value when the twisted pitch length was 200 mm, where the twisted rectangular tube had high Nusselt number. The secondary flow in the twisted rectangular tube promotes the heat exchange between the fluid inside and outside the thermal boundary layer, thus improving the comprehensive heat transfer performance of the twisted rectangular tube.

1. 引言

2. 数值模型

2.1. 物理模型

Figure 1. Physical model of twisted rectangular tube

Table 1. System resulting data of standard experiment

2.2. 控制方程

$\frac{\partial \rho }{\partial t}+\frac{\partial \left(\rho {\mu }_{j}\right)}{\partial {x}_{j}}=0$ (1)

$\rho \frac{\partial k}{\partial t}+\rho \frac{\partial \left({\mu }_{j}k\right)}{\partial {x}_{j}}=\frac{\partial p}{\partial {x}_{j}}\left[\left(\mu +\frac{{\mu }_{i}}{{\sigma }_{k}}\right)\frac{\partial k}{\partial {x}_{j}}\right]+{\eta }_{t}\frac{\partial {\mu }_{i}}{\partial {x}_{j}}\left(\frac{\partial {\mu }_{i}}{\partial {x}_{j}}+\frac{\partial {\mu }_{j}}{\partial {x}_{i}}\right)-\rho \epsilon$ (2)

$\rho \frac{\partial \epsilon }{\partial t}+\rho \frac{\partial \left({\mu }_{j}\epsilon \right)}{\partial {x}_{j}}=\frac{\partial }{\partial {x}_{j}}\left[\left(\mu +\frac{{\mu }_{t}}{{\sigma }_{\epsilon }}\right)\frac{\partial \epsilon }{\partial {x}_{j}}\right]+{c}_{1}\rho S\epsilon -{c}_{2}\rho \frac{{\epsilon }^{2}}{k+\sqrt{v\epsilon }}$ (3)

${c}_{1}=\mathrm{max}\left[0.43,\frac{\eta }{\eta +5}\right];\text{\hspace{0.17em}}\eta =\frac{Sk}{\epsilon };\text{\hspace{0.17em}}=\sqrt{2{S}_{i,j}{S}_{i,j}}；{S}_{i,j}=\frac{1}{2}\left(\frac{\partial {\mu }_{i}}{\partial {x}_{j}}+\frac{\partial {\mu }_{j}}{\partial {x}_{i}}\right)$ (4)

${c}_{2}=1.9;\text{\hspace{0.17em}}{\mu }_{l}=\frac{{c}_{\mu }\rho {k}^{2}}{\epsilon };\text{\hspace{0.17em}}{\sigma }_{k}=1.0;\text{\hspace{0.17em}}{\sigma }_{\epsilon }=1.2$ (5)

$\rho \frac{\partial T}{\partial t}+\rho \frac{\partial \left({u}_{i}T\right)}{\partial {x}_{i}}=\frac{\lambda }{{c}_{p}}\frac{{\partial }^{2}T}{\partial {x}_{i}^{2}}$ (6)

2.3 网格划分及边界条件

Figure 2. Meshing of twisted tube

Figure 3. 3D model of twisted rectangular tube

3. 数据处理

$\mathrm{Re}=\frac{\rho vd}{\mu }$ (7)

$v=\frac{{q}_{m}}{\rho ab}$ (8)

$d=\frac{2ab}{a+b}$ (9)

$f=\frac{2\Delta Pd}{\rho s{v}^{2}}$ (10)

$Nu=\frac{qd}{\left({T}_{w}-{T}_{b}\right)\lambda }$ (11)

$\eta =\left(Nu/N{u}_{0}\right)/{\left(f/{f}_{0}\right)}^{1/3}$ (12)

4. 模型计算结果分析

4.1. 数值方法可靠性验证

1) 网格独立性分析

Figure 4. Grid number of twisted rectangular tube

2) 模型验证

4.2. 长宽比对扭曲矩形管性能的影响

Figure 5. Comparison of Nu between numerical method and relative literature

Figure 6. Comparison of friction coefficient between numerical method and relative literature

Figure 7. Wall Nu number under different Re number at turbulent flow stage

Figure 8. Wall friction coefficient under different Re number at turbulent flow stage

Figure 9. Comprehensive performance of heat exchange tube at turbulent flow stage

4.3. 扭距对扭曲矩形管性能的影响

Figure 10. Wall Nu number under different Re number at turbulent flow stage

Figure 11. Wall friction coefficient under different Re number at turbulent flow stage

Figure 12. Comprehensive performance of heat exchange tube at turbulent flow stage

4.4. 扭曲矩形管管内强化传热机理分析

Figure 13. Streamlines and velocity distribution contours in Tube 3

Figure 14. Streamlines and velocity contours in Tube 1-5

Figure 15. Streamlines and velocity contours in Tube 1-2

Figure 16. (a) Temperature distribution in cross section of Tube 3; (b) Temperature distribution in cross section of Tube 1-5; (c) Temperature distribution in cross section of Tube 1-2

5. 结论

1) 通过SolidWorks软件建立了物理模型，使用CFD相关软件完成了网格划分和管内流体流动的模拟，得出了壁面平均Nu和f，与前人的实验研究结果进行了比对，确定了数值方法的可靠性。

2) 对得到的不同扭曲矩形管的壁面平均Nu和f进行了对比，发现当600 ≤ Re ≤ 40,000时，随着k的增加综合换热性能先增加后减小，在k = 0.4时达到最大值。随着s的增加，综合换热性能先增加后减少，在s = 200 mm时达到最大值。

3) 对扭曲矩形管管内流线、速度场和温度场进行了分析，结果表明二次流的出现改变了换热管横截面速度场分布，进而影响了流动截面的温度分布，实现了强化传热。

“高效节能的换热/反应装备关键技术”产学研合作项目(校企合作)。

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