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Investigation of heat transfer characteristics on various kinds of fin-and-tube heat exchangers with interrupted surfaces
各种断续表面翅片管式热交换器传热特性的研究

J.Y. Yun a,* a,*  ^("a,* "){ }^{\text {a,* }}, K.S. Lee b b  ^("b "){ }^{\text {b }} a a  ^("a "){ }^{\text {a }} Living System Research Laboratory, LG Electronics Co., Seoul, 153-023, Korea
a a  ^("a "){ }^{\text {a }} 生活系统研究实验室，LG 电子有限公司，韩国首尔，153-023 b b ^(b){ }^{\mathrm{b}} School of Mechanical Engineering, Hanyang University, Seoul, 133-791, Korea
b b ^(b){ }^{\mathrm{b}} 汉阳大学机械工程学院，韩国首尔，133-791

Received 28 May 1998; in final form 4 September 1998
1998 年 5 月 28 日收到；1998 年 9 月 4 日定稿

Abstract摘要

This study experimentally investigates the effects of the shapes of interrupted surfaces on the performance of the fin-and-tube heat exchanger used in home air conditioners. The scaled-up model experiments are conducted to evaluate the heat transfer coefficient and pressure drop, and prototype experiments are also performed to examine the validity of the scaled-up experiments. Their results are in agreement with the available experimental data. These results are confined to the sensible heat transfer characteristics. It is shown that the scaled-up model experiments are very useful for estimating the heat transfer characteristics of a heat exchanger. In this study, the heat transfer and pressure drop characteristics of the three kinds of newly designed fin shapes are also compared to one another, and an optimal fin shape for home air conditioners is recommended. © 1999 Elsevier Science Ltd. All rights reserved.
本研究通过实验研究了间断面形状对家用空调翅片管式热交换器性能的影响。通过放大模型实验来评估传热系数和压降，同时还进行了原型实验来检验放大实验的有效性。其结果与现有的实验数据一致。这些结果仅限于显热传递特性。实验表明，按比例放大模型实验对于估算热交换器的传热特性非常有用。本研究还对三种新设计翅片形状的传热和压降特性进行了比较，并推荐了适用于家用空调的最佳翅片形状。© 1999 爱思唯尔科学有限公司。保留所有权利。

Nomenclature术语

A f A f A_(f)A_{\mathrm{f}} fin surface area [ m 2 ] m 2 [m^(2)]\left[\mathrm{m}^{2}\right]
A f A f A_(f)A_{\mathrm{f}} 翅片表面积 [ m 2 ] m 2 [m^(2)]\left[\mathrm{m}^{2}\right]
A i A i A_(i)A_{\mathrm{i}} tube inside surface area [ m 2 ] m 2 [m^(2)]\left[\mathrm{m}^{2}\right]
A i A i A_(i)A_{\mathrm{i}} 管内表面积 [ m 2 ] m 2 [m^(2)]\left[\mathrm{m}^{2}\right]
A m A m A_(m)A_{\mathrm{m}} tube mean surface area [ m 2 ] m 2 [m^(2)]\left[\mathrm{m}^{2}\right]
A m A m A_(m)A_{\mathrm{m}} 管道平均表面积 [ m 2 ] m 2 [m^(2)]\left[\mathrm{m}^{2}\right]
A o A o A_(o)A_{\mathrm{o}} air-side total surface area [ m 2 ] m 2 [m^(2)]\left[\mathrm{m}^{2}\right]
A o A o A_(o)A_{\mathrm{o}} 空气侧总表面积 [ m 2 ] m 2 [m^(2)]\left[\mathrm{m}^{2}\right]
A t A t A_(t)A_{\mathrm{t}} tube outside surface area [ m 2 ] m 2 [m^(2)]\left[\mathrm{m}^{2}\right]
A t A t A_(t)A_{\mathrm{t}} 钢管外表面积 [ m 2 ] m 2 [m^(2)]\left[\mathrm{m}^{2}\right]
C p C p C_(p)quadC_{\mathrm{p}} \quad specific heat at constant pressure [ kJ kg − 1 K − 1 ] kJ kg − 1 K − 1 [kJkg^(-1)K^(-1)]\left[\mathrm{kJ} \mathrm{kg}^{-1} \mathrm{~K}^{-1}\right]
C p C p C_(p)quadC_{\mathrm{p}} \quad 恒压下的比热 [ kJ kg − 1 K − 1 ] kJ kg − 1 K − 1 [kJkg^(-1)K^(-1)]\left[\mathrm{kJ} \mathrm{kg}^{-1} \mathrm{~K}^{-1}\right]
D h D h D_(h)D_{\mathrm{h}} hydraulic diameter, D h = 4 V c / A o [ m ] D h = 4 V c / A o [ m ] D_(h)=4V_(c)//A_(o)[m]D_{\mathrm{h}}=4 V_{\mathrm{c}} / A_{\mathrm{o}}[\mathrm{m}]
D h D h D_(h)D_{\mathrm{h}} 液压直径， D h = 4 V c / A o [ m ] D h = 4 V c / A o [ m ] D_(h)=4V_(c)//A_(o)[m]D_{\mathrm{h}}=4 V_{\mathrm{c}} / A_{\mathrm{o}}[\mathrm{m}]
f f ff friction factor, dimensionless
f f ff 摩擦因数，无量纲
FPI fins per inchFPI 每英寸鳍片数
G G GG mass flux [ kg m − 2 s − 1 ] kg m − 2 s − 1 [kgm^(-2)s^(-1)]\left[\mathrm{kg} \mathrm{m}^{-2} \mathrm{~s}^{-1}\right]
G G GG 质量通量 [ kg m − 2 s − 1 ] kg m − 2 s − 1 [kgm^(-2)s^(-1)]\left[\mathrm{kg} \mathrm{m}^{-2} \mathrm{~s}^{-1}\right]
H H HH enthalpy [ kJ kg − 1 ] kJ kg − 1 [kJkg^(-1)]\left[\mathrm{kJ} \mathrm{kg}^{-1}\right]
H H HH 焓 [ kJ kg − 1 ] kJ kg − 1 [kJkg^(-1)]\left[\mathrm{kJ} \mathrm{kg}^{-1}\right]
h h hh heat transfer coefficient [ W m − 2 K − 1 W m − 2 K − 1 Wm^(-2)K^(-1)\mathrm{W} \mathrm{m}^{-2} \mathrm{~K}^{-1} ]
h h hh 传热系数 [ W m − 2 K − 1 W m − 2 K − 1 Wm^(-2)K^(-1)\mathrm{W} \mathrm{m}^{-2} \mathrm{~K}^{-1} ]
j j j j jjj j factor, dimensionless
j j j j jjj j 系数，无量纲
k k kk heat conductivity [ W m − 1 K − 1 W m − 1 K − 1 Wm^(-1)K^(-1)\mathrm{W} \mathrm{m}^{-1} \mathrm{~K}^{-1} ]
k k kk 热传导 [ W m − 1 K − 1 W m − 1 K − 1 Wm^(-1)K^(-1)\mathrm{W} \mathrm{m}^{-1} \mathrm{~K}^{-1} ]
L L LL heat exchanger depth in air flow direction [m]
L L LL 热交换器在气流方向的深度[米］
M w M w M_(w)M_{\mathrm{w}} water flow rate [ kg s − 1 ] kg s − 1 [kgs^(-1)]\left[\mathrm{kg} \mathrm{s}^{-1}\right]
M w M w M_(w)M_{\mathrm{w}} 水流量 [ kg s − 1 ] kg s − 1 [kgs^(-1)]\left[\mathrm{kg} \mathrm{s}^{-1}\right]
p p pp pressure [Pa] p p pp 压力 [Pa]
Δ p Δ p Delta p\Delta p pressure drop [ Pa ] [ Pa ] [Pa][\mathrm{Pa}]
Δ p Δ p Delta p\Delta p 压降 [ Pa ] [ Pa ] [Pa][\mathrm{Pa}]
Pr Prandtl number, Pr = C p μ / k Pr = C p μ / k Pr=C_(p)mu//k\operatorname{Pr}=C_{\mathrm{p}} \mu / k
普氏指数， Pr = C p μ / k Pr = C p μ / k Pr=C_(p)mu//k\operatorname{Pr}=C_{\mathrm{p}} \mu / k
Q Q QQ heat transfer rate [W]
Q Q QQ 传热速率 [W]
R c R c R_(c)R_{\mathrm{c}} thermal contact resistance, [ m 2 K W − 1 ] m 2 K W − 1 [m^(2)(K)W^(-1)]\left[\mathrm{m}^{2} \mathrm{~K} \mathrm{~W}^{-1}\right]
R c R c R_(c)R_{\mathrm{c}} 热接触电阻， [ m 2 K W − 1 ] m 2 K W − 1 [m^(2)(K)W^(-1)]\left[\mathrm{m}^{2} \mathrm{~K} \mathrm{~W}^{-1}\right]
R e R e Re quadR e \quad Reynolds number, R e = V D h / v R e = V D h / v Re=VD_(h)//vR e=V D_{\mathrm{h}} / v
R e R e Re quadR e \quad 雷诺数， R e = V D h / v R e = V D h / v Re=VD_(h)//vR e=V D_{\mathrm{h}} / v
R f R f R_(f)R_{\mathrm{f}} fouling factor [ m 2 K W − 1 ] m 2 K W − 1 [m^(2)(K)W^(-1)]\left[\mathrm{m}^{2} \mathrm{~K} \mathrm{~W}^{-1}\right]
R f R f R_(f)R_{\mathrm{f}} 污垢系数 [ m 2 K W − 1 ] m 2 K W − 1 [m^(2)(K)W^(-1)]\left[\mathrm{m}^{2} \mathrm{~K} \mathrm{~W}^{-1}\right]
Δ T am Δ T am DeltaT_(am)\Delta T_{\mathrm{am}} arithmetic mean temperature difference [K]
Δ T am Δ T am DeltaT_(am)\Delta T_{\mathrm{am}} 算术平均温差 [K]
T T TT temperature [K]
T T TT 温度[K]
V V VV air velocity [ m s − 1 ] m s − 1 [ms^(-1)]\left[\mathrm{m} \mathrm{s}^{-1}\right]
V V VV 空气流速 [ m s − 1 ] m s − 1 [ms^(-1)]\left[\mathrm{m} \mathrm{s}^{-1}\right]
V c V c V_(c)quadV_{c} \quad air-side volume [ m 3 ] m 3 [m^(3)]\left[\mathrm{m}^{3}\right]
V c V c V_(c)quadV_{c} \quad 空气侧容积 [ m 3 ] m 3 [m^(3)]\left[\mathrm{m}^{3}\right]
Δ x Δ x Delta x\Delta x tube thickness [m].
Δ x Δ x Delta x\Delta x 钢管厚度 [m].

