Selection of parameters and their levels

Selection of parameters and their levels

The perforated collector

The perforated collector was designed for vertical installation and includes the absorber plate itself, the back plate and the insulation layer. The overall size is 1.778 m × 0.60 m × 0.15 m,based on the work of Kutscher (1992). Air is drawn through a horizontal slot on the back plate into a duct in which the mass flow rate is measured. The external surface of the collector (the absorber plate) is made of galvanized steel 0.635 cm thick. The rear portion, the bottom, the top, and the sides of the apparatus are insulated with 38 mm of polystyrene foam. The overall thermal resistance is estimated at 1.2 m2 °C/W. The whole apparatus is fastened to a wooden base designed for positioning and moving the collector while ensuring stability.
With respect to former studies (Kutscher, 1992; Van Decker, Hollands and Brunger, 2001), a triangular (staggered) pattern was chosen for the perforations, with a 24.5 mm pitch (shortest distance between two adjacent holes). Three different galvanized steel absorbers were used, the first coated with non-reflective commercially available black paint, the second with Thurmalox® 250 selective black coating (Dampney), and the third left untreated.

The ventilation system (air collection and exhaust)

The plenum thickness was 15 cm and a 75.5 L/s (160 cfm) axial inline duct ventilator (DB206) was used (Sodha and Chandra, 1994). The ventilator creates a negative pressure in the plenum, drawing heated air through the perforations at a known rate. A variable drive (3PN116B, 110/120 V, 60Hz) ensured proper fan control. An exhaust pipe (15 cm diameter, 1.5 m length) was added to remove the heat from the unit to avoid any thermal perturbation during the experiments.

The radiative heat source (solar simulator)

Xenon long-arc lamps initially selected for their spectrum close to that of the sun would have required significant modification to laboratory security and air conditioning systems and were therefore abandoned in favour of conventional halogen lamps producing an irradiation between 300 and 700 W/m2. The irradiation source thus consisted of a light projector fitted with 27 T3/J-TYPE/78mm 150W halogen bulbs collectively providing a total radiative intensity of 4.08 kW. These provided a spectrum close to that of a black body at 3500 K.
Some parameters require a high level of instrument precision, while others require certain care with respect to measures concerning the installation and location of the UTC system.
The European standard described by the CSTB (Norme européenne, 2006) was observed to ensure proper installation of our apparatus.

Instrumentation

The instrumentation allowed us to measure the total hemispherical irradiation received by the absorber plate (GT), the relevant temperatures (Tamb, Tabs, Tout), and the mass flow rate (ṁ) at the ventilation duct exit.

Irradiation

A Kipp&Zonen CMP11 pyranometer with a 32-junction thermopile was used to evaluate the irradiation provided by the lamps. This pyranometer, with a normal sensitivity of 9.17 μV/(W/m²), may be used either with a multimeter or a data acquisition system. It is a class 1 instrument according to the WMO (ISO 9060). The irradiance value (GT) can be calculated simply by dividing the output signal (Uemf) of the pyranometer by its sensitivity. The uncertainty of this measurement is taken as ΔGT/GT = 0.01.

Mass flow rate

Hot wire anemometry (TSI, Velocicalc 8347) was used to measure air velocity. This very sensitive probe for both temperature and velocity allows measurements in the range of 0 m/s to 30 m/s, with a reading uncertainty of 3% or ±0.015 m/s, whichever is greater. The typical measured velocity was about 2 m/s for the maximum pressure drop. To obtain the mass flow rate, the mean velocity V in the fully developed region of the exhaust pipe was determined from the average velocities measured at the pipe axis and several the points located between the pipe axis and the solid surface. The mean velocity was then multiplied by the air density ρair at Tout and by the cross sectional area Acs. Since the flow was fully turbulent, the velocity profile was fairly flat across the pipe section.
The uncertainty of these measurements is taken as ΔV/V= 0.03. The uncertainty for ρair is assumed to be Δρair /ρair = 0.02 and that of the surface area is ΔAcs/Acs = 0.01 for a total uncertainty of the mass flow rate equal to Δṁ/ṁ = 0.04.

