pulsating heat pipe report
DESCRIPTION
numerical and experimental pulsating heat pipeTRANSCRIPT
Experimental and Numerical Investigation of a Single Loop
Pulsating Heat Pipe
8th semester project work
by
IDUL AZHARUL HOQUE
(Roll Number: SC11B029)
Department of Aerospace
Indian Institute of Space Science and Technology
Thiruvananthapuram
April 2015
BONAFIDE CERTIFICATE
This is to certify that this project report entitled Experimental and Numerical
Investigation of a Single Loop Pulsating Heat Pipe submitted to Indian
Institute of Space Science and Technology, Thiruvananthapuram, is a bonafide
record of work done by IDUL AZHARUL HOQUE under my supervision from
10/01/2015 to 20/04/2015.
Dr. Pradeep Kumar P
Dr. A. Salih
Head of Department
Aerospace Engineering, IIST
Place:
Date:
Declaration by Author
This is to declare that this report has been written by me. No part of the report is
plagiarized from other sources. All information included from other sources have
been duly acknowledged. I aver that if any part of the report is found to be
plagiarized, I shall take full responsibility for it.
Md. Idul Azharul Hoque
SC11B029
Place:
Date:
Contents
Acknowledgement............................................................................................................................I
Abstract........................................................................................................................................... II
Nomenclature................................................................................................................................. III
List of figures...................................................................................................................................V
Chapter 1: Introduction.........................................................................................................................1
1.1 Nature of a PHP...........................................................................................................................1
1.2 Objective of the work..................................................................................................................4
1.3 Organization of the report...........................................................................................................5
Chapter 2: Literature Survey.................................................................................................................7
2.1 History.........................................................................................................................................7
2.2 Review of studies conducted on pulsating heat pipes.................................................................9
2.2.1 Experimental studies:..........................................................................................................9
2.2.2 Numerical studies..............................................................................................................13
2.3 Inference....................................................................................................................................15
Chapter 3: Numerical Modelling..........................................................................................................16
3.1 Reference frame........................................................................................................................17
3.2 Forces acting on the liquid slug and equation of motion:..........................................................17
3.3 Energy equation of the vapor plugs...........................................................................................19
3.4 Mass balance at the interfaces..................................................................................................20
3.5 Energy equation of liquid slug:..................................................................................................21
3.6 Numerical solution:....................................................................................................................24
Chapter 4: Experiment.........................................................................................................................28
4.1 Experimental Setup....................................................................................................................28
I
4.2 Properties and dimensions of parts used:.................................................................................29
4.3 Procedure..................................................................................................................................34
4.4 Results.......................................................................................................................................35
4.5 Probability of errors:..................................................................................................................36
Chapter 5: Results and Discussion.......................................................................................................38
5.1 Theoretical results:....................................................................................................................38
5.2 Experimental results..................................................................................................................43
5.2.1 40% filling ratio:.................................................................................................................43
Chapter 6: Conclusion.........................................................................................................................44
Appendix........................................................................................................................................45
References.................................................................................................................................................46
II
Acknowledgement
I thank with gratitude for the guidance, suggestions and encouragement forwarded by several
respected persons and I know well that it is impossible to express my indebtedness for all those
valuable assistances in this finite piece of paper. I acknowledge in this page, the assistance
rendered by all the concerned persons, as a token of my gratitude. I am feeling honored to
express my sincere appreciation and deep gratitude to Dr. Pradeep Kumar P for his supervising
throughout the internship, for his valuable guidance, friendly encouragement and helping me to
acquire substantial knowledge in preparing whole process layout and experimental work. Entire
work has been carried out in the Manufacturing Lab and Heat and Thermal Lab of IIST,
Thiruvananthapuram. I would like to convey my thankfulness to the lab assistants Bipin Sir and
Dinesh Sir for their help without which I would have never been finish my project.
Md. Idul Azharul Hoque
SC11B029
I
Abstract
The oscillatory motion of the pulsating heat pipe (PHP) is highly non-linear. The objective of this project was to study the behavior of a typical closed PHP with a theoretical model based on Ma and Qu’s work and experimentally determine the temperature and pressure values in a closed PHP. A mathematical model is described and a MATLAB program is run to find the numerical solution. The results are compared with the source paper. Thermocouples and pressure transducer is used to find the temperature and pressure at various location in our experimental setup. The effect of filling ratio and inclination angle is experimentally determined. We compared the experimental results and theoretical results by finding the initial conditions in the experiment and incorporating it in our MATLAB program.
Key Words: PHP, latent heat, sensible heat, evaporator, condenser
II
Nomenclature
Bo Bond Number.
