A set of solutions of a reference case which will be called as “one day outdoor test” have been obtained in order to investigate the sensitivity of the numerical solutions on the temporal and spatial discretization adopted.

In the “one day outdoor test” the the ICS is exposed to outdoor sunny weather conditions during 24 hours without draw off. The simulation starts at 6 am (solar time) with the ICSs at an initial and homogeneous temperature jH; indicated by the user. Main features of the test are:

Transient effects are considered.

A constant ambient temperature of Ta = 20°С is assumed during all the day.

A daily solar irradiance in the collector plane of Я( = 25000kJ/m2 is assumed. Sunrise and sunset are set at 6 am and 6 pm. is assumed normal beam radiation, and is distributed during the day according to standard radiation correlations [2].

Among others values that can be obtained from the test, the following will be commented:

• Temperatures: T„: ambient temperature; Тет: average temperature of the water in the store; To()S: average temperature in the absorbing surface; : average temperature in the back surface; Tt: average temperatures in the top surface; and T6: average temperature in the bottom surface.

• Terms of the energy balance

(9)

where Eas is the accumulated energy by sensible heat at the water store, and Qt and Qi are respectively the thermal losses through the front surface (cover) of the store and through the other surfaces of the store respectively.

With the daily integrated values of the terms of the energy balance, the daily efficiency can be calculated as the ratio between the accumulated energy at the end of the day and the daily solar irradiance Я(.

In the results reported in this subsection the following data has been adopted: Я(= 25.000 ;Ta= = C; =1.8 and [/«=0.6387 W/mK. The store has a length (L)

of 1000 mm and a width ( ) of 100 mm.

A set of solutions of the “one day outdoor test” has been obtained varying the temporal and spatial discretization following an h-refinement procedure, that is, all other numerical parameters (numerical scheme, convergence criteria..) are fixed, and the mesh (spatial or temporal) are intensified. The study of temporal and spatial discretization was decoupled. Firstly the time step was fixed and the mesh was progressively refined. Once the spatial discretization was selected, the influence of the temporal discretization was analysed. The mesh was fixed and the time-step refined.

In the first step, three levels of refinement were considered (n = 5,10,20). Calculated values of the terms of the energy balance 9 are presented in Table 1. They are given integrated over the day and normalised with the daily solar irradiance Я(. As it can be seen, while for all levels of refinement the integrated terms of the energy equation obtained are almost the same, some differences appear in the maximum temperatures achieved during

the simulation. These differences are less important for the second and third levels of mesh refinement, n=10 and 20.

The computational time (CPU time) to perform the numerical simulations for the three levels of refinement was respectively: 39, 152 and 851 minutes in a AMD K7 2600 MHz processor.

Due to the level of accuracy obtained and the computational costs commented above, the second level of refinement was selected to analyse the influence of the temporal discretiza­tion. Three time-steps were taken into account (At= 1, 2, and 4 seconds). Results of this verification analysis is presented in table 2. As observed, while almost no differences ex­ist between results considering time-steps of 1 or 2 seconds, important disagreements are obtained when a time-step of 4 seconds is used.

R. Damle, J. Cadafalch, R. Consul, and A. Oliva

Centre TecnOlogic de Transferencia de Calor (CTTC)
Lab. de Termotecnia i Energetica
Universitat Politecnica de Catalunya (UPC)
labtie@labtie. mmt. upc. es, www. cttc. upc. edu

Finite volume numerical computations have been carried out in order to study the free convective heat transfer in differentially heated inclined air cavities. The air cavity inclination was varied from 0 =0 degrees ( heated from below) to 0 =90 degrees(heated from side) for aspect ratios of 10 to 300. Both two-dimensional and three-dimensional solutions have been obtained and compared with the literature.

Introduction

Natural convection in inclined differentially heated cavities is a subject of major interest and has been widely studied by many authors. Comprehensive review of both experimental and theoretical studies have been given by Ayyaswamy[6], and Hart[7]. Experiments on inclined cavities have been reported by Inaba [3]. Catton, Ayyaswamy and Clever[8] used a Galerkin method to investigate natural convection in inclined rectangular region, and there results show a pronounced aspect ratio dependency on the Nusselt number. The experimental cor­relation for natural convection in rectangular cavities by Hollands[1] gives Nusselt number for large aspect ratios for angles of inclination between 30 and 60 degrees.

