characterization of greywater heat implementation for
TRANSCRIPT
Characterization of greywater heat
exchangers and the potential of implementation for energy savings
Värmeväxlare för spillvatten –
karakterisering och energibesparingsmöjligheter
JOSE DANIEL GARCIA
MSc-Degree Thesis No.: TRITA-IES 2016:01
Division of Building Service and Energy Systems
Department of Civil and Architectural Engineering
August, 2016
Kungliga Tekniska Högskolan
SE – 100 44 Stockholm
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ABSTRACT
Buildings account for up to 32% of the total energy use in different countries.
Directives from the European Union have pointed out the importance of increasing
energy efficiency in buildings. New regulation in countries like Sweden establishes
that new buildings should fulfill regulations of Nearly Zero Energy Buildings (NZEB),
opening an opportunity for new technologies to achieve these goals. Almost 80-90%
of the energy in domestic hot water use is wasted from different applications with
almost no use and with a lot of potential energy to be recovered.
The present work studied the characteristics of greywater heat exchanger as a
solution to recuperate heat from greywater to increase efficiency in buildings. This
study explored the fluid mechanics involved in the vertical greywater heat
exchangers, analyzing the falling film effect present in drain pipes and the effects of
the secondary flow generated in the external helical coil. A heat transfer model from
a theoretical approach was proposed and validated. In addition, this study explored
the different variables influencing the economic feasibility of the technology and an
economic analysis was performed. A theoretical comparison between a greywater
heat exchanger application and a reference case without it was evaluated
highlighting the importance of all the variables involved in the potential of
implementation of the technology. The technology shows big potential in households
with high water consumptions, especially with electric boilers.
Keywords: Wastewater heat recovery, greywater heat exchanger, domestic hot
water, energy savings, energy efficiency, residential households, NZEB, heat
transfer modelling, feasibility study, potential of implementation, falling film effect,
flow helical coil.
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TABLE OF CONTENT
1 INTRODUCTION .............................................................................................. 8
1.1 Heat generation in buildings ....................................................................... 8
1.2 Greywater heat recovery systems (GHRS) ................................................ 9
1.3 Types of Greywater Heat Exchangers...................................................... 10
1.3.1 Vertical heat exchangers ................................................................... 11
1.3.2 Horizontal heat exchangers ............................................................... 11
1.3.3 Shower heat exchangers ................................................................... 11
1.4 Project goals ............................................................................................ 12
1.5 Project boundaries ................................................................................... 12
2 LITERATURE REVIEW .................................................................................. 13
3 FLUID MECHANICS ANALYSIS .................................................................... 15
3.1 Falling film effect ...................................................................................... 15
3.1.1 Falling Film Reynolds ........................................................................ 16
3.1.2 Falling Film Heat Transfer Coefficient ................................................ 17
3.2 Flow through a helical coil ........................................................................ 18
3.2.1 Helical Coil Reynolds Number ........................................................... 18
3.2.2 Dean & Nusselt numbers ................................................................... 20
3.2.3 Heat Transfer coefficient of helical coils ............................................ 22
4 HEAT TRANSFER MODEL ............................................................................ 23
4.1 Inputs of the model ................................................................................... 24
4.2 Thermodynamic properties of the fluid ..................................................... 24
4.3 Thermal Capacities .................................................................................. 26
4.4 Convection Falling Film – R1 ................................................................... 26
4.5 Conduction Drain Pipe – R2 ..................................................................... 26
4.6 Contact Resistance – R3 .......................................................................... 27
4.7 Conduction Coil Pipe – R4 ....................................................................... 28
4.8 Convection Helical Coil – R5 .................................................................... 28
4.9 NTU-Method ............................................................................................. 28
5 MODEL VALIDATION .................................................................................... 30
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5.1 Nusselt Correlation ................................................................................... 30
5.2 Standard Condition................................................................................... 31
5.3 Different Flow ........................................................................................... 32
5.4 Different dimensions................................................................................. 34
6 MODEL SIMULATIONS ................................................................................. 36
6.1 Dimensions .............................................................................................. 37
6.2 Number of coils ........................................................................................ 38
6.3 Outlet temperatures.................................................................................. 39
7 POTENTIAL OF IMPLEMENTATION ............................................................ 40
7.1 Water Usage ............................................................................................ 40
7.2 Persons per Household ............................................................................ 43
7.3 Energy price ............................................................................................. 44
7.4 GHRS Unit dimensions & Investment ....................................................... 45
8 ECONOMIC ANALYSIS ................................................................................. 46
8.1 Reference Case ....................................................................................... 46
8.2 GHRS Case ............................................................................................. 47
8.3 Net Present Value .................................................................................... 47
8.4 Discounted Payback Period ..................................................................... 48
8.5 N-number of households – Monte Carlo Simulation ................................. 50
8.6 Emission savings ..................................................................................... 51
8.7 District Heating ......................................................................................... 52
8.8 GHE for multi-dwelling households .......................................................... 54
9 CONCLUSIONS ............................................................................................. 56
10 FUTURE RESEARCH ................................................................................. 58
11 REFERENCES ............................................................................................ 59
APPENDIX A. Heat transfer model ....................................................................... 62
APPENDIX B. Model Validation ............................................................................ 65
APPENDIX C. Model simulations .......................................................................... 68
APPENDIX D. Potential of Implementation ........................................................... 70
APPENDIX E. Screenshots GUI MATLAB ............................................................ 72
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TABLE OF FIGURES
Figure 1.1 Energy used for heating and hot water in Sweden 2013. ....................... 9
Figure 1.2 Shape of a vertical Greywater Heat Exchanger (GHE). ....................... 10
Figure 3.1 Aspect simulation of a full wetting falling film in a GHRS. .................... 15
Figure 3.2 Falling film formation in vertical oriented GHRS (Left) and fluid
accumulation in horizontal oriented GHRS (right). ................................................ 16
Figure 3.3 Velocity contours [m/s] at different planes along the helical coil. .......... 18
Figure 4.1 Thermal resistors of the heat transfer model. ....................................... 23
Figure 4.2 Top view section with the different geometric diameter of the GHRS (Left)
and Different temperatures inside GHRS (Right). ................................................. 24
Figure 4.3 Heat transfer through contact plane between two solid surfaces. ........ 27
Figure 5.1 Cumulative histogram frequencies of the Heat Recovery Error (Top) and
effectiveness Error (Bottom) for different Nusselt Correlations. ............................. 30
Figure 5.2 Error frequency histogram of the heat transfer model. ......................... 32
Figure 5.3 Average error and standard deviation under different flows. ................ 34
Figure 5.4 Average error of the model under different dimensions. ....................... 34
Figure 6.1 Screenshot from the MATLAB GUI of the model. ................................. 36
Figure 6.2 Effectiveness dependency on GHE dimensions. .................................. 38
Figure 6.3 Effectiveness performance for different number of coils. ...................... 38
Figure 6.4 Simulation for outlet temperatures........................................................ 39
Figure 7.1 Water usage pattern during shower. .................................................... 42
Figure 7.2 Distribution of households in Sweden 2015. ........................................ 43
Figure 7.3. Energy prices for the residential and services sector [öre2013/kWh] ..... 44
Figure 7.4 Electricity price for household consumers 2015 [€/kWh] ...................... 45
Figure 8.1 DPP Analysis for two GHRS under different condition of shower time and
flow. ....................................................................................................................... 49
Figure 8.2 Distributions of DPP for n-number of household with 4 inhabitants. ..... 50
Figure 8.3 Distributions of DPP for n-number of household with 3 inhabitants. ..... 51
Figure 8.4 Graphic of gr CO2 per kWh in Europe - Electricity production 2009. .... 52
Figure 8.5 Comparison between electricity and district. ........................................ 53
Figure 8.6 Comparison between electricity and district heating for multi-dwelling
buildings. ............................................................................................................... 55
Figure D.1. Average person per Household in Europe 2014. ................................ 71
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TABLE OF TABLES
Table 3-1 Minimum flow required to fulfill the range of McAdams correlation. ...... 17
Table 3-2 Critical flow for the transition to Turbulent Regime. ............................... 19
Table 5-1 Table of Errors for GHRS Units with 0.08 m of nominal diameter. ........ 31
Table 5-2 Table of Error with different flows. ......................................................... 33
Table 5-3 Histogram table of validation process with different flows. .................... 33
Table 6-1 Simulation results for different GHE with different dimensions. ............. 37
Table 7-1 Patterns of water use by households in England and Wales, Finland and
Switzerland. ........................................................................................................... 41
Table 7-2 Frequency, Duration, and Intensity for Several Types and Subtypes of
End-Uses in the Netherlands. ................................................................................ 41
Table 7-3 Persons per Households in Sweden 2015. ........................................... 43
Table 8-1 Conditions for the comparison between electricity and district heating. 52
Table 8-2 Conditions for the analysis with multi-dwelling buildings. ...................... 54
Table A-1 Thermodynamic properties of water...................................................... 63
Table A-2 Table of thermal resistors. .................................................................... 64
Table B-1 Table of the error distribution for different Nusselt correlations. ............ 65
Table B-2 Table of Errors for different GHRS with different Nusselt Correlations. 66
Table B-3 Table of errors under different flows. .................................................... 67
Table C-1 Full table of simulation results for different GHE. .................................. 69
Table D-1 Full table of persons per household in Sweden 2015. .......................... 70
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NOMENCLATURE
µ Viscosity [Pa*s] Subscripts
A Area 0 Initial state
b Inner perimeter of a pipe [m] avg Average
C Thermal capacity coil Coil Side
Cp Specific Heat cold Cold inlet
Cr Thermal capacity relation copper Copper
d Diameter coil tube [m] drain Drain Side
D Diameter [m] em emissions
De Dean Number ff falling film
Dh Hydraulic diameter [m] hot Hot inlet
DPP Discounted Payback Period [Years] in Inlet
E Energy kWh per kWh
g Gravity on Earth L Laminar regime
h Heat transfer coefficient [W/m^2*°C] min Minimum
k Thermal conductivity constant [W/(m*°C] mix mixture
L Pipe Length [m] out Outlet
LPM Liters per minute ref Reference value
m Mass flow [Kg/s] shower Shower usage
ND Nominal Diameter [m] straight Straight pipe
NrCoils Number of Coils T Turbulent regime
NTU Number of transfer units theo Theoretical
Nu Nusselt Number tube coil tube
Pers Number of persons w water
Pr Prandtl number
q Heat exchanged [W]
R Resistor
r radius
Re Reynolds number
Savings Savings
T Temperature [°C]
t Time [s]
U Overall heat transfer coefficient [W/(m^2*°C]
v Volumetric flow [m^3/s]
ᵞ Cooling or Heating constant
ε Effectiveness [%]
η Efficiency [%]
ρ Density [kg/m^3]
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1 INTRODUCTION
Buildings account for up to 32% of the total energy use in the world. Different studies
have tried to calculate the impact of the built environment on the daily consumptions.
The influence differs from country to country, but it establishes a clear fact of the
importance of the buildings in the resource consumption of a nation.
In Canada, residential usage of energy and water accounts for 17% of the whole
consumption of the country (Leidl & David Lubitz 2009). The domestic sector in the
UK use 23% of the total consumption while in Hong Kong, it is determined to be 17%
(McNabola & Shields 2013). Households are responsible for almost 32% of the
energy consumed in Poland (Słyś & Kordana 2014).
The energy is used in several applications in residential buildings. The major
component of the consumption is directly linked to space heating, space cooling,
and water heating systems. Studies state that 51.9% of the energy used for these
applications, represent 55.7% of the costs and are responsible for 50.4% of the
greenhouse gas (GHG) emissions of the sector (Ni et al. 2012).
People are not aware of the fact that the energy consumption in the sector is high.
Just in Sweden, the Swedish Energy Agency (2014) estimates that in 2012, the
domestic household sector utilized over 46 TWh of district heating. It is important to
emphasize that 1 TWh is a lot of energy, putting it into perspective; 1 MWh can heat
a small house in Sweden for a couple of weeks. Despite that from the exergy point
of view, it is different to have electrical energy and thermal energy. It can be said
that all the Swedish Railways, subways and trams could be operated for 5 months
with just 1 TWh as an order of magnitude (Vattenfall 2015).
1.1 Heat generation in buildings
The previous statement says that space heating and water heating are the major
components of the consumptions in buildings. More studies support this statement
showing that, for example, in Canada, 57% of the energy is used for space heating
and 24% for water heating (representing almost 4% of the national energy demand).
The annual costs per household for 28 GJ were estimated at 2615 SEK2014 ($CAN
400) for gas water heaters and 4572 SEK2014 ($CAN 700) for electric one (Leidl &
David Lubitz 2009). For the UK, the percentage is almost the same accounting 26%
of the domestic energy consumption in water heating (McNabola & Shields 2013).
Different technologies have been applied to meet these demands: gas, oil, coal,
electric boilers, district heating, and others. In Sweden 2013, 51% of the energy in
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the residential sector came from electricity, being the most common form of energy
used for one and two dwelling buildings. District heating accounts for 33% and it is
more commonly used in multi-dwelling buildings and nonresidential premises as
depicted in Figure 1.1 (Swedish Energy Agency 2015). Alternatives for water heating
like the solar collectors have been increasing in importance. Studies have
demonstrated efficiencies of almost 38% and payback time of 9 years for this type
of installation depending on the location (Wong et al. 2010). In the US, gas boilers
dominate water heating share with 52.8%, just followed by electric boiler with a share
of 38.8% of the US market (Ni et al. 2012).
Figure 1.1 Energy used for heating and hot water in Sweden 2013.
Source: (Swedish Energy Agency 2015)
This shows a clear example that high-quality energy such as electricity, has been
used for applications that do not require high-quality of energy. It is also clear that
water heating is also related to the production of GHG. The reduction of energy
consumption in households is one of the main areas of energy conservation
programs (Wong et al. 2010). The increasing awareness on how to treat high-quality
energy and to reduce GHG have made that: saving measures that were not
previously taken into account be considered as an actual solution rising on the
market share. This is the case for Greywater Heat Recovery Systems (GHRS).
1.2 Greywater heat recovery systems (GHRS)
Much of the hot water used for domestic activities is wasted from different
applications and with a lot of potential energy to be recovered. In dishwashing
machines; the water is supplied at almost 80 °C for the sanitation cycle and it is
subsequently discharged at just a bit lower temperature. In washing machines, water
arrives at approximately 60 °C and discharges at a similar temperature. For typical
showers, the hot water is provided at 40 °C and it is discharged at around 30-38 °C
depending on the temperature of the surroundings (McNabola & Shields 2013).
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When the greywater is sent down the drain, the water still contains 80% to 90% of
the original thermal energy (Dieckmann 2012). These facts reconfirmed the energy
inefficiencies currently found in a typical household and highlight the opportunity of
systems such as GHRS.
Figure 1.2 Shape of a vertical Greywater Heat Exchanger (GHE).
A heat recovery system is basically a heat exchanger with two streams where on
one side, a “hot” fluid flows and exchanges heat with a cold fluid that comes in the
other stream. This concept has been applied for several years in building industry
for ventilation systems, recovering the waste heat from the exhaust air and transfer
it to fresh air. This concept applied for greywater is more recent and it is up until now
that is gaining recognition and penetration of the marketplace that until now, remains
low (Leidl & David Lubitz 2009).
The concept behind the GHRS is to preheat the water before it enters the hot water
heater to reduce the amount of energy required to heat it up to the control
temperature. As a description of the device, a conventional drain pipe is replaced by
a copper pipe with a secondary pipe coiled around the first one. Hot drain water is
drained through the inner pipe by gravity while fresh water flows through the
secondary pipe exchanging heat between them.
1.3 Types of Greywater Heat Exchangers
In the market, different technologies of greywater heat exchangers exist. The first
classification is in two types: Storage and on-demand. Storage systems are
submerged copper exchangers in a fresh water tank. The drain water flows through
the copper exchanger heating up the water in the tank. On-demand devices use the
drain water that flows down the inner pipe and the incoming fresh water that flows
11
through an external pipe (Dieckmann 2012). From the on-demand devices, three
types can be studied and the temperature efficiency can be defined as:
𝜂𝑇 =𝑇𝑝𝑟𝑒ℎ𝑒𝑎𝑡𝑒𝑑 − 𝑇𝑐𝑜𝑙𝑑𝑇𝑤𝑎𝑠𝑡𝑒𝑤𝑎𝑡𝑒𝑟 − 𝑇𝐶𝑜𝑙𝑑
(1.1)
Where Tpreheated is the preheated fresh water leaving the greywater heat exchange,
Tcold is the temperature of fresh water entering the GHE and Twastewater is the hot drain
water.
1.3.1 Vertical heat exchangers
The first one is known as Vertical heat exchangers. This ones are basically a vertical
pipe that is installed in the vertical sewer stack producing a falling film effect on the
drain side. A helical coil is located around the drain pipe in which the fresh water
flows. The heat is exchanged between the inner pipe and the surrounding helical coil
in a process that will be explained further in chapter 3 of the present study. In the
market, several dimensions of heat exchangers exist with different nominal
diameters, lengths and number of coils (ReneWABILITY 2016). The effectiveness of
heat transfer of these devices varies for length, diameters, the number of coils and
other. Values in the range from 30-70% can be achieved (Collins et al. 2013). The
order of magnitude for the length of the vertical heat exchangers is around 0.9-1.5
meters for residential applications (Leidl & David Lubitz 2009).
1.3.2 Horizontal heat exchangers
Horizontal heat exchangers are installed in the collecting sewer pipes of all the
outgoing water of a building. Freshwater flows through a pipe in contact with the
drain pipe. The system is insulated to ensure that most of the heat goes to preheat
the incoming cold water. These devices usually have low temperatures which require
large heat exchanger to compensate this fact. The average efficiency of these
systems is estimated around 20% (Korpar Malmström 2015).
1.3.3 Shower heat exchangers
Shower heat exchangers are units located in the discharge of the shower. The floor
of the shower is changed for a heat exchanger configuration in which the incoming
cold water is preheated with the shower water flowing through the drain. Different
configuration and specification are available on the market. Effectiveness values
around 45% can be achieved according to McNabola & Shields (2013).
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1.4 Project goals
The main objectives of the present master’s thesis are to:
Provide a better understanding of the fluid mechanics involved on the Vertical
greywater heat exchangers
Establish the basis of a heat transfer model that represents the physics of the
vertical greywater heat exchangers.
Analyze the potential of the technology for domestic households.
Study a methodology to perform an economic potential analysis of the
technology for a single household and multi-dwelling housing.
1.5 Project boundaries
The present project will focus on the analysis of vertically oriented greywater heat
exchangers. Two main fields will be subject to study: the heat transfer modeling of
the GHRS units and the potential implementation of the technology in residential
households from an economic perspective.
This heat transfer model will take a look at the available literature to describe the
phenomena of the vertical heat exchangers and a heat transfer model will be
proposed. A review on falling film effects and the secondary flow originated on the
flow through helical coils will be explained.
For the potential of implementation, this work will take a general look at the topic
from an economic perspective. Several conditions influencing this potential will be
explained. The economic results are proposed to evaluate the potential from a
general point of view and to understand the order of magnitude for the technology
and not as a market study.
This project will focus on the implementation on single-dwelling households with
electric boilers and the implication of low energy prices as it is the case with district
heating. For multi-dwelling housing, a short analysis on the potential of the
technology will be performed.
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2 LITERATURE REVIEW
Greywater heat recovery system is a growing technology that has shown several
cost-efficient benefits to increase the energy efficiency. The literature on the field
has become available and in this chapter, it is intended to describe some of the most
relevant articles/thesis/reports available that were important for the development of
the present thesis. As stated before, the present thesis studies two main fields: the
heat transfer modeling of the GHRS units and the potential implementation of the
technology in residential households. To perform this, literature in both fields was
required.
Manouchehri (2015) focused on experimental correlation to simulate GHRS
performance in buildings. In addition, a heat transfer model was presented to predict
the performance of GHRS that operates under equal flow conditions and explains
concepts of the technology. This model was used as a base for the methodology
applied to the present project. Collins et al. (2013) executed tests under the
Canadian Standard CSA B55.1 to achieve characteristic effectiveness curves of
different GHRS units at different equal flow conditions. Zaloum et al. (2007) present
a detailed explanation of the arrangement and test procedure for eight units to obtain
their characteristic curves based on experimental data.
