Fin efficiency in Type1223new is calculated using an analytical solution for circular plain fins. This can, however, overestimate the fin efficiency for high performance heat transfer surfaces (fins with waves, slits and louvers) [16]. If the overall heat transfer coefficient is determined using the same fin efficiency calculation as in developing of a heat transfer correlation, no error will be generated. Therefore, the fin efficiency calculation according to Schmidt [15] (taken from [9]) was implemented in the model, which was used in developing of the implemented correlations.

1.2. Liquid-side correlation

For a liquid-side heat transfer correlation a simplified Gnieliski correlation Eq. (1) was implemented, which corresponds to the chosen airside heat transfer correlations [10-13].

_k_](Rep -1000)Pr(f,/2) D. J1 + 12.7f2 (Pr2/3 -1)

(1)

u. =

This simplified correlation is only valid for turbulent and transitional flow. At small Re numbers (< 4000) heat transfer can be considerably over predicted with this correlation.

1.3. Heat transfer rate calculation

The overall heat transfer resistance is defined from the following relationship

1 ua	1
(3)

V

The authors of the airside heat transfer correlations applied s-NTU relationships for cross-counter flow heat exchangers from ESDU [17]. These relationships are used in the model instead of those in Type1223new for counter-flow heat exchanger. The number of heat transfer units, the capacity flow rate ratio C* and the efficiency s are defined as:

* C C* = (5), max	Q
NTU = UA/Cmn (4),	s =

Knowing NTU and C*, the efficiency can be calculated using a corresponding s-NTU relationship. The total heat transfer rate is determined as:

Q =sQ =sC ■ (t — T ) (7)

max min in, air in, liq

The simulation period is one year with a time step of three minutes; weather data from Zurich is used. A single family house with a heating demand of 60 kWh/m2a is simulated. The maximum power of the burner is set to 10 kW and the set temperature of the auxiliary volume of the store is 63°C. A collector area of 20 m2 and a 1 m3 store is chosen.

3.2. Compared values and comparison of results of the different modelling methods

The comparison of the results is done by comparing yearly values of energy delivered to and taken from the store by the several loops (collector, domestic hot water, space heating, auxiliary heating), the resulting energy balance as well as the fractional thermal energy savings (fsav, therm) of the system defined as the auxiliary energy consumption of the solar thermal system (Esoi) compared to the final energy consumption of a reference system (Eref):

The results show that the deviation of the compared values caused by the interfaces and different component order is negligible. The difference between the above named yearly values of the two systems is less than 1 %. This is also according to a simulation test made with only one controller component of the collector loop connected directly to the tank instead of the interfaces in the subsystem model in SIMULATION STUDIO. This also causes little effect compared to simulations where this component is connected via the interfaces only. Because it is only one component, in this case the difference of the compared values is less than 0.03 %.

2. Conclusion

The use of the new implemented subsystem based structure level in SIMULATION STUDIO — the graphical user interface of TRNSYS 16 — helps to improve the graphical representation of complex models as well as achieving a possibility to replace subsystems in a simple way. Regarding the educational field, the new feature leads to a shorter training time and simplified construction of models and permits students to work on projects using and maintaining complex systems, because they are not forced to get familiar with the ASCII input file. In recent simulation projects the new modular

approach was already applied. A comparison with a standard model representation via manually implemented text file showed negligible deviation, namely less than 1 %, comparing yearly values of the energy balance of the store and the fractional thermal energy savings of a solar thermal system for hot water preparation and space heating support used in the IEA-SHC Task 32. This is most likely caused by the additional EQUATIONS used as interfaces of the subsystems. Nevertheless, the new implemented feature should only be a first approach to get a new structure level to the graphical user interface of TRNSYS. It is worth striving for an integration of it in some way in newer versions of SIMULATION STUDIO without the use of extra equations as interfaces. In the future a database of subsystems could be generated like the TRNSYS component database and the subsystems could then also be linked to each other in the common TRNSYS way.

References

[1] S. A. Klein et al, (2005). TRNSYS 16 — A Transient Simulation System. Solar Energy Laboratory, Wisconsin-Madison University.

[2] W. Weiss et al, (2003). Solar Heating Systems for Houses — A Design Handbook for Solar Combisystems, International Energy Agency, Solar Heating & Cooling Programme — Task 26.

[3] R. Heimrath, M. Haller, (2007). IEA-SHC-Task 32 — Project Report of Subtask A2 of Subtask A: The Reference Building, the Reference Heating System. Institute of Thermal Engineering, Graz University.

[1] Each with ideal pump dimensioning and operating at design point.

