U Value Calculation Method

[sean.m.hayes]

Hi,

Can anyone advise please how Ecotect calculates U-Values of elements?

I am teaching a course in building energy modelling in Ecotect. When I define a new element (e.g. simple 100mm blockwork wall), the U-Value that Ecotect calculates is different to what I calculate manually using the thermal conductivity of each material, and the standard thermal resistances that would normally be taken for the internal and external surfaces.

In addition, can anyone please explain how the thermal resistance of an air gap is calculated in Ecotect? The thermal conductivity seems to default to 5.56 W/m.K, which doesn't seem to impact the overall U-Value of the element.

Many thanks for any help anyone can provide.

[Pennetier1]

Hello sean.m.hayes, 

As far as I know, Ecotect does not use any strange formulae for calculating the U-value of the assembly.  What thermal resistance are you using for interior and exterior air? I think Ecotect uses 0.12 for Rsi and 0.06 for Rso.

For the air gap, Ecotect uses the default 5.56 W/mK to simulate the conductivity of a typical 25 mm air gap in a cavity. Changing this value should change the overall U-value once you click on the "calculate Thermal Properties" button.

Let me know how things go with the U-value calculations.  I did visit that question in the past and will double check my numbers.  Calculating the Admittance is another thing altogether.  Also, keep in mind that it will be difficult to compare simple steady state processes with Ecotect's Admittance method since that is based on a dynamic flow.

I would recommend the book " Introduction to Architectural Science" by S. Szokolay, since Ecotect is quite a bit influenced by Steven's work.

Let me know if you have more questions on this topic, otherwise please accept as a solution so that others can benefit from this information.

Cheers,

[sean.m.hayes]

Hi Olivier,

Thanks for the reply.

I had been using 0.13 for Rsi and 0.04 for Rse as per EN ISO 6946 : 2007. When I used 0.12 for Rsi and 0.06 for Rso I still didn't get the same U-Value as I got from my basic calculation - my calculation came to 0.275 W / ((m^2).K) and Ecotect returned 0.260 W / W / ((m^2).K) for my example wall. I've attached screenshots of the wall I created in Ecotect, and my Excel calculations for reference.

Regarding the air gap, using 5.56 W / (m.K) for a 25mm air gap would give a thermal resistance of 0.004 ((m^2).k) / W. Section 4.8.1 of the 2006 BRE conventions for U-Value calculations (http://www.bre.co.uk/filelibrary/pdf/rpts/BR_443_%282006_Edition%29.pdf) gives the normal resistance of a cavity in a wall construction to be 0.18 ((m^2).K) / W, and if I use this value in my Excel calculation I get closer to the Ecotect U-Value of 0.260 (I get 0.262). So, the 5.56 does look correct but I can't see how it is used in the U-Value calculations?

If I change the 5.56 in the material properties, and click "Calculate Thermal Properties", a new, different U-Value is calculated but the value in the material properties reverts to 5.56. I'm not too concerned about being able to change the 5.56 as it gives an answer which is very close to mine, but I'd like to know how it is used in calculations if possible please?

Thanks again for your help, much appreciated.

Cheers,

Sean

[Pennetier1]

Hi Sean, 

I pretty much came up with the same conclusions as you did.

A couple of things:

1. In your spreadsheet, you have the air gap at 0.004 m, instead of 0.04 (for 40 mm) - that does not make a huge difference of course.

2. I would not use the same way of calculating the resistance of air gap as the other materials.  This value is already assumed to be 1/5.56 = 0.18 in the literature.  In reality, the conductivity or air is more like 0.025 W/mK, but air gap behaving differently, we assume 5.56, which gives us R 0.18 (I see 0.17 sometimes, but that is close enough).  Bottom line is you should not have to use the thickness here.  The 5.56 number is assumed for 25 mm (1"), after which there is so much convection that it throws things off.