On the fluid mechanics of the GHRS units, a lot of works have been pointing out the
falling film condition and the secondary flow generated on helical coils. The falling
film effect is specially developed by Prost et al. (2006). The flow conditions inside a
helical coil have been the subject of study for numerous authors (Naphon &
Wongwises 2006; Collins et al. 2013; Wallin & Claesson 2014; Austen & Soliman
1988; Jayakumar et al. 2008; Janssen & Hoogendoorn 1978; Kozo & Yoshiyuki
1988; Rogers & Mayhew 1964).
Daniel Słyś and Sabina Kordana (2014) performed a financial analysis of the
implementation of GHRS in residential households. It presented a calculation model
that allows to estimate the Payback time of units under the influence of different
usage parameters.
The water usage pattern was studied by different authors (Opitz et al. 1999; Lallana
et al. 2001; Athuraliya et al. 2012; Blokker et al. 2010). Athuraliya et al. (2012) and
Blokker et al. (2010) report the different water usage behavior and patterns of
residential households and how to simulate them for Australia and the Netherlands,
respectively.
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Additionally, several authors (Wong et al. 2010) (Ni et al. 2012) (McNabola & Shields
2013) (Leidl & David Lubitz 2009) (Dieckmann 2012) studied the impact of buildings
in the energy share and the potential of greywater to improve energy efficiency in
buildings.
Some of the findings and statement of these and other authors are going to be
developed further during the present work.
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3 FLUID MECHANICS ANALYSIS
Greywater heat exchangers (GHE) have mainly two streams, coil-side (cold water)
and drain-side (drain water), as previously explained in chapter 1. The fluid
mechanics of both streams is the subject of study in this section in order to
understand the process inside the system. The GHE are generally ruled by two flow
phenomena. The first one is known as falling film effect and it rules over the drain-
side of the unit. Second, the flow through a helical coil for the cold water that it is
going to be heated up. This chapter will make a review of some of the principles that
rule these effects to provide the reader with a deeper understanding of the theory of
greywater heat exchangers.
3.1 Falling film effect
The falling film effect is the development of a layer of fluid in the boundaries of a
plate or pipe. For the subject of study, vertical oriented GHE use the effect of the
falling film to form an annular film inside the pipe (Figure 3.1) by gravity and it is one
of the main characteristics of this kind of vertically oriented units.
Figure 3.1 Aspect simulation of a full wetting falling film in a GHRS. Source: (Author)
This effect has several characteristics that are valuable for the GHRS performance.
As a starting point, the falling film effect maximizes the contact area between the
falling fluid (water for this purpose) and the inside area of the copper pipe. This
maximization of surface represents an increase of the heat transfer surface area
16
resulting in bigger heat transfer rates compared to the performance of horizontally
oriented as shown in Figure 3.2. With the equation 3.1, it is clear that bigger Areas
(A) achieve higher transfer rates.
�� = ℎ ∗ 𝐴 ∗ (𝑇ℎ − 𝑇𝑐) (3.1)
Furthermore, falling film effect minimizes the thickness of the layer of fluid which heat
is conducted till the boundary of the pipe. Afterward, this heat is convected to the
inner wall of the pipe (Manouchehri 2015). This refers to the phenomena that in the
case of a completely filled pipe, the heat of the fluid at the center has to be
transferred to the boundary layer in order to be transferred to the pipe. Turning the
heat transfer mechanism less effective than with this thin layer of fluid at the annulus.
Figure 3.2 Falling film formation in vertical oriented GHRS (Left) and fluid accumulation in horizontal oriented GHRS (right).
Source: (Author)
3.1.1 Falling Film Reynolds
The Reynolds number is a dimensionless quantity that measures the ratio of inertial
forces to viscous forces in the fluid (3.2). At small Reynolds numbers, viscous forces
are strong enough to keep the fluid in the laminar regime but for large numbers the
inertial forces are leading the relationship, therefore it flows in a turbulent regime
(Cengel & Cimbala 2006).
𝑅𝑒 =𝐼𝑛𝑒𝑟𝑡𝑖𝑎𝑙 𝐹𝑜𝑟𝑐𝑒𝑠
𝑉𝑖𝑠𝑐𝑜𝑢𝑠 𝐹𝑜𝑟𝑐𝑒𝑠 (3.2)
To estimate when this transition will happen, the concept of critical Reynolds shows
up. Collins et al. (2013) used the correlation for falling films on the surface of vertical
plates of Incropera et al. (2007) for GHE where it is established that:
17
𝑅𝑒𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙𝑓𝑓 = 1800 (3.3)
𝑅𝑒𝑓𝑓 =4 ∗ mdrainµdrain ∗ b
(3.4)
Where b as the inner perimeter of the drain pipe.
3.1.2 Falling Film Heat Transfer Coefficient
Several correlations estimate the heat transfer coefficient at the falling film has been
developed by different authors. Prost et al. (2006) present a compilation of different
dimensionless heat transfer coefficient correlations. For the purpose of this work the
correlation of McAdams et al. (1940 Cited by Prost et al. 2006) on its non-
dimensionless form (3.5) is selected.
ℎ𝑓𝑓 = 0.01 ∗ 𝑅𝑒𝑑𝑟𝑎𝑖𝑛
13 ∗ 𝑃𝑟
𝑑𝑟𝑎𝑖𝑛
13 ∗ (
𝑘𝑑𝑟𝑎𝑖𝑛3 ∗ 𝑔 ∗ ρ𝑑𝑟𝑎𝑖𝑛
2
µ𝑑𝑟𝑎𝑖𝑛2 )
13
(3.5)
Where:
Redrain Reynolds number in the drain pipe
Prdrain Prandtl number
kdrain Thermal conductivity of the fluid [W/(m* °C)]
g Gravity [m/s^2]
ρdrain Fluid density [kg/m^3]
µdrain Dynamic viscosity [Pa*s]
The equation 3.5 was performed for water falling inside copper tubes and it is valid
for 1600 < Re < 50 000. For the different GHRS units available in the market, this
range works on their normal operation. The minimum volumetric flow required to
achieve this range is presented in table 3-1 for three different nominal diameters of
commercial GHE.
Nominal Diameter
[m]
V minimum [L/min]
0.05 3.21
0.08 5.24
0.10 6.61 Table 3-1 Minimum flow required to fulfill the range of McAdams correlation.
18
3.2 Flow through a helical coil
The second stream of study on the GHRS units it is the one through the outside coil.
Several authors (Naphon & Wongwises 2006; Collins et al. 2013; Wallin & Claesson
2014; Austen & Soliman 1988; Jayakumar et al. 2008; Janssen & Hoogendoorn
1978; Kozo & Yoshiyuki 1988; Rogers & Mayhew 1964) and many others have been
studied the phenomena of the flow through helical coils. A lot of information from the
experimental and theoretical side have been the subject of study. Nevertheless, it
still a complicated process and it is one of the bigger challenges for the study of
GHRS.
3.2.1 Helical Coil Reynolds Number
It is known that the centrifugal forces acting in the flow through helical coils generate
secondary flows (Kozo & Yoshiyuki 1988) (Janssen & Hoogendoorn 1978) (Austen
& Soliman 1988) as shown in figure 3.3. This fact increases the heat transfer
coefficient significantly in comparison with straight pipes. One of the main
consequences of the effect is that the transition to turbulent regime is achieved at
higher Reynolds number than in straight pipes (Collins et al. 2013) (Jayakumar et al.
2008).
Figure 3.3 Velocity contours [m/s] at different planes along the helical coil. Source: (Jayakumar et al. 2008)
In figure 3.3, the velocity contour alongside the helical coil is shown. At the inlet of
the coil, the velocity contour is homogenous and it does not present major
19
disturbances. This situation changes drastically inside the coil where due the effect
of the secondary flow, the velocity contour presents different values alongside the
helical coil.
Shah & Joshi (1987 cited by Collins et al. 2013) establish that the critical Reynolds
for helical coils is:
𝑅𝑒𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙𝑐𝑜𝑖𝑙 = 2300 ∗ (1 + (12 ∗ √
𝑑𝑡𝑢𝑏𝑒𝐷𝑐𝑜𝑖𝑙
)) (3.6)
Where dtube is the diameter of the tube and Dcoil is the diameter of the coil. This critical
Reynolds number varies from 10,000-13,000 for standardized tubes of 3/8” copper
Type L with a nominal diameter of GHRS from 0.05-0.1 [m]. Reynolds number can
be calculated with Incropera et al. (2007) for pipes where Dh_tube is the hydraulic
diameter of the tube.
𝑅𝑒𝑐𝑜𝑖𝑙 =4 ∗ ��𝑐𝑜𝑖𝑙
µ𝑐𝑜𝑖𝑙 ∗ 𝜋 ∗ 𝐷ℎ𝑡𝑢𝑏𝑒 (3.7)
Modern GHRS units use several tubes on the coil side to reduce the pressure drop
(Guo et al. 2001). The Table 3-2 shows clearly that these systems will most likely
operate under laminar flow, especially for GHRS units with 3 or more coils which are
the main focus systems of the present work.
Nominal Diameter GHRS = 0.1 [m]
Nominal Diameter GHRS = 0.08 [m]
Nominal Diameter GHRS = 0.05 [m]
Nr Coils
V critical [L/min]
V critical [L/s]
Nr
Coils V critical [L/min]
V critical [L/s]
Nr
Coils V critical [L/min]
V critical [L/s]
1 4.71 0.079 1 5.12 0.085 1 6.1 0.102
2 9.49 0.158 2 10.34 0.172 2 12.32 0.205
3 14.34 0.239 3 15.62 0.260 3 18.65 0.311
4 19.25 0.321 4 20.97 0.350 4 25.05 0.418
5 24.21 0.404 5 26.38 0.440 5 31.54 0.526
6 29.21 0.487 6 31.85 0.531 6 38.09 0.635
Table 3-2 Critical flow for the transition to Turbulent Regime.
From the present study, it can be concluded that units with 4 coils required more
than 19 liters per minute to reach the turbulent regime in the configuration with 0.1
meters of nominal diameter. It can be concluded that for this sort of heat exchangers,
20
they will always operate in the laminar regime under standard conditions. For units
with just 1 coil, the regime transition is easily achievable under the normal operation
conditions and the turbulent correlation must be applied.
3.2.2 Dean & Nusselt numbers
The secondary flow increases the heat transfer and in order to gain a better
understanding of the heat transfer and the hydrodynamics, the Dean & Nusselt
number should be studied. Firstly, the dimensionless characteristic known as Dean
Number is fundamentally important for this process. It can be defined as Janssen &
Hoogendoorn (1978) proposed:
𝐷𝑒 = 𝑅𝑒𝑐𝑜𝑖𝑙 ∗ 𝑠𝑞𝑟𝑡 (𝑑𝑡𝑢𝑏𝑒𝐷𝑐𝑜𝑖𝑙
) (3.8)
It is a number that relates the Reynolds number with the diameters of the geometry
of the coil, where Recoil is the Reynolds number, dtube the diameter of the tube and
Dcoil the diameter of the coil.
Secondly, the Nusselt number is a ratio of convective to conductive heat transfer at
the boundary layer of the fluid. It is equal to the dimensionless temperature gradient
at the surface layer and exposed a measure of the convection that occurs there
(Incropera et al. 2007).
In the literature, there are several different correlations for the Nusselt number in
laminar and/or turbulent regimes. For the purpose of the present work, these
correlations were evaluated in order to find out which relation displayed better results
for the GHRS units. This analysis will be developed further in chapter 5 during the
model validation. It is important to remark that these correlations are based on
cylindrical pipes that for the case of GHRS is not that common. For this reason, these
correlations are applied with the purpose to evaluate performance within an
academic approach; it is not meant to be used as design parameters.
3.2.2.1 Laminar
The correlation in equation 3.9 is from Manlapaz and Churchill (1980, cited by
Austen & Soliman 1988). This equation displayed significantly more accurate results
than the other correlations and for that reason, it was selected for the heat transfer
model of the GHRS. (To find out these results, refer to chapter 5).
21
𝑁𝑢𝐿 =
(
(
(
(48
11) +
(
5111
(1 + (1342
𝑃𝑟𝑐𝑜𝑖𝑙 ∗ 𝐷𝑒2))
2
)
)
3
+ 1.816 ∗
(
(
𝐷𝑒
1 + 1.15𝑃𝑟𝑐𝑜𝑖𝑙
)
32
)
)
)
13
(3.9)
The second correlation (3.10) is proposed by Kalb-Seader (1972, Cited by Elsayed
2011). This relation shows good performance during the model validation. In the end,
the model of Manlapaz and Churchill is used more often in literature, a point that was
taken into account in the merit order to select the correlation.
𝑁𝑢𝐿 = 0.913 ∗ 𝐷𝑒0.476 ∗ 𝑃𝑟𝑐𝑜𝑖𝑙
0.2 (3.10)
The third correlation (3.11) is proposed by Janssen & Hoogendoorn (1978):
𝑁𝑢𝐿 = 0.7 ∗ 𝑅𝑒𝑐𝑜𝑖𝑙
0.43 ∗ 𝑃𝑟𝑐𝑜𝑖𝑙
16 ∗ (
𝑑𝑡𝑢𝑏𝑒𝐷𝑐𝑜𝑖𝑙
)0.07
(3.11)
Finally, the correlation used by Manoucherhri (2015) on his theory calculations is the
one proposed by Dravid et al. (1971, cited by Manouchehri 2015).
𝑁𝑢𝐿 = (0.76 + (0.65 ∗ 𝑠𝑞𝑟𝑡(𝐷𝑒))) ∗ 𝑃𝑟𝑐𝑜𝑖𝑙0.175 (3.12)
3.2.2.2 Turbulent
Two correlations are shown in the present work for general knowledge purposes.
Due the limitation of the study, these correlations were not possible to validate the
model but, it is important to take them into account if the transition to turbulent regime
is reached, especially for GHRS with only one or two coils. These units were not
validated for the current model. For a more extensive analysis of the different
correlations available, it is recommended to read the work of Naphon & Wongwises
(2006).
𝑁𝑢𝑇 = 0.023 ∗ 𝑅𝑒𝑐𝑜𝑖𝑙
0.85 ∗ 𝑃𝑟𝑐𝑜𝑖𝑙0.4 ∗ (
𝑑𝑡𝑢𝑏𝑒𝐷𝑐𝑜𝑖𝑙
)0.1
(3.13)
(Rogers & Mayhew 1964)
22
𝑁𝑢𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 = 0.023 ∗ 𝑅𝑒𝑐𝑜𝑖𝑙
45 ∗ 𝑃𝑟𝑐𝑜𝑖𝑙
ᵞ
𝑁𝑢𝑇4 = 𝑁𝑢𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 ∗ (1 + 3.4 ∗ (𝑑𝑡𝑢𝑏𝑒𝐷𝑐𝑜𝑖𝑙
)) (3.14)
(Incropera et al. 2007)
Where ᵞ is 0.4 for heating and 0.3 for cooling processes.
3.2.3 Heat Transfer coefficient of helical coils
The heat transfer coefficient is shown in equation 3.15, where hcoil is the heat transfer
coefficient, Nu is the Nusselt number depending on the regime and the correlation
used, kcoil is the thermal conductivity of the fluid flowing through the coil and dtube is
the diameter of the tube.
ℎ𝑐𝑜𝑖𝑙 = 𝑁𝑢 ∗𝐾𝑐𝑜𝑖𝑙𝑑𝑡𝑢𝑏𝑒
(3.15)
23
4 HEAT TRANSFER MODEL
The heat transfer model is a starting point to predict the theoretical performance of
different GHRS units. The current model is based on the ε-NTU method from
Incropera et al. (2007) following some of the theory basis exposed by Manouchehri
(2015) and modified by the author of the present work. On this chapter, a heat
transfer methodology is proposed and the different steps of it are explained.
The ε-NTU method use ε as a characteristic parameter and it is defined in the
equation 4.1 as the ratio of the real heat transfer rate (q) with the maximum possible
heat transfer rate (qmax) (Incropera et al. 2007).
𝜀 =𝑞
𝑞𝑚𝑎𝑥 (4.1)
The effectiveness (ε) and the actual heat transfer rate (q) are two of the final
objectives of the heat transfer model. As the model presented by Manouchehri
(2015) based on Incropera et al. (2007), the use of a thermal resistor to describe the
heat transfer process is a simplified way to solve the problem as shown in figure 4.1.
Figure 4.1 Thermal resistors of the heat transfer model. Source: (Author)
Where the overall heat transfer coefficient for a GHRS can be found with a network
of thermal resistance in series configuration as explained by the equation 4.2.
1
𝑈𝐴= 𝑅𝑡𝑜𝑡𝑎𝑙 = 𝑅1 + 𝑅2 + 𝑅3 + 𝑅4 + 𝑅5 (4.2)
A schematic flow diagram of the whole model proposed is shown in APPENDIX A.
Tff Tsurfdrain Tinterference
Drain-side
Tinterference
Coil-side
Tinnercoil Tcoil
R1 R2 R3 R4 R5
CONVECTION
Falling Film
CONDUCTION
Drain-side
INTERFERENCE CONDUCTION
Coil-sideCONVECTION
Helical Coil
24
4.1 Inputs of the model
Three main categories are required for the model: Geometric inputs, specific flow
characteristic of the case and additional constants (g, kcopper...). The geometric inputs
are mainly the important measures of the GHRS. On figure 4.2, the different diameter
composing the GHRS are shown. For some cases, these measures are not possible
to find and/or to measure. In this case, some approximations based on the type of
copper pipe used can be made using the nominal pipe diameter of the unit. The total
length of the system and the number of coils are also required variables.
Figure 4.2 Top view section with the different geometric diameter of the GHRS (Left) and Different temperatures inside GHRS (Right).
On the other main category, the volumetric flows in both streams and the inlet
temperatures at the drain side and the fresh water at the coil side are required.
4.2 Thermodynamic properties of the fluid
For all fluid dynamics and heat transfer problems, the thermodynamic properties are
necessary to perform the calculations. Greywater heat exchangers mostly use water
as the fluid. The key aspect on this stage is that these properties in the Heat
Exchanger must be calculated at the average temperature between the inlet and the
output of the stream.
At this step of the model, the outlet temperatures are unknown and for that, an
iterative process is computed with an initial value of the outlet temperatures. These
25
outlet temperatures would be recalculated through the calculation until the outlet
temperatures converge with the real output temperatures of the exchanger.
Using the software Engineering Equation Solver the properties of specific heat,
dynamic viscosity, Prandtl number, thermal conductivity and fluid density are
calculated for water within a range of 0<T<60 [°C] and 1 atmosphere (Table 0-1
APPENDIX A).
A fifth order polynomial fit is applied and the following correlations are obtained as
result:
The specific heat in [kJ/ kg*K]:
𝐶𝑝𝑑𝑟𝑎𝑖𝑛 = 4.22783901 − 0.00783849467 ∗ 𝑇𝑎𝑣𝑔 + 0.00052713434 ∗ 𝑇𝑎𝑣𝑔2
− 0.0000169714919 ∗ 𝑇𝑎𝑣𝑔3 + 2.62003476𝐸 − 07 ∗ 𝑇𝑎𝑣𝑔
4
− 1.56365456𝐸 − 09 ∗ 𝑇𝑎𝑣𝑔5
(4.3)
The dynamic viscosity [kg/ m*s]:
µ = 0.0017922553 − 0.0000619423739 ∗ 𝑇𝑎𝑣𝑔 + 0.00000161169391 ∗ 𝑇𝑎𝑣𝑔2
− 3.12027493𝐸 − 08 ∗ 𝑇𝑎𝑣𝑔3 + 3.75757478𝐸 − 10 ∗ 𝑇𝑎𝑣𝑔
4
− 2.00244305𝐸 − 12 ∗ 𝑇𝑎𝑣𝑔5
(4.4)
The dimensionless Prandtl number:
𝑃𝑟 = 13.8366012 − 0.551920297 ∗ 𝑇𝑎𝑣𝑔 + 0.0163242036 ∗ 𝑇𝑎𝑣𝑔2
− 0.000354310865 ∗ 𝑇𝑎𝑣𝑔3 + 0.00000465354551 ∗ 𝑇𝑎𝑣𝑔
4
− 2.63157066𝐸 − 08 ∗ 𝑇𝑎𝑣𝑔5
(4.5)
Thermal conductivity [W/ m*K]:
𝑘 = 0.547511995 + 0.00204429925 ∗ 𝑇𝑎𝑣𝑔 − 0.0000044046946 ∗ 𝑇𝑎𝑣𝑔2
− 6.41854726𝐸 − 08 ∗ 𝑇𝑎𝑣𝑔3 − 4.68031789𝐸 − 10 ∗ 𝑇𝑎𝑣𝑔
4
+ 8.66907284𝐸 − 12 ∗ 𝑇𝑎𝑣𝑔5
(4.6)
Fluid density [kg/ m^3]:
𝜌 = 999.8297 + 0.0789410566 ∗ 𝑇𝑎𝑣𝑔 − 0.00982564195 ∗ 𝑇𝑎𝑣𝑔2
+ 0.00011599958 ∗ 𝑇𝑎𝑣𝑔3 − 0.00000120708114 ∗ 𝑇𝑎𝑣𝑔
4
+ 5.95968898𝐸 − 09 ∗ 𝑇𝑎𝑣𝑔5
(4.7)
26
It is important to remark that all of these properties have to be calculated separately
for each stream, the coil side and the drain side.