[2] Simulation Environment

In order to evaluate and optimise thermosiphon solar hot water systems, a simulation model in the Matlab/Simulink environment [3] was developed. In addition, the Simulink-based CARNOT

# Current address: Institut fur Solartechnik SPF, Rapperswil, Switzerland

[4] For example, air flow velocity > 2 m/s for even distribution and < 3.5 m/s (otherwise pressure drop too

high) [2]

[6] Fortran source code of the model can be downloaded from the TRNSYS website. http://sel. me. wisc. edu/trnsys/tmlib/ASHRAE_secondary_toolkit/heat_and_mass_trnsfr/1223NEW. for

[7] American Society of Heating, Refrigerating and Air-Conditioning Engineers

[8] Considering of condensation is of importance for the mentioned application in Bishkek, Kyrgyzstan as the dew point temperature often exceeds the water inlet temperature of 12°C.

[9] For example, the heat transfer coefficient calculated from (overall heat transfer) measurement data is lower if the heat exchanger is considered as a counter flow heat exchanger (the assumption valid for high number of tubes in air flow direction, e. g. [6]) than that for a cross-counter flow heat exchanger (e. g. [7-13])

’ Fanning factor is defined as the ratio of wall shear stress to the flow kinetic energy per unit volume [18]

[11] Thermal efficiency of a collector where ambient temperature equals the collector working temperature (i. e. no heat losses)

[12] This is necessary to be able to use time dependent values, e. g. temperatures, within equations.

Mathematical model has been experimentally validated in the frame of solar collectors testing according to European standard [5] in the Solar Laboratory operated under Department of Environmental Engineering at Faculty of Mechanical Engineering, Czech Technical University in Prague. Different construction of tested solar collectors has been chosen to validate the results from mathematical model with instantaneous efficiency data obtained experimentally under steady — state conditions. Experimental data and efficiency curves calculated from model are graphically compared.

Experimental data points of solar collector efficiency are coupled with uniform uncertainty bars in the graphs. Expanded efficiency uncertainty has been assessed for experimental data from both type A (statistical) and B (instrumental) uncertainties considering the coverage factor 2 with 95% level of confidence [5, 6] and for usual steady state conditions of measurements is between 3 and 4 %.

The theoretical calculation of efficiency curve by model is subjected to uncertainty of input parameters. While geometrical parameters are easily available with high degree of confidence, number of parameters defining the properties of collector parts is found uncertain within narrow range (e. g. absorber and glazing properties parameters, mostly ± 1 %), middle range (e. g. conductivity of insulation layer dependent on its temperature and density, ± 10 %) and quite broad range (e. g. emissivity of absorber back side, insulation or collector frame, > 50 %). Each of varying parameter has a different impact (sensitivity) to resulting efficiency value from high effect of absorber and glazing optical properties to negligible effect of frame external surface emissivity. Uncertainty of input parameters and its influence to calculated efficiency has been expressed by two borderlines where the collector efficiency values can be found in reality.

Fig. 4. Experimental evaluation of the mathematical model by collector testing (different absorber quality)

Fig. 4 shows validation of the model for two examples of different atmospheric flat-plate collectors. Collector on the left consists of nonselective absorber without conductive bond to register pipes (steel absorber is bond to copper pipe only by spot grip-contact). Standard safety glazing and mineral wool insulation are used in its construction. Determination of absorber-pipes bond conductance is a main source of uncertainty in the calculation.

Collector on the right is a representative of high-quality solar collectors with state-of-art copper laser welded absorber. High performance selective coating and solar antireflective glazing properties from optical testing reports were provided thus reducing the uncertainty of calculation to very low values. Due to sufficient back side insulation the influence of uncertain internal and external surfaces emissivity has decreased to minimum.

Mathematical model has been also tested in the field of solar flat-plate evacuated collectors. Validation has been performed on commercial evacuated collector with selective absorber and no insulation applied at the back of absorber (only air layers at given pressure). The collector envelope consists of moulded metal frame and low iron glazing. Support pillars to bear the underpressure stress are placed between glazing and back side of the collector and penetrating the absorber through holes (elimination of thermal bridges, not considered in modelling). The atmospheric variant of the collector (interior pressure 100 kPa) has been evaluated as a reference case (see Fig. 5, graph on the left). The evacuated variant has been tested with interior pressure reduced to 9 kPa (see Fig. 5, graph on the right.

