Politecnico di Torino Master's project on solar energy equipment

Politecnico di Torino
Master Degree in Mechanical Engineering
Solar energy equipment
Academic year 2014/2015
Francesco Beccarisi 214132
Lin Chen 214067
Lorenzo D’Angelo 220336
Aydin Farahmand 213933
Pietro Galli 220205
Mehdi Hadi 214742
Jean Paul Hamod 221495
Bakhtiyor Ismailov 221708
Shaoqiang Jin 218260
Angela Marco 220165
Giulio Marino 220128
Marco Merlotti 217196
Roberto Preite 214137
Marco Raimondo 220091
Antonio Russo 214173
Jorge Jesus Silva Silva 217696
Eduardo Terzidis 214001

Contents
1 Introduction 7
I PART S: Data collection and preliminary design 8
2 Geometric design of the building characteristics 9
2.1 Geographical localization of the building . . . . . . . . . . . . . . . . . . 9
2.2 Building description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3 Estimation of the hot water demand 16
4 Evaluation of the Irradiance 18
4.1 Theoretical informations . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.2 Global Radiation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2.1 Variables and assumed values . . . . . . . . . . . . . . . . . . . . 19
4.2.2 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
5 Computation of the volume of the hot storage tank and deﬁnition of its
insulation 23
5.1 Storage tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
5.2 Insulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6 Description of the plant 27
6.1 Collector loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
6.2 Gas boiler loop . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
6.3 Tank . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
II PART A: Oﬀ-design calculations 29
7 F chart 30
7.1 Solar collector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
7.2 Calculations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
8 Thermal balance of the solar panel 42
1

9 Heat exchanger 46
9.1 Thermal balance and design . . . . . . . . . . . . . . . . . . . . . . . . . 46
9.2 Balance through the First Law of TD . . . . . . . . . . . . . . . . . . . . 46
9.2.1 Forced convection (Ri) . . . . . . . . . . . . . . . . . . . . . . . . 49
9.2.2 Conduction (Rw) . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
9.2.3 Natural convection (Ro) . . . . . . . . . . . . . . . . . . . . . . . 50
9.2.4 Length evaluation . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
10 Thermal balance of the hot water storage system 53
10.1 First control volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
10.2 Second control volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
10.3 Calculation of Qwaste . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
10.4 Tank eﬃciency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
11 Boiler 60
11.1 General information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
11.2 Energy analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
11.2.1 Power from combustion . . . . . . . . . . . . . . . . . . . . . . . . 62
11.2.2 Thermal ﬂux . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
11.2.3 Lmtd method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
11.2.4 Transmittance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
11.2.5 Flow regimes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
11.2.6 Inner pipe side . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
11.2.7 Shell side . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
12 Thermal balance of the apartment 67
12.1 Windows and doors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
12.2 External/internal walls . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
12.3 Roof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
12.4 Power for ventilation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
III PART B: Exergy analysis 73
13 Collectors 75
14 Heat exchanger 80
15 Tank 83
16 Boiler 88
17 Cost analysis 91
2

IV PART C: Technical engineering design and heat transfer 93
18 Computation of the heat transfer of the fluid through the panel 94
18.1 Forced convection (Ri) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
18.2 Conduction (Rw) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
19 Determination of the temperature profile of the thermal fluid along the
pipe 97
3

List of Figures
1.1 Scheme of the plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
2.1 Piedmont region . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Plant of Turin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.3 Districts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2.4 Plant of the building . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.5 Plant of the basement . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.6 Front view of the building . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.7 Lateral view of the building . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.8 Plant of the roof . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.9 Rendering of the building . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.10 Rendering of the inner part of the building . . . . . . . . . . . . . . . . . 15
2.11 Rendering of the basement of the building . . . . . . . . . . . . . . . . . 15
3.1 Specific daily hot water demand . . . . . . . . . . . . . . . . . . . . . . . 16
4.1 Definition of angle of incidence . . . . . . . . . . . . . . . . . . . . . . . . 19
4.2 Azimuth definition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5.1 Image of the tank (1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.2 Image of the tank (2) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
5.3 Characteristics of the tank (1) . . . . . . . . . . . . . . . . . . . . . . . . 26
5.4 Characteristics of the tank (2) . . . . . . . . . . . . . . . . . . . . . . . . 26
6.1 Plant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
7.1 Solar collector specifications . . . . . . . . . . . . . . . . . . . . . . . . . 32
7.2 Input data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
7.3 case with one collector . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
7.4 case with one collector (1) . . . . . . . . . . . . . . . . . . . . . . . . . . 34
7.5 case with one collector (2) . . . . . . . . . . . . . . . . . . . . . . . . . . 34
7.6 case with two collectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
7.7 case with two collectors (1) . . . . . . . . . . . . . . . . . . . . . . . . . . 35
7.8 case with two collectors (2) . . . . . . . . . . . . . . . . . . . . . . . . . . 36
7.9 case with four collectors . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
7.10 case with four collectors (1) . . . . . . . . . . . . . . . . . . . . . . . . . 37
7.11 case with four collectors (2) . . . . . . . . . . . . . . . . . . . . . . . . . 37
7.12 case with six collectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
7.13 case with six collectors (1) . . . . . . . . . . . . . . . . . . . . . . . . . . 38
4

7.14 case with six collectors (2) . . . . . . . . . . . . . . . . . . . . . . . . . . 39
7.15 case with ten collectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
7.16 case with ten collectors (1) . . . . . . . . . . . . . . . . . . . . . . . . . . 40
7.17 case with ten collectors (2) . . . . . . . . . . . . . . . . . . . . . . . . . . 40
7.18 F vs area of the collectors . . . . . . . . . . . . . . . . . . . . . . . . . . 41
7.19 Roof area occupied by collectors . . . . . . . . . . . . . . . . . . . . . . . 41
8.1 Sketch of the solar panel . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
8.2 Irradiation, absorption and reflection definitions . . . . . . . . . . . . . . 43
8.3 Collector efficiency curve . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
8.4 Table summarizing obtained values . . . . . . . . . . . . . . . . . . . . . 45
9.1 Control volume of the heat exchanger . . . . . . . . . . . . . . . . . . . . 47
9.2 Resistance model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
9.3 Results and parameters of heat exchanger analysis . . . . . . . . . . . . . 51
9.4 Results and parameters of heat exchanger analysis (1) . . . . . . . . . . . 52
9.5 Results and parameters of heat exchanger analysis (2) . . . . . . . . . . . 52
10.1 Tank control volume scheme . . . . . . . . . . . . . . . . . . . . . . . . . 53
10.2 House control volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
10.3 Second control volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
10.4 Insulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
10.5 Resistance model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
10.6 Tank efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
11.1 Gas-boiler scheme . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
11.2 Table of efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
11.3 Typical shell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
11.4 Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
12.1 Apartment thermal fluxes . . . . . . . . . . . . . . . . . . . . . . . . . . 67
12.2 Limits of transmittance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
12.3 External walls resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
12.4 Internal walls resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
12.5 Roof resistance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
13.1 Control volume of the collectors . . . . . . . . . . . . . . . . . . . . . . . 75
13.2 Month temperatures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
13.3 Specific exergy flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
13.4 Results of exergy analysis of collectors . . . . . . . . . . . . . . . . . . . 78
13.5 Exergetic efficiency of the collectors . . . . . . . . . . . . . . . . . . . . . 79
13.6 Exergy destruction in the collectors . . . . . . . . . . . . . . . . . . . . . 79
14.1 Control volume of the heat exchanger . . . . . . . . . . . . . . . . . . . . 80
14.2 Data and results of heat exchanger exergetic analysis . . . . . . . . . . . 82
15.1 Tank control volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
15.2 Tank exergetic analysis results . . . . . . . . . . . . . . . . . . . . . . . . 85
5

15.3 Mass flow rates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
15.4 Efficiency result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
15.5 Trend of efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
16.1 Boiler control volume . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
16.2 Boiler exergy analysis results . . . . . . . . . . . . . . . . . . . . . . . . . 90
18.1 Scheme of the panel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
18.2 Resistance analogy results . . . . . . . . . . . . . . . . . . . . . . . . . . 96
19.1 Temperature profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
6

Chapter 1
Introduction
In this work it is performed design and calculation of a solar panel equipment for a 4-
storey building located in Turin. The building has 8 apartments (two per storey) of 70 m2
each, all of them having the same structure and characteristics. It can be considered that
each apartment has a kitchen, a living room, two bedrooms and a bathroom. The solar
water heating system that will be installed has the aim of partially covering the service
hot water demand. This new facility will comprise an array of thermal solar collectors in
the roof of the building (which is ﬂat) and a room in the cellar for the hot water storing
system. This room (called boiler room) is already used for the existing conventional water
heating system, namely, a central natural gas-ﬁred boiler. The objective of this project
is to carry out and to analyze the design of the solar water heating (SWH) system for
the building.
Figure 1.1: Scheme of the plant
7

