Numerical analysis of two phase flow characteristics in the oscillating capillary tube heat pipe

Thesis for the Degree of Doctor of Engineering
Numerical Analysis of Two-Phase Flow
Characteristics in the Oscillating
Capillary Tube Heat Pipe
by
Ngoc Hung Bui
Department of Refrigeration and Air Conditioning
Engineering
The Graduate School
Pukyong National University
June, 2003
Numerical Analysis of Two-phase Flow
Characteristics in the Oscillating
Capillary Tube Heat Pipe
(진동 세관형 히트 파이프에 있어서
2 상유동 특성에 대한 수치 해석)
Advisor : Jong Soo Kim
by
Ngoc Hung Bui
A thesis submitted in partial fulfillment of requirements
for the degree of
Doctor of Engineering
in the Department of Refrigeration and Air-Conditioning Engineering,
Graduate School, Pukyong National University
June 2003
Numerical Analysis of Two-phase Flow
Characteristics in the Oscillating
Capillary Tube Heat Pipe
A Dissertation
by
Ngoc Hung Bui
Approved as to style and content by :
Hoo-Kyu Oh
Chairman
Ki-Woo Lee Kyu-Il Han
Member Member
Eun-Pil Kim Jong-Soo Kim
Member Member
16 June, 2003
Numerical Analysis of Two-Phase Flow Characteristics in
the Oscillating Capillary Tube Heat Pipe
Ngoc Hung Bui
Department of Refrigeration and Air-Conditioning Engineering,
Graduate School, Pukyong National University
Abstract
진동세관형 히트파이프(OCHP) 내부에서 증기 기포들의 수축과 팽창에
의해서 길이 방향으로 진동되는 작동유체의 작동 방식을 유동 가시화
실험들을 통해 밝혔다. 수축과 팽창은 증발부와 응축부 각각에서 기포들의
형성과 소멸 때문에 일어난다. 실질적으로 물리적인 메커니즘을 보면, 각
채널에서의 진동과 순환등에 의해서 OCHP 는 복합적이면서도
불규칙적으로 열을 이동시킨다.
본 연구에서는 OCHP 의 작동메커니즘을 규명하기 위하여,
유동가시화를 통하여 밝혀진 유동양식을 근거로 2 개의 모델을 제안하였다.
첫 번째 모델은 균질 흐름에 기초하여 OCHP 에서 작동유체의 진동을
vii
해석한 모델이며, 두 번째 모델은 두개의 액체 슬러그와 세 개의 기체
플러그로 분리된 모델에 기초하는 OCHP 의 분석적인 모델이다.
첫 번째 모델에서 이상류의 미분방정식이 적용되었고 동시에 비선형
편미분방정식이 풀어진다. 수치해석 결과 분석으로부터 OCHP 작동유체의
진동은 열흐름, 작동유체의 봉입량, 플로우 채널의 수력직경과 같은
작동조건이나 설계 상황에 영향을 받는다는 것을 알 수 있다.
두 개의 액 슬러그와 세 개의 증기 기포로 OCHP 를 단순화한 형상을
제안하였다. 증기 기포와 액 슬러그들의 유동을 예측하기 위해,
지배방정식을 세우고, 유한차분법을 이용해 풀었다. 결과들은 세관의
직경과 작동유체의 봉입량, 열유속 등이 OCHP 의 성능에 큰 영향을
미친다는 것을 알 수 있다.
시뮬레이션 결과들은 제안된 2 개의 모델이 OCHP 의 작동 메커니즘을
평가하는 것에 유용함을 보여준다.
viii
Acknowledgments
This dissertation would not have been completed without the help of many
people. Especially, I own the greatest debt to Professor Jong-Soo Kim for his
financial support, sincere guidance, encouragement and suggestions through the
course of this study. I would like to take this opportunity to record my sincere
gratefulness to him for his creative influence on my professional activities and for
continued warm relationship. I also thank Professor Hoo-Kyu Oh, Professor
Young-Soo Kim, Professor Jong-Soo Kum, Professor Eun-Pil Kim, Professor
Kwang-Hwang Choi, Professor Suk-Kwon Jung, and Prof. Jeong-Seok Kwon of
Department of Refrigeration and Air-Conditioning, Professor Ki-Woo Lee of
Korea Institute of Energy Research, Professor Kyu-Il Han, Prof. Sang-Bong Kim
and Professor Myung-Suk Lee of Pukyong National University for their many
valuable suggestions, advice and kindness.