Temperature

Three types of temperature measurement were made: ambient air temperature Tamb, outlet air temperature Tout, and absorber surface temperature Tabs. For each case, the temperature was measured with 29 K-type calibrated thermocouples. The uncertainty of this measurement is ΔT/T = 0.02. Calibration was carried out in the 0–50°C range. To measure Tabs, 24 thermocouples were bonded to the inner surface of the absorber plate at equal distances from each other (to verify the isothermal assumption). A single thermocouple in front of the unit (shielded from the lamps) was used to measure Tamb while another behind the unit indicated whether or not this measurement was biased by radiative flux. Two other probes measured the exhaust temperature before the fan (Tout) and in the fully-developed downstream exhaust zone (to estimate air density). Another probe was located in the laboratory far from the apparatus and a final probe was positioned just outside the exhaust. A complete view is given in (Badache, 2010).

Analysis of the experimental plan

Since one of the aims of this study was to establish a relationship between the four control parameters and the response of the system (ηcoll), a second-order model that takes into account the main effects of factors and their two-factor interactions was chosen. This model can be expressed as follows:

Model quality

The overall predictive capability of a second-order model is commonly defined in terms of the coefficient of determination (R2), which indicates the proportion of the total variance that is explained by the model. The coefficient of determination ranges from 0 to 1, a value approaching 1 implying that the regression model performs well. However, one must bear in mind that R2 is not by itself a complete measurement of model accuracy (Myers, Montgomery and Anderson-Cook, 2009). Checking the validity and the adequacy of the bestfit model using diagnostic tests should be done as well. The R2 value obtained for the efficiency of the UTC was 0.9547, meaning that 95.47% of the variance is explained by the model.

Adjustments to the model

Since the model initially contains significant and non-significant terms, it can be adjusted by eliminating the non-significant terms. Draper (1998) suggested that full quadratic models should be used even if some terms are insignificant, because certain statistical properties are valid only in the full quadratic case. Myers, Montgomery and Anderson-Cook (2009) argue that reduced models containing only significant terms should be employed, especially when the goal is to find the optimal settings of major factors.
The Pareto chart in Figure 2.5 shows all of the parameter effects and their interactions in decreasing order of importance. This figure uses a vertical line to determine which effects are statistically significant. The length of each bar is proportional to the value of the statistic calculated for the associated effect. Any bars beyond the vertical line are statistically significant at the selected level of significance. The (+) sign indicates a positive contribution of the effect, while the (-) sign indicates a negative contribution. In the present case, there are three main effects (A: Absorber coating, D: Flow rate, and C: Irradiation) and four significant interactions (AA, AD, AC, and DD).

Model validation

The modeling step (next to last in Figure 2.2) is concluded by validation using standard statistical tests such as residuals analysis, analysis of variance (ANOVA), Student’s test or Fisher’s test (Vigier, 1988). The results of the analysis of variance performed for the efficiency of the UTC (with a threshold of 95%) are presented in Table 2.2 for the significant parameters only. In this table, the first column is the source of the variance of the investigated or desired output ηcoll, the second column is the treatment sum of squares of the parameter’s influence (SST), the third column shows degrees of freedom (Df), the fourth column is the mean square (column 2 divided by column 3), the fifth column shows the Fisher ratio (F-ratio) and the last column gives the P-value, here with a significance threshold of 0.05 (Vigier, 1988).
This analysis decomposes the variance of the response variable (ηcoll) among the different factors. The values of SST and SSR (residual sum of squares) indicate whether the observed difference between treatments is real or simply experimental error. A treatment effect is significant if it exceeds the experimental error to a sufficient extent. In the present case, error (SSR = 4298.86) represents 5.7% of the total variance of efficiency (SSTo = 74208.30), while 94.3% of the total variance is due to treatment effects, with less than 5% probability that this distribution of variance is due to chance. This means that absorber coating, irradiation, airflow rate plus the absorber coating × flow and absorber coating × irradiation interactions are responsible for 94.3% of the variance of the response function ηcoll in this experiment. This confirms our initial interpretation of the effects given by the Pareto chart (Figure 2.5).
Residuals are estimates of experimental errors obtained by subtracting the measured responses from the predicted responses. They can be thought of as elements of variance that are unexplained by the fitted model. In this analysis, we verify the three basic conditions (Wu and Hamada, 2009), namely independence of residuals, homogeneity of variances, and normality of residuals