Long inclined differentially heated cavities are frequently encountered in solar applications. Often these rectangular cavities have high aspect ratio with the length varying from 0.5m to 3m, finite depth varying from 0.5m to 2m or even larger and thicknesses from 10mm to 50 mm. The temperatures could range from ambient to about 300°C in such applications. More­over they are oriented at different angles of inclination to the horizontal. The heat transfer by natural convection then depends on parameters like the aspect ratio, inclination, temper­ature differences etc. A correlation of Nusselt number for all situations mentioned above for such rectangular cavities is not available currently and would be desirable.

The authors are carrying out numerical studies in order to develop a general correlation for convective heat transfer which would be applicable to most of the situations encountered in solar applications. For obtaining such a correlation, finite volume technique is being em­ployed to model the heat transfer and fluid flow in differentially heated inclined rectangular cavities. Different meshes, numerical schemes and convergence criteria are being worked out to find most appropriate numerical model, the solution to which would lead to a Nusselt number correlation over a wider range. The work presented here is a part of the numerical studies that have been conducted and the models that have been worked out. The solutions undergo a verification process with the post processing tool based on the Richardson ex­trapolation theory and on the grid convergence index (GCI) that estimates their uncertainty due to discretization[4][5].

Figure 1 Lair for 100 calves in South-Western part of Romania

For standard buildings in stock raising (see Figure 1), heat per time for temperature maintenance in a lair for 100 calves at Tin=160C is Qx = 5070W, [1]. The flow rate of warm air is m = 715kg/h. Warm air is supplied by air flat plane solar collectors and the temperature of the air entering the solar collectors is equal to the outdoor temperature (t1=te ).In this way the possibility of indoor air spoiling is eliminated. Warm air at the temperature to is introduced into the lair. The solar collecting surface area could be calculated [2] by:

In equation (1) the meaning of the quantities is:

— K is coefficient of thermal losses

— Cp is isobar specific heat for air

— 0 is equivalent air temperature related to solar radiation and is calculated [3], [4], [5] by:

в = {тОя /K + te (2)

In equation (2) (Ta)e is the effective value of the absorption-transmission product.

For the values GR=385W/m2, K=4.73W/(m2K), to=40oC, te=11.6oC, (та)=0.74, the obtained area is A=32m2. The surface of 32m2 is made up of n=8 solar collectors, each with an area of a=4m2, that means A=na.

The average specific power of the passive wall (Trombe) at delayed heating is roughly qT=52W/m2, [6]. The Trombe wall with an area AT=100m2 can heat the indoor air for four hours after sunset.

Water heating

The water quantity consumed daily in a lair for 100 calves is m=480kg. The required thermal energy for water heating by 15°C is Q2=30.2MJ. For this purpose are used five solar collectors with warm water storage, each supplying 90kg/day heated water.

Air ventilation

The air circulating through the lair towards the outside has to evacuate CO2, biological heat and water vapours. The air flow rate (m3/h) is calculated after the criteria: maximum admitted concentration of CO2, humidity and heat excess. The sanitary norms for stock raising are satisfied if the ventilated air flow rate in warm seasons is V1=9000m3/h and in cold seasons is V2=1500m3/h, [1]. For spring and autumn, the average velocity of the evacuated air is v=0.56m/s, but in summer it could reach 2 to 3m/s. The total area of the transversal surface of ventilation shafts (in m2)

A’=V/(3600v) (3)

For spring and autumn, there results A’=0.74m2.

Ventilation could be ensured by using sections of Trombe walls with a height of h=2.5m arranged on the South wall of the building. Along the Trombe wall the temperature gradient causes a hydrostatic depression which stimulates the air absorption from the inside through the lower skylight and its evacuation through the upper skylight towards the outside. There are eight sections and each section has squared area of side l=0.3m.

In the summer air solar collectors from the roof could fulfil the role of ventilation shafts. The hourly flow rate of the air ventilated through them is V3=4050m3/h.

It is shown that in the warm season 1m2 of solar wall ensures the evacuation from the lair of 400m3 of air per hour, [1]. It means that 10m2 of Trombe wall covered with metallized reflective foil evacuates 4000m3 air per hour.

Dr. Nguyen The Bao

Hochiminh University of Technology, Vietnam.

1. INTRODUCTION

Vietnam is a tropical country, stretching from Latitude 60 N to 230 N. Its land area is around 320,000 km2 and its population is about 78 million, of which 80 % are living in villages in remote rural and mountainous areas.

