enhanced condensation for organic rankine cycle
TRANSCRIPT
ENHANCED CONDENSATION FOR ORGANIC RANKINE CYCLE
Final Technical Report (Draft)
Project Grantor: Alaska Energy Authority 813 W. Northern Lights Blvd. AK 99503 907-771-3043 (voice), Email: [email protected]
Project Grantee: University of Alaska, Institute of the Northern Engineering Maggie Griscavage
P.O. Box 757880, Fairbanks, AK 99775 907-474-7301 (voice), Email: [email protected]\ Grant Agreement Number: 7310028 Project Code: 413006 Principal Investigators: Sunwoo Kim, PhD (PI)
Mechanical Engineering Department University of Alaska, Fairbanks 907-474-6096 (voice), Email: [email protected]
September 3, 2016
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Final Report Draft 09032016
EXECUTIVE SUMMARY
Generating electricity from low grade heat sources has attracted attention due to rising fuel price and increasing energy demand. The organic Rankine cycle (ORC) system is the most practical solution among technologies developed for low grade heat recovery. However, the efficiency of a typical small scale ORC is 10% or less. Most energy loss in the ORC is attributed to thermodynamically irreversible heat transfer processes occurring in its heat exchangers: the evaporator and condenser. In particular for waste heat recovery ORCs, economical success is mainly determined by effectiveness of the condenser because, while their heat source is provided at no cost, heat rejection accounts for most of operation cost. Almost half of total cost for operation and maintenance of an ORC system can stem from its condenser. We investigated and demonstrated heterogeneous condensing surfaces that potentially reduce the irreversibility during the condensation of organic fluids.
The proposed work is the investigation, optimization and testing of organic fluid condensation on a heterogeneous surface that enhances the vapor-to-liquid phase changing heat and mass transfer. The heterogeneous condensing surface possesses two different wetting characteristics against the working fluid: hydrophobicity and hydrophilicity. A theoretical and experimental investigation were carried out to design a condensing surface that could produce cost reduction in construction and operation of heat recovery ORC systems.
In order to meet the objectives, an analytical model that mathematically describes the phase changing heat transfer phenomenon on the heterogeneous condensing surface was developed. The condensation heat transfer rate per surface area and the gravity effect on the condensate flow were calculated. An experimental setup was constructed to perform condensation heat transfer testing for designed heterogeneous condensing surfaces. It consists of the condenser chamber, the evaporator, the cooling fluid supplier, the condensing surface and the temperature and pressure sensors. Initial performance tests were conducted using deionized water as working fluid at around 100°C and 102 kPa. Comparisons were made to evaluate the effect of orientation with respect to the direction of gravity. Similar experiments were carried out in a row pressure condition with HFC-134a refrigerant being a working fluid. A set of long term tests was conducted to investigate into performance degradation after continuous operation for more than 500 hours. The samples used in the long term tests were visually inspected with a high quality scanning electron microscope tool for fouling and corrosion.
The initial tests revealed two findings: 1) proposed condensing surface outperform a non-treated condensing surface, 2) the angle of the stripes that was formed by the design of the heterogeneous condensing surface is a key factor. The enhancement of the horizontal heterogeneous sample over the vertical sample was more than 50% for subcooling of 2~4 K. The following low pressure condensation experiments showed that the heat flux on the horizontal heterogeneous surface was 172% of that on the plain surface sample at subcooling of 2K.
The most significant source of irreversibility in the condensers in an ORC system is the thermal resistance due to a homogeneous condensing surface. The heterogeneous condensing surface showed a significant reduction in the thermal resistance. This improvement will increase the overall thermodynamic efficiency of ORC system, leading to shorter payback period.
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Final Report Draft 09032016
TABLE OF CONTENTS
EXECUTIVE SUMMARY ............................................................................................................................ ii
LIST OF FIGURES ....................................................................................................................................... iv
LIST OF TABLES ......................................................................................................................................... v
1 INTRODUCTION .................................................................................................................................. 1
2 ANALYTICAL STUDY OF CONDENSATION ..................................................................................... 3
2.1 Heat Transfer on Heterogeneous Condensing Surfaces................................................................ 3
2.1.1 Convection by Wavy Surface .......................................................................................................... 4
2.1.2 Coexistence of Dropwise and Filmwise Condensation .................................................................. 6
3 EXPERIMENTS OF THE CONDENSING SURFACES ...................................................................... 9
3.1 Design and Construction of Apparatus ........................................................................................ 9
3.2 Condensation Experiments .........................................................................................................13
3.2.1 Initial Performance ........................................................................................................................13
3.2.2 Heterogeneous Condensing Surface for HFC-134a .......................................................................20
4 LONGEVITY AND FOULDING ANALYSIS ........................................................................................24
4.1 Longevity Analysis .......................................................................................................................24
4.2 Fouling Analysis ..........................................................................................................................26
5 DISCUSSION AND SUMMARY ..........................................................................................................31
Appendix I: Sample of Raw Data Store .........................................................................................................33
REFERENCES ..............................................................................................................................................38
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Final Report Draft 09032016
LIST OF FIGURES
Figure 2.1: Heterogeneous condensing surface ............................................................................... 3
Figure 2.2: Convection induced by the wavy vapor-liquid interface .............................................. 4
Figure 3.1: Design of condensation experiment apparatus .............................................................. 9
Figure 3.2: Condensation apparatus that consists of evaporator, condensing chamber, condensing
surface, cooling chamber, and water circulation bath (top: before insulation, bottom: after
insulation in a lab hood) ................................................................................................................ 10
Figure 3.3: Heat conduction rod with holes on step surface ......................................................... 12
Figure 3.4: Heat flux for the plain copper sample ......................................................................... 14
Figure 3.5: Heat transfer coefficient for the plain copper sample ................................................. 15
Figure 3.6: Heat flux for the hydrophobic sample......................................................................... 16
Figure 3.7: Heat transfer coefficient for hydrophobic sample ....................................................... 17
Figure 3.8: Horizontal (left) and vertical (right) orientation of heterogeneous condensing surface
samples .......................................................................................................................................... 17
Figure 3.9: Heat flux for heterogeneous samples in comparison with full-hydrophobic and non-
treated samples .............................................................................................................................. 18
Figure 3.10: Heat transfer coefficient for heterogeneous samples in comparison with full-
hydrophobic and non-treated samples ........................................................................................... 19
Figure 3.11: Heterogeneous condensing surface ........................................................................... 21
Figure 3.12: Screen shot of NI LabView DAQ [11] ..................................................................... 21
Figure 3.13: Heat flux on the heterogeneous and plain surfaces ................................................... 22
Figure 3.14: Heat transfer coefficient on the heterogeneous and plain surfaces ........................... 23
Figure 4.1: Heat transfer coefficient change for 528 operation hours ........................................... 25
Figure 4.2: Heat flux change for 528 operation hours ................................................................... 25
Figure 4.3: New sample, magification: 50X.................................................................................. 26
Figure 4.4: New sample, magification: 400X................................................................................ 27
Figure 4.5: Used sample (300 hours with steam), magification: 50X ........................................... 27
Figure 4.6: Used sample (300 hours with steam), magification: 1600X ....................................... 28
Figure 4.7: Used sample (528 hours with HFC-134a), magification: 50 X .................................. 29
Figure 4.8: Used sample (528 hours with HFC-134a), magification: 182 X ................................ 29
Figure 4.9: Used sample (528 hours with HFC-134a), magification: 11691 X ............................ 30
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Final Report Draft 09032016
LIST OF TABLES
Table 4.1: The changes of the heat transfer coefficient and heat flux.................................................. 24
Table A.1: Sample of raw data from one of high pressure condensation experiments while system raises temperature............................................................................................................................. ................. 33
Table A.2: Sample of raw data from one of high pressure condensation experiments at a steady state............................................................................................................................. ............................................ 34
Table A.3: Sample of raw data from one of low pressure condensation experiments at a steady state............................................................................................................................. ............................................ 36
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1 INTRODUCTION Condensation is one of the most important heat transfer processes. Most energy conversion systems require a condenser as one of main components. However, no break-through improvement in condenser design has been made since its first application to engineering systems. Therefore, it is desirable to develop a technology that can be an alternative to conventional surface condensers that serve as a heat-removing device in power generation, refrigeration, and air conditioning systems. Particularly in the conventional power generation industry, high oil prices have forced condenser manufacturers to reevaluate their low-efficiency products, and to invest in designing small-sized, more efficient condensers. The rising energy costs also lead to growth in low grade energy recover and maintenance services market. In addition, renewable energy systems whose input source is thermal energy such as geothermal power plants and solar thermal power systems also demand a great deal of improvement in their condensation performance. While their energy resources (hot fluid) are naturally obtained at almost no cost, heat rejecting components (cold fluid) become relatively expensive. Furthermore, unlike the conventional power plants in which closeness to a cooling resource is one of most important factors in locating the site, the heating resource determines the location in renewable power plants; consequently they suffer from insufficient supply of cooling resource. As a result, the demand for high-efficiency condensers is expected to increase. There exists considerable desire for high-performance condensers not only in the power generation industry but also in the emerging technology applications. The development of high-speed microprocessors and ultrasonic aircraft and the miniaturization of energy conversion systems require a heat-rejecting mechanism having heat transfer coefficient on the order of 105 W/m2-K (10 times typical heat transfer coefficient by condensation), which cannot be achieved by the conventional mechanism of vapor-to-liquid heat transfer. First of all, improvement in condensation heat transfer has been an unsolved problem in the application in the Organic Rankine Cycle (ORC) system. ORC is the most practical solution among technologies developed for low grade heat recovery. However, the efficiency of a typical small scale ORC is 10% or less. Most energy loss in the ORC is attributed to thermodynamic irreversibility during the heat transfer processes occurring in its heat exchangers: the evaporator and condenser. In particular for waste heat recovery ORCs, economical success is mainly determined by effectiveness of the condenser because, while their heat source is provided at no cost, heat rejection accounts for most of operation cost. According to a report1 by the Department of Energy [1], almost half of total cost for operation and maintenance of an ORC system stems from its condenser. We propose use of heterogeneous condensing surfaces that significantly reduce the irreversibility during the condensation of organic fluids. The condensing surface of a conventional condenser is homogeneous surface made of copper or copper alloy in a form of tube or flat plate. The organic vapor condenses into liquid called condensate on the condensing surface. The condensate, in fact, is the culprit of efficiency loss because it forms a liquid film over the condensing surface acting as an insulator. Heterogeneous condensing surface minimizes the insulation effect of the condensate film by causing convection inside the condensate. In contrast to the conventional condensing surface, the heterogeneous condensing surface generates convection flows inside the condensate film, thanks to variation of surface tension and its interaction with gravity. We estimated that this technology enhances the condensation heat transfer by 50%, which leads to approximately 10% improvement toward the overall system performance. The object of this project is the investigation, optimization and testing of organic fluid
2
condensation on a heterogeneous surface that enhances the vapor-to-liquid phase changing heat and mass transfer. The heterogeneous condensing surface was studied for the application into the ORC system. A theoretical and experimental investigation were carried out to design an optimal condensing surface that results in cost reduction in construction and operation of heat recovery ORC. The technical objectives of this project are to:
(i) study the convection phenomenon over a surface on which wettability is heterogeneously distributed,
(ii) design a heterogeneous condensing surface with a high heat transfer capacity, and (iii) experimentally verify that the designed condensing surface performs 50% or more
better than the plain condensing surface.
