FACULTY OF ENGINEERING AND SUSTAINABLE DEVELOPMENT
Department of Building, Energy and Environmental Engineering
Improvement of the energy efficiency of a drain water heat exchanger
Pablo Díez Soto
2015
Student thesis, Master degree (one year), 30 HE Energy Systems
Master Programme in Energy Systems
Supervisor: Ulf Larsson
Examiner: Mathias Cehlin
PREFACE
First of all I want to thank my family who has supported me during this year abroad, for their encouragement and attention.
Thanks also to TECNUN (Universidad de Navarra) for giving me the chance to take this year abroad and Högskolan i Gävle for hosting me.
Special thanks to Mats Eriksson and Bengt Olsson from EFFAB - Effektiv Energiåtervinning AB for all their help and providing the case and information. Also special thanks to Björn Jedvik from COMSOL AB for all his help and suggestions. And Last but not least, I would like to express my deepest gratitude to Ulf Larsson for advising me and supervising this master thesis.
Pablo Díez Soto
ABSTRACT
The aim of this master thesis project is to build a model and provide a study of a drain water heat exchanger for both buildings and industrial activity.
Heat exchangers are devices that are used for recovering heat from warm water. This warm water can be the water for cooling down in an industrial activity or warm water from houses activity among other.
Once the model was built, the next step was to change several parameters and run the simulations in order to provide EFFAB - Effektiv Energiåtervinning AB with useful information for improving the energy efficiency of the heat exchanger according to different needs and working conditions.
The heat exchanger is to be used in both residential buildings and industrial installations where there is a use of warm water and considerable flow rates. This warm water represents a great potential for heat recovery since a lot of energy is lost.
The first part of the thesis was to create a model with help of an appropriate software. It was decided to work with COMSOL MULTIPHYSICS because of its multiple options for working with fluids and heat exchange. The model has been built as an approximation since it was not possible to have access to the internal geometry of the pipes (EFFAB - Effektiv Energiåtervinning AB buys the heat exchanger, so the geometry among other details are secrets that the selling company did not reveal to us). It was necessary to have some real values to use as reference so that the model could be validated. This data was taken from tests that were run on one of the heat exchangers that EFFAB - Effektiv Energiåtervinning AB owns and that is stored in Sandviken (Sweden). Details regarding the test are gathered in a chapter of the report.
The test was run under what is considered to be a standard water use in a residential building. All the data was provided by EFFAB - Effektiv Energiåtervinning AB.
The main target is to recover the maximum possible heat from the waste water. It has
been studied different situations, usually considering the warm waters values fixed so
that the dimensions of the pipes and the cold water flow had to be changed. The
parameters that have been changed are the diameters, flow rates and different inlet
temperatures. Also were considered obstacles in the inner pipe [20] and the influence of the insulation layer.
The current results were obtained by running the test with 1.5 l/s and 22.2 °C inlet temperature for the warm flow and 0.5 l/s and 4°C inlet temperature for the cold water.
It was obtained an outlet temperature of 20.1°C for the drain water and 10.1°C for the cold water. This means around 13 kW (considering cp=4.18 kJ/(kg*K)). This gives an effectiveness of 34% [1]. In the chapter of results and discussion are shown graphs that show different values for the parameters so that the efficiency can be improved depending on the conditions of the installation.
Because of the interest of EFFAB - Effektiv Energiåtervinning AB, it was also analysed
the model with different drain water temperatures and flow rates. Also a case with the
parameters values related to an industrial activity. Finally, this same heat exchanger
that is usually used as counter-flow was simulated as parallel flow. Even the results
show that the counter flow is more effective (as expected from theory [1]), in some
situations, the company has to install this type of heat exchanger.
CONTENTS
1. INTRODUCTION... 1
1.1. BACKGROUND ... 1
1.2. WATER USE IN SWEDEN ... 2
1.3. AIM OF THE THESIS PROJECT ... 4
2. METHOD ... 5
2.1. LIMITATIONS ... 5
2.2. SOME CONSIDERATIONS ... 6
2.3. THE HEAT EXCHANGER TO BE SIMULATED ... 6
2.4. CURRENT SITUATION ... 8
2.5. THE MODEL ... 9
2.5.1. Obstacle ... 9
2.5.2. Outer flow ... 10
2.5.3. Defining the physic model ... 11
2.5.4. Solvers ... 12
2.5.5. Mesh ... 13
2.6. TEST ... 14
2.7. VALIDATION ... 16
3. THEORY ... 18
3.1. HEAT RECOVERY WASTE WATER SYSTEM ... 18
3.2. HEAT EXCHANGER ... 19
3.2.1. Parallel flow heat exchanger ... 19
3.2.2. Counter flow heat exchanger ... 20
3.3. TURBULENCE ... 21
3.4. NON-ADIABATIC HEAT EXCHANGER ... 22
4. RESULTS AND DISCUSSION ... 24
4.1. VARIATION OF INLET TEMPERATURE FOR COLD WATER ... 24
4.2. VARIATION IN COLD WATER: DIFFERENT INLET TEMPERATURES AND FLOW RATE ... 26
4.3. SPECIAL CASE ... 28
4.4. DIFFERENT INNER PIPE DIAMETER ... 29
4.5. EFFECT OF THE OBSTACLE ... 30
4.6. DIFFERENT MASS FLOW RATE IN WASTE WATER ... 31
4.7. DIFFERENT MASS FLOW RATE AND INLET TEMPERATURE IN WASTE WATER ... 32
4.8. INFLUENCE OF CHANGES IN THE COLD WATER MASS FLOW RATE ... 35
4.9. PARALLEL FLOW VS COUNTER-FLOW HEAT EXCHANGER ... 36
4.10. INDUSTRIAL CASE ... 37
4.10.1. Parallel flow VS counter-flow ... 37
4.10.2. Industrial case with different cold water flow rates ... 38
5. ECONOMICAL DISCUSSION ... 40
5.1. ECONOMICAL ANALYSIS ... 40
5.2. CURRENT SAVINGS ... 41
5.3. SAVINGS AFTER CHANGES ... 42
6. CONCLUSION ... 44
7. REFERENCES ... 46
8. APPENDIX ... 49
1
1. INTRODUCTION
1.1. BACKGROUND
Nowadays there is a general aim to reduce the negative impact of energy in the environment, especially in those industries which activities have greater contribution to its degradation. An analysis of the CO
2emissions during the last decades shows how it has increased due to human activity. According to a research from the International Energy Agency [2], the CO
2emissions in 2012 where 31 734 Mt, twice the emissions 40 years before since in 1973 the CO
2where 15 633Mt.
