Category Archives: EuroSun2008-11

Simulations evaluation: performance indicators

Three different performance indicators defined initially in Task 26 and adapted to Task 32 are shown in the Excel tool developed to evaluate the simulation results. They are compared with a reference system which has no collectors and all the energy is provided by fossil energy [6]. The three performance indicators evaluated are the thermal energy savings (fsav, therm), the extended thermal energy savings (fsav, ext) and the fractional solar savings indicator (fsi) and are defined in Eq. 1 to Eq.3.

The fractional thermal energy savings (fsav, therm) are a measure of the percentage the auxiliary (non­solar) energy input for heating can be reduced with the solar system, this term does not account for electricity use unless it is used directly for heating and it is defined as:

image015 Подпись: Eq. 1

Qboiler + Qel, heater

П boiler, ref

The extended fractional energy savings (fsav, ext) are defined in a similar way than the fractional thermal energy savings (fsav, therm), but they also include electricity use for pumps, valves, controllers etc.

image017 Подпись: Eq. 2

Qboiler. Qel, heater + Wpar

image019 Подпись: Eq. 3

Finally, it is theoretically possible to achieve a high fsav, therm and at the same time not meeting the comfort criteria for space heating or warm-water production. Therefore the fractional solar savings indicator (fsi) includes a penalty term that compensates and even punishes for not meeting comfort criteria and it is defined as:

nboiler, ref n el

where:

Qboiler [kWh]: Energy delivered to the system by the auxiliary boiler (energy balance on the water-side of the boiler)

Qboiler, ref [kWh]: Energy delivered to the reference system (system without solar) by the boiler in the reference system (energy balance on the water-side of the boiler)

Qel, heater [kWh]: Energy delivered to the system by an electrical heater

nboiler [-]: Efficiency of auxiliary boiler of the solar system (dependent on the overall system) nboiler, ref [-]: Efficiency of auxiliary boiler of the reference system (= 0.85)

nel [-]: Efficiency of electricity production and transport to the site of use (= 0.4 independent of the source)

Wpar [kWh]: Electricity used for pumps, valves, etc. as well as for direct heating or driving a heat pump Wpar, ref [kWh]: Electricity used for pumps, valves, etc. of the reference system Qpenalty [kWh]: Penalty for the solar system for not meeting comfort criteria Qpenalty, ref [kWh]: Penalty for the reference system for not meeting comfort criteria

Two different kinds of penalties were considered, a penalty function for not meeting the required tapping water temperature of 45 °C (Qpen45), and a penalty function for not meeting comfort criteria (Qpen20) [5]. The penalties evaluation is also an important parameter whose influence is reflected in the fractional solar savings indicator (fsi) as shown in Eq. 3 where Qpenalty are the total penalties (DHW plus heating).

2. Simulation results

For the first set of simulations, where the aim was to observe the influence of some parameters in the result of the simulations, the most influencing parameter was the position of the outlet to the space heating (Z_SbB). This parameter had a strong influence on the three different performance indicators. On the other hand, the position of the auxiliary temperature sensors that operates the auxiliary system shows a slight influence on the results. Analyzing the influence of the position of Z_SbB (Table 1), it was easy to conclude that the lower the relative position of the outlet to the space heating, the better the value of the performance indicators fsav, therm and fsav, ext. However, the value of the fsi performance indicator was worst because of high penalty values, taking into account that Qpenalty, ref (Eq. 3) has always the same value. It was also seen that the fossil fuel used decreased with a lower position for the outlet to the space heating. When the outlet to the space heating was placed at a higher position, the value of the penalties was lower and the fsi indicator was also better.

Table 1. Variations on the position of the outlet to the space heating (Z_SbB)

Modification

fsav, therm

f

-Lsav, ext

fsi

Qburn kWh

Qpen45

Qpen20

Z_SbB=0.8

0.506

0.435

-0.059

3411.99

2947.15

240.68

Z_SbB=0.74

0.647

0.548

-0.146

2191.72

113.62

5058.91

A lower position of the space heating outlet reduces the penalties regarding the DHW demand at 45 °С. This is because the water placed above the Z_SbB outlet is at a higher temperature and therefore, it is easier to provide water at the set point temperature of 45 °С. However, the water temperature going to the space heating system is at a lower temperature, thus it has less energy to release to the ambient and it is more difficult to reach the comfort temperature of at least 19.5°C inside the building.