Part I
PART S: Data collection and
preliminary design
8

Chapter 2
Geometric design of the building
characteristics
2.1 Geographical localization of the building
The building is located in Turin, the capital of Piedmont; more precisely in the micro-
zone 27, on the border with the neighborhood Moncalieri. The following ﬁgures illustrate
the position of the building.
Figure 2.1: Piedmont region
9

Figure 2.2: Plant of Turin
The building is located in Piero Monticelli street, 5, as indicated in the following image.
Figure 2.3: Districts
In the following table the characteristics of the city of Turin are reported:
Altitude 250 m
Longitude 7◦
39.9
Latitude 45◦
1.1
Climatic zone E
10

2.2 Building description
In the building there is a total of eight apartments (two per storey), all of them
having the same structure and characteristics. Each apartment has a kitchen, a living
room, a double bedroom, a single bedroom, a bathroom and a corridor (Figure 2.4). The
regulatory plan of the city of Turin establishes a minimum height for the domestic walls
of 2.70 m and a thickness of 10 cm for partitions, 20 cm for the walls shared with another
house and 30 cm for exterior walls.
In the basement (Figure 2.5) there are 8 rooms (one for each resident, a local for electric
meters and an open space for the regulation of the hot water storage system).
According to the normative the thickness of the screed must be at least 15 cm and for
the last floor there must be a railing with at least 100 cm of height (Figures 2.6 and 2.7).
Finally the roof of the building (Figure 2.8) is flat, this is a feature that leaves ample
degrees of freedom to the location of the solar panels. The total area of the roof, net of
the walls, the roof for the satellite and the walkways, is 106 m2
.
In the following figures, the non specified dimensions are in cm.
Figure 2.4: Plant of the building
11

Figure 2.5: Plant of the basement
Figure 2.6: Front view of the building
12

Figure 2.7: Lateral view of the building
13

Figure 2.8: Plant of the roof
Finally some render images of the building and the basement are attached.
Figure 2.9: Rendering of the building
14

Figure 2.10: Rendering of the inner part of the building
Figure 2.11: Rendering of the basement of the building
15

Chapter 3
Estimation of the hot water demand
When calculating the hot water demand for the entire building, we referred to law
n.13 05/28/2007 issued by Piedmont region. The just mentioned law led us to get all
the used formulas from UNI/TS 11300-2. The whole building is made up of four floors
and each of them contains two apartments of 70 m2
each. The required hot water volume
has been computed as follows:
Vw = a Nu [l/d]
where:
• Vw is the mean daily required hot water in litres;
• a [l/d] is the specific daily hot water demand (from figure 3.1, it depends on the
useful surface (Su [m2
] of the building itself));
• Nu is a parameter that depends on the kind of building. Since the building we are
dealing with is a residential building, Nu will be computed as the useful area Su.
According to the normative, the value of the gross surface (Sg = 70 m2
) has to be
corrected by using the following factor (fn) defined as:
fn = 0.9761 − 0.3055 dm = 0.899725
Where dm = 0.25 m is the wall external mean thickness.
This factor permits to evaluate the useful area:
Su = Sg fn = 63 m2
= Nu
Figure 3.1: Specific daily hot water demand
16

Finally it is possible to obtain the daily demand of hot water per apartment as follows:
Vw = a Nu = 107.1
l
d
Since there are eight apartments the total daily demand of hot water is:
Vw,t = 8 a Nu = 857.0
l
d
17

Chapter 4
Evaluation of the Irradiance
4.1 Theoretical informations
Requirements and general recommendations are based on the Regional Law May 28,
2007 n. 13 (Provisions on energy efficiency in buildings) Article 21, paragraph 1, letters g)
and p). According to the law, in the case of a flat roof, solar panels and their components
can be installed on suitable substrates to achieve the inclination considered optimal,
assuring that the plant is not visible, even using shielding in front of neighboring public
spaces building placed at lower elevation. In case of installation of solar collectors on the
flat roof, also the following recommendations must be applied:
• in order to obtain the best efficiency solar collectors should be oriented to the south
with a maximum tolerance of ±10◦
;
• in the case where the load is constant during the months of the year, the inclination
is preferably equal to 35◦
÷ 40◦
;
• in the case where the load is mainly in the summer (definitely our case), the incli-
nation is preferably equal to 30◦
÷ 35◦
;
• in winter the inclination is preferred to be 50◦
÷ 60◦
.
In general the (direct) radiation from the sun is not completely incident along the
normal onto a solar collector, but arrives at a certain angle of incidence. This angle is
measured between the radiation beam and the normal to the collector surface, as in the
following figure.
18

Figure 4.1: Definition of angle of incidence
The incidence direction is not only described by this single angle, but also by two
different ones: transversal and longitudinal. For flat plate collectors the longitudinal and
transversal angles have no influence on the calculation of the incidence direction, while
e.g. for concentrating or evacuated tube collectors these angles have different influences.
4.2 Global Radiation
In order to compute the Daily Global Radiation in Monthly average (Rggmm) on the
ground and on the inclined surface, the procedure complies with the requirements of UNI
8477/1 laying instructions for the ”Calculation of energy gains for building applications,
Evaluation of radiant energy received”, but uses the maps of the Global Radiation in
Monthly average (Rggmm) on horizontal plane calculated by ENEA. Those maps have
a space-resolution of 2.5 km2
and they are estimated starting from the cloudy satellite
images obtained from the European authority EUMETSAT. It allows - among other
things - to evaluate the effect due to the presence of obstacles that at certain times of
day may shield the rays of the sun.
The calculation is performed at an assigned location and with reference to a known
surface orientation; geographic coordinates of locations and angles that define the orien-
tation of the receiving surface are chosen by the user.
4.2.1 Variables and assumed values
• Inclination: angle that the receiving surface forms with the horizontal plane of
location. According to the Regional Law in the case where the load is mainly in the
summer, the inclination is preferably equal to 30◦
÷35◦
. We assume the mean value,
32◦
, just for calculation. When we will look at the inventories of the different firms
we will assume the right angle associated to the type of panel we will physically
use.
• Azimuth: is the angle with the normal projection to the receiving surface of the
horizontal plane in the southward projection. It can take values between −180◦
19

and +180◦
:
– null if the projection coincides with the direction South (our case);
– positive if the projection falls on the half-plane East;
– negative in the opposite case.
In the following figure the concepts just expressed are exemplified.
Figure 4.2: Azimuth definition
• Reflection coefficient of the ground: reflected fraction upwards of Rggmm that
reaches the ground, in the horizontal plane. This coefficient depends on the type of
ground and it can vary from 0 to 1. Here it is attached a table for some types of
soil/ground (Source: UNI 8477/1; for a more extensive collection, see also: M. Iqbal,
An Introduction to Solar Radiation, 1983, p 288 and following; or F.M.Butera:
Architettura e ambiente, Etats, 1995 Appendix 1.3.a):
20

Type of ground Reflective coefficient
Snow (freshly fallen or film of ice) 0.75
Water surfaces 0.07
Soil (clay, marl) 0.14
Dirt roads 0.04
Conifer forest in winter 0.07
Forest in autumn and fields with mature crops and plants 0.26
Asphalt aged 0.10
Old concrete 0.22
Dead leaves 0.30
Dry grass 0.20
Green grass 0.26
Roofs or terraces in bitumen 0.13
Rubble 0.20
Dark surfaces of buildings (dark brick, dark colors, ...) 0.27
Light surfaces of buildings (light brick, clear varnishes, ...) 0.60
Last coefficient of the table refers to our case.
4.2.2 Results
In this section it is described the computation of the Daily Global Radiation in
Monthly average (Rggmm) on inclined surface (Five-year average in 1995 - 1999).
Input data are:
• Latitude: 45◦
1.1 ; longitude: 7◦
39.9
• Azimuth 0◦
0 0
• Inclination from the horizontal: β = 32◦
• Model for the calculation of the fraction of the scattered radiation than the global:
ENEA-SOLTERM
• Reflection coefficient soil: 0.60
• Unit: MJ/m2
In the model for the calculation of the fraction of the diffuse radiation with respect
to the global the following parameters are present:
• Hglob: global radiation at the ground [on the horizontal plane]
• Ho: extra-atmospheric radiation (also extra-earth) [on the horizontal plane]
• Kt = Hglob/Ho: global trasmission coefficient at the ground
• Hdiff : diffuse radiation [on the horizontal plane]
• K = Hdiff /Hglob: fraction of diffused radiation with respect to the global one.
21