Society is energy dependent. The energy use is high, due to the contribution of not only industrial activities but also day a day activities of individuals. Our daily routine requires transport, electronic devices, heating, cooling among other, which all require different types of energy, but at the end energy that entails processes of transformation, transport, use… It is well known the aim of developing more generation plants based on renewable energy and the improvement of the energy efficiency of both already existing technologies and future ones.
Big energy losses are taking place in big industrial activities. Big effort is used to reduce that losses or recover the energy somehow and for plenty of different uses. But not only in big industrial activities exists the potential for energy recovery and energy savings. Individuals can also take part of this challenge. In every house can be applied more efficient behavior, making sure that only the energy necessary is used.
Following the previous fact, buildings are becoming more and more energy efficient.
And while time is passing they are becoming more economically accessible for particulars so that the payback time will worth the initial investment.
One of the most common energy requirements in houses is domestic hot water. Grey-
water is a term used to define the outlet water from showers, bath tubs, sinks
dishwashers and washing machines. Recovering energy form grey-water has not been
a priority when comes to energy savings in buildings. But actually, a lot of energy is lost
in this dirty water. Recovering heat from that water will lead to energy savings when
2 heating up fresh cold water [3], what can also be translated into economical savings after a deep analysis of the particular conditions of each dwelling [4], especially when considering dwellings where water is heated by using certain heaters, like electrics [18]
. It can be combined with other technologies, such as heat pumps in order to have a system capable of recovering the maximum heat possible [5]. Also, different researches have been performed in order to analyse how this technology can be used in houses since some times the wastewater available will require a really big dimensions heat exchanger which is usually a problem because a lack of space. There are available in the market both vertical and horizontal heat exchangers in order to get adapted to the requirements [17][19]. In this project and horizontal heat exchanger will be considered.
EFFAB - Effektiv Energiåtervinning AB is a company which target is the installation of heat exchangers in buildings and small industries such as industrial washing companies and swimming pools.
This report will be focused on a waste water heat exchanger. There are several options for heat recovery in buildings such as shower and dishwasher heat exchangers. But in this case, the one to be analysed will be a centralized heat exchanger.
It has to be considered that the flow rate in buildings is much smaller than in industries.
Also the temperature of waste water is low, what gives small temperature difference.
In the following chapters of the report will be introduced the analysis that have been made. A model will be built and validated with real data. Afterwards, a study by means of changing different parameters will provide information so that EFFAB - Effektiv Energiåtervinning AB will be able to know in advance how the heat exchanger will react.
1.2. WATER USE IN SWEDEN
EFFAB - Effektiv Energiåtervinning AB is a Swedish company and its main market will
be national. For this reason it is interesting to provide some numerical data regarding
the warm water use in regular Swedish houses. According to results obtained from
3
"Mäning av kall-och varmvatten I tio hushåll”[6], domestic water use can be divided as follows:
- Wash basin: 23% (13% hot water and 10% cold water).
- Kitchen sink: 41% (24% hot water and 17% cold water).
- Shower/bathtub: 36% (23% hot water and 13% cold water).
Image 1, Water use in Sweden.
Around 60% of the total water use is hot water (note that cold water for toilet flushing and laundry is not included). Water use in dwellings can vary from 5.5 to 25.1 m
3per person and year.
More than 57% of all tapings are shorter than 1 minute long and most of them, up to 53% are in the kitchen sink. The average time for a shower/bath is 4.7 minutes for hot water and 4.6 minutes for cold water.
An schematic representation can be analysed in the following image:
4
Image 2, Schematic representation of warm water use in a house.
1.3. AIM OF THE THESIS PROJECT
The aim of the project is to improve the energy efficiency of a heat exchanger. It will be necessary to build a model with an appropriate software and then save the results running the model changing certain parameters that are of the interest of EFFAB - Effektiv Energiåtervinning AB. All the results will be provided with a discussion as well as a conclusion. The results will provide numerical values that are expected under different working conditions.
In any case, it will be up to EFFAB - Effektiv Energiåtervinning AB to take the solution
that better fits with their requirements.
5
2. METHOD
In order to simulate a model similar enough to reality, an appropriate software for heat transfer and Computational Fluid Dynamics was chosen. For this thesis project the software selected was Comsol Multi-physics.
It was necessary to have some real reference to know if the model built was in fact close to real results. Some tests where run in a real heat exchanger and the results of these tests where used for validating the model.
2.1. LIMITATIONS
There were significant limitations when developing the model in the software. The goal was to build it according to the real device.
It is known that the inner pipe has certain obstacles that prevent fouling and so, reduces the maintenance considerably. Also, the cold water which flows along the outer pipe is forced to develop a helix around the inner pipe. Since EFFAB - Effektiv Energiåtervinning AB buys the heat exchanger to a company, it is this companies secret how to build the obstacles and the helix flow. At the end, it was possible to obtain good results regardless of this limitation.
Also, only data of two tests was available, so the validation was based on those results .
It will be explained in the following chapter how these limitations were solved.
6
2.2. SOME CONSIDERATIONS
It is important to have knowledge of some considerations that will be used along the analysis: [16]
- It has not been considered losses in the installation further than in the main heat exchanger.
- Temperature of the municipal tap water remains constant during the whole investment cycle.
- Temperature of the used hot utility water and temperature of the wastewater discharged do not change in time.
- Contaminants present in wastewater like shampoo or gels have no effect on the heat recovery effectiveness.
2.3. THE HEAT EXCHANGER TO BE SIMULATED
The heat exchanger to be analysed is a concentric tubes counter-flow heat exchanger.
It will be used for heat recovery from waste water, which will be flowing through the
inner pipe meanwhile the new cold water (the one to be preheated) will be flowing
through the outer pipe. In Image 3 is shown the heat exchanger and the installation that
has been used in order to run the tests.
7
Image 3, Heat exchanger.
The dimensions of the heat exchanger are:
Table 1, dimensions.
Length 6 m
Inner pipe diameter 200 mm Inner pipe thickness 2 mm Outer pipe diameter 354 mm Outer pipe thickness 2 mm Insulation thickness 40 mm
And the materials:
- Pipes: Steel 4541. h=16 W/(m*K) [21]
- Isolation material: Armaflex (cellular rubrer). h=0.033 W/(m*K)[22]
Geometry:
- In the inner pipe have been built some obstacles in order to increase the turbulence of the flow. All that was known from them is that the obstacles are 9 mm deep. No distribution was known. They were manufactured in the pipe, just benching it (like triangles).
- The outer flow is influenced by the opposite shape of the obstacles that were
built in the inner pipe (the inside of the triangle). There was some geometry
8 (also unknown) forcing the stream to flow as a helix around the inner pipe, as can be observer in Image 4.