During the days of working on this study, I have received generous help from
all research members of Air Conditioning Lab., including Dr. Wook-Huyn Lee,
Dr. Ju-Won Kim, Dr. Jeong-Hoon Kim. I express my sincere thanks to all of them.
Hochiminh City University of Technology (HUT) has recommended me to
The Pukyong National University. In particular, I am grateful to Prof. Thanh Ky
Tran, Prof. Dinh Tin Hoang, and Prof. Chi Hiep Le for their recommendation.
My thanks are also due to my Vietnamese colleagues who have researched
and studied in Pukyong National University. In particular, I am grateful to Dr. Tan
Tien Nguyen, Ms Tan Tung Phan, Ms Thien Phuc Tran, Ms. Thanh Tong Phan,
Ms. Tuong Long Nguyen and Ms. Trong Hieu Bui for their help and advice.
Finally, I would like to thank my parents, sisters, and also my parents-in-law
for their great support and encouragement. I express my appreciation to my wife
Ba Dieu Uyen Nguyen and my daughter Tuong Nhi Bui and my son Dang Khoa
Bui for their continued patience, understanding and endless encouragement.
90
Contents
Contents i
List of figures iv
List of tables vi
Abstract vii
Nomenclatures ix
Chapter 1 Introduction
1.1 Background 1
1.2 Review of previous studies 4
1.3 Objectives and outline of the present study 17
Chapter 2 The working principle of the OCHP
2.1 The flow pattern in working process 19
2.2 Tube diameter for stable operation 22
2.3 Fundamental processes in the OCHP 24
2.4 Effect of the type of the OCHP 29
2.5 Effect of the turn number of the OCHP 30
i
Chapter 3 Numerical analysis of the OCHP based on the homogeneous
flow model
3.1 Theoretical model 32
3.2 Derivation of governing equations 33
3.3 Numerical procedure 35
3.4 Numerical results 40
3.5 Comparisons with previous experimental results 45
3.6 Summary 49
Chapter 4 Numerical analysis of the OCHP based on the separated flow
model
4.1 Theoretical model 50
4.2 Derivation of governing equations 53
4.3 Numerical procedure 57
4.4 Results and discussion 60
4.5 Summary 75
Chapter 5 Conclusions
5.1 Conclusions 76
5.2 Future works 78
ii
References 79
Appendix 1 86
Appendix 2 87
Appendix 3 88
Acknowledgments 90
iii
List of figures
Figures
Fig. 1.1 Oscillating capillary tube heat pipe and conventional heat pipe
Fig. 1.2 Schematic of the model presented by Dobson et al.
Fig. 1.3 Model with single spring mass damper system presented by Zuo et al.
Fig. 1.4 Model with multiple spring mass system presented by Wong et al.
Fig. 2.1 Capillary slug flow
Fig. 2.2 Transport processes in an OCHP
Fig. 2.3 Pressure-enthalpy diagram
Fig. 2.4 Schematic of the two type of OCHP
Fig. 2.5 Schematic diagram of oscillating wave in the OCHP of 10 turns
Fig. 3.1 Schematic of the homogeneous model of OCHP
Fig. 3.2 Approximation of heat flux distribution
Fig. 3.3 Variations of effective thermal conductivity with heat flux at different
charging ratios.
Fig. 3.4 Variations of pressure according to heat flux at the charging ratio of 40
vol.%
Fig. 3.5 Mass velocity according to the different charging ratios of working fluid
Fig. 3.6 Mass velocity according to the different heat fluxes
iii
Fig. 3.7 Comparison between experimental and numerical results.