All quantities refer to the monthly mean daily data. The procedure requires to express
K with respect to Kt, so we have chosen to calculate it with the: ENEA-SOLTERM
correlation, done for Italy, based on the measurements of the Rete attinometrica of ENEA:
K = 1 − 1.165 (0.0695 + 0.8114 Kt)
The obtained results are summed up in the following table:
Month Rggmm (MJ/m2
) Sunlight Daylight N of days Rainy days/month
January 10.20 3.52 9.11 31 6
February 13.52 4.10 10.20 28 4
March 17.61 5.32 11.51 31 5
April 19.33 6.02 13.28 30 11
May 20.53 6.52 14.50 31 13
June 21.85 10.42 15.33 30 10
July 22.15 8.23 15.14 31 8
August 20.03 7.13 14.02 31 10
September 17.03 5.28 12.28 30 9
October 13.33 4.31 10.52 31 9
November 10.46 2.48 9.30 30 8
December 8.42 3.21 8.49 31 6
In the previous table, Sunlight and Daylight refer to the average values expressed in hours
per day.
22

Chapter 5
Computation of the volume of the
hot storage tank and definition of its
insulation
5.1 Storage tank
The total energy required in one day can be evaluated by the following formula:
Ed = mH2O cp,w ∆T = (Vw,t ρ) cp,w (TU − Tw,c)
where:
• Ed is the required total energy per day;
• mH2O is the daily mass of the required water;
• Vw,t = 900 l/d is the volume occupied by the daily required water, which is rounded
up from the value of 857 l/day computed before;
• ρ = 1 kg/l is the density of water;
• cp,w = 4.184 kJ/kg K is the specific heat of water;
• TU = 40◦
C is the post-heating temperature;
• Tw,c = 15◦
C is the inlet water temperature, according to the normative.
Now we can consider the energy required respectively daily and in seven days, the results
are summed in the following table:
Ed(energy/day) 94 MJ/day
Ew(energy/week) 659 MJ/week
Now, in order to choose the model of the tank, it can be assumed that energy necessary
for one week (Ew) has to be stored; furthermore, in first approximation, by following
SMACNA directives, energy losses will be about 2% in 12 hours: so heat losses p after
23

one week will take the 28% of the initial energy; it follows that mass and the volume
can be computed for different temperatures of the water stored in the tank (Tt) with the
following formula:
m =
Ew (1 + p)
cp,w (Tt − Tw,c)
Values are reported in the following table:
Tt(◦
C) m(kg) V olume(m3
)
55 5040 5.04
60 4480 4.48
65 4032 4.03
70 3665 3.67
75 3360 3.36
80 3102 3.10
85 2880 2.88
90 2688 2.69
Then the temperature stored in the tank is taken equal to 65◦
C: in particular it is found
that Tt has to be higher than 60◦
C in order to avoid possible proliferation of bacteria
colonies; moreover the temperature is chosen in order to optimize the efficiency of the
solar panels as it will be evident in the following part of the analysis; hence according to
standardized sizes by catalogues this temperature leads to a tank of 4000 l. So, given the
size of the tank (4m3
) and the required performance, the tank NSIXE4000 by SICC is
taken. In the following figures and tables the main characteristics are shown:
24

Figure 5.1: Image of the tank (1)
Figure 5.2: Image of the tank (2)
25

Figure 5.3: Characteristics of the tank (1)
Figure 5.4: Characteristics of the tank (2)
In the previous ﬁgure, each heat exchanger surface is indicated with the letters Sc 1,2,3.
5.2 Insulation
The insulation is taken into account considering that the material is soft polyurethane,
with a thermal conductivity λ = 0.037 W/m/K, 50 mm thick and PVC laminated.
26

Chapter 6
Description of the plant
At this point it is possible to provide a rough definition of the plant, as represented
in the following image:
Figure 6.1: Plant
This combined solar panel-gas boiler energy is designed to provide service water for
a four storey building with eight apartments, each hosting two people. The system can
be divided into three main subsystems interacting one with each other:
• Collector loop;
• Gas boiler loop;
• Tank.
6.1 Collector loop
It is the subsystem providing energy taken by solar radiation to the water in the tank.
It is mainly made up of:
• Collectors which transform solar radiation into heat stored by a non-freezing fluid;
• A closed loop of pipeline that allows the collector fluid to transport the heating
energy from the collectors to the tank;
27

• Heat exchanger involved with the energy transfer between collector fluid and the
water inside the tank;
• A pump necessary to put fluid of the loop in motion;
• A fluid refilling system in case of natural leakages of the fluid in the circuit;
• A control system CS1 switching on/off the pump and the fluid refilling system:
– It checks temperature T of the water in the tank and, if it is lower than the
maximum design temperature (65◦
C), it activates or keeps activated the pump;
– It checks the pressure in a certain point of the pipeline and, in case it is lower
than a limit value, it activates refilling system.
6.2 Gas boiler loop
The gas boiler loop consists of:
• A gas boiler providing energy to the fluid of the loop by using gas combustion;
• A closed loop of pipeline that allows the fluid to transport the heating energy from
the boiler to the tank;
• Heat exchanger dealing with the energy transfer between boiler fluid and the water
inside the tank.
6.3 Tank
The tank stores heating energy necessary to provide water to the building for one
week. It receives fluxes from the heat exchangers connected to collector and boiler loops
and mass flow rate from the aqueduct; then it supplies mass flow rate to the building:
actually a control system CS2 controls a valve to ensure the right temperature to the
users.
28

Part II
PART A: Oﬀ-design calculations
29

Chapter 7
F chart
Evaluation of the solar system is usually done in terms of useful fraction of energy
produced compared to the total requirement. One simple method to do it is f-chart
method that allows the calculation of the monthly fraction of energy produced by the
solar system with regards to the thermal load required for monthly hot water supply.
The results of the correlations express the value of a coefficient f, as the monthly
fraction of the thermal load supplied by a solar system as a function of two dimensionless
parameters X and Y. The first parameter expresses the ratio between the losses of the
collector and thermal load, the second expresses instead the relationship between the
absorbed solar radiation and thermal load.
In order to compute X and Y parameters the following formulas are implemented:
X =
Ac Fr UL (Tref − Ta) ∆τ
L
Y =
Ac Fr (τα) HT N
L
where:
• Ac is the collector area;
• Fr is the corrected Fr factor, being Fr is the collector overall heat removal efficiency
factor;
• UL are collector losses;
• ∆τ is the number of seconds in a month;
• Tref is the empirical reference temperature;
• Ta is the environmental temperature (monthly average);
• N are the days in a month;
• L = Ld N is the monthly thermal load for tap water (where Ld is the daily thermal
load for tap water);
30

• HT is the monthly average daily total solar radiation on the collector surface;
• τα is the monthly average of the product of transparency factor and absorption
factor, corrected with kθ coefficient: τα = kθ (τα)n that considers the incidence of
the solar collector, through the following formula:
kθ (τα)n = 1 − b0
1
cos θ
− 1
where:
– b0 depends on the optic properties of the glass and it is generally assumed 0.1
for single glazed collectors;
– θ is the inclination of the solar panels.
• Fr is the collector heat removal coefficient. We cannot compute directly its value
but by comparing the following formulas we know that η0 = Fr τα and a1 = Fr UL:
Fr =
ηc
kθ (τα)n − UL
tin − ta
G
ηc = η0 − a1
Tm − Ta
G
− a2 G
Tm − Ta
G
2
To take into account even the efficiency of the heat exchanger Fr is substituted by
Fr which is calculated by the following formula (according to Standard EN 12975):
Fr
Fr
= 1 +
AA Fr Ul
˙m cf c
( ˙m cf )c
( ˙m cf )min
− 1
−1
where:
– ˙m is the mass flow rate in the collector;
– AA is the surface of the heat exchanger;
– cf is the specific heat of the glycol ethylene.
The f factor in case of liquid system for hot tap water is:
f = 1.092 Y − 0.065 Xc − 0.245 Y 2
+ 0.0018 X2
c + 0.0215Y 3
where:
Xc
X
=
11.6 + 1.18 Tw,c + 3.86 Tu − 2.32 Ta
100 − Ta
where Tw,c and Tu are temperature of the water supply and the minimum temperature
required by the user.
Finally we can define F as the annual total thermal load met by solar energy, i.e. the
sum of the monthly contributions relating to the annual:
F =
Σfi Li
ΣLi
31

7.1 Solar collector
A flat plate solar collector from the Eclipse Company with the following specifications
is selected:
Figure 7.1: Solar collector specifications
7.2 Calculations
Substituting the data from the catalogue of the collector provided into the above-
mentioned formulas, the following results are obtained for the different cases of 1, 2, 4, 6
and 10 collectors:
32

Figure 7.2: Input data
Figure 7.3: case with one collector
33

Figure 7.4: case with one collector (1)
Figure 7.5: case with one collector (2)
34