Image 4, helix flow.
The flows pressure is around 6 bar.
2.4. CURRENT SITUATION
The tests that have been run have provided the following results:
Table 2, current situation.
Further data:
- Waste water mass flow rate, mfr1=1.5 kg/s - Cold water mass flow rate, mfr2=0.5 kg/s - Heat capacity of water, cp=4.18 kJ/(kg*K)
( 1)
( 2)
Using the values in equation (1)
Tinner inlet(°
C)Tinner outlet(°C) Touter inlet(°C) Touter outlet(°C)
test 22,2 20,1 4 10,1
9
( 3)
Where,
( 4)
So, calculating equation (3),
( 5)
Right now, by using a counter flow heat exchanger, the effectiveness is 33.5%.
2.5. THE MODEL
The model was built as an approximation to reality. In Image 5 can be seen how the model looks like and the different layers that have been considered. From inside to outside, the order is as follows: waste water, inner pipe, cold water, outer pipe and insulation layer. Also, since there is no certainty on the obstacles and how the flow is actually flowing, several different configurations will be considered before validating the model.
Image 5, Model.
2.5.1. Obstacle
10 As it has already been said previously in the report, it is known that there are some obstacles along the pipes. Since there was not possible access to the real geometry and distribution, it was decided to simulate with some obstacles to check the influence that may have on the heat exchange. It was built a helix, with the same depth as real obstacles (9 mm, only data known) as can be observed in Image 6.
Image 6, obstacle.
2.5.2. Outer flow
It is also known that the outer flow is forced to follow and helix (labyrinth) around the inner pipe. This will make the fluid to spend longer time inside the heat exchanger.
After trying to set some obstacles so that the flow could be driven as desired, but with no success, it was decided to force it mathematically to follow a helix by using the following equations:
x: ux_out*1/sqrt(2) y: uy_out*1/sqrt(2) z: -u_out*1/sqrt(2)
Were u_out is the velocity that has to be set for the outer flow. The result for these
equations is the flow of Image 7.
11
Image 7, outer flow.
2.5.3. Defining the physic model
At the beginning, both flows where defined as turbulent flows. As turbulence model was chosen k-epsilon. Finally it was decided to change the model due to errors and convergence problems. After consulting the support service from Comsol Multy- physics, it was decided to use a model available in the software called Algebraic yPlus [10]. This is a model that works well combined with heat exchange and that allowed the simulation to converge.
Also, after some simulations the result that was obtained for the turbulence in the outer
pipe was laminar. Because the parameter values that were to be used were not going
to vary much, the possibility of forcing the flow mathematically (as it has been
explained in the previous section of the report) was considered. By setting the
equations the flow is not considered a flow in its physical meaning anymore. The
software will not solve the Navier-Stokes equations, so there is no way to say whether
it is laminar or turbulent. The flow field is defined as a mathematical expression.
12
2.5.4. Solvers
Comsol Multi-physics offers direct and iterative methods for solving the equations of the problem. In this thesis were used direct methods that even they require more memory, they are at the same time more robust.
Direct methods are based on LU decomposition. Comsol uses MUMPS, PARDISO and SPOOLES. All of them will arrive at the same answer. In this case MUMPS where used. Related to solving speed, MUMPS is in the middle of them three and can store the solution out-of-core, which means that they can offload some of the problem onto the hard disk [11].
As it has been introduced previously in the report, there were some convergence problems when running the simulation. One of the solutions that were taken was to improve the convergence of the model. Originally it was used a Segregated Approach, which solves each physics sequentially until convergence, Image 8. Then it was changed to a Fully Coupled Approach, which starts from an initial guess and applies Newton-Raphson iterations until the solution has converged, Image 9. This change made the model converge [12].
Image 8, Segregated Approach.
13
Image 9, Fully Coupled Approach.
2.5.5. Mesh
The mesh used for this model was Physics-controlled Mesh. This model is adapted to the current physics interface settings in the model. The mesh size was set as Coarse, giving good results.
Image 10, Mesh.
14
Table 3, mesh statistics.
2.6. TEST
The test took place in an installation in Sandviken (Sweden).
The test was performed as follows. It was used a 1m
3water tank were the warm water was stored, which in reality would have been the waste water (Image 11). The tank was filled stored with water at around 30 °C. Then with help of pumps, the water was pumped through the heat exchanger. Ambient temperature was around 18 °C.
At the same time, cold water supply was taken directly from the tab and then driven directly to the drain.
Image 11, Test installation.
15 As it can be observed in Image 12, thermometers (Thermokon, Pt 100) and flow- meters were used for measuring both the temperature and flow rates. Thermometers were measuring temperature directly from the water.
Image 12, Measurement devices.
In Image 13 is shown schematically how the installation for the test was set up.
Image 13, Schema of the installation for the test.
t4 t2
Q2
t1 Q1 t3
KV
FÖRV. VV
AVLOPP VV
16
2.7. VALIDATION
Several options were analysed so that the final models result was as similar as possible to the results from the tests, which have been gathered in Table 4. Ambient temperature was around 18 °C, waste water flow rate 1.5 l/s and cold water 0.5 l/s. Inlet temperatures were set to 22.2°C for the waste water and 4°C for the cold water for the first test and 17.6°C for the waste water and 3.9 for the cold water in a second test.
Table 4, Test results.
Where
- Tinner inlet: waste water inlet (inner flow).
- Tinner oulet: waste water outlet.
- Touter inlet: cold water inlet (outer flow).
- Touter outlet: cold water outlet.
In order to validate the model, since there were several crucial details that were unknown, it was decided to run simulations with different configurations a see what results were more similar to those from the tests.
So the model was run for the inlet temperatures as the test (both cases) and same flow rates. Then It was simulated with and without the obstacle and with real values for insulation and absolutely isolated (so that the influence of surroundings could be considered).The results are shown in the following tables.
Table 5, Real insulation, higher temperature values.
Tinner inlet(°
C)Tinner outlet(°C) Touter inlet(°C) Touter outlet(°C) delta T inner delta T outer
22,2 20,1 4 10,1 2,1 6,1
17,6 16 3,9 8,8 1,6 4,9
Tinner inlet(°
C)Tinner outlet(°C) Touter inlet(°C) Touter outlet(°C) delta T inner delta T outer error Tin error Tout
test 22,2 20,1 4 10,1 2,1 6,1
with obst 22,2 19,883 4 10,895 2,317 6,895 0,093655589 0,115300943
no obst 22,2 20,021 4 10,045 2,179 6,045 0,036255163 0,009016393
17
Table 6, Real insulation, lower temperature values.
Table 7, Absolutely isolated, higher temperatures values.