A higher position of the space heating outlet benefits the heating system. The operation time of the space heating system is lower because the water going to the heating is at a higher temperature and more energy is released to the ambient reaching easier the comfort temperature. However, this is a drawback for the DHW demand and the penalties for it increase.

For the second set of simulations the aim was to check the influence of the PCM modules characterization. That is the placement of the PCM modules, the length of the modules and the amount of PCM. Several simulations were performed with variations of the length and diameter of the modules, which involved a variation of the number of PCM modules, and as a consequence, a variation of the PCM volume into the store (Table 2). Only slight improvements up to 2% in the performance indicators were obtained, when compared with the reference simulation without PCM in the tank. However, this small advantage is within the numerical uncertainties in the calculations [7]. Also the amount of energy provided by the auxiliary system had very few variations. Some more simulations without the stratifier device were carried out with and without PCM but the performance indicators showed no difference. The water store resulted to be at least as good as a water-PCM store.

The highest variation (2%) is observed in the fsi indicator, which is the one that considers the penalties when the demand, DHW or space heating, is not fulfilled. Concerning a PCM-water store, penalties are always smaller compared with a water store (Table 2). They can be even completely avoided in a PCM-water store with the same characteristics of a water tank. Therefore, the introduction of PCM helps to decrease the penalties for not reaching the specified conditions.

Table 2. Variations of the PCM modules geometry

Modification

fsav, therm

f

-Lsav, ext

fsi

Qburn

(kWh/a)

Qpen45

(kWh/a)

Qpen20

(kWh/a)

PCM vol. (%)

Water

0.515

0.495

0.322

3784.92

46.81

0

1 PCM at the top

0.25 P

a area

0.516

0.495

0.327

3776.14

0

0

2.22

(DHW)

0.5 Parea

0.519

0.497

0.329

3757.25

0

0

4.45

Z_SbB=0.9125

0.75 Parea

0.518

0.497

0.329

3760.55

0

0

6.67

1 PCM at the top (DHW) and 1 in the middle

0.25 P

a area

0.517

0.496

0.328

3769.29

0.52

0

8.25

0.5 Parea

0.517

0.495

0.327

3771.27

0.68

0

16.5

(space heating)

0.75 Parea

0.514

0.494

0.324

3791.09

14.26

0

24.77

Water

0.535

0.508

0.324

3632.39

91.62

68.91

1 PCM at the top

0.25 P

a area

0.531

0.505

0.326

3660.51

55.21

54.70

3.17

(DHW)

0.5 Parea

0.532

0.505

0.330

3655.81

2.25

61.07

6.35

Z_SbB=0.82

0.75 Parea

0.531

0.505

0.329

3657.53

33.36

50.07

9.52

2. Conclusions

Advantages offered by PCM have been already tested theoretically and experimentally in DHW installations. Several simulations were performed to check its suitability in a DHW and space heating demand system. A complete and powerful tool with Trnsys was developed in the framework of Task 32 of the International Energy Agency (IEA) to perform simulations with this system.

Two different set of simulations were carried out. For the first one, where the aim was to observe the influence of some parameters in the result of the simulations (three performance indicators: fsav, fsav, ext, fsi), the most influencing parameter was the position of the outlet to the space heating. The lower the relative position of the outlet to the space heating, the better the value of the performance indicators fsav, therm and fsav, ext but the worst the value of fsi because of high penalty values. This parameter has a strong influence on the performance of the system since the outlet position benefits one of the demands but affects negatively the other one. Another important conclusion is that the fossil fuel used decreased with a lower position for the outlet to the space heating.