This report summarizes the detail description of model development, design and construction of a condensation apparatus and the experiment results for the heterogeneous condensing surface. It also include some of data collected from the experiments in Appendix.
3
2 ANALYTICAL STUDY OF CONDENSATION The key indicator of condenser performance is the rate of condensation heat transfer. It is mathematically expressed by Newton’s Law of Cooling; the rate of heat transfer Q is proportional to the condensing surface area A and the temperature difference between the vapor of organic fluid entering to the condenser and the coolant, Tvap - Tcoolant:
A factor called the heat transfer coefficient h turns the proportional relation above to:
It represents how effectively the condenser transfers heat at a given surface area and temperature difference. The heat transfer coefficient h can be affected by a number of variables including the thermal properties of the working fluid, the geometry of the condensing surface, and the interactions between vapor and liquid and between liquid and solid, where the solid and the liquid are the condensing surface and the condensate, respectively. The solid-to-liquid interfacial phenomena and its impact on the condensation performance are analytically studied.
2.1 Heat Transfer on Heterogeneous Condensing Surfaces A heterogeneous surface is proposed to enhance the vapor-to-liquid phase changing heat and mass transfer of organic fluids. The heterogeneous condensing surface has two different wettabilities: hydrophilic and hydrophobic, Figure 2.1 illustrates the heterogeneous condensing surface. Condensation occurs in different manners depending on the wettability of condensing surface. Most metals used for condensing surface in industrial power plants possess high surface energy, and thus they attract the liquid with high bonding energy. As a result the liquid wets the surface, leading to the conventional filmwise condensation. The area with a low surface energy coating has the opposite characteristics. Due to low wettability the hydrophobic surface may promote dropwise condensation.
Figure 2.1: Heterogeneous condensing surface
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Depending on operation conditions, three different condensation modes may be observed on the proposed heterogeneous surface. Due to the variation of wettability the condensate can form a wavy profile on the vapor-liquid interface as shown in Figure 2.2. The other two possible condensate modes are coexistence of dropwsie and filmwise condensation and filmwise dominant condensation. The filmwise condensation model has been established by Nusselt [2]. Mathematical models are developed for the condensation with a wavy profile and the coexistence of dropwise and filmwise condensation.
Figure 2.2: Convection induced by the wavy vapor-liquid interface
2.1.1 Convection by Wavy Surface The heterogeneous condensing surface alternates two different surface characteristics: low and high surface free energy. They induce variation of wettability on the condensing surface. In contrast to the film formed on a homogeneous surface, a heterogeneous surface creates wavy profile on the vapor-to-liquid interface. The heterogeneous surface promotes intense convection inside the condensate and, consequently, reduces the thermal resistance drastically. Figure 2.2 shows the mechanism of the convection induced by the heterogeneous surface. Typical condenser materials, such as copper, copper alloy and titanium alloy, possess relatively high surface energy; therefore liquid on it has low surface tension with vapor. In contrast, liquid on the surface with a low surface energy (hydrophobic) coating presents high surface tension. The fluctuating surface tension force of the liquid condensate acts like a stirrer in a hot pot and enhances the heat and mass transfer. The convection current in Figure 2.2 can be mathematically identified through the continuity, momentum, and energy conservation as well as surface tension and interfacial tension. We consider Figure 2.2 as the physical domain containing a Newtonian fluid. The coordination is set with x being the horizontal axis and y being the vertical axis. The horizontal center is coordinated x = 0, and the bottom (the condensing surface) y = 0. Symmetry is assumed along the imaginary line of x = 0. The continuity, momentum, and energy conservation equations are given in a two-dimensional Cartesian coordinate. The fluid motion is described as an incompressible fluid in the following equations:
5
Continuity:
where u and v are the fluid velocity of x and y components, respectively. And, time is denoted by t.
x-Momentum:
y-Momentum:
where P is the fluid pressure, is the density, and is the viscosity. The terms X
and Y are the body force in x and y components. In the present model the body forces are caused by the tangential surface tension gradient volume forces. Since these forces are dominant, the buoyancy force in the y direction is negligible. The conservation of energy in the two-dimensional domain is expressed as:
Energy:
where the temperature of fluid and the thermal diffusivity are denoted by T and . The heat generation term is zero, , because no heat or other energy
source is considered.
Boundary conditions are set based on the symmetry line at x = 0, and no-slip condition on the condensing surface. The temperature on the condensing surface is constant at Ts.
The heat transfer rate to the condensing surface from the condensate is determined by the convection motion, and this heat transfer rate must be equal to the rate of conduction through the solid region for y < 0. Thus, a heat flux at the condensing surface is given by:
where k, h, and Tsat are the thermal conductivity, the condensation heat transfer coefficient, and the saturation temperature of the fluid.
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The surface pressure analysis can derive the surface tension in the normal direction, n. The surface pressure can be expressed with:
where Psurf, Pv, , and γ are the surface pressure, the vapor pressure, the surface tension, and the curvature of the free surface. γ can be identified by both experimental observation and theoretical prediction. We suppose that γ will be determined experimentally. In general, it depends on the temperature difference between the condensing surface and the fluid and on the vapor pressure. The surface pressure analysis is used to calculate the surface tension gradient force as well as normal stress boundary condition:
The surface tension coefficient can be viewed as a value that is proportional to the saturated temperature of the fluid. This simplification produces a linear relation of the surface tension with its gradient:
where and denote the reference values of the surface tension and fluid temperature. The mathematical model can be solved with the finite element method, which is a numerical analysis method for partial difference equations. 2.1.2 Coexistence of Dropwise and Filmwise Condensation
Dropwise and filmwise mode of condensation may happen in a condenser when the proposed condensing surface with the coated area having high hydrophobicity is used under a moderate condensation rate condition. For this case, both filmwise and dropwise condensation heat transfers determine the average heat transfer coefficient of the condenser. Dropwise condensation can be predicted by knowing the population of droplets and the heat transfer rate of individual drops.
Population of droplets is determined by the population balance theory [3,4]. The growth rates of drops of radius r1 and r2 are called G1, and G2, respectively. The population density of drops n(r) in an arbitrary area A is defined as the number of drops of radius r per unit area. In order for the number of drops to be conserved in a certain size range, the number of drops entering by growth must equal the sum of the number of drops leaving by growth and the number of drops swept away by larger drops; i.e.,
rdtSndtGAndtGAn 212211
where S and t are the sweeping rate and the time. As Δr approaches zero, n1-2 becomes a point value, and the equation can now be written by
0
nGn
dr
d
7
where the sweeping period τ = A/S.
The heat transfer rate through a drop of radius r with the contact angle equals to the rate at which the enthalpy Hfg of newly condensing vapor changes, and therefore one can write the single drop heat transfer qd as a function of the drop growth rate G:
GrHq fgd cos12 2
Meanwhile, heat transfer rate through a single drop can be obtained by evaluating the network of thermal resistances residing on the vapor-liquid interface and inside of the drop. From the vapor side to the liquid and solid surface, there are four thermal resistances affecting the condensation heat transfer. They are the vapor-liquid interfacial resistance, thermal resistance due to the drop curvature, conduction resistance of the liquid, and conduction resistance of the coating material. Each component of thermal resistance contributes to temperature drop between the thermal boundaries. Temperature drop by the vapor-liquid interfacial resistance ΔTif varies with the drop radius, drop contact angle, and interfacial heat transfer coefficient hif
cos12 2
rh
qT
if
dif
Drop curvature also creates temperature drop ΔTc as a function of the surface tension σ and the average temperature of the drop Tavg [5]
rH
TT
fg
avg
c
2
Since, the wall subcooling determines the minimum viable drop radius [6],
TH
Tr
fg
avg
2min
This equation is reduced to
Tr
rTc min
The conduction effect inside of the drop ΔTdrop depends strongly on the shape of drop and the thermal conductivity kd. [7]
sin4 d
d
droprk
qT
Temperature decrease due to the resistance of the coating material on the contact surface is proportional to the thickness of coating layer δ and the inverse of thermal conductivity kcoat of the coating material
22 sinrk
qT
coat
dcoat
8
Combining the equations above the total temperature drop between the vapor and the condensing surface can be computed
cos12
1
sin4sin/1
112
min
2
ifdcoat
d
ccoatdropif
hk
r
krrrq
TTTTT
Solving the growth rate differential equation we have the drop population equation
minminmin
1
3
min
2
minminmin
2
min
1
2min
ln
ln22
exp
rrrrrA
A
rrrrrrrr
A
A
G
Gnrn
wherefgH
TA
21
,
sin4
cos12
dkA
, and
23
sin
cos1
2
1
coatif khA
The steady state dropwise condensation heat transfer rate per unit area of the hydrophobic condensing surface can be obtained by multiplying the heat transfer rate through a single drop with the population density,
max
min
"r
rddropwise drrnrqq
Condensation on the non-coated condensing area must be filmwise. For this area we can take the Nusselt condensation model,
4/1
4/32
" 943.0
L
TgHkq
vcfgc
filmwise
When dropwise condensation on the coated area and filmewise condensation on the non-treated area coexist in the proposed condensing surface, the average heat transfer coefficient is determined as:
sw
sqwqq
filmwisedropwise
""
"
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3 EXPERIMENTS OF THE CONDENSING SURFACES 3.1 Design and Construction of Apparatus
Design for a condensation experiment apparatus was carried out in a SolidWorks environment as shown in Figure 3.1. The test setup consists of the condensing chamber, condensing surface, evaporator, heat conduction rod, and cooling chamber.