Figure 7.6: case with two collectors
Figure 7.7: case with two collectors (1)
35

Figure 7.8: case with two collectors (2)
Figure 7.9: case with four collectors
36

Figure 7.10: case with four collectors (1)
Figure 7.11: case with four collectors (2)
37

Figure 7.12: case with six collectors
Figure 7.13: case with six collectors (1)
38

Figure 7.14: case with six collectors (2)
Figure 7.15: case with ten collectors
39

Figure 7.16: case with ten collectors (1)
Figure 7.17: case with ten collectors (2)
It is plotted the values of F against the area of the collectors:
40

Figure 7.18: F vs area of the collectors
The share of the roof computed for diﬀerent values of thermal load provided by the solar
system is presented as follows:
Figure 7.19: Roof area occupied by collectors
Since the surface area of each collector is the ﬁxed value of 2.51 m2
, the minimum
number of collectors in order to provide the above mentioned percentages of F is:
• two collectors for 20%;
• four collectors for 40%;
• six collectors for 60%;
• ten collectors for 80%.
41

Chapter 8
Thermal balance of the solar panel
A sketch of solar panel under investigation is the one shown below:
Figure 8.1: Sketch of the solar panel
The solar panel chosen is the flat collector already defined in the f-chart method and
the number of collectors is defined in order to satisfy 80% of the thermal load by solar
panels and it results to be equal to ten collectors.
In order to clarify the concepts of irradiation, absorption, reflection and transmission,
which play an important role in the thermal balance of a solar collector, the following
sketch helps with clarifying the ideas.
42

Figure 8.2: Irradiation, absorption and reflection definitions
The energy balance on the medium can be expressed as follows:
Gλ = Gλ,ref + Gλ,abs + Gλ,tr
The thermal balance of a solar collector can be expressed through the following equa-
tion, which depends on the thermal power absorbed by the collector, the thermal power
dissipated and the useful one which is the one transferred to the fluid:
˙Qsun − ˙Qdiss = ˙Qu
At this point an important assumption is made: the temperatures at the inlet and at
the outlet of the collector are set to be fixed during all the months of the year and their
values are, respectively, Tc,c = 70◦
C and Tc,h = 94◦
C.
The efficiency of the solar collector is provided by the producer as a function of the
difference between the average temperature of the liquid (arithmetic mean between inlet
and outlet temperatures) and the ambient temperature:
43

Figure 8.3: Collector efficiency curve
So it is possible to evaluate the useful power by means of the following equation:
˙Qu = η ˙Qsun
where ˙Qsun = G Ac N, whose elements are:
• G [W/m2
] is the daily irradiance incident on the collector: the number of rainy days
in a month and the number of hours of daylight in a day are considered in order to
find the nominal value of the irradiance;
• Ac [m2
] is the area of a collector;
• N is the number of collectors considered for the thermal balance.
The useful power can also be computed with the following formula:
˙Qu = Gc cp,g (Tc,h − Tc,c)
where:
• Gc [kg/s] is the mass flow rate of the heat transfer fluid which is chosen to be wa-
ter/propylene glycol which has a high value of specific heat and good heat exchange
property.
The properties of the non-freezing fluid are shown in the following table:
44

Percentage of glycol 30%
Freezing temperature −15◦
C
Fluid speciﬁc heat cp,g 3683.2 J/(kg K)
A table summarizing the values of absorbed, dissipated and useful power is displayed as
well as the value of the mass ﬂow rate in the collector loop:
Figure 8.4: Table summarizing obtained values
The results are used in order to design the heat exchanger.
45

Chapter 9
Heat exchanger
9.1 Thermal balance and design
This part deals with the analysis of thermal balance and designing of the heat ex-
changer(s), interface between the hot water in the storage tank and glycol (thermal fluid
coming from collectors) in a technical way to satisfy the requirements of the system.
First, it is worth pointing out that designing here is not free enough to let us choose plate
heat exchangers with better performances compared to the tube configuration, because
the model of the tank chosen in part S, which comes with an equal couple of tube heat
exchangers. As it is clear in fig. 5.1 and 5.2 (page 25), the configuration is installed hor-
izontally inside the tank. Another restrictive address is the material of the combination
which is stainless steel. So, the main concern is directed to find the length necessary to
satisfy heat transfer required. It is worth noticing that, since a couple of identical heat
exchangers in parallel configuration is present, then the mass flow rate is supposed to be
split equally into the two devices; for this reason the analysis done on one heat exchanger
can be repeated equally for the other one. We have taken from catalogue a standard 1/4
pipe (dimension of external diameter) of stainless steel.
9.2 Balance through the First Law of TD
First of all heating flux exchanged can be obtained by using the First Law of Thermo-
dynamics to the control volume defined by the external wall and by the section of inlet
and of outlet of a single heat exchanger, as in the following figure:
46

Figure 9.1: Control volume of the heat exchanger
Φ =
Qu,December
2
= Gh cp,g (Tc,h − Tc,c)
where:
• Qu,December is the smallest value of useful power absorbed in the year (the choice is
based on the idea of being on the safe side of the design);
• Gh = Gc/2 is the mass flow rate of glycol solution from the collectors and its value
is assumed as the minimum one in the whole year (December);
• cp,g is the specific heat of the fluid;
• Tc,c and Tc,h are the temperatures of the glycol solution at the outlet and the inlet
respectively.
47

Obtained the flux, in order to use the LMTD method, the Logarithmic Mean Tem-
perature Difference is evaluated:
∆Tlmtd =
∆T1 − ∆T2
ln(∆T1/∆T2)
The temperature of the water is considered almost constant in the tank. Hence, the total
resistance can be found from the following analogy with an electric circuit:
Figure 9.2: Resistance model
Now, since the temperatures and consequently the heat flux inside the tank and along
the pipes is not homogeneously distributed, in first approximation we assume the thermal
resistance to be uniformly distributed along the length of the exchanger and equal to the
one of the section of the devices having a temperature equal to the arithmetic mean
between Tc,h and Tc,c; consequently all the properties of the fluid that will be used are
evaluated in this condition.
∆Tlmtd = Rtot Φ
The total thermal resistance is the sum of different contribution:
• Ri due to the forced convection inside the heat exchanger pipe;
• Rw due to the conduction through the wall of pipes;
• Ro due to the natural convection with the water stored in the tank.
48

9.2.1 Forced convection (Ri)
Resistance of forced convection inside heat exchanger can be calculated as follows:
Ri =
1
hi Ai
where:
• Ai is the internal surface of heat exchanger (internal perimeter times the length of
the pipe);
• hi is the heat transfer coefficient expressed in [ W
K m2 ] that can be derived from Nusselt
number.
In order to calculate Nusselt, the following unknowns must be evaluated: Prandtl and
Reynolds numbers and the friction coefficient:
Pr =
cph µh
λh
Re =
ρh uh di
µh
where:
• µh is the dynamic viscosity of the glycol solution at T = 82◦
C (arithmetic mean
between inlet and outlet temperatures);
• λh is the thermal conductivity of the glycol solution;
• ρh is the glycol solution density;
• uh is the velocity of the solution inside the pipe;
• di the inner diameter of the pipe.
Friction coefficient fh:
fh = (1.58 ln(Reh − 3.28))−2
Hence Nu is calculated with the empirical formula valid for forced convection:
Nuh =
h di
λ
=
(f/2) Reh Prh
1 + 8.7 (f/2)0.5 (Pr − 1)
Finally Ri is expressed as function of only the length of heat exchanger L:
Ri =
1
hi L (π di)
49

9.2.2 Conduction (Rw)
The next resistance component (R2) is due to the conduction through the walls of
the pipe and it is evaluated as follow:
Rw =
ln(do/di)
2 π k L
where:
• do and di are respectively the outer and inner diameters of the pipe;
• k is the thermal conductivity of the steel and is expressed in [W/m K];
• L is the length of the pipe.
9.2.3 Natural convection (Ro)
The final component of thermal resistance (Ro) is due to natural convection between
the pipe wall and the water inside the tank and is equal to:
Ro =
1
ho Ao
where:
• Ao is the outer surface of heat exchanger (external perimeter times the length of
the pipe);
• ho is the heat transfer coefficient expressed in [W/K m2
] that can be derived from
Nusselt number for natural convection.
In order to calculate Nusselt number, it is necessary to know Prandtl, Grashof and
consequently Rayleigh numbers. They are evaluated by using the following formulas:
Pr =
µ cp
λ
Gr =
g β |Tw − Tf | L3
ν2
Ra = Gr Pr
where:
• g is the gravity acceleration in [m/s2
];
• β is the thermal expansion coefficient of the water in [K−1
];
• ν is the kinematic viscosity coefficient of water in [m2
/s] at T = 65◦
C;
• Tw is the temperature of the walls;
• Tf is the temperature of the fluid.
50