c pv Specific heat of the vapour at constant pressure [J/KgK]
cvv Specific heat of the vapour at constant volume [J/KgK]
d Internal diameter [m]
Ac Cross sectional area [m2]
σ Surface tension [N/m]
ρl iq Density of liquid [kg/m3]
g Acceleration due to gravity [m/s2]
Lp Length of liquid plug [m]
Lh Length of the pipe in the heater region [m]
Lad Adiabatic length [m]
Lc Length of the pipe in the condenser region [m]
x p Position of the vapor bubble [m]
h fg Latent heat of vaporization [J/kg]
T e Temperature of the heater [K]
T v Temperature of vapor plug [K]
T c Temperature of condenser [K]
ṁ Mass transfer rate [kg/s]
mv Mass of vapor plug [kg]
m p Mass of liquid plug [kg]
III
he Overall heat transfer coefficient for heater region [W/m2˚C]
hc Overall heat transfer coefficient for condenser region [W/m2˚C]
C f Co-efficient of friction
Re Reynolds’s Number
μl Viscosity of liquid [Kg/m sec]
Pe External Pressure [Pa]
Pv Pressure of the vapour bubble [Pa]
iv Specific enthalpy [J/KgK]
IV
List of figures
Figure 1-1: (A) Typical PHP (B) Open loop PHP (C) Closed loop PHP..........................................................................2
Figure 2-1: Dunking Bird.............................................................................................................................................4
Figure 2-2: Loop type heat pipe [Akachi, 1990].........................................................................................................6
Figure 3-1: A multi-turn CLPHP with symmetrical distribution of liquid and vapor..................................................8
Figure 3-2: Single liquid slug and two adjacent vapor plug model with co-ordinate frame.....................................9
Figure 3-3: Vapor plugs at xp<0............................................................................................................................13
Figure 3-4: Vapor plugs at xp≥ 0............................................................................................................................13
Figure 3-5: Conduction and convection relating to the liquid slug..........................................................................14
Figure 4-1: Pressure cooker as evaporator...............................................................................................................20
Figure 4-2: Copper tube shape and dimensions.......................................................................................................21
Figure 4-3: Glass tube dimension.............................................................................................................................22
Figure 4-4: Condenser box made of acrylic plates...................................................................................................22
Figure 4-5: Setup to change the angle of inclination...............................................................................................23
Figure 4-6: Final assembly........................................................................................................................................25
Figure 4-4-7: (1) Data base system (2) Ice junction (3) Complete setup (4) voltage distributor.............................26
V
Chapter 1: Introduction
Modern world is gripped by machines and electronics. Every machines or electronic
device gets heated due to the high heat density. Each upcoming nano-design is with
higher power dissipation and higher heat density. Pulsating Heat Pipes (PHPs),
characterized by highly effective evaporation and condensation cycles offer an
effective heat remover greater than the traditional ways. PHPs do not require
mechanical pumps or valves or consume any power and also quieter and reliable.
1.1 Nature of a PHP
A PHP consists of a metallic tube of capillary dimensions bend in serpentine
manner and joined end to end (closed loop) or open end (open loop) .These structures
are characterized by the given basic features:
(a) The structure is made of meandering tube of small capillary dimensions with
turns .This tube can be either:
Open Loop: tube ends are not connected to each other.
Closed Loop: tube ends connected to each other.
(b) There is no internal wick structure.
(c) At least one heat receiving (heater) region is present.
(d) At least one heat dissipating (condenser) region is present.
A PHP is essentially a non-equilibrium heat transfer device driven by complex
combination of various types of two-phase flow instabilities. The construction of the
device inherently ensures that no external mechanical power source is needed for the
fluid transport. The driving pulsations are fully thermally driven.
1
Figure 1-1: (A) Typical PHP (B) Open loop PHP (C) Closed loop PHP (1)
The parameters that influences the overall performance and dynamics of the PHP
are:
1. Tube diameter:
The flow mode is ‘pulsating’ only under certain range of diameters. Bond number (or
Eötvös) criterion (2) gives the design rule for diameter
(Eö)crit=(Bo)crit2=
dcrit2 . g .( ρliq− ρvap)
σ≅ 4
∴ dcrit=2×√ σg .(ρliq−ρ vap)
This criteria ensures that plug flow (figure1-2) is exhibited and they do not
agglomerate leading to stratified phase separated flow (figure1-3).
For d<dcrit there will be a plug flow resulting in pulsation. But it can’t be so
small because for a given specified heat power, decreasing the diameter will increase
the dissipative losses and lead to poor performance.
2
Figure 1-2: Plug flow (1)
As the diameter increases beyond dcrit ,the surface tension is reduced and all the
working fluid tend to stratify by gravity and the pipe will stop functioning as a PHP
rather it will operate as interconnected array of two-phase thermosyphons.
Figure 1-3: Stratified flow (1)
2. Filling ratio (3):
Filling ratio is the fraction (by volume) of the heat pipe which is initially filled with
the liquid. Experimental results so far indicate that there is an optimum filling ratio
for proper PHP operation (in the pulsating mode of operation). This optimum,
however, is not sharply defined but generally is around 40% - 70% fill charge.
A too high filling ratio above the optimum leads to a decrease in the overall
degree of freedom as there are not enough bubbles for liquid pumping. At 100%
filling ratio, the device acts as a single phase buoyancy driven thermosyphon. In this
3
mode too, substantial heat transfer can take place, but the action is limited to bottom
heat mode only.
3. Heat Flux (2):
The applied heat flux affects the following:
(a) Internal bubble dynamics, sizes and agglomeration,
(b) Level of perturbations and flow instabilities , and
(c) Flow pattern.
PHPs are inherently suitable for high heat flux operation. Since the input heat
provides the pumping power, below a certain level, no oscillations commence. In
case of CLPHPs, a unidirectional circulating flow has been observed at high heat
fluxes.
4. Number of turns (2):
The number of turns increases the level of perturbations inside the device. If the
number of turns is less than a critical value, then there is a possibility of a stop-over
phenomenon to occur. In such a condition, all the evaporator U-sections have a vapor
bubble and the rest of the PHP has liquid. This condition essentially leads to a dry out
and small perturbations cannot amplify to make the system operate self-sustained.
If the total heat throughput is defined, increasing the number of turns leads to a
decrease in heat flux handled per turn. Thus, an optimum number of turns exits for a
given heat throughput.
Other parameters which too affect the operation are
Working fluid thermal properties.
Device orientation.
Tube material thermal characteristics.
4
1.2 Objective of the work
The dynamics and working of a PHP is very complex and highly non-linear.
