To validate the mathematical model, the store element of the ICS is analysed under two different working conditions. In the first, experimental data from other authors is available??. In the second, numerical solutions from more detailed numerical data (i. e. Direct Numerical Simulation, DNS) have been obtained in order to compare them with the solutions of the model here presented.

Case A. Constant heat flux problem.

The experimental test defined in [8] is reproduced numerically. The store element has a length of L = 154 cm and a width of cm. Heat losses through the sides of the

store are set to Ut = 0 and Ut = 0.375. Ambient and initial temperature are set at T0=7)=13

0C. At the beginning of the test, the water is at rest with a uniform temperature T*. The test consist of applying a constant uniform net solar irradiance of Gt-Gtrc/= 603.2 W/rri2 on the absorber. In the experiment, the absorber is modelled by means of electrical resistances. Experimental data is provided for the distribution of temperatures in the ж direction halfway the width of the store (i. e. y=4.05 cm) after 225 min of heating process.

To perform the numerical simulations, the second level of refinement (n = 10) is consid­ered. The time-step has been fixed to 2 seconds.

In Figure 2 numerical results are compared with experimental data. A general agreement is observed.

Case B. 450-Inclined differentially heated cavity problem.

A differentially heated cavity problem with water (Pr = 7.0), an inclination of 45° with respect to horizontal and an aspect ratio of L/W=A=10 is modelled both with the model here presented on five different levels of refinement, n=5, 10, 20, 40 and 80 and with a detailed numerical simulation (DNS). To do so, boundary conditions at the front and back plates have been changed from those described in the definition of the problem: the absorber and back plate surfaces are set at a uniform temperature (Dirichlet boundary condition) of To()S=80 0C and ТЬаск=20 0C, resulting into a Rayleigh number of, according

to the standard definition of Да for this kind of problems. Other sides are assumed adiabatic. Initially the fluid is considered at rest at 20 0C. And the transient evolution of the heat transfer and fluid flow is evaluated until the steady-state (or a steady-oscillating-state) is reached.

The goal of this study is to show the capacity of the numerical model here presented to simulate the water store in extreme working conditions.

Numerical solutions are compared to detailed numerical data from a Direct Numerical Simulation, where no assumptions of laminar flow are made. This DNS results are to be considered as the highest possible level of modelling, and are here taken as the reference solution (“real” solution) to see how far are the solutions of the numerical laminar model from reality. DNS results were obtained from a code developed in the Centre Tecnologic de Transferencia de Calor. In this code, the spatial discretization is carried out using a staggered mesh [4], and a spectro-consistent second-order scheme [10]. In this way the global kinetic-energy balance is exactly satisfied even for coarse meshes. For the tempo­ral discretization, a central difference scheme is used for the time derivative term and a fully explicit second-order Adams-Bashforth scheme for convection, diffusion and body force terms. An implicit first-order Euler scheme is employed for the pressure gradient term and the mass conservation equation. For more details see [9]. The computational domain is

discretized with 400 * 160 CVs. The mesh is also intensified at the walls along y-direction with a concentration factor of 1.0.

In figure 3, time averaged Nusselt and temperature profiles of the DNS are compared to instantaneous data obtained for three levels of refinement {n = 10, 20, 40) when the problem has reached a quasi-steady-state solution ( non-dimensional time 10^4). Good agreement is observed when the level of refinement is higher than.

This agreement is also observed in the mean Nusselt numbers (see table 3). The same agreement has been observed when comparing the solutions of the velocity fields.

Figure 3: Validation. Case B. Inclined differentially heated cavity problem. Numerical results for different levels of refinement (n=10, 20, 40) vs DNS data. (a) Nusselt at the cold wall. (b) Non-dimensional temperature profile aty=W/2.

Conclusions

Numerical methods on heat transfer and fluid flow have been consolidated during the last decades as an indispensable tool for the resolution of thermal and mechanical problems, being nowadays an essential complement to the experimental studies. These methods solve the multidimensional equations governing the fluid flow and heat transfer by converting them into a set of algebraic equations which are to be solved by means of some kind solver. In order to assess that the numerical solution is an appropriate solution of the mathematical
model, a large number of equations may be required (large number of CV), resulting in very large and time consuming calculations. However, and due to the huge recent improvement in the computation capacities and on the improvement of the numerical methods, nowadays is already possible to apply this kind of methods to solve problems of engineering interest.