Hence Nu is calculated with the empirical formula valid for water natural convection:
Nu = 0.10 Ra
1
3
Again from the reverse general formula of Nusselt we can derive ho.
Nu =
ho do
λ
9.2.4 Length evaluation
Finally, since the three components of thermal resistance are expressed as functions of
L and since total resistance has been evaluated, the value of L is derived by the following
equation:
Rtot = Ri + Rw + Ro =
1
hi L di π
+
ln(do/di)
2 π k L
+
1
ho L do π
L results equal 15 m.
The parameters used for calculations and the results are summed up in the following
table:
Figure 9.3: Results and parameters of heat exchanger analysis
51

Figure 9.4: Results and parameters of heat exchanger analysis (1)
Figure 9.5: Results and parameters of heat exchanger analysis (2)
52

Chapter 10
Thermal balance of the hot water
storage system
Figure 10.1: Tank control volume scheme
The thermal balance of the hot water storage system (see ﬁgure above) can be ex-
pressed through the following equation, which depends on the thermal power provided by
the collector per each month, the thermal power provided by the boiler and the thermal
53

losses due to a lack of insulation:
˙Li + ˙Qwaste − ˙Qu = ˙Qb
where:
• ˙Qu is the thermal power provided by the heat exchanger [kW];
• ˙Qb is the thermal power provided by the boiler [kW], which is the only unknown.
From the calculations it will be evident that during the whole year the thermal
energy provided by the collectors is too high and maybe the temperature inside
the tank will increase more than 65◦
C. If the temperature is higher than 65◦
C the
system turns off the pump and the thermal power is no more provided by the boiler,
this is the reason why ˙Qb is considered equal to zero. In the F chart analysis it
is performed a calculation based on empirical formulas to provide the number of
collectors required to supply a defined percentage of the average energy demand.
However the approach followed in the energy analysis is based on nominal values of
thermal fluxes; for this reason it emerges that the energy provided by the collectors
is higher than the percentage of energy required in the F chart computations;
• ˙Qwaste is the thermal power lost from the tank due to its lack of insulation [kW]. In
a first approximation it has been evaluated as the 2% of the storage energy inside
the tank per 12 h:
˙Qwaste = 0.02 · 2 · Q/(24 · 3600) [kW]
– Q is the stored thermal energy in the tank that can be considered as always
present inside:
Q = m cp,w (Tt − Tw,c) · 10−3
[kJ]
– m = 4000 l · ρw is the mass of hot water stored in the tank;
– cp,w is the specific heat of water;
– Tt is the mean temperature of water in the tank;
– Tw,c is the temperature of the water coming from the city;
• ˙Li is the thermal power provided by the storage system [kW].
54

10.1 First control volume
Figure 10.2: House control volume
˙Li = Gu cp,w (40 − 15)
10.2 Second control volume
Figure 10.3: Second control volume
(Gw,h + Ga) 40 − Gw,h 65 − Ga 15 = 0
Ga = Gw,h
Gu = 2 Ga
55

As stated before, the evaluation of ˙Qwaste has been made in ﬁrst approximation by
considering the 4% in a day. Now the situation will be analysed more in detail.
10.3 Calculation of Qwaste
Figure 10.4: Insulation
Losses deriving from both the top and the bottom are assumed to be negligible.
Lateral part has three layers, of which thickness and thermal conductivity are shown (in
the second image it seems there are just two layers, but actually this is due to values of
R3 and R4 very close one to each other):
• Outermost layer: Polyurethane 50 mm (with λ1 = 0.037 [W/m/K]);
• Middle layer: PVC 50 mm (with λ2 = 0.19 [W/m/K]);
• Base layer: Steel 5 mm (with λ3 = 16 [W/m/K]).
Referring to last ﬁgure:
• temperature in the basement: Tbasement = 10◦
C;
• temperature inside the tank: Tt = 65◦
C;
• tank Height L = 2640 mm;
• R1 = 800 mm, R2 = 750 mm, R3 = 700 mm, R4 = 695 mm;
• convective heat transfer: for air h1 = 1.9[W/m2
/K], for water h2 = 278.2[W/m2
/K].
56

The convective heat transfer has been evaluated starting from the assumption that
a vertical cylinder of big dimensions can be considered as a flat vertical surface. In
particular, considering natural convection (by the assumption of quasi-static flow of water
inside the tank), the dimensionless Nusselt’s number is a function of Rayleigh number.
In turn, this number is related to the Grashof and Prandtl numbers in the following way:
Gr =
g β |Ts − Tf | L3
ν2
Pr =
µ cp,w
λ
Ra = Gr Pr
Nu = 0.10 Ra1/3
where:
• Gr is the Grashof number;
• Pr is the Prandtl number;
• Ra is the Rayleigh number;
• Nu is the Nusselt number;
• β is the volumetric thermal expansion coefficient;
• g is the acceleration due to Earth’s gravity;
• Ts is the surface temperature;
• Tf is the fluid temperature;
• L is the characteristic length (in our case it is the height of the tank);
• ν is the kinematic viscosity;
• µ is the dynamic viscosity;
• λ is the thermal conductivity;
• cp,w is the specific heat.
The transition to turbulent flow occurs in the range 108
< Gr < 109
for natural
convection from vertical flat plates. At higher Grashof number, the boundary layer is
turbulent, at lower Grashof number the boundary layer is laminar.
The surface areas are evaluated as follows:
A1 = 2 π R1 L
A4 = 2 π R4 L
57

The following image describes how the principle of total resistance works, then the cal-
culation is performed.
Figure 10.5: Resistance model
Rtot =
1
h1 A1
+
ln(r3/r4)
2 π λ3 L
+
ln(r2/r3)
2 π λ2 L
+
ln(r1/r2)
2 π λ1 L
+
1
h2 A4
Substituting values we get Rtot = 0.167 K/W.
As we know
1
Rtot
= U A = U1 A1 = U2 A2 = U3 A3 = U4 A4
where U is the overall heat transfer coefficient [W/(m2
K)]
and
˙Qwaste = U A ∆T
By combining the two equations we get:
˙Qwaste =
1
Rtot
∆T =
1
Rtot
(Tt − Tbasement)
Finally, thermal energy of disposal is:
Qwaste = ˙Qwaste time = ˙Qwaste · 3600 · 24 = 25.9 MJ/day
The obtained result is equal to 3.1% of the total energy Q = 837 MJ/day. Since we
assume the energy loss is 2% every 12 hours (which should be 4% per day), so the 3.1%
per day is accessible. For a cautelative reason it has been assumed 4% of losses instead
of 3.1%.
10.4 Tank efficiency
The efficiency has been evaluated through the following formula:
Eff =
˙Li
˙Qu + ˙Qb
100%
In the following table the values of efficiencies are reported.
58

Figure 10.6: Tank eﬃciency
59

Chapter 11
Boiler
11.1 General information
The conventional gas-fired boilers are water heaters fueled by gas or oil. In this sense,
the fuel is burned and the hot gases produced pass through a heat exchanger where much
of their heat is transferred to water, thus raising the temperature of water.
Figure 11.1: Gas-boiler scheme
We are going to use the typical conventional model, which has efficiency around 90%
by using wasted heat in fuel gases to pre-heat cold water entering the boiler, which brings
most brands of condensing gas boiler into the highest available categories for energy
efficiency.
60

Figure 11.2: Table of efficiencies
Since collectors, during nominal conditions, are able to provide the total amount of power
required by the users, the boiler has only an auxiliary function being activated only when
necessary (for instance in case of rainy days or damages in the solar panel system).
However it is supposed that the boiler is already present to fully supply the building
need of hot water and since it provides instantaneous power, the design of the boiler is
based on the assumption that a possible extreme situation of four showers simultaneously
sucking water may occur. Since the mass flow rate is estimated to be of about 0.3 kg/s
for each shower, the total service hot water will amount to 1.2kg/s.
So, the power demand can be evaluated by the following formula:
Φ = Gu cp,w (Tu − Tw,c) = 126 kW
where:
• Gu = 1.2 kg/s is the mass flow rate required by the users;
• cp,w is the specific heat of water;
• Tw,c = 15◦
C and Tu = 40◦
C.
However the value of the power provided by the boiler is rounded up to 150 KW.
Given the value of the thermal request, it is possible to compute the gas mass flow rate.
Considering that:
Φ = η Ggas Hi
where:
• Φ: thermal flux [W];
• η: efficiency of the gas boiler;
• Ggas: gas mass flow rate [kg/s];
• Hi: heating value of CH4 [J/kg].
61

