Sensitivity analysis

Table 2. Material data and allowable stress for Copper and Aluminium.

Material Outs [MPA] ae [MPA] Op0.2 =Ox500,p0.2 [MPA] Ox500,aiiow [MPA]

Al 95 50 35 35

Cu 220 70 50 50

Allowable levels of stress in glass are counted with time dependency and distribution of brittleness and by these two reasons the stress in a glass when used as a construction material never shall exceed 8-9 MPa [3].

A safety factor defined as (4) will be used

Sf =—————— (4)

^T 500

Since a construction never will be stronger than its weakest point we also defined a weakest safety factor as in (5).

Sf weakest = min(Sfg, Sfp, Sft) (5)

2.3 Modelling

As a modeling tool we used a finite element analysis program called “MSC Marc Mentat” version 2005r2 (32bit). A solar collector has double symmetry axis, therefore only one quarter of the collector were modeled. The model was set up with thick shell Quad 4 elements, called element type 75 in the program. Thick shell elements using Mindlin’s shell theory is common used in applications like these

[4] . The elements in the mesh were up to 20*20 mm.

3. Results

A sensitivity analysis where done in order to see which factors had most affection of the stresses in the material. The sensitivity is a dimensionless number describing the response of the disturbance, e. g. if you make a disturbance of 1 % and the response is -1.9 the stress in that particular case will be reduced by 1.9 %. Material in absorber was copper. The result is compiled in to table 3.

The x and y both have trends that seem complex and needs more analysis for understanding.

z is more or less proportional i. e. all trends ~ 1.

Selection of material and thickness in absorber affect the price / thermal performance relation. That relation will not be questioned in this article, instead geometry properties of tubes and absorber will be kept constant on common used values described in table 1.[5]

tg have trends that seem complex and needs more analysis for understanding.

Eg will not be further investigated since there are no real good alternatives to soda glass with better price / thermal performance relation.

Disturbed factor

Unaffected values

P

P gas

^glassmax

^absmax

^tubemax

x

1440 mm

-0.46

0.26

0.05

-0.45

y

1400 mm

-1.90

-0.36

-0.31

0.24

z

10 mm

1.03

0.91

0.89

1.03

Dtt

120 mm

-0.68

-0.86

-0.96

0.54

0t

12 mm

0.36

0.41

0.36

-1.81

tg

4 mm

0.56

-0.75

-0.55

0.55

tp

0.25 mm

2.10

1.23

1.18

2.08

tt

0.85 mm

0.09

0.14

0.11

-0.82

Eg

69 GPa

0.16

-0.18

-0.15

0.16

Ep

118 GPa

0.72

1.02

1.06

0.71

Et

118 GPa

0.09

0.14

0.11

0.10

Table 3. Sensitivity of different disturbances

Trends