For the second set of simulations the aim was to check the influence of the PCM modules characterization. New placement and modules configuration was tested. Only slight improvements up to 2% in the performance indicators were obtained when compared with the reference simulation without PCM in the tank. Even some simulations without the stratifier device were carried out but no differences were observed concerning the performance indicators. A water store was at least as efficient as a PCM-water store. The highest variation (2%) is observed in the fsi indicator, which is the one that considers the penalties when the demand, DHW or space heating, is not fulfilled. DHW penalties are always smaller in the PCM water store than in the water store with the same characteristics and they can be even completely avoided in a PCM-water store. Therefore, the introduction of PCM helps to decrease the penalties for not reaching the comfort conditions in the demand.

With the system designed as it is and the control applied (typical differential control for simple water tank), only slightly better results were obtained for a PCM-water store compared to a water store regarding the performance indicators used. However, this system is not the commonly used only-water store, it is a PCM-water store so the differential control applied could be no the suitable for this application. A new control strategy taken into account the PCM should be applied. Another possibility could be a new composition of the system, this is for example placing the auxiliary system out of the store.

Acknowledgements

The work was partially funded with the project ENE2005-08256-C02-01/ALT and 2005-SGR-00324. Dr. Marc Medrano would like to thank the Spanish Ministry of Education and Science for his Ramon y Cajal research appointment.

References

[1] M. Nogues, L. F. Cabeza, J. Roca, J. Illa, B. Zalba, J. M. Marin, S. Hiebler, H. Mehling, Efecto de la Insercion de un Modulo de PCM en un Deposito de ACS. Anales de la Ingenieria Mecanica, vol 1 (2002) 398-402.

[2] L. F. Cabeza, M. Ibanez, C. Sole, J. Roca, M. Nogues, Experimentation with a water tank including a PCM module, Solar Energy Materials and Solar Cells, 90 (2006) 1273-1282.

[3] M. Ibanez, L. F. Cabeza, C. Sole, J. Roca, M. Nogues, Modelization of a water tank including a PCM module, Applied Thermal Engineering, 26 (2006), 1328-1333.

[4] C. Sole, M. Medrano, A. Castell, M. Nogues, H. Mehling and L. F. Cabeza, Energetic and exergetic analysis of a domestic water tank with phase change material, International Journal of Energy Research, 32 (2008) 204-214.

[5] R. Heimrath and M. Haller (2007). Project Report A2 of Subtask A: The Reference Heating System, the Template Solar System.

[6] W. Weiss, (2003). Solar Heating Systems for Houses. A design handbook for solar combisystems, JamesXJames, London (United Kingdom).

[7] E. Talmatsky and A. Kribus, PCM storage for solar DHW: An unfulfilled promise?, Solar Energy, in press.

Unglazed Solar Collectors in Heat Pump Systems:. Measurement, Simulation and Dimensioning

E. Bertram1*, J. Glembin1, J. Scheuren1, G. Rockendorf1, G. Zienterra2

1 Institut fur Solarenergieforschung Hameln (ISFH),

Am Ohrberg 1, 31860 Emmerthal; Germany

2 RHEINZINK GmbH & Co. KG, Bahnhofstrafie 90, 45711 Datteln; Germany
* Corresponding Author, s. bertram@isfh. de

Abstract

Two heat pump-systems with borehole and unglazed solar thermal collector are measured and simulated in TRNSYS as part of a research project. Compared to systems without collector the collector yield increases the average temperature level of the heat pump system on the evaporator side. A collector model is developed and evaluated considering the long­wave radiation exchange and the condensation heat gains. The annual collector yield is measured as 545 kWh/m2a, of which 4% are determined as heat gains through condensation. Further simulations in TRNSYS show the interdependency of collector area, borehole length and heat pump system performance. The additional heat source component collector reduces the required borehole length and simultaneously improves the heat pump system perform­ance in comparison to a solely borehole supported heat pump. In addition the system sensi­tivity for the heat source parameters is reduced significantly, thus resulting in a more certain system planning and operation.

