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Солнечная и другая альтернативная энергия

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Heat losses investigation

1.1. Problem description

When solar radiation come to an absorber layer, the spectral response of the ideal material should allow an absorbance on the bandwidth of incoming radiation and an emittance completely shifted in a different bandwidth. In this case all incoming radiation would be transferred into thermal radiation. Part of this radiation is lost under the form of emittance of the absorbing layer to the environment, part becomes thermal energy and is transferred to the below layers. The structure of the solar tube avoids conduction and convection losses to the environment due to the evacuated area between two concentric glass cylinders inside which area the absorbing material is deposited, usually on the external surface of the inner tube. The consequence is that, all conduction and convection losses concentrate in the various layers from the absorber to the vector fluid. The investigation of the problem starts with the evaluation of the efficiency for the analysed solar collector as certified according to EU certification EN.12975-2:2006. The solar collector efficiency is the ratio between the energy Q (energy density) absorbed from the vector fluid and the energy (solar energy density) incident on its external surface.

image231"(1)

and similarly, as usually reported, from the relation:

(2)

where tjq is the solar collector efficiency at TM = 0, ai and a2 are heat transfer coefficients, G is the total solar radiation and:

image232"(3)

where tm is the panel average temperature and is the ambient temperature. The relation (2) is

the main instrument to evaluate the quality of a solar collector, and is within the certification reports. The efficiency of the solar collector investigated in the actual work can be viewed in the Fig. 1. It starts at 71,8 % at ambient temperature and it’s referred to an incident radiation of 1000 W/m2. In the same graph are represented the various heat losses calculated from optical and geometric factors, tube materials, reflector characteristics and cermet thermal properties. "Other losses", the orange area, resume some other factors, the most relevant of whose is the thermal resistance between the cermet layer and the vector fluid.

Подпись: Efficiency and thermal loss on a vacuum solar collectorПодпись: ■ Other Losses ■ Conduction Loss to External ■ CPC Concentrator ■ Cermet Emissivity ■ Borosilicate Glass ■ Collector Efficiency Подпись: 0 0.025 0.075 0.125 0.175 0.275 tm-ta / G image233100%

90%

80%

70%

60%

50%

40%

30%

20%

10%

0%

Fig. 1. Evaluation of the thermal losses on the real solar collector.

The Fig. 2 represents a section of the Evacuated Solar Tube (EST), selected for the modelling and used in the experimental prototype.

Temp

Parabolic

Concentrator

(W)*

Borosilicate Glass (W)

Cermet

(W)

100

7.6

12.8

8.3

150

7.6

12.8

38.1

200

7.6

12.8

68.5

300

7.6

12.8

120.2

Table 1. Main contribution to radiation heat losses due to different optical behaviour and properties of the evacuated solar tube.

* surface reflectance = 0.9

Подпись: Fig. 2. Sectional view of the analysed evacuated solar tube (EST)

From external to internal the different layers of the EST are:

• borosilicate glass 3.3 tube — Glass TubeEXT ^EXT = 58mm; tb = 0.92, p = 0.062, a = є = 0.018 );

• vacuum (pINT~10-7 Torr, фЕХ1- = 56.4mm, фют = 47mm);

• cermet layer (a > 0.93);

• borosilicate glass tube — GlassTubeINT (фЕХЇ = 47mm, 5 = 1.5mm);

• computed air layer for materials tolerance between GTINT and aluminium profile (5 = 0.7mm);

• aluminium foil;

• copper tube (фЕХт = 7mm, фШт = 6mm);

• water (v = 0.556 m/s).

The problem of the evaluation of the heat loss and the development of a modified object with higher thermal efficiency is the first step to begin the research for a new device able to produce electrical, thermal and cooling power, with an efficiency higher than 70%. The first step is to build an evacuated solar tube with the capability to work at 250°C and more, without loosing thermal energy with consequences on its efficiency. The actual evacuated solar tube, at a vector fluid temperature of 523 K, has a thermal efficiency n = 0.23.