Although there are many studies conducted on PHPs, the mechanism of fluid flow
and heat transfer of PHPs is not well understood. Many authors have tried to reason
the behavior of the dynamics of the PHP but is not able to converge to a definite
solution. Questions have been raised if gravity have any effect on the pulsation mode
of heat transfer, what is the contribution of latent and sensible heat on the total heat
transfer amount, how the filling ratio effects the pulsation mode, how the boundary
conditions effect the temperature distribution and heat transfer rate, etc. Many authors
have different answers to the questions. We tried to validate and understand the
reasoning by doing and experiment based on one of various models forwarded and
compare the results to validate the theory or find out errors and to have a better
understanding of the dynamics of a PHP.
A mathematical model is made based on previous studies. Some assumptions
and symmetrical behavior is considered to simplify the model. A MATLAB program
is executed to find out numerical solution of the equations based on the model. The
results are analyzed and compared to the previous model’s results and effects of
various physical parameters are evaluated from the results.
An experiment is conducted based on the model and the results are analyzed
and compared with our theoretical results. Experimental results for different
conditions are extracted and analyzed.
1.3 Organization of the report
The report contains a substantial amount of previous studies both numerical and
experimental on PHP. We did a survey of these previous literature and compared the
inferred the differences among them and took a model among them for our study. We
made a theoretical model based on Qu & Ma’s paper ‘Flow and heat transfer of liquid
plug and neighboring vapor slugs in a pulsating heat pipe’ [2009] and wrote a
MATLAB code to solve the equations derived numerically, Effect of different
5
parameters like inclination, temperature gradient and initial conditions were seen. The
aim for the experiment is discussed after the model. Parts, assemblies, procedure and
results of our experiment is broadly discussed. Then in our result and discussion
section the results from both the modelling and experiment. The results from our
program were analyzed and compared with the paper’s result. The experimental
results were compared with our experimental results with the same given conditions.
The need of PHP, our study and understanding and the future works related are also
discussed in the conclusion section. Appendix contains the MATLAB code,
thermocouple calibration sheet, experimental temperature sheet from data acquisition
system and derivation of the equations in our model.
6
Chapter 2: Literature Survey
2.1 History
‘Drinking’ or ‘dunking duck’ (1), a popular toy may be the vital link in the
evolutionary of the modern PHPs. The bird’s body is made up of a glass tube with
two bulb like container on both ends (head and tail). The device is partially filled with
volatile working fluid (having boiling point around 40˚C). When the bird is upright
the vapor in the head doesn’t connect with that in the tail section as seen in the
figure2-1. The evaporation hence mass transfer from the head end generates a low
vapor pressure inside hence the working fluid is pushed up in the neck rising the
centre of gravity.
Figure 2-4: Dunking Bird (1)
A time comes when the mouth end weighs more than the tail and the duck’s head
goes down and touches the water beaker and re-wet the fuzzy cloth attached to the
7
beak. In this horizontal position, the two vapor pockets are connected so that the
liquid in the body can freely move. All the liquid is pulled back by gravity to the tail
container and again the evaporation from beak will cause pressure difference and the
cycle continues.
While it is difficult to trace the origin of the ‘drinking duck ’, another
presentation of an analogous concept is found in a patent filed in the former
USSR ,Smyronv and Savchenkov, 1975 (1). It consists of an evaporator and a
condenser bulb connected by a tube. At first evaporator end bulb of the connecting
tube is completely filled by a working fluid while the condenser bulb is partially
filled and the rest is filled by some passive gas.
Figure 2-5: Details of the patent shown by Smyronv and Savchenkov (1)
Heating at the evaporator expands the working fluid and pushes it to the condenser.
Further heating generates vapor in the evaporator bulb and pushes the liquid further
and hence compressing the trapped passive gas. The passive gas is substantially
compressed at this stage. The potential energy stored in the passive gas at some stage
push back the liquid back to the evaporator and the cycle continues.
8
With this brief introduction we shall now review the modern PHP studies and
experiment conducted.
2.2 Review of studies conducted on pulsating heat pipes
Pulsating Heat Pipes, after their development in the early 90s, have been actively
employed in thermal management of microelectronics. Although a variety of designs
are in use, understanding of the fundamental processes and parameters affecting the
PHP operation are still vague. Experimental and numerical analyses of such flows
require more stringent time and spatial resolutions and hence there exists fewer
investigations of pulsating heat pipe. As the need of effective and efficient heat
removal mechanism is increasing with the sophistication in electronics and other
nano-designs the attention towards the PHP’s realization and use is increasing.
2.2.1 Experimental studies:
Although the basic idea of PHP is in the patent presented by Smyronv and
Savchenkovn [1975] the exploitation of the concept of PHP from an engineering
point of view was done by Hisateru Akachi in 1990. In this patent, the inventor
disclosed twenty four different preferred embodiments of what is referred to as Loop
Type Heat Pipe. While the fundamental aspects common to all the embodiments are
similar to the PHPs, these proposed structures are essentially characterized by the
presence of at least one non return flow control check valve integrated in the tubes for
imposing a preferred flow direction. The typical tube cross sections employed were
2.0mm or more, always ensuring that the diameter is below a prescribed limit for
liquid and vapor phases to form distinct plugs due to surface tension effects. All the
proposed structures were characterized by the presence of at least one non-return flow
check valve for imposing a preferred flow direction.
9
Figure 2-6: Loop type heat pipe and its different designs (1)
Figure 2-7: PHP’s as designed by Akachi (1)
Many works on PHP was done based on Akachi’s concept. C Wilson and his group
conducted a visual and thermal experimental investigation of four pulsating heat
10
pipes (PHPs) to observe fluid flow of liquid plugs and vapor bubbles in the PHP and
its effect on the temperature distribution and heat transfer performance in a PHP (4).
Four PHPs were constructed for this experiment, two open loop Figure 2-5(A) and
two closed loop PHPs Figure 2-5(B).