Figure 3.1: Design of condensation experiment apparatus
Based on the design, we constructed a complete vertical flat plate condensation apparatus as photographed in Figure 2. The apparatus requires a constant vapor source and a heat sink, to dump the heat absorbed by the condensing block from the vapor. The heating chamber constantly heats and vaporizes the organic fluid. The vapors are then transferred to the condensing chamber though the upper pipe line. The cooling chamber, which removes the latent heat from the organic vapors, is fed with cooling water. Cooling water is circulated by the chiller pump (also called chilled water circulation bath), which maintains the set cooling water temperature. The condensate then flows back to the boiling chamber through the lower pipe line. This configuration allows the condensation process to be continuous and steady.
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Figure 3.2: Condensation apparatus that consists of evaporator, condensing chamber, condensing
surface, cooling chamber, and water circulation bath (top: before insulation, bottom: after insulation
in a lab hood)
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Boiling and Condensation Chambers
The chamber in which the organic liquid is heated to its boiling point and evaporates is known as the evaporator or boiling chamber. The evaporator must withstand high pressures as well as vacuum pressures, for example, if we run the condenser with a high pressure fluid such as water as working fluid, the fluid tends to get superheated, which also raises the pressure. On the other hand, if we run a low pressure fluid such as most organic fluids, we would observe vacuum pressures. (Normal operating conditions of industrial power plant condensers are vacuum conditions.) In both cases, we need a boiling chamber which would withstand the aforementioned conditions. Moreover, the chamber should be air tight under positive and negative pressures. The outer diameter of the transparent cylinder is six inches. The thickness of the cylinder is a quarter of an inch. Two aluminum disks are used to cover the two open ends of the cylinder. The aluminum disks are each eight inches in diameter and half inch thick. These aluminum disks have a groove so that the cylinder wall would sit tight in to the aluminum disks.
The condensing chamber is similar to the boiling chamber in size, dimensions, and materials. In the condensing chamber, instead of having two aluminum disks we have one aluminum disk and one stainless steel disk. The reason for choosing aluminum disk is that, aluminum has a high thermal conductivity; so a system with aluminum would come to equilibrium faster when compared to stainless steel and plastics. This is the reason why we chose aluminum for the boiling chamber as well. The aluminum disk in the condensing chamber also has two tapped holes of half inch diameter in which a nipple is screwed in, and to which pipes are connected from the boiling chamber. The stainless disk has a three inch diameter hole in the center which houses the heat conduction rod. The heat conduction rod is made out of copper. Because the heat conduction rod and the plate housing are made of dissimilar metals, the thermal expansion coefficient of copper and the thermal expansion coefficient of stainless steel are to be considered. The thermal expansion coefficients of both copper and stainless steel are close enough that no leaking problems should occur at the copper and stainless steel interface.
Heat Conduction Rod
The copper rod of width 3.5 inches diameter and length of 4.5 inches was machined in lathe in such a way so that the diameter of the copper rod is 3 inches except for a 1 inch section where there is a step of 0.5 inches. The step begins at 0.75 inches from right end. The step is machined so that the vacuum in the condensing chamber cannot force the copper condensing block through the housing hole in the stainless steel plate. The step rests against the O-ring of the stainless steel disk. O.75 inches of the copper block fits into stainless steel disk. The other part of the copper goes into the cooling chamber. There are three holes on the step surface of the copper, to allow thermocouples to measure the temperatures of the copper at known spacing intervals. Figure 3.3 shows the copper heat conduction rod with holes for the thermocouples.
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Figure 3.3: Heat conduction rod with holes on step surface
Cooling Chamber
The cooling chamber requires a material that is easy to machine and possesses resistance to oxidation. For this reason, stainless steel type 304 was selected. The dimension of the cooling chamber is a 6”×6”×4” cube. The front face of the cooling chamber has a three inch diameter hole, in which the copper block is held. It has two inlet ports on the bottom and two exit port on the top, through which the coolant pumped by the chilled water circulator flows. The chamber is the room where the heat delivered by the heat conduction rod is released to the coolant. A sufficient area of the heat conduction rod is exposed to the coolant to facilitate the cooling. The chilled water circulator (manufacturer: Polyscience) is capable of adjusting the coolant temperature with an increment of 0.01 degree Celsius from -15 degree Celsius to more than 100 degree Celsius.
Measurement
For the measurement of the temperatures, we use Omega’s hermitically sealed tip “K” type thermocouples. These thermocouples were chosen because the tips for these thermocouples are sealed with an insulating material, which does not expose metal tip of the thermocouple. Because of this we can make sure that the metal tip is not in contact with the copper rod since thermocouples are inserted in the copper rod. An Omega pressure transducer, which is installed on the tube from the condensation chamber, measures the condensation pressure and feeds data to an NI DAQ system. The DAQ reads the measured temperatures and pressures simultaneously. It collects three temperature values from the heat conduction rod, the condensation chamber temperature, and the ambient air temperature as well as the condensation pressure.
Three immersion type heaters (cartridge heaters) for heating the liquid in the boiling chamber. The heaters have NPT threads for the connection into the boiling chamber. Of three heaters, two heaters are 250 watts, and the third one is 75 watts. These heaters provide heat to boil the working fluid. Two variacs (variable autotransformer) are used to control the output voltage, for a steady input power.
Once the all component is connected and assembled, the condensation test apparatus is well insulated, preventing any heat transfer from the heat conduction rod to the environment. Thanks to the insulation, the radial heat transfer in the condensing block is negligible. The heat travels in one direction that is from the condensation chamber to the cooling chamber.
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3.2 Condensation Experiments 3.2.1 Initial Performance
Initial performance tests were conducted using deionized water as working fluid at around 100°C and 102 kPa. Data collection procedure and description of apparatus are as follows.
Steam is generated from distilled water in the heating chamber. The steam then flows over the condensing surface (3-inch diameter copper), which is located in the condensing chamber. The condensing surface’s temperature is maintained at the required temperature by maintaining the temperature of the coolant, which flows on the other end of the condensing block in the cooling chamber. A chiller pump is used to control the coolant’s temperature. The condensate from the test condenser flows down in to the condensing chamber. The condensate is then pumped into the heating chamber to be turned into steam again using a very small pressure differential pump. The vacuum pump is operated from time to time to remove non-condensable gases from the system. This vacuum pump is also used to maintain a set pressure in the condensing chamber. The pump which is used to drain the condensate from the condensing chamber is also used to fine adjust the pressure in the condensing chamber. The thermocouples inserted in the heat conduction rod provide the linear temperature decrease along the direction of heat.
Maintaining the condensation temperature and pressure is a delicate job. With the help of the variacs, an operator controls the total heat output from the heating elements. When the temperature is above 100°C in the evaporation chamber, the steam starts flowing into the condensing chamber through the hose. At this moment the chiller pump is still turned off, which means the condensing block is at room temperature. The steam which flows into the condensing chamber starts condensation on the condensing surface. The condensing chamber temperature is allow to raise up to 90°C before turning on the chiller pump. The reason behind this is to let the temperature rise in the condensing chamber to be gradual, not exponential The operator first adjusts the variac so that the temperature is around 100°C and then when the condensing chamber temperature is high enough, he/she keeps adjusting the chiller pump’s temperature to get the desired condensing surface temperature.
The operator waits a period of time after changing each individual setting, giving enough time to the system to respond to the changes. It is very important that the system is at equilibrium before the operator takes measurements for the heat transfer coefficient. Giving the system a long enough time after any changes in temperature and pressure, the operator starts monitoring the pressure and temperatures closely for another half an hour. By doing this the temperature is also controlled. Taking the average pressure and temperature reading for the last half an hour would provide one set of data for a specific subcooling. The operator then changes the variac and chiller pump settings to find out temperature and pressure values at different ΔT.
Determination of heat transfer coefficient
The one-directional heat conduction law is used to calculate the surface temperature of the condensing block and the heat flux. The local flux is determined by the known thermal conductivity of the heat conduction rod and collected temperature data:
i
ii
L
Tkq
where k is the thermal conductivity of the heat conduction rod, ΔTi is the temperature difference of two thermocouples, and Li is the distance between the two thermocouples. The heat flux q is
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computed by taking the average of all local heat fluxes measured. The surface temperature Ts is then extrapolated from the computed heat flux q:
k
LqTT s
s1
1
where T1 and Ls-1 are the temperature of the thermocouple that is the closest to the surface and its distance from the surface, respectively. The condensation heat transfer coefficient h is given by
TA
qh
where A denotes the condensing surface area.
Comparisons were made between a plain copper condensing surface and a hydrophobic-treated sample to investigate the treated condensing surface. An example of the raw data collected is found in Appendix.
Plain copper condensing surface
The condensation on the plain copper sample was first observed at different subcooling temperatures (the difference between the vapor saturation temperature and the condensing surface temperature) to provide a baseline. The mode of condensation was dropwise. The formation of the drops and the coalescence of the drops were visually studied. The sliding of the coalesced drops away from the plain copper sample and the movement of other drops in the process of sliding were slower at smaller subcooling temperatures than at larger subcooling temperatures. The number of drops formed at the smaller subcooling temperature was noticeably less when compared to that at larger subcooling temperature. Consequently, the area of the plain copper sample exposed directly to the vapor appeared greater when the subcooling temperature was relatively small. The drops did not depart on the surface until they reached about 6 mm in diameter.
