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
ṁ 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]
v̇ 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
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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− 𝑇𝑐𝑜𝑙𝑑
𝑇𝑤𝑎𝑠𝑡𝑒𝑤𝑎𝑡𝑒𝑟− 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).
12 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
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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.
𝑄̇ = 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:
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𝑅𝑒𝑐𝑟𝑖𝑡𝑖𝑐𝑎𝑙𝑓𝑓 = 1800 (3.3)
𝑅𝑒𝑓𝑓 =4 ∗ ṁdrain
µdrain∗ 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
1
3 ∗ 𝑃𝑟𝑑𝑟𝑎𝑖𝑛
1
3 ∗ (𝑘𝑑𝑟𝑎𝑖𝑛3 ∗ 𝑔 ∗ ρ𝑑𝑟𝑎𝑖𝑛2 µ𝑑𝑟𝑎𝑖𝑛2 )
1
3 (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]
V̇ 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 ∗ √𝑑𝑡𝑢𝑏𝑒
𝐷𝑐𝑜𝑖𝑙)) (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 ∗ 𝑚̇𝑐𝑜𝑖𝑙
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
V̇ critical [L/min]
V̇
critical [L/s]
Nr Coils
V̇ critical [L/min]
V̇
critical [L/s]
Nr Coils
V̇ critical [L/min]
V̇
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,
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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 (𝑑𝑡𝑢𝑏𝑒
𝐷𝑐𝑜𝑖𝑙) (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) + (
51 11 (1 + ( 1342
𝑃𝑟𝑐𝑜𝑖𝑙∗ 𝐷𝑒2))
2
))
3
+ 1.816 ∗ (
( 𝐷𝑒
1 + 1. 15 𝑃𝑟𝑐𝑜𝑖𝑙
)
3 2
)))
1 3
(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∗ 𝑃𝑟𝑐𝑜𝑖𝑙0.2 (3.10)
The third correlation (3.11) is proposed by Janssen & Hoogendoorn (1978):
𝑁𝑢𝐿= 0.7 ∗ 𝑅𝑒𝑐𝑜𝑖𝑙0.43∗ 𝑃𝑟𝑐𝑜𝑖𝑙
1
6 ∗ (𝑑𝑡𝑢𝑏𝑒
𝐷𝑐𝑜𝑖𝑙)
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 ∗ 𝑅𝑒𝑐𝑜𝑖𝑙0.85∗ 𝑃𝑟𝑐𝑜𝑖𝑙0.4 ∗ (𝑑𝑡𝑢𝑏𝑒 𝐷𝑐𝑜𝑖𝑙)
0.1
(3.13)
(Rogers & Mayhew 1964)
22 𝑁𝑢𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡 = 0.023 ∗ 𝑅𝑒𝑐𝑜𝑖𝑙
4
5 ∗ 𝑃𝑟𝑐𝑜𝑖𝑙ᵞ 𝑁𝑢𝑇4= 𝑁𝑢𝑠𝑡𝑟𝑎𝑖𝑔ℎ𝑡∗ (1 + 3.4 ∗ (𝑑𝑡𝑢𝑏𝑒
𝐷𝑐𝑜𝑖𝑙))
(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 ∗ 𝐾𝑐𝑜𝑖𝑙
𝑑𝑡𝑢𝑏𝑒 (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.
T
ffT
surfdrainT
interference Drain-sideT
interference Coil-sideT
innercoilT
coilR1 R2 R3 R4 R5
CONVECTION Falling Film
CONDUCTION Drain-side
INTERFERENCE CONDUCTION Coil-side
CONVECTION 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 ∗ 𝑇𝑎𝑣𝑔4
− 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 ∗ 𝑇𝑎𝑣𝑔4
− 2.00244305𝐸 − 12 ∗ 𝑇𝑎𝑣𝑔5
(4.4)
The dimensionless Prandtl number:
𝑃𝑟 = 13.8366012 − 0.551920297 ∗ 𝑇𝑎𝑣𝑔+ 0.0163242036 ∗ 𝑇𝑎𝑣𝑔2
− 0.000354310865 ∗ 𝑇𝑎𝑣𝑔3 + 0.00000465354551 ∗ 𝑇𝑎𝑣𝑔4
− 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 ∗ 𝑇𝑎𝑣𝑔4
+ 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 ∗ 𝑇𝑎𝑣𝑔4
+ 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 ṁcoil 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= 𝑚̇𝑑𝑟𝑎𝑖𝑛∗ 𝐶𝑝𝑑𝑟𝑎𝑖𝑛 𝐶𝑐𝑜𝑖𝑙 = 𝑚̇𝑐𝑜𝑖𝑙∗ 𝐶𝑝𝑐𝑜𝑖𝑙∗ 𝑁𝑟𝐶𝑜𝑖𝑙𝑠
(4.8)
𝐶𝑟 = 𝐶𝑚𝑖𝑛
𝐶𝑚𝑎𝑥 (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 ∗ (𝐷1 2 ) ∗ 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 ( 𝐷2 𝐷12 2
) 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 ( 𝐷4 𝐷32 2
) 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 ∗ (𝐷4
2 ) ∗ 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
Nominal Diameter [m] Length [m] Effectiveness [%] Heat Recovery [W] Effectiveness [%] Effectiveness ERROR [%] Heat Recovery [W] Heat Recovery ERROR [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.