Due to the complex topography, climate factors, including solar radiation levels, vary significantly from region to region. The annual average daily global radiation values increase from 12 MJ/m2 for northern locations up to 19 MJ/m2 for some southern locations, with the annual average daily sunshine hours varying from 4 to 8, respectively. Figures 1 and 2 show the monthly average daily solar radiation and sunshine hours for 3 locations across the country They are: Lang (210 N); Danang (160 N) and Hochiminh City (10.80 N), and they represent the three general climatic regions in Vietnam [1].

On the basis of these data, Vietnam can be considered as a country having good solar resources and consequently good possibilities for solar energy applications. However, no systematic analysis has been conducted into the application of these technologies in Vietnam. This work will hopefully be one of the first steps in systematically and rigorously researching the feasibility of the application of solar hot water ( SHW ). This work will also assist in assessing the potential of the SHW market in this country for local as well as foreign investors.

Figure 2. Monthly Average Daily Sunshine Hours for three representative locations in

Vietnam

During the first days of testing — reported here — weather conditions were not ideal for high evaporation rates, has can be observed from the observed values for solar radiation, air temperature, relative humidity and wind speed in Figs.3.1 and 3.2:

100 90 80 70 60 50 : 40 30 20 10 0

5.0

4.5

4.0

3.5

3.0

2.5

2.0

1.5

1.0 0.5 0.0

This first set of data was analysed, allowing comparison of evaporation results in the prototype with the predicted ones, after simulation with the numerical model in [2]:

Evaporation results illustrated in Fig.3.1 clearly show that the ingredients in the model clearly overestimate the evaporation that took place.

The air flow within the ASD prototype was monitored after measurement of air velocities in the evaporation section, 30 cm above the brine surface, and solar chimney section, according to the scheme in Fig.2.5. Air flow velocities in those sections over the 12 days monitoring period were in accordance to Fig.3.4:

The assessment of thermal solar systems based on economic aspects is difficult, since the cost effectiveness of this type of systems strongly depends on the development of the fossil fuel prices.

An additional aspect complicating an economic assessment is that the advanced storage technologies are not introduced to the market up to now. But only when a technology is established on the marked and is produced in large quantities the results of an economic analysis are reliable /2/.

Due to this the following cost considerations are limited to system concepts that can be realised with today’s system technology and with the use of water as heat storage medium.

Table 1 shows the solar heat prices for various collector areas and collector types as well as for different store volumes. For each configuration an average and an inexpensive value are given. The average value is determined without taking into account subsidies or self services (e. g. installation by the owner). For the calculation of the inexpensive value these possibilities for saving were taken into account. Additionally discount prices of the components were used.

WLS is a weighted regression method, as the name says. The method is used for collector coefficients and uncertainties calculations. Theoretical background of this method is given by Press [ 3 ]. Compared to LS it has the following advantages:

— the collector coefficients are determined also using the measurement uncertainties of the transducers

— the measurement uncertainty of the transducer can be different in different measurement ranges

— the statistic distribution of the measurement uncertainties doesn’t have to be normally distributed

— measurement uncertainties may be weakly correlated with each other

Equation (2) shows the individual error squares as function of the collector coefficients a1…a6 and the measurement variables Xi…. Хє. Like in the least square method (LS), first this „squares of the deviation between model and measurement” (2) have to be determined also by the WLS. To do this, the variables for the collector model have to be calculated with the data from the measurement

(1) . The initial coefficients could be determined by the LS regression.

In the next step, the uncertainties of all determined error-values Uerror[i] have to be calculated for every 5 min mean value (3). The measurement uncertainty of every variable U^me; Ux1… Ux6 has to be determined with help of the measurement uncertainties of the transducers to calculate the combined uncertainty Uerror (3).

After the squared quotients of the error — and Uerror-values have been determined, the new weighted evaluation function can be implemented (4).

The collector coefficients are varied iteratively by a spreadsheet program (e. g. EXCEL™) in a way that the sum of x2 is minimized. If the uncertainty of the measurements Uerror is very large for one 5 min mean value, the weight or participation of this data point in the regression process is reduced due to the decreased contribution of the respective error value to the overall value of %2 (see equation 4). That works because the %2-value of this data point is lower.