Figure 3.4: Heat flux for the plain copper sample
15
Figure 3.4 shows the heat flux with the variation of the subcooling temperature. It is observed that the heat flux increases with the subcooling temperature. This result accords with the visual observation that the rate of drop falling from the surface was higher at higher subcooling.
Figure 3.5: Heat transfer coefficient for the plain copper sample
The condensation heat transfer coefficient on the plain copper sample is plotted for the subcooling temperature ranging 1 to 10 K in Figure 3.5. The graph can be divided into two sections: one with a steep declination at low subcooling temperatures and the other with a flat trend line. The least square regression method is employed to generate trend lines for this graph. Steep declination is observed in subcooling temperatures from 1 to 4 K. In this range of subcooling temperatures, the formation of the drops was at the beginning stage. Thus, the plain copper surface allowed more surface area that was exposed directly to the vapor, because there formed a less number of drops on it. As a result, the overall resistance to the heat transfer from the vapor to the surface remained low. The graph reflects that the overall thermal resistance increases significantly with the subcooling temperatures up to 4 K (the overall thermal resistance is inversely proportional to the heat transfer coefficient). In the subcooling range of 1 to 4 K, the number of drops formed on the plain copper sample gradually increased with the increase in the subcooling due to direct condensation. This explains the steep declination of the heat transfer coefficient.
The transition of the trend occurs at the subcooling temperature 4 K. As shown by the second trend line representing h’s for ΔT > 4 K, the heat transfer coefficient remained at around 12 kW/m2-K after the transition. With an increase in ΔT, the rate of condensation proportionally increases. When ΔT = 4 K, however, the total volume of droplets on the surface no longer escalated because of the rapid sweeping by falling drops. Therefore, the overall thermal resistance was kept nearly constant, leading to the flat trend of the heat transfer coefficient h.
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Hydrophobic copper condensing surface
Figure 3.6: Heat flux for the hydrophobic sample
The hydrophobic-treated sample outperformed the non-treated plain sample. Figure 3.6 displays the heat flux measured on the hydrophobic-tread sample in comparison with the plain sample. No signs of film condensation were observed as expected. The average diameter of departing drops was visually measured around 3 - 4 mm. This meant that the size of departing drops was smaller by 2 mm than that on the plain sample. The cause of this difference lies in the wettability. Whereas the drops on a greater wettability do not start moving until they are heavy enough, ones on hydrophobic surface depart and clean off other drops on its path at less weight. The experimental results obviously reflect this in Figure 3.6. The hydrophobic surface generated heat fluxes almost twice as much as the plain copper sample, which is represented by the dotted line. This is improvement is significant in that both the plain and hydrophobic samples promoted dropwise condensation. Even, visually examined contact angles were found almost identical on the both surfaces.
A data pattern similar to in Figure 3.5 is viewed in Figure 3.7 that shows the heat transfer coefficient on the hydrophobic-treated surface with respect to the subcooling temperature. This graph also can be divided into two parts, but for the hydrophobic surface, transition takes place at the subcooling temperature of 2 K. The same reasoning can be adopted to explain the variation of h; the curve before ΔT = 2 K has a steep slope and after there it is flat. For the plain copper, sample the transition in the curve takes place at ΔT = 4. This implies that the moment when the total volume of drops on the condensing surface stops rising is reached at lower subcooling when hydrophobicity of the condensing surface is reinforced. According to our visual observation, the size of departure drops was smaller on the hydrophobic surface. A less population of large drops resulted in a smaller total volume of drops and consequently a decrease in the overall thermal resistance, which caused the rise of the heat transfer coefficient h. At ΔT = 1 K, h for the hydrophobic-treated copper sample was approximately 50 kW/m2-K while that for the plain
17
copper sample about 25 kW/m2-K. Even at their respective transition temperatures, the h for the hydrophobic-treated copper sample was twice.
Figure 3.7: Heat transfer coefficient for hydrophobic sample
Heterogeneous condensing surface
The performance of a heterogeneous condensing surface was experimentally examined for different orientations: horizontal and vertical. Figure 3.8 illustrates the horizontal and vertical samples, where the dark and bright stripes represent the hydrophobic coating and copper substrate, respectively. Details on the heterogeneous condensing surface samples can be found in the previous reports.
Figure 3.8: Horizontal (left) and vertical (right) orientation of heterogeneous condensing surface
samples
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The difference between the horizontal and the vertical heterogeneous samples is only the angle of the stripes with respect to the direction of gravitational acceleration. Nonetheless, it behaved differently. The drop departure on the hydrophobic stripe was similar to that of the horizontal case, but the drop departure on the hydrophilic stripe was hardly witnessed on vertically oriented samples.
Figure 3.9 shows the experimental heat transfer rate per unit condensing area, which is also called the heat flux. It is obvious that the horizontal heterogeneous sample transferred as much heat as the fully hydrophobic sample, which is plotted with the steeper dotted straight line in the figure. Below subcooling temperature of 3 K the heat flux for the horizontal heterogeneous surface was found nearly identical to the hydrophobic-treated copper sample. This was undoubtedly due to the same degree of bare surface area. At lower subcooling temperatures, the area of bare surface that was exposed to the vapor was the same in both cases. As the subcooling temperature increased (> 3 K), the drops began to fall off the surface. The drops from the hydrophobic stripes swept away the drops on the hydrophilic stripes, except for the drops of the first few stripes on the top half that were unable to be swept away. Thus, the resistance created by the drops that were unable to be swept away became substantial, resulting in a higher thermal resistance. After the subcooling temperature of 3 K, the heat flux for the horizontal heterogeneous sample started generating discrepancy from the hydrophobic sample.
Figure 3.9: Heat flux for heterogeneous samples in comparison with full-hydrophobic and non-
treated samples
The experimental results of heat transfer coefficient for the heterogeneous surfaces in Figure 3.10 also demonstrate that the horizontally aligned sample effectively reduces thermal resistance at low subcooling temperatures and that the vertical sample is outperformed by the horizontal one. When the vertical heterogeneous sample is compared with the plain sample, the heat transfer coefficient at ΔT = 4 ~ 5 K was 16 and 12 kW/m2-K for the vertical and plain sample, respectively. At ΔT = 8 K it was 12.5 and 11 kW/m2-K for the vertical and plain sample, respectively. The greater heat transfer coefficients compared to the plain copper sample are due to the easy departure of drops on the hydrophobic stripes.
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Figure 3.10: Heat transfer coefficient for heterogeneous samples in comparison with full-
hydrophobic and non-treated samples
Until now experimental investigation has been conducted for a plain copper sample, fully hydrophobic-treated copper sample, and heterogeneous samples in a flat plate condenser. The heterogeneous surface has been tested for the first time to investigate the heat transfer coefficients and drop formation behavior on it. From the observations and measured results the following conclusions were drawn.
1. Condensation heat transfer of steam on the hydrophobic-treated sample is superior to that on the plain copper surface despite the fact that both the surfaces stably promote dropwise condensation, even though visually examined contact angles are almost identical on the both surfaces. This is attributed to the size of the droplets that are about to depart. The difference in the droplets behavior is due to the surface free energy difference between the samples. The lower surface free energy causes low wettability of the droplet, reducing the size of departing droplets.
2. The heat transfer coefficients for the horizontal heterogeneous surface at lower subcooling temperatures are as high as the heat transfer coefficients for the homogeneous hydrophobic-treated surface. This is because the drops generated on the non-treated stripes are carried away by drops from the hydrophobic stripes due to the orientation of the horizontal heterogeneous surface. The heat transfer coefficients decrease with increase in the subcooling temperatures. This is partially attributed to the drops which are unable to be swept away on the top part of the condensing surface.
3. The heat transfer coefficient for the vertical heterogeneous sample at ΔT = 4 K is about 25% greater than that of the plain sample. The enhancement of the horizontal heterogeneous sample over the plain sample is approximately 100%. The enhancement is not comparable to that of the horizontal heterogeneous surface, because of the orientation of the sample. The drops generated on the hydrophobic stripes do not have
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any influence on the drops on the hydrophilic stripes due to the orientation. Thus, less enhancement in the heat transfer coefficients are obtained.
4. Higher heat transfer coefficients are observed at lower subcooling temperatures for all the samples. This is due to the number of drops covering the condensing surface. At lower at subcooling temperatures the drop generation is slow and thus the bare surface area of the condensing surface exposed to the vapor. The lower drop generation at lower subcooling temperatures results in higher heat transfer coefficients.
The uncertainty of the heat transfer coefficient (δh/h) can be determined by the standard approach presented by Coleman and Steele [8].
2/12222
q
q
h
h
T
T
T
T
h
h
c
c
s
s
st
st
where h is the heat transfer coefficient, Tst is the steam temperature, Ts is the surface temperature, q is the average heat flux, and hc is the thermal contact conductance. For thermocouples, (δT/T) is given by the manufacturers and the value is approximately 0.75%. For calculation of the thermal contact resistance, we assumed the thermal contact conductance of the copper to copper contact to be 200,000 W/m2-K. This value is chosen from the range of values given in a literature [9]. For δhc/hc, the maximum uncertainty that is possible so that Ts < Tst is calculated 3%. The uncertainty of the average heat flux is calculated by using higher-order uncertainty principle as explained by Figliola and Beasley [10]. The uncertainty of the average heat flux (δq/q) is 3.74%. From the equation, the uncertainty of the measurement of the heat transfer coefficient is δh/h =4.68%.
3.2.2 Heterogeneous Condensing Surface for HFC-134a One of the primary technical objectives of this project is to develop a high-heat transfer condensing surface employing the proposed heterogeneous hydrophobicity design. Previous experiments for steam condensation showed that heat transfer on the heterogeneous surface outperforms the plain (non-treated) surface. Figure 3.11 depicts the design of the heterogeneous surface. It has alternative hydrophobic coating and hydrophilic copper substrate layers. The orientation of the stripes with respect to gravity considerably affects the heat transfer performance.