Greek symbols希腊文符号

η η eta\eta surface efficiency
η η eta\eta 表面效率
η f η f eta_(f)\eta_{\mathrm{f}} fin efficiency
η f η f eta_(f)\eta_{\mathrm{f}} 翅片效率
μ μ mu\mu dynamic viscosity [ kg m − 1 s − 1 ] kg m − 1 s − 1 [kgm^(-1)s^(-1)]\left[\mathrm{kg} \mathrm{m}^{-1} \mathrm{~s}^{-1}\right]
μ μ mu\mu 动态粘度 [ kg m − 1 s − 1 ] kg m − 1 s − 1 [kgm^(-1)s^(-1)]\left[\mathrm{kg} \mathrm{m}^{-1} \mathrm{~s}^{-1}\right]
v v vv kinematic viscosity [ m 2 s − 1 ] m 2 s − 1 [m^(2)s^(-1)]\left[\mathrm{m}^{2} \mathrm{~s}^{-1}\right]
v v vv 运动粘度 [ m 2 s − 1 ] m 2 s − 1 [m^(2)s^(-1)]\left[\mathrm{m}^{2} \mathrm{~s}^{-1}\right]
ρ ρ rho\rho air density [ kg m − 3 ] kg m − 3 [kgm^(-3)]\left[\mathrm{kg} \mathrm{m}^{-3}\right].
ρ ρ rho\rho 空气密度 [ kg m − 3 ] kg m − 3 [kgm^(-3)]\left[\mathrm{kg} \mathrm{m}^{-3}\right] 。
Superscript上标
  • Nondimensional quantity.无量。

Subscripts下标

a air空气
ex exit退出
f f ff fin f f ff 鳍
h hydraulich 液压
i inside内
in inlet进气
m model模型
o outside外部
p prototypep 原型
t tube电子管
w tube wallw 管壁
W water.W 水。

1. Introduction1.导言

Fin-and-tube exchangers are used extensively in home appliances and transportation applications, where compactness is very important. Fabricating technologies of special shapes, such as a louver or a slit in the fin surface, have been devised to minimize relatively large air-side thermal resistance in fin-and-tube heat exchangers. These efforts have resulted in an increase of the heat transfer coefficient and a reduction in size, and thus the development of compact heat exchangers has been accelerated.
翅片管式热交换器广泛应用于对结构紧凑度要求极高的家用电器和交通运输领域。为了尽量减小翅片管式热交换器中相对较大的空气侧热阻，人们设计了特殊形状的制造技术，如翅片表面的百叶窗或狭缝。这些努力的结果是提高了传热系数，缩小了尺寸，从而加快了紧凑型热交换器的发展。
The enhancement of the air-side heat transfer coefficient, in general, can be made using the following three methods [1]: (i) scaling down the geometry [2]; (ii) increasing turbulence; (iii) using interrupted surfaces. Since the use of interrupted surfaces has higher potential for the enhancement of the heat transfer coefficient than the other two methods, it is one of the most widely used techniques. This provides enhancement of heat transfer by the repeated growth and destruction of the laminar boundary layer, the so-called ‘leading edge’ effect.
提高空气侧传热系数一般可采用以下三种方法[1]：(i) 缩减几何尺寸[2]；(ii) 增加湍流；(iii) 使用间断表面。与其他两种方法相比，使用间断表面具有更高的传热系数提升潜力，因此是最广泛使用的技术之一。这种方法通过层流边界层的反复增长和破坏（即所谓的 "前缘 "效应）来增强传热。
Recent studies on heat exchangers have focused on the development of new interrupted surfaces, and so, fin shapes with new design criteria are being suggested. The search for new fin configurations takes much time and effort, hence, experimental studies to analyze the heat transfer characteristics of heat exchangers have not been very active. The geometry similitude method has been employed to alleviate those difficulties in this study, and it has turned out to be effective. Since Wong [3] demonstrated the feasibility of a scaled-up experiment through a comparative study between prototype and the scaledup model, many researchers have used this method. Torigoe et al. [4] showed experimental results of four scaled-up models with tube diameters of 6.25 , 5.0 6.25 , 5.0 6.25,5.06.25,5.0 and 4.0 mm each and three different kinds of step and row pitches to examine the effects of tube diameter and tube arrangement on the heat transfer performance. Koido et al. [5] performed flow visualization tests and numerical analysis using 20 scaled-up heat exchangers with slitted fins to investigate the temperature and velocity field, and selected optimal fin shapes.
近期对热交换器的研究主要集中在开发新的间断面上，因此提出了具有新设计标准的翅片形状。寻找新的翅片结构需要花费大量的时间和精力，因此分析热交换器传热特性的实验研究并不活跃。本研究采用几何模拟法来缓解这些困难，结果证明这种方法是有效的。自 Wong [3] 通过原型与放大模型的对比研究证明了放大实验的可行性后，许多研究人员都采用了这种方法。Torigoe 等人[4]展示了管直径分别为 6.25 , 5.0 6.25 , 5.0 6.25,5.06.25,5.0 和 4.0 毫米以及三种不同阶梯和行距的四种放大模型的实验结果，以研究管直径和管排列对传热性能的影响。Koido 等人[5]使用 20 个带狭缝翅片的按比例放大热交换器进行了流动可视化测试和数值分析，以研究温度场和速度场，并选出了最佳翅片形状。
In this study, air-side heat transfer characteristics such as the heat transfer coefficient and pressure drop are experimentally analyzed using fin-and-tube heat exchangers with 2-row, staggered arrangements. The geometry similitude experiment using three scaled-up models with three kinds of interrupted fins and a plate
本研究使用双排交错布置的翅片管式热交换器对空气侧的传热特性（如传热系数和压降）进行了实验分析。几何模拟实验使用了三个按比例放大的模型，其中有三种间断翅片和一个板片。
fin is conducted in the present study, and the heat transfer coefficient and pressure drop of these fins are measured by utilizing a small-sized wind tunnel. Prototype experiments with these fins are done to verify the scaled-up experiments. By comparing their performance characteristics with the three kinds of fin shapes, the optimal shapes are selected for application to home air conditioners. This work also suggests a process for the development of a new heat exchanger.
本研究利用小型风洞测量了这些翅片的传热系数和压降。使用这些翅片进行了原型实验，以验证放大实验的结果。通过比较三种翅片形状的性能特点，选出了适用于家用空调的最佳形状。这项工作还提出了一种新型热交换器的开发流程。