Turbulence model applied to a fluid in a modified evacuated solar collector

L. Crema1*, G. Cicolini1, A. Bozzoli1

1 Renewable Energies & Environmental Technologies research unit (REET), Fondazione Bruno Kessler (FBK),
Via alla Cascata 56/C, I-38050 Povo (Tn), Italy
* Corresponding Author, :rema@,fbk. eu

Abstract

In this work, we propose a solution to convection and conduction heat losses on an solar thermal collector. We have based our work starting from the technology of the evacuated solar tubes, the technology actually with the highest thermal efficiency in the market. The tubes have got a CERMET absorbing layer sputtered on the surface of a glass tube, in the evacuated area. A modified structure for the evacuated tube has been analysed in order to investigate the heat transfer and the thermal resistance from the cermet layer to the vector fluid in different fluid dynamic conditions than the actual used. Some models have been created and their behaviour has been verified using Finite Element Modelling software. The computed results show a lower thermal resistance for the proposed geometries. A higher convective heat transfer has been obtained providing the vector fluid of a turbulent flow, using special shapes (turbulators) applied to the evacuated tubes. The temperature gradient between the cermet layer and the vector fluid has been decreased from 20 to 1,06 K in the better case. The thermal efficiency of the panel has an improvement of about 10% from such modified geometry.

Keywords: solar collector, finite element modelling, fluid dynamic

1. Introduction

During last years the development of new technologies have taken solar thermal collectors to new frontiers [1]. Collectors based on evacuated solar tubes, cermet layers and other applied technologies have taken good results. Many studies had proposed solutions to the evacuated solar tube development [2]. Nevertheless commercial collectors frequently suffer from some problems related to heat transfer phenomena, radiation loss at high temperatures or vector fluid choice. A relevant heat loss comes from conduction/convection phenomena between the absorber material and the vector fluid and from both of them to the environment. In the actual work it has been performed an analysis on a real evacuated solar tube with a relevant presence on the international markets and particularly good characteristics. The aim is to analyse aspects related to heat losses and to propose both a partial solution to the problem and a technical improvement of the system. The analysis will be performed under an analytical point of view, by the use of FEM (Finite Element Modelling) simulation and by an experimental setup for a direct verification of modelling.

Determination of the maximum usable hot water volume

In order to evaluate the system behaviour under different draw off volumes and to determine the maximum usable hot water over a whole year, several simulations have been carried with a collector tilt angle of 42° under the climatic conditions of Rome. It has been assumed that hot water is only needed in the evening in between 6.00 — 8.00 pm. The system is included into an existing hot water system consisting e. g. of a gas boiler for hot water and room heating or a simple electronic hot water boiler.

image229

An automatic tempering valve at the hot water outlet of the storage prevents the users from scalding themselves. A selector valve automatically takes the hot water from the backup heating if the hot water temperature turns below 45°C. Figure 6 shows a schematic drawing of the system.

The daily draw off pattern was varied in the range of 120l/d.480l/d. As a first result of these variations it can be seen that the hot water draw off out of the 180l storage is limited to about 35,000l/a respectively the draw off gets saturated at about 240l/d, because of the climatic

conditions. With a draw off profile of only 120l/d, an annual solar hot water fraction of about 66% can be achieved. In terms of saved energy this equals a reduction of about 95l of fuel oil. With a hot water demand of 180l/d, it is still possible to cover nearly 50% of the annual hot water demand or an equivalent of 125l of fuel oil with only one collector of about 2m2 and a 180l storage tank.

4. Conclusion

The paper presents the implementation of a double mantle heat exchanger into the simulation environment CARNOT and first simulation results calculated with the new storage type.

The developed double mantle heat exchanger storage is based on the TRNSYS double mantle heat exchanger storage but was enhanced by the possibility of including user settable material and geometric data.

Concerning the system simulation, some “to dos” remain, like the validation of a modified “thermosiphonic pump”, which is able to calculate the fact of reverse thermosiphoning e. g. at night. In order to improve the system and to identify other main influencing variables, further simulation runs have to be carried out, e. g. with regard to overheating.

References

[1] S. Gurtner, F.-D. Treikauskas, W. Zorner: „Prufstand fur Thermosiphonanlage am Kompetenzzentrum Solartechnik an der Fachhochschule Ingolstadt“, 16. Symposium Thermische Solarenergie, Kloster Banz / Staffelstein (Germany), May 2006, p. 118 — 122.