Fig. 5. Experimental evaluation of the mathematical model by collector testing (different interior pressure) 6. Conclusion and outlook

The principles of mathematical model and design tool KOLEKTOR 2.2 for design and virtual prototyping of solar flat-plate collectors have been described. Design tool allows the determination of solar collector efficiency curve, parametric analysis to obtain information on different parameters influence on collector performance and especially for investigation of thermal performance of advanced solar collectors (building integrated, evacuated collectors, etc.). The model has been validated by experimental data from testing of solar collectors with different construction concepts (atmospheric collector with spectrally non-selective and selective absorber; evacuated collector with selective absorber under different interior pressures).

The model and design tool is under continuous development. Validation of the model for unglazed solar thermal collector type is planned and huge experimental investigations are expected due to high uncertainty in modelling of wind convection heat transfer coefficients known from literature. Mathematical model of solar thermal flat-plate collector (glazed, unglazed) and design tool KOLEKTOR will stand as a basis for development of universal solar photovoltaic-thermal liquid collector model. Advanced PV/T model will allow PV collector modelling (fluid mass flow equal zero, considering influence of temperature on electric efficiency), PT collector modelling (PV reference efficiency equal zero) or PV/T collector modelling.

Acknowledgement

The development of mathematical model and design tool KOLEKTOR has been supported by research project MSM 684077011 “Environmental Engineering” granted by Ministry of Education, Youth and Sports. The experimental validation of the model has been supported by research project CTU 880590 „Experimental validation of mathematical model for flat-plate evacuated solar thermal collector“.

References

[1] J. A. Duffie, W. A. Beckman, Solar Engineering of Thermal Processes. 3rd edition, Wiley & Sons, Inc., 2006.

[2] D. Y. Goswami, F. Kreith, J. F. Kreider, Principles of Solar Engineering, 2nd edition, Taylor & Francis, 1999.

[3] Solar Energy — The State of Art, ed. by J. Gordon (ISES), James & James, 2001.

[4] TRNSYS 16 release, Mathematical reference, Wisconsin University, 2004.

[5] G. Fraisse, Ch. Plantier, Development and experimental validation of a detailed flat-plate solar collector model, 5th European TRNSYS user meeting, 2003.

[6] J. Koo, Development of a Flat-Plate Solar Collector Design Program, Master Thesis. University of Wisconsin-Madison, 1999.

[7] E. Mathioulakis, K. Vorostopoulos, V. Belessiotis, Assessment of Uncertainty in Solar Collector Modeling and Testing. Solar Energy 66, 337-347, 1999.

[8] Ch. Muller-Scholl, U. Frei, Uncertainty Analyses in Solar Collector Measurement. Proc. of Eurosun 2000, Copenhagen, 2000.

[9] T. Matuska, V. Zmrhal, Software tool KOLEKTOR 2.2, available from http://www. fsid. cvut. cz/~matuskat/kolektor. htm

1.2. Introduction

Sizing of component is done for one floor. Extrapolation can be done to the whole building. For the different locations, the device power is equal to the maximum heating and cooling load computed before. Nevertheless the same performances are chosen whatever the nominal power. The three cases differ only by the heating and cooling production plant. Emission and distribution of heat/cold is kept as described above. In this way decoupling can be done about two parts of the simulation: building consumption; heating/cooling system consumption. For cases where solar energy is used, the collectors field is assumed to be located on the roof. This implies a limitation of collectors area. To go through this limitation, two versions are presented for case 2 and 3: one roof for 12 floors (case B.), one roof for 3 floors (case A).

1.3. Case 1: Gas boiler and vapour compression chiller

Heating and cooling production for this case has also been defined in the frame of the IEA Annex 48 report. Gas boiler performance is the same for each case: yield at 100 % load is 89.2 %; yield at 30% load is 88.2 %; losses at 0% load are 1.3 kW. Interpolation is done between these points. Heating curve has set point between 45°C and 90°C depending on external temperature.

The cold production is provided by an air-chiller with COP = 3.5. The set point of cold water is always 7°C whatever the case and external conditions. Due to lack of data, part load performance decrease is not taken into account.

1.4. Case 2: Gas boiler, vapour compression chiller, PV field

Gas boiler and chiller have similar behaviour as for case 1. The only difference is that Photovoltaic panels are placed on the roof to feed electrical grid (Panel chosen: SHARP NDL3E62). Given the roof surface, optimisation is done to produce maximum electricity on a yearly basis. A special TRNSYS shading model dedicated to PV is implemented (Type 551). A location has an optimal inclination angle

[5] , the optimal number of rows is found (10 rows). Inverter efficiency is set to 0.78. It is assumed that PV panels work at their optimal point (current-voltage) each time. For case 2A building has 3 floors for case 2B, 12 floors. Roof panel field contains 700 elements and has a total net area of 610 m2.