Figure 2-8: Wilson’s OHP prototypes: (A) schematic of the open loop OHP,
(B) Schematic of the closed loop OHP, (C) photo of the finished
OHP, and (D) neutron radiography image of the OHP (4)
The heat pipes were charged with high performance liquid chromatography (HPLC)
grade water or HPLC grade acetone at different filling ratios. Each OHP was
instrumented with 24 T-type calibrated thermocouples. Figure 2-7 illustrates the
temperature variations between the water PHP and acetone PHP including the effects
of orientation and loop type at a condenser temperature of 20°C and a power of 100
W.
11
Figure 2-9: Evaporator temperature oscillations at 100 W and a condenser
temperature of 20°C: (A) water OHP and, (B) Acetone PHP (4)
They experimentally found the effects of the temperature gradient, fluid properties
and orientation in the heat transfer rate and the amount of heat transfer.
Robert Thomson Dobson conducted an experiment on open loop PHP based on his
own theoretical model on open loop PHP. He made a comparison of the temperature
distribution and pressure force of both his theoretical modelling and experimental
result to validate his theory.
12
Figure 2-10: Dobson’s comparison of theoretical and experimental result (5)
Many other experiments have been conducted recently to understand how a PHP
behaves and to find out effects of various physical parameters.
2.2.2 Numerical studies
Robert Thomson Dobson forwarded a theoretical model on open loop PHP. His
famous Dobson boat model describes how an open PHP mechanism works in a ‘putt
putt’ boat (6).
Figure 2-11: ‘putt putt’ boat (an open PHP) (6)
13
Theoretical results of his model includes the liquid plug velocity, position and the
thrust due to pressure difference resulting the motion of the boat with respect to time.
He also conducted an experiment to validate his theory.
Figure 2-12: Dobson’s theoretically determined thrust as a function of time (6)
Dazhong Yuan, Wei Qu and Tongze Ma also proposed a theoretical model on closed
loop PHP. They studied previous works on PHP and found the difference in the views
of different authors. In their work they pointed out how gravity effects the behavior
of PHP and its heat transfer capabilities. They also found the fraction of heat transfer
by sensible and latent heat (7). In their model some assumptions were made to
simplify the problem. Their results included the temperature, pressure and position
variation inside the PHP and the amount of heat transfer by sensible and latent heat
and their response to the initial conditions and gravity.
14
Figure 2-13: Comparison of sensible heat replaced by latent heat by Ma and
group with previous Zhang’s work (7)
2.3 Inference
From the above discussion of the works done on PHP we can easily see the objective
of the works and the differences in the results. In the experiments it is tried to validate
the theories proposed on the mechanism and behavior of a PHP. New theories are
developed and experimental data has to be compared to validate the same. Studying
various models and experiments we decided to study Ma and Qu’s model and do a
MATLAB program to find numerical solution of the equations based on is model.
Validation of his model by experimental data is not yet done and we conducted an
experiment to validate his theory. We also conducted experiment to study the effects
of filing ratio and gravity and fluid thermal properties.
15
Chapter 3: Numerical Modelling
A closed loop pulsating heat pipe (CLPHP) contains one or more loop closed in both
ends. Based on Ma and Qu’s study a model is made on closed loop pulsating heat
pipe. It is assumed that fluid is symmetrically distributed into liquid and vapor inside
the pipe and our model considers a part consisting only one liquid slug between two
vapor plugs as shown in Figure 3-1.
Figure 3-14: A multi-turn CLPHP with symmetrical distribution of liquid and
vapor
Some assumptions are made such as:
1 The vapor plugs in two evaporators observe the ideal gas law.
2 The mass and energy exchanges occurred on the interface between the vapor
plugs and the liquid slug are due to the phase change.
3 The shear stress on the tube wall is related to the fluid flow state.
16
3.1 Reference frame
A one-dimensional coordinates with the right direction as the positive is set up along
the tube. The origin of the coordinates is set at the right intersection of the heater and
the condenser. The liquid slug is assumed as a particle, the displacement of which is
the displacement of the right end of the liquid slug form the origin.
Figure 3-15: Single liquid slug and two adjacent vapor plug model with co-ordinate frame
3.2 Forces acting on the liquid slug and equation of motion:
When x p is positive i.e. liquid plug moves up in the right side gravity force of 2 x p
length of liquid acts downward i.e. in the negative direction. Therefore the
gravitational force acting is:
Fgravity=−ρL Ac (2 x p) g
The driving force is the pressure difference of the two vapor plugs acting on the
liquid slug. Therefore the driving force is:
F pressure=(P¿¿ v1−Pv 2) Ac¿
17
The motion of a vibrating particle is restrained by the wall shear stress which is a
damping force:
F friction=−πd Lp τ p
Where shear stress is proportional to the velocity as:τ p=12
Cρ( dxdt
)2
Where C is called the viscous coefficient and dependent on the flow state (laminar,
transition and turbulent), or on the Reynolds number .We adopted Swami and Jain’s
explicit co-relation accounting for the surface roughness as:
C=14
¿¿
F friction=−πd Lp12
ρL C (d x p
dt)
2
Hence we have our pressure force and one friction force and one gravitational force
acting on the liquid slug during its motion. Hence by newton’s law our equation of
motion is:
Lp Ac ρL
d2 x p
d t 2 =(P ¿¿v 1−Pv 2) Ac− ρL Ac(2 x p)g−πd Lp12
C ρL (d x p
dt)
2
¿
Rearranging we get[APPENDIX]
d2 x p
d t 2 + 2 Cd
(d xp
dt)
2
+ 2gLp
x p=(P¿¿ v1−Pv 2)
Lp ρL
¿
The equation is similar to the governing equation for forced damped mechanical
vibrations. It is a second-order nonlinear differential equation. The damping force
term 2Cd
changes with the flow velocity.