4.3 Thermal Capacities
The thermal capacities are calculated through the standard methodology. It is
essential that for the capacity of the coil, the number of coils (Nrcoils) must be taken
into account. The flow inside each of the coils is considered to be equal for all of
them and mcoil represents the mass flow on each coil. With the values of the equation
4.8, Cmin and Cmax can be assigned and determined the relation of Cr following
equation 4.9.
𝐶𝑑𝑟𝑎𝑖𝑛 = ��𝑑𝑟𝑎𝑖𝑛 ∗ 𝐶𝑝𝑑𝑟𝑎𝑖𝑛
𝐶𝑐𝑜𝑖𝑙 = ��𝑐𝑜𝑖𝑙 ∗ 𝐶𝑝𝑐𝑜𝑖𝑙 ∗ 𝑁𝑟𝐶𝑜𝑖𝑙𝑠 (4.8)
𝐶𝑟 =𝐶𝑚𝑖𝑛𝐶𝑚𝑎𝑥
(4.9)
4.4 Convection Falling Film – R1
The falling film effect was explained in Chapter 3. Following that methodology, the
first thermal resistance is determined using the heat transfer coefficient (hff)
established by equation 3.4.
𝑅1 =1
ℎ𝑓𝑓 ∗ 2 ∗ 𝜋 ∗ (𝐷12) ∗ 𝐿
(4.10)
4.5 Conduction Drain Pipe – R2
The conduction process that occurs on the pipe is estimated using the equation 4.11
in which the relation of external and internal diameter is used. L is the length of the
pipe and kcopper is the thermal conductivity of copper which value for the normal
condition is approximately 401 [W/ m*K].
𝑅2 =
𝑙𝑛 (
𝐷22𝐷12
)
2 ∗ 𝜋 ∗ 𝐿 ∗ 𝑘𝑐𝑜𝑝𝑝𝑒𝑟
(4.11)
27
4.6 Contact Resistance – R3
The presence of an interface between the drain pipe and the coils can be simulated
through the theory of contact resistance propose by Incropera et al. (2007). In the
Greywater heat exchanger, a copper-copper interface is present.
Two surfaces will never form a perfect thermal contact when they are put together.
Roughness becomes important due the fact that it will always include gaps of air
between the surfaces as shown in figure 4.3. In a thermal contact resistance, the
heat follows two different paths: a conduction between the points of solid-to-solid
contact which is very effective and a convection through the air between the gaps in
which the mechanism of heat transfer performs poorly (Lienhard IV & Lienhard V
1986).
Figure 4.3 Heat transfer through contact plane between two solid surfaces.
Source: (Lienhard IV & Lienhard V 1986)
The main factors that influence the contact resistance are the roughness of the
surface, the material, the pressure at which the surface are forced together, the
interstitial fluid and the temperature of contact. Considering the greywater heat
exchangers, the contact resistant accounts for roughly a 6.24% (APPENDIX A: Table
A-2) of the total thermal resistance.
𝑅3 =1
ℎ𝐶 ∗ 𝐴 (4.12)
The coefficient of interfacial conductance (hc) has values of 10,000-25,000
[W/(m^2*K)] (Rohsenow & Hartnett 1973 cited by Lienhard IV & Lienhard V 1986).
A value of 25,000 [W/(m^2*K)] for the interfacial coefficient (hc) is used for the
present work.
28
For the Greywater heat exchanger, this interface presents contact discontinuity due
the fact of several coils pile together. For the present work, this contact resistance
was assumed to be the same alongside the unit, but it is important to remark the fact
that the heat transfer mechanism is less effective in the gaps between coils.
4.7 Conduction Coil Pipe – R4
Following the same methodology as section 4.5, the conduction on the coil pipe is
calculated with the equation 4.13 representing the resistor 4.
𝑅4 =
𝑙𝑛 (
𝐷42𝐷32
)
2 ∗ 𝜋 ∗ 𝐿𝑐𝑜𝑖𝑙 ∗ 𝑘𝑐𝑜𝑝𝑝𝑒𝑟
(4.13)
4.8 Convection Helical Coil – R5
The phenomena of the secondary flow originated in the helical coil was explained in
section 3.2. The thermal resistance for the convective heat of the flow through the
helical coil is calculated using the equation 4.14 where hcoil is defined by the equation
3.14.
𝑅5 =1
ℎ𝑐𝑜𝑖𝑙 ∗ 2 ∗ 𝜋 ∗ (𝐷42 ) ∗ 𝐿𝑐𝑜𝑖𝑙
(4.14)
4.9 NTU-Method
Once the different resistors have been calculated, the overall heat transfer coefficient
(U) and the heat transfer Area (A) is estimated using equation 4.15 with the total
resistor of equation 4.2. A table with the thermal resistors calculated and the
percentage of the total resistor can be found on the table A-2 of APPENDIX A.
𝑈𝐴 =1
𝑅𝑡𝑜𝑡𝑎𝑙 (4.15)
Following the methodology of Incropera et al. (2007) the number of transfer units
(NTU) is determined where Cmin is the minimum thermal capacity, it can be Ccoil or
Cdrain depending on the conditions.
𝑁𝑇𝑈 =𝑈𝐴
𝐶𝑚𝑖𝑛 (4.16)
29
The effectiveness is calculated in equation 4.17 for counterflow GHRS units. If the GHRS is installed in a parallel flow configuration a different relation must be used as presented in equation 4.18. It is important to remark, that higher values of effectiveness are achieved with the counterflow configuration and that is why the parallel configuration must be avoided.
𝜀𝑡ℎ𝑒𝑜_𝑐𝑜𝑢𝑛𝑡𝑒𝑟𝑓𝑙𝑜𝑤 =
1 − 𝑒𝑥𝑝(−𝑁𝑇𝑈(1 − 𝐶𝑟))
1 − 𝐶𝑟 ∗ 𝑒𝑥𝑝(−𝑁𝑇𝑈 ∗ (1 − 𝐶𝑟)) (4.17)
𝜀𝑡ℎ𝑒𝑜𝑝𝑎𝑟𝑎𝑙𝑙𝑒𝑙 =
1 − 𝑒𝑥𝑝(−𝑁𝑇𝑈(1 + 𝐶𝑟))
1 + 𝐶𝑟 (4.18)
The heat recovery (q) of the GHRS unit is evaluation using the qmax which is the
relation between the minimum thermal capacity and the two limit temperatures. This
value is applied alongside the effectiveness value to obtain q.
𝑞 = 𝜀𝑡ℎ𝑒𝑜 ∗ 𝐶𝑚𝑖𝑛 ∗ (𝑇𝑑𝑟𝑎𝑖𝑛𝑖𝑛 − 𝑇𝑐𝑜𝑖𝑙𝑖𝑛) (4.19)
Outlet temperatures are calculated using the expression 4.20 for both streams.
𝑇𝑐𝑜𝑖𝑙𝑜𝑢𝑡 = (𝑞
𝐶𝑐𝑜𝑖𝑙) + 𝑇𝑐𝑜𝑖𝑙𝑖𝑛
𝑇𝑑𝑟𝑎𝑖𝑛𝑜𝑢𝑡 = 𝑇𝑑𝑟𝑎𝑖𝑛𝑖𝑛 − (𝑞
𝐶𝑑𝑟𝑎𝑖𝑛)
(4.20)
30
5 MODEL VALIDATION
Models are an approximation of reality, therefore, it is important that the models are
well-founded and represent with a certain margin of error the phenomena it tries to
describe. For this process, the current heat transfer model was validated with the
empirical data available from Collins (2009) and the reference values from the
nominal effectiveness which are also available there. Collins (2009) performed tests
under different flow and standard conditions for different Greywater heat
exchangers. On this chapter, the validation process of the heat transfer model is
presented.
5.1 Nusselt Correlation
On this section different laminar Nusselt correlations (Section 3.2.2) were evaluated
in order to find out which relation displays better results. For the evaluation of the
flow through a helical coil, the correlations of (Eq. 3.8) Manlapaz and Churchill (1980,
cited by Austen & Soliman 1988); (Eq. 1.9) Karl-Saeder (1972, Cited by Elsayed
2011); (Eq. 3.10) Janssen & Hoogendoorn (1978) and (Eq.3.11) Dravid et al. (1971,
cited by Manouchehri 2015) were validated in order to look for the correlation that
gives the most accurate results.
Figure 5.1 Cumulative histogram frequencies of the Heat Recovery Error (Top) and effectiveness Error (Bottom) for different Nusselt Correlations.
31
A validation process with 54 different geometries was evaluated. The correlation of
Manlapaz & Churchill and Karl-Saeder outperformed the other correlations. For
Manlapaz & Churchill, 75.93% of the times the error in the heat recovery (q) is below
6.0% and 92.59% of the times is below 10%. For the Karl-Saeder case, the same
order of magnitude is achieved. For Janssen correlation, only 51.85% of the times
the error was below 10% which is not significantly accurate. Dravid et al. expression
obtain error below 10%, 85.19% of the times but the error was only below 6%,
46.30% of the times. A Cumulative Histogram of the frequencies is depicted in figure
5.1 and for the full table of results refer to the tables B-1 and B-2 of APPENDIX B.
For the present work, the correlation of Manlapaz & Churchill was used for the
current model due the results achieved in this section.
5.2 Standard Condition
On the validation process, the 54 models were evaluated and some of the results
are shown in table 5-1 (to see the full table of results refer to Table B-2 in APPENDIX
B).
The conditions for this validation test were 9 [L/min] of water flow in both streams,
inlet drain temperature of 36°C and inlet coil temperature of 8°C.
(COLLINS 2009) Manlapaz and Churchill
MODEL
No
min
al
Dia
me
ter
[m]
Le
ng
th [
m]
Eff
ecti
ve
ne
ss
[%]
Heat
Rec
ov
ery
[W
]
Eff
ecti
ve
ne
ss
[%]
Eff
ecti
ve
ne
ss
ER
RO
R [
%]
Heat
Rec
ov
ery
[W
]
Heat
Rec
ov
ery
ER
RO
R [
W]
R2-36 0.05 0.91 32.6% 5720 31.1% 4.73% 5430.13 5.07%
R2-48 0.05 1.22 37.8% 6540 37.7% 0.36% 6586.90 0.72%
R2-120 0.05 3.05 64.4% 10810 60.1% 6.63% 10526.35 2.62%
R3-36 0.08 0.91 38.7% 6790 38.4% 0.89% 6708.24 1.20%
R3-42 0.08 1.07 43.1% 7500 42.3% 1.97% 7390.78 1.46%
R3-120 0.08 3.05 67.8% 12060 67.5% 0.40% 11824.44 1.95%
R4-36 0.1 0.91 43.0% 7580 42.1% 2.10% 7363.98 2.85%
R4-108 0.1 2.74 69.6% 12120 68.6% 1.48% 12008.19 0.92%
R4-120 0.1 3.05 72.4% 12760 70.8% 2.18% 12403.49 2.79%
C3-84 0.08 2.13 56.3% 9720 56.9% 1.06% 9959.25 2.46%
C3-96 0.08 2.44 60.7% 10520 60.2% 0.83% 10538.24 0.17%
C3-120 0.08 3.05 66.4% 11570 65.4% 1.50% 11452.22 1.02%
C4-96 0.1 2.44 65.8% 11350 63.9% 2.95% 11180.78 1.49%
C4-108 0.1 2.74 68.9% 12010 66.5% 3.50% 11642.45 3.06%
C4-120 0.1 3.05 70.8% 11940 68.8% 2.78% 12053.73 0.95%
Table 5-1 Table of Errors for GHRS Units with 0.08 m of nominal diameter.
32
The process was evaluated for nominal diameters from 0.05 – 0.10 m and length of
0.91 – 3.05 m with some model of 4 coils and some with 6 coils.
For the effectiveness, the error was below 6% for 62.96% of the times and below
10% for 92.59% of the times. Obtaining the average error of 4.95% with standard
deviation of +/- 3.4%. The Heat recovery error was below 6% for 75.93% of the times
and below 10% for 92.59% of the times. The average error of this category was
4.52% with standard deviation of +/- 3.3%. These frequency histograms are depicted
in figure 5.2.
Figure 5.2 Error frequency histogram of the heat transfer model.
5.3 Different Flow
A validation using different models under different flow conditions was performed
obtaining the results presented in the table 5-2 (Refer to Table B-3 in APPENDIX B
for the results). The histogram distribution of errors is presented in table 5-3.
Simulations for different geometries were performed and its results were compared
with the empirical data from Collins (2009) for flows around 4, 8, 11 and 14 [L/min].
The variables evaluated were the Outlet temperature at the Drain side and at the
Coil side, the effectiveness and the heat recovered.
33
Table 5-2 Table of Error with different flows.
Percentage of error
Temp. Drain Out Temp. Coil Out Effectiveness Heat Recovery
Fre
quency
Cum
ula
tive
[%]
Fre
quency
Cum
ula
tive
[%]
Fre
quency
Cum
ula
tive
[%]
Fre
quency
Cum
ula
tive
[%]
2% 14 43.75% 11 34.38% 8 25.00% 8 25.00%
4% 9 71.88% 14 78.13% 7 46.88% 7 46.88%
6% 4 84.38% 2 84.38% 10 78.13% 9 75.00%
8% 2 90.63% 4 96.88% 2 84.38% 3 84.38%
10% 0 90.63% 1 100.00% 3 93.75% 2 90.63%
12% 2 96.88% 0 100.00% 2 100.00% 3 100.00%
More 1 100.00% 0 100.00% 0 100.00% 0 100.00%
Table 5-3 Histogram table of validation process with different flows.
RE
F.
Tem
p. D
rain
In
[°C
]
Tem
p. C
oil
In
[°C
]
Flo
w [LP
M]
(CO
LLIN
S 2
009)
[°C
]
MO
DE
L [°C
]
DIF
F. [°
C]
Err
or
[%]
(CO
LLIN
S 2
009)
[°C
]
MO
DE
L [°C
]
DIF
F. [°
C]
Err
or
[%]
(CO
LLIN
S 2
009)
[°C
]
MO
DE
L
DIF
F.
Err
or
[%]
(CO
LLIN
S 2
009)
[°C
]
MO
DE
L [W
]
DIF
F. [W
]
Err
or
[%]
35.7 8.1 3.99 19.1 19.84 -0.74 3.89% 24.6 23.91 0.69 2.80% 0.601 0.574 0.027 4.41% 4610 4395 215 4.67%
36.2 8.2 7.92 22.2 23.12 -0.92 4.14% 21.9 21.23 0.67 3.05% 0.492 0.467 0.025 5.06% 7600 7191 409 5.38%
36.1 8.0 10.84 23.5 24.39 -0.89 3.79% 20.4 19.66 0.74 3.62% 0.443 0.417 0.026 5.94% 9420 8810 610 6.48%
35.9 8.2 14.23 25.4 25.54 -0.14 0.53% 19.2 18.52 0.68 3.54% 0.396 0.374 0.022 5.51% 10860 10236 624 5.75%
35.9 8.2 4.16 15.8 15.83 -0.03 0.18% 28.4 28.24 0.16 0.57% 0.729 0.725 0.004 0.60% 5840 5803 37 0.63%
36.0 7.7 7.88 18.5 18.00 0.50 2.69% 25.3 25.66 -0.36 1.40% 0.624 0.636 -0.012 1.92% 9690 9854 -164 1.69%
36.0 8.0 10.73 20.1 19.50 0.60 2.96% 23.9 24.45 -0.55 2.30% 0.569 0.589 -0.020 3.53% 11900 12295 -395 3.32%
36.5 8.0 13.80 22 20.83 1.17 5.32% 23 23.62 -0.62 2.70% 0.527 0.550 -0.023 4.32% 14430 15016 -586 4.06%
36.0 7.8 4.06 20.1 18.61 1.49 7.41% 23.6 25.15 -1.55 6.55% 0.559 0.617 -0.058 10.31% 4450 4905 -455 10.22%
35.6 7.8 7.96 20.8 21.36 -0.56 2.69% 22.6 21.99 0.61 2.70% 0.531 0.512 0.019 3.56% 8180 7870 310 3.79%
35.5 7.7 10.63 22.7 22.55 0.15 0.65% 20.6 20.60 0.00 0.01% 0.464 0.466 -0.002 0.37% 9540 9557 -17 0.18%
36.3 7.9 14.03 24.6 24.27 0.33 1.33% 19.6 19.88 -0.28 1.42% 0.415 0.423 -0.008 2.04% 11500 11711 -211 1.84%
35.7 7.6 4.06 16.4 13.77 2.63 16.04% 27.3 29.49 -2.19 8.02% 0.7 0.780 -0.080 11.46% 5580 6188 -608 10.90%
35.7 8.1 8.45 17 16.61 0.39 2.29% 27.1 27.15 -0.05 0.18% 0.687 0.692 -0.005 0.67% 11160 11210 -50 0.44%
36.1 8.0 10.85 17.6 17.63 -0.03 0.17% 26.6 26.42 0.18 0.68% 0.662 0.657 0.005 0.76% 14050 13920 131 0.93%
35.7 7.6 13.77 17.6 18.33 -0.73 4.15% 25.8 24.93 0.87 3.38% 0.65 0.618 0.032 4.90% 17520 16618 902 5.15%
36.1 8.1 4.16 16.9 16.73 0.17 0.99% 27 27.42 -0.42 1.56% 0.677 0.692 -0.015 2.17% 5480 5598 -118 2.16%
36.1 8.0 7.79 19 19.18 -0.18 0.97% 25.1 24.87 0.23 0.92% 0.611 0.602 0.009 1.47% 9280 9154 126 1.36%
35.9 8.0 10.81 19.3 20.53 -1.23 6.36% 24.6 23.33 1.27 5.17% 0.594 0.551 0.043 7.26% 12450 11541 909 7.30%
36.1 7.7 14.09 20.8 21.65 -0.85 4.09% 23.7 22.09 1.61 6.79% 0.562 0.509 0.053 9.49% 15650 14135 1516 9.68%
36.2 8.3 3.97 15.5 13.67 1.83 11.81% 28.8 30.79 -1.99 6.91% 0.734 0.807 -0.073 9.98% 5640 6216 -576 10.20%
36.2 8.1 8.44 15.7 15.90 -0.20 1.27% 28.6 28.36 0.24 0.84% 0.732 0.722 0.010 1.31% 12080 11907 173 1.43%
35.8 7.9 11.23 16.2 16.73 -0.53 3.25% 27.7 26.94 0.76 2.76% 0.709 0.684 0.025 3.57% 15460 14885 575 3.72%
35.9 8.1 14.08 16 17.77 -1.77 11.06% 27.9 26.18 1.72 6.16% 0.711 0.652 0.059 8.31% 19400 17731 1669 8.60%
Heat RecoveryINITIAL PARAMETERS
R4-66
R4-120
Temp. Drain OUT Temp. Coil OUT Effectiveness
R2-60
R2-120
R3-54
R3-120
34
On this procedure, the result achieved are consistent within the margin of error of
the present model. The average error and the standard deviation of the outlet
temperature of the drain and coils side, the effectiveness, and the heat recovery are
presented in figure 5.3.
Figure 5.3 Average error and standard deviation under different flows.
The main idea of this validation process was to analyze if there is a dependency of
the error with the volumetric flow. The results show that the error is in the same order
of magnitude for the different flows evaluated [4-14 L/min].