2. Performance evaluation procedure
2.绩效评估程序

2.1. Scaled-up experiment [6]
2.1.放大实验 [6]

2.1.1. Theoretical analysis
2.1.1.理论分析

The nondimensional governing equations of steady, incompressible flows can be written as follows:
不可压缩的稳定流的非一维控制方程可写成以下形式：
∇ ∗ ⋅ v ∗ = 0 ∇ ∗ ⋅ v ∗ = 0 grad^(**)*v^(**)=0\nabla^{*} \cdot \mathrm{v}^{*}=0
( v ∗ ⋅ ∇ ∗ ) v ∗ = − ∇ ∗ p ∗ + ( 1 R e ) ∇ ∗ 2 v ∗ v ∗ ⋅ ∇ ∗ v ∗ = − ∇ ∗ p ∗ + 1 R e ∇ ∗ 2 v ∗ (v^(**)*grad^(**))v^(**)=-grad^(**)p^(**)+((1)/(Re))grad^(**2)v^(**)\left(\mathrm{v}^{*} \cdot \nabla^{*}\right) \mathrm{v}^{*}=-\nabla^{*} p^{*}+\left(\frac{1}{R e}\right) \nabla^{* 2} \mathrm{v}^{*}
v ∗ ( ∇ ∗ ⋅ T ∗ ) = ( 1 RePr ) ∇ ∗ 2 T ∗ v ∗ ∇ ∗ ⋅ T ∗ = 1 RePr ∇ ∗ 2 T ∗ v^(**)(grad^(**)*T^(**))=((1)/(RePr))grad^(**2)T^(**)\mathrm{v}^{*}\left(\nabla^{*} \cdot T^{*}\right)=\left(\frac{1}{\operatorname{RePr}}\right) \nabla^{* 2} T^{*}
where其中
x ∗ = x D h , v ∗ = v V , ∇ ∗ = D h ∇ x ∗ = x D h , v ∗ = v V , ∇ ∗ = D h ∇ x^(**)=(x)/(D_(h)),quadv**=(v)/(V),quadgrad^(**)=D_(h)grad\mathrm{x}^{*}=\frac{\mathrm{x}}{D_{\mathrm{h}}}, \quad \mathrm{v} *=\frac{\mathrm{v}}{V}, \quad \nabla^{*}=D_{\mathrm{h}} \nabla,
p ∗ = p − p 0 ρ V 2 , T ∗ = T w − T T w − T in p ∗ = p − p 0 ρ V 2 , T ∗ = T w − T T w − T in p^(**)=(p-p_(0))/(rhoV^(2)),quadT^(**)=(T_(w)-T)/(T_(w)-T_(in))p^{*}=\frac{p-p_{0}}{\rho V^{2}}, \quad T^{*}=\frac{T_{\mathrm{w}}-T}{T_{\mathrm{w}}-T_{\mathrm{in}}},
R e = V D h v , Pr = C p μ k , D h = 4 V c A o R e = V D h v , Pr = C p μ k , D h = 4 V c A o Re=(VD_(h))/(v),quad Pr=(C_(p)mu)/(k),quadD_(h)=(4V_(c))/(A_(o))R e=\frac{V D_{\mathrm{h}}}{v}, \quad \operatorname{Pr}=\frac{C_{\mathrm{p}} \mu}{k}, \quad D_{\mathrm{h}}=\frac{4 V_{\mathrm{c}}}{A_{\mathrm{o}}}
Similitude of the flow field is obtained as the Reynolds number in equation (2) set to be equal value. Similitude of air temperature is also required to obtain similitude of heat transfer. Similitude of fin surface temperature has to be met with the Reynolds and Prandtl numbers in energy equation (3). In this study, similarity of the Prandtl number is automatically satisfied since the working fluid is air. Similitude of fin surface temperature is obtained from the heat conduction equation inside the fin as follows:
当方程（2）中的雷诺数设定为等值时，就可获得流场的模拟值。要获得传热的模拟性，还需要空气温度的模拟性。翅片表面温度的相似性必须与能量方程（3）中的雷诺数和普朗特尔数相匹配。在本研究中，由于工作流体是空气，因此自动满足了普朗德数的相似性。翅片表面温度的相似性可通过翅片内部的热传导方程求得，如下所示：
∇ ∗ ( k f ∗ ∇ ∗ T f ∗ ) = 0 ∇ ∗ k f ∗ ∇ ∗ T f ∗ = 0 grad^(**)(k_(f)^(**)grad^(**)T_(f)^(**))=0\nabla^{*}\left(k_{\mathrm{f}}^{*} \nabla^{*} T_{\mathrm{f}}^{*}\right)=0
where其中
T f ∗ = T f − T in T w − T in , k f ∗ = k f , m k f , p T f ∗ = T f − T in T w − T in , k f ∗ = k f , m k f , p T_(f)^(**)=(T_(f)-T_(in))/(T_(w)-T_(in)),quadk_(f)^(**)=(k_(f,m))/(k_(f,p))T_{\mathrm{f}}^{*}=\frac{T_{\mathrm{f}}-T_{\mathrm{in}}}{T_{\mathrm{w}}-T_{\mathrm{in}}}, \quad k_{\mathrm{f}}^{*}=\frac{k_{\mathrm{f}, \mathrm{m}}}{k_{\mathrm{f}, \mathrm{p}}}
T f ∗ T f ∗ T_(f)^(**)T_{\mathrm{f}}^{*} and k f ∗ k f ∗ k_(f)^(**)k_{\mathrm{f}}^{*} represent dimensionless fin temperature and thermal conductivity, respectively. Since fin thickness and thermal conductivity must have the same values as those of the prototypes in order to have similarity for fin surface temperature, fin thickness may be scaled-up as much as the scale factor.
T f ∗ T f ∗ T_(f)^(**)T_{\mathrm{f}}^{*} 和 k f ∗ k f ∗ k_(f)^(**)k_{\mathrm{f}}^{*} 分别代表无量纲翅片温度和导热系数。由于翅片厚度和导热系数必须与原型相同，翅片表面温度才会相似，因此翅片厚度可按比例系数放大。

2.1.2. Experimental apparatus and procedure
2.1.2.实验仪器和程序

Figure 1 shows the schematic diagram of the experimental apparatus which is an open type, small-sized wind tunnel [7]. It consists of a suction fan, flow straightener, first reduction area, a test section, second reduction area, and exit chamber. The air flow rate and velocity are determined by using the measured pressure difference at the nozzle installed inside the exit chamber. The pressures at eight pressure taps are measured by a micro-manometer with resolution of 0.1 Pa and the average pressure difference is determined from these data. The air flow rate is calibrated by a pitot tube at the downstream of nozzle and the deviation between these two data is within 0.3 % 0.3 % 0.3%0.3 \%. The air velocity is varied from 0.2 to 1.0 m s − 1 1.0 m s − 1 1.0ms^(-1)1.0 \mathrm{~m} \mathrm{~s}^{-1} using a fan connected to the power regulator. Static pressure is measured using six pressure taps which are installed at the inlet and the outlet of the test section. Pressure drop is measured using a differential pressure gauge. Average temperature difference of air is measured using type T thermocouple installed at the same positions. To control the inlet temperature with the same conditions as the actual product, an air-cooled heat exchanger with a water tank at constant temperature is placed at the inlet section of the chamber. The outlet temperature is estimated by averaging the temperatures at two locations in exit chamber. Styrofoam of 40 mm thickness is used to minimize the heat loss.
图 1 显示了实验装置的原理图，它是一个开放式的小型风洞[7]。它由吸风机、气流矫直机、第一减速区、测试区、第二减速区和出口室组成。空气流量和速度是通过安装在出口室内部的喷嘴处的测量压差确定的。八个压力抽头的压力由分辨率为 0.1 Pa 的微压计测量，并根据这些数据确定平均压差。空气流速由喷嘴下游的皮托管校准，这两个数据之间的偏差在 0.3 % 0.3 % 0.3%0.3 \% 以内。使用连接到功率调节器的风扇将空气流速从 0.2 到 1.0 m s − 1 1.0 m s − 1 1.0ms^(-1)1.0 \mathrm{~m} \mathrm{~s}^{-1} 变化。使用安装在测试部分入口和出口的六个压力抽头测量静压。使用压差计测量压降。使用安装在相同位置的 T 型热电偶测量空气的平均温差。为了在与实际产品相同的条件下控制入口温度，在试验室入口处放置了一个带有恒温水箱的风冷式热交换器。出口温度通过出口室两个位置的平均温度来估算。使用厚度为 40 毫米的泡沫塑料以尽量减少热量损失。
The test section is composed of nine fins and eight rings that correspond to the tube in the prototype. To maintain the wall temperature under the same condition as that of the actual product, the rings are heated by Joule heating.
测试部分由与原型管相对应的九个翅片和八个环组成。为了使管壁温度与实际产品的温度保持一致，环是通过焦耳加热进行加热的。
Electric power on the front and back rows can be controlled independently for the convenience of heat transfer calculation. Aluminium fins and tubes are screwed tightly to minimize contact resistance. Tube wall temperature is measured using type T thermocouples.
前排和后排的电力可独立控制，便于进行传热计算。铝翅片和管子被拧紧，以尽量减少接触电阻。管壁温度使用 T 型热电偶测量。
The experiment starts with supplying electricity to the heating wire after fan speed reaches the maximum value. The amount of electric power is measured after the wall temperature reaches a steady state at every measuring point. The steady state is generally obtained in 30 min , and the test is repeated with increasing or decreasing velocity to identify the reproducibility. The heat transfer coefficient is obtained as follows:
实验开始时，在风扇转速达到最大值后向发热丝供电。在每个测量点的壁温达到稳定状态后测量电功率。一般在 30 分钟内达到稳定状态，然后以增大或减小速度重复试验，以确定重现性。传热系数的计算公式如下：
h = Q A o Δ T am h = Q A o Δ T am h=(Q)/(A_(o)DeltaT_(am))h=\frac{Q}{A_{\mathrm{o}} \Delta T_{\mathrm{am}}}
where其中
Δ T am = T w − ( T ex + T in ) 2 Δ T am = T w − T ex + T in 2 DeltaT_(am)=T_(w)-((T_(ex)+T_(in)))/(2)\Delta T_{\mathrm{am}}=T_{\mathrm{w}}-\frac{\left(T_{\mathrm{ex}}+T_{\mathrm{in}}\right)}{2}
Q Q QQ and Δ T am Δ T am  DeltaT_("am ")\Delta T_{\text {am }} represent the amount of power supplied and the arithmetic mean temperature difference, respectively. All the temperature measurements with the thermocouples are made with an uncertainty of ± 0.1 ∘ C ± 0.1 ∘ C +-0.1^(@)C\pm 0.1^{\circ} \mathrm{C}.
Q Q QQ 和 Δ T am Δ T am  DeltaT_("am ")\Delta T_{\text {am }} 分别代表供电功率和算术平均温差。所有使用热电偶进行的温度测量的不确定度均为 ± 0.1 ∘ C ± 0.1 ∘ C +-0.1^(@)C\pm 0.1^{\circ} \mathrm{C} 。

2.2. Prototype experiment
2.2.原型实验

The prototype experiment is performed to confirm the validity of the geometry similitude experiment. Samples are made to actual size using a fin die, and their heat transfer and pressure drop characteristics are measured at the open-type wind tunnel inside a psychrometric type
为证实几何模拟实验的有效性，进行了原型实验。样品是用鳍片模具按实际尺寸制作的，其传热和压降特性是在心理测量型风洞内进行测量的。