This work has described a numerical model that solves the two-dimensional Navier — Stokes equations together with the energy equation in order to predict the heat transfer and fluid flow in a rectangular water store of a integrated collector storage system. With this model is possible to obtain a prediction of the behaviour of the store exposed to real outdoor weather data during 24 hours, only just with a few hours of computation (about 12 hours) on a standard personal computer.

Results have been presented in order to show that the numerical solutions obtained by the model are an appropriate approximation of the mathematical model used (verification), and in order to demonstrate that the numerical solutions fit with results obtained from exper­iments and from highest level simulation techniques (validation).

Acknowledgments

This work has been funded in part by The European Commission under the “Energy, Environment and Sustainable Development” Programme, Framework Programm V, 1998­2002, project contract number CRAFT-1999-70604.

[1]

A schematic of the problem under study is shown in Fig. 1a. It consists of an air cavity that can be vertical or inclined, bounded by two isothermal walls (top and bottom) and remaining walls adiabatic. The cavity length varies from L=0.5m to L=3m and the inter-wall spacing can vary from b=0.01m to b=0.05m, leading to aspect ratios of 10 to 300. The depth of the cavity varies from w=0.5m to w=2m. The inclination of the cavity 0 with respect to the horizontal goes from 0 =0 degrees ( heated from below) to 0 =90 degrees(heated from side). The hot wall temperature goes from Tft=0°C to Tft= 300°C. The temperature difference between the hot and the cold walls goes from 20°C to 200°C provided >0.

The Nusselt number in these problems is defined in terms of the inter-wall spacing, as follows:

firef

where, q= heat flux passing from the hot wall to the cold wall.

=heat flux assuming only conduction between the hot and cold walls with conductivity at the mean temperature.

_ (Th — Tc) * Xref

Figure 1: Schematic (a): The air layer between hot and cold surfaces, with other faces adiabatic, (b): mesh utilized, solid triangles indicate intensification at the boundaries, mesh not shown in the third direction.

The daily needs of drinking water for the staff could be estimated at V4=80 litres/day. For producing the necessary drinking water a solar experimental still from the West University in Timisoara could be used, [7]. The still is supplying roughly V5=4l water per day. The solar energy converted into heat and used for water evacuation at the temperature of 540C is Q3=mAev (Aev is a latent heat of evaporation; at t=540C we have Aev=2.372 MJ/kg and Q3=9.5MJ/m2*day). The drinking water could be obtained by 5 solar stills, each with an area of 4m2. In the collecting ponds of water there is a layer of finely crushed rock of marble for water mineralization. The solar stills are installed either on the ground, or on the building porch.

Indoor illumination

The light has to be distributed equally in the lair and the illumination level, E is in the range from 5 to 60 lx. The electrical energy used by the light bulbs is from 9 to 16 kJ/m2*hour. Fluorescent lamps can give the same light as a 40W bulb; such a lamp could cover an area of 5m2. Taking into account that the total surface of the lair is of 500m2, 100 fluorescent lamps would be necessary to cover this surface. The total installed power could be 100*8W=800W (maximum value to be considered would be 1kW), [8] ,[9], [10]. The average time estimated for the daily illumination of the lair is of 4h. The average daily energy consumption could be estimated as: 100 lamps * 8W *4h/day = 3.2 kWh/day.

If we choose Siemens PV modules (12 Vdc, 53Wp), the total number of such units to be used for the lair illumination is 18.

For sizing the storage batteries, we would consider: an autonomy of 2 days, battery voltage 24Vdc, discharging coefficient Kd=0.3. The capacity of the batteries would be Cb=3200Wh/day * 2 days/ 24 Vdc * 0.3=888Ah.

The selected inverter would have the following characteristics: 24Vdc/220Vc. a, 1.2K, efficiency 0.85%.