5.4 Different dimensions
Figure 5.4 Average error of the model under different dimensions.
The last validation process shows the behavior of the model under different
dimensions of the heat exchanger. 8 units with different nominal diameter and
35
different lengths were the subject of study under different flow conditions and the
average error was calculated for 4 variables (Outlet drain Temperature, Outlet coil
Temperature, Effectiveness, and Heat Recovery).
The figure 5.4 shows that the error for the 4 evaluated variables is at the same order
of magnitude alongside the different dimensions evaluated. With this process, the
model shows that its results are stable for the dimension evaluated that were:
nominal diameter of 0.05-0.10 [m], length 0.91-3.05 [m] and 4-6 coils.
36
6 MODEL SIMULATIONS
In the previous chapter, the heat transfer model proposed was validated. In this
chapter, the effectiveness dependency for variables such as the dimensions,
number of coils and analyzes about the outlet temperature of the results of the model
are explained.
For this model, the code was developed in MATLAB with a Graphic User Interface
(GUI) following the process described in chapter 4.
Figure 6.1 Screenshot from the MATLAB GUI of the model.
Figure 6.1 shows one of the screenshots of the MATLAB GUI. This figure is the main
program in which general calculation for a heat exchanger can be done. In this
interface, the other calculations such as the economic analyses can be reached. For
these additional screenshots, refer to APPENDIX E.
With this model, different simulation can be run. Table 6-1 shows the results for
several heat exchangers with different diameters and different lengths. This test
used standard conditions of 9 [L/min], 36 °C as inlet temperature on the drain side
and 8°C at the coil side. The dimensions evaluated were for a heat exchanger with
4 coils with a nominal diameter of 0.05, 0.08 and 0.10 [m] and lengths in the range
of 0.91-3.05 [m].
A complete table of results can be found in APPENDIX C. With this full table of
results, some graphics were created to analyze some of the performance trends of
the greywater heat exchangers.
37
GE
OM
ET
RY
Le
ng
th [
m]
Eff
ecti
ven
ess
q [
kW
]
Td
rain
_o
ut
[°C
]
Tc
oil
_o
ut
[°C
]
NT
U
UA
[W
/K]
ReD
rain
ReC
oil
Reg
imeC
oil
R1 [
K/W
]
R2 [
K/W
]
R3 [
K/W
]
R4 [
K/W
]
R5 [
K/W
]
Rto
tal
[K/W
]
Cco
il
Cd
rain
No
min
al
Dia
me
ter
= 0
.05
[m
]
Nu
mb
er
of
co
ils
= 4
0.91 31.06% 5.43 27.30 16.65 0.450 281.0 4933.9 4876.6 Laminar 1.53E-03 3.36E-05 2.59E-04 3.27E-05 1.70E-03 3.56E-03 627.46 624.40
1.07 34.63% 6.06 26.30 17.65 0.529 330.5 4883.3 4943.9 Laminar 1.31E-03 2.85E-05 2.20E-04 2.78E-05 1.44E-03 3.03E-03 627.36 624.50
1.22 37.66% 6.59 25.45 18.50 0.603 376.9 4840.4 5001.2 Laminar 1.16E-03 2.50E-05 1.93E-04 2.44E-05 1.25E-03 2.65E-03 627.29 624.59
1.37 40.42% 7.07 24.68 19.27 0.678 423.3 4801.6 5053.6 Laminar 1.04E-03 2.23E-05 1.72E-04 2.17E-05 1.11E-03 2.36E-03 627.22 624.67
1.52 42.95% 7.51 23.97 19.98 0.752 469.6 4766.1 5101.8 Laminar 9.41E-04 2.01E-05 1.55E-04 1.96E-05 9.94E-04 2.13E-03 627.16 624.74
1.68 45.41% 7.95 23.28 20.67 0.831 519.0 4731.5 5148.9 Laminar 8.56E-04 1.82E-05 1.40E-04 1.77E-05 8.95E-04 1.93E-03 627.11 624.81
1.83 47.54% 8.32 22.69 21.26 0.905 565.3 4701.8 5189.7 Laminar 7.89E-04 1.67E-05 1.29E-04 1.62E-05 8.18E-04 1.77E-03 627.06 624.87
2.13 51.33% 8.98 21.63 22.32 1.053 657.9 4649.1 5262.7 Laminar 6.84E-04 1.43E-05 1.11E-04 1.40E-05 6.97E-04 1.52E-03 626.99 624.97
2.44 54.70% 9.57 20.68 23.27 1.205 753.4 4602.2 5328.1 Laminar 6.01E-04 1.25E-05 9.66E-05 1.22E-05 6.05E-04 1.33E-03 626.92 625.06
2.74 57.55% 10.07 19.89 24.07 1.353 845.8 4562.9 5383.4 Laminar 5.39E-04 1.11E-05 8.61E-05 1.08E-05 5.35E-04 1.18E-03 626.86 625.13
3.05 60.13% 10.53 19.16 24.79 1.505 941.1 4527.2 5433.9 Laminar 4.87E-04 1.00E-05 7.73E-05 9.75E-06 4.78E-04 1.06E-03 626.81 625.20
No
min
al
Dia
me
ter
= 0
.08
[m
]
Nu
mb
er
of
co
ils
= 4
0.91 38.36% 6.71 25.26 18.69 0.621 388.1 3019.2 5014.3 Laminar 1.14E-03 2.13E-05 1.67E-04 2.13E-05 1.23E-03 2.58E-03 627.27 624.61
1.07 42.25% 7.39 24.17 19.78 0.731 456.4 2984.9 5088.5 Laminar 9.75E-04 1.81E-05 1.42E-04 1.81E-05 1.04E-03 2.19E-03 627.18 624.72
1.22 45.48% 7.96 23.27 20.69 0.833 520.4 2956.6 5150.2 Laminar 8.61E-04 1.59E-05 1.24E-04 1.59E-05 9.04E-04 1.92E-03 627.11 624.81
1.37 48.36% 8.46 22.46 21.50 0.935 584.3 2931.5 5205.6 Laminar 7.72E-04 1.41E-05 1.11E-04 1.41E-05 8.01E-04 1.71E-03 627.05 624.89
1.52 50.95% 8.92 21.73 22.22 1.037 648.2 2908.9 5255.5 Laminar 7.00E-04 1.27E-05 9.97E-05 1.27E-05 7.18E-04 1.54E-03 626.99 624.96
1.68 53.45% 9.35 21.04 22.92 1.146 716.3 2887.3 5303.7 Laminar 6.37E-04 1.15E-05 9.02E-05 1.15E-05 6.46E-04 1.40E-03 626.94 625.03
1.83 55.56% 9.72 20.44 23.51 1.248 780.1 2868.9 5344.8 Laminar 5.87E-04 1.06E-05 8.28E-05 1.06E-05 5.91E-04 1.28E-03 626.90 625.08
2.13 59.26% 10.37 19.41 24.55 1.452 907.6 2837.0 5416.9 Laminar 5.09E-04 9.09E-06 7.12E-05 9.09E-06 5.04E-04 1.10E-03 626.83 625.18
2.44 62.48% 10.94 18.51 25.45 1.662 1039.1 2809.3 5480.0 Laminar 4.47E-04 7.94E-06 6.21E-05 7.94E-06 4.37E-04 9.62E-04 626.77 625.26
2.74 65.15% 11.41 17.76 26.20 1.865 1166.3 2786.5 5532.4 Laminar 4.01E-04 7.07E-06 5.53E-05 7.07E-06 3.87E-04 8.57E-04 626.72 625.33
3.05 67.53% 11.82 17.09 26.87 2.075 1297.7 2766.1 5579.4 Laminar 3.62E-04 6.35E-06 4.97E-05 6.35E-06 3.46E-04 7.71E-04 626.68 625.38
No
min
al
Dia
me
ter
= 0
.10
[m
]
Nu
mb
er
of
co
ils
= 4
0.91 42.10% 7.36 24.21 19.74 0.726 453.6 2389.0 5085.5 Laminar 9.88E-04 1.71E-05 1.35E-04 1.73E-05 1.05E-03 2.20E-03 627.18 624.72
1.07 46.09% 8.06 23.10 20.86 0.854 533.3 2361.1 5161.8 Laminar 8.48E-04 1.45E-05 1.14E-04 1.47E-05 8.84E-04 1.88E-03 627.09 624.83
1.22 49.35% 8.64 22.18 21.77 0.973 608.0 2338.3 5224.6 Laminar 7.49E-04 1.28E-05 1.00E-04 1.29E-05 7.70E-04 1.64E-03 627.03 624.92
1.37 52.24% 9.14 21.37 22.58 1.092 682.6 2318.1 5280.5 Laminar 6.71E-04 1.14E-05 8.94E-05 1.15E-05 6.82E-04 1.47E-03 626.97 625.00
1.52 54.82% 9.59 20.65 23.30 1.211 757.1 2300.3 5330.4 Laminar 6.08E-04 1.02E-05 8.05E-05 1.03E-05 6.11E-04 1.32E-03 626.92 625.06
1.68 57.28% 10.03 19.96 23.99 1.338 836.6 2283.3 5378.2 Laminar 5.53E-04 9.27E-06 7.29E-05 9.35E-06 5.50E-04 1.20E-03 626.87 625.13
1.83 59.35% 10.39 19.38 24.57 1.457 911.0 2269.0 5418.6 Laminar 5.10E-04 8.51E-06 6.69E-05 8.59E-06 5.03E-04 1.10E-03 626.83 625.18
2.13 62.94% 11.02 18.38 25.58 1.695 1059.7 2244.3 5489.0 Laminar 4.42E-04 7.31E-06 5.75E-05 7.38E-06 4.29E-04 9.44E-04 626.76 625.27
2.44 66.04% 11.56 17.51 26.45 1.940 1213.3 2223.1 5549.9 Laminar 3.89E-04 6.38E-06 5.02E-05 6.44E-06 3.73E-04 8.24E-04 626.71 625.35
2.74 68.57% 12.01 16.80 27.16 2.177 1361.7 2205.7 5600.1 Laminar 3.48E-04 5.68E-06 4.47E-05 5.73E-06 3.30E-04 7.34E-04 626.66 625.41
3.05 70.82% 12.40 16.17 27.79 2.422 1515.0 2190.4 5644.7 Laminar 3.14E-04 5.10E-06 4.01E-05 5.15E-06 2.95E-04 6.60E-04 626.62 625.46
Table 6-1 Simulation results for different GHE with different dimensions.
6.1 Dimensions
Figure 6.2 shows the change in effectiveness for different dimensions. One of the
first conclusions that can be stated is that bigger diameters performed better than
small ones. With the length, a similar phenomenon is depicted. A longer heat
exchanger can transfer more heat than short ones. For this reason, long units
performed with higher effectiveness than short heat exchangers.
38
Figure 6.2 Effectiveness dependency on GHE dimensions.
6.2 Number of coils
A reference unit of 0.05 m of nominal diameter was used to evaluate the impact of
numbers of coils. Figure 6.3 shows that higher number of coils will perform worse
than with less number of coils. The main reason why it is important to have several
numbers of coils is that the pressure drop will be lower for those cases (Guo et al.
2001).
Figure 6.3 Effectiveness performance for different number of coils.
39
6.3 Outlet temperatures
The outlet temperatures were evaluated for a reference unit with a nominal diameter
of 0.08 m and 4 coils. As it is expected, shorter unit will perform worse than longer
units. The temperatures achieve for short units are less than the ones achieve with
longer exchangers as shown in figure 6.4.
Figure 6.4 Simulation for outlet temperatures.
40
7 POTENTIAL OF IMPLEMENTATION
Directives from the European Union have pointed out the importance of increasing
the energy efficiency in buildings. In addition, Sweden has established a law in which
all new buildings should fulfill the regulation of nearly zero energy buildings (NZEB)
from 2020, implemented according to the EU Energy performance of buildings
directive (Wallin & Claesson 2014). GHRS raise in importance in order to achieve
this goal.
In the real world, what makes a technology or idea succeed between others is how
economically feasible it is. A study in Poland (Słyś & Kordana 2014) analyzed the
economic aspect of the GHRS for household consumers. As the first conclusion, the
potential of recovering the investment is directly proportional to the amount of hot
water used. Logically, it would be the total water consumption of the whole
household which determined how economically feasible the concept is.
The findings of this study state that the discount payback period can range from
almost 2.5 years to less than 10 years depending directly on the shower duration
and the volume of hot water used (Słyś & Kordana 2014).
On this chapter, some of the characteristics of the variables that influence the
implementation of GHRS are the subject of study.
7.1 Water Usage
One of the most important variables for the economic feasibility of GHRS is the water
usage. The main concern is that not everyone use the same amount of water and
neither take the same time during showers. The variability of water usage is
tremendous and several factors influence them (Opitz et al. 1999). It is important to
estimate a pattern of water usage during shower time. Studies (Blokker et al. 2010;
Athuraliya et al. 2012; Lallana et al. 2001) have acquired theoretical and empirical
data to simulate these patterns.
Firstly, countries use water for different purposes with different applications. This can
be easily explained with table 7-1. A comparison in the water pattern in percentage
depending on the application is done between England, Finland, and Switzerland.
Finland uses only 14% of their household water for toilet flushing, different from
England and Switzerland that use a 33%. The situation changes drastically with a
higher use of washing machine and dishwashing in Finland than in the other
countries.
41
HOUSEHOLD USES ENGLAND
AND WALES (%)
FINLAND (%) SWITZERLAND
(%)
Toilet flushing 33 14 33
Bathing and showering 20 29 32
Washing machines and dishwashing
14 30 16
Drinking and cooking 3 4 3
Miscellaneous 27 21 14
External use 3 2 2
Table 7-1 Patterns of water use by households in England and Wales, Finland and Switzerland.
Source: ((UK Department of the Environment, 1997; Etelämäki, 1999) cited by Lallana et al. 2001)
For bathing and showering, England uses a 20% of the water, while Finland and
Switzerland use a 29% and 32% respectively. These facts show a clear difference
between different countries on how the water usage share differs from one to
another. Specific information on the water consumption with this differentiation of
applications for Sweden was not found and a simulated profile was required.
Blokker et al. (2010) proposed a water demand end-use model that predicts water
demand for small time scale at a residential level. The model is based on information
from statistical data of users and end-uses.
The model proposes different distribution for different end-uses. Specifically talking
about most important concerning greywater for GHE, the model proposes the next
distributions for the Netherlands.
APPLICATION Frequency
[1/day] Duration Intensity [L/s]
End Use Type Avg, Distribution Avg Distribution Avg. Distribution
Dishwasher Brand and
type 0.3 Poisson
Specific dishwashing pattern ( 4 cycles of water entering, total 84 seconds,
0.167 L/ sec=14 L )
Washing Machine
Brand and type
0.3 Poisson Specific washing pattern ( 4 cycles of water entering, total 5 minutes, 0.167
L/ sec=50 L )
Shower
Normal
0.7 Binominal 8.5 min
x^2 Distribution
0.142 N.A.
(Fixed) Water Saving
0.123
Table 7-2 Frequency, Duration, and Intensity for Several Types and Subtypes of End-Uses in the Netherlands.
Source: (Blokker et al. 2010)
42
The shower duration has a strong dependency with the age of the inhabitants.
Children and teenagers take longer showers than adults. Additionally, the water
intensity for shower depends on the type of water heater (Blokker et al. 2010).
Another study was presented by Athuraliya et al. (2012) where they performed a
major research to measure the residential water usage at the end-level for the city
of Melbourne, Australia. 337 households were evaluated for two weeks of the winter
2010 and two of summer 2012.
The result shows a major use of water during the summer season, but for the
simplicity of the present work, only the average between seasons was taken into
account. Figure 7.1 shows the different Poisson distributions of water usage. The
shower time simulated shows a distribution in the top left graphic with an average
value of 6.5 minutes per person. The flow distribution is depicted in the top right
graphic with an average value of 7.29 L/min (0.1215 L/s) during showering. The total
water usage per shower is shown in the bottom graphic where the mean value is
47.17 Liters per person. The total water usage for 80% of the cases is below 70
Liters.
Figure 7.1 Water usage pattern during shower. Source: (Athuraliya et al. 2012)
The present distribution will be used further to analyses the economic feasibility of
GHE if applied to n-number of household with this distributed pattern of showering.
The condition presented on Athuraliya et al. (2012) distribution is a worse scenario
than the distribution proposed by Blokker et al. (2010) and this is the main reason of
selecting this pattern to simulate the consumption of Sweden.
43
7.2 Persons per Household
The number of persons per household is another important variable in order to
understand the potential of GHRS in residential households. It is easily recognizable
that the more people living in the same household, the higher water consumption will
be and the more economically feasible the GHRS will be.
Table 7-3 Persons per Households in Sweden 2015.
Source: (SCB-Sweden 2016)
Figure 7.2 shows the distribution of persons per households and households with n-
persons. These results can be found in the table 7-3 where it is clearly stated that
most people live in 2-persons households with 30.87%. The most common type of
household is the single person one with 37.39%. The average number of persons
living per household in Sweden is 2.21 (SCB-Sweden 2016). The full statistical
distribution of households can be found in Table D-1 in APPENDIX D.
Figure 7.2 Distribution of households in Sweden 2015. Source: (SCB-Sweden 2016)
These numbers are important to understand that the implementation of GHRS is
related as well to the persons living in the different households. This number varies
with several conditions and it is also different from country to country in Europe, as
44
it can be seen in Figure D-1 in APPENDIX D. For Europe the average number of
persons per household is around 2.3 persons for the year 2014 (Eurostat 2016).
7.3 Energy price
Another important aspect to take into account for the potential of implementation is
the energy price. Different countries have different prices for energy. In Sweden, It
is not that common to find gas boilers in households; district heating and electric
boilers are more representative of the market. This can be a completely different
reality from another country’s perspective.
Payback times would be several years higher with cheaper energy prices. The prices
for energy in Sweden are shown in figure 7.3 where it can be seen that District
heating is cheaper than electricity for households. This clearly means that the GHE
will have a bigger opportunity when electric boilers are present. The lower cost of
district heating means longer payback periods. For the present work, the electricity
will be the main case of comparison. Nevertheless, the potential within district
heating is studied as well.
Figure 7.3. Energy prices for the residential and services sector [öre2013/kWh] Source: (Swedish Energy Agency 2015)
From the electricity perspective, it is clear that GHRS will benefit from higher
electricity prices. Therefore countries such as Denmark, Germany and Italy which
have shown higher electricity prices (Fig. 7.4) will find it more attractive to invest in
this technology.
45
Figure 7.4 Electricity price for household consumers 2015 [€/kWh] Source: (Eurostat 2016) (Online data code: nrg_pc_204)
7.4 GHRS Unit dimensions & Investment
In the market, several different GHRS units can be found with different sizes, number
of coils, diameters and effectiveness values, as well that with a diverse price range.
The configuration of the units plays an important role. It is different to analyze the
potential of implementation in a single household than in a multi-dwelling one. All of
these characteristics are key aspects to develop an economic analysis, due that
different models will generate diverse results.
The cost of the unit varies on its dimensions. Bigger units with a better performance
are more expensive than smaller ones with lower performance in comparison. In
addition, the installation cost varies from country to country and influence directly the
investment cost. For the cheaper units, the installation cost could account for almost
50% of the total investment cost according to the cost proposed by a manufacturer
(ReneWABILITY 2016). These variables influence directly the economic potential of
the technology.
46
8 ECONOMIC ANALYSIS
As seen in the previous chapter, several variables influence the performance and
economic feasibility for the implementation of GHRS. This section will join all these
variables in order to understand an economic analysis for this technology. The work
of Słyś & Kordana (2014) presents a calculation model to estimate the financial
efficiency of projects with GHRS. This model was used as based for the present
work and additionally, a Monte Carlo simulation was performed in order to estimate
the potential for an n-number of households using one exchanger per household.
The main methodology consists of a reference case without a GHRS unit and a
further comparison with the savings produce due the higher temperature of the
incoming water preheated from the coil side. The main objective was to obtain the
Discounted Payback Period (DPP) for different units on several operational
conditions.
It is important to remark that the result in this section should not be taken as given,
but just as results to explore the potential of the technology from an economic point
of view due some of the assumptions made through the simulation.
