Category Archives: Particle Image Velocimetry (PIV)

REGRESSION METHODS FOR THE DETERMINATION OF COLLECTOR COEFICIENTS

The Euronorm [ 1 ] proposes the Multilinear Regression (MLR) for the QDT. The efficiency of the collector is determined by a model containing 6 parameters (1). The six variables of the model have to be determined from the measured data. With the regression, the six collector coefficients can be determined. By minimizing the square errors of the differences between the calculated and the modeled efficiencies of all data pairs the coefficients are determined. As the uncertainties of the primary measurement data (radiation, flow rate, temperatures) join the calculation of the efficiency, a procedure would be useful, which considers appropriate weighting of a data pair in respect to the inherent uncertainty of that data pair.

For example, pyranometers with an offset of approximately 10 W/m2 show a higher relative measuring uncertainty in their lower measurement range than in their upper range. The weighted least square method (WLS) weights “measuring points by lower radiation (<300 W/mF)” less than for higher radiation for the regression process. Articles [ 5 ], [ 6 ] and [ 8 ] show that the MLR regression based on the least square method (LS) is not sufficient enough to determine the collector coefficients with their uncertainties for the SST. This paper shows the advantage of WLS for the QDT. In the following we discuss the different results obtained by the LS and the WLS for the QDT.

01

POLYCARBONATE SOLAR FLAT PLATE COLLECTOR

To reduce costs to a minimum level, making solar systems a viable domestic option, the materials, dimensions, and method of fabrication must be chosen with great care. Therefore, alternative methods of construction need to be looked into.

A typical flat plate collector is made from a number of parts. To simplify the construction and reduce costs an extruded polycarbonate structure is to be incorporated into the design of the flat plate collector. The purpose of the extruded triple walled polycarbonate construction is to substitute for both the glass cover and the absorber plate. Figure 3.1.1, shows a section of the extruded polycarbonate panel.

Both types of thermal collector configurations being looked at in this study are shown as a section in figure

3.1.2 and 3.1.3. Figure 3.1.2 shows the set up of the collector with a black — coated backing between the insulation and the polycarbonate. Figure 3.1.3, shows the collector with an aluminum backing (absorber) between the insulation and the polycarbonate.

Under steady state conditions the energy balance is used to describe the performance of a solar collector. The useful energy output of a collector of area Ac is the difference between the absorbed solar radiation and the thermal loss [1]:

Qu = A [5 — UL (Tpm — Ta)]

The overall heat loss from a solar collector, UL, consists of top heat loss through cover systems and back and edge heat loss through back and edge insulation of the collector can be expressed as:

Ul = Utop + UEdge + UBack (3’1’2

Since polycarbonate material is being used instead of glass, it is necessary to calculate UTop for a plastic glazing, in order to analyse the thermal performance of the solar collector. The net radiation method was used to calculate the top loss coefficient of plastic-covered solar flat-plate collectors. To evaluate the heat loss through the cover system, all of the convection and radiation heat transfer mechanisms between parallel plates and between the plate and the sky must be considered as shown in Figure 3.1.

Analysing each of the variable

Performing an energy balance on the cover, Utop can be easily obtained:

Q£ox? ftp ^"Qcw, to Qcovrfip Qc/Ntrfxt ^Qsoieypr ‘oer fib/т/

QLve’,dsflnf Ьр-с (p T)

Or* =Ш ~7I)

Qpjcss Q, dsthr ^Qovrjisficnr Qphafar

U Qfils-/ tp~ T _TJ

(3.1.11)

When evaluating the back heat loss, the thermal resistances from convection and radiation heat transfer are much smaller than that of conduction. Therefore, it can be assumed that all the thermal resistance from the back is due to the insulation. The back heat loss, Qb, can be obtained from:

Qb — kb Ac (Tpm-Ta)

Lb (3.1.12)

With the assumption of one-dimensional sideways heat flow around the perimeter of the collector, the edge losses can be estimated by

Qe — kg Ae (Tpm-Ta)

Le (3.1.13)

Existing Procedures for Determination

According to EN 12975-2, the following procedures can be applied for the determination of the effective collector capacity (the first three of these are alternative methods for the stationary collector test).

• Calculation from the physical data (with weighting factors for the components),

• determination from the response of the collector to a step-change of the fluid inlet temperature (Annex J.2),

• determination from the response of the collector to a step-change of the irradiance (Annex J.3),

• determination as a fit parameter of the quasi-dynamic collector test.

For details of the procedures see figure 2.

Unfortunately, the results of these procedures are not at all comparable. According to investigations at Fraunhofer ISE and at ISFH, the J.3 procedure leads to values that are
two to four and a half times as high as the calculated value. The most marked difference is found for vacuum-tube collectors of the dewar type ("Sydney” and similar collectors). According to ITW members, the results of the quasi-dynamic test agree quite well with those of the J.3 procedure. In a test at ISFH, the J.2 procedure gave a value that is even slightly below the calculated one.

These differences influence the thermal gains of the collector, which decrease with increasing capacity. For a dewar-type vacuum-tube collector, tested at ISFH, the calculated capacity was 9 kJ/m2K, while the result of the J.3 procedure was 40 kJ/m2K. The difference of calculated yearly collector yields1, caused by the difference of capacities, amounts to 9 %, which is quite remarkable.

Figure 1: Comparison of energetic balances in the 1-node and 2-node models.