[2] S. Brandmayr, W. Zorner: “Thermosiphon Systems: Market, State-of-the-Art and Trends“, 3rd European Solar Thermal Energy Conference (estec2007), Freiburg (Germany), June 2007, p. 182 — 188.

[3] N. N.: “Matlab/Simulink user manuals”, The Mathworks Inc., http://www. mathworks. com, Natick (USA), 2002.

[4] B. Hafner, J. Plettner, C. Wemhoner: “CARNOT Blockset: Conventional And Renewable eNergy systems OpTimization Blockset — User’s Guide”, Solar-Institut Julich, Aachen University of Applied Sciences (Germany), 1999.

[5] A. Carillo Andres, J. M. Cejudo Lopez: “TRNSYS model of a thermosiphon solar domestic water heater with a horizontal store and mantle heat exchanger”, Solar Energy, Vol. 72/2 (2002), p. 89 — 98.

[6] G. L. Morrison, D. B.J. Ranatunga: “Thermosyphon circulation in solar collectors”, Solar Energy, Vol. 24 (1980), p. 191 — 198.

Determination of the optimum collector tilt angle

The subsequent simulation runs were carried out in order to calculate the best collector tilt angle for the thermosiphon system under the climatic conditions of Rome, a typical target region for thermosiphon systems. The goal behind these simulations was to achieve the best solar fraction even during winter times. The basis for the simulated collector tilt angles was the latitude of Rome, which is 41° 51’N. Therefore the first tilt angle was chosen to be 42°, all the other angles were simulated in steps of 10° plus or minus. The simulated draw off takes place every evening at 6.00 pm and lasts until the mixed water temperature turns below 45°C.

image226

Table 2. Determination of the best collector tilt angle in terms of hot water production

month collector tilt angle [-]

22°

32°

42°

52°

62°

72°

82°

mo

nthly hot water production [l]

Jan

0

129

402

512

515

519

393

Feb

1,037

1,140

1,183

1,198

1,191

1,184

1,129

Mar

1,866

2,068

2,200

2,196

2,050

1,835

1,180

Apr

2,538

2,444

2,422

2,122

1,533

1,382

588

May

3,688

3,643

3,239

2,861

2,516

1,604

587

Jun

4,020

3,917

3,616

3,331

2,868

2,055

1,112

Jul

4,656

4,603

4,487

4,231

3,844

2,598

1,715

Aug

4,701

4,701

4,641

4,389

4,092

3,319

2,420

Sep

3,339

3,429

3,448

3,331

3,230

2,923

2,260

Oct

2,145

2,268

2,322

2,343

2,337

2,308

2,098

Nov

767

970

1,131

1,248

1,262

1,360

1,132

Dec

0

110

253

278

284

277

278

Total

28,755

29,421

29,343

28,041

25,721

21,362

14,893

Table 2 shows the simulation results in terms of monthly hot water production. It can be seen that the thermosiphon system is able to produce almost the same amount of hot water in the range from 22°.. .52°. Lower system angles, e. g. 22°, should be preferred if hot water is only needed between spring and autumn, e. g. for campsites. If hot water is needed throughout the whole year, a collector tilt angle comparable to the latitude should be preferred, in case of Rome 42°. With collector tilt angles of 62° and more it is not really possible to increase hot water production during winter times as is known from pumped solar hot water systems.

Validation of the Storage Tank Model

After finishing the code, the storage model was validated in two steps. In a first step, the simulation behaviour was compared to measured data from previous system tests using measured hot water draw off curves and storage heat loss curves from several different testing days (Figure 3).

image221

Fig. 3. Comparison between a measured and a simulated storage behaviour a) temperature increase and energy draw off at night, b) temperature drop caused by heat loss within a period of 18h

In a second step, the thermal behaviour of the double mantle heat exchanger store was compared with CARNOT’s existing simple water store model — insulated cylindrical hot water storage without any additional heat exchangers — validated by Hafner et al [4]. In order to compare both storage types, the gap between the inner and outer mantle of the double mantle storage model was assumed to be zero.

Both types of validation tests showed a deviation between simulation and measurements of less then 5%.

3. System Simulation

Подпись: Fig. 4. CARNOT simulation model of a thermosiphon solar water heater.