8.1 Reference Case
The first step to describe the energy cost for the reference case begins with the
equation 8.1 (Słyś & Kordana 2014) which define Vref_cold as the flow of cold water
for the mixture of shower. Where Vshower is the water flow of the shower [m^3/s] (Refer
to section 7.1); Twmix is the temperature of the shower and it is assumed to be 38°C
(301 K) for the present work; Twhot the temperature of hot water 60°C (333 K); Twcold
the temperature of the cold water 8°C (281 K) or the inlet temperature of the coil
side; with Cp as the specific heat and ρ as the density of the fluid.
��𝑟𝑒𝑓_𝑐𝑜𝑙𝑑 = ��𝑠ℎ𝑜𝑤𝑒𝑟 ∗ (
𝐶𝑝0 ∗ 𝜌0 ∗ (𝑇𝑤𝑚𝑖𝑥 − 𝑇𝑤𝑐𝑜𝑙𝑑)
𝐶𝑝0 ∗ 𝜌0 ∗ (𝑇𝑤ℎ𝑜𝑡 − 𝑇𝑤𝑚𝑖𝑥) + 𝐶𝑝0 ∗ 𝜌0 ∗ (𝑇𝑤𝑐𝑜𝑙𝑑 − 𝑇𝑤𝑚𝑖𝑥)) (8.1)
Secondly, the energy required for one year to heat up the cold water up to the hot
water temperature (Eref) is computed from equation 8.2 where: Days is the numbers
of days of the computation (yearly base, therefore, it is 365); Pers is the number of
inhabitants in the household (Refer to section 7.2); tshower is the duration of the
shower [s] (Refer to section 7.1); ηboiler is the efficiency of the boiler.
𝐸𝑟𝑒𝑓 = 𝐷𝑎𝑦𝑠 ∗ 𝑃𝑒𝑟𝑠 ∗ 𝑡𝑠ℎ𝑜𝑤𝑒𝑟 ∗ 𝑉𝑟𝑒𝑓_𝑐𝑜𝑙𝑑 ∗ 𝐶𝑝0 ∗ 𝜌0 ∗𝑇𝑤ℎ − 𝑇𝑤𝑐
𝜂𝑏𝑜𝑖𝑙𝑒𝑟 ∗ 3.6𝐸6 (8.2)
47
Finally, the total cost of the electricity for one year is calculated using equation 8.3
where: PricekWh is the price of electricity per kWh (1.7 SEK2014/kWh). For district
heating, the average cost is 0.74 SEK2014 (Swedish Energy Agency 2015).
𝑃𝑟𝑖𝑐𝑒𝑟𝑒𝑓 = 𝐸𝑟𝑒𝑓 ∗ 𝑃𝑟𝑖𝑐𝑒𝑘𝑊ℎ (8.3)
8.2 GHRS Case
The cost of energy using GHRS is computed in the same way as the reference case.
The difference is that the cold water temperature is now the preheated water coming
from the outlet of the GHRS which is defined as Tcoil_out. In equation 8.4.
𝑉𝐺𝐻𝑅𝑆 =
𝑉𝑠ℎ𝑜𝑤𝑒𝑟 ∗ (𝐶𝑝𝑐𝑜𝑖𝑙 ∗ 𝜌𝑐𝑜𝑖𝑙) ∗ (𝑇𝑤𝑚𝑖𝑥 − 𝑇𝑐𝑜𝑖𝑙𝑜𝑢𝑡)
((𝐶𝑝𝑐𝑜𝑖𝑙 ∗ 𝜌𝑐𝑜𝑖𝑙) ∗ (𝑇𝑤ℎ𝑜𝑡 − 𝑇𝑤𝑚𝑖𝑥)) + ((𝐶𝑝𝑐𝑜𝑖𝑙 ∗ 𝜌𝑐𝑜𝑖𝑙) ∗ (𝑇𝑤𝑚𝑖𝑥 − 𝑇𝑐𝑜𝑖𝑙𝑜𝑢𝑡)) (8.4)
In the same way, with the GHE, the water does not have to heat up from the initial
temperature. It is preheated on the GHE and it will require less energy to achieve
the required temperature.
𝐸𝐺𝐻𝑅𝑆 = 𝐷𝑎𝑦𝑠 ∗ 𝑃𝑒𝑟𝑠 ∗ 𝑡𝑠ℎ𝑜𝑤𝑒𝑟 ∗ 𝑉𝐺𝐻𝑅𝑆 ∗ 𝐶𝑝𝑐𝑜𝑖𝑙 ∗ 𝜌𝑐𝑜𝑖𝑙 ∗
𝑇𝑤ℎ𝑜𝑡 − 𝑇𝑐𝑜𝑖𝑙𝑜𝑢𝑡𝜂𝑏𝑜𝑖𝑙𝑒𝑟 ∗ 3.6𝐸6
(8.5)
The operational cost is calculated, obtaining lower cost than the reference case
without GHRS.
𝑃𝑟𝑖𝑐𝑒𝐺𝐻𝑅𝑆 = 𝐸𝐺𝐻𝑅𝑆 ∗ 𝑃𝑟𝑖𝑐𝑒𝑘𝑊ℎ (8.6)
𝑆𝑎𝑣𝑖𝑛𝑔𝑠𝑝𝑒𝑟𝑖𝑜𝑑 = 𝑃𝑟𝑖𝑐𝑒𝑟𝑒𝑓 − 𝑃𝑟𝑖𝑐𝑒𝐺𝐻𝑅𝑆 (8.7)
The saving on the period of the first year is defined by equation 8.7.
8.3 Net Present Value
To evaluate the economic benefits of GHE the Net Present Value must be
considered due the fact that money has different value through time. Money from
one specific year has a net value different than the same amount of money in another
period of time.
48
On this step, the net present savings during the lifetime of the device that is 50 years
according to one manufacturer (ReneWABILITY 2016) but for the computation, only
20 years are taking into account. The internal rate of return (r) is assumed to be 8%.
𝑁𝑃𝑉𝑟𝑒𝑓 = 𝑃𝑟𝑖𝑐𝑒𝑟𝑒𝑓 ∗ (
1 − (1 + 𝑟)−𝑡
𝑟)
𝑁𝑃𝑉𝐺𝐻𝑅𝑆 = 𝑃𝑟𝑖𝑐𝑒𝐺𝐻𝑅𝑆 ∗ (1 − (1 + 𝑟)−𝑡
𝑟)
(8.8)
𝑆𝑎𝑣𝑖𝑛𝑔𝑠𝑆𝐸𝐾 = 𝑁𝑃𝑉𝐺𝐻𝑅𝑆 −𝑁𝑃𝑉𝑟𝑒𝑓 (8.9)
8.4 Discounted Payback Period
In economics, there is an important variable known as the Discounted Payback
Period (DPP) which gives the number of years to achieve the breakeven point of the
investment. It is computed using equation 8.10 where Invest is the initial investment
cost, Savingsperiod is the saving on a period of one year and r is the internal return
rate.
𝐷𝑃𝑃 =
𝑙𝑛(1
1 − (𝐼𝑛𝑣𝑒𝑠𝑡 ∗𝑟
𝑆𝑎𝑣𝑖𝑛𝑔𝑠𝑝𝑒𝑟𝑖𝑜𝑑))
𝑙𝑛(1 + 𝑟)
(8.10)
Due the complexity of water usage for different household and the numerous
variables involve the analysis of GHRS, giving a single result is a challenging
situation. Variables such as shower time, shower flow, investments, dimension,
effectiveness and others must be taken into account.
As seen in figure 8.1, the DPP is extremely sensitive to many factors. The proper
dimensioning of the unit is fundamental to make it economically feasible. This
computation was based on the retail prices available at the website of the
manufacturer (ReneWABILITY 2016) and an approximate installation fee. In figure
8.1(a), a unit of 0.05 of nominal diameter and 1.22 m of length for 4 inhabitants per
household, the payback time is below 10 years for all the possible configuration of
flow and shower time proposed. On the other hand, for only 2 inhabitants per
household it is still profitable and under 5 years of payback time for water intensive
49
users. On the low usage region (Short shower time and low water intensity), it is
impossible to reach a break-even point.1
This trend can be seen more easily in figure 8.1(b) whereas a product of the lower
prices of district heating; the region that is unable to reach the breakeven point is
bigger.
Figure 8.1 DPP Analysis for two GHRS under different condition of shower time and flow.
1 The results should not be taking as given for a market analysis. The only purpose is to give
a rough estimation of the potential implementation of GHRS from the economic point of view.
DPP with electricity price.
b) DPP with electricity price.
50
8.5 N-number of households – Monte Carlo Simulation
The potential of implementation analysis should take into account the variability of
water usage (Refer to section 7.1). To study the potential with this variability, a Monte
Carlo simulation was performed in order to introduce a variability factor of the water
usage.
The simulation randomizes 1 000 000 combinations of water usage following the
pattern presented in Figure 6.1 which simulates the variability of water usage for n-
number of households
For a given unit with ε-effectiveness of 49% and conditions of 36°C at the drain side,
8°C on the coil side, and an estimated total investment of 7600 SEK, the simulation
was performed. Figure 8.2 and figure 8.3 displayed the distribution of results for
households with 4 and 3 number of persons per households respectively with the
random variation of water usage.
The 4 persons per household’s results show similar outcomes from the ones
presented in section 8.4, but due the random water usage, a worst case scenario is
presented. On figure 8.2 a clear trend can be depicted. On this situation, it is
expected that if the GHRS were implemented in an n-number of household with 4
inhabitants; for 33.94% of the cases the DPP will be below 5 years for the device
used. Around 62.67% of the times, the DPP will remain below 10 years and only
would not reach a break-even point for 11.76% of the cases.
Figure 8.2 Distributions of DPP for n-number of household with 4 inhabitants.
51
For the figure 8.3 that correspond for 3 persons per household, it is expected to
decrease the values achieved. Even though the results display a good opportunity
for implementation. On this case, for 19.13% of the cases, the DPP will be below 5
years and 46.34% below 10. It would not reach a break-even point for 21.48% of the
occasions. 2
Figure 8.3 Distributions of DPP for n-number of household with 3 inhabitants.
8.6 Emission savings
The allocation of emissions that comes from the electricity production of the country
can be seen as emission savings (Eq. 8.11).
𝑆𝑎𝑣𝑖𝑛𝑔𝑠𝑒𝑚𝑖𝑠𝑠𝑖𝑜𝑛𝑠 = 𝑆𝑎𝑣𝑖𝑛𝑔𝑠𝑘𝑊ℎ ∗ 𝐶𝑂2𝑘𝑊ℎ (8.11)
The energy saved by GHRS, which can range from 30-70% of the energy required
depending on the model used, is multiply by the gr CO2 emitted per kWh produced
from the electricity production graphic depending on the country (Figure 8.4).
District heating manages different concentrations of gr CO2 that can be computed
and give an estimation of the emissions saved.
2 The results should not be taking as given for a market analysis. The only purpose is to give a rough estimation of the potential implementation of GHRS from the economic point of view.
52
Figure 8.4 Graphic of gr CO2 per kWh in Europe - Electricity production 2009.
Source: (European Environment Agency 2011)
8.7 District Heating
In countries like Sweden, District heating accounts for 58% of the total energy use
in non-residential buildings and dwelling. Multi-dwelling buildings use half of this
share (29% of the total energy used) while the other half is shared between the non-
residential building and one/two-dwelling building with a 38% and 12% respectively
(Swedish Energy Agency 2015).
One big advantage of district heating over electricity is that it is available at a lower
price. The price of electricity per kWh is 1.7 SEK2014/kWh while for district heating is
0.74 SEK2014/kWh (Swedish Energy Agency 2015). Electricity price is around 229%
more expensive per kWh than district heating. This fact shows a challenge for
technologies like the GHRS which will face up harder scenarios to achieve a break-
even point from an economic point of view.
Nr
Co
ils
Nu
mb
er
of
pers
on
s
in h
ou
seh
old
Td
rain
IN
[°C
]
Tco
il I
N [
°C]
Insta
llati
on
Fee
[SE
K]
Sh
ow
er
Tim
e [
min
]
Vo
lum
etr
ic F
low
[L/m
in]
Inte
rest
rate
[%
]
Ele
ctr
icit
y P
ric
e
[SE
K/k
Wh
]
Dis
tric
t H
eati
ng
Pri
ce [
SE
K/k
Wh
]
4 4 36 8 3500 6.5 7.29 8 1.7 0.74
Table 8-1 Conditions for the comparison between electricity and district heating.
53
On this section, a comparison about the estimated discounted payback period (DPP)
for different greywater heat exchanger between electricity and district heating prices.
Table 8-1 present the conditions and parameters taken into account for the
comparison. Figure 8.5 shows the results achieved in this analysis.
Figure 8.5 Comparison between electricity and district.
For the order of magnitude, the usage of district heating as energy source increases
the DPP in an average of 4.67 times more than with electricity for the heat exchanger
evaluated. The average payback time for this conditions was around 5.8 years with
electricity and 27.1 years with district heating. This situation exposed the impact of
cheap energy for the implementation of the technology from an economic
perspective.
It is important to remark that the installation fee takes an important role for small
units and that is why bigger units amortize this cost better achieving lower payback
periods.
0.00
5.00
10.00
15.00
20.00
25.00
30.00
35.00
40.00
DP
P [
years
]
GHE Dimensions
Electricity District Heating
54
8.8 GHE for multi-dwelling households
The most usual type of housing in Sweden is to live in an owned single-or two-
dwelling building with a 43% of the share. A rented dwelling in a multi-dwelling
building is the next most common type of housing with a 29%. While the other 20%
lives in owner-occupied apartments in multi-dwelling buildings (SCB-Sweden 2016).
On this section, a short analysis for big units applied in multi-dwelling buildings is
performed.
The approach is a bit different from single households one. The first consideration is
the lower temperature available at the inlet of the drain side. This happens due that
big units require longer pipes from the drain pipes from the households until the
entrance of the GHRS. This situation increases the losses and it is represented with
a lower inlet temperature on the drain side.
Table 8-2 present the conditions and parameters taken into account for the multi-
dwelling analysis and figure 8.6 shows the results achieved in this analysis.
Nr
Co
ils
No
min
al
Dia
me
ter
[m]
Len
gth
[m
]
Td
rain
IN
[°C
]
Tco
il I
N [
°C]
Insta
llati
on
Fee
[SE
K]
Sh
ow
er
Tim
e
[min
]
Vo
lum
etr
ic F
low
[L/m
in]
Inte
rest
rate
[%
]
Ele
ctr
icit
y P
ric
e
[SE
K/k
Wh
]
Dis
tric
t H
eati
ng
Pri
ce [
SE
K/k
Wh
]
4 0.10 2.44 26 8 3500 6.5 7.29 8 1.7 0.74
Table 8-2 Conditions for the analysis with multi-dwelling buildings.
In this case, the lower temperature at the inlet of the drain side allows that the
difference electricity and district heating is not that big. The average increment in
payback period is around 2.86 times more, compared with the 4.67 for single
households.
Additionally, the installation fee does not have that big influence in the payback
period due the fact that these units are more costly and with better performance than
the ones for single households.
From the figure 8.6, it is also stated that the more inhabitants connected to the
device, the lower time it requires to achieve the economic breakeven point. A
cost/benefit analysis is required to achieve the optimal solution between the
permissible losses and the cost.
55
In general, units for multi-dwelling buildings achieve lower payback periods than
single households as it is also mentioned by one of the manufacturers
(ReneWABILITY 2016).
Figure 8.6 Comparison between electricity and district heating for multi-dwelling buildings.
0
2
4
6
8
10
12
14
161
0
12
14
16
18
20
22
24
26
28
30
DP
P [
years
]
Number of persons in the multi-dwelling
Electricity District Heating
56
9 CONCLUSIONS
The present study explored the different fluid mechanics characteristics of vertical
greywater heat exchangers. The first characteristic refers to the falling film effect
present in the drain side that maximizes the contact area between the fluid and the
inside area of the pipe. These conditions also minimize the thickness of the layer
turning the heat transfer mechanism more effective. Secondly, the helical coil
creates a secondary flow that increases the heat transfer coefficient significantly in
comparison with straight pipes and allows the transition to the turbulent regime to be
achieved at a higher Reynolds number than in straight pipes.
A theoretical heat transfer approach of the greywater heat exchanger was proposed
where a mathematical model was developed to simulate the performance of different
GHE. Different correlations available in the literature were evaluated to represent in
the most accurate way the performance of GHE. The model achieves a permissible
margin of error under different conditions of flow, temperatures, dimensions and
others. The heat recovery errors were below 6% for 75.93% of the times and below
10% for 92.59% of the times. The effectiveness of greywater heat exchanger
increase with its length and nominal diameter, being the influence of nominal
diameter bigger to achieve higher effectiveness values. The increase in the number
of coils decrease the effectiveness of the heat exchanger but it is beneficial for
decreasing the pressure drop on the device.
Greywater heat exchanger’s potential of implementation is influenced by several
variables. Water usage is one of the main variables and the variability of this aspect
has a deep implication on the potential of the technology. Not every inhabitant use
the same amount of water for different applications and there is a big fluctuation
between users. Additionally, the number of persons per household is important due
that the more people living in the same household, the higher water consumption will
be and the more economically feasible the GHRS will be. Another variable study in
the present work was the energy price. GHE will have a bigger opportunity when
electricity is used as the source of domestic hot water due its elevated priced
compared to district heating. The lower cost of district heating means longer payback
periods. The total cost of the device include the installation fee and this cost is
important for small units where it can account for 40-50% of the total price. With
lower effectiveness, small units present challenging situation to achieve break-even
points.
With the economic analysis performed, it can be stated that GHE present a higher
opportunity in a household with 3-4 inhabitant. This is not a rule due the variability
57
of water consumption patterns, but from a general point of view, it is more feasible
than for 1-2 inhabitants per household. Under average user consumptions, small
units can achieve a break-even point in around 5-6 years. District heating prices
increase this time by 4.7 times in comparison with electric boilers. For a multi-
dwelling household with big units, the technology is more feasible with a higher
number of households connected. Additionally, the technology has more potential
with big units even with lower energy prices. In the case of district heating, it only
represents an increment of 2.86 times compared to the 4.67 times of the single
households for one of the studies performed.
58
10 FUTURE RESEARCH
Empirical tests about the performance of greywater heat exchanger will validate the
characteristics studied about the technology. A deeper understanding of the
performance according to dimensions and flow conditions will generate better
information to quantify the benefits of GHRS. Additionally, long term effects can be
evaluated because until now, the analyses are taken as an assumption that the heat
exchanger will perform equally during its lifetime. The fouling effect can introduce
additional knowledge to understand the long-term performance of the devices.
This project studied the general concepts of fluid mechanics and heat transfer
involve in the technology. To go further, a CFD (Computational Fluid Dynamics)
analysis can be proposed in order to perform a deeper analysis on the different
devices and to work on optimizing the design to increase the efficiency and
performance of them.
The domestic hot water usage is one of the most important variables understanding
the potential of GHRS. During the development of the present work, a detailed study
concerning the water usage in Sweden was not found. There is information about
consumption per capita, total water usage but not about the patterns and usage in
different applications for households. This study would be interesting for the field and
with that information, a more accurate potential of implementation analysis can be
performed in addition to all the valuable knowledge for different fields around
conservation measures of water.
Most studies on the topic include baths and showers as the most important
application for GHRS. But greywater refers additionally to washbasins, kitchens,
washing machines, dishwashers and others. An additional study simulating these
conditions and impact of all greywater will enrich the discussion of the topic. The
waste water is also an opportunity to study in order to increase the efficiency in the
built environment.
As shown in the present work, several variables influence the economic feasibility of
GHRS. An extensive economic analysis with real-life cases could generate an
important database of the relation with the performance of the devices, the variability
of water usage and the economic performance. This information could generate
more accurate and meaningful conclusions about the economic potential as a cost
and effective solution.
59
11 REFERENCES
Athuraliya, A., Roberts, P. & Brown, A., 2012. Yarra Valley Future Water - Residential water use study volume 2. , 2(August), pp.1 – 46.
Austen, D.S. & Soliman, H.M., 1988. Laminar flow and heat transfer in helically coiled tubes with substantial pitch. Experimental Thermal and Fluid Science, 1(2), pp.183–194.