(a) Front view(a) 正视图

(b) Side view(b) 侧视图
Fig. 1. Schematic diagram of the test apparatus for scaled-up experiment.
图 1.放大实验的测试仪器示意图。
calorimeter which has similar principles to the scaled-up experimental apparatus. This unit is composed of a test section, a control chamber, cooling equipment, a blower section, hot and cold water supply unit, and a refrigerant supply unit. The accuracy and test conditions of this unit are shown in Table 1. This experiment has been performed to measure only the sensible heat transfer characteristics using hot water to compare it with the scaled-up experimental results under the same conditions. The acceptance criteria of the prototype experimental data are judged by the heat balance ratio of air-to-water under the steady state condition, which is available in the ASHRAE Standard 33-78 [8]. An overall error of less than ± 4 % ± 4 % +-4%\pm 4 \% in the heat balance is permitted in this study. Since the present results satisfy the heat balance and the data reading under the steady state, these experiments are considered as a ‘valid’ run. This balance is automatically calculated utilizing the data acquisition and reduction program. The steady state is obtained between 30 and 60 min at every measuring point. The heat transfer rate in the tube-side and air-side is obtained using the inlet and outlet temperature and enthalpy, respectively, which can be expressed as follows:
热量计的原理与按比例放大的实验装置相似。该装置由测试部分、控制室、冷却设备、鼓风机部分、冷热水供应装置和制冷剂供应装置组成。该装置的精度和测试条件如表 1 所示。本实验仅测量了使用热水的显热传递特性，以便与相同条件下的放大实验结果进行比较。原型实验数据的验收标准是根据稳态条件下空气与水的热平衡比来判断的，ASHRAE 标准 33-78 [8]。本研究允许热平衡的总体误差小于 ± 4 % ± 4 % +-4%\pm 4 \% 。由于目前的结果符合热平衡和稳态下的数据读数，因此这些实验被视为 "有效 "运行。该平衡是利用数据采集和还原程序自动计算得出的。每个测量点的稳态时间为 30 至 60 分钟。管侧和空气侧的热传导率分别通过入口和出口温度和焓来获得，可表示如下：
Q W = M W C pW ( T Wi − T Wo ) Q W = M W C pW T Wi − T Wo Q_(W)=M_(W)C_(pW)(T_(Wi)-T_(Wo))Q_{\mathrm{W}}=M_{\mathrm{W}} C_{\mathrm{pW}}\left(T_{\mathrm{Wi}}-T_{\mathrm{Wo}}\right)
Q a = G a ( H ao − H ai ) Q a = G a H ao − H ai Q_(a)=G_(a)(H_(ao)-H_(ai))Q_{\mathrm{a}}=G_{\mathrm{a}}\left(H_{\mathrm{ao}}-H_{\mathrm{ai}}\right)
The subscripts Wi, Wo, ai and ao denote the water inlet, the water outlet, the air inlet and the air outlet, respectively. The air-side heat transfer coefficient is calculated using a modified Wilson plot method [9]:
下标 Wi、Wo、ai 和 ao 分别表示进水口、出水口、进气口和出气口。空气侧传热系数采用改进的威尔逊图法计算[9]：
Q = F U A o Δ T am Q = F U A o Δ T am Q=FUA_(o)DeltaT_(am)Q=F U A_{\mathrm{o}} \Delta T_{\mathrm{am}}
where F F FF represents the correction factor, and Q Q QQ is obtained from the arithmetic mean of equation (8) and (9). Since water flow rate is increased with maximum possible rate to minimize the temperature difference between the inlet and outlet and the arithmetic mean temperature difference is used in the calculation process, the value of F F FF is assumed to be unity. The overall heat transfer coefficient U U UU is expressed by
其中 F F FF 代表校正系数， Q Q QQ 由公式 (8) 和 (9) 的算术平均值得出。由于水流量以最大可能的速度增加，以尽量减小入口和出口之间的温差，并且在计算过程中使用算术平均温差，因此假定 F F FF 的值为一。总传热系数 U U UU 表示为
1 U = 1 h o + R f + R c + Δ x A m k t / A o + A o A i h i 1 U = 1 h o + R f + R c + Δ x A m k t / A o + A o A i h i (1)/(U)=(1)/(h_(o))+R_(f)+R_(c)+(Delta x)/(A_(m)k_(t)//A_(o))+(A_(o))/(A_(i)h_(i))\frac{1}{U}=\frac{1}{h_{\mathrm{o}}}+R_{\mathrm{f}}+R_{\mathrm{c}}+\frac{\Delta x}{A_{\mathrm{m}} k_{\mathrm{t}} / A_{o}}+\frac{A_{\mathrm{o}}}{A_{\mathrm{i}} h_{\mathrm{i}}}
where其中
h o = η h = ( A t + η f A f ) A o h , h i = 0.023 Re 0.8 Pr 0.4 k d i h o = η h = A t + η f A f A o h , h i = 0.023 Re 0.8 Pr 0.4 k d i h_(o)=eta h=((A_(t)+eta_(f)A_(f)))/(A_(o))h,quadh_(i)=0.023Re^(0.8)Pr^(0.4)(k)/(d_(i))h_{\mathrm{o}}=\eta h=\frac{\left(A_{\mathrm{t}}+\eta_{\mathrm{f}} A_{\mathrm{f}}\right)}{A_{\mathrm{o}}} h, \quad h_{\mathrm{i}}=0.023 \operatorname{Re}^{0.8} \operatorname{Pr}^{0.4} \frac{k}{d_{\mathrm{i}}}
Since the heat exchangers of the same size are used in this study, the second to fourth terms of the right hand side in equation (11) can be treated as constants. In equation (12), h h hh represents the pure heat transfer coefficient of the tube outside at the 100 % 100 % 100%100 \% fin efficiency, η f η f eta_(f)\eta_{\mathrm{f}}. Since the fin efficiency is difficult to be obtained experimentally, the heat transfer coefficient including the effect of fin efficiency is adopted in the present study. Consequently, the air-side heat transfer coefficient h o h o h_(o)h_{\mathrm{o}} is determined using the overall heat transfer coefficient U U UU of equation (10) and the tube side heat transfer coefficient h i h i h_(i)h_{\mathrm{i}} of equation (12). Colburn j j jj factor and friction factor are, respectively, given by
由于本研究中使用的是相同尺寸的热交换器，因此方程 (11) 右侧的第二项至第四项可视为常数。在公式 (12) 中， h h hh 表示在 100 % 100 % 100%100 \% 翅片效率、 η f η f eta_(f)\eta_{\mathrm{f}} 条件下管外的纯传热系数。由于翅片效率难以通过实验获得，因此本研究采用了包含翅片效率影响的传热系数。因此，空气侧传热系数 h o h o h_(o)h_{\mathrm{o}} 是利用公式 (10) 中的整体传热系数 U U UU 和公式 (12) 中的管侧传热系数 h i h i h_(i)h_{\mathrm{i}} 确定的。Colburn j j jj 因子和摩擦因数分别为
j = h o P r 2 / 3 ρ C p V j = h o P r 2 / 3 ρ C p V j=(h_(o)Pr^(2//3))/(rhoC_(p)V)j=\frac{h_{\mathrm{o}} P r^{2 / 3}}{\rho C_{\mathrm{p}} V}
f = D h L 2 Δ p ρ V 2 f = D h L 2 Δ p ρ V 2 f=(D_(h))/(L)(2Delta p)/(rhoV^(2))f=\frac{D_{\mathrm{h}}}{L} \frac{2 \Delta p}{\rho V^{2}}
where ρ ρ rho\rho and C p C p C_(p)C_{\mathrm{p}} represent air density and specific heat at constant pressure, respectively.
其中 ρ ρ rho\rho 和 C p C p C_(p)C_{\mathrm{p}} 分别代表恒压下的空气密度和比热。