The previous experiments demonstrate that the heat transfer coefficient by steam condensation on the vertically oriented (the stripes are vertical, which is in the same direction as gravity) heterogeneous sample at a subcooling of 4 K is about 25% greater than that of the plain sample. A more significant finding is that the enhancement of the horizontal heterogeneous sample over the plain sample is approximately 100%. Based on these experimental findings we decided to examine the horizontal heterogeneous surface for organic fluid condensation in comparison to a plain non-treated surface.
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Figure 3.11: Heterogeneous condensing surface
(Left: design, Right: photograph when it is attached in the condensation apparatus)
The testing apparatus was set up to measure the heat transfer rates and heat transfer coefficients for various subcooling conditions. Data to be collected included the condensation pressure and temperature, three thermocouples’ reading in the copper rod, the ambient air temperature, and the heater power. The data acquisition system (DAQ) processed and stored the data as shown in the Figure 3.12 The raw data were processed for a steady state heat transfer analysis. Two to four hours were required to collect one set of data because a steady state condition must be ensured. Once a steady state was observed 2 minutes long data were taken from the raw data to determine mean values (time-averaged values). Details about the setting can be found in previous progress reports.
Figure 3.12: Screen shot of NI LabView DAQ [11]
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A data reduction process was carried out to determine the heat flux on the condensing surface. This value was studied for difference subcooling conditions. Subcooling is the degree of how much less the condensing surface temperature is from the saturation temperature of the vapor HFC-134a. In other words, that is the temperature difference between the vapor in the condenser and the condensing surface.
Figure 3.13: Heat flux on the heterogeneous and plain surfaces
The heat flux for both the horizontal heterogeneous sample and plain sample is plotted in Figure 3.13. For both cases, heat flux increases with the subcooling. This is explained by the fact that the temperature difference between the vapor and the surface is the driving force of convection heat transfer. A comparison between the heterogeneous surface and plain sample is obvious. The heat flux on the horizontal heterogeneous surface was 172% of that on the plain surface sample at subcooling of 2K. This means that a condenser equipped with the proposed condensing surface would transfer 72% more heat than the existing condenser. This improvement may lead to size reduction of the condenser because the proposed condenser would handle the same heat transfer with only 58% of condensing surface area used in a conventional condenser. However this enhancement wanes as the degree of subcooling increases. At subcooling of 3K and 4K, the heat flux enhancements reduce to 33.4% and 15.8%, respectively. And, one can expect no improvement when subcooling is greater than 6K. This suggests using the proposed condenser at low subcooling conditions.
This experimental results imply that the horizontally oriented heterogeneous condensing surface successfully creates an internal convection, which cannot be expected in a non-treated surface. The variation in surface tension, which is generated by the heterogeneous hydrophobicity design, breaks the balance of momentum of the condensate film that flows on the surface. As a result, a wavy profile of flow is formed and causes the internal convection. This phenomenon becomes
Subcooling [K]
23
more apparent when the mass flow rate of condensate is low. However, when the condensation rate is high, another factor take in charge of internal convection. It is the effect of a high Reynolds number. The convection promoted by the surface tension variation becomes lesser because the turbulence in the high Reynolds number region dominates the internal convection. This makes the enhancement by the proposed design less effective. Moreover, the addition in the thermal resistance due to the coating layer on the heterogeneous surface sample leads to lower heat flux values than that on the plain sample at 6K or greater subcooling.
Figure 3.14: Heat transfer coefficient on the heterogeneous and plain surfaces
However, the improvement at low subcooling appears remarkable. This observation looks more obvious in comparing the heat transfer coefficient, as in Figure 3.14. The heat transfer coefficient is the opposite concept of thermal resistance. Thus, a high value in this implies small thermal resistance and, in other words, low entropy generation. While it nearly remains unchanged on the plain surface, the heat transfer coefficient h [W/m2-K] on the heterogeneous surface rapidly rises as the degree of subcooling decreases. It reaches almost 4,000 W/m2-K on the heterogeneous condenser at subcooling of 1.6 K. We were not able to obtain experimental data for a subcooling lower than that because of experimental constraints. However, it may be anticipated that the heat transfer coefficient can be more than 5 KW/m2-K at subcooling of 1 K.
To sum up, the experiments show that the heterogeneous condensing surface improves condensation 30 ~ 70% depending on the degree of subcooling. In the next reporting period, design modifications will be made to accommodate the high subcooling region. In addition, longevity of the current design will be investigated.
Subcooling [K]
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4 LONGEVITY AND FOULDING ANALYSIS A long term experiment was carried out to test the longevity of the proposed condensing surface. The sample used for this experiment was the heterogeneous condensing surface with its stripes being perpendicular to the direction of gravity as shown in Figure 3.11. As shown in Chapter 3, the sample produced an enhanced heat flux compared to the plain surface with 72% improvement at the subcooling of 2 K. The objective of the longevity test is to determine 1) if the proposed sample surface deteriorates the heat transfer capability, 2) if corrosion occurs on the condensing surface, and 3) if the sample surface is vulnerable to fouling with the organic working fluid.
4.1 Longevity Analysis The experiment conditions were as follows. HFC-134a refrigerant was used as working fluid. The pressure and temperature in the condensation chamber were maintained at 80 ± 0.8 psia and 18.8 ± 0.4 °C. The heating element that vaporizes the refrigerant was rated at 60 W for the entire length of experiment. The room temperature was measured to be between 22.5 and 24.0 °C. However, the apparatus was well insulated so that the room temperature and its variation would not affect the experimental data. All temperature sensors collected the temperature values every 5 seconds and pressure data were collected at the rate of one per 0.2 seconds. The test continued for 528 hours without a stop.
Table 1 summarizes the results of the experiment. The operation duration began when a steady state operation was first observed, and this moment was defined as zero hours. The second and third columns contain the condensation heat transfer coefficient h [W/m2-K] and the heat flux [W/m2] on the sample surface. The last column shows the error of the heat transfer coefficient h from its mean value. For example, at 168 hours the heat transfer coefficient h was calculated 2.65 % lower than the mean value. The error flutuates at the maximum of only 3.56 %. This implies the proposed condensing surface shows no sign of degradation over its operation time up to 528 hours.
Table 4.1: The changes of the heat transfer coefficient and heat flux
Operation
hours h [W/m2K]
q" [W/m2]
Error of h (%)
Operation
hours h [W/m2K]
q" [W/m2]
Error of h (%)
0 2356.1 10795.5 3.56 312 2248.7 10376.6 -0.46
24 2217.9 10258.5 -1.60 336 2242.5 10414.5 -0.10
48 2278.1 10423.6 -0.01 360 2299.4 10646.7 2.13
144 2229.8 10379.2 -0.44 384 2241.6 10444.0 0.18
168 2186.1 10148.0 -2.65 456 2240.0 10326.8 -0.94
192 2267.7 10493.6 0.66 480 2338.5 10493.0 0.65
216 2263.4 10519.8 0.91 504 2305.6 10327.2 -0.94
288 2238.9 10406.8 -0.17 528 2316.2 10342.3 -0.79
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Figure 4.1 plots the heat tranfer coefficients measured during the longevity test period. The value steadily remains between 2,000 and 2,500 W/m2-K, drawing a horizontal straight line. In addition, a similar straight line is formed in the heat flux graph in Figure 4.2. The both figures indicate that the sample condensation did not deteriorate for the first 528 hours.
Figure 4.1: Heat transfer coefficient change for 528 operation hours
Figure 4.2: Heat flux change for 528 operation hours
Operation hours
h [W
/m2
-K]
q" [W/
m2]
Operation hours
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The longevity test demonstrates that the proposed condensing surface maintained its enhanced heat transfer performance for more than 500 hours. For this reason, it is assumed that no fouling or corrosion has happened during this longevity test. In a near future, we will take scanning electron microscope images on the surface to visually examine the 500 + hours operated sample and compare it with a new sample.
4.2 Fouling Analysis
Visual Investigation for Fouling and Corrosion
Visual investigation of the sample condensing surface was conducted in the Advanced Instrumentation Laboratory at University of Alaska Fairbanks. Three different groups of samples were examined: 1) new surfaces, 2) 300 operations hours with steam, and 3) 528 operation hours with the organic fluid.
The SEM images below show the conditions of the condensing surface having about 300 operation hours in comparison with a sample that has never been used. Figures 4.3 and 4.4 show the images of a new sample with magnification of 50 x and 400 x, respectively. The both display a homogeneous coating surface with some dust particles (in white), which can be expected in non-cleanroom laboratory environment. In Figures 4.5 and 4.6, which are for the sample used for steam condensation of 300 hours, it is observed that stains and deposit of containments have formed on the surface. We believe that the stains may be introduced before the condensation experiments since the condensation chamber did not allow any other condensable matter than steam. We cannot say if there has been degradation of the coating material only via this visual investigation.
Figure 4.3: New sample, magification: 50X
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Figure 4.4: New sample, magification: 400X
Figure 4.5: Used sample (300 hours with steam), magification: 50X
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Figure 4.6: Used sample (300 hours with steam), magification: 1600X
More noticeable changes on the condensing surface were found with the sample that experienced 528 hours condensation with HFC-134a organic fluid. Figures 4.7 to 4.9 are the SEM images with magnification of 50 x, 182 x, and 11691 x, respectively. As seen in Figure 4.7, part of the surface was covered by relatively large foreign matters, which are in white. The crack like dark spots are believed to be indication of removal of the original coating material. Figure 4.8 zooms in the largest white stain shown in Figure 4.7. The closest view with the maximum magnification in Figure 4.9 reveals the nature of the white foreign matter. They form in a grain of about 1 μm in size. It is obvious the matter is not yielded as the result of corrosion or a kind of chemical reaction in that it does not uniformly cover the surface. If this was a chemical reaction between the organic fluid and the coating material, it should spread out over the entire surface. One possible presumption is condensable containment from either the storage tank of the organic fluid or the charging horse. However, as we concluded from the longevity experiments, the treated sample did not affect heat transfer performance and maintained its superior condensation capacity for more than 500 operation hours.
