基于POD降阶模型的正弦波翅片扁管管翅式换热器流动与传热特性分析

doi:10.11949/0438-1157.20211203

摘要/Abstract

摘要：

为了提高正弦波翅片扁管管翅式换热器的数值设计效率，以FVM (finite volume method，有限体积法)的计算结果作为样本数据构建POD降阶模型，研究换热器空气侧的流动与传热特性。结果表明：单参数和双参数变化时POD降阶模型重构的温度场与FVM计算结果的偏差集中表现在正弦波翅片表面区域，且沿主流方向呈减小趋势，2种方法所得速度分布的差异主要集中在主流区域。随着变量参数个数的增多，POD降阶模型的计算精度及计算效率均有所降低。POD降阶模型重构的物理场与FVM结果间的平均相对偏差最大值为2.921%，平均计算速度比传统FVM计算速度最大提高了11752倍。

关键词: 本征正交分解, 管翅式换热器, 正弦波, 有限体积法, 数值模拟

Abstract:

In order to improve the numerical design efficiency of flat tube-bank-fin heat exchanger with sine wave fin, the calculation results of FVM (finite volume method) were used as sample data to build a POD reduced-order model to study the flow and heat transfer characteristics on the air side. The results show that the relative deviation between the temperature field reconstructed by POD and the calculation results of FVM is concentrated in the sinusoidal fin surface region. And the relative deviation decreases along the mainstream direction. The velocity distribution difference between the two methods is mainly concentrated in the mainstream region. The calculation accuracy and efficiency of POD reduced-order model decrease with the increase of the number of variable parameters. The maximum average relative deviation between the physical field reconstructed by POD reduced-order model and FVM results is 2.921%, and the average computational speed is 11752 times faster than the traditional FVM calculation speed.

Key words: proper orthogonal decomposition, flat tube-bank-fin heat exchanger, sine wave, finite volume method, numerical simulation

中图分类号:

TK 124

王烨, 朱欣悦, 孙振东. 基于POD降阶模型的正弦波翅片扁管管翅式换热器流动与传热特性分析[J]. 化工学报, 2022, 73(5): 1986-1994.

Ye WANG, Xinyue ZHU, Zhendong SUN. Flow and heat transfer characteristics analysis of flat tube-bank-fin heat exchanger with sine wave fin based on POD reduced-order model[J]. CIESC Journal, 2022, 73(5): 1986-1994.

图/表 19

图1 正弦波翅片扁管管翅式换热器物理模型

Fig.1 The physical model of flat tube-bank-fin heat exchanger with sine wave fin

图2 换热器单元及正弦波翅片几何尺寸

Fig.2 Geometric dimensions of the heat exchanger unit and sine wave fins

表1 换热单元几何尺寸

Table 1 Geometry size of heat exchanger unit

名称	符号	数值/mm	名称	符号	数值/mm
横向管间距	S₁	35/40/45	纵向管间距	S₂	55
扁管宽度	a	6.3	扁管长度	b	46.3
翅片间距	T_p	4/5/6	正弦波波长	W	16.43/32.86
正弦波波幅	A	1/2

表2 样本参数变化

Table 2 Sample parameters

参数名称	单参数	双参数	三参数
Re_a	R	R	R
T_p/mm	6	T	T
S₁/mm	35	45	S
样本数	10	30	120

表3 基函数组数的选取

Table 3 Selection of the basis function numbers

项目	温度场		速度场
项目	结构1	结构2	结构1	结构2
单参数	6	7	7	8
双参数	15	21	22	24
三参数	80	80	90	90

图3 数值方法验证

Fig.3 Numerical method verification

表4 网格独立性验证

Table 4 Grid independence verification

Re_a	T_p/mm	S₁/mm	网格数	壁面平均Nu
800	6	40	245628	17.61
			359187	16.75
			441561	16.81

图4 空气通道壁面平均Nu对比(Tp=6 mm，S1=40 mm)

Fig.4 Comparison of the average Nu on the wall of the air channel (Tp=6 mm，S1=40 mm)

图5 空气侧压降随Rea变化关系

Fig.5 The air side pressure drop varies with Rea

图6 强化传热JF因子随Rea变化关系

Fig.6 JF factor of enhanced heat transfer varies with Rea

图7 单参数变化时y=S1/2截面温度分布对比（A=1 mm，W=16.43 mm）

Fig.7 Comparison of temperature distribution in y=S1/2 section for single parameter (A=1 mm，W=16.43 mm)

图8 单参数变化时y=S1/2截面速度分布对比（A=1 mm，W=16.43 mm）

Fig.8 Comparison of velocity distribution in y=S1/2 section for single parameter (A=1 mm，W=16.43 mm)

图9 双参数变化时y=S1/2截面温度分布对比(A=1 mm，W=16.43 mm)

Fig.9 Comparison of temperature distribution in y=S1/2 section for two parameters (A=1 mm，W=16.43 mm)

图10 双参数变化时y=S1/2截面速度分布对比(A=1 mm，W=16.43 mm)

Fig.10 Comparison of velocity distribution in y=S1/2 section for two parameters (A=1 mm，W=16.43 mm)

图11 三参数变化时y=S1/2截面温度分布对比(A=1 mm，W=16.43 mm)

Fig.11 Comparison of temperature distribution in y=S1/2 section for three parameters (A=1 mm，W=16.43 mm)

图12 三参数变化时y=S1/2截面速度分布对比(A=1 mm，W=16.43 mm)

Fig.12 Comparison of velocity distribution in y=S1/2 section for three parameters (A=1 mm，W=16.43 mm)

表5 两种方法平均计算耗时对比

Table 5 Comparison of average calculation time between the two methods

翅片结构	参数变化情况	FVM平均计算耗时/s	POD平均重构耗时/s
翅片结构	参数变化情况	温度场/速度场	温度场	速度场
A=1 mm， W=16.43 mm	单参数	21620	2.41	2.32
	双参数		7.15	6.91
	三参数		38.52	36.97
A=2 mm， W=32.86 mm	单参数	22094	1.88	2.34
	双参数		8.06	7.99
	三参数		35.74	34.69

表6 两种方法所得温度场偏差对比（三参数）

Table 6 Comparison of temperature field deviation obtained by two methods （three parameters）

工况变量	参数值和平均相对偏差/%
S₁/mm	37.5	42.5
T_p/mm	4.5
Re_a	1250
A=1 mm，W=16.43 mm	0.937	1.145
A=2 mm，W=32.86 mm	1.257	1.470

表7 两种方法所得速度场偏差对比（三参数）

Table 7 Comparison of velocity field deviation obtained by two methods （three parameters）

工况变量	参数值和平均相对偏差/%
S₁/mm	37.5	42.5
T_p/mm	4.5
Re_a	1250
A=1 mm，W=16.43 mm	1.860	1.741
A=2 mm，W=32.86 mm	2.705	2.921

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