18
3.3 Energy equation of the vapor plugs
We consider the heat input or output to the vapor plugs due to phase change. Our
general heat equation is:
dHdt
= pdvdt
+ dqdt
For the 1st vapor plug (left side) as it is compressing the liquid slug i.e. work is done
by the vapor plug we have our energy equation as:
d mv1 cv T v 1
dt=−Pv 1
d Ac xp
dt+
d mv1 hfg
dt
Simplifying we get:
mv 1 cv
d T v 1
dt+cv T v 1
d mv 1
dt=−Pv 1 Ac
d x p
dt+
d mv 1
dth fg
For the 2nd vapor plug (right side) as it is being compressed i.e. work is done on the
vapor plug we have our energy equation as:
d mv2 cv T v2
dt=Pv 2
d Ac xp
dt+
d mv2 hfg
dt
Simplifying we get:
mv 2 cv
d T v2
dt+cv T v 2
d mv 2
dt=Pv 2 Ac
d x p
dt+
d mv 2
dth fg
As we have assumed the vapor as ideal gas we can write:
For the 1st plug
Pv 1(Lh+x p) Ac=mv1 R T v1
Differentiating with respect to time we get:
(Lh+x p) Ac
d Pv 1
dt+Pv 1 Ac
d x p
dt=mv 1 R
d T v 1
dt+R T v 1
d mv 1
dt
19
And for the 2nd plug
Pv 2(Lh−x p) Ac=mv 2 R T v 2
Differentiating we get:
( Lh−x p ) Ac
d Pv2
dt−Pv 2 Ac
d xp
dt=mv2 R
d T v 2
dt+R T v 2
d mv2
dt
3.4 Mass balance at the interfaces
The mass change of the vapor plugs is related with the evaporation and/or
condensation processes. We assumed that this change occurred only at the interfaces.
Therefore the mass of the vapor plugs will change according to mass flux equation:
m' '= q ' '
h fg
=U (Th , c−T v)
h fg
For the 1st vapor:
d mv1
dt={ −hc πd x p(T v 1−T c)
h fg
,∧x p≥ 0
he πd (Lh+ xp)(T e−T v 1)hfg
,∧x p<0
For the 2nd vapor:
d mv2
dt={he πd
(Lh−x¿¿ p)(Te−T v 2)hfg
,∧x p ≥0¿hc πd x p(T v2−Tc )
hfg
,∧x p<0
20
O
For positive x
O
For negative x
3.5 Energy equation of liquid slug:
To find the temperature distribution within the liquid slug with respect to time and
space we have to build another equation. The energy input/output to/from the liquid
slug will give the energy hence temperature distribution. The heat transfer to/from the
liquid plug is the sensitive heat transfer. Both conduction and convection is occurring.
Conduction is from the adjacent vapor plugs and convection to the outside or
environment.
Figure 3-18: Conduction and convection relating to the liquid slug
Conduction equation:
AC
∂(K∂T∂ x
)
∂ x=AC ρ c p
∂ T∂t
Convection equation:
21
−hliq A (T−T wi)=AC ρ c p∂ T∂t
Note that the co-ordinate frame here is different from the previous frame. The new
frame of reference is having origin at the intersection of heater and condenser:
Figure 3-19: Co-ordinate frame for the energy equation of liquid slug
Hence our energy equation of the liquid slug is:
ρ c p AC∂ T∂t
=AC
∂(K∂ T∂ x
)
∂ x−hliq A (T−T wi)/ AC
As T wi is not known we can extend to the environment temperature T ∞ by
22
ρ c p∂ T∂ t
=∂ (K
∂ T∂ x
)
∂ x−
4 Ud AC
(T−T ∞)
Where,
1U
= 1hliq
+d i
d0h∞
+ Kt
The initial and boundary conditions are:
T ( x=0 ,t )=T v 1
T ( x=LP , t )=T v2
T ( x , t=0 )=T ∞
And the variation of the outside temperature is:
T ∞={ T c ,∧0<x<Lc
T e ,∧x>Lc , x<0
Once the results of the temperature distribution are obtained, the sensible heat is
calculated. The heat input to the liquid slug from outside is:
Q¿ ,liq=∫x¿0
x¿Lp
πdK (T ∞−T )dx ,T ≤T ∞
And heat output from the liquid slug to outside is:
Qout , liq=∫x¿ 0
x¿Lp
πdK (T−T∞)dx ,T ≥ T ∞
Hence total heat transfer is both due to the latent heat transfer in vapor and sensible
heat transfer in the liquid slug.