11.2 Energy analysis
11.2.1 Power from combustion
From the First Law of Thermodynamics, it is possible to compute the energy balance
as follows:
Φ = Gb cp,w (Tb,h − Tb,c) = η Ggas Hi
To consider any possible power failure, we choose a boiler whose power is higher than
the required one.
11.2.2 Thermal flux
Attention is now shifted to the heat flux supplied to the tank:
φ = U At ∆Tlmtd = U At
∆T1 − ∆T2
ln(∆T1/∆T2)
where:
• U is the transmittance;
• At is the total surface for the heat transfer;
• ∆Tlmtd is the logarithmic mean temperature difference (LMTD).
11.2.3 Lmtd method
The method is particularly useful when the inlet and outlet temperatures of the fluids
are known. Our system is the counter flow. Therefore, calculation of the logarithmic
mean temperature difference is:
∆Tlmtd =
∆T1 − ∆T2
ln(∆T1/∆T2)
where:
• ∆T1 = Thot,in − Tcold,out;
• ∆T2 = Thot,out − Tcold,in.
11.2.4 Transmittance
The transmittance is the reciprocal of the specific thermal resistance of the wall.
To get the transmittance in case of a hollow cylinder, we should consider to have both
convection inside the pipe and convection between the outer wall of the pipe and water
in the tank. Conduction within walls has been considered as well.
Transmittance of the hollow cylinder with convection can be found by using the formula
hereafter shown:
Ui =
1
1
hg
+ ln(do/di) Ai
2 π kc L
+ Ai
hw Ao
62

where:
• hg is the convective heat transfer coefficient of the fluid in the pipe;
• hw is the convective heat transfer coefficient of the water in the tank;
• kc is the thermal conductivity of copper;
• do is the outer diameter of the pipe;
• di is the inner diameter of the pipe.
11.2.5 Flow regimes
Now Reynolds number has to be defined to know whether the flow is laminar or
not. This is due to the fact that convection heat transfer depends on the flow regime.
Helical coil pipes will be adopted due to more efficient heat transfer offered. Due to the
centrifugal forces the pressure drop in coil pipes is higher than pressure drop in the same
length of straight pipes, because the presence of secondary flow which dissipates kinetic
energy, thus increasing the resistance to flow. Therefore, the transition from laminar to
turbulent flow that is marked by the critical Reynolds number (Recr), in coil pipes is as
high as 6000 to 8000 while in straight pipes Recr is approximately 2100. It is suggested
a correlation to obtain the critical Reynolds number:
Recr = 20000
d
D
0.32
where:
• d is the inner diameter of the pipe in m;
• D is the diameter of the coil in m.
Prandtl number
The Prandtl (Pr) number gives a measure of the ratio between diffusive molecular
transport of momentum and the analogous diffusive heat transport term.
Pr =
ν
α
=
µ cp,w
λ
where:
• ν is the kinematic viscosity;
• µ is the dynamic viscosity;
• cp,w is specific heat capacity of water;
• λ is thermal conductivity of water.
63

Nusselt number
The Nusselt (Nu) number expresses the ratio between the convective and the con-
ductive heat flux terms and it is defined as:
Nu =
q (convective)
q (conductive)
=
hL
λ
11.2.6 Inner pipe side
A typical shell and coiled tube heat exchanger is shown in the following figure.
Figure 11.3: Typical shell
In particular d is the diameter of the coiled tube, Rc is the curvature radius of the
coil, D is the inner diameter of shell, and b is the coil pitch. The curvature ratio (d)
is defined as the coil-to-tube diameter ratio d/2/Rc, and the non-dimensional pitch c is
defined as b/(2 p Rc). The other important dimensionless parameters of coiled tube are
Reynolds number (Rei) and Nusselt number (Nui), defined as follows:
Rei =
ρ νi di
µ
Nui = 0.023 Re0.8
i Pr0.4
11.2.7 Shell side
We will consider for shell-side the natural convection, and Rayleigh number, Nusselt
number, NuL, are defined as:
Ra =
g α ∆T d3
ν k
64

NuL = 0.0825 +
0.387 Ra
1/6
L
(1 + (0.492/Pr)9/16)8/27
2
Finally, all parts of our equation are known, and we can easily ﬁnd length of pipe.
φ = U At ∆Tlmtd = U At
∆T1 − ∆T2
ln(∆T1/∆T2)
L =
At
π do
Required length is 73 m.
Finally results are presented in the following lines.
65

Chapter 12
Thermal balance of the apartment
Figure 12.1: Apartment thermal fluxes
The thermal energy demand concerning the climate control of an apartment is es-
timated by an energy balance applied on the above-mentioned apartment as a Control
Volume. In order to calculate the heat fluxes, temperatures in the considered spaces must
be defined. Hence, some values have been fixed, in particular:
• −8◦
C: external temperature (by regulations, considering the city of Turin since it
is in the ’E’ climatic zone);
• 20◦
C: design temperature in the apartment;
67

• 15◦
C: temperature in the stairs and in the hallway.
The (outgoing) thermal power transmitted through the control volume of the apart-
ment is evaluated with the following formula:
˙Q =
n
j=1
Uj Aj (Ti − Te)
where U (W/(m2
K)) is the transmittance and A the surface. Summation is needed
because there are different values of U and temperatures, which are dependent on the
considered surface:
U =
1
1
hi
+ Σsi
ki
+ 1
he
where:
• the terms h (W/(m2
K)) are the convective coefficients (internal and external) that
depend on the air velocity (if there is not ventilation it would be 4 ÷ 6 cm/s, oth-
erwise it would be higher). For comfort aim the air velocity was set at 0.15 m/s.
Hence, all used values of h are directly taken from Manuale del termotecnico, and
they respect the regulation UNI 6946;
• si (m) is the layer thickness of the single material;
• k (W/(m K)) is the conductivity of the considered material;
In Italy, the value of U must be chosen in accordance with a decree. The Decree of
January 26th 2010 sets some values of limit transmittance, according to the thermal zone
the houses belong to. Turin belongs to the E zone and the limit values of trasmittance
are fixed as follows.
Figure 12.2: Limits of transmittance
Below, the analysis of the various terms which influence thermal power that must be
considered in the summation is considered.
68

12.1 Windows and doors
From Nurith catalogues, it has been chosen windows with a trasmittance equal to
1.2 W/m2
/K. From an energetic point of view, those are mid-range windows, since
this company produces less dissipative models that would have been more expensive.
Nevertheless, the chosen windows are not the worst among the catalogue. The total
area of windows has been calculated summing the surfaces of the three different sizes of
windows. The considered temperature is the external one.
The transmitted power that is obtained is equal to 0.53 kW.
Windows type 1 type 2 type 3
height (m) 1.5 1.5 1.5
width (m) 2 1.5 1
number 1 3 4
Area (m2
) 3 6.75 6
Total area (m2
) 15.75
From Silvelox catalogues by folllowing the choice made for the windows (trade-off
between costs and performances), it has been chosen an entrance door that has a trasmit-
tance equal to 1.68 W/m2
/K. The stairs temperature, in this case is fixed to 15◦
C, and
the transmitted power results 0.02 kW, while the dimensions are 2.2 m of height, 1.2 m
of width for an area of 2.64 m2
.
The parameters used to perform the computation and the results are summed up in
the following table:
Uw (W/(m2
K)) 1.2
Ti (◦
C) 20
Te (◦
C) -8
As (m2
) 15.75
˙Qs (kW) 0.53
Ud (W/(m2
K)) 1.68
Tstairs (◦
C) 15
Ad (m2
) 2.64
˙Qd (kW) 0.02
12.2 External/internal walls
To estimate the value of walls resistance, it is considered a type of wall with four
different layers:
• layer 1 of plaster;
• layer 2 of terra-cotta block;
• layer 3 of insulating layer;
• layer 4 of brick.
69

From the regulation UNI 10351 the value of conductance for every material is taken, and
then the resistance of every layer is calculated with the ratio thickness/conductance.
The final resistance of walls is equal to the sum of all the calculated resistances.
Figure 12.3: External walls resistance
The value of trasmittance is evaluated as the reciprocal of total resistance (U = 1/Rtot).
The other variables used are shown in the following tables, with a resulting value of
trasmitted power equal to 0.68 kW.
Ue,w (W/(m2
K)) 0.42
Ti (◦
C) 20
Te (◦
C) -8
Ae,w (m2
) 58.1
˙Qe,w (kW) 0.68
The analysis of internal walls follows the same principles, but different thicknesses
and different temperatures must be considered as shown in the following tables.
Figure 12.4: Internal walls resistance
Ui,w (W/(m2
K)) 0.64
Ti (◦
C) 20
Tstairs (◦
C) 15
Ai,w (m2
) 13.16
˙Qi,w (kW) 0.04
70