Table 8, Absolutely isolated, lower temperature values.
As it can be seen from the previous tables, the results are considerably similar in all the cases. Only one case was to be chosen. Finally the case from
Table 7 and
Table 8 were rejected since as it will be seen later in the results, there is an influence of the surroundings in the heat balance. Then it had to be decided with or without obstacle. The option with real insulation and without obstacles was chosen. The first reason is that the results are closer to the real results for the tests. Furthermore, since the flow rates that are to be considered later in the different cases cannot be much different to the one already given (since the waste water flow rate cannot be varied much), it was considered that the flow behavior would be pretty much as it is in this case, and in this case the best option is without obstacle. It has to be considered that in any case, the real obstacles are unknown.
Tinner inlet(°
C)Tinner outlet(°C) Touter inlet(°C) Touter outlet(°C) delta T inner delta T outer error Tin error Tout
test 17,6 16 3,9 8,8 1,6 4,9
with obst 17,6 15,85 3,9 9,1 1,75 5,2 0,085714286 0,057692308
no obst 17,6 15,957 3,9 8,473 1,643 4,573 0,026171637 0,066734694
Tinner inlet(°
C)Tinner outlet(°C) Touter inlet(°C) Touter outlet(°C) delta T inner delta T outer error Tin error Tout
test 22,2 20,1 4 10,1 2,1 6,1
with obst 22,2 20,026 4 10,526 2,174 6,526 0,034038638 0,065277352
no obst 22,2 20,145 4 9,75 2,055 5,75 0,021428571 0,057377049
Tinner inlet(°C) Tinner outlet(°C) Touter inlet(°C) Touter outlet(°C) delta T inner delta T outer error Tin error Tout
test 17,6 16 3,9 8,8 1,6 4,9
with obst 17,6 15,96 3,9 8,8 1,64 4,9 0,024390244 0
no obst 17,6 16,47 3,9 8,256 1,13 4,356 0,29375 0,111020408
18
3. THEORY
This section provides some important concepts and theory explanation for a better understanding of the report. It is important to have an idea of the basic physics behind these technologies as well as some equations that will be use further in the results [7][8].
3.1. HEAT RECOVERY WASTE WATER SYSTEM
Heat recovery allows reusing the thermal energy, that otherwise would be unused as waste, in another process (for example the outcome of an exothermic process, activity or water that has been warmed up for its use and afterwards still has useful heat). This is possible by using heat exchangers.
Wastewater heat recovery systems allow reusing the heat in domestic gray-water before going to drain. This heat will be for pre-heating the incoming domestic hot water.
How much heat will be recovered depends on the system, the temperature and flow rate of both cold and warm streams and of course of the heat exchanger.
Reusing the heat form wastewater provides some advantages:
- Less heat will be wasted.
- Ecologically friendly: less CO
2(Especially depending on the heating technology considered in the system after the heat exchanger).
- Economical savings.
- The system works automatically and the need of maintenance is getting lower with new designs.
- It works regardless of the weather conditions.
It can be seen in the following figure and table, a schematic representation the type of
heat exchanger considered and what will be each flow.
19
Image 14, Schematic heat exchanger.
Where,
Table 9, Flows of the heat exchanger.
T
a1Inlet cold water
T
a2Outlet cold water(warmed up)
T
b1Inlet wastewater
T
b2Outlet warm water (cooled up)
3.2. HEAT EXCHANGER
A heat exchanger is used to transfer thermal energy from one medium to another.
Common mediums are water and air but it can be other fluid or even solid particles.
[7][8][9]
3.2.1. Parallel flow heat exchanger
In this configuration, both liquids are flowing in the same direction. In general, this type
of heat exchanger is less efficient than counter flow heat exchangers. However, there
are applications where can be useful, for example if the maximum heat to be
20 exchanged is to be limited. Schematic representation can be observed in the following image.
Image 15, Parallel flow heat exchanger.
Heat exchange will happen meanwhile there is temperature difference. Once both liquids have reached the same temperature there will be no longer heat exchange. So for example, let’s consider both streams are the same liquid and same flow rate. Then the heat that can be exchanged will be up to half of the temperature of both liquids in the inlet.
3.2.2. Counter flow heat exchanger
In this case, the streams flow in opposite direction. In this case more heat can be
exchanged since the outlet temperature for the cold fluid can be higher than the outlet
temperature for the warm fluid. Theoretically is possible to warm up the cold fluid up to
the warm fluids inlet temperature, however, it is not the common case. Next image
shows a schematic counter flow heat exchanger.
21
Image 16, counter flow heat exchanger.
This configuration has higher efficiency than the parallel flow case. It is commonly used when the maximum possible heat is to be recovered.
3.3. TURBULENCE
The flow inside the pipes of a heat exchanger can be laminar or turbulent (or transitions between them). The turbulence can be calculated with Reynolds number:
Where:
ρ: fluid density (kg/m
3).
v
s: velocity of the fluid (m/s).
D: characteristic linear dimension (m).
η: dynamic viscosity of the fluid (kg/(m·s)).
Turbulence improves the heat transfer of a heat exchanger. Furthermore, turbulence prevents fouling, what reduces significantly the maintenance of the heat exchanger.
Usually, in heat exchangers the flow speed is fixed by the system, so the turbulence is
achieved by modifying the design of the pipe (the geometry) as can be observed in the
following image.
22
Image 17, Different ways of achieving a turbulent flow.
3.4. NON-ADIABATIC HEAT EXCHANGER
Usually when studying theory related to heat exchangers it is considered that the outer layer is adiabatic, so basically it can be stated that the heat released by the hot fluid will be equal to the heat absorbed by the cold fluid.
In this thesis project, in order to build the model as similar to reality as possible it will be considered a non-adiabatic heat exchanger. What should be expected then? [13]. The answer can be observed in Figure 1.
Figure 1, influence of surroundings.
So, setting a non-adiabatic outer layer condition will lead to reduce the outlet
temperature of the hot fluid meanwhile the cold fluid will remain almost with the outlet
23
temperature. This statement will justify that the heat transfer rate for each fluid will no
longer be necessarily equal.
24
4. RESULTS AND DISCUSSION
Once the model was validated with the results from the test it was ready to simulate the cases of interest. In this chapter are given the results obtained from simulating the model according to the interest of EFFAB.
It has been decided to gather together in this section both results and the discussion of the results since it was considered easier to follow this way.
The reference situation is the one with the values under which the test was run since it is considered as a common real situation in Swedish houses (those that are considered for installing this heat exchanger). This situation is:
Table 10, Standard situation.