The charge controller will have the following characteristics: 24Vdc, 40A.

The annual energy consumption in Vietnam for 1990 was about 4.623 million tones of oil equivalent. This corresponds to an annual consumption of 70 kgoe per capita (.e., about 1667 MJ per capita), which was one of the lowest energy consumption per capita values in the world [2]. The percentage contributions of commercial forms of energy used in Vietnam in 1990 are shown in Fig 3. The breakdown of energy consumption in the various sectors is illustrated in Fig.4. In the domestic sector, the patterns of consumption are shown in Fig. 5. In this sector, 51% of energy is consumed for cooking, while the remaining 49% is divided between lighting and electrical appliances, including electrical water heaters. Electricity contributes 23% of the energy used in cooking and 55% of that in lighting and other electrical appliances.

However, the pattern of energy consumption in the domestic sector is changing dramatically. Coal is being replaced by natural gas for cooking in cities; the level of consumption for lighting and electrical appliances is increasing; and the demand for hot water and space conditioning is also increasing in the main cities. Figure 6 shows the pattern of energy consumption in a typical middle-income household in Hochiminh city [2].

Furthermore, the number of electrical hot water systems imported into Vietnam is increasing significantly. For instance, in Hochiminh city alone, for the first nine months of 1996, the number of imported electrical hot water systems with storage tank capacity ranging from 30 litres to 50 litres averaged 960 units per month [3]. This means that every month, the potential peak electricity demand on the grid system in this city alone increased approximately 1440 kW due to the installation of these hot water systems.

The above analysis indicates that if the Vietnamese government does not have a wise strategy to correct the trend of electrical water heating use, this could become an increasing burden on the already inadequate electricity supply in the coming years.

With the advantage of plentiful solar radiation, the introduction of solar water heaters could be part of the solution to this problem.

The analysis of monitoring results for the different parameters under study in the ASD prototype, allowed the identification of two main differences between monitoring and simulation results:

• volumetric airflow within the ASD was lower than the predicted;

• air flow velocities over brine surface were much lower than expected average values.

Such differences where evaluated under two different and complementary approaches:

• air flow differences seemed to imply much larger head losses in the prototype than those assumed for the numerical model calculations;

• lower airflow velocities over brine surface really mean a certain velocity profile between the brine surface and the evaporation channel cover, which must be taken properly into account.

Results for air average velocity in the solar chimney from ASD prototype monitoring and numerical simulation, for the first 12 day monitoring period, are presented in Fig.4.1:

From the graphic in Fig.4.1 it is possible to see that the observed and simulated results for air flow average velocity are in phase, validating the comment above about the numerical model underestimation of head losses in the ASD prototype (instead of an error in the calculation of air flow motion driving force) according to [2].

A correction of the head loss calculation was made after analysis of ASD monitoring results of average air flow velocity in the Solar Chimney section for different driving force conditions (the driving force was calculated after numerical model presented in [2], for the observed climate conditions), after Fig.4.2, with all the data collected over an extended 30 days period:

Given that ASD inner air flow velocity is such that head loss equals available driving force, correction in the numerical model of the average air flow velocity calculation (in the chimney section and, consequently, in the evaporation section), was made with the equation below representing the solid line in Fig.4.2:

Uchim =V 0.05 + 0.3DF (1)

where DF stands for driving force, in [Pa], in line with the quadratic evolution of head loss with velocity.

Results for the observed air flow velocity over the brine surface (30 cm above it) and average airflow velocity in the same evaporation channel section (corrected from the average air flow velocity in the chimney section) were previously presented in Fig.3.4. Those results clearly show that, instead of a uniform velocity profile with convection occurring at an average airflow velocity, as assumed in the original numerical model, a more complex velocity profile occurs over the brine surface, with lower velocities around the interface region brine/airflow.