Keywords: heat pump system, unglazed solar thermal collector, condensation heat gains

1. Introduction

Unglazed solar collectors (SC) provide a high collector yield at a low temperature level. They may therefore be applied to the best advantage as heat source in heat pump systems (HPS) [1]. During winter, in the period of maximum heating demand, unglazed SC can gain heat on a very low tem­perature level only. Thus a second heat source is needed, which offers ambient temperature inde­pendent heat to the HPS. As such heat sources vertical borehole heat exchangers (BHE) are applied.

The role of an unglazed SC is to increase the source temperature level of a HPS, showing an enormous potential for reducing the electrical consumption of the heat pump. If the average tem­perature level of the heat source is increased by 5 K the annual HPS performance factor (HPF) im­proves from 3.4 to 4.0. The HPF is defined as the heat supplied by the heat pump divided by its electricity consumption for one year of operation.

In such a two source HPS application the solar heat is either supplied directly to the heat pump condenser or to the BHE. The heat is transferred to the BHE for thermal regeneration of the cooled soil surrounding the BHE. A direct use of the solar heat for space heating or domestic hot water preheating is not regarded in this paper. These solar assisted ground coupled systems offer a high dynamic, a complex interdependency and particularly unknown behaviour, which can not be de­scribed properly with common steady state methods used for BHE dimensioning. Hence detailed numerical simulations are required. The realization and evaluation of two HPS pilot plants were in

the focus of a research project, where a TRNSYS-simulation configuration could be validated and used for further extrapolating studies.

Development of a Double Mantle Heat Exchanger Storage Model

The first step leading to a realistic thermosiphon simulation model is the implementation of a double mantle heat exchanger storage tank. This development was carried out based on a simple hot water storage model already available in CARNOT and a validated TRNSYS double mantle heat exchanger storage tank model developed at Malaga University, Spain [5].

Подпись:
In order to consider stratification effects within the hot water storage, it is necessary to divide it into n user settable vertical layers with either a uniform height or volume. Figure 1a shows one volume segment of height dh and the storage section it affects in terms of energetic calculations (dotted lines). The model is one-dimensional and, therefore, the storage is not divided into additional layers alongside its length. Hence every volume element of the model is calculated using the full length of the storage (Figure 1b).

Подпись: dUt dt Подпись: V dT Q Q c-P-V ■ = Qm - Qo dt Подпись: (1) Подпись: dT = Qtn - Qou dt c- p - V Подпись: (2)

The thermal behaviour of the model is described by mathematical-physical correlations within every node. For every element in the collector fluid and the tap water, the energy balance is drawn. Within this energy balance, the changes of the inner energy of every element have to be equal to the difference of the entering and leaving heat flow (1, 2).

The main advantage of the CARNOT model in comparison to the TRNSYS model can be found in the way the storage model is discretised.

The storage model in TRNSYS does not consider the heat conductivity of the mantle and storage as well as the transfer coefficients of all materials (including liquids) directly. In order to describe the heat flux within the TRNSYS model, the convective heat transmission on the surfaces and the heat conduction through the different layers, like e. g. steel or insulation materials, are combined resulting in an overall heat transfer coefficient. This coefficient has to be estimated and validated by measurement data. The advantage of this method is the reduced amount of variables, e. g. if there are unknown conditions, there is just one parameter to estimate.

The major advantage of the more complex model built for CARNOT is the possibility to use this model in optimization and development simulations, as almost every important parameter — like materials and geometric values — can be tuned. Figure 2 shows the calculated heat transfer mechanisms heat conduction and convection.

The TRNSYS model uses the same length for the inner and outer mantle of the storage. In the CARNOT model, these lengths can be varied. This has the advantage of adapting the length and fluid capacity of real double mantle storages, as shown in Figure 1. The model calculates the heat transfer from the heat exchanger to the tap water only according to the heat exchanger length lma„ae (Figure 1a). For the rest of the storage length the occurring heat loss from the hot water through the storage material, the insulation and the convective losses into the surrounding ambience is calculated.