7me[i]: measured efficiency; ^mo[i] = ^: modeled or calculated efficiency;

Gd : beam radiation [w/m2 ] ; Gb : diffuse radiation [w/m2 ] ; Gb = G — Gd Tm : average collector temperature = Tm = (Tin + Tout) / 2 [°Cj; AT = Tm — Ta Ta : ambient temperature; в : incidence angle

Coeficients a1….. a6 obtained from the regression :

1: rj0 = a1 : zero loss efficiency[-],

1 : V0 • b0 = a2 : (b0 : factor to determine the incident angle modifier of the beam irradiance [-]),

2 : r/0 ■ IAMGd = a3 : (IAMGd : incident angle modifier for diffuse radiation [-] )

4: k1 = a4 : heat loss coeficient[W/(m2K)], negative

5: k2 = a5 : heat loss coeficient[W/(m2K)], negative 6: k3 = a6 : coeficient for the thermal capacity [kJ/(m2K)]

(errO[i] )2 =( rime[i] — Vmof )2=(^ V me[i] “Z (Xk[l] ‘ ak )2 j

„2 = у (erroti])2

& (Uerro [i])2

N : quantity of 5 min mean values

Calculation of the collector coefficients uncertainties with WLS-method:

For the determination of the uncertainties of collector coefficients in the framework WLS method the method described by [ 3 ] is applied here. The application of this method for the SST is described by article [ 6 ]; here it is used for the QDT and calculated the uncertainties for the collector coefficients that were determined by the WLS regression. With equation (5) the collector coefficients uncertainties are calculated using the variables Xk(i) from a data set of one collector test and the uncertainties Uerror[i] (3) of each “5 min mean value” from the same data set. The author [ 5 ] shows that C = (AT ■ A) _1 of eqn. (5) yields a 6×6 matrix with squared uncertainties of the free parameters as diagonal elements and the co-variances between the parameters as off-diagonal elements.

n = number of measurement points

To determine the mean temperature of the absorber plate is a complicated function of the conductivity of the material, heat transfer inside of the channels and geometric configuration. To consider these factors along with the energy collected at the
absorber plate and heat loss, the collector efficiency factor and the collector heat removal factor are introduced.

The collector efficiency factor, F, represents the temperature distribution along the absorber plate between channels. This collector efficiency factor F’ is defined in the familiar Hottel-Willier-Bliss model, where

The collector heat removal factor, FR, is the ratio of the actual useful energy gain of a collector to the maximum possible useful gain if the whole collector surface were at the fluid inlet temperature. It is defined as [1]:

Fr = mCp (To — Ti )

Ap [S — Ul’ (Ti — Ta)] (3.2.3)

By introducing the collector heat removal factor and the modified overall heat transfer coefficient into Equation 3.1.1, the actual useful energy gain Qu can be represented as

Qu = Ap Fr [S — Ul’ (Ti — Ta)] + (3.2.4)

Since Sc = S (Ap/ Ac) and Ul’ = Ul(Ac/ Ap) implies equation 3.2.1 can be expressed as

Qu = Ac Fr [Sc — Ul (Ti — Ta)] + (3.2.5)

This allows, the useful energy gain to be calculated as a function of the inlet fluid temperature not the mean plate temperature.

For accurate predictions of collector performance, it is necessary to evaluate properties of the working fluid to calculate the forced convection heat transfer coefficients inside the tubes and the overall loss coefficient. The mean fluid temperature Tfm at which the fluid properties are evaluated can be obtained by [1]:

Tfm = Ti + [(Qu / Ap)/ (Fr Ul’)] ( 1 — F”) (3.2.6)

Where the collector flow factor F” defined as the ratio of FR to F’, is given by

F”= Fr / F’ = (mCp /ApUl’F’) [1 — exp (ApUl’F’/mCp)] (3.2.7)

Equating equations 3.2.4 and 3.2.6 and solving for the mean plate temperature TPM yields:

Tpm = Ti + [(Qu / Ap)/(FR Ul’)] (1- Fr) (3.2.8)

In the following, the procedures mentioned above and their results for the effective capacity are analysed qualitatively. The arguments are based on fundamental physical considerations. In this analysis, the dynamic behaviour of the two nodes absorber (Tabs) and fluid (TF) is investigated. The effective collector capacity is nearly completely determined by the dynamics of these two nodes.

The amplitudes ATabs and ATF of changes of these temperatures in transients between two steady states are regarded. The thermal energy that is needed in the real collector to achieve the temperature steps ATabs and ATF corresponds with the effective capacity to be determined, which is, in the underlying one-node models, the capacity of the fluid node. Hence the larger ATabs in the test procedure, the higher will be the resulting effective capacity.