3. Experimental model3.实验模型

The basic model in this work is chosen as the heat exchanger with a 2-row, staggered arrangement and tube diameter of 7 mm , which is extensively used in room air conditioners. A scale factor is selected by considering the manufacturing process of the sample and measuring accuracy. In the case of a three scaled-up model, all geometries have to be enlarged to three times the prototype. Table 2 shows geometric configurations of the samples. In the present scaled-up procedure, the heat transfer coefficient and the pressure drop must be one third and one ninth, respectively, of the actual value to satisfy the similarity with the prototype as shown in Table 3.
本研究选择的基本模型是室内空调中广泛使用的双列交错布置、管径为 7 毫米的热交换器。考虑到样品的制造工艺和测量精度，选择了比例系数。在三比例模型的情况下，所有几何形状都必须放大到原型的三倍。表 2 显示了样品的几何结构。如表 3 所示，在本缩放程序中，传热系数和压降必须分别为实际值的三分之一和九分之一，以满足与原型的相似性。
Figure 2 represents five kinds of fin shapes used in the present work. Type ’ R R RR ’ fin is a standard fin for comparisons of validity, and a leading edge effect is maximized by being formed by cutting the metal plate and
图 2 显示了本研究中使用的五种翅片形状。 R R RR "型鳍片是用于有效性比较的标准鳍片，通过切割金属板和" R R RR "型鳍片形成的前缘效果最大化。
Table 1表 1
Accuracy and test conditions of psychrometric type calorimeter
心率式热量计的精度和测试条件
Physical parameter物理参数 Accuracy准确性 Physical parameter物理参数 Test condition测试条件
Temperature ( ∘ C ) ∘ C (^(@)C)\left({ }^{\circ} \mathrm{C}\right)温度 ( ∘ C ) ∘ C (^(@)C)\left({ }^{\circ} \mathrm{C}\right) ± 0.1 ± 0.1 +-0.1\pm 0.1 Air dry bulb temperature ( ∘ C ) ∘ C (^(@)C)\left({ }^{\circ} \mathrm{C}\right)
空气干球温度 ( ∘ C ) ∘ C (^(@)C)\left({ }^{\circ} \mathrm{C}\right) 		21
Pressure ( Pa ) ( Pa ) (Pa)(\mathrm{Pa})压力 ( Pa ) ( Pa ) (Pa)(\mathrm{Pa}) ± 0.1 ± 0.1 +-0.1\pm 0.1 Air wet bulb temperature ( ∘ C ) ∘ C (^(@)C)\left({ }^{\circ} \mathrm{C}\right)
空气湿球温度 ( ∘ C ) ∘ C (^(@)C)\left({ }^{\circ} \mathrm{C}\right) 		15.5
Air flow rate ( m 3 min − 1 ) m 3 min − 1 (m^(3)min^(-1))\left(\mathrm{m}^{3} \mathrm{~min}^{-1}\right)空气流速 ( m 3 min − 1 ) m 3 min − 1 (m^(3)min^(-1))\left(\mathrm{m}^{3} \mathrm{~min}^{-1}\right) ± 0.1 ± 0.1 +-0.1\pm 0.1 Air velocity ( m s − 1 ) m s − 1 (ms^(-1))\left(\mathrm{m} \mathrm{s}^{-1}\right)气流速度 ( m s − 1 ) m s − 1 (ms^(-1))\left(\mathrm{m} \mathrm{s}^{-1}\right) 0.5 ∼ 1.5 0.5 ∼ 1.5 0.5∼1.50.5 \sim 1.5
Water flow rate ( kg h − 1 ) kg h − 1 (kgh^(-1))\left(\mathrm{kg} \mathrm{h}^{-1}\right)
水流量 ( kg h − 1 ) kg h − 1 (kgh^(-1))\left(\mathrm{kg} \mathrm{h}^{-1}\right) 		± 0.6 ± 0.6 +-0.6\pm 0.6 Inlet water temperature ( ∘ C ) ∘ C (^(@)C)\left({ }^{\circ} \mathrm{C}\right)
进水温度 ( ∘ C ) ∘ C (^(@)C)\left({ }^{\circ} \mathrm{C}\right) 		45
Physical parameter Accuracy Physical parameter Test condition Temperature (^(@)C) +-0.1 Air dry bulb temperature (^(@)C) 21 Pressure (Pa) +-0.1 Air wet bulb temperature (^(@)C) 15.5 Air flow rate (m^(3)min^(-1)) +-0.1 Air velocity (ms^(-1)) 0.5∼1.5 Water flow rate (kgh^(-1)) +-0.6 Inlet water temperature (^(@)C) 45| Physical parameter | Accuracy | Physical parameter | Test condition | | :--- | :--- | :--- | :--- | | Temperature $\left({ }^{\circ} \mathrm{C}\right)$ | $\pm 0.1$ | Air dry bulb temperature $\left({ }^{\circ} \mathrm{C}\right)$ | 21 | | Pressure $(\mathrm{Pa})$ | $\pm 0.1$ | Air wet bulb temperature $\left({ }^{\circ} \mathrm{C}\right)$ | 15.5 | | Air flow rate $\left(\mathrm{m}^{3} \mathrm{~min}^{-1}\right)$ | $\pm 0.1$ | Air velocity $\left(\mathrm{m} \mathrm{s}^{-1}\right)$ | $0.5 \sim 1.5$ | | Water flow rate $\left(\mathrm{kg} \mathrm{h}^{-1}\right)$ | $\pm 0.6$ | Inlet water temperature $\left({ }^{\circ} \mathrm{C}\right)$ | 45 |
Table 2表 2
Basic geometries on experimental heat exchanger
实验热交换器的基本几何形状
Geometric parameter几何参数
放大模型
Scaled-up
model
Scaled-up model| Scaled-up | | :--- | | model |
原型模型
Prototype
model
Prototype model| Prototype | | :--- | | model |
Scale factor比例系数 3 1
Frontal area ( mm 2 ) mm 2 (mm^(2))\left(\mathrm{mm}^{2}\right)前额 ( mm 2 ) mm 2 (mm^(2))\left(\mathrm{mm}^{2}\right) 36 × 315 36 × 315 36 xx31536 \times 315 290 × 231 290 × 231 290 xx231290 \times 231
Tube diameter ( mm ) ( mm ) (mm)(\mathrm{mm})管径 ( mm ) ( mm ) (mm)(\mathrm{mm}) 22.5 7.5
Fin pitch ( mm ) ( mm ) (mm)(\mathrm{mm})鳍片间距 ( mm ) ( mm ) (mm)(\mathrm{mm}) 3.6 1.2
Fin thickness ( mm ) ( mm ) (mm)(\mathrm{mm})鳍片厚度 ( mm ) ( mm ) (mm)(\mathrm{mm}) 0.3 0.1
Row pitch ( mm ) ( mm ) (mm)(\mathrm{mm})行距 ( mm ) ( mm ) (mm)(\mathrm{mm}) 38.1 12.7
Step pitch ( mm ) ( mm ) (mm)(\mathrm{mm})步距 ( mm ) ( mm ) (mm)(\mathrm{mm}) 63 21
Number of rows行数 2 2
Number of steps步骤数 5 11
Hydraulic diameter ( mm ) ( mm ) (mm)(\mathrm{mm})
液压直径 ( mm ) ( mm ) (mm)(\mathrm{mm}) 		6.3 2.1
Geometric parameter "Scaled-up model" "Prototype model" Scale factor 3 1 Frontal area (mm^(2)) 36 xx315 290 xx231 Tube diameter (mm) 22.5 7.5 Fin pitch (mm) 3.6 1.2 Fin thickness (mm) 0.3 0.1 Row pitch (mm) 38.1 12.7 Step pitch (mm) 63 21 Number of rows 2 2 Number of steps 5 11 Hydraulic diameter (mm) 6.3 2.1| Geometric parameter | Scaled-up <br> model | Prototype <br> model | | :--- | :--- | :--- | | Scale factor | 3 | 1 | | Frontal area $\left(\mathrm{mm}^{2}\right)$ | $36 \times 315$ | $290 \times 231$ | | Tube diameter $(\mathrm{mm})$ | 22.5 | 7.5 | | Fin pitch $(\mathrm{mm})$ | 3.6 | 1.2 | | Fin thickness $(\mathrm{mm})$ | 0.3 | 0.1 | | Row pitch $(\mathrm{mm})$ | 38.1 | 12.7 | | Step pitch $(\mathrm{mm})$ | 63 | 21 | | Number of rows | 2 | 2 | | Number of steps | 5 | 11 | | Hydraulic diameter $(\mathrm{mm})$ | 6.3 | 2.1 |
Table 3表 3
Comparison of similitude relations on parameters used in this study
本研究所用参数的相似关系比较
Geometric parameters几何参数
放大模型
Scaled-up
model
Scaled-up model| Scaled-up | | :--- | | model |
原型模型
Prototype
model
Prototype model| Prototype | | :--- | | model |

比例系数 翅片长度 ( mm ) ( mm ) (mm)(\mathrm{mm})
Scale factor
Fin length ( mm ) ( mm ) (mm)(\mathrm{mm})
Scale factor Fin length (mm)| Scale factor | | :--- | | Fin length $(\mathrm{mm})$ |
 3 1
Fin thermal conductivity鳍片导热率 3 1
( W m − 1 K − 1 ) W m − 1 K − 1 (Wm^(-1)K^(-1))\left(\mathrm{W} \mathrm{m}^{-1} \mathrm{~K}^{-1}\right)
(Wm^(-1)K^(-1))| $\left(\mathrm{W} \mathrm{m}^{-1} \mathrm{~K}^{-1}\right)$ | | :--- |
 1 1

