[TRNSYS-users] U-value for windows in type 56

[jean-francois.gobeau@legrand.fr]

Dear all,

I need to check the overall U-value of the windows in my Type 56 building
models.

In order to do that, I decided to plot the Ntype 50 output (uWIN = U-value
of glazing + frame) of type 56.
But I got strange results, that I didn't understand. Maybe someone of you
has an explanation?

1/ To make things as simple as possible, I created a type 56 with one
single window.
The window is a SINGLE type window in the American Library (it is just an
example and I got the same kind of results with other window types).
According to TRNBUILD, the estimated U-value (for reference only...)  of
the glazing is 5.8 W/m2.K = 20.88 kJ/hr.m2.K
The U-value of the frame without conv and rad heat transfer coefficients is
8.17 kJ/hr.m2.K = 2.27 W/m2.K
Supposing 1/hint = 0.11 K.m2/W and 1/hext=0.06 K.m2/W (internal and
external heat transfer coefficients), I can estimate the real U-value of
the frame = 1.638 W/m2.K.
Knowing that the area ratio of the frame to the window is f=0.15, I should
be able to calculate a rough estimate of the window U-value according to
the following equation :

      Uwindow = f * Uframe + (1-f)*Uglass = 0.15 * 1.638 + 0.85 * 5.8 =
5.17 W/m2.K = 18.6 kJ/hr.m2.K (Eq. 6.3.2-95 in the TRNSYS Manual, volume 6,
page 6.86)

And yet, when I run my type 56 model, the result for the Ntype 50 output is
Uwindow = 20.55 kJ/hr.m2.K = 5.71 W/m2.K.

2/ To go further, I decided to vary the frame ratio from 0 to 1 and I was
surprised to notice that the Ntype 50 output doesn't vary linearly with f
as it should according to the above equation : the variations of uWin as a
function of f are highly non linear, even if the values when f=0 (only
glass, uWin=Uglass=20.8 kJ/hr.m2.K) and f=1 (only frame, uWin=Uframe = 18.6
kJ/hr.m2.K) seem to be correct.
For example, with f=0.5, uWin = 20.13 kJ/hr.m2.K = 5.6 W/m2.K : it is very
close to the glazing U-value (5.8 W/m2.K) although there is 50% frame / 50%
glass!

3/ To go even further, I built a very simple type 56 model with one single
zone and one single wall. The wall has a 100 m2 area and is almost entirely
covered with one 99.9 m2 window.
In other words, the only heat transfer is through the window. The external
temperature (ambiant) is stationnary and fixed at 0°C. There is no solar
radiation. There is only one convective heat source in the zone defined as
a constant heat gain = 1000W = 3600 kJ/hr.m2.K.
The window is again a SINGLE type window from the american library.
When I run the simulation, the equilibrium air temperature in the zone is =
3.797°C.
Consequently, I should be able to calculate the window U-value : Uwindow =
1000W/(99.9*3.797) = 2.633 W/m2.K = 9.49 kJ/hr.m2.K.
And yet, the Ntype 50 output uWin gives a very different result : uWin =
20.55 kJ/hr.m2.K
And unfortunately, these two results are different from my first estimate
for Uwindow (see above) : Uwindow = 18.6 kJ/hr.m2.K


I am very confused with these results : what is the correct value for
Uwindow? what are the explanations for these disparities between U-values?

Thanks in advance for your comments, help and advice!

Best regards,

Jean-Francois GOBEAU
LEGRAND
Limoges - FRANCE

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