3. With all that said, we still get 0.260 W/m2K instead of the manually calculated 0.262, so something is still off, and I can say it is the air gap because I use a similar spreadsheet as yours and when no air gap is present, I get the exact same numbers as Ecotect.  Perhaps Ecotect accounts for the increase in thickness of the air gap from the standard 25 mm? Note that if you change the air gap thickness, the U-value does not change because it still see that standard 25 mm air gap value, but perhaps the conductivity changes in the background.

4. Not to add more confusion for you... if you were to change the "type" from air gap (5) to something else, you would see another change in the U-value.  This I reckon is another way to simulate something but I have never asked Andrew what it was for exactly.

Bottom line is that the Air Gap is causing a shift in what would be expected from manual calculations, I suspect the software tries to account for something else I am not aware of.  I will investigate.

Let me know if you have more questions on this topic, otherwise please accept as a solution so that others can benefit from this information.

Cheers,

[sean.m.hayes]

Hi Olivier,

Many thanks for this advice, much appreciated.

I'm sorry but I'm still not clear on how the 5.56 is used. 

The thermal conductivity of the air gap is entered in Ecotect as 5.56 W/(m.K). If this is to achieve an air gap thermal resistance of 0.18 ((m^2).K)/W, then for a 25mm air gap it would be 0.025/5.56 = 0.004.

0.18 ((m^2).K)/W is what is normally given in the literature, but 1/5.56 = 0.18 uses inches for the numerator and SI units for the denominator. To get 0.18 I would have thought 0.1388* should be used, would this be right please?

Thanks again for your help,

Cheers,

Sean

[Pennetier1 · Accepted solution]

Hello Sean, 

I know this is a bit confusing, because air does not act like other material properties when computing thermal processes.  The main reason is that beyond a certain thickness, about 1" or 25 mm, thermal convection happen in air gap, and radiation from the adjoining surfaces also play a role in the performance of this air gap.

The conductivity of air at 20* c is about 0.0257 W/mK, but again, in construction, air behaves differently than other materials.  Instead, we use a conductance of 5.56, or a R-value of 0.18 m2 K/W. The "1" in 1/5.56 = 0.18 is not meant to be 1 inch, but rather the inverse of the Conductance, that is the Resistance.  Recall that R = 1/C.

Changing the thickness of your air gap should NOT change anything, unlike with other materials; that is because the R value of an air gap is thought to be fairly constant beyond 1 inch or 25 mm.  That is why insulation is actually "broken up" air gap, small pockets of air gap trapped in a medium.  If thick air gaps had an increased resistance with their thickness, we would not have to use insulation materials.  Again, this is due to the convection processes happening in air gap thicker than 25 mm.

So in Ecotect, you really do not have to do anything with the air gap layer, simply drop it in.  The software will automatically use a R-value of 0.18 for it, regardless of its thickness - that is, as long as the "type" is set to Air Gap.  If set to anything else, Ecotect will account for the thickness as for other materials, but that would not be correct.

I hope this makes more sense!

Let me know if you have more questions on this topic, otherwise please accept as a solution so that others can benefit from this information.

Cheers,

[sean.m.hayes]

Hi Olivier,

Thanks very much, that makes sense now. So when other materials are used in Ecotect, the thermal conductivity is entered, but when an air gap is used, the conductance is entered.

Thanks again for your time, much appreciated!

Cheers,

Sean

[Pennetier1]

Hi Sean, 

That is correct! Because we always associate the 5.56 value to a specific thickness.  All other materials use their conductivity and divide it by the thickness entered to get the conductance.  For the air gap, we forget about the thickness and simply use the conductance of 5.56 since beyond 25 mm, the thermal resistance remains the same everything else being equal.

Keep in mind that this air gap resistance of 0.18 will vary depending on whether the heat flow is horizontal - such as in walls - or vertical such as in roof assemblies.  Also, the emittance of the material facing the air gap will affect the overall resistance of the air gap.  Low emittance materials such as foil (aluminum) will increase the resistance of the air gap, because it will reduce the radiation process, compared to, say a brick or stud that has a relatively high emittance (~0.89) and readily conducts heat through the air space via radiation. That is why radiant barriers work so well and can increase the thermal resistance of an assembly. 

Glad I could help.

Cheers,