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Figure 4.7: Used sample (528 hours with HFC-134a), magification: 50 X
Figure 4.8: Used sample (528 hours with HFC-134a), magification: 182 X
30
Figure 4.9: Used sample (528 hours with HFC-134a), magification: 11691 X
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5 DISCUSSION AND SUMMARY This project aimed to develop and test a heterogeneous condensing surface for use in Organic Rankine Cycle (ORC) systems. An analytical model that mathematically describes the phase changing heat transfer phenomenon on the heterogeneous condensing surface was developed. The model can be used to calculate the heat transfer rate on a condensing surface with different wettabilities (hydrophilic, hydrophobic, or heterogeneous having both hydrophilicity and hydrophobicity). The gravity effect on the condensate flow were understood by thermo-fluidic analysis in the model. An experimental setup was constructed to perform condensation heat transfer testing for designed heterogeneous condensing surfaces. It consists of the condenser chamber, the evaporator, the cooling fluid supplier, the condensing surface and the temperature and pressure sensors. Initial performance tests were conducted using deionized water as working fluid at around 100°C and 102 kPa. Comparisons were made to evaluate the effect of orientation with respect to the direction of gravity. Similar experiments were carried out in a row pressure condition with HFC-134a refrigerant being a working fluid. After completion of initial performance tests, a set of long term tests was conducted to investigate into performance degradation after continuous operation for more than 500 hours. The samples used in the long term tests were visually inspected with a high quality scanning electron microscope tool for fouling and corrosion. The initial tests revealed two findings: 1) proposed condensing surface outperform a non-treated condensing surface, 2) the angle of the stripes that was formed by the design of the heterogeneous condensing surface is a key factor. The enhancement of the horizontal heterogeneous sample over the vertical sample was more than 50% for subcooling of 2~4 K. The low pressure condensation experiments showed that the heat flux on the horizontal heterogeneous surface was 72% higher than that on the plain surface sample at subcooling of 2K. The enhancement became even greater with lower subcooling. For example, the heat transfer rate on the heterogeneous surface marked a value twice that on the plain surface sample at subcooling 1.5 K. This proves that the designed heterogeneous surface sample successfully minimizes the irreversibility caused during the phase-changing heat transfer. The experimental results suggest that the heterogeneous condensing surface should be used in a low subcooling condition to obtain its maximum benefit. This work partially achieved the objective of the project: to develop and experimentally investigate a specially treated surface to enhance the condensation heat transfer for ORC by 50% or more. The proposed condensing surface exceeded the set goal but it did in a limited subcooling range. A best heat transfer performance at a low subcooling condition can yield a double benefit. First, if the condenser in an ORC system operates at a low subcooling, this implies that the condenser temperature is very close to the system’s lowest temperature, which is the coolant supply temperature. In such a circumstance, the condenser pressure accordingly remains the lowest. Since the power generation is propositional to the pressure difference between the inlet and exit of the turbine, the lowest condenser pressure bring down the turbine exit pressure, and consequently, the pressure difference is maximized. In other words, a low subcooling produces an increased power generation and improves the thermodynamic system efficiency. Secondly, the enhanced condensation heat transfer reduces the size of the condenser. With a smaller condenser, we can save significant costs in manufacturing. A large condenser requires more materials and a longer manufacturing time. In addition, a smaller condenser benefits from low operation and maintenance costs. Condensers require periodic cleaning. This should be easier with a shorter condenser. More importantly, operation cost can be drastically reduced with a smaller sized condenser. The reduced heat transfer surface area lowers pumping
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power for the coolant, which accounts for nearly 100% of operation cost in the condenser. This is because the flow resistance of the coolant is linearly proportional to the total travel length of the coolant in the condenser. Reduced heat transfer area directly means reduced total travel length of the coolant. Among many power generation technologies, the ORC system is considered as the most feasible method to utilize a low grade heat source, such as geothermal water or waste heat from conventional coal power plants. However, the low thermodynamic efficiency of the ORC remains as a long last problem. The findings from the project will alleviate this problem and make the ORC a more feasible solution.
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Appendix I: Sample of Raw Data Store
Table A.1: Sample of raw data from one of high pressure condensation experiments while system raises temperature
Sample Date/Time HC TC1 TC2 TC3 TC4 Number 1 52:29.7 20.8501 21.1554 22.0054 21.694 21.2997 2 52:30.7 20.8411 21.2911 21.9496 21.6796 21.2802 3 52:31.7 20.8554 21.2862 22.0803 21.6729 21.2698 4 52:32.7 20.8443 21.2968 22.0639 21.7474 21.3217 5 52:33.7 20.8494 21.2848 22.0697 21.7518 21.3062 6 52:34.7 20.8413 21.282 22.068 21.7439 21.3196 7 52:35.7 20.8469 21.2913 22.0613 21.7479 21.3087 8 52:36.7 20.8591 21.2931 22.068 21.6944 21.3897 9 52:37.7 20.9013 21.3355 22.0937 21.7719 21.3154 10 52:38.7 20.908 21.3359 22.1356 21.7668 21.3136 11 52:39.7 20.9087 21.3158 22.0979 21.7152 21.408 12 52:40.7 20.8756 21.3394 22.103 21.8034 21.3205 13 52:41.7 20.8473 21.3339 22.0891 21.7594 21.3599 14 52:42.7 20.9353 21.3531 22.1263 21.793 21.3807 15 52:43.7 20.8631 21.36 22.0972 21.8059 21.3305 16 52:44.7 20.8573 21.4355 22.0643 21.8027 21.3133 17 52:45.7 20.8371 21.2929 22.0972 21.7622 21.3617 18 52:46.7 20.8777 21.2915 22.0664 21.8115 21.3427 19 52:47.7 20.8265 21.2806 22.0481 21.7786 21.3187 20 52:48.7 20.861 21.2917 22.0965 21.7659 21.3686 21 52:49.7 20.8418 21.288 22.0653 21.7638 21.3168 22 52:50.7 20.8436 21.2693 22.0995 21.7754 21.349 23 52:51.7 20.8427 21.2818 22.0738 21.6773 21.3791 24 52:52.7 20.8223 21.2425 22.025 21.7115 21.2763 25 52:53.7 20.8242 21.3369 22.1358 21.8168 21.3578 26 52:54.7 20.8325 21.279 22.0569 21.7099 21.255 27 52:55.7 20.8228 21.2855 22.0787 21.7523 21.3163 28 52:56.7 20.8612 21.2755 22.0683 21.7622 21.3064 29 52:57.7 20.8327 21.2506 22.1055 21.7722 21.2923 30 52:58.7 20.8628 21.3204 22.0773 21.8124 21.3494 31 52:59.7 20.8376 21.1115 22.2214 21.792 21.3683 32 53:00.7 20.7195 21.3359 22.0764 21.7442 21.3745 33 53:01.7 20.8406 21.2695 22.0694 21.7377 21.3718 34 53:02.7 20.8675 21.2549 22.1034 21.7437 21.375 35 53:03.7 20.8536 21.2769 22.0495 21.7032 21.412 36 53:04.7 20.8316 21.2617 22.0697 21.7504 21.365 37 53:05.7 20.7957 21.2806 22.0995 21.7328 21.3854 38 53:06.7 20.8392 21.2506 22.0549 21.7127 