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62
APPENDIX A. Heat transfer model
START
GEOMETRIC INPUTSGHRS Diameters
LengthNumber of Coils
CASE INPUTSVolumetric Flow
Inlet Temperatures(Coil & Drain)
OTHERSIteration Output Temp
Constants (k_cooper, g,..)
FLUID THERMODYNAMIC PROPERTIES[Cp, µ, ρ, k, Pr] at average Temperature (T_in+T_out)/2 for both flows (Coil and Drain)
THERMAL CAPACITIESC_drain=m_dot_drain*Cp_drain
C_coil=m_dot_coil*Cp_coil*NrCoils
RESISTOR 1CONVECTION FILM
MINIMUM THERMAL CAPACITYC_min
VARIABLESReynolds
Heat Transfer Coefficient – Falling Film
CALCULATERESISTOR
Convection
RESISTOR 2CONDUCTION
DRAIN PIPE
NTU METHOD
Output Temperatures = Initial Output Temp
RESULT
CALCULATE RESISTOR
Conduction
RESISTOR 4CONDUCTION
COIL PIPE
RESISTOR 5CONVECTION
COIL
CALCULATE RESISTOR
Conduction
VARIABLESReynolds
Dean NumberNusselt Number
CALCULATEHeat Transfer
Coefficient
CALCULATERESISTOR
Convection
TOTAL THERMAL
RESISTANCEUA NTU
EffectivenessqOutput
TemperaturesIntial Output Temp = Output Temp
NO
YES
END
63
Temperature [°C] µ [kg/m-s] k [W/m-K] Cp [kJ/kg-K] Pr [-] ρ [kg/m^3]
0 0.0017930 0.5475 4.228 13.840 1000.00
1.224 0.0017190 0.5500 4.219 13.180 1000.00
2.449 0.0016500 0.5525 4.211 12.570 1000.00
3.673 0.0015850 0.5550 4.205 12.010 1000.00
4.898 0.0015240 0.5574 4.200 11.480 1000.00
6.122 0.0014670 0.5598 4.196 10.990 1000.00
7.347 0.0014130 0.5623 4.193 10.530 1000.00
8.571 0.0013620 0.5647 4.190 10.110 1000.00
9.796 0.0013140 0.5670 4.188 9.707 1000.00
11.02 0.0012690 0.5694 4.187 9.330 999.60
12.24 0.0012260 0.5718 4.185 8.976 999.50
13.47 0.0011860 0.5741 4.185 8.643 999.40
14.69 0.0011470 0.5764 4.184 8.329 999.20
15.92 0.0011110 0.5787 4.184 8.032 999.00
17.14 0.0010760 0.5809 4.183 7.751 998.80
18.37 0.0010430 0.5831 4.183 7.485 998.60
19.59 0.0010120 0.5853 4.183 7.233 998.30
20.82 0.0009824 0.5875 4.183 6.994 998.10
22.04 0.0009540 0.5897 4.183 6.767 997.80
23.27 0.0009268 0.5918 4.183 6.551 997.50
24.49 0.0009010 0.5939 4.183 6.346 997.20
25.71 0.0008762 0.5960 4.183 6.150 996.90
26.94 0.0008526 0.5980 4.183 5.964 996.50
28.16 0.0008299 0.6000 4.183 5.786 996.20
29.39 0.0008082 0.6020 4.183 5.616 995.80
30.61 0.0007874 0.6039 4.183 5.454 995.50
31.84 0.0007675 0.6059 4.183 5.299 995.10
33.06 0.0007484 0.6077 4.183 5.151 994.70
34.29 0.0007300 0.6096 4.183 5.009 994.30
35.51 0.0007124 0.6114 4.183 4.873 993.90
36.73 0.0006954 0.6132 4.183 4.743 993.40
37.96 0.0006791 0.6150 4.182 4.619 993.00
39.18 0.0006634 0.6167 4.182 4.499 992.50
40.41 0.0006483 0.6184 4.182 4.384 992.10
41.63 0.0006337 0.6200 4.182 4.274 991.60
42.86 0.0006197 0.6217 4.182 4.169 991.10
44.08 0.0006062 0.6232 4.182 4.067 990.60
45.31 0.0005931 0.6248 4.182 3.969 990.10
46.53 0.0005805 0.6263 4.182 3.876 989.60
47.76 0.0005683 0.6278 4.182 3.785 989.00
48.98 0.0005566 0.6293 4.181 3.698 988.50
50.2 0.0005452 0.6307 4.181 3.615 987.90
51.43 0.0005342 0.6321 4.181 3.534 987.40
52.65 0.0005236 0.6335 4.182 3.456 986.80
53.88 0.0005133 0.6348 4.182 3.381 986.20
55.1 0.0005034 0.6361 4.182 3.309 985.60
56.33 0.0004937 0.6374 4.182 3.239 985.00
57.55 0.0004844 0.6386 4.182 3.172 984.40
58.78 0.0004753 0.6398 4.182 3.107 983.80
60 0.0004666 0.6410 4.183 3.045 983.20
Table A-1 Thermodynamic properties of water.
64
Geometry R1 - CONVECTION
FALLING FILM R2 - CONDUCTION
DRAIN PIPE R3 - CONTACT
RESISTOR R4 - CONDUCTION
COIL PIPE R5 - CONVECTION
HELICAL COIL
TOTAL RESISTANCE
[K/W]
Length
[m] Resistor
[K/W] % of total resistance
Resistor [K/W]
% of total resistance
Resistor [K/W]
% of total resistanc
e
Resistor [K/W]
% of total resistance
Resistor [K/W]
% of total resistance
Nom
inal D
iam
ete
r =
0.0
5 m
Num
ber
of
Coils
= 4
0.91 1.531E-03 43.02% 3.357E-05 0.94% 2.591E-04 7.28% 3.267E-05 0.92% 1.702E-03 47.84% 3.5588E-03
1.07 1.312E-03 43.37% 2.855E-05 0.94% 2.204E-04 7.28% 2.778E-05 0.92% 1.437E-03 47.49% 3.0257E-03
1.22 1.158E-03 43.66% 2.504E-05 0.94% 1.933E-04 7.28% 2.437E-05 0.92% 1.252E-03 47.19% 2.6532E-03
1.37 1.038E-03 43.93% 2.230E-05 0.94% 1.721E-04 7.28% 2.170E-05 0.92% 1.109E-03 46.93% 2.3625E-03
1.52 9.405E-04 44.17% 2.010E-05 0.94% 1.551E-04 7.28% 1.956E-05 0.92% 9.941E-04 46.68% 2.1294E-03
1.68 8.556E-04 44.41% 1.818E-05 0.94% 1.403E-04 7.28% 1.770E-05 0.92% 8.948E-04 46.45% 1.9266E-03
1.83 7.891E-04 44.61% 1.669E-05 0.94% 1.288E-04 7.28% 1.624E-05 0.92% 8.179E-04 46.24% 1.7688E-03
2.13 6.837E-04 44.98% 1.434E-05 0.94% 1.107E-04 7.28% 1.396E-05 0.92% 6.973E-04 45.88% 1.5200E-03
2.44 6.014E-04 45.31% 1.252E-05 0.94% 9.663E-05 7.28% 1.218E-05 0.92% 6.046E-04 45.55% 1.3273E-03
2.74 5.390E-04 45.58% 1.115E-05 0.94% 8.605E-05 7.28% 1.085E-05 0.92% 5.353E-04 45.28% 1.1824E-03
3.05 4.870E-04 45.83% 1.001E-05 0.94% 7.731E-05 7.28% 9.747E-06 0.92% 4.785E-04 45.03% 1.0626E-03
Nom
inal D
iam
ete
r =
0.0
8 m
Num
ber
of
Coils
= 4
0.91 1.137E-03 44.13% 2.128E-05 0.83% 1.666E-04 6.47% 2.128E-05 0.83% 1.230E-03 47.75% 2.5764E-03
1.07 9.752E-04 44.51% 1.810E-05 0.83% 1.417E-04 6.47% 1.810E-05 0.83% 1.038E-03 47.37% 2.1909E-03
1.22 8.614E-04 44.83% 1.587E-05 0.83% 1.242E-04 6.47% 1.587E-05 0.83% 9.042E-04 47.06% 1.9216E-03
1.37 7.720E-04 45.11% 1.413E-05 0.83% 1.106E-04 6.46% 1.413E-05 0.83% 8.005E-04 46.78% 1.7114E-03
1.52 6.998E-04 45.36% 1.274E-05 0.83% 9.972E-05 6.46% 1.274E-05 0.83% 7.177E-04 46.52% 1.5427E-03
1.68 6.367E-04 45.61% 1.153E-05 0.83% 9.022E-05 6.46% 1.153E-05 0.83% 6.461E-04 46.28% 1.3961E-03
1.83 5.873E-04 45.81% 1.058E-05 0.83% 8.283E-05 6.46% 1.058E-05 0.83% 5.906E-04 46.08% 1.2819E-03
2.13 5.088E-04 46.17% 9.091E-06 0.83% 7.116E-05 6.46% 9.091E-06 0.83% 5.037E-04 45.72% 1.1019E-03
2.44 4.474E-04 46.49% 7.936E-06 0.82% 6.212E-05 6.46% 7.936E-06 0.82% 4.369E-04 45.40% 9.6234E-04
2.74 4.009E-04 46.75% 7.067E-06 0.82% 5.532E-05 6.45% 7.067E-06 0.82% 3.871E-04 45.15% 8.5739E-04
3.05 3.621E-04 46.99% 6.349E-06 0.82% 4.970E-05 6.45% 6.349E-06 0.82% 3.461E-04 44.92% 7.7061E-04
Nom
inal D
iam
ete
r =
0.1
m
Num
ber
of
Coils
= 4
0.91 9.878E-04 44.81% 1.711E-05 0.78% 1.345E-04 6.10% 1.727E-05 0.78% 1.048E-03 47.53% 2.2047E-03
1.07 8.475E-04 45.20% 1.455E-05 0.78% 1.144E-04 6.10% 1.469E-05 0.78% 8.840E-04 47.14% 1.8751E-03
1.22 7.487E-04 45.52% 1.276E-05 0.78% 1.003E-04 6.10% 1.288E-05 0.78% 7.702E-04 46.82% 1.6448E-03
1.37 6.710E-04 45.80% 1.136E-05 0.78% 8.936E-05 6.10% 1.147E-05 0.78% 6.818E-04 46.54% 1.4651E-03
1.52 6.083E-04 46.06% 1.024E-05 0.78% 8.054E-05 6.10% 1.034E-05 0.78% 6.114E-04 46.29% 1.3208E-03
1.68 5.534E-04 46.30% 9.266E-06 0.78% 7.287E-05 6.10% 9.353E-06 0.78% 5.504E-04 46.05% 1.1954E-03
1.83 5.104E-04 46.50% 8.506E-06 0.77% 6.690E-05 6.09% 8.586E-06 0.78% 5.033E-04 45.85% 1.0977E-03
2.13 4.421E-04 46.86% 7.308E-06 0.77% 5.748E-05 6.09% 7.377E-06 0.78% 4.293E-04 45.50% 9.4363E-04
2.44 3.887E-04 47.16% 6.380E-06 0.77% 5.017E-05 6.09% 6.440E-06 0.78% 3.725E-04 45.20% 8.2423E-04
2.74 3.482E-04 47.41% 5.681E-06 0.77% 4.468E-05 6.08% 5.735E-06 0.78% 3.301E-04 44.95% 7.3438E-04
3.05 3.144E-04 47.63% 5.104E-06 0.77% 4.014E-05 6.08% 5.152E-06 0.78% 2.953E-04 44.73% 6.6009E-04
Nom
inal D
iam
. =
0.0
8 m
Num
ber
of
Coils
= 6
0.91 1.131E-03 39.67% 2.128E-05 0.75% 1.666E-04 5.84% 2.128E-05 0.75% 1.511E-03 52.99% 2.8511E-03
1.22 8.567E-04 40.35% 1.587E-05 0.75% 1.242E-04 5.85% 1.587E-05 0.75% 1.111E-03 52.31% 2.1234E-03
1.52 6.960E-04 40.87% 1.274E-05 0.75% 9.972E-05 5.86% 1.274E-05 0.75% 8.816E-04 51.77% 1.7027E-03
1.83 5.841E-04 41.32% 1.058E-05 0.75% 8.283E-05 5.86% 1.058E-05 0.75% 7.254E-04 51.32% 1.4135E-03
2.13 5.061E-04 41.69% 9.091E-06 0.75% 7.116E-05 5.86% 9.091E-06 0.75% 6.186E-04 50.95% 1.2140E-03
2.44 4.451E-04 42.01% 7.936E-06 0.75% 6.212E-05 5.86% 7.936E-06 0.75% 5.365E-04 50.63% 1.0596E-03
2.74 3.988E-04 42.27% 7.067E-06 0.75% 5.532E-05 5.86% 7.067E-06 0.75% 4.752E-04 50.36% 9.4347E-04
3.05 3.603E-04 42.51% 6.349E-06 0.75% 4.970E-05 5.86% 6.349E-06 0.75% 4.248E-04 50.12% 8.4756E-04
Nom
inal D
iam
ete
r =
0.1
m
Num
ber
of
Coils
= 6
0.91 9.826E-04 40.30% 1.711E-05 0.70% 1.345E-04 5.52% 1.727E-05 0.71% 1.287E-03 52.77% 2.4382E-03
1.07 8.429E-04 40.68% 1.455E-05 0.70% 1.144E-04 5.52% 1.469E-05 0.71% 1.085E-03 52.39% 2.0720E-03
1.22 7.446E-04 41.00% 1.276E-05 0.70% 1.003E-04 5.53% 1.288E-05 0.71% 9.456E-04 52.07% 1.8162E-03
1.37 6.674E-04 41.28% 1.136E-05 0.70% 8.936E-05 5.53% 1.147E-05 0.71% 8.372E-04 51.78% 1.6167E-03
1.52 6.050E-04 41.53% 1.024E-05 0.70% 8.054E-05 5.53% 1.034E-05 0.71% 7.506E-04 51.53% 1.4567E-03
1.68 5.504E-04 41.77% 9.266E-06 0.70% 7.287E-05 5.53% 9.353E-06 0.71% 6.758E-04 51.28% 1.3177E-03
1.83 5.077E-04 41.98% 8.506E-06 0.70% 6.690E-05 5.53% 8.586E-06 0.71% 6.178E-04 51.08% 1.2095E-03
1.98 4.713E-04 42.17% 7.862E-06 0.70% 6.183E-05 5.53% 7.936E-06 0.71% 5.688E-04 50.89% 1.1177E-03
2.13 4.399E-04 42.34% 7.308E-06 0.70% 5.748E-05 5.53% 7.377E-06 0.71% 5.269E-04 50.72% 1.0390E-03
2.29 4.107E-04 42.50% 6.798E-06 0.70% 5.346E-05 5.53% 6.862E-06 0.71% 4.885E-04 50.55% 9.6632E-04
2.44 3.868E-04 42.65% 6.380E-06 0.70% 5.017E-05 5.53% 6.440E-06 0.71% 4.571E-04 50.41% 9.0690E-04
2.74 3.465E-04 42.91% 5.681E-06 0.70% 4.468E-05 5.53% 5.735E-06 0.71% 4.050E-04 50.15% 8.0762E-04
3.05 3.130E-04 43.13% 5.104E-06 0.70% 4.014E-05 5.53% 5.152E-06 0.71% 3.622E-04 49.92% 7.2557E-04
Average percetange [%] 43.98% 0.80% 6.24% 0.80% 48.19%
Table A-2 Table of thermal resistors.
65
APPENDIX B. Model Validation
Effectiveness Error Histogram Heat Revovery Error Histogram
Bin Frequency Cumulative % Bin Frequency Cumulative %
Ma
nla
pa
z &
Ch
urc
hill 2.0% 12 22.22%
Ma
nla
pa
z &
Ch
urc
hill 2.0% 13 24.07%
4.0% 14 48.15% 4.0% 14 50.00%
6.0% 8 62.96% 6.0% 14 75.93%
8.0% 11 83.33% 8.0% 5 85.19%
10.0% 5 92.59% 10.0% 4 92.59%
12.0% 2 96.30% 12.0% 2 96.30%
More 2 100.00% More 2 100.00%
Ka
rl-S
aed
er
2.0% 13 24.07%
Ka
rl-S
aed
er
2.0% 12 22.22%
4.0% 11 44.44% 4.0% 17 53.70%
6.0% 12 66.67% 6.0% 13 77.78%
8.0% 9 83.33% 8.0% 4 85.19%
10.0% 5 92.59% 10.0% 3 90.74%
12.0% 2 96.30% 12.0% 3 96.30%
More 2 100.00% More 2 100.00%
Jan
ssen
2.0% 3 5.56%
Jan
ssen
2.0% 4 7.41%
4.0% 5 14.81% 4.0% 5 16.67%
6.0% 7 27.78% 6.0% 5 25.93%
8.0% 7 40.74% 8.0% 10 44.44%
10.0% 7 53.70% 10.0% 4 51.85%
12.0% 8 68.52% 12.0% 12 74.07%
More 17 100.00% More 14 100.00%
Dra
vid
et
al.
2.0% 7 12.96%
Dra
vid
et
al.
2.0% 7 12.96%
4.0% 5 22.22% 4.0% 7 25.93%
6.0% 10 40.74% 6.0% 11 46.30%
8.0% 9 57.41% 8.0% 10 64.81%
10.0% 12 79.63% 10.0% 11 85.19%
12.0% 5 88.89% 12.0% 4 92.59%
More 6 100.00% More 4 100.00%
Table B-1 Table of the error distribution for different Nusselt correlations.
66
(COLLINS 2009) Manlapaz and Churchill Karl-Saeder Janssen Dravid et al.