Fig. 3.8 Mass velocity according to the different hydraulic diameters
Fig. 4.1 Theoretical model of OCHP
Fig. 4.2 Control volume of ith liquid slug
Fig. 4.3 Control volume of ith vapor plug
Fig. 4.4 Variation of pressure and the end positions of the first vapor plug with
time
Fig. 4.5 Variation of pressure and the end positions of the second vapor plug
with time
Fig. 4.6 Variation of pressure and the end positions of the third vapor plug with
time
Fig. 4.7 Variation of the evaporative and condensation heat transfer rate of the
first vapor plug with time
Fig. 4.8 Variation of the evaporative and condensation heat transfer rate of the
second vapor plug with time
Fig. 4.9 Variation of the evaporative and condensation heat transfer rate of the
third vapor plug with time
Fig. 4.10 Variation of the velocity of each liquid slugs with time
Fig. 4.11 Effect of diameter on the performance of the first vapor plug
Fig. 4.12 Effect of diameter on the evaporative heat transfer rate
Fig. 4.13 Variation of pressure of vapor plugs at different charging ratios
Fig. 4.14 Effect of surface tension on the performance of the first vapor plug
Fig. 5.1 Combination model of OCHP
iv
Nomenclatures
A : tube cross sectional area [m2]
cp : specific heat at constant pressure [J/kgK]
cv : specific heat at constant volume [J/kgK]
d : diameter [m]
f : friction coefficient
F : friction force per unit volume [N/m3]
g : gravitational acceleration [m/s2]
G : mass velocity [kg/m2s]
h : specific enthalpy [J/kg]
h : heat transfer coefficient [W/m2K]
hfg : laten heat of vaporization [J/kg]
k : thermal conductivity [W/mK]
L : length [m]
m : mass [kg]
m& : mass flow rate [kg/s]
n : integer
p : pressure [Pa]
q : heat flux [W/cm2]
Q : heat transfer rate [W]
r : radius [m]
R : gas constant [J/kgK]
Re : Reynolds number
t : time [s]
ix
T : temperature [K] or [oC]
u : internal energy [J/kg]
v : specific volume [m3/kg]
V : volume [m3]
v : velocity [m/s]
x : axial coordinate [m]
X : vapor quality
Greek letters
α : charging ratio of working fluid [vol.%]
θ : inclination angle, contact angle [o]
μ : dynamic viscosity [kg/ms]
υ : kinematic viscosity [m2/s]
ρ : density [kg/m3]
σ : surface tension [N/m]
τ : shear stress [N/m2]
Subscripts
c : cooling
cond : condensation
evp : evaporation
f : liquid
fg : vapor-liquid
g : gas
h : heating
in : inlet
l : liquid slug
x
le : left end
out : outlet
re : right end
sat : saturated
v : vapor plug
w : wall
xi
Chapter 1
Introduction
1.1 Backgrounds
Heat pipe is one of the effective heat transfer devices being used in electronic
equipments. Heat pipes such as thermosyphon, wick-type heat pipe, micro heat
pipe [1], and dream pipe [2] are the representative configurations that they have
already been applied.
However, there are various parameters that put limitations on the operation of
conventional heat pipes. The capillary limit is the most commonly encountered
limitation in the operation of heat pipes. It occurs when the capillary pumping rate
is not sufficient to provide enough liquid to the evaporating section. This is due to
the fact that the sum of the liquid and vapor pressure drops exceeds the maximum
capillary pressure that the wick can sustain [1]. The entrainment limit is due to the
influence of the shear force because the liquid and vapor flow in opposite
directions. The interaction between this countercurrent liquid and vapor flow and
the viscous shear forces occurring at the liquid-vapor interface may inhibit the
return of liquid to the evaporating section [3].
For the limitation of installation space in electronic equipments, the
conventional heat pipes have to be made of small structure for compactness.
However, the limitation of heat transfer due to the decrease of structure causes
difficulty for manufacturing the conventional heat pipes. Micro heat pipe can be
1
used to solve this problem but it has a complex structure and small quantity of
heat transfer area [4]. The dream pipe has higher heat transfer coefficient by the
axial oscillation of working fluid. However, its effective thermal conductivity is
still lower than the effective thermal conductivity of heat pipes with two-phase
heat transfer of working fluid. Also, it needs a power source, which can produce
vibration.
The above limits can overcome by using the oscillating capillary tube heat
pipe. It has high heat removal rate and can be also used for cooling of power
electronics [5] as well as using for low temperature waste heat recovery systems
with high performance and low cost.
The oscillating capillary tube heat pipe (OCHP), which is a very promising
heat transfer device, was proposed by Akachi for the first time [6]. In addition to
its excellent heat transfer performance, it has a simple structure: in contrast with
conventional heat pipes, there is no wick structure to return the condensed
working fluid back to the evaporating section. The OCHP is made from a long
continuous capillary tube bent into many turns of serpentine structure as shown in
Fig. 1.1. The working fluid is charged into the OCHP. The diameter of the OCHP
must be sufficiently small so that vapor plugs can be formed by capillary action.
The OCHP is operated within a 0.1 ∼ 5 mm inner diameter range. If the diameter
is too large, the liquid and vapor phases will tend to stratify. The OCHP can
operate successfully for all heating modes. Due to the effect of surface tension, the
working fluid will arrange in slug-train units in the OCHP. The heat input, which
is the driving force, increases the pressure of the vapor plugs in the evaporating
section. In turn, this pressure increase will push neighboring vapor plugs and
liquid slugs toward the condensing section, which is at a lower pressure.