翅片厚度 ( mm ) ( mm ) (mm)(\mathrm{mm}) 翅片表面温度 ( K ) ( K ) (K)(\mathrm{K})
Fin thickness ( mm ) ( mm ) (mm)(\mathrm{mm})
Fin surface temperature ( K ) ( K ) (K)(\mathrm{K})
Fin thickness (mm) Fin surface temperature (K)| Fin thickness $(\mathrm{mm})$ | | :--- | | Fin surface temperature $(\mathrm{K})$ |
 3 T ( x , y ) T ( x , y ) T(x,y)\mathrm{~T}(\mathrm{x}, \mathrm{y})
Air velocity ( m s − 1 ) m s − 1 (ms^(-1))\left(\mathrm{m} \mathrm{s}^{-1}\right)气流速度 ( m s − 1 ) m s − 1 (ms^(-1))\left(\mathrm{m} \mathrm{s}^{-1}\right) 1 / 3 1 / 3 1//31 / 3 T ( x , y ) T ( x , y ) T(x,y)\mathrm{~T}(\mathrm{x}, \mathrm{y})
Heat transfer rate ( W ) ( W ) (W)(\mathrm{W})
传热速率 ( W ) ( W ) (W)(\mathrm{W})
Heat transfer rate (W)| Heat transfer rate $(\mathrm{W})$ | | :--- |
 3 1
Heat transfer coefficient
传热系数		 1 / 3 1 / 3 1//31 / 3 1
( W m m − 2 K − 1 ) W m m − 2 K − 1 quad((W)(m)m^(-2)K^(-1))\quad\left(\mathrm{~W} \mathrm{~m} \mathrm{~m}^{-2} \mathrm{~K}^{-1}\right) 1
Pressure drop ( Pa ) ( Pa ) (Pa)(\mathrm{Pa})压降 ( Pa ) ( Pa ) (Pa)(\mathrm{Pa}) 1 / 9 1 / 9 1//91 / 9 1
R e R e ReR e, Pr number R e R e ReR e ，Pr 编号 1 1
j , f j , f j,fj, f factor j , f j , f j,fj, f 系数 1 1
Geometric parameters "Scaled-up model" "Prototype model" "Scale factor Fin length (mm)" 3 1 Fin thermal conductivity 3 1 "(Wm^(-1)K^(-1))" 1 1 "Fin thickness (mm) Fin surface temperature (K)" 3 T(x,y) Air velocity (ms^(-1)) 1//3 T(x,y) "Heat transfer rate (W)" 3 1 Heat transfer coefficient 1//3 1 quad((W)(m)m^(-2)K^(-1)) 1 Pressure drop (Pa) 1//9 1 Re, Pr number 1 1 j,f factor 1 1| Geometric parameters | Scaled-up <br> model | Prototype <br> model | | :--- | :--- | :--- | | Scale factor <br> Fin length $(\mathrm{mm})$ | 3 | 1 | | Fin thermal conductivity | 3 | 1 | | $\left(\mathrm{W} \mathrm{m}^{-1} \mathrm{~K}^{-1}\right)$ | 1 | 1 | | Fin thickness $(\mathrm{mm})$ <br> Fin surface temperature $(\mathrm{K})$ | 3 | $\mathrm{~T}(\mathrm{x}, \mathrm{y})$ | | Air velocity $\left(\mathrm{m} \mathrm{s}^{-1}\right)$ | $1 / 3$ | $\mathrm{~T}(\mathrm{x}, \mathrm{y})$ | | Heat transfer rate $(\mathrm{W})$ | 3 | 1 | | Heat transfer coefficient | $1 / 3$ | 1 | | $\quad\left(\mathrm{~W} \mathrm{~m} \mathrm{~m}^{-2} \mathrm{~K}^{-1}\right)$ | 1 | | | Pressure drop $(\mathrm{Pa})$ | $1 / 9$ | 1 | | $R e$, Pr number | 1 | 1 | | $j, f$ factor | 1 | 1 |
raising the cut elements to both sides alternatively. It has a X shape when viewed from the front. Experimental results on these shapes are already reported in the literature [10]. Type ‘SA’ fin is a kind of slitted fin and is designed to promote convective heat transfer from the tube-side by allowing more air over the tube. The slitted structure is similar to the type ’ R ’ fin. Although the type ’ R R RR ’ fin is formed at an angle of 50 ∘ 50 ∘ 50^(@)50^{\circ} with slit forming surfaces based on a center line connected between tubes, this fin is formed at 80 ∘ 80 ∘ 80^(@)80^{\circ}. This also reduces pressure drop by decreasing the allowable forming area of interrupted surfaces. Type ‘SB’ fin is also a kind of slitted fin and is designed to induce the turbulence of inflow air and the uniform velocity of outflow air as the slits of the inlet and outlet sections are cut into three parts [11]. The four array slit group in the central section is formed with a simple rectangular shaped slit to conform to the air flow
在两侧交替提高切割元件。从正面看，它呈 X 形。有关这些形状的实验结果已见诸文献 [10]。SA "型鳍片是一种狭缝鳍片，其设计目的是通过让更多的空气进入管子，促进管侧的对流传热。其狭缝结构与 "R "型鳍片类似。虽然" R R RR "型鳍片是以 50 ∘ 50 ∘ 50^(@)50^{\circ} 的角度形成的，缝隙形成面基于管子之间连接的中心线，但这种鳍片是以 80 ∘ 80 ∘ 80^(@)80^{\circ} 的角度形成的。这也通过减小间断面的允许成型面积来减少压降。SB "型鳍片也是一种狭缝鳍片，其设计目的是将进气和出气部分的狭缝切割成三部分，从而引起进气的紊流和出气的匀速[11]。中央部分的四个阵列狭缝组由简单的矩形狭缝组成，以适应气流的流动
direction. Slitted fins are made up of six array slits. Type ’ L ’ fin is a kind of parallel louvered fin and is used to compare heat transfer with the slitted fins. This is designed for use in home air conditioners operated under a relatively low velocity by reducing the number of multi louvers to three couples, which has been used mainly in high velocity flow such as automotive air conditioners. Type ’ P P PP ’ fin is a plate fin. Three fins, except type ’ R R RR ’ and ’ P P PP ’ fins, are designed in this study.
方向狭缝翅片由六个阵列狭缝组成。L "型鳍片是一种平行百叶鳍片，用于与狭缝鳍片进行传热比较。这种翅片设计用于在相对低速条件下运行的家用空调，将多百叶的数量减少到三对，主要用于汽车空调等高速气流中。 P P PP 型翅片是一种板翅片。除" R R RR "型和" P P PP "型鳍片外，本研究还设计了其他三种鳍片。

4. Results and discussion
4.结果和讨论

In this study, air-side heat transfer characteristics are analyzed using five different kinds of fin-and-tube heat exchangers, and the scaled-up experiment is conducted for this purpose. These results are compared with experimental results using the prototype to confirm its availability as a development tool for a new heat exchanger. The results of Hiroaki on the type ‘R’ fin are used to verify the validity of the scaled-up experiment. The heat transfer coefficient and pressure drop on both experiments are measured by varying the air velocity at the test section. The heat transfer coefficient and pressure drop in the scaled-up model should be converted to the actual value to compare with them in the prototype model. A conversion to the actual value from the scaledup experimental results can be obtained by multiplying the heat transfer coefficient and velocity by three and multiplying pressure drop by nine. They are marked with actual values in all figures.
本研究使用五种不同的翅片管式热交换器分析了空气侧的传热特性，并为此进行了放大实验。这些结果与使用原型的实验结果进行了比较，以确认其作为新型热交换器开发工具的可用性。Hiroaki 关于 "R "型鳍片的结果被用来验证放大实验的有效性。通过改变试验段的空气流速，测量了两次实验的传热系数和压降。放大模型中的传热系数和压降应转换为实际值，以便与原型模型中的传热系数和压降进行比较。将传热系数和速度乘以 3，再将压降乘以 9，就可以将按比例放大的实验结果换算成实际值。所有图中都标有实际值。

4.1. Verification of scaled-up experiment
4.1.放大实验验证

Figures 3 and 4 show the heat transfer coefficient and pressure drop of the scaled-up model and the prototype model with respect to air velocity for the type ’ R R RR ’ fin. The data from the scaled-up model is enlarged three times. Hiroaki’s result on the heat transfer coefficient is also obtained using the modified Wilson-plot method. The heat transfer coefficient on the scaled-up model shows relatively good agreement with the prototype results at an air velocity of about 1.0 m s − 1 1.0 m s − 1 1.0ms^(-1)1.0 \mathrm{~m} \mathrm{~s}^{-1}, but it is underestimated by 2.7 % 2.7 % 2.7%2.7 \% at the velocity of 1.5 m s − 1 1.5 m s − 1 1.5ms^(-1)1.5 \mathrm{~m} \mathrm{~s}^{-1}. Considering that the performance estimation on the prototype generally has a measurement error of 3.0 % 3.0 % 3.0%3.0 \%, the present scaled-up model predicts the heat transfer characteristics of the prototype very well. The uncertainty of the heat transfer coefficient on the scaled-up experiment is 3.6-4.0% according to the velocity range.
图 3 和图 4 显示了" R R RR "型鳍片的放大模型和原型模型的传热系数和压降随风速的变化情况。放大模型的数据放大了三倍。此外，还使用改进的威尔逊绘图法获得了 Hiroaki 关于传热系数的结果。在气流速度约为 1.0 m s − 1 1.0 m s − 1 1.0ms^(-1)1.0 \mathrm{~m} \mathrm{~s}^{-1} 时，按比例放大模型的传热系数与原型结果的一致性相对较好，但在气流速度为 1.5 m s − 1 1.5 m s − 1 1.5ms^(-1)1.5 \mathrm{~m} \mathrm{~s}^{-1} 时，传热系数被低估了 2.7 % 2.7 % 2.7%2.7 \% 。考虑到对原型机的性能估计一般有 3.0 % 3.0 % 3.0%3.0 \% 的测量误差，本放大模型可以很好地预测原型机的传热特性。按比例放大实验的传热系数的不确定性根据速度范围为 3.6-4.0%。
It is shown that the pressure drop in the prototype experiment is higher by approximately 3.2 % 3.2 % 3.2%3.2 \% than that of the scaled-up experiment at the velocity of 1.0 m s − 1 1.0 m s − 1 1.0ms^(-1)1.0 \mathrm{~m} \mathrm{~s}^{-1}. However, the two results are in good agreement at the velocity of over 1.5 m s − 1 1.5 m s − 1 1.5ms^(-1)1.5 \mathrm{~m} \mathrm{~s}^{-1}. The uncertainty of pressure drop on the scaled-up experiment was 2.8 − 5.0 % 2.8 − 5.0 % 2.8-5.0%2.8-5.0 \% accord-
实验结果表明，在速度为 1.0 m s − 1 1.0 m s − 1 1.0ms^(-1)1.0 \mathrm{~m} \mathrm{~s}^{-1} 时，原型实验的压降比按比例放大实验的压降高约 3.2 % 3.2 % 3.2%3.2 \% 。然而，当速度超过 1.5 m s − 1 1.5 m s − 1 1.5ms^(-1)1.5 \mathrm{~m} \mathrm{~s}^{-1} 时，两者的结果却非常一致。按比例放大实验的压降不确定度为 2.8 − 5.0 % 2.8 − 5.0 % 2.8-5.0%2.8-5.0 \% ，与 1.5 m s − 1 1.5 m s − 1 1.5ms^(-1)1.5 \mathrm{~m} \mathrm{~s}^{-1}一致。
Fig. 2. Five kinds of fin shapes used in this study.
图 2.本研究中使用的五种鳍片形状。
Fig. 3. Comparison of the heat transfer coefficients for scaled-up and prototype models using type ’ R R RR ’ fin.
图 3.使用" R R RR "型鳍片的放大模型和原型模型的传热系数比较。
ing to the velocity range. Since pressure drop of a resisting body is proportional to the square of velocity, the scaledup model results fitted to a quadratic curve can be closer
与速度范围成正比。由于阻力体的压降与速度的平方成正比，因此根据二次曲线拟合的缩放模型结果可以更接近于
to the actual state compared to the prototype results. Hence, a scaled-up model can predict the heat transfer coefficient and pressure drop more accurately. These
与原型结果相比，该模型更接近实际状态。因此，放大模型可以更准确地预测传热系数和压降。这些
Fig. 4. Comparison of the pressure drop for scaled-up and prototype models using type ’ R R RR ’ fin.
图 4.使用" R R RR "型鳍片的放大模型和原型模型的压降比较。
results can also be used effectively in the development of a new heat exchanger.
这些结果还可有效地用于新型热交换器的开发。