MODEL N
om
ina
l
Dia
me
ter
[m]
Le
ng
th [
m]
Eff
ec
tive
ne
ss
[%]
Hea
t R
ec
ov
ery
[W]
Eff
ec
tive
ne
ss
[%]
Eff
ec
tive
ne
ss
ER
RO
R [
%]
Hea
t R
ec
ov
ery
[W]
Hea
t R
ec
ov
ery
ER
RO
R [
W]
Eff
ec
tive
ne
ss
[%]
Eff
ec
tive
ne
ss
ER
RO
R [
%]
Hea
t R
ec
ov
ery
[W]
Hea
t R
ec
ov
ery
ER
RO
R [
W]
Eff
ec
tive
ne
ss
[%]
Eff
ec
tive
ne
ss
ER
RO
R [
%]
Hea
t R
ec
ov
ery
[W]
Hea
t R
ec
ov
ery
ER
RO
R [
W]
Eff
ec
tive
ne
ss
[%]
Eff
ec
tive
ne
ss
ER
RO
R [
%]
Hea
t R
ec
ov
ery
[W]
Hea
t R
ec
ov
ery
ER
RO
R [
W]
R2-36 0.05 0.91 32.6% 5720 31.1% 4.73% 5430.13 5.07% 31.3% 3.90% 5477.26 4.24% 27.0% 17.19% 4719.54 17.49% 29.4% 9.92% 5134.38 10.24%
R2-42 0.05 1.07 37.7% 6590 34.6% 8.13% 6056.23 8.10% 34.9% 7.45% 6101.01 7.42% 30.3% 19.62% 5298.90 19.59% 32.8% 12.92% 5740.80 12.89%
R2-48 0.05 1.22 37.8% 6540 37.7% 0.36% 6586.90 0.72% 37.9% 0.28% 6629.02 1.36% 33.1% 12.32% 5796.23 11.37% 35.8% 5.34% 6257.44 4.32%
R2-54 0.05 1.37 42.1% 7400 40.4% 3.98% 7070.46 4.45% 40.6% 3.45% 7109.70 3.92% 35.8% 15.06% 6254.53 15.48% 38.5% 8.60% 6730.39 9.05%
R2-60 0.05 1.52 47.4% 7770 42.9% 9.39% 7512.89 3.31% 43.2% 8.95% 7549.20 2.84% 38.2% 19.46% 6678.20 14.05% 41.0% 13.59% 7164.95 7.79%
R2-66 0.05 1.68 48.9% 8590 45.4% 7.13% 7945.12 7.51% 45.6% 6.74% 7978.36 7.12% 40.6% 17.05% 7096.20 17.39% 43.4% 11.26% 7591.24 11.63%
R2-72 0.05 1.83 53.8% 9410 47.5% 11.64% 8317.59 11.61% 47.7% 11.31% 8348.04 11.29% 42.6% 20.75% 7459.70 20.73% 45.5% 15.44% 7959.98 15.41%
R2-84 0.05 2.13 56.5% 9890 51.3% 9.16% 8981.47 9.19% 51.5% 8.90% 9006.76 8.93% 46.4% 17.92% 8115.28 17.94% 49.3% 12.81% 8620.48 12.84%
R2-96 0.05 2.44 61.3% 10670 54.7% 10.77% 9573.38 10.28% 54.8% 10.58% 9593.97 10.08% 49.8% 18.83% 8708.26 18.39% 52.6% 14.13% 9212.97 13.66%
R2-108 0.05 2.74 63.7% 10630 57.5% 9.66% 10072.63 5.24% 57.6% 9.51% 10089.27 5.09% 52.6% 17.36% 9214.74 13.31% 55.5% 12.87% 9715.38 8.60%
R2-120 0.05 3.05 64.4% 10810 60.1% 6.63% 10526.35 2.62% 60.2% 6.51% 10539.50 2.50% 55.3% 14.13% 9680.14 10.45% 58.1% 9.75% 10174.14 5.88%
R3-36 0.08 0.91 38.7% 6790 38.4% 0.89% 6708.24 1.20% 38.6% 0.14% 6758.85 0.46% 34.7% 10.30% 6070.89 10.59% 36.5% 5.79% 6376.40 6.09%
R3-42 0.08 1.07 43.1% 7500 42.3% 1.97% 7390.78 1.46% 42.5% 1.35% 7437.29 0.84% 38.5% 10.77% 6727.43 10.30% 40.3% 6.55% 7045.26 6.06%
R3-48 0.08 1.22 48.1% 8310 45.5% 5.45% 7956.46 4.25% 45.7% 4.94% 7999.03 3.74% 41.6% 13.52% 7277.64 12.42% 43.5% 9.65% 7602.81 8.51%
R3-54 0.08 1.37 50.0% 8710 48.4% 3.27% 8462.02 2.85% 48.6% 2.83% 8500.76 2.40% 44.4% 11.14% 7774.16 10.74% 46.3% 7.37% 8103.63 6.96%
R3-60 0.08 1.52 54.6% 9460 51.0% 6.68% 8916.55 5.74% 51.2% 6.31% 8951.69 5.37% 47.0% 13.92% 8224.49 13.06% 48.9% 10.45% 8555.98 9.56%
R3-66 0.08 1.68 55.9% 9710 53.4% 4.39% 9353.43 3.67% 53.6% 4.07% 9384.99 3.35% 49.5% 11.47% 8660.87 10.80% 51.4% 8.08% 8992.62 7.39%
R3-72 0.08 1.83 59.4% 10330 55.6% 6.46% 9724.34 5.86% 55.7% 6.19% 9752.82 5.59% 51.6% 13.10% 9034.14 12.54% 53.5% 9.92% 9364.80 9.34%
R3-84 0.08 2.13 61.5% 10610 59.3% 3.65% 10373.07 2.23% 59.4% 3.43% 10396.19 2.02% 55.4% 9.96% 9693.22 8.64% 57.2% 6.93% 10019.04 5.57%
R3-96 0.08 2.44 66.4% 11550 62.5% 5.90% 10938.55 5.29% 62.6% 5.74% 10957.08 5.13% 58.7% 11.62% 10274.28 11.05% 60.5% 8.88% 10592.76 8.29%
R3-108 0.08 2.74 67.9% 11920 65.1% 4.06% 11406.35 4.31% 65.2% 3.93% 11421.23 4.18% 61.5% 9.50% 10759.66 9.73% 63.2% 6.89% 11069.84 7.13%
R3-120 0.08 3.05 67.8% 12060 67.5% 0.40% 11824.44 1.95% 67.6% 0.30% 11836.21 1.86% 63.9% 5.69% 11197.12 7.15% 65.7% 3.15% 11498.14 4.66%
R4-36 0.1 0.91 43.0% 7580 42.1% 2.10% 7363.98 2.85% 42.4% 1.42% 7414.95 2.18% 38.8% 9.81% 6783.99 10.50% 40.1% 6.66% 7020.28 7.38%
R4-42 0.1 1.07 46.6% 8120 46.1% 1.10% 8062.90 0.70% 46.4% 0.54% 8109.02 0.14% 42.7% 8.42% 7466.41 8.05% 44.1% 5.44% 7709.44 5.06%
R4-48 0.1 1.22 53.5% 9310 49.4% 7.75% 8635.68 7.24% 49.6% 7.31% 8677.39 6.79% 45.9% 14.21% 8031.31 13.73% 47.3% 11.58% 8277.59 11.09%
R4-54 0.1 1.37 55.8% 9570 52.2% 6.37% 9142.70 4.47% 52.5% 5.99% 9180.29 4.07% 48.8% 12.59% 8535.72 10.81% 50.2% 10.05% 8783.14 8.22%
R4-60 0.1 1.52 59.1% 10310 54.8% 7.24% 9594.69 6.94% 55.0% 6.91% 9628.50 6.61% 51.4% 13.10% 8988.88 12.81% 52.8% 10.71% 9235.91 10.42%
R4-66 0.1 1.68 60.5% 10550 57.3% 5.33% 10025.74 4.97% 57.5% 5.04% 10055.90 4.68% 53.8% 11.01% 9424.16 10.67% 55.2% 8.69% 9669.56 8.35%
R4-72 0.1 1.83 63.5% 11070 59.3% 6.54% 10389.13 6.15% 59.5% 6.29% 10416.21 5.91% 55.9% 11.89% 9793.52 11.53% 57.3% 9.71% 10036.58 9.34%
R4-84 0.1 2.13 67.0% 11500 62.9% 6.06% 11019.13 4.18% 63.1% 5.87% 11040.96 3.99% 59.6% 11.01% 10439.16 9.22% 61.0% 8.99% 10676.02 7.17%
R4-96 0.1 2.44 69.0% 12300 66.0% 4.30% 11562.57 6.00% 66.1% 4.15% 11580.04 5.85% 62.8% 8.94% 11001.55 10.56% 64.1% 7.04% 11230.85 8.69%
R4-108 0.1 2.74 69.6% 12120 68.6% 1.48% 12008.19 0.92% 68.7% 1.36% 12022.26 0.81% 65.5% 5.92% 11466.54 5.39% 66.7% 4.10% 11688.09 3.56%
R4-120 0.1 3.05 72.4% 12760 70.8% 2.18% 12403.49 2.79% 70.9% 2.09% 12414.70 2.71% 67.8% 6.29% 11881.94 6.88% 69.1% 4.61% 12095.41 5.21%
C3-36 0.08 0.91 31.3% 5410 36.0% 14.99% 6293.91 16.34% 36.4% 16.34% 6367.93 17.71% 32.5% 3.75% 5678.76 4.97% 34.0% 8.71% 5950.29 9.99%
C3-48 0.08 1.22 41.6% 7330 43.0% 3.41% 7524.97 2.66% 43.4% 4.33% 7592.22 3.58% 39.2% 5.75% 6858.64 6.43% 40.9% 1.71% 7152.47 2.42%
C3-60 0.08 1.52 46.9% 8280 48.5% 3.39% 8484.17 2.47% 48.8% 4.12% 8543.95 3.19% 44.6% 5.00% 7796.01 5.85% 46.3% 1.30% 8099.38 2.18%
C3-72 0.08 1.83 48.7% 8600 53.1% 9.11% 9299.32 8.13% 53.4% 9.73% 9351.77 8.74% 49.2% 0.97% 8605.55 0.06% 50.9% 4.56% 8911.43 3.62%
C3-84 0.08 2.13 56.3% 9720 56.9% 1.06% 9959.25 2.46% 57.2% 1.53% 10005.36 2.94% 53.0% 5.93% 9269.94 4.63% 54.7% 2.85% 9573.93 1.50%
C3-96 0.08 2.44 60.7% 10520 60.2% 0.83% 10538.24 0.17% 60.4% 0.44% 10578.66 0.56% 56.3% 7.21% 9859.65 6.28% 58.0% 4.39% 10159.03 3.43%
C3-108 0.08 2.74 62.9% 11130 62.9% 0.07% 11019.83 0.99% 63.1% 0.39% 11055.51 0.67% 59.1% 5.97% 10355.11 6.96% 60.8% 3.30% 10648.49 4.33%
C3-120 0.08 3.05 66.4% 11570 65.4% 1.50% 11452.22 1.02% 65.6% 1.23% 11483.69 0.75% 61.7% 7.07% 10803.84 6.62% 63.3% 4.61% 11090.14 4.15%
C4-36 0.1 0.91 34.8% 6120 39.7% 13.99% 6937.98 13.37% 40.1% 15.22% 7012.79 14.59% 36.5% 4.81% 6379.40 4.24% 37.6% 8.09% 6579.04 7.50%
C4-42 0.1 1.07 40.8% 7110 43.6% 6.91% 7630.39 7.32% 44.0% 7.90% 7700.86 8.31% 40.3% 1.22% 7050.38 0.84% 41.5% 1.69% 7257.72 2.08%
C4-48 0.1 1.22 43.5% 7510 46.9% 7.77% 8202.06 9.22% 47.3% 8.64% 8268.19 10.10% 43.5% 0.01% 7609.76 1.33% 44.7% 2.77% 7821.57 4.15%
C4-54 0.1 1.37 47.9% 8320 49.8% 3.93% 8711.23 4.70% 50.1% 4.67% 8773.05 5.45% 46.4% 3.21% 8112.23 2.50% 47.6% 0.66% 8326.53 0.08%
C4-60 0.1 1.52 50.4% 8830 52.4% 3.94% 9167.59 3.82% 52.7% 4.59% 9225.26 4.48% 48.9% 2.88% 8566.06 2.99% 50.2% 0.44% 8781.37 0.55%
C4-66 0.1 1.68 52.6% 9120 54.9% 4.33% 9604.93 5.32% 55.2% 4.92% 9658.43 5.90% 51.4% 2.19% 9004.10 1.27% 52.7% 0.14% 9219.28 1.09%
C4-72 0.1 1.83 57.1% 9980 57.0% 0.19% 9975.22 0.05% 57.3% 0.31% 10025.10 0.45% 53.6% 6.17% 9377.42 6.04% 54.8% 4.03% 9591.64 3.89%
C4-78 0.1 1.98 59.1% 10120 58.9% 0.32% 10312.36 1.90% 59.2% 0.13% 10358.88 2.36% 55.5% 6.05% 9719.30 3.96% 56.7% 4.00% 9931.93 1.86%
C4-84 0.1 2.13 63.1% 10890 60.7% 3.85% 10620.61 2.47% 60.9% 3.46% 10664.03 2.08% 57.3% 9.17% 10033.54 7.86% 58.5% 7.26% 10244.14 5.93%
C4-90 0.1 2.29 60.5% 10700 62.4% 3.11% 10921.57 2.07% 62.6% 3.49% 10961.95 2.45% 59.1% 2.36% 10341.91 3.35% 60.3% 0.40% 10549.96 1.40%
C4-96 0.1 2.44 65.8% 11350 63.9% 2.95% 11180.78 1.49% 64.1% 2.62% 11218.55 1.16% 60.6% 7.91% 10608.73 6.53% 61.8% 6.13% 10814.15 4.72%
C4-108 0.1 2.74 68.9% 12010 66.5% 3.50% 11642.45 3.06% 66.7% 3.22% 11675.64 2.78% 63.3% 8.10% 11086.86 7.69% 64.5% 6.45% 11286.57 6.02%
C4-120 0.1 3.05 70.8% 11940 68.8% 2.78% 12053.73 0.95% 69.0% 2.54% 12082.91 1.20% 65.8% 7.12% 11515.95 3.55% 66.9% 5.56% 11709.44 1.93%
Table B-2 Table of Errors for different GHRS with different Nusselt Correlations.
67
Table B-3 Table of errors under different flows.
RE
F.
Tem
p. D
rain
In
[°C
]
Tem
p. C
oil
In
[°C
]
Flo
w [LP
M]
(CO
LLIN
S 2
009)
[°C
]
MO
DE
L [°C
]
DIF
F. [°
C]
Err
or
[%]
(CO
LLIN
S 2
009)
[°C
]
MO
DE
L [°C
]
DIF
F. [°
C]
Err
or
[%]
(CO
LLIN
S 2
009)
[°C
]
MO
DE
L
DIF
F.
Err
or
[%]
(CO
LLIN
S 2
009)
[°C
]
MO
DE
L [W
]
DIF
F. [W
]
Err
or
[%]
36.0 8.1 4.03 21.6 22.41 -0.81 3.75% 22.7 21.63 1.07 4.71% 0.522 0.487 0.035 6.76% 4100 3800 300 7.31%
36.1 8.0 7.71 25.1 25.24 -0.14 0.54% 19.3 18.79 0.51 2.64% 0.402 0.386 0.016 4.06% 6090 5799 291 4.78%
36.0 8.1 10.76 26.6 26.62 -0.02 0.09% 17.8 17.43 0.37 2.06% 0.347 0.336 0.011 3.15% 7270 7000 270 3.71%
36.9 8.0 13.75 27.6 28.16 -0.56 2.01% 17 16.69 0.31 1.82% 0.312 0.303 0.009 3.02% 8610 8339 271 3.15%
35.7 8.1 3.99 19.1 19.84 -0.74 3.89% 24.6 23.91 0.69 2.80% 0.601 0.574 0.027 4.41% 4610 4395 215 4.67%
36.2 8.2 7.92 22.2 23.12 -0.92 4.14% 21.9 21.23 0.67 3.05% 0.492 0.467 0.025 5.06% 7600 7191 409 5.38%
36.1 8.0 10.84 23.5 24.39 -0.89 3.79% 20.4 19.66 0.74 3.62% 0.443 0.417 0.026 5.94% 9420 8810 610 6.48%
35.9 8.2 14.23 25.4 25.54 -0.14 0.53% 19.2 18.52 0.68 3.54% 0.396 0.374 0.022 5.51% 10860 10236 624 5.75%
35.9 8.2 4.16 15.8 15.83 -0.03 0.18% 28.4 28.24 0.16 0.57% 0.729 0.725 0.004 0.60% 5840 5803 37 0.63%
36.0 7.7 7.88 18.5 18.00 0.50 2.69% 25.3 25.66 -0.36 1.40% 0.624 0.636 -0.012 1.92% 9690 9854 -164 1.69%
36.0 8.0 10.73 20.1 19.50 0.60 2.96% 23.9 24.45 -0.55 2.30% 0.569 0.589 -0.020 3.53% 11900 12295 -395 3.32%
36.5 8.0 13.80 22 20.83 1.17 5.32% 23 23.62 -0.62 2.70% 0.527 0.550 -0.023 4.32% 14430 15016 -586 4.06%
36.0 7.8 4.06 20.1 18.61 1.49 7.41% 23.6 25.15 -1.55 6.55% 0.559 0.617 -0.058 10.31% 4450 4905 -455 10.22%
35.6 7.8 7.96 20.8 21.36 -0.56 2.69% 22.6 21.99 0.61 2.70% 0.531 0.512 0.019 3.56% 8180 7870 310 3.79%
35.5 7.7 10.63 22.7 22.55 0.15 0.65% 20.6 20.60 0.00 0.01% 0.464 0.466 -0.002 0.37% 9540 9557 -17 0.18%
36.3 7.9 14.03 24.6 24.27 0.33 1.33% 19.6 19.88 -0.28 1.42% 0.415 0.423 -0.008 2.04% 11500 11711 -211 1.84%
35.7 7.6 4.06 16.4 13.77 2.63 16.04% 27.3 29.49 -2.19 8.02% 0.7 0.780 -0.080 11.46% 5580 6188 -608 10.90%
35.7 8.1 8.45 17 16.61 0.39 2.29% 27.1 27.15 -0.05 0.18% 0.687 0.692 -0.005 0.67% 11160 11210 -50 0.44%
36.1 8.0 10.85 17.6 17.63 -0.03 0.17% 26.6 26.42 0.18 0.68% 0.662 0.657 0.005 0.76% 14050 13920 131 0.93%
35.7 7.6 13.77 17.6 18.33 -0.73 4.15% 25.8 24.93 0.87 3.38% 0.65 0.618 0.032 4.90% 17520 16618 902 5.15%
35.3 7.7 4.41 17.4 17.73 -0.33 1.90% 26 25.22 0.78 3.00% 0.664 0.636 0.028 4.16% 5610 5383 227 4.05%
35.4 8.1 8.31 20.4 20.62 -0.22 1.09% 23.6 22.84 0.76 3.24% 0.569 0.541 0.028 4.86% 8970 8530 440 4.91%
35.9 7.9 10.97 21.7 21.96 -0.26 1.18% 22.7 21.80 0.90 3.98% 0.527 0.498 0.029 5.51% 11270 10621 649 5.76%
35.6 8.0 13.62 23 22.82 0.18 0.79% 21 20.74 0.26 1.26% 0.472 0.463 0.009 1.89% 12350 12086 264 2.14%
36.1 8.1 4.16 16.9 16.73 0.17 0.99% 27 27.42 -0.42 1.56% 0.677 0.692 -0.015 2.17% 5480 5598 -118 2.16%
36.1 8.0 7.79 19 19.18 -0.18 0.97% 25.1 24.87 0.23 0.92% 0.611 0.602 0.009 1.47% 9280 9154 126 1.36%
35.9 8.0 10.81 19.3 20.53 -1.23 6.36% 24.6 23.33 1.27 5.17% 0.594 0.551 0.043 7.26% 12450 11541 909 7.30%
36.1 7.7 14.09 20.8 21.65 -0.85 4.09% 23.7 22.09 1.61 6.79% 0.562 0.509 0.053 9.49% 15650 14135 1516 9.68%
36.2 8.3 3.97 15.5 13.67 1.83 11.81% 28.8 30.79 -1.99 6.91% 0.734 0.807 -0.073 9.98% 5640 6216 -576 10.20%
36.2 8.1 8.44 15.7 15.90 -0.20 1.27% 28.6 28.36 0.24 0.84% 0.732 0.722 0.010 1.31% 12080 11907 173 1.43%
35.8 7.9 11.23 16.2 16.73 -0.53 3.25% 27.7 26.94 0.76 2.76% 0.709 0.684 0.025 3.57% 15460 14885 575 3.72%
35.9 8.1 14.08 16 17.77 -1.77 11.06% 27.9 26.18 1.72 6.16% 0.711 0.652 0.059 8.31% 19400 17731 1669 8.60%
R4-66
R4-120
R2-42
R2-60
R2-120
R3-54
R3-120
R4-54
68
APPENDIX C. Model simulations G
EO
ME
TR
Y
Le
ng
th [
m]
Eff
ec
tive
ne
ss
q [
kW
]
Td
rain
_o
ut
[°C
]
Tc
oil_
ou
t [°
C]
NT
U
UA
[W
/K]
ReD
rain
ReC
oil
Reg
ime
Co
il
R1 [
K/W
]
R2 [
K/W
]
R3 [
K/W
]
R4 [
K/W
]
R5 [
K/W
]
Rto
tal [K
/W]
Cco
il
Cd
rain
No
min
al
Dia
me
ter
= 0
.05
[m
]
Nu
mb
er
of
co
ils
= 2
0.91 34.35% 6.01 26.38 17.57 0.523 326.4 4887.3 9877.1 Laminar 1.54E-03 3.36E-05 2.59E-04 3.27E-05 1.20E-03 3.06E-03 627.37 624.49
1.07 38.06% 6.66 25.34 18.61 0.614 383.3 4834.8 10017.5 Laminar 1.32E-03 2.85E-05 2.20E-04 2.78E-05 1.01E-03 2.61E-03 627.28 624.60
1.22 41.18% 7.20 24.47 19.48 0.699 436.7 4791.0 10135.9 Laminar 1.17E-03 2.50E-05 1.93E-04 2.44E-05 8.80E-04 2.29E-03 627.20 624.69