Besides the thermal part of the storage, the calculation of the pressure drop is one of the most important variables in thermosiphon systems, as the circulation of the system is maintained by very small pressure differences, due to density decrease or temperature increase along the collector, in the range of 10 — 300 Pa (or 1 — 30mm water column) [6]. The model considers the pressure drop according to height differences in the storage between entering and returning pipes (Figure 1). The dynamic pressure drop resulting from differences in velocity between the piping and the heat exchanger is calculated using the flow rate and the geometrical parameters of entering pipes and storage tank. Bends and other obstacles at the connection between the piping and the storage’s heat exchanger mantle are described by additional friction coefficients. As the velocity of the heat

transfer fluid within the double mantle heat exchanger is nearly zero, there is no dynamic pressure drop calculated.

The solar thermal power plant

Подпись: Fig. 2: Arrangement of the solar thermal collectors

image294The existing district heating grid will now be extended by a solar thermal feed-in. The heating grid will be supplied by the produced energy of a solar thermal power plant (collector area: 3.700m2m, Fig. 2) via a heat exchanger. Since the solar thermal heat is almost always used immediately, no additional buffer storage are necessary, energy oversupply can be stored in the thermal storage tank in case of need.

Analysis of simplified calculation procedures of solar gain in buildings

G. Oliveti, N. Arcuri, M. De Simone, R. Bruno,

Department of Mechanical Engineering — University of Calabria
87036 — P. Bucci 44/ C — Rende (CS) — ITALY
M. De Simone, marilena. desimone@unical. it

Abstract

A critical analysis of the calculation procedure of solar gain in buildings with reference to an attached sunspace bordering air conditioned environments was developed. The EN ISO 13790:2008 Standard provides a simplified calculation method for the estimation of solar gain based upon the monthly energy balance in a stationary regime, to be applied both during winter heating and summer cooling. Moreover, the Standard hypothesises possible simplifications to be evaluated in relation to climatic conditions and the type of greenhouse-environment system. The direct, indirect and total solar contribution evaluated by means of the Standard are compared with those obtained with a dynamic calculation code, with the aim of highlighting the limits of the schematization adopted by the Standard. Furthermore, the gain in an airconditioned environment obtained by means of a windowed wall is compared with that produced by the use of a sunspace opposite the same wall.

Keywords: Energy balance, solar heat gain, Standard, sunspace.

1. Introduction

The use of solar radiation in buildings is of particular interest in the case of the use of glazed systems such as glazed balconies and sunspaces. Sunny spaces adjacent to air conditioned volumes are passive solar systems, usable in order to reduce the thermal energy requirement of adjacent spaces in winter and to control solar gain in the summer months.

For solar contribution we are refering to the energy that, in a determined time interval, reaches the airconditioned environment by means of the separating walls of the lodge or the greenhouse. Such a gain is produced by solar radiation which directly penetrates the environment through the glass surfaces, and the energy transmitted by conduction through the dividing walls consequent to the absorption of solar radiation. The energy absorbed by the greenhouse shell is in part given to the adjacent rooms, in part transferred to the outside, in part removed by the ventilation flow and in part remains accumulated within the opaque walls [1].

The EN ISO 13790:2008 Standard [2] in Annex E provides a calculation method of solar gain obtainable with specific elements including unconditioned sunspace attached to buildings; it confirms the UNI EN 832:2001 calculation method [3] based upon the monthly energy balances in a stationary regime and also extends its validity to the summer. Furthermore, the EN ISO 13790 suggests conservative simplifications in calculating the monthly energy requirements of the adjacent environment whose validity requires checking in different national realities.

The Standard method distinguishes between direct solar contribution which reaches the airconditioned environment through the glazed and opaque surfaces which separate the sunspace from the environment, and indirect solar contribution deriving from heating of the air in the sunspace. For the evaluation of direct contribution, consider the energy entering through the glass separation surface of the sunspace-environment completely absorbed by the environment (black cavity hypothesis), and the energy absorbed by the opaque separation components, which is conducted in the walls, evaluated by a simplified model that does not consider the effects of thermal capacity.