12.3 Roof
To estimate the value of roof resistance, it is considered a type of roof with five
different layers as shown in the following table:
Figure 12.5: Roof resistance
Results are summed up in the next table:
Ur (W/(m2
K)) 0.37
Ti (◦
C) 20
Te (◦
C) -8
Ar (m2
) 70
˙Qr (kW) 0.52
12.4 Power for ventilation
For working and residential environment an adequate change of air is done by pro-
viding it externally both naturally or mechanically. In order to compute the wasted
ventilation thermal power the following formula is used:
˙Qv =
n
3600
V cp,a (Ti − Te)
where:
• n is amount of air renewal per hour. It is 0.5 1/h for residential cases;
• V (m3
) is the volume of the apartment;
• cp,a = 0.35 J/(m3
K) is the air specific heat;
• Ti = 20◦
C is the internal temperature of the apartment;
• Te = −8◦
C is the external temperature.
Values for calculation and results are summed up in the following table:
71

V (m3
) 189
Ti (◦
C) 20
Te (◦
C) -8
n (l/h) 0.51
cp,a (J/(m3
K)) 0.35
˙Qv (kW) 0.003
Finally by summing all the ﬂuxes, the following result is obtained:
˙Qtot = 1.8 kW
72

Part III
PART B: Exergy analysis
73

The purpose of this part is to evaluate the irreversibility produced in each component
and to calculate their efficiency in term of Exergy. In particular the analysis is focused
on the following components:
• boiler;
• collectors;
• heat exchanger;
• water tank.
Finally an analysis of the cost in terms of exergy is performed.
The general formula of exergy balance is:
d(Et − T0 S)cv
dt
=
i
Φi 1 −
T0
Ti
− Wt +
IN
j=1
Gj bt
j −
OUT
k=1
Gk bt
k − T0 Σirr
where:
• T0 Σirr = Ψirr is the rate of exergy destruction;
•
Φi 1 −
T0
Ti
− Wt +
IN
j=1
Gj bt
j −
OUT
k=1
Gk bt
k
is the rate of exergy transfer;
•
d(Et − T0S)cv
dt
is the rate of exergy change;
• Wt is the pump power.
Considering the specific flow exergy of each component equal to:
bt
1 = h − h0 − T0 (s − s0) + ec + ep
where:
• h − h0 is the enthalpy difference with respect to the environmental value;
• T0 is the reference temperature;
• s − s0 is the entropy difference with respect to the environmental value;
• ec is the kinetic energy;
• ep is the potential energy.
74

Chapter 13
Collectors
It has been considered as control volume an area containing the collector and the
tubes for the inlet and the outlet of the glycol. In this way the power of the pump of the
glycol circuit is not taken into account.
Figure 13.1: Control volume of the collectors
The purpose of this part is to evaluate the irreversibility produced by the solar panel and
to calculate the efficiency of it in terms of Exergy.
It is possible to consider the fluid as SIMPLE LIQUID under the assumption of steady
state condition and isobaric flow; these are acceptable simplifications for the purpose.
75

By adjusting the equation with this hypothesis it possible to obtain:
bi = cg T0
Ti
T0
− 1 − ln
Ti
T0
T0 is the reference temperature, it is expressed in Kelvin and it is equal to the environ-
mental temperature; the table reporting the various temperatures for each month is here
attached:
Figure 13.2: Month temperatures
By having all the temperatures and the temperature of the water at the inlet (Tc,c)
and at the outlet (Tc,h) of the collector all the values of the speciﬁc exergy ﬂux at the
inlet and at the outlet can be computed as reported in the formula upward.
Here are attached the results:
76

Figure 13.3: Specific exergy flow
Then we consider the power coming from the sun ( ˙Qsun), from studies it is globally
accepted to transform the solar radiation into flux of entropy, it is sufficient to multiply
by the coefficient 0.78 ( ˙Qsun,exergy = 0.78 · ˙Qsun).
By having also the specific flux of entropy going in and out of the control volume and the
mass flow rate taken from the calculation done in solar collector part A we can compute
the value of Ψirr remembering that in the solar collector the equation that rules the
exergy is:
Ψirr = ˙Qsun,exergy + Gc (b1 − b2)
And then we can compute the exergetic efficiency of the collector with this formula:
= 1 −
Ψirr
˙Qsun,exergy + Gc b1
Here are reported the tables with all the results for each month and the monthly efficiency
and exergy destruction plots:
77

Figure 13.4: Results of exergy analysis of collectors
78

Figure 13.5: Exergetic eﬃciency of the collectors
Figure 13.6: Exergy destruction in the collectors
79

Chapter 14
Heat exchanger
From the general formula of exergy reported at the beginning of this part, some
simplifications are introduced, in particular:
• steady state condition so the first term in the equation is neglected;
• the contributions of kinetic energy and potential energy are negligible since the
length of the heat exchanger is very small and the position of the h.e. is horizontal.
0 =
i
Φi 1 −
T0
Ti
+
IN
j=1
Gj bj −
OUT
k=1
Gk bk − T0 Σirr
b1 = h − h0 − T0 (s − s0)
The control volume used to make the calculations in this section is reported in the
following figure:
Figure 14.1: Control volume of the heat exchanger
The exergetic efficiency is evaluated with the following formula:
= 1 −
Ψirr
Gc bin
80

In the table the data and then the results of the calculation are collected; it is remarkable
that such a very high eﬃciency is due to the fact that the gradient of temperature (source
of exergy destruction) is present in the tank and not in the heat exchanger. Finally it is
possible to state that the origin of the exergy destroyed is the incoming ﬂux at 94◦
C.
81

Figure 14.2: Data and results of heat exchanger exergetic analysis
82

Chapter 15
Tank
The aim of this section is to compute the destroyed exergy and the exergy efficiency
of the tank (it will be the considered C.V. Control Volume). Considering the general
formula of exergy, the following simplifications are made:
• system is at steady state conditions, so the first term of the equation is assumed
equal to zero;
• Wt = 0 since there are not pumps/other machines inside the tank;
• kinetic and potential energies are negligible;
• Simple Liquid;
• Isobaric Flow.
Further details are:
• Ψirr = T0 Σirr to be computed;
• only one thermal flux, ˙Qwaste = 0.39 kW already found in part A;
• T0 varies monthly in accordance with the available history data.
Figure 15.1: Tank control volume
83

The values of the specific flow exergy are computed for:
• temperatures In and Out of the heat exchanger (94◦
C and 70◦
C);
• temperature In and Out of the Boiler (90◦
C and 70◦
C);
• temperature In from aqueduct (15◦
C);
• temperature Out to User (65◦
C).
The reference temperature T0 is chosen considering the environmental mid temperature
for every month, instead the value of cp is chosen equal to 4197 J/Kg/K in case of water,
3683 J/Kg/K in case of the 30% Ethylene Glycol fluid.
The obtained values are shown in the following table, in which all b are expressed in J/kg:
84

Figure 15.2: Tank exergetic analysis results
85

Using the previous assumptions, the final formula used to compute irreversibilities is:
Ψirr = Σ G (bin − bout) − ˙Qwaste(1 −
T0
Tbasement
)
In the summation, the values of the mass flow rate of all components are taken from part
A, as shown in next table.
Figure 15.3: Mass flow rates
Note that in nominal conditions, namely the panels are able to supply all the needed
energy to heat the tank, the boiler will not provide any mass flow rate. That is why
Gb = 0.
The supplied exergy will be equal to all the ingoing quantities:
Ψsuppl = Σ Gin bin
Thus the efficiency is computed as:
η = 1 −
Ψirr
Ψsuppl
Results and trends are attached below:
86

Figure 15.4: Efficiency result
Figure 15.5: Trend of efficiency
This trend is mainly due to the dead state choice: naturally the reference temperature
reaches a maximum in the summer months, however the temperatures of the ingoing/out-
going mass flow rates remain constant in the year. This means that in summer there is
an inferior value of the temperature difference to be exploited, namely all values of the
specific exergy flows b are directly affected.
87

Chapter 16
Boiler
Given the control volume in ﬁgure, we can evaluate the irreversibilities by applying
the exergy balance equation:
Figure 16.1: Boiler control volume
d(Et − T0)cv
dt
=
i
Φi 1 −
T0
Ti
− Wt +
IN
j=1
Gj bj −
OUT
k=1
Gk (bk + ech) − T0 Σirr
The chemical exergy ech is introduced because the following combustion is present:
CH4 + 2 O2 → CO2 + 2 H2O
ech can be computed as follows:
ech = hF − hCO2 − 2 hH2O (T0, p0)−T0 [sF − sCO2 − 2 sH2O] (T0, p0)+R T0 ln
(ye
O2
)2
(ye
CO2
)(ye
H2O)2
where:
• hi are the enthalpy formation of the species (F stands for fuel);
88