This becomes clear when regarding figure 1: In all the procedures of determination and in the underlying 1-node model, the energy AEcol needed to raise the fluid temperature by ATf is given by eq. (1). In a 2-node description (which is close to reality), this energy also includes the energy needed to heat up the absorber by the corresponding amplitude ATabs (see eq.(2)). As AEcol must be equal for both cases, eq. (3) follows. From eq. (3) the influence of ATabs on the effective capacity Ccol can be seen directly.

TRNSYS simulation of a standard SDHW system, collector area 5 m2.

SHAPE * MERGEFORMAT

In the following discussion, the fact is made use of that during steady state the difference Tabs — TF is proportional to the collector’s thermal performance.

The procedures, the courses of temperatures, the amplitudes ATabs and ATF and the resulting values of the thermal capacity are shown in figure 2.

In the calculation procedure (clause 6.1.6.2 of EN 12975-2) the weighting factors for fluid and absorber are equal, hence by definition the relation ATabs = ATF holds. The resulting effective capacity is relatively low.

The procedure according to Annex J.2 starts with a steady state where the inlet temperature Tin is equal to the ambient temperature Ta. In a step change, Tin is raised by 10 K. The irradiance G remains zero. So in the new steady state resulting after the temperature step, the heat flux is reversed, compared with normal collector operation: the collector loses heat, and consequently the fluid temperature is higher than the absorber temperature. Hence it follows for the amplitudes of the temperature steps that ATabs < ATF. The resulting effective capacity can be expected to be even lower than the one from the calculation procedure.

The procedure according to Annex J.3 starts with the same steady state as the J.2- procedure. Unlike above, the inlet temperature is kept constant here, and the irradiance is switched from zero to a high level. Here the thermal power of the collector increases from zero to a high value. Consequently, the same is true for the difference Tabs — TF. Hence for the amplitudes the relation ATabs >> ATF follows. A high effective thermal capacity is the result.

Collectors with a relatively low heat transfer coefficient habsF between absorber and fluid, as for example vacuum-tube collectors with a dewar construction, show particularly high values of Tabs-TF and, consequently, very high effective J.3-capacities. (When the irradiance is increased from 0 to 1000 W/m2, increases of ATabs « 30 K and ATF « 8 K can be expected for habsF « 30 W/m2K.)

In the quasi-dynamic collector test, the fluid inlet temperature is kept constant. The only dynamic effect that is taken into account are natural fluctuations of the irradiance. Hence it can be expected that the results for the effective capacity are similar to those of the procedure of Annex J.3.

Solar energy incident on a field of highly efficient plane solar collectors, with orientation towards south, is transferred across the primary circuit into an isolated tank located in the basament of the building with a constant air temperature of 20°C.

The control system actives the flow rate in the primary circuit each time the solar radiation is sufficient to increase tanking water temperature, under the condition that it does not reached the maximum value of 90°C. Storage system has made with an isolated steel tank, whose transmittance value is equal to 0.833 W/m2 K.

Three different types of solar collectors have been considered, each of them being present on Italian market: the first representing the selective plane type (a), the second is a evacuated model (b) and the third is a heat pipe evuacuated model (c).

Fig. 3 shows the expression of the tendency of each collector efficiency,

T — T ^ (T — T )2

m ae I___________ a У m ae /

G ) 2 G

whit G (W/m2) the irradiance, Tm (°C) collectors mean temperature and Tae representing (°C) outside air temperature. Table IV shows the three coefficients a0, a1, a2 appeared in the expression of efficiency of collector (2) and its cost per surface unit.

In order to choose the collector employing in simulations, the system has been simulated, equipped with collector field, the accumulator, radiant floor heating system, the building, with the three collectors to the variation of important parameters such as collectors’ surface and tank’s storage volume. For every configuration the ratio of the collectors’ cost to annual solar energy has been determined. Fig. 3 shows data relative to Milan. The comparison has showed that plane collectors have resulted more convenient, because a lower efficiency is compensated by a lower cost, owing to Italian climatic conditions. Thus the plane selective collectors has been used.

In the period in which building heating is expected, the control system of the secondary circuit, knowing outside air temperature, verifies if thermal level in the tank can provide the energy requirement. In this case it will activate the secondary circuit, that will supply the inlet flow rate to the building at the wished temperature, extracting it from the tank. Flow rate will be otherwise heated by an auxiliary boiler. Regulation of heat transfer fluid temperature in radiant floor is provided by a mixing valve being located on the entrance of each room. By a regulator, the valve is running as above described as to the combined control. A thermostat interrupts the flow rate when the inside air temperature goes above 21 °C. It will be activate again when temperature falls under 19 °C.