21.3898 39 53:07.7 20.8839 21.2536 22.0484 21.7391 21.369 40 53:08.7 20.9101 21.2677 22.0639 21.7604 21.3674 41 53:09.7 20.9825 21.2737 22.0306 21.6866 21.4208 42 53:10.7 21.0585 21.2818 22.0588 21.7162 21.3641 43 53:11.7 21.1422 21.2494 22.062 21.7298 21.3697 44 53:12.7 21.2506 21.245 22.0676 21.724 21.3829 45 53:13.7 21.2894 21.2469 22.0382 21.7467 21.378 46 53:14.7 21.3133 21.264 22.0232 21.7506 21.3403 47 53:15.7 21.3517 21.2401 22.0484 21.6928 21.3817 48 53:16.7 21.3871 21.242 22.0199 21.7178 21.3588 49 53:17.7 21.3626 21.2184 22.0546 21.7113 21.3343 50 53:18.7 21.3225 21.2332 22.0192 21.7333 21.3225 51 53:19.7 21.2982 21.2198 22.0357 21.7194 21.3363 52 53:20.7 21.3068 21.1871 22.0514 21.712 21.3373 53 53:21.7 21.3434 21.2258 22.0109 21.725 21.3313 54 53:22.7 21.3255 21.2325 22.0477 21.7155 21.3248 55 53:23.7 21.3334 21.2344 22.0435 21.7141 21.312 56 53:24.7 21.2959 21.2589 21.9917 21.7018 21.3104 57 53:25.7 21.3156 21.2668 22.0091 21.7102 21.3421 58 53:26.7 21.3172 21.2383 22.0165 21.7018 21.3139 59 53:27.7 21.3211 21.1913 22.2479 21.4159 21.3565 60 53:28.7 21.3223 21.2089 22.035 21.6479 21.3053 61 53:29.7 21.3093 21.1925 22.0042 21.712 21.307 62 53:30.7 21.3846 21.2689 22.0346 21.7112 21.3065 63 53:31.7 21.3726 21.3078 22.0541 21.6936 21.3088 64 53:32.7 21.3837 21.286 22.0506 21.713 21.2908 65 53:33.7 21.4216 21.2539 22.0665 21.7371 21.3368 66 53:34.7 21.4765 21.2754 22.0589 21.7473 21.251 67 53:35.7 21.5382 21.258 22.0756 21.7242 21.2655 68 53:36.7 21.6731 21.2944 22.0781 21.7082 21.2857 69 53:37.7 21.9019 21.3208 22.0781 21.7651 21.3002
34
70 53:38.7 22.2294 21.286 22.0622 21.7584 21.3023 71 53:39.7 22.4747 21.2738 22.042 21.6631 21.2727 72 53:40.7 22.7248 21.2691 22.0117 21.6497 21.3219 73 53:41.7 22.9085 21.2978 22.0941 21.6726 21.3286 74 53:42.7 23.0895 21.2668 22.0679 21.71 21.2985 75 53:43.7 23.2216 21.2805 22.0492 21.7205 21.3263 76 53:44.7 23.3558 21.2631 22.0552 21.729 21.3406 77 53:45.7 23.4665 21.2722 22.0478 21.7255 21.3337 78 53:46.7 23.5293 21.2201 22.0622 21.7329 21.339 79 53:47.7 23.6824 21.2819 22.0603 21.7327 21.3251 80 53:48.7 23.806 21.1178 22.0957 21.7186 21.351 81 53:49.7 23.9306 21.2944 22.0598 21.7209 21.3455 82 53:50.7 24.0837 21.2951 22.073 21.7047 21.3346 83 53:51.7 24.2728 21.2807 22.0591 21.7311 21.389 84 53:52.7 24.4874 21.283 22.073 21.7535 21.3471 85 53:53.7 24.7156 21.3964 22.0968 21.7794 21.3725 86 53:54.7 24.8821 21.4256 22.255 21.7753 21.467 87 53:55.7 24.8819 21.3661 22.2136 21.8993 21.5049 88 53:56.7 24.9823 21.3545 22.117 21.8174 21.5084 89 53:57.7 25.1146 21.3393 22.1066 21.8014 21.3827 90 53:58.7 25.2622 21.3626 22.1096 21.7757 21.4066 91 53:59.7 25.4921 21.3034 22.1059 21.7762 21.3922 92 54:00.7 25.6731 21.2849 22.1038 21.7799 21.3705 93 54:01.7 25.9215 21.2847 22.0427 21.7824 21.3568 94 54:02.7 26.0881 21.2856 22.0737 21.7366 21.3735 95 54:03.7 26.2236 21.2643 22.0665 21.7274 21.3797 96 54:04.7 26.3427 21.2557 22.0816 21.7348 21.3422 97 54:05.7 26.501 21.1861 21.9972 21.714 21.3751 98 54:06.7 26.6408 21.2282 21.965 21.748 21.3476 99 54:07.7 26.8773 21.2048 21.9791 21.6818 21.28 100 54:08.7 27.1011 21.23 21.9826 21.689 21.1955
Table A.2: Sample of raw data from one of high pressure condensation experiments at a steady state
Sample Date/Time HC TC1 TC2 TC3 TC4 Number 1 34:00.8 101.3506 80.585 79.7063 74.9948 73.47 2 34:01.8 101.3477 80.5499 79.6649 74.8666 73.4521 3 34:02.8 101.3907 80.5555 79.7086 74.9496 73.5206 4 34:03.8 101.3199 80.6349 79.7177 74.8362 73.4749 5 34:04.8 101.3585 80.7184 79.773 74.8467 73.5651 6 34:05.8 101.3416 80.7549 79.8659 74.9543 73.5067 7 34:06.8 101.3553 80.7766 79.882 74.9344 73.5519 8 34:07.8 101.3456 80.7865 79.9346 74.997 73.5329 9 34:08.8 101.3731 80.8592 79.9319 74.9677 73.6146 10 34:09.8 101.3402 80.8767 79.923 75.0284 73.6351 11 34:10.8 101.3788 80.8704 79.9637 75.0814 73.613 12 34:11.8 101.3984 80.8238 79.9254 75.125 73.628 13 34:12.8 101.4466 80.7871 79.9433 75.1217 73.6454 14 34:13.8 101.4256 80.7468 79.8706 75.1011 73.6656 15 34:14.8 101.4504 80.7276 79.8881 75.0644 73.7231 16 34:15.8 101.4484 80.8102 79.8659 75.0783 73.6927 17 34:16.8 101.4243 80.8117 79.8256 75.0848 73.722 18 34:17.8 101.422 80.8758 79.9001 75.0588 73.5913 19 34:18.8 101.4292 80.9152 79.9265 75.136 73.6649 20 34:19.8 101.4536 80.9649 79.933 75.1074 73.7325 21 34:20.8 101.4204 80.9483 79.9829 75.0903 73.6931 22 34:21.8 101.4768 80.9839 79.985 75.0941 73.6958 23 34:22.8 101.463 81.0195 80.0633 75.1194 73.7526 24 34:23.8 101.4941 81.0459 80.0528 75.1461 73.7658 25 34:24.8 101.4567 81.0862 80.0566 75.1519 73.7401 26 34:25.8 101.4367 81.0663 80.089 75.1707 73.7381 27 34:26.8 101.4461 81.1003 80.0693 75.2011 73.7291 28 34:27.8 101.4649 81.0369 80.0543 75.2067 73.6996 29 34:28.8 101.477 81.0586 80.0758 75.2257 73.8303 30 34:29.8 101.4996 81.1265 80.0942 75.1901 73.7578 31 34:30.8 101.482 81.1399 80.1351 75.2141 73.7217 32 34:31.8 101.4779 81.1782 80.1696 75.2322 73.8421 33 34:32.8 101.4851 81.1959 80.1674 75.238 73.8148 34 34:33.8 101.5158 81.2303 80.1609 75.2761 73.8305 35 34:34.8 101.479 81.2523 80.1933 75.2673 73.8571 36 34:35.8 101.482 81.2464 80.2462 75.251 73.8578 37 34:36.8 101.5056 81.2496 80.2773 75.2651 73.8645 38 34:37.8 101.5302 81.2948 80.3043 75.3313 73.9072 39 34:38.8 101.5095 81.2704 80.3017 75.3606 73.8761 40 34:39.8 101.5045 81.229 80.2656 75.3935 73.8692 41 34:40.8 101.5005 81.1903 80.2336 75.4043 73.8826 42 34:41.8 101.5395 81.1236 80.1974 75.3781 73.8448
35
43 34:42.8 101.5392 81.0844 80.1378 75.3629 73.7949 44 34:43.8 101.5735 81.0445 80.1298 75.3528 73.8517 45 34:44.8 101.5802 80.989 80.1577 75.3092 73.8336 46 34:45.8 101.5983 81.0278 80.1289 75.3248 73.8893 47 34:46.8 101.5651 81.0766 80.1777 75.323 73.9379 48 34:47.8 101.5886 81.1703 80.1965 75.3306 73.9542 49 34:48.8 101.6032 81.1133 80.2231 75.398 73.9428 50 34:49.8 101.5971 81.1269 80.2253 75.3586 73.9938 51 34:50.8 101.5881 81.139 80.2522 75.3729 73.9757 52 34:51.8 101.6075 81.1762 80.254 75.375 74.0285 53 34:52.8 101.6005 81.1869 80.2766 75.3711 73.9918 54 34:53.8 101.6343 81.235 80.3003 75.4005 73.9835 55 34:54.8 101.6251 81.263 80.3229 75.4383 74.0086 56 34:55.8 101.6337 81.2993 80.3319 75.4094 74.0225 57 34:56.8 101.6395 81.2841 80.3428 75.4687 73.9629 58 34:57.8 101.6569 81.2867 80.3352 75.5173 73.9495 59 34:58.8 101.647 81.2364 80.2934 75.526 74.0507 60 34:59.8 101.6285 81.1979 80.2683 75.4875 74.009 61 35:00.8 101.6463 81.1972 80.2634 75.4448 74.0348 62 35:01.8 101.7222 81.1712 80.2717 75.4336 74.0764 63 35:02.8 101.6941 81.302 80.3099 75.4316 74.1234 64 35:03.8 101.7011 81.3716 80.3663 75.4273 74.0903 65 35:04.8 101.6869 81.4298 80.4241 75.4949 74.0596 66 35:05.8 101.7132 81.4403 80.4803 75.5139 74.0918 67 35:06.8 101.697 81.4499 80.4339 75.5287 74.1021 68 35:07.8 101.7315 81.4217 80.4089 75.5499 74.0849 69 35:08.8 101.6278 81.3937 80.4653 75.5584 74.0234 70 35:09.8 101.7313 81.3761 80.4505 75.5757 74.112 71 35:10.8 101.7827 81.3371 80.4572 75.577 74.1823 72 35:11.8 101.7786 81.2988 80.457 75.5942 74.1805 73 35:12.8 101.7752 81.2959 80.4324 75.5714 74.2085 74 35:13.8 101.7646 81.3107 80.4359 75.5327 74.2396 75 35:14.8 101.8234 81.3085 80.4377 75.5284 74.2534 76 35:15.8 101.7946 81.3756 80.4718 75.5228 74.2434 77 35:16.8 101.7563 81.4528 80.4496 75.5535 74.3053 78 35:17.8 101.7401 81.5204 80.5689 75.5976 74.3246 79 35:18.8 101.7527 81.5339 80.5673 75.6562 74.3382 80 35:19.8 101.796 81.5713 80.5539 