4.1. VARIATION OF INLET TEMPERATURE FOR COLD WATER
One of the first parameters to consider was the cold water inlet temperature. This is a parameter which value can vary along the year. This is important to consider since smaller the delta T between the waste water inlet temperature and the cold water inlet temperature the less heat that can be exchanged. In the original case was considered 4 °C, but this value may increase during the warmer periods of the year and depending on the geographical location.
Table 11 provides the parameters that have been considered for calculating the results of Figure 2 and Figure 3. (Appendix 1)
mfr waste 1,5 kg/s
mfr cold 0,5 kg/s
Waste inlet 22,2 °C
Cold inlet 4 °C
25
Table 11, parameters.
Figure 2, Power with variation of cold water inlet temperature without obstacle.
.
Figure 3, Power with variation of cold water inlet temperature, with obstacle.
mfr waste 1,5 kg/s
mfr cold 0,5 kg/s
cp 4,2 kJ/(kg*K)
26 As it can be observed from the images and as it was expected, the heat rate that can be exchanged decreases as the temperature difference decreases with an increment of the cold water temperature.
From the results with obstacles can be observed that the values are slightly higher and the heat exchange rate of both flows almost the same, which seems to be a good configuration. But actually, the case without obstacle provides better values when compared with the test, with a heat rate difference of around 500 W between waste and cold water. This fact supports the selection of the case with no obstacle as the most similar to reality.
4.2. VARIATION IN COLD WATER: DIFFERENT INLET TEMPERATURES AND FLOW RATE
This section is somehow based on the previous one, but in this case it is only considered the case with no obstacle.
In Figure 4 and Figure 5 have been plotted the heat rate exchange expected for
another case interesting for analysis. The same procedure of changing the cold water
inlet temperature but in this case it was taken extra step. The cold water flow rate was
also changed so that it can be shown the values that can be expected in case that
higher flow rates are possible or necessary. (Appendix 2)
27
Figure 4, Power cold water.
Figure 5, Power waste water.
Also in this case, the result from the simulation was as expected, with a decreasing
heat exchange rate when the temperature difference decreases and also, and
increment of the heat exchange rate when there is a higher flow.
28
4.3. SPECIAL CASE
In EFFAB where thinking in a new installation for the test, where a recirculation circuit was installed for the cold water (Image 18), so that the cold water flow rate could be increased. In this case the parameters have been changed from the previous section.
The aim of this section is to check if it is possible to obtain from the heat exchanger what it is theoretically expected.
Image 18, recirculation.
The objective values are 20 °C for outlet waste water temperature and 10 °C for outlet cold water temperature. The parameters that have been considered are shown in
Table 12 and the results from the simulation are shown in
Table 13.
Table 12, parameters values. .
mfr waste 0,57 kg/s
mfr cold 0,6 kg/s
Tinner inlet 27 °C
Touter inlet 5 °C
cp 4,2 kJ/(kg*K)
29
Table 13, simulation result.
The results obtained match pretty well with those that were expected.
4.4. DIFFERENT INNER PIPE DIAMETER
It was very interesting to know how the result will vary when changing the dimension from manufacturing. In this section, it was decided to change the diameter of the inner pipe, keeping the outer pipe with the same value and the flow rates for both flows constant.
Results for both waste water and cold water are shown in Figure 6 and Figure 7.
(Appendix 3)
Figure 6, Waste water power as function of inner radius.
Tinner out(°C) Touter out(°C) Power inner (kW) Power outer (kW)
22,819 9,1157 10,009314 10,371564
30
Figure 7, Cold water power as function of inner radius.
In this case, it can be observed how the waste water heat exchange rate has a maximum with an inner pipe radius on 120 mm. Also, the curve for the cold water does not have the exact same shape as the waste water one, what makes to think about the influence of the surroundings and the insulation layer.
4.5. EFFECT OF THE OBSTACLE
In this section has been considered how the waste flow would be influenced by an obstacle when the flow rate increases compared to the case with no obstacle.
In this case the cold flow was not considered since as it has already been said, it has been forced mathematically to follow a certain helical way and it cannot be consider as a fluid properly said any more. For this reason, the results obtained for the cold fluid would not be representative.
Figure 8 shows the results obtained for both cases, with and without obstacle and
different flow rates for the waste water. (Appendix 4)
31
Figure 8, Waste water power.
It can be observed how the obstacles have an influence over the heat exchange rate of the fluid, but basically both curves tend to have the same shape and slope.
4.6. DIFFERENT MASS FLOW RATE IN WASTE WATER
Now, it has been considered the situation where the waste water flow rate increases and it has been answered what will happen with the heat exchange rate for both fluids.
Solution is shown in Figure 9. (Appendix 5)
32
Figure 9, Power for different waste water mfr.
Once again, there is a difference between the flows which may be due to the influence of the surroundings on the heat exchange.
4.7. DIFFERENT MASS FLOW RATE AND INLET TEMPERATURE IN WASTE WATER
In this section are shown results for two parameters variation. Usually waste water
temperature and flow rate will be fixed by the system, but of course it should be known
what performance can be expected under different conditions. Results can be
observed in the following figures. (Appendix 6)
33
Figure 10, waste water mfr 1.5 kg/s
Figure 11, waste water mfr 2 kg/s.
34
Figure 12, waste water mfr 2.5 kg/s
Figure 13, waste water mfr 3 kg/s.
The result is that the heat exchange rate in both flows increases when the waste water flow rate increases. But also the difference between them is bigger, since the heat exchange rate for the waste water increases more with an increment of both flow rate and temperature.
0 5 10 15 20 25 30
15 20 25 30 35
Power (kW)
Waste Water inlet temp. (°C)
Waste Cold
35
4.8. INFLUENCE OF CHANGES IN THE COLD WATER MASS FLOW RATE
As it has already been introduced, waste water parameters will be fixed. On the other hand, the cold water parameters can be modified. One of the ideas was to increase the flow rate. Of course, it can be increased as much as desired, but there will a point after which the heat transfer will not change that much because of a flow rate change.
Parameters for waste water are as in the original case, mfr=1.5 kg/s and T
in=22.2°C and for cold water T
in=4°C. Results are given in the following images: (Appendix 7)
Figure 14, cold water power.
Figure 15, waste water power.
36
Figure 16, Comparison after changing cold water mfr.
It should be highlighted that in Figure 14 and Figure 15 the mass flow rate has been increased up to values that are not expected to be set in a real installation but that helped to demonstrate that there is an asymptote after 7 kg/s approximately. Anyway, the really interesting one for the purpose of the thesis is Figure 16 where expected flows are shown in better detail.
Actually, Figure 16 shows how when the mfr of the cold water reaches approximately 1 kg/s both heat exchange rates are equal. Then, for higher mfr the cold water heat exchange rate remains higher that for waste water. When both mfr are equal, there is already a significant difference.