In order to include such airflow dynamics in the calculation of the evaporation rate, a general expression for boundary layer was included, after an estimated evolution throughout the evaporation channel, according to Fig.4.3 (the behaviour considered results also from some qualitative observations made with the injection of smoke):

The average velocity profile is described according to the following expression:

where Uo stands for undisturbed air velocity, y stands for height above brine surface and CH for total channel height. For the average air flow velocity in the evaporator section:

Air flow velocity to convection mass transfer calculation is, then, calculated as a function of the distance from brine surface and average air flow velocity, after (2) and (3):

(4)

Average velocity profiles in the evaporation section, calculated after (4) for different average air flow velocities, are presented In Fig.4.4:

Simulation results for the observed monitoring period, after implementation of these corrections to the model, can be seen in Fig.4.5, for two different representative heights from the brine surface to velocity profile calculations, 40 mm and 50 mm:

This shows that indeed the model, corrected as described, reproduces nicely the observed results. Air flow velocity calculation, for convection mass transfer, at 40 mm above the brine surface seems to fit better the observed evaporation results.

All of this will be further confirmed with more data, coming from the next measuring period It should be noted that this paper is being written according to the deadline of April 1st for its submission. More data is being recorded and, in particular, corresponding to sunnier spring and summer conditions, and will be presented at the Congress in June.

The energy payback time is the period, the system has to be in operation in order to save the amount of primary energy that has been spent for production, operation and maintenance of the system. Based on an overall consideration a system only contributes to the saving of our resources if it is operated longer than its energy payback time.

With regard to the determination of the energy payback time arguments are the same valid as discussed for the cost assessment in the previous section: Concerning the systems with hot water stores the listed energy payback times represent only a rough estimation. For systems based on advanced storage technologies it was not possible to determine reliable values of the energy payback time due to the lack of appropriate data.

5 Conclusions

With regard to systems that achieve fractional energy savings of approximately 50 %, the lowest value of the heat price is found for the reference system with 1 m3 store volume and 35 m2 vacuum tube collector with 0.18 EURO/kWh. Partly more expensive are system designs that lead to the same fractional energy savings by using larger store volumes and smaller collector areas. At present, it is more cost effective to enlarge the collector area instead of an enlargement of the store volume. The reasons for this are the following: On one hand the subsidies that were accounted for the determination of the inexpensive value of the heat price are related to the size of the collector area and not to the store volume. On the other hand collectors are already today produced in large quantities and therefore offered relatively cheap. A totally different situation arises if the store volume is enlarged: Large hot water stores are only produced in small quantities or sometimes even as a custom made product. A consequence of this fact is that a high potential for cost reduction can be realised by using large standardised stores.

With regard to the solar heat prices the presented results showed that even today it is already possible to cover approximately 50 % of the heat demand by solar energy at moderate costs. Depending on the chosen configuration of store volume and collector area or collector type respectively, the resulting heat prices are similar to the ones of typical combisystems already offered on the market /2/. However, the fractional energy savings of these systems only amounts to 20 — 30 %.

The step over the “50 % fractional energy saving borderline” from the solar supported conventional heating system to a fossil supported solar heating system is quite small. The

potential of the environmental benefits of such advanced solar combisystems is shown by the fact that the energy payback times for all investigated systems were significantly below the expected lifetime of the systems.

The cost-effective, efficient and environmentally friendly storage of heat is one of the key technologies for the further development of solar technology. Looking on the current building situation and the amount of buildings that have to be retrofitted, it is obvious that a very large potential market exists for relatively small thermal solar systems.

Due to this facts the IEA (International Energy Agency) established within their Solar Heating and Cooling Program an corresponding working group named Task 32 „Advanced Storage Concepts for Solar Buildings". Within this task European manufacturers and research institutes will work together during the next four years in order to bring storage technology, and in this context also solar technology, at least one important step forward.