1.5. Case 3: Gas boiler, solar thermal field, absorption chiller

For this case, gas boiler power is designed to feed the absorption chiller when the load is maximum. It implies a higher power value than for previous cases. The heating/cooling system of case 3 requires additional equipment:

• Solar thermal panels : evacuated tube collector SCHOTT ETC 16

• Absorption chiller : YAZAKI WFC-SH 30 (Nominal point : 105 kWcold; thermal COP = 0.695)

• Storage tank

• Cooling tower : AEC Cooling Tower Systems FG 2004

• Heat exchanger

The central element of the simulation scheme is the storage tank (TRNSYS type 534); four circuits are linked to it: gas boiler, building heating network, absorption chiller hot water circuit and solar panel circuit. 20 cm width rockwool insulation has been modelled in order to decrease storage losses.

Storage tank volume is optimized: this value ranges from 3 to 11 m3 depending on the simulation case and location.

Absorption chiller behaviour has been implemented in a new TRNSYS type 255 (nearly the same as existing type 107) based on manufacturer curves [6] . The model takes into account the energy balance, but not the chiller inertia nor other dynamic effects. Cooling tower fan speed is controlled by rejection circuit temperature. Solar energy passes trough a heat exchanger (95% efficiency) and heats the bottom of the storage tank. Its upper part is heated at 89°C by gas boiler in order to feed the absorption chiller at nominal point. No temperature control neither flow variation is provided on the hot water. Nominal power for absorption chiller is 105 kW for Paris and Stockholm, 150 kW for Lisbon.

The whole solar field has a net collector area of 427 m2 and the slope is optimized for each location. There are four rows (less than case 2 due to size of panels). Mass flow of the fluid has been chosen to 30 litres/(m2_coll_net_area hour) [7] . New auxiliaries’ consumptions have to be taken into account in this case. Common values are given by H.-M. Henning [8] : 0.02 kWhelec/kWhth for solar system, 0.03 kWhelec/kWhth for heat rejection, 0.01 kWhelec/kWhth for absorption chiller.

2. Results

2.1. Introduction

Hereafter are presented simulations results for each case and each location. They emphasize the energy consumption of building. Variable selection for presentation is based on reference book [9]; for example, primary energy savings are related to collector area. When converting net energy consumption in primary energy consumption, the selected coefficient is 2.5 for electricity and 1 for fossil fuels. These are legal values for Belgium. All values are given in kWh by building squared meter per year (building area is 15000 m2 for twelve floor, internal zones area is used), or other units if necessary.

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.

Figure 5 display the velocity profile of the new ICS-SWH. An increase in velocity, compared to the four fin design, was observed resulting in an increase of the maximum velocity of 2%. The main velocity pattern occurs between 1.90mm/s to 3.8mm/s compared with a 1.86mm/s to 3.72mm/s for the five and four fins collectors respectively.

The longitudinal temperature stratification of the five fin collector is shown in Figure 6. Stratification occurs from a maximum water temperature of 295.9°K to a minimum temperature of 293.8°K at the top and bottom of the collector respectively resulting in a 2.1°K temperature difference from top to bottom. This corresponds to a 19% decrease in stratification.

2.95e+02 2.95e+02 2.94e+02 2.94Є+02 2.94Є+02 2.94Є+02 2.94Є+02 2.94Є+02 2.94Є+02

2.94Є+02 2.94Є+02 2.94Є+02 2.94Є+02 2.94Є+02 2.94Є+02 2.93e+02 2.93e+02 2.93e+02 2.93e+02 2.93e+02 2.93e-t02

Figure 6: Longitudinal water temperature stratification — 5 fins, side view, after 20mn

In this paragraph the main characteristics of the studied solar heating system and the elaborated physically-based model applied to the system are described in details.

1.1. Main characteristics of the solar heating system

The monitored combined solar heating system installed at the campus of Szent Istvan University (SIU), Godollo, Hungary is sketched in Fig. 1.

The term combined means actually that the installation has more than one consumers. It preheats water for an outdoor swimming pool and, in the idle period of this operation, provides domestic hot water for a kindergarten nearby. The main system components are the flat plate solar collector field, with a total area of 33.3 m2, oriented to the south and its inclination angle is 45°, plate heat exchangers, a 700 m3 outdoor swimming pool with a surface of 350 m2 and a 2000 litre solar storage tank. Auxiliary gas heated boilers are also included which operate in the same time with the solar heating if necessary. According to the notations above the following parameters are monitored on the system: temperatures (T, °C), specific solar irradiance (I, W/m2), volumetric flows (v, m3/s). Measured data are available from the year 2001, apart from minor interruptions.