4.9. PARALLEL FLOW VS COUNTER-FLOW HEAT EXCHANGER
In some cases it is interesting to have control over the maximum heat to be exchanged
and this is something that parallel flow heat exchangers offer. With this idea in mind
was taken into account this section. It can be stated in advanced that the efficiency for
the parallel flow heat exchanger will be lower. Once again, that is not the real aim of
the section but to have a numerical reference of the difference. Table 14 provides the
different results obtained after simulating the same heat exchanger, under the same
conditions just changing the direction of the inner flow.
37 Table 14, Parallel flow VS counter flow.
As it was expected, the heat exchange rate decreases when using parallel flow. The difference is not that big since in general the parameter values are low and even the counter flow heat exchanger is far from its optimal configuration.
4.10. INDUSTRIAL CASE
As it was stated previously, this heat exchanger can be installed in houses but it is also interesting to analyse how it will perform in an industrial case, where flow rates and temperatures are higher.
It has been considered the same geometry and the conditions for an industrial situation are: (Appendix 8)
Table 15, Industrial conditions.
4.10.1. Parallel flow VS counter-flow
mfr WASTE (kg/s)
mfr COLD (kg/s)
Tinner inlet(°C)
Tinner outlet(°C)
Touter inlet(°C)
Touter outlet(°C)
Power waste (kW)
Power cold (kW)
Counter 1,5 0,5 22,2 20,021 4 10,045 13,66233 12,63405
Parallel 1,5 0,5 22,2 20,553 4 9,5832 10,32669 11,668888
Waste mfr 3 kg/s
Cold mfr 3 kg/s
Waste inlet T 45 °C
Cold inlet T 8 °C
38 Table 16 provides a comparison between a counter flow and parallel heat exchanger.
Table 16, Parallel flow VS counter flow.
Again, counter flow results are better that parallel. Any way this is the comparison, we can see up to how much we can restrict the maximum heat exchanged.
4.10.2. Industrial case with different cold water flow rates
In this section it has been considered different flow rates for the cold water, maintaining all the other parameters as in the original industrial case and parallel heat exchanger.
This will provide information about the best configuration that can be set according to the possibilities of the installation. Results are shown in Figure 17.
Figure 17, Industrial case with different cold water flow rates.
mfr WASTE (kg/s)
mfr COLD (kg/s)
Tinner inlet(°C)
Tinner outlet(°C)
Touter inlet(°C)
Touter outlet(°C)
Power waste (kW)
Power cold (kW)
Parallel 3 3 45 40,09 8 13,284 61,5714 66,26136
Counter 3 3 45 39,459 8 13,635 69,48414 70,6629
39
The pattern described by the curves shows that the power increases as the mass flow
rate increases but the slope decreases, tending once again to an asymptote.
40
5. ECONOMICAL DISCUSSION
Installing a waste water heat exchanger will have a direct impact in the environmental impact, especially in regions where the heating is based in technologies run by using fossil fuels. But it has to be considered the investment cost and the payback time of the installation. For this reason, it has been considered interesting to have a brief discussion regarding these aspects.
5.1. ECONOMICAL ANALYSIS
Some important points regarding the installation will be highlighted in this section.
First, it will be especially relevant the technology that is currently used for heating up the water. Those places where gas or electricity is used will be more likely for this technology than those where district heating is used. Focusing in the case of Sweden, some representative data can be observed in the following figures, where data regarding the different types of energy use in Swedish residential buildings and how the price of each energy has evolve [14]:
Figure 18, Residential energy use by type.
41
Figure 19, Price of different energy types.
There is no doubt that the main way for heating up water is district heating followed by electricity. Considering the prices for each one, those where electricity is used are a priori, who will have the most benefits if installing a waste water heat exchanger.
Nevertheless, also those where district heating is used will have benefits but the payback time will be longer.
For 2014, the electricity price in Sweden was 0.119 EUR/kWh, which is 1.1 SEK/kWh.
And for district heating it will be considered 80 öre/kWh. [15]
5.2. CURRENT SAVINGS
It will be considered that the heat exchanger will be working during 16 hours a day (it has been considered that this is the time that there will be hot water use in building per day, EFFAB), 365 days per year.
First of all, it will be considered the original case, with the data form the test, where around 13 kW were saved.
⁄
( 6)42 So, with the heat exchanger current working conditions, the economical
savings depending on the energy type used is:
- Electricity: 76 000 kWh/year * 1.1 SEK/kWh=83 600 SEK/Year - District heating=76 000 kWh/year * 0.8 SEK/kWh=60 800 SEK/Year This will mean a payback time for the heat exchanger when compared to each technology of:
- Payback time with electricity t=350 000 SEK/ 83 600 SEK/Year =4.18 Years - Payback time with district heating t=350 000 SEK/60 800 SEK/Year= 5.75
Years.
5.3. SAVINGS AFTER CHANGES
As it was already said, is up to EFFAB the decision of what changes can be done and in that case an economic analysis could be better developed.
Per each kW extra that can be recovered in the heat exchanger at the end of the year will be:
( 7)
What in economic terms will mean that when compared with the current heating technologies, the savings will be:
- Electricity: 5840 kWh/year * 1.1 SEK/kWh = 6424 SEK/year
- District heating: 5840 kWh/year * 0.8 SEK/kWh = 4672 SEK/year
43
44
6. CONCLUSION
All the results that have been considered as relevant have been shown in the previous section. As far as the model can be considered satisfactory it can be simulated any other case of interest.
To sum up, it has to be said that the results are as expected from theory. It can be suggested to increase the flow rates. In case of waste water it may be fixed by the system. On the other hand, the cold water flow is suitable for changes. One of the options discussed with EFFAB was to install a recirculation circuit, where the temperature of the inlet cold water will be higher (worse efficiency) but the mass flow rate can be increased compared to the waste water mass flow rate (increase the efficiency). How should be expect the results to change due to this changes are shown in the previous section. It has been proven in the section “Special case” (which is based in this idea) that it is possible to obtain the results that EFFAB is expecting by using this same heat exchanger.
Many more situations can be considered. It has not been considered more parameters in this thesis project since it is the beginning and maybe it will be interesting to simulate different cases once the conditions are well defined for those new operational cases. At least, it has been considered that the aim of the thesis project has been answered.
It should not be forgotten that the model was built according to the results of two real
tests. Even the results from the model where pretty satisfactory, it has to be considered
that because of the lack of information regarding the geometry it cannot be guarantee
that the numerical values of the real heat exchanger under the conditions stated in the
model, will give the same numerical value. Nevertheless, since the values for
temperatures and mass flow rates are expected to be changed, but always with new
values in the same order of magnitude, it can be expected that the behavior will in fact
be as defined in this report. Results from new tests will help to check how good this
model really is and otherwise, it will allow improving it.
