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Scaling Criteria
The third stage in the study was to determine at which speed the wind should be set inside the tunnel to achieve similarity between the model and the prototype To achieve similarity in the data obtained between the model and the full scale prototype house there must be scaling criteria to satisfy. There should be a geometrical similarity in all details and all dimensions between the model and the prototype house. Also, there are non-dimensional parameters that should be similar, one of which is the Reynolds’s Number (Re) (1), that is:
That is Re for the model = Re for the prototype:
where
is the air density, V is the air
speed, D is a typical dimension( for example the length of the house), and m
is air dynamic viscosity
The criteria for scale modeling in the wind tunnel is that similarity is achieved between the Reynolds numbers, and that the Reynolds number for the prototype house and the model should both exceed 50,000. This is done using the Reynolds number which in this case is;
Re
(model) = Re (prototype) = r
V
D
/m
= r
V
D
/m
where the subscripts m and p are the model and the prototype house values respectively
and
since V
= 2.0 m/s at the building site and the scale
of the model is 1:75
hence
ideally V
= V
(D
/D
)(r
/r
)(m
/m
) = 2 X 75 X 1 X 1 = 150 m/s
which
is a very high speed to be achieved in the wind tunnel; the speed in the wind
tunnel is limited to 10 m/s. So if r
= 1.17 at 30°
C and m
= 1.86 X 10
at the same temperature and D
= 30 meters then :
Re
= 1.17 X 2 X 30 / 1.86 X 10
= 3.8 X 10
Re
= 1.2 X 10 X 0.4 / 1.86 X 10
= 0.24 X 10
the
criteria > 0.05 X 10
So both the model and the prototype house are fully turbulent and therefore the model is valid at a wind boundary speed of 7 m/s. For the Reynolds number higher than 50,000, Cp is constant (5). Therefore, the test used 70% of the top speed of the fans (about 7m/s) in the wind tunnel to achieve constant Cp.