In the next step a complete thermosiphon system composed of solar collector, the necessary piping, the so-called thermosiphon pump (a block setting the thermosiphonic flow rate according to pressure differences in the system) and the newly developed double mantle heat exchanger storage was built up (Figure 4). The implemented technical data is identical to a system which was tested according to ISO 9459-2 at the CENTRE OF EXCELLENCE FOR SOLAR ENGINEERING in Ingolstadt (Table 1).

Table 1. Technical characteristics of the measured and simulated thermosiphon system.

Collector aperture area

1.89m2

Collector cover material

Prismatic tempered glass, 3.2mm thickness

Collector hydraulics

Diameter header: 18x1mm; diameter riser: 8×0.5mm; number of risers: 10

Collector slope

38°

Heat transfer fluid

Water

Storage

Horizontal double mantle heat exchanger storage, volume: 180l, diameter: 0.48m, length: 1.46m

Tank insulation

30mm polyurethane

Heat exchanger

Double mantle, volume: 8.5l

Connecting pipes

Well insulated tube, 22x1mm, total length: 2.64m

Location

Ingolstadt, Germany

All blocks in the system are connected via data vectors according to their position in the system. The most important vector is the so called thermo hydraulic vector (THV), in which all relevant values are bundled. It includes the fluid identity, e. g. water or water-glycol mixture, fluid pressure, pressure drop (calculated in the block before), fluid temperature and density. Due to this THV, a realistic system behaviour can be achieved.

In the following, two different thermosiphon systems were simulated according to data measured at Ingolstadt University, using irradiation on the collector plane, the thermosiphonic flow rate and temperatures at collector / storage in — and outlet. The corresponding simulation runs show a good correlation between measured and simulated data, as can be seen in Figure 5 showing the flow rate and the accumulated flow through collector and storage over a whole day.

Подпись: 08:00 10:00 Подпись: 12:00 14:00 time M Подпись: 16:00 Подпись: 18:00

Fig. 5. Measured and simulated flow rate in a thermosiphon solar hot water heater

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.

Simulation of Thermosiphon Solar Hot Water Systems. UsingMatlab/Simulink and Carnot

S. Brandmayr1*, M. Konrad1, W. Zorner1 and V. Hanby[2]

1 Ingolstadt University of Applied Sciences — KompetenzzentrumSolartechnik, Esplanade 10,

85049 Ingolstadt, Germany

2 De Monfort University, Institute of Energy and Sustainable Development, The Gateway,
Leicester LE1 9BH, United Kingdom
* Corresponding Author, sebastian. brandmayr@fh-ingolstadt. de

Abstract

This paper describes with the R&D activities at Ingolstadt University of Applied Sciences in terms of thermosiphon solar hot water systems. The simulation tool Matlab/Simulink and CARNOT was enhanced by a double mantle heat exchanger storage in order to be able to investigate the behaviour of all kinds of thermosiphon systems in theory. Taking data measured at the university’s thermosiphon testing rig into the simulation models, provides the possibility to improve systems by all relevant parameters without performing additional outdoor tests.

Keywords: simulation, Matlab/Simulink, thermosiphon system, storage, development

1. Introduction

Thermosiphon solar hot water systems have been a subject to R&D activities of the Kompetenzzentrum Solartechnik (Centre of Excellence for Solar Engineering) at Ingolstadt University of Applied Sciences since 2004. After building up a test rig, several thermosiphon systems were tested according to the specifications given in ISO 9459-2 [1]. In addition to that, tests according to methods and procedures developed at Ingolstadt University have been carried out in order to learn about the system’s behaviour under special conditions, e. g. its stagnation behaviour.

In the end of 2007, a R&D project was started which aims at the development of an optimised thermosiphon system based on scientific results. A market analysis carried out beforehand showed that most thermosiphon systems are still developed through trial and error [2]. This project, however, aims at demonstrating a closed development cycle. This cycle includes the analysis of thermosiphon systems in theory, the transfer of the mathematical model into simulation, the design of a prototype based on the simulation results and, eventually, the testing of the prototype in order to maximize the system performance and to achieve validation of the computer model. This validated system model is going to offer the project partner, a manufacturer of solar thermal applications, the possibility of adapting their thermosiphon systems to the customers’ and climatic conditions.

blockset (Conventional And Renewable eNergy systems Optimization Toolbox [4]), which is a tool for the calculation and simulation of the thermal components of heating systems with regard to conventional and regenerative elements, was used. It provides models for heat sources, storage systems, hydraulics and fundamental material calculation as well as the possibility of integrating further models. The models used, except the developed double mantle heat exchanger storage, were validated by Hafner et al [4].