1.37 43.99% 7.70 23.68 20.27 0.784 489.9 4751.5 10243.2 Laminar 1.05E-03 2.23E-05 1.72E-04 2.17E-05 7.79E-04 2.04E-03 627.14 624.77
1.52 46.54% 8.14 22.97 20.98 0.869 543.1 4715.8 10341.0 Laminar 9.48E-04 2.01E-05 1.55E-04 1.96E-05 6.99E-04 1.84E-03 627.08 624.84
1.68 49.01% 8.58 22.28 21.68 0.960 599.7 4681.3 10436.1 Laminar 8.62E-04 1.82E-05 1.40E-04 1.77E-05 6.29E-04 1.67E-03 627.03 624.91
1.83 51.13% 8.95 21.68 22.27 1.044 652.7 4651.8 10517.8 Laminar 7.95E-04 1.67E-05 1.29E-04 1.62E-05 5.75E-04 1.53E-03 626.99 624.97
2.13 54.87% 9.60 20.64 23.32 1.214 758.6 4599.9 10662.7 Laminar 6.89E-04 1.43E-05 1.11E-04 1.40E-05 4.90E-04 1.32E-03 626.91 625.06
2.44 58.17% 10.18 19.71 24.24 1.388 867.7 4554.2 10791.2 Laminar 6.06E-04 1.25E-05 9.66E-05 1.22E-05 4.25E-04 1.15E-03 626.85 625.15
2.74 60.93% 10.67 18.94 25.02 1.556 973.1 4516.2 10899.1 Laminar 5.43E-04 1.11E-05 8.61E-05 1.08E-05 3.76E-04 1.03E-03 626.80 625.22
3.05 63.42% 11.10 18.24 25.72 1.730 1081.9 4482.0 10996.9 Laminar 4.91E-04 1.00E-05 7.73E-05 9.75E-06 3.37E-04 9.24E-04 626.75 625.28
No
min
al
Dia
me
ter
= 0
.05
[m
]
Nu
mb
er
of
co
ils
= 4
0.91 31.06% 5.43 27.30 16.65 0.450 281.0 4933.9 4876.6 Laminar 1.53E-03 3.36E-05 2.59E-04 3.27E-05 1.70E-03 3.56E-03 627.46 624.40
1.07 34.63% 6.06 26.30 17.65 0.529 330.5 4883.3 4943.9 Laminar 1.31E-03 2.85E-05 2.20E-04 2.78E-05 1.44E-03 3.03E-03 627.36 624.50
1.22 37.66% 6.59 25.45 18.50 0.603 376.9 4840.4 5001.2 Laminar 1.16E-03 2.50E-05 1.93E-04 2.44E-05 1.25E-03 2.65E-03 627.29 624.59
1.37 40.42% 7.07 24.68 19.27 0.678 423.3 4801.6 5053.6 Laminar 1.04E-03 2.23E-05 1.72E-04 2.17E-05 1.11E-03 2.36E-03 627.22 624.67
1.52 42.95% 7.51 23.97 19.98 0.752 469.6 4766.1 5101.8 Laminar 9.41E-04 2.01E-05 1.55E-04 1.96E-05 9.94E-04 2.13E-03 627.16 624.74
1.68 45.41% 7.95 23.28 20.67 0.831 519.0 4731.5 5148.9 Laminar 8.56E-04 1.82E-05 1.40E-04 1.77E-05 8.95E-04 1.93E-03 627.11 624.81
1.83 47.54% 8.32 22.69 21.26 0.905 565.3 4701.8 5189.7 Laminar 7.89E-04 1.67E-05 1.29E-04 1.62E-05 8.18E-04 1.77E-03 627.06 624.87
2.13 51.33% 8.98 21.63 22.32 1.053 657.9 4649.1 5262.7 Laminar 6.84E-04 1.43E-05 1.11E-04 1.40E-05 6.97E-04 1.52E-03 626.99 624.97
2.44 54.70% 9.57 20.68 23.27 1.205 753.4 4602.2 5328.1 Laminar 6.01E-04 1.25E-05 9.66E-05 1.22E-05 6.05E-04 1.33E-03 626.92 625.06
2.74 57.55% 10.07 19.89 24.07 1.353 845.8 4562.9 5383.4 Laminar 5.39E-04 1.11E-05 8.61E-05 1.08E-05 5.35E-04 1.18E-03 626.86 625.13
3.05 60.13% 10.53 19.16 24.79 1.505 941.1 4527.2 5433.9 Laminar 4.87E-04 1.00E-05 7.73E-05 9.75E-06 4.78E-04 1.06E-03 626.81 625.20
No
min
al
Dia
me
ter
= 0
.05
[m
]
Nu
mb
er
of
co
ils
= 6
0.91 28.92% 5.06 27.90 16.06 0.406 253.8 4964.3 3224.4 Laminar 1.52E-03 3.36E-05 2.59E-04 3.27E-05 2.09E-03 3.94E-03 627.52 624.33
1.07 32.38% 5.66 26.93 17.02 0.478 298.7 4915.2 3267.7 Laminar 1.31E-03 2.85E-05 2.20E-04 2.78E-05 1.77E-03 3.35E-03 627.42 624.44
1.22 35.34% 6.18 26.11 17.85 0.546 340.9 4873.3 3304.8 Laminar 1.15E-03 2.50E-05 1.93E-04 2.44E-05 1.54E-03 2.93E-03 627.34 624.52
1.37 38.04% 6.65 25.35 18.61 0.613 383.0 4835.1 3338.9 Laminar 1.03E-03 2.23E-05 1.72E-04 2.17E-05 1.36E-03 2.61E-03 627.28 624.60
1.52 40.53% 7.09 24.65 19.30 0.681 425.2 4800.0 3370.5 Laminar 9.36E-04 2.01E-05 1.55E-04 1.96E-05 1.22E-03 2.35E-03 627.22 624.67
1.68 42.98% 7.52 23.97 19.99 0.753 470.2 4765.7 3401.5 Laminar 8.51E-04 1.82E-05 1.40E-04 1.77E-05 1.10E-03 2.13E-03 627.16 624.74
1.83 45.09% 7.89 23.37 20.58 0.820 512.3 4736.0 3428.5 Laminar 7.85E-04 1.67E-05 1.29E-04 1.62E-05 1.01E-03 1.95E-03 627.12 624.80
2.13 48.88% 8.55 22.31 21.64 0.955 596.7 4683.1 3477.1 Laminar 6.80E-04 1.43E-05 1.11E-04 1.40E-05 8.57E-04 1.68E-03 627.04 624.90
2.44 52.29% 9.15 21.36 22.60 1.094 683.8 4635.7 3520.9 Laminar 5.98E-04 1.25E-05 9.66E-05 1.22E-05 7.43E-04 1.46E-03 626.97 625.00
2.74 55.18% 9.66 20.55 23.40 1.229 768.1 4595.6 3558.2 Laminar 5.36E-04 1.11E-05 8.61E-05 1.08E-05 6.58E-04 1.30E-03 626.91 625.07
3.05 57.81% 10.12 19.81 24.14 1.368 855.2 4559.1 3592.5 Laminar 4.84E-04 1.00E-05 7.73E-05 9.75E-06 5.88E-04 1.17E-03 626.86 625.14
No
min
al
Dia
me
ter
= 0
.08
[m
]
Nu
mb
er
of
co
ils
= 4
0.91 38.36% 6.71 25.26 18.69 0.621 388.1 3019.2 5014.3 Laminar 1.14E-03 2.13E-05 1.67E-04 2.13E-05 1.23E-03 2.58E-03 627.27 624.61
1.07 42.25% 7.39 24.17 19.78 0.731 456.4 2984.9 5088.5 Laminar 9.75E-04 1.81E-05 1.42E-04 1.81E-05 1.04E-03 2.19E-03 627.18 624.72
1.22 45.48% 7.96 23.27 20.69 0.833 520.4 2956.6 5150.2 Laminar 8.61E-04 1.59E-05 1.24E-04 1.59E-05 9.04E-04 1.92E-03 627.11 624.81
1.37 48.36% 8.46 22.46 21.50 0.935 584.3 2931.5 5205.6 Laminar 7.72E-04 1.41E-05 1.11E-04 1.41E-05 8.01E-04 1.71E-03 627.05 624.89
1.52 50.95% 8.92 21.73 22.22 1.037 648.2 2908.9 5255.5 Laminar 7.00E-04 1.27E-05 9.97E-05 1.27E-05 7.18E-04 1.54E-03 626.99 624.96
1.68 53.45% 9.35 21.04 22.92 1.146 716.3 2887.3 5303.7 Laminar 6.37E-04 1.15E-05 9.02E-05 1.15E-05 6.46E-04 1.40E-03 626.94 625.03
1.83 55.56% 9.72 20.44 23.51 1.248 780.1 2868.9 5344.8 Laminar 5.87E-04 1.06E-05 8.28E-05 1.06E-05 5.91E-04 1.28E-03 626.90 625.08
2.13 59.26% 10.37 19.41 24.55 1.452 907.6 2837.0 5416.9 Laminar 5.09E-04 9.09E-06 7.12E-05 9.09E-06 5.04E-04 1.10E-03 626.83 625.18
2.44 62.48% 10.94 18.51 25.45 1.662 1039.1 2809.3 5480.0 Laminar 4.47E-04 7.94E-06 6.21E-05 7.94E-06 4.37E-04 9.62E-04 626.77 625.26
2.74 65.15% 11.41 17.76 26.20 1.865 1166.3 2786.5 5532.4 Laminar 4.01E-04 7.07E-06 5.53E-05 7.07E-06 3.87E-04 8.57E-04 626.72 625.33
3.05 67.53% 11.82 17.09 26.87 2.075 1297.7 2766.1 5579.4 Laminar 3.62E-04 6.35E-06 4.97E-05 6.35E-06 3.46E-04 7.71E-04 626.68 625.38
No
min
al
Dia
me
ter
= 0
.08
[m
]
Nu
mb
er
of
co
ils
= 6
0.91 35.99% 6.29 25.92 18.03 0.562 350.7 3040.0 3313.0 Laminar 1.13E-03 2.13E-05 1.67E-04 2.13E-05 1.51E-03 2.85E-03 627.33 624.54
1.07 39.82% 6.96 24.85 19.10 0.661 412.8 3006.3 3361.4 Laminar 9.70E-04 1.81E-05 1.42E-04 1.81E-05 1.27E-03 2.42E-03 627.24 624.65
1.22 43.02% 7.52 23.96 20.00 0.754 470.9 2978.2 3402.0 Laminar 8.57E-04 1.59E-05 1.24E-04 1.59E-05 1.11E-03 2.12E-03 627.16 624.74
1.37 45.89% 8.03 23.15 20.80 0.847 529.1 2953.0 3438.7 Laminar 7.68E-04 1.41E-05 1.11E-04 1.41E-05 9.83E-04 1.89E-03 627.10 624.82
1.52 48.49% 8.48 22.42 21.53 0.940 587.3 2930.4 3472.0 Laminar 6.96E-04 1.27E-05 9.97E-05 1.27E-05 8.82E-04 1.70E-03 627.04 624.89
1.68 51.00% 8.92 21.72 22.23 1.039 649.3 2908.5 3504.2 Laminar 6.33E-04 1.15E-05 9.02E-05 1.15E-05 7.94E-04 1.54E-03 626.99 624.96
1.83 53.14% 9.30 21.12 22.83 1.132 707.5 2889.9 3531.8 Laminar 5.84E-04 1.06E-05 8.28E-05 1.06E-05 7.25E-04 1.41E-03 626.95 625.02
2.13 56.90% 9.96 20.07 23.89 1.318 823.7 2857.4 3580.6 Laminar 5.06E-04 9.09E-06 7.12E-05 9.09E-06 6.19E-04 1.21E-03 626.88 625.12
2.44 60.20% 10.54 19.14 24.81 1.510 943.8 2828.9 3623.5 Laminar 4.45E-04 7.94E-06 6.21E-05 7.94E-06 5.36E-04 1.06E-03 626.81 625.20
2.74 62.94% 11.02 18.38 25.58 1.695 1059.9 2805.3 3659.4 Laminar 3.99E-04 7.07E-06 5.53E-05 7.07E-06 4.75E-04 9.43E-04 626.76 625.27
3.05 65.41% 11.45 17.69 26.27 1.887 1179.9 2784.2 3691.7 Laminar 3.60E-04 6.35E-06 4.97E-05 6.35E-06 4.25E-04 8.48E-04 626.72 625.33
69
GE
OM
ET
RY
Len
gth
[m
]
Eff
ecti
ven
ess
q [
kW
]
Td
rain
_o
ut
[°C
]
Tco
il_o
ut
[°C
]
NT
U
UA
[W
/K]
ReD
rain
ReC
oil
Reg
imeC
oil
R1 [
K/W
]
R2 [
K/W
]
R3 [
K/W
]
R4 [
K/W
]
R5 [
K/W
]
Rto
tal [K
/W]
Cco
il
Cd
rain
No
min
al
Dia
mete
r =
0.1
0 [
m]
N
um
ber
of
co
ils =
4
0.91 42.10% 7.36 24.21 19.74 0.726 453.6 2389.0 5085.5 Laminar 9.88E-04 1.71E-05 1.35E-04 1.73E-05 1.05E-03 2.20E-03 627.18 624.72
1.07 46.09% 8.06 23.10 20.86 0.854 533.3 2361.1 5161.8 Laminar 8.48E-04 1.45E-05 1.14E-04 1.47E-05 8.84E-04 1.88E-03 627.09 624.83
1.22 49.35% 8.64 22.18 21.77 0.973 608.0 2338.3 5224.6 Laminar 7.49E-04 1.28E-05 1.00E-04 1.29E-05 7.70E-04 1.64E-03 627.03 624.92
1.37 52.24% 9.14 21.37 22.58 1.092 682.6 2318.1 5280.5 Laminar 6.71E-04 1.14E-05 8.94E-05 1.15E-05 6.82E-04 1.47E-03 626.97 625.00
1.52 54.82% 9.59 20.65 23.30 1.211 757.1 2300.3 5330.4 Laminar 6.08E-04 1.02E-05 8.05E-05 1.03E-05 6.11E-04 1.32E-03 626.92 625.06
1.68 57.28% 10.03 19.96 23.99 1.338 836.6 2283.3 5378.2 Laminar 5.53E-04 9.27E-06 7.29E-05 9.35E-06 5.50E-04 1.20E-03 626.87 625.13
1.83 59.35% 10.39 19.38 24.57 1.457 911.0 2269.0 5418.6 Laminar 5.10E-04 8.51E-06 6.69E-05 8.59E-06 5.03E-04 1.10E-03 626.83 625.18
2.13 62.94% 11.02 18.38 25.58 1.695 1059.7 2244.3 5489.0 Laminar 4.42E-04 7.31E-06 5.75E-05 7.38E-06 4.29E-04 9.44E-04 626.76 625.27
2.44 66.04% 11.56 17.51 26.45 1.940 1213.3 2223.1 5549.9 Laminar 3.89E-04 6.38E-06 5.02E-05 6.44E-06 3.73E-04 8.24E-04 626.71 625.35
2.74 68.57% 12.01 16.80 27.16 2.177 1361.7 2205.7 5600.1 Laminar 3.48E-04 5.68E-06 4.47E-05 5.73E-06 3.30E-04 7.34E-04 626.66 625.41
3.05 70.82% 12.40 16.17 27.79 2.422 1515.0 2190.4 5644.7 Laminar 3.14E-04 5.10E-06 4.01E-05 5.15E-06 2.95E-04 6.60E-04 626.62 625.46
No
min
al
Dia
mete
r =
0.1
0 [
m]
Nu
mb
er
of
co
ils =
6
0.91 39.67% 6.94 24.89 19.06 0.657 410.1 2406.1 3359.5 Laminar 9.83E-04 1.71E-05 1.35E-04 1.73E-05 1.29E-03 2.44E-03 627.24 624.65
1.07 43.62% 7.63 23.79 20.17 0.773 482.6 2378.3 3409.7 Laminar 8.43E-04 1.45E-05 1.14E-04 1.47E-05 1.09E-03 2.07E-03 627.15 624.76
1.22 46.88% 8.20 22.87 21.08 0.881 550.6 2355.5 3451.4 Laminar 7.45E-04 1.28E-05 1.00E-04 1.29E-05 9.46E-04 1.82E-03 627.08 624.85
1.37 49.78% 8.71 22.06 21.89 0.990 618.5 2335.3 3488.6 Laminar 6.67E-04 1.14E-05 8.94E-05 1.15E-05 8.37E-04 1.62E-03 627.02 624.93
1.52 52.39% 9.17 21.33 22.62 1.098 686.5 2317.2 3522.1 Laminar 6.05E-04 1.02E-05 8.05E-05 1.03E-05 7.51E-04 1.46E-03 626.96 625.00
1.68 54.88% 9.60 20.63 23.32 1.214 758.9 2299.9 3554.4 Laminar 5.50E-04 9.27E-06 7.29E-05 9.35E-06 6.76E-04 1.32E-03 626.91 625.07
1.83 56.99% 9.98 20.04 23.91 1.323 826.8 2285.3 3581.7 Laminar 5.08E-04 8.51E-06 6.69E-05 8.59E-06 6.18E-04 1.21E-03 626.87 625.12
2.13 60.67% 10.62 19.01 24.94 1.539 962.5 2259.9 3629.6 Laminar 4.40E-04 7.31E-06 5.75E-05 7.38E-06 5.27E-04 1.04E-03 626.80 625.21
2.44 63.86% 11.18 18.12 25.84 1.763 1102.7 2238.0 3671.4 Laminar 3.87E-04 6.38E-06 5.02E-05 6.44E-06 4.57E-04 9.07E-04 626.74 625.29
2.74 66.49% 11.64 17.38 26.58 1.980 1238.2 2220.0 3705.9 Laminar 3.47E-04 5.68E-06 4.47E-05 5.73E-06 4.05E-04 8.08E-04 626.70 625.36
3.05 68.83% 12.05 16.73 27.24 2.204 1378.2 2204.0 3736.8 Laminar 3.13E-04 5.10E-06 4.01E-05 5.15E-06 3.62E-04 7.26E-04 626.65 625.42
Table C-1 Full table of simulation results for different GHE.
70
APPENDIX D. Potential of Implementation
Table D-1 Full table of persons per household in Sweden 2015.
Source: (SCB-Sweden 2016)
Number of
households
Percentage of
Households
Number of
persons
Percentage
of persons
Persons per
Household
Single w ithout
children 1,648,130 38.06% 1,648,130 17.19% 1.00
Single w ith 1
children aged 0-
24
137,691 3.18% 275,382 2.87% 2.00
Single w ith 2
children aged 0-
24
87,780 2.03% 263,340 2.75% 3.00
Single w ith 3 or
more children
aged 0-24
31,110 0.72% 136,536 1.42% 4.39
Single w ith 1
children aged 25
and older
43,983 1.02% 87,966 0.92% 2.00
Single w ith 2
children aged 25
and older
3,078 0.07% 9,234 0.10% 3.00
Single w ith 3 or
more children
aged 25 and
older
217 0.01% 897 0.01% 4.13
Cohabiting/marr
ied w ithout
children
1,075,485 24.84% 2,150,970 22.44% 2.00
Cohabiting w ith
1 children aged
0-24
310,969 7.18% 932,907 9.73% 3.00
Cohabiting w ith
2 children aged
0-24
446,962 10.32% 1,787,848 18.65% 4.00
Cohabiting w ith
3 or more
children aged 0-
24
177,499 4.10% 942,351 9.83% 5.31
Cohabiting w ith
1 children aged
25 and older
55,789 1.29% 167,367 1.75% 3.00
Cohabiting w ith
2 children aged
25 and older
4,942 0.11% 19,768 0.21% 4.00
Cohabiting w ith
3 or more
children aged 25
and older
378 0.01% 1,941 0.02% 5.13
Other
household
w ithout children
171,168 3.95% 445,408 4.65% 2.60
Other
household w ith
1 children aged
0-24
47,529 1.10% 193,852 2.02% 4.08
Other
household w ith
2 children aged
0-24
44,488 1.03% 232,659 2.43% 5.23
Other
household w ith
3 or more
children aged 0-
24
35,430 0.82% 258,651 2.70% 7.30
Other
household w ith
1 children aged
25 and older
6,724 0.16% 26,527 0.28% 3.95
Other
household w ith
2 children aged
25 and older
947 0.02% 4,753 0.05% 5.02
Other
household w ith
3 or more
children aged 25
and older
102 0.00% 647 0.01% 6.34
Total 4,330,401 9,587,134
71
Avg. Persons per household in Europe
Figure D.1. Average person per Household in Europe 2014.
Source: (Eurostat 2016)