75.6564 74.2677 81 35:20.8 101.8135 81.5751 80.6081 75.698 74.3095 82 35:21.8 101.8068 81.6189 80.6161 75.7139 74.3359 83 35:22.8 101.8122 81.6057 80.63 75.7477 74.3695 84 35:23.8 101.8246 81.6592 80.6461 75.7421 74.3679 85 35:24.8 101.8298 81.6924 80.6479 75.7332 74.4102 86 35:25.8 101.8014 81.773 80.7195 75.7432 74.4601 87 35:26.8 101.834 81.858 80.7786 75.718 74.4351 88 35:27.8 101.8257 81.9032 80.8603 75.8336 74.4422 89 35:28.8 101.8395 81.858 80.8666 75.8898 74.397 90 35:29.8 101.8814 81.8506 80.837 75.9106 74.4794 91 35:30.8 101.8762 81.839 80.8346 75.886 74.472 92 35:31.8 101.8298 81.815 80.8117 75.8717 74.4557 93 35:32.8 101.8169 81.7683 80.7782 75.8822 74.4488 94 35:33.8 101.8703 81.7374 80.7339 75.905 74.4559 95 35:34.8 101.8895 81.7239 80.7182 75.8614 74.436 96 35:35.8 101.8818 81.7709 80.7433 75.7927 74.4579 97 35:36.8 101.8721 81.8247 80.7621 75.8059 74.4808 98 35:37.8 101.8582 81.8441 80.8133 75.8632 74.4566 99 35:38.8 101.8568 81.8943 80.8617 75.8211 74.5933 100 35:39.8 101.8701 81.9057 80.8449 75.9012 74.5246 101 35:40.8 101.8602 81.9312 80.8664 75.9596 74.5219 102 35:41.8 101.9418 81.8952 80.8073 75.9641 74.5161 103 35:42.8 101.9298 81.8345 80.799 75.9737 74.4754 104 35:43.8 101.906 81.7745 80.7634 75.92 74.524 105 35:44.8 101.9107 81.7219 80.7793 75.8804 74.5392 106 35:45.8 101.9188 81.7768 80.7912 75.8652 74.538 107 35:46.8 101.9386 81.7947 80.837 75.9384 74.5372 108 35:47.8 101.9468 81.8249 80.867 75.924 74.5864 109 35:48.8 101.9359 81.8791 80.8771 75.867 74.6721 110 35:49.8 101.9265 81.9503 80.9505 75.9046 74.5488 111 35:50.8 101.9697 81.9885 80.9331 75.9252 74.6213
36
Table A.3: Sample of raw data from one of low pressure condensation experiments at a steady state
Date/Time HC TC1 TC2 TC3 44:56.7 21.6551 12.6415 12.5679 12.5467 45:01.8 21.6529 12.6279 12.5753 12.5519 45:07.0 21.6597 12.6286 12.5852 12.5522 45:12.1 21.6528 12.6489 12.5787 12.558 45:17.2 21.656 12.6292 12.5856 12.5483 45:22.3 21.6575 12.6359 12.5487 12.5275 45:27.5 21.6481 12.6273 12.5781 12.5535 45:32.6 21.6645 12.6307 12.5707 12.5435 45:37.7 21.6756 12.6452 12.5678 12.5527 45:42.9 21.679 12.6483 12.5933 12.556 45:48.0 21.6568 12.643 12.5901 12.5577 45:53.1 21.6686 12.6502 12.5815 12.5494 45:58.2 21.693 12.6579 12.5873 12.5474 46:03.4 21.6747 12.6475 12.5912 12.5621 46:08.5 21.6798 12.642 12.6057 12.5613 46:13.6 21.6658 12.6611 12.5873 12.5595 46:18.7 21.6706 12.6392 12.5857 12.5624 46:23.9 21.6625 12.64 12.5886 12.5474 46:29.0 21.6601 12.6264 12.5819 12.5397 46:34.1 21.646 12.6413 12.5803 12.5438 46:39.3 21.6663 12.6489 12.5923 12.555 46:44.4 21.6686 12.6444 12.5808 12.5497 46:49.5 21.6819 12.649 12.5932 12.5556 46:54.6 21.6695 12.6499 12.5856 12.5593 46:59.8 21.6798 12.6286 12.5822 12.5615 47:04.9 21.6705 12.6641 12.5882 12.5614 47:10.0 21.6711 12.656 12.6031 12.5691 47:15.2 21.6744 12.6405 12.5969 12.551 47:20.3 21.6714 12.6635 12.6012 12.5852 47:25.4 21.6702 12.6577 12.5982 12.5776 47:30.5 21.6783 12.6449 12.5836 12.5733 47:35.7 21.6869 12.6589 12.6005 12.5614 47:40.8 21.6874 12.6602 12.5874 12.5641 47:45.9 21.6615 12.6569 12.5923 12.5727 47:51.1 21.6721 12.6676 12.6119 12.5647 47:56.2 21.6828 12.6767 12.6088 12.5788 48:01.3 21.6909 12.6647 12.5976 12.5594 48:06.4 21.6877 12.669 12.5844 12.5768 48:11.6 21.666 12.6499 12.6199 12.5697 48:16.7 21.6628 12.6513 12.6002 12.5617 48:21.8 21.6636 12.6704 12.5866 12.5625 48:27.0 21.6668 12.6483 12.6038 12.5646 48:32.1 21.6483 12.649 12.6173 12.5661 48:37.2 21.67 12.6509 12.6084 12.5616 48:42.3 21.6591 12.6574 12.5971 12.5747 48:47.5 21.6728 12.6477 12.6131 12.5803 48:52.6 21.6716 12.6654 12.5987 12.558 48:57.7 21.6607 12.6553 12.5854 12.5692 49:02.9 21.6628 12.6537 12.5982 12.5589 49:08.0 21.6796 12.647 12.5948 12.5461 49:13.1 21.659 12.6436 12.5957 12.5565 49:18.2 21.6592 12.6553 12.5979 12.5453 49:23.4 21.6747 12.6542 12.6194 12.5556 49:28.5 21.6747 12.6426 12.5992 12.5772 49:33.6 21.6756 12.6503 12.5828 12.5858 49:38.7 21.663 12.6556 12.5965 12.5535 49:43.9 21.6563 12.6462 12.5784 12.5523 49:49.0 21.667 12.6449 12.5635 12.5452 49:54.1 21.6737 12.6644 12.5818 12.5494 49:59.3 21.6567 12.6599 12.5962 12.5583 50:04.4 21.6799 12.6404 12.5966 12.562 50:09.5 21.6758 12.6696 12.5877 12.5465 50:14.6 21.6755 12.6632 12.6039 12.5648 50:19.8 21.6642 12.656 12.5986 12.5526 50:24.9 21.6534 12.6534 12.5873 12.5528 50:30.0 21.6748 12.6388 12.6021 12.5458 50:35.2 21.6615 12.6489 12.5926 12.569 50:40.3 21.6766 12.6624 12.5955 12.569 50:45.4 21.6781 12.6785 12.5857 12.5618 50:50.5 21.6815 12.6558 12.5945 12.5699 50:55.7 21.6737 12.6513 12.5908 12.5622 51:00.8 21.6574 12.6455 12.5866 12.562 51:05.9 21.6603 12.6557 12.5787 12.5709 51:11.1 21.6517 12.6655 12.6001 12.5703 51:16.2 21.6672 12.6469 12.6042 12.5706
37
51:21.3 21.6595 12.6607 12.6063 12.5681 51:26.4 21.6742 12.6597 12.5984 12.5728 51:31.6 21.6581 12.6499 12.6151 12.5581 51:36.7 21.6875 12.6595 12.5993 12.5714 51:41.8 21.6725 12.6706 12.6104 12.574 51:47.0 21.6493 12.6642 12.6131 12.5684 51:52.1 21.663 12.6451 12.6118 12.5658 51:57.2 21.657 12.6477 12.5959 12.5741 52:02.3 21.6553 12.6532 12.5995 12.5714 52:07.5 21.6511 12.649 12.6114 12.5663 52:12.6 21.6631 12.6631 12.6059 12.5714 52:17.7 21.6519 12.6601 12.6027 12.5602 52:22.8 21.652 12.656 12.5959 12.58 52:28.0 21.6575 12.6657 12.6063 12.5753 52:33.1 21.6471 12.6659 12.593 12.5804 52:38.2 21.6539 12.6677 12.595 12.56 52:43.4 21.6604 12.6632 12.609 12.5656 52:48.5 21.6407 12.6505 12.6017 12.5704 52:53.6 21.6642 12.6438 12.6046 12.5661 52:58.7 21.6679 12.6471 12.5793 12.5575 53:03.9 21.6596 12.6571 12.6082 12.5583 53:09.0 21.6556 12.6696 12.5874 12.5669 53:14.1 21.6787 12.6638 12.5956 12.562 53:19.3 21.6647 12.6592 12.601 12.5725 53:24.4 21.6724 12.654 12.6171 12.5686 53:29.5 21.6636 12.6512 12.5912 12.5554 53:34.6 21.6565 12.6658 12.5974 12.5717 53:39.8 21.676 12.6563 12.603 12.5851 53:44.9 21.6874 12.6651 12.6114 12.5883 53:50.0 21.6776 12.6792 12.617 12.5891 53:55.2 21.6767 12.6638 12.6094 12.577 54:00.3 21.6674 12.6701 12.6001 12.5769 54:05.4 21.6672 12.6591 12.6162 12.5774 54:10.5 21.6667 12.675 12.6012 12.5774 54:15.7 21.6582 12.6564 12.5945 12.5718 54:20.8 21.665 12.6523 12.5924 12.5664 54:25.9 21.6612 12.6469 12.5834 12.5704 54:31.1 21.6752 12.6609 12.5837 12.5619 54:36.2 21.6732 12.6551 12.5897 12.5537 54:41.3 21.6656 12.644 12.5993 12.565 54:46.4 21.6698 12.6409 12.5839 12.5544 54:51.6 21.6797 12.6471 12.6078 12.58 54:56.7 21.6643 12.6679 12.5902 12.5639 55:01.8 21.6833 12.6709 12.6068 12.5788 55:07.0 21.6717 12.6545 12.6201 12.5921 55:12.1 21.6683 12.668 12.5931 12.5633 55:17.2 21.6676 12.6463 12.5849 12.5538 55:22.3 21.6689 12.664 12.5969 12.5637 55:27.5 21.6583 12.6541 12.5991 12.565 55:32.6 21.6787 12.6569 12.5975 12.5553 55:37.7 21.6574 12.6498 12.6073 12.5717 55:42.8 21.6659 12.646 12.5909 12.5622 55:48.0 21.6721 12.6711 12.5913 12.566 55:53.1 21.644 12.6475 12.6152 12.5657 55:58.2 21.6566 12.6668 12.6038 12.5697 56:03.4 21.6621 12.6702 12.5999 12.5798 56:08.5 21.6799 12.6749 12.6073 12.5765 56:13.6 21.6677 12.6628 12.6076 12.5825 56:18.7 21.6822 12.6478 12.6006 12.5784 56:23.9 21.671 12.67 12.6139 12.5529 56:29.0 21.6626 12.656 12.6066 12.563 56:34.1 21.6537 12.6787 12.6006 12.5837 56:39.3 21.655 12.6517 12.5997 12.566 56:44.4 21.6687 12.6711 12.6019 12.5747 56:49.5 21.6772 12.6595 12.5984 12.5732 56:54.6 21.6681 12.6578 12.6123 12.5577
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