Table des matières

REMERCIEMENTS
TABLE DES MATIÈRES
LISTE DES ABRÉVIATIONS, SIGLES ET ACRONYMES
LISTE DES SYMBOLES ET UNITÉS DE MESURE
INTRODUCTION
0.1 Contexte
0.1.1 Constat environnemental
0.1.2 Constats énergétiques
0.2 Mesure de réduction des émissions de GES
0.2.1 Énergie solaire
0.3 Les systèmes de chauffage solaire de l’air à perforations
0.3.1 Description des UTCs et TTCs
0.3.2 Performances des UTCs et TTCs
0.4 Problématique
0.5 Objectifs et méthodologie
0.6 Contenu de la thèse
CHAPITRE 1 REVUE BIBLIOGRAPHIQUE
1.1 Introduction
1.2 Synthèse bibliographique sur les UTCs
1.2.1 Résumé des études théoriques
1.2.2 Résumé des études de modélisation numérique
1.2.3 Résumé des études expérimentales
1.2.4 Résumé des études d’implantations et d’applications
1.3 Revue bibliographique sur les TTCs
CHAPITRE 2 A FULL 34 FACTORIAL EXPERIMENT FOR OPTIMIZING THE EFFICIENCY OF AN UNGLAZED TRANSPIRED SOLAR COLLECTOR PROTOTYPE
2.1 Introduction
2.1.1 Solar heat recovery
2.1.2 A brief review of unglazed transpired collectors
2.1.3 The need for an experimental design methodology
2.2 The design-of-experiments method applied to a specific UTC
2.2.1 Objective
2.2.2 Principle of the design-of-experiments method
2.2.3 The design-of-experiments method applied to a specific UTC
2.3 Experimental apparatus
2.3.1 The perforated collector
2.3.2 The ventilation system (air collection and exhaust)
2.3.3 The radiative heat source (solar simulator)
2.3.4 Instrumentation
2.3.5 Irradiation
2.3.6 Mass flow rate
2.3.7 Temperature
2.4 Analysis of the experimental plan
2.4.1 Model quality
2.4.2 Adjustments to the model
2.4.3 Model validation
2.5 Results and discussion
2.6 Efficiency optimization
2.7 Conclusion
CHAPITRE 3 EXPERIMENTAL AND NUMERICAL SIMULATION OF A TWODIMENSIONAL UNGLAZED TRANSPIRED SOLAR AIR COLLECTOR
3.1 Introduction
3.1.1 Literature review
3.2 Experimental setup and test procedure
3.2.1 Experimental set-up
3.2.2 Test procedure
3.3 Numerical method
3.3.1 Physical Problem
3.3.2 Turbulence modeling
3.3.3 Mesh design and boundary conditions
3.3.4 Numerical methodology and grid independence study
3.4 Results
3.4.1 Comparison with experimental results
3.4.2 Effect of mass fluxes
3.4.3 Effect of irradiance
3.4.4 Effect of plenum thickness
3.5 Conclusion
3.5.1 Research outcome (summary)
3.5.2 Experiments and simulations
3.5.3 Upcoming work
CHAPITRE 4 AN EXPERIMENTAL INVESTIGATION A TWO-DIMENSIONAL PROTOTYPE OF A TRANSPARENT TRANSPIRED COLLECTOR
4.1 Introduction
4.1.1 A new type of collector
4.1.2 A transparent cover
4.1.3 The performance of a TTC
4.2 Design of Experiment (DoE)
4.2.1 Selection of parameters and their levels
4.2.2 Planning matrix
4.3 Experimental set-up and procedure
4.3.1 Measurements
4.3.2 Measurements of temperature
4.3.3 Measurements of solar and radiative properties of polycarbonate
4.3.4 Test procedure and initial observations
4.4 Results and discussion
4.4.1 Main factors effects on the efficiency
4.4.2 Interactions between Factors
4.5 Conclusion and recommendation
CHAPITRE 5 SYNTHÈSE ET CONCLUSION
5.1 Synthèse des articles
5.2 Comparison des résultats
5.3 Conclusion générale
5.4 Recommandations
ANNEXE I RÉFÉRENCES DES ARTICLES PUBLIÉS DANS DES COMPTESRENDUS DE CONFÉRENCES AVEC COMITÉ DE LECTURE
ANNEXE II LISTE DES SYSTÈMES D’UTCs INSTALLÉES ENTRE 1990 ET 1997
ANNEXE III MATERIAUX POLYMERES CONDIDAT
BIBLIOGRAPHIE

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