#### 期刊菜单

Numerical Study of the Flow Characteristics in a Circular Tube Fitted with Different Shape Vortex Generator
DOI: 10.12677/MOS.2020.94047, PDF, HTML, XML, 下载: 281  浏览: 412  科研立项经费支持

Abstract: The vortex generator inserted into a circular tube is a passive heat transfer enhancement method. The secondary flow induced by the vortex generator in the tube is the main reason for the heat transfer enhancement, and the intensity of secondary flow is subject to flow parameters and the structural parameters of vortex generators. In this paper, the numerical method is used to study the flow characteristics of the different shapes vortex generators inserted into the circular tube. It is found that the average secondary flow intensity and the local secondary flow intensity along the flow direction generated by the vortex generators with different shapes are the strongest in the order of isosceles trapezoidal vortex generators, followed by right-angle trapezoid vortex generator and the weakest in the rectangular vortex generator. When the geometric area of material cut from the traditional twisted tape to form different vortex generator inserts is identical, the shape of vortex generator has little influence on the average friction factors and the local friction factors along the flow direction. By comparing the secondary flow cloud graphs at different locations, it is found that compared with the baseband, the vortex generator induces stronger secondary flow in the tube. When vortex generators with different shapes are built in, the secondary flow intensity distribution and streamline distribution of the fluid in the tube change. Compared with the other three vortex generators with different shapes, the isosceles trapezoidal vortex generator can induce stronger secondary flow.

1. 引言

2. 物理模型与数学模型

2.1. 物理模型

Figure 1. Schematic diagram of twisted vortex generator

${T}_{\text{r}}=H/W$ (1)

$\alpha =\mathrm{arctan}\left[\pi /\left(2H/W\right)\right]$ (2)

(3)

Table 1. Geometrical parameters of vortex generator

Figure 2. Computational domain

2.2. 物理模型建立过程

Figure 3. Model diagram established by SolidWorks

2.3. 数学模型

$\frac{\partial {u}_{i}}{\partial {x}_{i}}=0$ (4)

$\frac{\partial }{\partial {x}_{i}}\left(\rho {u}_{i}{u}_{k}\right)=\frac{\partial }{\partial {x}_{i}}\left(\mu \frac{\partial {u}_{k}}{\partial {x}_{i}}\right)-\frac{\partial p}{\partial {x}_{k}},\left(k=1,2,3\right)$ (5)

${u}_{\text{in}}={u}_{\text{c}}\left(1-\frac{{r}^{2}}{{R}^{2}}\right),v=w=0$ (6)

$\frac{\partial u}{\partial x}=\frac{\partial v}{\partial x}=\frac{\partial w}{\partial x}=0$ (7)

$u\left(x,y,z\right)=v\left(x,y,z\right)=w\left(x,y,z\right)=0$ (8)

$u\left(x,y,z\right)=v\left(x,y,z\right)=w\left(x,y,z\right)=0$ (9)

$Re=\frac{\rho {u}_{\text{m}}D}{\mu },f=\frac{2\Delta pD}{\rho {u}_{\text{m}}^{2}{L}_{2}}$ (10)

${f}_{0}=64/Re$ (11)

${J}_{\text{ABS}}^{n}=\iint |{\omega }^{n}|\text{d}A/A$ (12)

${J}_{\text{ABS}}^{n}=\iint |{\omega }^{n}|\text{d}V/V$ (13)

$Se=\rho {J}_{\text{ABS}}^{\text{n}}{D}_{h}^{2}/\mu$ (14)

2.4. 网格划分

Figure 4. Schematic diagram of grid division by ICEM

3. 网格独立性考核及算法考核

3.1. 网格独立性考核

Table 2. Grid independence test

3.2. 数值结果准确性验证

4. 数值结果分析

4.1. 涡产生器形状对平均阻力系数与二次流强度的影响

Figure 5. Comparison of Num and f between simulation results and empirical formulas

Figure 6. The variation of average resistance coefficient and secondary flow intensity with Reynolds number Re

Figure 7. When Re = 400, the fluid flow diagram after inserting vortex generators of different shapes into the tube

4.2. 涡产生器形状对局部阻力系数和二次流强度的影响

Figure 8. When Re = 400, the influence of vortex generators of different shapes on the local resistance coefficient and the local secondary flow strength

Figure 9. Section position

Figure 10. Flow diagram at different positions in the tube

Figure 11. When x = 0.270 m, flow diagram of the fluid inside the vortex generator with different shapes. (a) Isosceles trapezoidal vortex generator; (b) Rectangular vortex generator; (c) Parallelogram vortex generator; (d) Right-angle trapezoidal vortex generator

Figure 12. Cloud map of secondary flow distribution at different positions in the tube

Figure 13. When x = 0.270 m, cloud map of secondary flow distribution of vortex generators of different shapes. (a) Isosceles trapezoidal vortex generators; (b) Rectangular vortex generator; (c) Parallelogram vortex generator; (d) Right-angle trapezoidal vortex generator

5. 结论

1) 在Re = 200~800范围内，在扭带裁去部分面积相同的情况下，等腰梯形涡产生器诱导产生的二次流最强，直角梯形涡产生器次之，矩形涡产生器最差；涡产生器的形状对管内流体的平均阻力系数影响较小。

2) 涡产生器的形状对管内流体沿流动方向的局部阻力系数影响较小；管内诱导产生的局部二次流大小依次为：等腰梯形涡产生器 > 直角梯形涡产生器 > 平行四边形涡产生器 > 矩形涡产生器。

NOTES

*通讯作者。

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