Qtotal ,∈¿=Q ¿ , liq+Q¿ ,vap ¿
Qtotal , out=Qout ,liq+Qout , vap
23
3.6 Numerical solution:
So we have our equations as:
d2 x p
d t 2 + 2 Cd
(d xp
dt)
2
+ 2gLp
x p=(P¿¿ v1−Pv 2)
Lp ρL
¿
mv 1 cv
d T v 1
dt+cv T v 1
d mv 1
dt=−Pv 1 Ac
d x p
dt+
d mv 1
dth fg
mv 2 cv
d T v2
dt+cv T v 2
d mv 2
dt=Pv 2 Ac
d x p
dt+
d mv 2
dth fg
Pv 1(Lh+x p) Ac=mv1 R T v1
Pv 2(Lh−x p) Ac=mv 2 R T v 2
d mv1
dt={ −hc πd x p(T v 1−T c)
h fg
,∧x p≥ 0
he πd (Lh+ xp)(T e−T v 1)hfg
,∧x p<0
d mv2
dt={he πd
(Lh−x¿¿ p)(Te−T v 2)hfg
,∧x p ≥0¿hc πd x p(T v2−Tc )
hfg
,∧x p<0
Also C is related to the Reynolds number as:
C=14
¿¿
Solving the above equations given the initial and boundary conditions we can
numerically determine the positon (x p), velocity of the liquid slug and we can
determine the pressures ( pv 1 , pv 2), temperatures (T v 1 , T v 2) and the masses (mv 1 ,m v2)
transiency of the vapor plugs. Algorithm for numerical solution is given below:
1 Given initial values x p0, Lp 0 , d x p
dt 0, T v 10 , T v 20, Pv 10 & Pv 20 find x pand
d x p
dt
using 4th order Runge-kutta method on:
24
d2 x p
d t 2 + 2 Cd
(d xp
dt)
2
+ 2gLp
x p=(P¿¿ v1−Pv 2)
Lp ρL
¿
Our functions needed will be equation for Lp(can be assumed constant) and C.
2 We find mass of the vapor plug from the mass balance equation:
d mv1
dt={ −hc πd x p(T v 1−T c)
h fg
,∧x p≥ 0
he πd (Lh+ xp)(T e−T v 1)hfg
,∧x p<0
d mv2
dt={he πd
(Lh−x¿¿ p)(Te−T v 2)hfg
,∧x p ≥0¿hc πd x p(T v2−Tc )
hfg
,∧x p<0
3 We use the energy equation of the vapor plugs to find the temperatures:
mv 1 cv
d T v 1
dt+cv T v 1
d mv 1
dt=−Pv 1 Ac
d x p
dt+
d mv 1
dth fg
mv 2 cv
d T v2
dt+cv T v 2
d mv 2
dt=Pv 2 Ac
d x p
dt+
d mv 2
dth fg
4 We use the temperature , mass and position to find the pressures:
Pv 1(Lh+x p) Ac=mv1 R T v1
Pv 2(Lh−x p) Ac=mv 2 R T v 2
5 In order to find the temperature distribution and transiency of the liquid plug
we use energy equation of liquid slug with the suitable boundary and initial
conditions.
25
26
Chapter 4: Experiment
An experiment was conducted to compare the experimental results and the analytical
solution. The experiment is based on CLPHP. Single loop is considered in our
experiment. Temperature at 8 different locations and pressure at one location has
been found. Snapshot of pulsation at different time is taken. Values for different
filling ratios and different angles are evaluated.
4.1 Experimental Setup
We made a closed pipe of single turn. We needed constant temperature at both ends
(evaporator and condenser), a transparent pipe to see the pulsations happening inside
the pipe. Requirements and what we used are given in the table 4-1.
Table 4-1: Required parts for the experiment
Parts required Parts used
Evaporator to maintain constant
temperature.
Pressure cooker with an electric heater
Condenser to maintain a constant
temperature.
Acrylic box made and ice cold water is
passed through it
Pipes for flow allowing heat transfer in
hater and condenser sides.
Copper tubes
Inlet and outlet for filling and sucking Valves
Transparent adiabatic pipes Glass tubes
Temperature measuring instrument Pre-calibrated thermocouples connected
to a data acquisition system
Pressure measuring instrument Pressure tapping and pressure transducer
Pipes for inlet and outlet to cool the Plastic pipes carrying ice cold water.
27
condenser
Filling and sucking mechanism Syringes
4.2 Properties and dimensions of parts used:
Cooker as evaporator:
Figure 4-20: Pressure cooker as evaporator
Copper tubes for conduction of heat:
28
Figure 4-21: Copper tube shape and dimensions
Glass tubes for adiabatic past and visualization:
Figure 4-22: Glass tube dimension
Condenser box:
29
Figure 4-23: Condenser box made of acrylic plates
Angle setup to give different angle of inclinations:
Figure 4-24: Setup to change the angle of inclination
Thermocouples to measure temperature:
30
Eight thermocouples are used to determine the temperatures at 8 different locations of
the CLPHP. Thermocouples were made and calibrated. The accuracy of each
thermocouple is given below:
Table 4-2: Thermocouple accuracy
Thermocouple number Error in °C
1 -1.067
2 -1.295
3 -0.871
4 -1.340
5 -0.904
6 -0.981
7 -0.877
8 -0.914
Pressure tapping to measure pressure:
2 mm tube is used to measure the pressure at one side of the evaporator connecting it
to a pressure transducer.
Fluid:
Alcohol and water is mixed prepared to have a fluid having boiling point temperature
below 95°C. Our 70% to 30% water to alcohol mixture is having a boiling point
temperature as 85°C.
Assembly:
Copper tube is inserted through two holes in the pressure cooker and fixed using m-
seal. One valve is welded to this copper tube outside of the pressure cooker. The
acrylic plates are assembles using chloroform to make the condenser box. Two holes
at the side plates are drilled for cold water inlet and outlet. Plastic pipes are used for
31
cold water inlet and outlet. Two more small holes are drilled on the top plate for
inserting thermocouples. Another copper tube is inserted in the condenser box and
fixed with araldite. One valve and one pressure tapping tube (2 mm diameter) is
welded to the copper tube. The glass tubes are connected to the copper tubes using a
nylon seal and araldite. Leaks at each joint were check by blowing air. Araldite or m-
seal is used to prevent leakage. Two thermocouples at both evaporator and condenser
side copper tubes and four thermocouples at four junctions of the glass tube were
fixed using high temperature seal. The assembly was kept on the angle setup plywood
to reduce movements of the parts (which may lead to leakage) and to set different
angle of inclinations. Two water tubs are placed, one above a table and one on the
floor for cold water blowing to cool the condenser. The heater is connected to the
adjustable output voltage distributor through wires.