SYSTEM SIMULATION

The system is modeled and simulated with TRNSYS and the typical meteorological year (TMY) of Nicosia, Cyprus. In this section both TRNSYS and TMY are shortly presented and details of the model are given.

3.1 TRNSYS Program Description

TRNSYS is an acronym for a “transient simulation program” and is a quasi-steady simulation model [3]. The program consists of many subroutines that model subsystem components. The mathematical models for the subsystem components are given in terms of their ordinary differential or algebraic equations. With a program such as TRNSYS, which has the capability of interconnecting system components in any desired manner, solving differential equations and facilitating information output, the entire problem of system simulation reduces to a problem of identifying all the components that comprise the particular system and connecting them together to form the complete system model.

The latest version of TRNSYS (version 16) works in a graphic interface environment called the simulation studio. In this environment, icons of readymade components are dragged and dropped from a list and connected together according to the real system configuration. Each icon represents the detailed program of each component of the system and requires a set of inputs (from other components or data files) and a set of constant parameters, which are specified by the user. Each component has its own set of output parameters, which can be saved in a file, plotted, or used as input in other components. Thus, once all the components of the system have been identified and as the mathematical description of each component is readily available, the user all he has to do is to construct an information flow diagram for the system, the purpose of which is to facilitate identification of the components and the flow of information between them. The flow diagram also contains information on the weather data file and the output format.

TRNSYS is employing the standard second-order collector performance equation to model the collector, given by:

Подпись: ■"0 ат 1 Подпись: Gt Подпись: 2 Подпись: Gf

(T — Ta) (T — Ta )2

where kaT is the incidence angle modifier given by:

The values of c0, cb c2 and bo are obtained by experimental testing of collectors in accredited laboratories. The values employed in the present system are shown in Table 1. The useful energy extracted from the collectors is given by:

ft = FAKtTG — ft ( — Г, )] (3)

The total useful energy for the whole year is obtained from:

365 24

Подпись: (4)

Подпись: (2)

Q„,a = YY. Q.

d=1 h=1

Подпись: Qaux Подпись: Qload -Qa - Q loss Qrel J Подпись: (5)

and the auxiliary energy required, Qaux is:

where Qload is the energy required by the load, Qloss is the energy lost from the storage tank and pipes and Qrei is the energy relieved from the storage tank relief valve.

As can be seen from the above equations the energy obtained from the solar collector field depends on the collector area (A), collector slope (affects cos0), flow rate (affects FR) and the storage tank size (affects Ti). The collector inlet temperature depends also on the load pattern, make-up water temperature, the losses from the storage tank and pipes and the energy relieved from the relief valve. The storage tank losses and energy relieved from relief valve depend on the temperature of the stored water, i. e., it depends on the energy collected and storage tank size.

The system presented in this paper is simulated with TRNSYS using Typical Meteorological Year (TMY) data for Nicosia, Cyprus. The selection of typical weather conditions for a given location is very crucial in computer simulations for performance predictions and has led various investigators either to run long periods of observational data or to select a particular year, which appears to be typical from several years of data. The TMY for Nicosia, Cyprus, was generated from hourly measurements, of solar irradiance (global and diffuse on horizontal surface), ambient temperature, wind speed and direction and humidity ratio, for a seven-year period, from 1986 to 1992 using the Filkenstein — Schafer statistical method [4]. The measurements were recorded by the Cyprus Meteorological Service at the Athalassa region, an area at the suburbs of the town of Nicosia. The TMY is considered as a representative year for the Cypriot environment.