4.2. Comparison of heat transfer characteristics
4.2.传热特性比较

4.2.1. Interrupted fins4.2.1.间断翅片

Figures 5-7 show the heat transfer coefficient and pressure drop of the scaled-up model and the prototype model, respectively, with respect to air velocity for type ‘SA’, ‘SB’ and ‘L’ fins.
图 5-7 分别显示了 "SA"、"SB "和 "L "型鳍片的放大模型和原型模型的传热系数和压降随风速的变化情况。
As far as the type ‘SA’ fin is concerned, the heat transfer coefficient of the prototype is higher by approximately 2.3 % 2.3 % 2.3%2.3 \% than that of the scaled-up model at the velocity of 1.0 m s − 1 1.0 m s − 1 1.0ms^(-1)1.0 \mathrm{~m} \mathrm{~s}^{-1}. However, the two results are in good agreement at the velocity of 1.5 m s − 1 1.5 m s − 1 1.5ms^(-1)1.5 \mathrm{~m} \mathrm{~s}^{-1}. The value of the heat transfer coefficient on this type fin is about 63 W m − 2 K − 1 63 W m − 2 K − 1 63Wm^(-2)K^(-1)63 \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-1} at the velocity of 1.0 m s − 1 1.0 m s − 1 1.0ms^(-1)1.0 \mathrm{~m} \mathrm{~s}^{-1}, and is approximately the same as that of the type ’ R ’ fin which is about 65 W m − 2 K − 1 65 W m − 2 K − 1 65Wm^(-2)K^(-1)65 \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-1} at the same velocity. This indicates that a minute change of a slitted area shows little influence on heat transfer enhancement in the fin-and-tube heat exchangers. It is shown that the heat transfer coefficient can also be predicted accurately using a scaled-up experiment. The pressure drop of the prototype model is higher by about 9.5 − 16.5 % 9.5 − 16.5 % 9.5-16.5%9.5-16.5 \% in comparison to that of the scaled-up model with increasing velocity.
就 "SA "型鳍片而言，在速度为 1.0 m s − 1 1.0 m s − 1 1.0ms^(-1)1.0 \mathrm{~m} \mathrm{~s}^{-1} 时，原型的传热系数比放大模型的传热系数高约 2.3 % 2.3 % 2.3%2.3 \% 。然而，在速度为 1.5 m s − 1 1.5 m s − 1 1.5ms^(-1)1.5 \mathrm{~m} \mathrm{~s}^{-1} 时，两者的结果非常一致。在 1.0 m s − 1 1.0 m s − 1 1.0ms^(-1)1.0 \mathrm{~m} \mathrm{~s}^{-1} 速度下，该类型翅片的传热系数值约为 63 W m − 2 K − 1 63 W m − 2 K − 1 63Wm^(-2)K^(-1)63 \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-1} ，与 "R "型翅片的传热系数值大致相同，在相同速度下，"R "型翅片的传热系数值约为 65 W m − 2 K − 1 65 W m − 2 K − 1 65Wm^(-2)K^(-1)65 \mathrm{~W} \mathrm{~m}^{-2} \mathrm{~K}^{-1} 。这表明，狭缝面积的微小变化对翅片管式热交换器的传热性能影响很小。实验表明，利用放大实验也可以准确预测传热系数。随着速度的增加，原型模型的压降比放大模型的压降高约 9.5 − 16.5 % 9.5 − 16.5 % 9.5-16.5%9.5-16.5 \% 。
The heat transfer coefficient of the prototype model on
原型模型的传热系数在
a type ‘SB’ fin shows a higher value by about 4 % 4 % 4%4 \% than that of the scaled-up model at the velocity of 1.0 m s − 1 1.0 m s − 1 1.0ms^(-1)1.0 \mathrm{~m} \mathrm{~s}^{-1}, but it is overestimated by approximately 4.6 % 4.6 % 4.6%4.6 \% at the velocity of 1.5 m s − 1 1.5 m s − 1 1.5ms^(-1)1.5 \mathrm{~m} \mathrm{~s}^{-1}. Since the value of the heat transfer coefficient is nearly the same as that of the type ‘SA’ fin, it is clear that slitted fins have little effect on the variation of pattern. The pressure drop of the prototype model on this type of fin is higher by about 16 − 18 % 16 − 18 % 16-18%16-18 \% compared with that of the scaled-up model with increasing velocity. It is expected from this result that the slit pattern formed on the fin surface has a substantial influence on the pressure drop of slitted fins.
在速度为 1.0 m s − 1 1.0 m s − 1 1.0ms^(-1)1.0 \mathrm{~m} \mathrm{~s}^{-1} 时，"SB "型鳍片的数值比按比例放大模型的数值高出约 4 % 4 % 4%4 \% ，但在速度为 1.5 m s − 1 1.5 m s − 1 1.5ms^(-1)1.5 \mathrm{~m} \mathrm{~s}^{-1} 时，则高估了约 4.6 % 4.6 % 4.6%4.6 \% 。由于传热系数值与 "SA "型鳍片的传热系数值几乎相同，很明显，狭缝鳍片对模式变化的影响很小。与按比例放大的模型相比，原型模型在这种翅片上的压降随着速度的增加而增大约 16 − 18 % 16 − 18 % 16-18%16-18 \% 。从这一结果可以预计，翅片表面形成的狭缝图案对狭缝翅片的压降有很大影响。
The heat transfer coefficient of the prototype model on the type ’ L L LL ’ fin shows good agreement with that of the scaled-up model within ± 2 % ± 2 % +-2%\pm 2 \% error for the overall velocity ranges. This is the lowest among the fins considered in this work. The pressure drop of the prototype model on this type fin is about 23 % 23 % 23%23 \% higher than that of the scaled-up model for overall ranges. Compared to the slitted fins, the type ’ L L LL ’ fin has yielded the slightly large deviation between the pressure drop in the prototype and that in the scaled-up model. This may be attributed to the following: the flow pattern in the slitted fin is parallel to the wall of wind tunnel, but the louvered fin shows a slanted flow pattern. The effect of flow pattern is negligible in the prototype with many fins. However, it might be possible that the pressure drop in the scaled-up exper-
在整个速度范围内，" L L LL "型鳍片上原型模型的传热系数与按比例放大模型的传热系数非常一致，误差在 ± 2 % ± 2 % +-2%\pm 2 \% 以内。这是本文所考虑的翅片中误差最小的一种。就总体范围而言，该类型翅片上原型模型的压降约 23 % 23 % 23%23 \% 高于按比例放大模型的压降。与狭缝翅片相比，" L L LL "型翅片的原型模型压降与放大模型压降之间的偏差稍大。这可能归因于以下几点：狭缝翅片的流型与风洞壁平行，而百叶翅片的流型是倾斜的。在有许多翅片的原型中，流型的影响可以忽略不计。不过，在按比例放大的实验中，压降可能会增加。
Fig. 5. Heat transfer coefficient and pressure drop characteristics of type ‘SA’ fin.
图 5.SA" 型鳍片的传热系数和压降特性。
Fig. 6. Heat transfer coefficient and pressure drop characteristics of type ‘SB’ fin.
图 6.SB 型鳍片的传热系数和压降特性。
Fig. 7. Heat transfer coefficient and pressure drop characteristics of type ‘L’ fin.
图 7.L 型鳍片的传热系数和压降特征。
iment using 10 fins could be slightly affected due to the difference of flow characteristics.
由于流动特性的不同，使用 10 片鳍片的试验结果可能会受到轻微影响。