Figure 4-25: Final assembly
The thermocouples are attached in such a way that the tip of the thermocouples are
just touching the inner flow at the junction of the glass tubes and are touching the
32
evaporator and condenser copper tubes externally. Thermocouples are connected to
the data base system and calibrated by dipping the mid-junction in an ice junction so
that we get the values of voltage from the data base system corresponding to 0˚C.
4.3 Procedure
The assembly is kept in the angle setup board at an initial inclined position of about
5-10 degree with the condenser side above. Air is sucked out through the vacuum
valve and closed immediately. Initially water is filled completely to measure the total
volume (glass pipes + copper tubes + other extensions). After measuring, working
fluid (ethanol +water mixture) is filled up to 60% by volume through the filling valve
and closed with the help of two syringes (to fill and suck).
Figure 4-26: (A) Setup to change angle (B) Adjustable voltmeter (0-240 V)
Water is filled in the pressure cooker and the heater is switched on. Output voltage
given to the heater is 220V. Ice cold water (20˚C) from the tub above the table is
passed through the plastic pipes to fill the acrylic box (condenser) and fill the water
tub below. As temperature rises near the boiling point of the working fluid in the
copper tubes (heated section) we try to keep the temperature constant by slowly
decreasing the voltage a little bit. Pulsations are observed in the transparent glass tube
and as the oscillations are somewhat steady we switch on the scan mode in the pre-
configured data acquisition system for extraction of data.
Figure 4-27: (A) Ice bridge (B) Data acquisition system
Temperature variations are extracted as voltage difference and are plotted in the data
acquisition system.
33
Figure 4-28: (A) Pressure transducer (B) Connection of glass tubes to condenser
box and cooker
Data (in volts) are exported to excel file and corresponding temperature values are
related by the TC table. These temperature variation with respect to time are plotted
in graphs. Angle of inclination and filling ratio was varied and corresponding
temperature values are extracted to get the results.
4.4 Results
As the pulsations were steady we took the reading at different angles and filling
ratios. The corresponding temperature and pressure values are calculated and
analyzed in the result and discussion section. Snapshots showing the pulsations is in
figure 4-10.
Figure 4-29: Snapshots showing pulsations
34
4.5 Probability of errors:
There are some possibility that the results won’t be of high accuracy due to some
fault in our experiment. We have some fault in our setup and some errors due to
environment and instrument errors. Some lengths of conductive copper tube was
exposed to the atmosphere so the adiabatic section was not completely adiabatic. The
filling and sucking valve fittings were longer than usual hence the pressure was not
that precise.
Figure 4-30: Difference between our CLPHP and a typical CLPHP
The temperature of the evaporator and condenser was not exactly constant at 90°C
and 20°C respectively. We tried to keep them constant but some fluctuations occur
due to the environmental effects. The losses due to the sharp bends and tapings of
thermocouples and pressure are also notable. The data extracted for the temperature
from the thermocouples are also having a little error due to the temperature change in
the reference ice bridge due to melting of ice in period of time.
35
36
Chapter 5: Results and Discussion
Our work contains both theoretical and experimental results with some assumptions
and errors respectively. We tried to minimize the experimental errors to get results as
accurate as possible.
5.1 Theoretical results:
Pulsating mode of the various characters e.g. position of vapor bubble, mass of liquid
in the heater section, temperature and pressure of the vapor are seen from the graphs
plotted by the MATLAB program.
Figure 5-31: Position of liquid slug w.r.t time
37
Figure 5-32: Velocity of pulsating liquid slug w.r.t time
Initially the pulsation is slow and of small amplitude because the vapors are just
beginning to form as seen in the figure 5-1 and figure 5-2. As time increasers both the
velocity and positional amplitude increases because the pressure difference increases
with time until a steady state is achieved. After the steady state, the amplitude of
position oscillation and velocity is almost constant.
The pressure develops slowly in the heater part with the evaporation of the fluid. For
a fluid of low boiling point evaporation will be fast and hence development of
pressure will be fast. We can see the oscillation of pressure and pressure difference
with time in figure5-3 and 5-4. After steady state the pressure in the vapor oscillates
with almost constant amplitude. The oscillation of pressure in the vapors leads to the
oscillatory motion of the liquid plug.
38
Figure 5-33: Pressure of the vapor plugs w.r.t time
Figure 5-34: Pressure difference between the vapor plugs w.r.t time
The temperature of the vapors slowly rises to a value then starts to oscillate. The
phase difference in the oscillation is about 180° which gives a higher temperature in
one vapor and a lower temperature in the other at a particular time and vice versa. By
39
the ideal gas law pressure increases with temperature and hence the pressure thrust
moving the liquid slug is pulsating in nature.
Figure 5-35: Temperature of the vapor plugs w.r.t time
We can see that temperature rises slowly at first and after the steady state the
temperature amplitude of both the vapor is constant. Mass of the vapor plug also
changes with the latent heat changes as seen in figure 5-6.
Figure 5-36: Mass of the vapor plugs w.r.t time
40
Effect of gravity on the position and velocity of the liquid slug is also found. Effect of
gravity is very less in the behavior of pulsation. For condenser up position increasing
the angle of inclination gives a higher amplitude of both slug position and velocity
and vice versa. As we have taken heater in the top in our model our g=9.8 is the
vertical position with heater at top, g=0 is the horizontal position and g=-9.8 is the
vertical position with condenser at top.