• si are the entropy formation of the species;
• yi are the molar fractions of the species.
But since the last two terms of the equation, those dependant on entropy, are very small,
it is possible to neglect them. The final formula for the computation of the chemical
exergy is the following:
ech = ∆hr
By applying the first formula of this chapter to the component in a stationary condition,
it is possible to obtain:
GCH4 ∆hr − Gb(bOUT − bIN ) − Ψirr = 0
where:
• GCH4 is the mass flow rate of methane;
• Gb is the mass flow rate of water through the boiler;
• b is the specific exergy flow;
• T0 is the environmental temperature for each month;
• Ψirr is the irreversibility flux;
• ∆hr is the lower heating value, since the water, product of combustion, is supposed
to be send out of the combustion chamber in form of steam.
Since we are dealing with water, we can now consider our fluid as simple liquid under the
assumption of steady state condition and isobaric flow. By adjusting the equation with
this hypothesis we finally evaluate the exergy specific flow coming in and going out with
the following expression:
bi = c T0
Ti
T0
− 1 − ln
Ti
T0
where:
• c is the specific heat of water;
• T0 is the environmental temperature for each month expressed in Kelvin;
• Ti is the temperature at the inlet or at the outlet of the boiler respectively in the
evaluation of bIN or bOUT .
At this point, by applying the previous exergy balance equation for each month, the
irreversibility flux can be computed.
Moreover the efficiency can be also evaluated as follows:
= 1 −
Ψirr
Ψsupplied + Gb bIN
where Φsupplied is the exergy flux coming from the methane.
89

The obtained results are summed up in the following tables:
Figure 16.2: Boiler exergy analysis results
The origin of the exergy losses can be found mainly in the combustion of the methane.
90

Chapter 17
Cost analysis
In order to analyse the cost of the plant, first the initial investment and maintenance
costs have to be taken into account:
• solar plant components requires an initial expense of about 700 e/m2
of collectors
surface (where the cost of the boiler is not considered because already present before
the solar panel installation);
• maintenance cost amount to 20 e/m2
of collectors surface each year; so, since the
plant life is supposed to be at least 15 years, the total maintenance expenses (by ne-
glecting monetary value fluctuations and eventually extraordinary technical action)
will be 300 e/m2
of collectors surface.
Now, from the previous part, the surface of the collectors is 25.1 m2
and this leads to a
total cost of the plant in 15 years of 25100 e. Actually according to the actual Italian
law, a detraction of a maximum of 65% on the component cost is possible: this leads to
a saving of 11420 e which will lead to a real expense of 13680 e.
Values and results are summed up in the following table.
Plant components 700 e/m2
Maintenance/year 20 e/m2
Expected life 15 years
Maintenance 300 e/m2
Surface 25 m2
Total cost 25100 e
Deductions (−65% of plant cost) 11420 e
Final cost 13680 e
At this point the total cost of the unit of exergy flux lost is evaluated by dividing the
sum of the Ψirr = T0 Σirr produced by each component for the global cost found before.
Hence, in order to evaluate the economical contribution of each component, the ratio just
found is multiplied for the exergy of each component, obtaining the following output.
Component Exergy (kW) Cost (e)
Collectors 10.330 11980
Heat exchanger 0.028 33
Tank 1.437 1667
91

The total wasted exergy is the sum of the contribution of each component, as the total
cost:
Total exergy (kW) 11.8
Total cost (e) 13680
Total exergy/Total cost 1160
(kW/e)
From the calculations in the previous tables, it can be noticed that the component
which mostly contributes to the cost in terms of exergy is the set of collectors.
92

Part IV
PART C: Technical engineering
design and heat transfer
93

Chapter 18
Computation of the heat transfer of
the fluid through the panel
The heat transfer of the fluid through the panel is computed with an electrical analogy
based on the following scheme:
Figure 18.1: Scheme of the panel
Since the thermal flux is considered as the useful one, absorbed by the thermal fluid,
the thermal resistances which come into play are forced convection inside the pipes and
conduction through the pipe thickness.
18.1 Forced convection (Ri)
Resistance of forced convection inside collectors can be calculated as follows:
Ri =
1
hi Ai
where:
• Ai is the internal surface of heat exchanger (internal perimeter times the length of
the pipe);
94

• hi is the heat transfer coefficient expressed in [ W
K m2 ] that can be derived from Nusselt
number.
In order to calculate Nusselt, the following unknowns must be evaluated: Prandtl and
Reynolds numbers and the friction coefficient:
Pr =
cph µh
λh
Re =
ρh uh di
µh
where:
• µh is the kinematic viscosity of the glycol solution at T = 82◦
C;
• λh is the thermal conductivity of the glycol solution;
• ρh is the glycol solution density;
• uh is the velocity of the solution inside the pipe, considering the month of Decem-
ber. In particular, since the ten collectors are in parallel, the velocity is computed
considering 1
10
Gc (total mass flow rate through the collectors);
• di = 8 mm the inner diameter of the pipe.
Friction coefficient fh:
fh = (1.58 ln(Reh − 3.28))−2
Hence Nu is calculated with the empirical formula valid for forced convection:
Nuh =
hi di
λ
=
(f/2) Reh Prh
1 + 8.7 (f/2)0.5 (Pr − 1)
Finally Ri is expressed as follows, where L = 14 m is the length of the pipe, defined with
geometric considerations on the panel:
Ri =
1
hi L (π di)
18.2 Conduction (Rw)
The next resistance component (R2) is due to the conduction through the walls of
the pipe and it is evaluated as follow:
Rw =
ln(do/di)
2 π k L
where:
• do = 9.56 mm and di = 8 mm are respectively the outer and inner diameters of the
pipe;
95

• k = 350 W/m/K is the thermal conductivity of copper;
• L = 14 m is the length of the pipe, deﬁned with geometric considerations on the
panel based on figure 7.1.
Finally it is possible to calculate the overall thermal resistance as follows:
U =
1
Rtot A
where Rtot = Rh + Rw.
Results are summarized in the following table.
Figure 18.2: Resistance analogy results
96

Chapter 19
Determination of the temperature
profile of the thermal fluid along the
pipe
The temperature profile of the thermal fluid along the pipe is evaluated through the
effectiveness-NTU method.
In the case under study the heat exchanger consists of:
• a solution of water and glycol flowing inside the tube is heated up from the inlet
temperature Tc,c to the outlet temperature Tc,h;
• the plate is the heating medium and its temperature is considered constant. This
hypothesis is equivalent to a case of a heat exchanger with a fluid changing phase
(condensation or evaporation), that is with an infinite thermal capacity.
In the special case of heat exchanger the implemented formula is the following one:
= 1 − e−NTU
where:
• = q
qmax
is the effectiveness, equal to the ratio of actual transmitted heat and
maximum possible one;
• NTU is the number of transfer units, equal to:
NTU =
U A
Cmin
where:
– U A is the inverse of the total thermal resistance, for the month of December
to be on the safe side;
– Cmin = cp,g
Gc,dec
Nc
is the minimum thermal capacity per collector (Nc = 10).
97

It is possible to define a relation between the effectiveness and the temperatures in the
heat exchanger, in particular:
=
Tc,x − Tc,c
Tp − Tc,c
= 1 − e
−
Ui π di x
Cmin
where:
• Tc,x is the temperature at each step δx;
• Tp = 94◦
C is the constant temperature of the panel, this value is a typical one for
solar panels;
• x is the step position along the pipe.
From the previous formula it is possible to find the temperature evolution along the pipe
inside the collector:
Tc,x = Tc,c + (Tp − Tc,c) 1 − e
−
Ui π di x
Cmin
The shape of the temperature profile is plotted in the following diagram:
Figure 19.1: Temperature profile
Finally Matlab/Octave code used to perform the calculation is attached.
clc;
clear all;
U=6.5545*10^2; % [W/m^2/K]
T_cc=70; % [C]
98

T_p=94; % [C]
d_i=0.008; % [m]
C_min=1.6791; % [W/K]
L=14; % [m]
T_cx=@(x) T_cc+(T_p-T_cc)*(1-exp((-U*pi*d_i*x/C_min)));
fplot(T_cx, [0,L],’blu’);
hold on
fplot(@(x) T_p+0.1,[0,L],’red’)
xlabel(’x [m]’)
ylabel(’T [C]’)
title(’Temperature profile’)
legend(’T_c_h’,’T_p’)
99

Politecnico di Torino Master's project on solar energy equipment

Recommended

Recommended

More Related Content

What's hot

What's hot (19)

Similar to Politecnico di Torino Master's project on solar energy equipment

Similar to Politecnico di Torino Master's project on solar energy equipment (20)

More from Pietro Galli

More from Pietro Galli (10)

Recently uploaded

Recently uploaded (20)

Politecnico di Torino Master's project on solar energy equipment