4.2.2. Plate fin4.2.2.板翅式

Figure 8 shows the heat transfer coefficient and pressure drop of the scaled-up model and the prototype model with respect to air velocity for a plate fin. The heat transfer coefficient of the prototype model is almost the same as that of the scaled-up model at the velocity of 1.0 m s − 1 m s − 1 ms^(-1)\mathrm{m} \mathrm{s}^{-1}, however, it is higher by about 4.5 % 4.5 % 4.5%4.5 \% at the velocity of 1.5 m s − 1 1.5 m s − 1 1.5ms^(-1)1.5 \mathrm{~m} \mathrm{~s}^{-1}. The heat transfer coefficient of plate fin shows a little different trend with that of interrupted fins. It is believed that this is due to the fact that the thermal boundary layer of plate fin has a different growth process with that of interrupted fins. Therefore, it is expected that the more accurate data on the heat transfer coefficient may be obtained by using the l-row heat exchanger sample or reducing the scale factor. The heat transfer coefficient of the prototype model is higher by about 19 25 % 25 % 25%25 \% in comparison to that of Webb’s correlation [12] with increasing velocity. It is shown that some deviation between the two results exists, since Webb’s correlation has been proposed at a higher velocity region compared to the present experimental condition. It is measured when the FPI of the heat exchanger is less than 21.
图 8 显示了放大模型和原型模型的传热系数和压降随板翅片空气流速的变化情况。当风速为 1.0 m s − 1 m s − 1 ms^(-1)\mathrm{m} \mathrm{s}^{-1} 时，原型模型的传热系数与放大模型基本相同，但当风速为 1.5 m s − 1 1.5 m s − 1 1.5ms^(-1)1.5 \mathrm{~m} \mathrm{~s}^{-1} 时，原型模型的传热系数比放大模型高出约 4.5 % 4.5 % 4.5%4.5 \% 。板翅片的传热系数与间断翅片的趋势略有不同。据认为，这是由于板翅片的热边界层与间断翅片的热边界层具有不同的生长过程。因此，通过使用 l 排热交换器样品或减小比例系数，有望获得更准确的传热系数数据。随着速度的增加，原型模型的传热系数比 Webb 的相关系数[12]高出约 19 25 % 25 % 25%25 \% 。结果表明，这两个结果之间存在一定的偏差，因为与目前的实验条件相比，Webb 的相关性是在速度较高的区域提出的。它是在热交换器的 FPI 小于 21 时测量的。
However, the difference is very small, and the characteristics between the two results have similar tendencies.
然而，两者之间的差异非常小，而且两个结果之间的特征具有相似的趋势。
The pressure drop of the prototype model is higher by about 22 − 14.6 % 22 − 14.6 % 22-14.6%22-14.6 \% in comparison to that of the scaled-up model with increasing velocity.
随着速度的增加，原型模型的压降比按比例放大模型的压降高约 22 − 14.6 % 22 − 14.6 % 22-14.6%22-14.6 \% 。
It is shown that performance is possible to predict using the present result, although it depends greatly on the suitability of the scaled-up experimental apparatus on plate fin and the measurement accuracy at the low velocity. As shown above, the scaled-up experimental apparatus in this study can predict the results very well in the case of the interrupted surface fins, but careful evaluation of experimental procedure must be considered for accurate measurement for plate fin.
尽管这在很大程度上取决于按比例放大的板翅片实验装置的适用性和低速时的测量精度，但本研究结果表明，使用本结果可以预测性能。如上所述，本研究中的按比例放大实验装置可以很好地预测断续表面翅片的结果，但要精确测量板翅片，必须考虑对实验程序进行仔细评估。

4.2.3. Comparison of j and f factors
4.2.3.j 因子和 f 因子的比较

Figure 9 shows the variations of j j jj and f f ff factors on the prototype model with respect to the Reynolds number for four kinds of fin shapes. Note that the data on the Reynolds number below 100 are not presented in this figure, although the experiment has been performed at the velocity of 0.5 m s − 1 0.5 m s − 1 0.5ms^(-1)0.5 \mathrm{~m} \mathrm{~s}^{-1}, corresponding to the Reynolds number of 61 . This is due to the fact that natural convection is dominant if the Reynolds number is below 100. In such cases, unreasonable results may be obtained since
图 9 显示了四种鳍片形状的原型模型上 j j jj 和 f f ff 因子随雷诺数的变化情况。请注意，虽然实验是在 0.5 m s − 1 0.5 m s − 1 0.5ms^(-1)0.5 \mathrm{~m} \mathrm{~s}^{-1} 速度下进行的，相当于雷诺数 61，但图中没有显示雷诺数低于 100 的数据。这是因为如果雷诺数低于 100，自然对流将占主导地位。在这种情况下，可能会得到不合理的结果，因为
Fig. 8. Heat transfer coefficient and pressure drop characteristics of plate fin.
图 8.板翅片的传热系数和压降特征。
heat exchangers are generally operated under forced convection. Therefore, the results in this figure are limited to the operating range of home air conditioners. The results show that the magnitude of the j j jj factor is in the order of SB , SA , L SB , SA , L SB,SA,L\mathrm{SB}, \mathrm{SA}, \mathrm{L} and P fins, and the f f ff factor shows in the order of L, SA, SB and P fins. The j j jj factors of the type ‘SA’ and ‘SB’ fins are almost the same, however the f f ff factor of the type ‘SB’ fin is less than that of the ‘SA’ fin. The thermal performance of the type ’ SB ’ fin is relatively better than that of the other fins when considering only sensible heat transfer performance, and it is also shown that the type ‘SB’ fin has the lowest pressure drop. The results displayed in Fig. 9 suggest that the heat transfer characteristics of the type ‘SB’ fin is superior to that of the ‘SA’ fin in the Reynolds number of over 200, although there is little difference between them. It is believed that this phenomenon at a relatively high velocity is due to the increase of turbulent flow, resulting from the fact that the slits of the inlet and outlet section are divided into three parts. Hence, the type ‘SB’ fin shows superior characteristics in the view of heat transfer and pressure drop when it is applied to an actual design. However, this is in contrast to the case of the type ’ L L LL ’ fin, where there is little difference in thermal performance among the interrupted surface fins over the ranges of the Reynolds number considered in the present work. Therefore, any
热交换器通常在强制对流条件下运行。因此，本图中的结果仅限于家用空调的运行范围。结果显示， j j jj 系数的大小依次为 SB , SA , L SB , SA , L SB,SA,L\mathrm{SB}, \mathrm{SA}, \mathrm{L} 和 P 翅片， f f ff 系数依次为 L、SA、SB 和 P 翅片。SA "型鳍片和 "SB "型鳍片的 j j jj 因子几乎相同，但 "SB "型鳍片的 f f ff 因子小于 "SA "型鳍片。如果只考虑显热传递性能，"SB "型鳍片的热性能相对优于其他鳍片，而且 "SB "型鳍片的压降也最小。图 9 中显示的结果表明，在雷诺数超过 200 时，"SB "型鳍片的传热特性优于 "SA "型鳍片，但两者之间的差别不大。据认为，在相对较高的速度下出现这种现象的原因是，由于入口和出口部分的狭缝被分为三部分，导致湍流增加。因此，在实际设计中，"SB "型鳍片在传热和压降方面表现出更优越的特性。然而，这与" L L LL "型鳍片形成了鲜明对比，在本研究中考虑的雷诺数范围内，间断表面鳍片的热性能差别不大。因此，任何
type of fin is applicable to home air conditioners. Since the f f ff factor of the type ‘SA’ fin is approximately the same as that of the type ‘SB’ fin with increasing velocity, it is shown that the slitted fins with 6 array have similar flow resistance. However, the f f ff factor of the louvered fin is relatively higher than that of the slitted fins over all ranges, hence, it is not good in view of the heat transfer and the pressure drop characteristics.
这种翅片适用于家用空调。由于 "SA "型鳍片的 f f ff 因子与 "SB "型鳍片的 f f ff 因子随着速度的增加而大致相同，这表明带有 6 个阵列的狭缝鳍片具有相似的流动阻力。然而，在所有范围内，百叶翅片的 f f ff 因子都相对高于狭缝翅片，因此，从传热和压降特性的角度来看，百叶翅片并不理想。

5. Conclusions5.结论

This study presents heat transfer characteristics according to fin shapes in fin-and-tube heat exchangers. The scaled-up and prototype experiments have been performed to analyze the characteristics of heat transfer coefficient and pressure drop for each fin. The conclusions from the present work are as follows:
本研究介绍了翅片管式热交换器中不同翅片形状的传热特性。通过按比例放大和原型实验，分析了每种翅片的传热系数和压降特性。本研究的结论如下：
(1) The heat transfer and pressure drop characteristics of the scaled-up model on the type ’ R ’ fin show good agreement with those of Hiroaki’s prototype within an error of 3 % 3 % 3%3 \% over all ranges of operating velocity. The heat transfer coefficient from the scaled-up experiment for the proposed interrupted fins predicts an actual value within an error of 4.5 % 4.5 % 4.5%4.5 \%; however,
(1) 在所有工作速度范围内，"R "型鳍片上按比例放大模型的传热和压降特性与 Hiroaki 原型的传热和压降特性非常吻合，误差在 3 % 3 % 3%3 \% 范围内。拟议的间断式翅片的放大实验所预测的传热系数与实际值的误差在 4.5 % 4.5 % 4.5%4.5 \% 范围内；但是，"R "型翅片的传热系数与实际值的误差在 3 % 3 % 3%3 \% 范围内、
Fig. 9. j , f j , f j,fj, f factor vs Reynolds number in the prototype model.
图 9.原型模型中的 j , f j , f j,fj, f 因子与雷诺数的关系。
the pressure drop decreases by about 10 − 23 % 10 − 23 % 10-23%10-23 \% compared to the prototype, irrespective of fin shapes. Although there is a large deviation in the pressure drop, it is believed that the present result is reliable since it shows a similar trend. Consequently, it is confirmed that these tools may be very helpful in the development of a new heat exchanger.
与原型相比，无论翅片形状如何，压降都下降了约 10 − 23 % 10 − 23 % 10-23%10-23 \% 。虽然压降偏差较大，但由于显示出相似的趋势，因此相信目前的结果是可靠的。因此，可以肯定的是，这些工具可能对新型热交换器的开发非常有帮助。
(2) It is indicated that all of the proposed interrupted fins have suitable characteristics for home air conditioners, and the deviations in the heat transfer and pressure drop performance between them are also very small. However, the type ‘SB’ fin, of the three kinds of interrupted fins, is recommended as an optimal shape.
(2) 结果表明，所有建议的间断翅片都具有适用于家用空调的特性，它们之间的传热和压降性能偏差也非常小。不过，在三种间断翅片中，"SB "型翅片被推荐为最佳形状。

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