However, due to the continuous heating, small vapor bubbles formed by
nucleate boiling grow and coalescence to become vapor plugs. The flow of vapor
plugs and liquid slugs moves to the condensing section by pressure difference.
2
The heat transfer continuously occurs. As a result, the heat is transported
from the evaporating section to the condensing section by means of axial
oscillations and phase changes of working fluid in the OCHP [6 ∼ 8].
Until now, the OCHP have been used in heat transfer related application for
the cooling of electronic equipments and low temperature waste heat recovery.
However, its working mechanism is not specified clearly and there are no reliable
data or tools for designing the OCHP according to given cooling requirements.
Liquid Vapor
Heat out
Condensing Liquid Condensation
Section Oscillation
Vapor
Adiabatic Oscillation &
Section Departure of Heat
Small vapor in Fine Fiber Wick
Liquid Return
Vapor Flow
Oscillation by Evaporation
Evaporating Nucleate
Section Boiling
Conventional
OCHP Heat Pipe
Fig. 1.1 Oscillating capillary tube heat pipe and conventional heat pipe
3
1.2 Review of previous studies
Both experimental and numerical investigations on the OCHP have been
carried out by some researchers. The experiments mainly focus on examinations
of flow pattern by flow visualization and heat transfer characteristics according to
the design and operation conditions such as tube diameter, turn number,
inclination angle, and the charging ratio of working fluid to find the optimal
operation condition of the OCHP. And a few numerical investigations are
developed to model the operating mechanism of the OCHP. However, these
models are mostly based on rough assumptions and simplifications.
Takahashi et al. [9] conducted flow visualization experiments using the proton
radiography method on the aluminum-extruded type OCHP. The cross section of
flow channels was rectangular of 0.6 x 0.7 mm. The used working fluid was R-
134a at the charging ratio of 30 vol.%. They concluded that the flow pattern
depends on the inlet heat flux and inclination angle of the test section. However,
in their study, the detailed flow pattern could not be understood by the indirectly
projected flow pattern. So their experimental results only described the flow of
vapor plugs and liquid slugs at each experimental condition.
Nishio et al. [10, 17, 21] compared the performance of the OCHP and dream
pipe and proposed that the OCHP was more excellent in heat transfer performance
than dream pipe. Nishio proposed the related equation to determine pipe diameter
for the stable operation of the OCHP. They presented the special result that the
OCHP of 2 turns was higher in effective thermal conductivity than that of 10 turns
with glass pipes and water was used as working fluid. Furthermore, they also
examined the influence of the charging ratio and inclination angle on effective
thermal conductivity. They report that the heat transfer performance was high at
the charging ratios of 30 ∼ 50 vol. % and over inclination angles of 60 ∼ 90°.
4
Hosoda et al. [11] estimated the heat transfer performance depending on the
charging ratio of working liquid and heat flux. The OCHP of 10 turns was made
of glass tubes (inner diameter of 2.4mm) and the used working fluid was distilled
water. At the charging ratio of 60 vol.%, the maximal heat transfer performance
was shown. They reported that the effective thermal conductivity at this condition
was ten times even in glass pipe as well as in copper pipe.
Gi et al. [8, 13, 20] examined the heat transfer performance by experiments
depending on the working temperature and the inclination angle of the OCHP.
Teflon tubes (10 turns of 2 and 4 mm inner diameter) and copper tubes (40 turns
of 1.6 and 2 mm inner diameter) were used. The used working fluid was R-142b.
They reported that when the charging ratio was increased in the OCHP with teflon
tubes, the vapor plugs were broke out and only liquid phase existed. As the
operation temperature was high, short liquid and short vapor plugs were
distributed within the OCHP. In the OCHP with copper tube, the effective thermal
conductivity decreased by increasing the working temperature. When the tube
diameter was decreased, the effective thermal conductivity increased. The heat
transfer rate was the best with the charging ratios from 50 to 60 vol.% and the
circulation velocity increased with increasing of the inclination angle of the
OCHP.
Numata et al. [12] investigated flow visualization experiments according to
the variation of tube diameter. The glass tube type OCHPs (of 2.4mm and 5mm
inner diameters) were used and the working fluids were water and R-141b. They
concluded that as the tube diameter was increased, the flow pattern changed from
slug flow to churn flow and annular flow. However, the experimental results
obtained in their study were somewhat different from the flow pattern in real
metal tube because the glass tubes of low thermal conductivity were used. And the
detailed flow pattern was not observed.
5