2.1. Territorial cover

The GIS prototype tool covers an area of 183,500 km2 and corresponds to the total area of three states, Alagoas, Pernambuco and Paraiba. In a second phase it will be extended to 1,561,178 km2 which corresponds to the total area of the Northeast region.

2.2. Modality

The totality of the developed GIS tools previously described are principally focussed on the planning of the insertion of renewable sources and does not deal with the management problems of a program for insertion of renewable energies on a wide spatial scale as the PRODEEM — The Energy Development Program for States and Municipalities.

The SIGA-SOL (Geographic Information System Applied to Solar Energy) is a methodology based in GIS for management and planning of programs for insertion of renewable energy sources. The SIGA-SOL has the capacity of carrying out macro-spatial analyses (at state level) and local (municipality) as can be seen in Fig. 5.

There are some contributions to the heat losses from conduction phenomena. One of those is the heat that comes out from the solar tube, mainly from the junction between the two cylinders, external and internal, and from the support structures at the bottom of the two cylinders in the evacuated area. This is not a relevant effect (see Figure 1, conduction loss to external). The other is the thermal resistance between the cermet layer and the vector fluid that maintains the cermet at a higher temperature than the fluid with the creation of a temperature gradient between the surface and the fluid itself. In the results of the certified collectors in accordance with EN-12975-2:2006 the efficiency curve depends on irradiance, external temperature and fluid average temperature, but indirectly depends on the unmeasured cermet layer temperature. So, if there’s a temperature gradient from the cermet layer and the vector fluid of several degrees, the measured efficiency curve suffers from such results. The temperature gradient comes out from the geometry of the tube, the material used, the vector fluid and fluid dynamic applied to the circuit.

Another problem is the convection heat transferred from the copper tube to the fluid, in our case water. A laminar flow with low Reynolds number involves a low heat transfer coefficient and the increasing of the temperature gradient between the cermet and the fluid at the steady state. For example, for a commercial sample reported in the Figure 2, the vector fluid, water, flows in a copper tube with internal diameter of 6 mm at the average velocity of 0,056 m/s. At a temperature of 70°C it has a Reynolds number of 815, sign for a laminar flow. The calculated heat transfer coefficient, based on Nusselt number obtained from the Bohm expression, becomes 92,50 (W/m2-K). Such value may be critical in the convection from the cermet to the fluid.

2. Modelling

2.1. Real case modelling

To have a more accurate analysis of the previous model description, it has been simulated a partial three-dimensional model of a real evacuated solar tube with some initial hypothesis and some approximations:

• 313 K temperature on the vector fluid at the inlet;

• modelization of a partial section of the tube (20 cm);

• air layer between the glass and the aluminium profile;

• the influence of the air layer with different thicknesses;

• approximated model with no computation for the external borosilicate glass tube and the evacuated area;

• the Multiphysic analysis combining heat transfer (conduction and convection) and fluid dynamic (incompressible Navier-Stokes).

The solar tube have been modelled correlating the heat transfer to the fluid dynamic. Fluid dynamic models only the vector fluid, in our case water. Heat transfer works on all the layers and calculate conduction and convection phenomena.

The relation assumes that mass is always conserved, which means that density and velocity must be related through:

(8)

The FE modelling uses Fourier’s law of conduction which states that the conductive heat flux, q, is proportional to temperature gradient:

(9)

Not considering the viscous heating and pressure work, the heat equation can be derived in a more similar form:

(10)

When only the conduction heat transfer in solid material is active in the modelling, the convective term рС? лі * Vr is equal to zero.

In the modelling it has been considered the inward heat flux in the cermet surface:

(11)

The modelling has reported the following results in terms of data, for the model of 20 cm in length:

• net heat flux: 9,1 W

• temperature gradient between income and outcome of the vector fluid: 3,25 K

• cermet Average Temperature: 315,6 K

•

temperature gradient between the cermet layer and the outward vector fluid flow (average

The sensitivity analysis methods briefly described above are applied to analysis of two solar heating systems.

In Fig. 2, a schematic layout is shown of the reference solar combisystem of Task 32. Besides the collector and storage tank, it has also an auxiliary heating loop with heated volume inside the tank. The weather data for Zurich (Switzerland) were taken for simulation and the time resolution was 3 minutes. The influence of a few design and operation parameters is investigated by the FAST algorithm.

This system is an example of planning case, when all design and operational parameters can be chosen for sensitive analysis and consequent optimization. The methodological approach would be first to apply the Morris method and then FAST for more accurate estimation of the parameters influence.