TMY is defined as a year, which sums up all the climatic information characterizing a 30 year period record and not the operation lifetime of solar systems. Every about 10 years TMY files need updating to reflect climate changes, especially in cases where urbanization, pollution, increasing/decreasing of aerosols, drought, etc. takes place. Therefore an added advantage of the present method is that if this periodic updating of TMY fails to be done in regular intervals, some extreme effects can be accounted. Additionally, uncertainty in the weather patterns could include large-scale geophysical, human or nature caused events, like volcanic eruptions (Mt. Pinatubo eruption created aerosols which took two years to settle out), forest burning, increased storm occurrence, etc. which can have a much larger impact on short term and long-life system performance.

In this paper the effect of introducing uncertainty or noise in the weather data and load pattern is examined. The noise is introduced by using Type 578 (Random number generator). This model creates a random number drawn from a normal distribution based on user supplied values of the

mean (average) and standard deviation. For the parameters considered here these are shown in Table 3.

Table 3 Mean and standard deviation of the parameters considered in this work

Parameter

Mean (average) value of the normal distribution function

Standard deviation of the normal distribution function

Solar radiation (kJ/m2)

0

100

Ambient temperature (°C)

0

8.5

Load demand (l)

0

3.5

It should be noted that higher values of radiation resulted in messages that the horizontal component of radiation is higher than the extraterrestrial value and that the latter will be used, as a maximum value.

For the ambient temperature the noisy value is added to the normal value using the equation component of TRNSYS as:

Ta, new Ta, normal + Ta, noisy (6)

For the case of solar radiation the following equation was used in order to avoid adding radiation in hours where the normal value is zero, i. e., during nighttime:

Radnew Radnormal+LT(0,Radnormal)*Radnoisy (7)

The term LT (0,Rad) is a standard TRNSYS function which returns 1 when Rad>0 and 0 when Rad=0. Similarly for the load demand:

DHW new=DHW normal+DHW noisy*LT(0,DHW normal) ( 8 )

This avoids adding demand at the hours where its value is zero (early in the morning, see Fig. 2).

It should be noted that this analysis could also be performed by specifying the mean or average values of the various parameters shown in Table 3, without the need of equations (6) to (8). In this case however, the introduction of negative values into the simulation would have been unavoidable.

3.2 System Simulation

The normal system simulation is carried out with the aid of TRNSYS and the TMY for Nicosia, Cyprus. The system is also simulated by introducing noise in various parameters as shown above.

In all graphs that follow the mark “n” in the various parameters represent the values corresponding to the operation with noisy conditions. Figures 3 and 4 show a comparison of the normal and noisy radiation and ambient temperature respectively as obtained from the program for the first two days of the year. Similarly, Fig. 5 show a comparison of the normal and noisy hot water consumption profile for the same period. As can be seen the radiation values are not affected significantly whereas both ambient temperature and demand profile show large variations. It can also be seen that the noise is different from day to day, it is however impractical to show this variation for all days of the year.

A comparison of the annual performance of the normal (without noise) and noisy systems is shown in Table 4. As can be seen the annual differences are minimal which means that the noise introduced as described above has not created large differences. The solar energy incident on the

image198

collector is very much the same whereas the greatest difference is for the auxiliary energy which for the noisy system is reduced by 6.3%.

Fig. 5 Comparison of the normal and noisy hot water consumption profile for days 1 and 2

Of course the differences on a daily basis are expected to be more significant and these are presented and analyzed below. As it is impractical to show a comparison for all months of the year only January and July are presented showing typical winter and summer performance respectively.

image199 Подпись: 86.1 87.0

As can be seen from Figs. 6 and 8, in both January and July, although the difference in the total radiation falling on the collector is not much there is considerable difference in the useful energy supplied from solar collectors.

January

A jy’AsA’^A. a. Ay

1

3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 Day number

250000

200000

150000

Fig. 7 Comparison of the daily normal and noisy domestic hot water load and auxiliary energy supplied from

the collector for January

Also as shown in Figs. 7 and 9 for January and July respectively, the hot water load for the non­noisy case is almost constant and much larger for the noisy case, but this has almost a negligible effect on the auxiliary energy required during the summer period and a more pronounced effect during the winter, as both the makeup water temperature replacing the demand and the performance of the solar system during this period are much lower.

image215,image216

Fig. 9 Comparison of the daily normal and noisy domestic hot water load and auxiliary energy supplied from

the collector for July

2. CONCLUSIONS

As it is proved in this paper annual performance of the system is not very much different compared to the normal non-noisy model whereas the daily and hourly performance shows some considerable variations. It is believed that the present method gives more reliable results to the long-term performance evaluation of the systems and should be followed once the optimum system is obtained as it produces more reliable results. This is more important in cases where guaranteed solar results schemes are followed where possible mistakes could result in significant penalties.