Literature:

/1/ H. DrQck, H. Kerskes, W. Heidemann, H. MQller-Steinhagen: Solare Kombianlagen der nachsten Generation — Advanced Solar Combisystems, Tagungsband zum zwolften Symposium Thermische Solarenergie, Seiten 59 — 63, Otti, Regensburg, 2002,

ISBN 3-934681-20-4

/2/ H. DrQck, W. Heidemann, H. MQller-Steinhagen: Comparison Test of Thermal Solar Systems for Domestic Hot Water Preparation and Space Heating, proceedings of EuroSun 2004, to be published

SHAPE * MERGEFORMAT

Assume the case that the measured efficiency ^me is equal to the modeled efficiency ^mo during the whole test, we will get a straight line as presented in Figure

1. This line we call identity line. In the real case (Figure 2 and Figure 3) ^me and ■qmo are different. Measured and modeled efficiency can be determined with their uncertainties for a chosen confidence limit. A confidence limit of 95% is chosen here. Combining the uncertainties of ^me and ^mo we get an uncertainty ellipse for each measuring point. The uncertainty ellipse shows, with a probability of 95%, where the single measuring point can be located. If the uncertainty ellipse has an intersection with the identity line, we assume for this measuring point that the measured efficiency is equal to the modeled efficiency. To prove the value and the confidence limit of the estimated uncertainties, we tested for which percentage of the pairs (measured / modeled efficiency) the uncertainty ellipse (with 95% confidence limit) covers the identity line with:

Л measured = ‘Л modeled (see figure 1).

The intersections of the ellipse were calculated using equation (6).

SHAPE * MERGEFORMAT

SHAPE * MERGEFORMAT

i)MeSP [2] : intersection of the identity line with the elipse

VMe [2]; ЛмОо [2] : pair of the modeled and measured eficieny

UriMfe[i] ; Um [2]: measured and modeled uncertainties of the eficiencies

The modeled uncertainties for the i-th data point were calculated with:

UX1[;]….. UX6[;] : uncertainity of the variables;

UX1[;]….. UX6[;]: uncertainity of the coeficients

The uncertainty of the coefficients is taken from the vector C as discussed above for the WLS method. For the LS method we take the uncertainty of the coefficients from the result of the Excel™ spread sheet program.

We calculated the measured uncertainty for the i-th data point with equation (8).

Um [2]: Uncertainty of the collector power

Ug [2] : Uncertainty of the global radiation Ua [2] : Uncertainty of the collector area

Standard transducer uncertainties as defined by EN 12975 [ 1 ] are used for the calculation of equations (7) and (8).

For about 4,5% with the LS method and for about 7% with the WLS method the uncertainty ellipse does not cover the identity line (expected value is 5%). In the examples discussed here, we tested 134 of the efficiency pairs from one collector test. To get the 95% confidence limit result with both methods, we had to increase the uncertainty of the pyranometer from 10 W/m2 to 10 W/m2 + 1%. This indicates that the estimated uncertainty assumes the same value, with the same confidence limit (95%), with which the uncertainty was calculated using the WLS and the LS methods. The outliner points for the Ls and the WLS methods are indicated in Figure 2 and Figure 3.

The instantaneous efficiency and the incidence angle modifier can represent the thermal performance of the collector.

4.1 INSTANTANEOUS EFFICIENCY

The instantaneous collector efficiency, q,, is a measure of collector performance that is defined as the ratio of the useful gain over some specified time period to the incident solar energy over the same time period [1]:

By introducing the Equation 3.2.5, the instantaneous efficiency becomes [1]

П; = Qu/AcGT = [Fr (та ) — FrUl (T; — T) Gt] (4.1.2)

Where the absorbed energy Sc based on the gross collector area has been replaced by

Sc = Gt (та) (4.1.3)

(та) is the effective transmittance-absorptance product based on the collector gross area. It is defined as:

(та) = SAp / GtAc = (та )avg Ap/Ac (4.1.4)

In Equation 4.1.2, two important parameters, Fr (та) and FrUl, describe how the collector works. Fr (та) indicates how the collector absorbs energy while FrUl is an indication of how energy is lost from the collector.

4.2 INCIDENCE ANGLE MODIFIER

To express the effects of the angle of incidence of the radiation on thermal performance of the flat-plate solar collector, an incidence angle modifier KTa is employed. This describes the dependence of (та ) on the angle of incidence of radiation on the collector. It is defined as [1]:

KTa = (та) /(та)п (4.2.1)

Where subscript n indicates that the transmittance-absorptance product is for the normal incidence of solar radiation.

