Calculation of ψ (psi) value

Hello all,

Hi.
I think you could find the answer in some old post. Anyway.

With Therm you can calculate in two ways the thermal coupling coefficient, named L2D in EN ISO 10211 and measured in W/(mK).

1) By dividing the Heat Flow value Φ, that you can find in the U-factors tab, once the calculation done, by activating its display in "Options/Preferences/Results Display", value that should actually be named Φl and be measured in W/m, by the difference of temperature, delta T, that should actually be measured in Kelvin degrees K. In the example of the image L2D = Φl  / ΔT = 51.4030 W/m / 25 K = 2.05612 W/(mK)

2) Or by multipling the U-factor value, measured in W/(m2K), you can find in the U-factor tab, once the calculation done, and the total length , expressed in m, of the 2D detail. In the example of the image L2D = U-factor x total length = 0.4782 W/(m2K) x 4.3 m = 2.05626 W/(mK)

To obtain the Ψ value, measured in W/(mK) and associated to the 2D detail representing a thermal bridge, you must subtract to the L2D value, obtained as above, the L1D value obtained by multipling the U-value of every element of the detail, in W/(m2K) calculated with EN ISO 6946, for its linear dimension, in m, as represented in the 2D detail:

Ψ = L2D - Σ U x l

In the example of the image the U value of the wall in Aerated Autoclaved Concrete (AAC) without the thermal bridge is U1 = U2 = 0.263 W/(m2K), so it will be:

Ψ = 2.05626 W/(mK) - (0,263 W/(m2K) x 2,15 m + (0,263 W/(m2K) x 2,15) = 0.926 W/(mK)

Pay attention that if internal dimensions of the detail are different from the external ones, as in the case of a corner between two walls, the Ψ values associated to the detail are 2: one calculated with internal dimensions (Ψi) and one with the external ones (Ψe). According to EN ISO 13789, Ψi or Ψe values must be always used in consistency with dimensional system adopted in the calculation of thermal losses otherwise final results are wrong.

Have a nice day
Fabrizio

Dear Fabrizio,

Hi Zafer.

Measures that can be used in calculation of thermal losses according to EN ISO 13789 are:
- Net internal measures (in your first example 0,8m for the vertical reddish structure and 1.0 m for the horizontal yellowish one): in this case Psi value must be calculated using net internal measures, and should be indicated as Psi(i)
 - Gross external measures: (in your example 1.0 m for the vertical reddish structure and 1.2 m for the horizontal yellowish one): in this case Psi value must be calculated using gross external measures and will be indicated as Psi(e)

The model you need help for is that of the image in your first post or the therm model you attached here?

Fabrizio


Il giorno lunedì 31 agosto 2015 10:05:30 UTC+2, Zafer yüce ha scritto:Dear Fabrizio,

Dear Fabrizio,

Hi again Zafer

Actually EN ISO 14683 thermal bridges are very very conservative cases, and must be considered only if you have no hint about the actual detail.
So if you make a (correct) numerical simulation of EN ISO 14683 thermal bridges results are certainly better then those given by the standard.

I will take a look to your files.

Fabrizio

Hi Zafer.

Please find the attached 2 images and therm file (therm 7.3)
One refers to how EN ISO 10211 says to model thermal bridge's detail (distance of cutting planes from central element) and boundary conditions when calculation is done to determine Psi value.
The other one is your model adapted to EN ISO 10211 conditions. Calculations of Psi values, both internal and external, are done in the 2 red points assuming your conductivity values (but structures stratigraphy should always be fully modeled). U-factor surface names are "internal" for all internal boundaries and "external" for all the external ones.
Internal and external real temperatures are not crucial for flux and psi values calculation but it is important to have at least 1 degree Kelvin of delta T between internal and external surfaces. I used 20°C as internal temperature and 0°C as external temperature to simulate real condition and have some hints on the internal surface temperature (that actually should be determined using Rsi = 0.25 (m2K)/W and the external monthly average local temperature of year's coldest month).

Finally: this is a real bad thermal bridge, with high Psi value and low internal surface temperatures, if it refers to a real case it should be corrected.

Hope it can help you.
Have a nice day.
Fabrizio

Dear Fabrizio,
7 Eylül 2015 Pazartesi 13:03:50 UTC+3 tarihinde Fabrizio Prato yazdı:

Hi Zafer.

To answer to your doubt about the wall U value calculation U=0.7676 W/(m2K): I used the wall thickness (29 cm) of your Therm file model so
R = (0.13 + 0.29/0.256 + 0.04) (m2K)/W = 1,3028125 (m2K)/W       and     U = 1 / R = 0,76757 W/(m2K)
If wall thickness is actually 30cm Therm file model and L2D value should be updated, U value recalculated to U = 0.7452 W/(m2K) and Psi values found again.

Ciao
Fabrizio

Dear Fabrizio,

Hi again Zafer.

First of all:
- When numerical calculation (Therm simulation) is done for thermal flux and Psi value determination, internal Rsi can't be R=0.25 (m2K)/W: this value is only used for numerical calculations done for internal surfaces temperatures (Tsi) determination.
- furthermore it is quite impossible for Rse to be 0,13 (m2K)/W

According to EN ISO 10211, When numerical calculation is done for thermal flux and Psi value determination, Rs values have to be set as follow:
- in case flux direction is known Rsi values according to EN ISO 6946
- in case flux direction is unknown, always Rsi = 0.13 (m2K)/W and Rse=0.04 (m2K)/W
Your case falls in the first option beeing thermal flux direction easily predictable before any calculation is done, because it will presumably go horizontally through wall and verticcally through concrete slab, so for internal horizontal surfaces Rsi = 0.10 (m2K)/W (flux direction vartical upward), for all internal vertical surfaces Rsi = 0.13 (m2K)/W, for external surfaces Rse = 0.04 (m2K)/W, but if roof slab is not facing external air but another unheated room Rse = Rsi = 0.10 (m2K)/W.

After making these corrections to your therm model and to U value calculation of roof slab according to 6946 (U should approximatly be = 4,5455 W/(m2K) try again Psi values calculation and this time I think results will be more orthodox.

I suggest you to read carefully both EN ISO 6946 and 10211, actually it is no fun reading, but it is really useful for these calculations!

Ciao
Fabrizio

Thanks for your explanation :) It looks clear.

However, I have one question. When we have the case of corner between two walls we need to find  Ψi and Ψe. To get the final  Ψ, do we sum  Ψi and Ψe?

Thanks for your answer.

Frank

Hi Frank. Better late then never.

" do we sum  Ψi and Ψe?" the answer is no. Psi(i) and Psi(e) are linear transmission values referred to Internal or external dimensions.

If in your heat loss calculation inside net dimensions are used then Psi(i) value has to be used to consider heat loss through the associated thermal bridge.

If external gross dimensions are used then Psi(e) value has to be used.

Ciao

Fabrizio