The estimation of indirect solar contribution is obtained considering the solar energy absorbed by only the opaque components of the sunspace, after the conductive transfers in the conditioned environments, which one is supposed to be transferred to the greenhouse air.

In this article, by means of the DEROB-LTH (Dynamic Energy Response of Buildings) dynamic simulation code [4], a critical analysis was developed of the procedures used by the EN ISO 13790 Standard for the calculation of direct and indirect solar contribution, and furthermore, with reference to the Italian climate, verifies the possibility of adopting some simplifications proposed by the same Standard relating to the heating and the cooling. The system considered is an attached sunspace separated from an adjacent airconditioned environment by a mixed opaque-glazed wall, and bordering by means of the flooring with a second airconditioned space. The DEROB-LTH code resolves the transmission of solar radiation through the glazed surfaces taking into consideration the directional aspects, and the absorption in the greenhouse and the adjacent environment considering the directly irradiated portions of the surfaces and the redistribution of solar radiation consequent on reflection phenomena. Moreover, the code resolves the thermal field in the glazed and opaque walls of the sunspace taking into consideration the effective surrounding conditions that act upon both the internal and external surfaces [5].

The comparison of monthly energy was carried out in the same application conditions of the Standard, that is to say considering only solar power as an agent on the sunspace. This was obtained in the simulations by eliminating the other powers, or rather by imposing the same temperature constant as the aircondtioned environment for the external air and the sky. The simulations were conducted on an hourly basis using both direct and diffuse radiation values relative to the average monthly day [6].

Description of SIGA SOL 1.0

1.1. Principal menu

The SIGA SOL 1.0 ( Geographic Information System Applied to Solar Energy) is made up of three principal blocks: management, planning, and updating of data bank., according to what can be seen in Fig. 1. Management and planning occur at two levels: macro-spatial (state) and local (municipal). The updating of data bank can be done by rectification, exclusion or inclusion of information to data banks that are associated to already installed energy systems.

1.2. Functionalities

Подпись: Figure 1 - Principal menu of the SIGA SOL 1.0

The use of a GIS tool requires the formulation of questions, whose answers are products of crossing one or more data banks and or maps. The result is not normally completely conclusive (closed) and the product is a group of spatial information and/or reports that almost always still require the interpretation of who made the question. The SIGA SOL 1.0 was constructed to give the user answers to questions, of general and simple character, that in the majority of times corresponds to one layer of information or complex questions whose answers are products of crossing of diverse layers of information. The answer to questions of simple general character are denominated default functionality and are recorded as sub-menus in the menus of management and planning at macro-spatial and local level. The non default functionalities generated by complex questions by the users can be printed or recorded and can be transformed into default functionalities. Other default functionalities associated to the tasks of updating the data bank and dimensioning renewable energy systems are in the sub-menus of the updating and planning menu.

Numerical simulation of fluid dynamics

It is of major importance to determine the influence of the fluid medium and the fluid dynamics inside the collector on the heat transfer. The heat transfer through a surface depends not only on the thickness and the heat conductivity of the material but also — and in some cases even predominantly — on the heat transfer coefficient between the fluid and the wall which is determined by the fluid dynamics in the vicinity of the surface. Thus one of the main objectives of this work was to study in detail the behaviour and the characteristics of the fluid flow by means of numerical simulations. By using computational fluid dynamics methods (CFD) it was possible to calculate the fluid flow in the absorber, the heat distribution in the solid materials and the radiation interaction between the internal and external surfaces.

In order to develop a systematic way to compare the mechanisms and the performance of different collector types, calculations for a simple flat plate collector were first made and the influence of various parameters was examined.

Подпись: Fig. 1. Mesh consisting of approx. 100,000 elements For symmetry reasons, the numerical model was reduced to a stripe of 1cm width and symmetric boundary conditions were set for both sides. The model consists of approx. 100’000 finite volumes (Fig. 1). CFD simulations were performed in order to quantify how the heat transfer depends on

• the length of the collector.

• the position of the absorber (above, in between or below the carrier fluid).

• the height of the fluid channel.

• the mass flow rate.