3.50
E-04
1.14
E-02
2.25
E-02
3.35
E-02
4.46
E-02
5.56
E-02
6.67
E-02
7.77
E-02
8.88
E-02
9.98
E-02
1.11
E-01
1.22
E-01
1.33
E-01
1.44
E-01
1.55
E-01
1.66
E-01
1.77
E-01
1.88
E-01
1.99
E-01
2.10
E-01
2.21
E-01
2.32
E-01
2.43
E-01
2.55
E-01
2.66
E-01
2.77
E-01
2.88
E-01
2.99
E-01
3.10
E-01
3.21
E-01
3.32
E-01
3.43
E-01
3.54
E-01
3.65
E-01
3.76
E-01
3.87
E-01
3.98
E-01
-0.3-0.2-0.1
00.10.2
Effect of gravity on slug postion
position g=-9.8 positon g=0 position g=9.8
time in sec
Posi
tion
of l
iqui
d sl
ug
Figure 5-37: Effect of gravity on slug position
3.50E-043.78E-027.52E-021.13E-011.50E-011.87E-012.25E-012.62E-013.00E-013.37E-013.74E-01
-10-8-6-4-202468
10
Effect of gravity on velocity of liquid slug
velocity g=-9.8 velocity g=0 velocity g=9.8
time in sec
Velo
city
of l
iqui
d sl
ug
Figure 5-38: Effect of gravity on slug velocity
The amount of latent and sensible heat transfer is also found.
41
5.2 Experimental results
In our experiment we tried to validate our theoretical results and also to find the
effect of filling ratio and gravity in the mode of pulsation. Three filling ratios with
two angles is taken. The results we got explains the reason of an optimum filling ratio
and the effect of gravity at a low temperature gradient.
The position of the thermocouples is shown in the figure
Figure 5-39: Thermocouple location
5.2.1 40% filling ratio:
The fluid we used is a mixture of alcohol and water in the ratio of 1:1. It has a boiling
point around 75-80 degree Celsius. We can see that the pulsation is very slow for
40% filling ratio at a small angle of inclination. The condenser side and evaporator
side thermocouples (1st, 8th, 3rd and 5th) showing almost constant values (figure 5-
10). The 2nd, 4th and 7th thermocouple shows a little oscillation due to the half pulsatile
motion of the liquid slug. The low amount of fluid at this filling ratio leads to less
amount of vapor formation and hence the low pressure in the vapors. This vapor
pressure can’t move the liquid plug hence the gravitational force have to pull the
liquid plug into the heater side. Since the angle is small this process is also very slow.
42
0 20 40 60 80 100 1200
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
1001 (VDC) 1002 (VDC) 1003 (VDC) 1004 (VDC) 1005 (VDC) 1006 (VDC)1007 (VDC) 1008 (VDC)
time in seconds
emf i
n m
v
Figure 5-40: Temperature vs time for 40% filling ratio and an angle of
But as we increase the angle of inclination the force due to gravity on the liquid plug
applies pressure on the vapor and comes from the condenser to the heater section and
again vapor is formed and it goes back to the condenser and condenses to liquid and
the cycle continues .this process is slow as it takes time for the pressure development
and condensation of vapor. This is more like a stratified flow rather than slug flow.
0 50 100 150 200 250-0.0005
0
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
1001 (VDC) 1002 (VDC) 1003 (VDC) 1004 (VDC) 1005 (VDC)1006 (VDC) 1007 (VDC) 1008 (VDC)
time in sec
emf n
mv
Figure 5-41: Temperature vs time for 40% filling ratio and an angle of
43
5.2.2 80% filling ratio:
Same fluid as before (during 40% filling ratio) is used.
1 6 11 16 21 26 31 36 41 46 51 56 61 66 71 76 81 86 91 96 101 106 111 1160
0.0005
0.001
0.0015
0.002
0.0025
0.003
1001 (VDC) 1002 (VDC) 1003 (VDC) 1004 (VDC)1005 (VDC) 1006 (VDC) 1007 (VDC) 1008 (VDC)
time in sec
emf i
n m
v
Figure shows that the pulsation is very slow, only a small movement is seen in the 8 th
thermocouple. This is because there is not enough vapor inside the pipe to give vapor
pressure for the pulsation to occur and the liquid will stay in the evaporator side for a
long time. Increasing the angle of inclination doesn’t help much as we can see in
figure
44
0 20 40 60 80 100 120 1400
0.0005
0.001
0.0015
0.002
0.0025
0.003
0.0035
1001 (VDC) 1002 (VDC) 1003 (VDC) 1004 (VDC)1005 (VDC) 1006 (VDC) 1007 (VDC) 1008 (VDC)
45
46
Chapter 6: Conclusion
47
Appendix
48
References
1. Thermo-hydrodynamics of closed loop pulsating heat pipes,PHD thesis.
Khandekar, Sameer. 2004.
2. Closed and open loop pulsating heat pipes. Manfred Groll, Sameer Khandekar.
2004.
3. Review and assesment of pulsating heat pipe mechanism for high heat flux
electronic cooling. G. Karimi, J.R. Kulham. s.l. : university of waterloo.
4. Thermal and Visual Observation of Water and Acetone Oscillating Heat Pipes. C.
Wilson, B. Borgmeyer,R. A. Winholtz,H. B. Ma,D. Jacobson,D. Hussey. 2011,
Vol. 133. 061502-5.
5. Theoretical and experimental modelling of an open oscillatory heat pipe including
gravity. Dobson, Robert Thomas. s.l. : University of Stellenbosch, 2003.
6. An open oscillatory heat pipe steam-powered boat. Dobson, Robert Thomson.
s.l. : University of Stellenbosch.
7. Flow and heat transfer of liquid plug and neighboring vapor slugs in a pulsating
heat pipe. Dazhong Yuan, Wei Qu , Tongze Ma. Beijing : Chinese Academy of
Sciences, 2009.
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50