45 Elements like the obstacles in the inner pipe have been considered to play a minor roll since the velocity of the fluid that have been consider is low and so, the fluid may not be affected significantly by the obstacles.
It is in the outer pipe where it will be interesting to know how the cold fluid is driven, since in this project it has not been considered as fluid at all by forcing it with mathematical equations. Knowing how the fluid actually behaves may be interesting.
Regarding parallel or counter-flow heat exchanger, in order to obtain the best efficiency it should always be chosen counter-flow. Only in those cases where it has to be a maximum heat transfer should be used the parallel flow heat exchanger.
Finally, from an economic perspective, recovering one extra kW will be translated in
relevant energy savings by the end of the year, what will make the payback time
shorter and then, it will mean up to almost 6500 SEK/year savings in case of electricity
heating systems and more than 4500 SEK/year in case of district heating systems.
46
7. REFERENCES
[1] Ahmad Fakheri (2007), Heat Exchanger Efficiency, Journal of Heat Transfer, Vol.129, pp: 1268-1276.
[2] “Key world energy statistics”, International Energy Agency (IEA), 2014.
[3] “Measurements of water use in eight dwellings, by quantity and time”,2007. Anna Johansson, Åsa Wahlström, Ulrik Petterson and Tomas Berggren. The eceee 2007 Summer study, paper 6.284, La Colle sur Loup, France.
[4] “Financial analysis of the implementation of a Drain Water Heat Recovery unit in residential housing”, Energy and Buildings 71 (2014) 1-11. Daniel Slys, Sabina Kordana.
[5] “Analyzing the efficiency of a heat pump assisted drain water heat recovery system that uses a vertical inline heat exchanger”, Sustainable Energy Technologies and assessments 8 (2014) 109-119. Jörgen Wallin, Joachim Claesson.
[6] “Mätning av kall- och varmvatten i tio hushåll”, SP Sveriges Tekniska Forskningsinstitut, 2008. Åsa Wahlström, Roger Nordman and Ulrik Pettersson.
[7] “Heat transfer”(Book).-McGraw-Hill Education, 2010. J.P. Holman.
[8] “Heat and mass transfer, a practical Approach”, (Book).-McGraw-Hill Education, 2007. Çengel, Yunus A.
[9] “The engineering Toolbox”, Heat Exchangers - Arithmetic and Logarithmic Mean Temperature Difference, 2015.
http://www.engineeringtoolbox.com/arithmetic-logarithmic-mean-temperature- d_436.html
[10] Comsol Multi-Physics, “Which turbulence model should I choose for my CFD application?”, 2015.
https://www.comsol.se/blogs/which-turbulence-model-should-choose-cfd-application/
47 [11] Comsol Multi-Physics, “Solution to linear systems of equations: Direct and Iterative Solvers”, 2015.
https://www.comsol.se/blogs/solutions-linear-systems-equations-direct-iterative- solvers/
[12] Comsol Multi-Physics, “Improving Convergence of Multiphysics Problems”, 2015.
https://www.comsol.se/blogs/improving-convergence-multiphysics-problems/
[13] “ANALYTICAL SOLUTION FOR A DOUBLE-PIPE HEAT EXCHANGER WITH NON-ADIABATIC CONDITION AT THE OUTER SURFACE”, Int. Comm. Heat Mass Transfer, Vol. 14, pp. 665-672 (1987). R.C. Prasad.
[14] “The Swedish policy case for Cogeneration and District Heating”, Swedish Energy Agency, 2013, Daniel Friberg.
[15] EUROSTAT, Statistics Explained, “Energy Price Statistics”, 2015.
http://ec.europa.eu/eurostat/statistics-explained/index.php/Energy_price_statistics
[16] “Rationalization of water and energy consumption in shower systems of single- family dwelling houses” 2014. Sabina Kordana, Daniel Sły_s*, J_ozef Dziopak, Journal of Cleaner Production, Volume 82, Pages 58–69
[17] “Efficient drain water heat recovery in horizontal domestic shower drains”, 2012.
Aonghus McNabola , Killian Shields. Energy and Buildings, Volume 59, Pages 44–49
[18] “Water heating through electric shower and energy demand” 1998 Racine T.A.
Prado *, Orestes M. Goçalves. Energy and Buildings Volume 29, Issue 1, Pages 77–82
[19 ] “Feasibility study of a localized residential grey water energy-recovery system”
2012 L. Ni, S.K Lau, H. Li, T. Zhang, J.S Stansbury, Jonathan Shi, Jill Neal. Applied Thermal Engineering Volume 39, Pages 53–62
[20] “Summary and evaluation on single-phase heat transfer enhancement
techniques of liquid laminar and turbulent pipe flow” 2015. Wen-Tao Ji, Anthony M.
Jacobi, Ya-Ling He, Wen-Quan Tao. International Journal of Heat and Mass Transfer
88 (2015) 735–754
48 [21] “Steel 1.4541” ThyssenKrupp Materials International
http://www.skh.com/media/de/Service/Werkstoffblaetter_englisch/Edelstahlrohre/1.454 1_engl.pdf
[22] “HIGH DENSITY INDUSTRIAL GRADE FEF INSULATION FOR ELEVATED TEMPERATURES, HT/Armaflex
®, Industrial”, Armacell Enterprise GmbH & Co. KG.
http://www.armacell.com/C1256AF100412A28/F/NT018CBEBA/$FILE/HTArmaflexIndu
strial_ES.pdf
49
8. APPENDIX
In this chapter all the temperatures are given in °C, power in kW and mass flow rate in kg/s.
Appendix 1, Variation cold water inlet temperature with and without obstacle.
Table 17, With obstacle.
Table 18, without obstacle.