Through series of systematic calculations the following dependencies were discovered:

Подпись: • AT ~ L • Ap ~ L • AT ~ 1/d • Ap ~ 1/d • AT = const. • Ap ~ Фm The temperature difference between inlet and outlet is proportional to the length (Fig. 2).

The pressure drop in the fluid channel is proportional to the length.

The temperature difference increases if the height d of the channel decreases.

The pressure drop increases reciprocally with the channel height d.

AT is constant if the mass flow rate Фщ is held constant for different collector geometries.

The pressure drop is proportional to the mass flow rate.

Furthermore, the simulations showed that the position of the absorber does not influence the outlet temperature of the carrier fluid. However the temperature of the surrounding solid materials depends on the position of the absorber. Thus this parameter is of relevance for the design of the absorber for material or stability reasons. This topic is discussed in Section 4.

Ray-tracing and Variation of Parameters

In order to carry out investigations and to describe an established collector we developed an input mask in which all relevant geometrical and material data can be entered. A macro is generated from this information that completely describes the collector and that can be executed by OptiCAD.

For instance, different types of CPC-reflectors can be easily generated just by entering the designated half acceptance angle and the reflector arc length in such a parametrical model. Every other parameter of the reflector geometry such as angle of truncation, concentration ratio and height of the reflector are automatically determined. For more information on CPC-collectors, see [2] and [3].

The next step after fixing the geometrical and optical properties of the different collector components is to define the simulation mode. Simulations in the transversal or longitudinal plane are possible or also for all other angles (3D-IAM).

Two different alternatives exist for the determination of the IAM-values over the hemisphere (3D — IAM):

image312Either, the simulation can be carried out in polar coordinates (0 — theta, ф — phi) or in the projections of the incident angle (0t — theta_t, 0l — theta_l). The latter are used e. g. in different solar simulation programs such as TRNSYS. Figure 3 shows the angle conventions for the projected incidence angles theta_t and theta_l of solar radiation incident from an optional direction.

Transversal

Подпись: Fig. 3. Projected angles of incidence in the longitudinal and transversal plane [4]

Longitudinal

Direction

When OptiCAD is started, the macro which also contains the description of the ray-tracing calculation is imported and executed. The interpretation of results (e. g. plot of 3D-IAM) happens automatically within the file of the input mask. Thus, it is assured that simulation settings and the output of a simulation as well as the analysis of results are documented together in one file.

The Temperature Field in a Tube’s Coating

To describe the temperature field in a tube’s coating we choose a system of polar coordinates with O as the initial point and write Laplace’s equation in the polar coordinates assuming that the process is stationary [7]:

image079

(12)

 

image080

(13)

(14)

(15)

(16)

(17)

 

image081

d© 2jf>1,pP = Q (p <ф<п-ф1); dp

d©2d(/?1,p) = 0 {n + p1 <p< 2п-ф1);

dp

 

image082

image083

image084 Подпись: (18)

Applying the Fourier method of separation of variables [8] one obtains:

where k is a positive integer.

Variations in measured hot water use

The time-use data is only available for one weekday and one weekend day per household, and therefore the model only generate average profiles for one day of each type, not depending on season

or day of the week. To enable further model development the time dependent variations in load measured in the 24 apartments are investigated below.

Подпись: Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Month Figure 3. The measured daily hot water consumption per average household member in the 24 apartments for the different months of the year.

The energy use for hot water for different months, expressed as average daily demand per average household member, is found in Figure 3. The lowest hot water consumption is found during the summer months and the highest consumption during winter. The average daily energy use for hot water is 5.4 and 4.4 kWh/person for 2005 and 2006 respectively, with a variation of the maximum and minimum consumption of ±17-26 % around the average. The results correspond well to the monthly relative variations found in [9].

Подпись: Figure 4. The energy use for hot water different weeks during the half-year including summer. A decrease can be observed for the vacation time in July for both measured years.

The half-year including summer is investigated more in detail in Figure 4, showing the weekly variations in hot water demand in April to October. A clear minimum is found in July and August, which is the usual vacation period in Sweden.