References

[1] Kalogirou, S., The potential of solar industrial process heat applications, Applied Energy, 76 (2003) 337-361.

[2] Kalogirou, S., Optimisation of solar systems using artificial neural networks and genetic algorithms, Applied Energy, 77 (2004) 383-405.

[3] Klein S. A., et al. (2004) TRNSYS program manual, University of Wisconsin.

[4] Kalogirou, S., Generation of typical meteorological year (TMY-2) for Nicosia, Cyprus, Renewable Energy,

28 (2003) 2317-2334.

SOLAR SYSTEM DESCRIPTION

In order to demonstrate uncertainty in modelling solar systems a large solar hot water system, is employed. A schematic diagram of the system is shown in Fig. 1. The system consists of a collector array, a storage tank, solar pump and auxiliary heater. A differential thermostat is used which compares the temperature at the exit of the collectors and the storage tank and gives a signal to switch on the pump. The collectors employed in this application are flat plate collectors. Their characteristics are shown in Table 1.

Подпись: Solar pump Fig. 1 Schematic diagram of the large solar hot water system

The characteristics of the solar system are shown in Table 2. These are obtained from an optimization exercise of the same solar system presented in [2].

Table 2 Characteristics of the hot water system

Parameter

Range

Collector area Collector slope Mass flow rate Storage tank capacity

36 m2 45°

54 kg/hr-m2 1.8 m3

The solar system examined can satisfy the hot water needs of 10 houses or flats or any other similar application of same hot water requirement. For this application, a hot water consumption (load) profile is required. This load is subject to a high degree of variation from day to day and from consumer to consumer, however, it is impractical to use anything but a repetitive load profile. This is not quite correct for the summer period, where the consumption pattern is somewhat higher due to frequent bathing. However, during this period, the temperature requirement for hot water is not as high as during winter. Consequently, the total thermal energy requirement is reasonably constant throughout the year. For the present study, the hot water consumption profile, illustrated in Fig. 2 is used. The same daily hot water consumption profile, of 120 liters at 50°C, is assumed for each house (families of four persons, 30 liters/person).

image206

Fig. 2 Hot water daily consumption profile for one family

UNCERTAINTY IN SOLAR THERMAL SYSTEMS SIMULATIONS

Soteris A. Kalogirou

Department of Mechanical Engineering and Materials Science and Engineering, Cyprus University of
Technology, P. O. Box 50329, Limassol 3603, Cyprus

Tel. +357-2500 2621, Fax. +357-2500 2769, Email: soteris. kalogirou@cut. ac. cy

Abstract

Usually solar systems are modeled with programs, like TRNSYS, using a typical meteorological year data and a constant consumption profile. This is the most practical method as all systems modeled are simulated with the same weather conditions and the same load demand profile, thus it is easier to compare systems of different configurations. In this paper the effect of introducing uncertainty or noise in the weather data and load pattern is examined. As it is proved the annual performance of the system is not very much different compared to the normal non-noisy model whereas the daily and hourly performance shows some considerable variations. It is believed that the present method gives more reliable results to the long-term performance evaluation of the systems and should be followed once the optimum system is obtained as it produces more reliable results. This is more important in case where guaranteed solar results schemes are followed where possible mistakes could result in significant financial penalties.

Keywords: Modeling of solar systems, simulation, uncertainty, long-term performance.

1. INTRODUCTION

As part of the design process of a solar system, simulation tools are often employed both to investigate the implication of a design change on the system and its long-term performance. The simulation is usually performed by using typical meteorological year (TMY) data and a constant hot water demand profile. Such applications can be seen in [1,2].

The proper sizing of the components of a solar system is a complex problem, which includes both predictable (collector and other performance characteristics) and unpredictable (weather data) components. For the modeling and simulation of the systems presented in this paper, the well — known TRNSYS program is employed [3]. This program is considered as the most accurate for modeling of solar systems.