During operation of real solar thermal systems, the following dynamic processes are relevant.

• Fast fluctuations of irradiance on a time scale of a few minutes,

• fast decreases of the operating temperatures caused by draw-offs (also on a time scale of minutes),

• slow increases of operating temperatures over several hours due to the warming of the contents of the storage tank,

• the switch-on process of the solar circuit pump.

Which value of an effective one-node collector capacity best describes these four processes? Is there a unique value at all for all the processes?

In order to answer these questions, the mentioned processes are (just like the procedures for determination above) analysed qualitatively, based on fundamental physical arguments. Again the dynamic behaviour of Tabs and TF is investigated, as their amplitudes correspond with the effective capacity (see also figure 2).

Fast fluctuations of irradiance are similar to the processes of the J.3-procedure. Consequently, for the amplitudes ATabs >> ATF holds. A high effective thermal capacity best describes the process.

After a draw-off during collector operation, Tabs and TF decrease. As at the same time the collector performance will increase slightly (as the point of operation on the collector
efficiency curve is shifted to the left), Tabs-TF also increases, and hence the amplitude ATabs will be smaller or almost equal to ATF; so the result is ATabs < ATF. This process is best described by a low effective capacity.

When the storage tank is charged, all the system temperatures (including Tabs and TF) will slowly rise. The relation between ATabs and ATF depends on the (slow) dynamics of the irradiance G. If G is more or less constant or decreases, the collector thermal performance will slowly decrease, and ATabs < ATF holds. For increasing irradiance, the amplitudes will be similar: ATabs « ATF. Hence the corresponding effective capacity is low.

The switch-on process shows parallels with the draw-off, since colder fluid suddenly enters the collector. Again the result is ATabs < ATF, and the best suiting effective capacity is low.

The simulation code has allowed to estimate, in transient condition, the performances of the system including solar collectors — tank — building to be heated. Table V shows for each localities and for each system configuration the quantities concerning the period of heating: incident solar energy, energy supplied to the building and for domestic hot water, solar fraction of the system (ratio of the energy supplied by the tank to seasonal requirement) and eventually the system efficiency (ratio of the energy supplied by the system to solar incident energy on the tilted plane); DHW annual energy and annual solar fraction are also reported in the tables. In the period in which building heating is not expected, domestic hot water requirement is completely satisfied, while in the ramaining period of the year an DHW fraction depending on collectors’ surface and tank’s storage volume takes place. Annual solar fractions calculated vary between 30 % and 72% for Cosenza, between 25% and 68% for Rome and between 14% and 41% for Milan.

Figures 4, 5 and 6, each refered to one locality, show the solar fraction and system efficiency values, in ralation to the variation of the collector’s surface and at the different storage volumes. These data only concern the period of heating. Solar fraction grows at increasing of storage volume. The four curves, each referring to a different tank storage volume, have the same solar fraction for collectors’ surface of 4 m2. The bigger the surface, the more the curves are different from each other. A value of solar fraction
variable between 12% and 62% for Cosenza and Rome and between 7% and 36% for Milan has been found. The benefit produced by the increment of storage volume increases with the growing of the collectors’ surface. Figures also show a diminuition of the efficiency of the whole system with the growth of collectors’ surface; for S=4 m2 it evaluates 55% for Cosenza, 42% for Rome, 45 % for Milan. While for, S=28 m2, it assumes a value between 28% and 36% for Cosenza, 23 and 29% for Rome and 30 and 35% for Milan. The more the storage volume increases, the more the system is efficient, both because of the better collection efficiency, as a consequence of a lower mean temperature of the tanking water; and for the smaller frequency with which the maximum temperature in the tank is touched. Even though among the three localities there is a difference in value of solar fraction and efficiency of the system, seasonal energy supplied only for building heating is not so different instead, because of the different period of heating. As example Figure 7 shows the energy supplied to the building for a storage volume 2m3 ; the best performance takes place in Rome. With a 28 m2 collector’s surface it can supply 16.7 GJ, followed by Cosenza with 15.5 GJ and Milan with 13.8 GJ.