Tinner inlet(°
C)Tinner outlet(°C) Touter inlet(°C) Touter outlet(°C)
Power outer (kW)
Power inner (kW)
22,2 19,755 3 10,273 15,2733 15,4035
22,2 19,883 4 10,895 14,4795 14,5971
22,2 20,01 5 11,57 13,797 13,797
22,2 20,138 6 12,139 12,8919 12,9906
22,2 20,265 7 12,761 12,0981 12,1905
22,2 20,392 8 13,382 11,3022 11,3904
22,2 20,52 9 14 10,5 10,584
22,2 20,647 10 14,624 9,7104 9,7839
22,2 20,775 11 15,224 8,8704 8,9775
Tinner inlet(°
C)Tinner outlet(°C) Touter inlet(°C) Touter outlet(°C)
Power outer (kW)
Power inner (kW)
22,2 19,9 3 9,38 13,398 14,49
22,2 20,021 4 10,045 12,6945 13,7277
22,2 20,14 5 10,7 11,97 12,978
22,2 20,25 6 11,39 11,319 12,285
22,2 20,375 7 12,1 10,71 11,4975
22,2 20,495 8 12,727 9,9267 10,7415
22,2 20,615 9 13,394 9,2274 9,9855
22,2 20,735 10 14,061 8,5281 9,2295
22,2 20,855 11 14,728 7,8288 8,4735
50
51 Appendix 2, VARIATION IN COLD WATER: DIFFERENT INLET TEMPERATURES AND FLOW RATE
All the cases with waste water flow rate 1.5 l/s, inlet temperature 22.2 °C and cp=4.2 kJ/(kg*K). Parameters that will wavy are cold water flow rate and inlet temperature.
Table 19, Cold water mfr 0.5 l/s.
Table 20, Cold water mfr 0.55 l/s.
Tinner inlet(°
C)Tinner outlet(°C) Touter inlet(°C) Touter outlet(°C)
Power outer (kW)
Power inner (kW)
22,2 19,9 3 9,38 13,398 14,49
22,2 20,021 4 10,045 12,6945 13,7277
22,2 20,14 5 10,7 11,97 12,978
22,2 20,25 6 11,39 11,319 12,285
22,2 20,375 7 12,1 10,71 11,4975
22,2 20,495 8 12,727 9,9267 10,7415
22,2 20,615 9 13,394 9,2274 9,9855
22,2 20,735 10 14,061 8,5281 9,2295
22,2 20,855 11 14,728 7,8288 8,4735
Tinner inlet(°
C)Tinner outlet(°C) Touter inlet(°C) Touter outlet(°C)
Power outer (kW)
Power inner (kW)
22,2 19,821 3 9,0761 14,035791 14,9877
22,2 19,945 4 9,7606 13,306986 14,2065
22,2 20,069 5 10,445 12,57795 13,4253
22,2 20,187 6 11,136 11,86416 12,6819
22,2 20,311 7 11,819 11,13189 11,9007
22,2 20,435 8 12,502 10,39962 11,1195
22,2 20,559 9 13,186 9,66966 10,3383
22,2 20,684 10 13,868 8,93508 9,5508
22,2 20,808 11 14,551 8,20281 8,7696
52
Table 21, Cold water mfr 0.6 l/s.
Table 22, Cold water mfr 0.7 l/s.
Table 23, Cold water mfr 0.75 l/s.
Tinner inlet(°
C)Tinner outlet(°C) Touter inlet(°C) Touter outlet(°C)
Power outer (kW)
Power inner (kW)
22,2 19,747 3 8,8 14,616 15,4539
22,2 19,875 4 9,5 13,86 14,6475
22,2 20,003 5 10,202 13,10904 13,8411
22,2 20,131 6 10,9 12,348 13,0347
22,2 20,253 7 11,601 11,59452 12,2661
22,2 20,381 8 12,299 10,83348 11,4597
22,2 20,509 9 12,997 10,07244 10,6533
22,2 20,638 10 13,694 9,30888 9,8406
22,2 20,766 11 14,391 8,54532 9,0342
Tinner inlet(°
C)Tinner outlet(°C) Touter inlet(°C) Touter outlet(°C)
Power outer (kW)
Power inner (kW)
22,2 19,619 3 8,3298 15,669612 16,2603
22,2 19,754 4 9,0534 14,856996 15,4098
22,2 19,888 5 9,766 14,01204 14,5656
22,2 20,019 6 10,498 13,22412 13,7403
22,2 20,153 7 11,221 12,40974 12,8961
22,2 20,288 8 11,944 11,59536 12,0456
22,2 20,423 9 12,666 10,77804 11,1951
22,2 20,557 10 13,389 9,96366 10,3509
22,2 20,692 11 14,111 9,14634 9,5004
Tinner inlet(°
C)Tinner outlet(°C) Touter inlet(°C) Touter outlet(°C)
Power outer (kW)
Power inner (kW)
22,2 19,563 3 8,1212 16,13178 16,6131
22,2 19,7 4 8,8556 15,29514 15,75
22,2 19,838 5 9,5898 14,45787 14,8806
22,2 19,972 6 10,32 13,608 14,0364
22,2 20,11 7 11,054 12,7701 13,167
22,2 20,247 8 11,788 11,9322 12,3039
22,2 20,385 9 12,521 11,09115 11,4345
22,2 20,522 10 13,255 10,25325 10,5714
22,2 20,66 11 13,988 9,4122 9,702
53 Appendix 3, INNER PIPE: DIFFERENT RADIUS.
Table 24, parameters values.
Table 25, varying the radius of inner pipe.
cp 4,18 kJ/kgK
mfr waste 1,5 kg/s
mfr cold 0,5 kg/s
Rinner (mm)Router (mm)Tinner inlet(°C)Tinner outlet(°C)Touter inlet(°C)Touter outlet(°C)Power inner (kW)Power outer (kW) 6017722,220,41648,642711,185689,703243 7017722,220,29748,8711,9318110,1783 8017722,220,20649,328312,5023811,136147 9017722,220,10649,553513,1293811,606815 10017722,220,021410,04513,6623312,63405 10517722,220,016410,15613,6936812,86604 11017722,219,929410,3914,2391713,3551 12017722,219,895410,82814,4523514,27052 13017722,219,937410,85214,1890114,32068
54
55 Appendix 4, Influence of the obstacle.
Table 26, with obstacle.
Table 27, without obstacle.
mfr WASTE
(kg/s)
mfr COLD (kg/s)
Tinner inlet(°
C)Tinner outlet(°C)
Touter inlet(°C)
Touter outlet(°C)
Power waste (kW)
Power cold (kW)
1,5 0,5 22,2 19,883 4 10,895 14,52759 14,41055
2 0,5 22,2 20,197 4 10,628 16,74508 13,85252
2,5 0,5 22,2 20,499 4 10,853 17,77545 14,32277
mfr WASTE (kg/s)
mfr COLD (kg/s)
Tinner inlet(°
C)Tinner outlet(°C)
Touter inlet(°C)
Touter outlet(°C)
Power waste (kW)
Power cold (kW)
1,5 0,5 22,2 20,021 4 10,045 13,66233 12,63405
2 0,5 22,2 20,328 4 10,675 15,64992 13,95075
2,5 0,5 22,2 20,553 4 11,145 17,21115 14,93305
56
57 Appendix 5, Influence of the variation of the waste water flow rate.
Table 28, Influence of the variation of the waste water flow rate
