Definition of SHGC

[Daniel Kuang Chen Liu]

Hi All,

I'm trying to understand to the relationship between SHGC and Uval, q, and I_sol.

According to WINDOW Technical Documentation.pdf, the general definition of SHGC is stated on page 2-2 as

SHGC = T_sol + A_sol x N [Eqn 2-2]

where 

• T_sol is the solar transmittance
• A_sol is the solar absorptance
  
• N is the inward flowing fraction

On page 5-19, the procedure for calculating the SHGC of a Glazing System is stated as

SHGC = T_sol + (q_in(I_sol=0) - q_in)/I_sol [Eqn 5-106]

where

• q_in(I_sol=0) is the heat flux into the indoor environment WITHOUT incident solar radiation (W/m^2)
  
• q_in is the heat flux into the indoor environment WITH incident solar radiation (W/m^2)
• I_sol is the incident solar radiation (W/m^2)

There are a few issues here:

Issue 1

Substituting [Eqn 2-2] into [Eqn 5-106] implies 

N= (q_in(I_sol=0) - q_in)/(I_sol * A_sol)

but heat flux towards the indoor with solar radiation should be greater than heat flux without solar radiation. This means

q_in > q_in(I_sol=0) --> N is negative

But N should be between 0 and 1!

It seems there is a sign error in Eqn 5-106, and the correct eqn should be

SHGC = T_sol + (q_in - q_in(I_sol=0) )/I_sol

Issue 2

Assuming that the above sign error was real, we can correct it and rearrange Eqn 5-106 as

q_in = I_sol (SHGC - T_sol) + q_in(I_sol=0)

Question:

Does q_in(I_sol=0) = Uval * delta_T ? (where delta_T is the temperature difference between the inside and the outside)

If this is the case we get

q_in = I_sol (SHGC - T_sol) + Uval * delta_T (Eqn A)

But intuitively I would have assumed

q_in = I_sol * SHGC + Uval * delta_T (Eqn B)

Which is correct? Eqn A or Eqn B?

Regards,

Daniel Liu
R&D Engineer
www.fgsglass.com.au­­­­­­­­­­­­­­­
M: +61 422 319 550 T: + 61 3 8562 0872
A: 117 Bangholme Road, Bangholme VIC 3175

[Daniel Kuang Chen Liu]

I have reformatted the equations to be a bit more readable, hopefully someone in the know can help me with this question.

[D. Charlie Curcija]

Hi Daniel,

Yes, that was a typo in the equation. It should have been qin-qin(Is=0). Somehow, nobody noticed it before. 

qin(Is=0) is U*Delta  T, but remember that this is a U calculated under Summer conditions, which is slightly different than reported (Winter) U-factor.

Charlie

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[Daniel Kuang Chen Liu]

Hi Charlie,

Thanks for the clarification regarding the sign error.

So does this mean

    qin = (SHGC - Tsol)*Is + U_summer*DeltaT?

I believe most people would have assumed that

    qin = SHGC*Is + U*DeltaT

[D. Charlie Curcija]

qin=SHGC *Is+U*DeltaT

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[Daniel Kuang Chen Liu]

Hi Charlie,

But if you look at the definition of SHGC

    SHGC = Tsol + (qin - qin(Is=0))/Is

Substituting qin(Is=0) = U*Delta T gives us

    qin = (SHGC - Tsol)*Is + U_summer*DeltaT

The only other way to resovle this is to redefine SHGC by removing reference to Tsol entirely

    SHGC = (qin - qin(Is=0))/Is

[D. Charlie Curcija]

Hi Daniel,

My mistake, I was referring to how qin is defined in ISO 15099. In WINDOW qin does not include Tsol. Tsol is Solar spectrum transmittance (UV, VIS and NIR), while qin includes only long wave IR. As it turns out the equation as written in the Technical procedures document is correct (no  typo in the equation), because heat flow inward is negative by our convention, so the qin-qin(Is=0) becomes a positive quantity (inward flowing fraction).

You bring up an important and interesting point, though which is that ISO 15099 notation (which is the guiding document for our procedures) and our notation is not in agreement.  We are starting the process of updating ISO 15099 and we are updating documentation for WINDOW 8, so this is a good opportunity to make them consistent.

Many thanks for going into details and I hope to stay in touch...

Charlie

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[Daniel Kuang Chen Liu]

Hi Charlie,

Okay thanks. I would suggest calling heat flux inward that's negative qout to make it a little easier to reason about.

Can you please confirm if the following are correct for WINDOW

1. SHGC = (qout (Is=0) - qout) / Is (NOTE: no Tsol)
   
2. qout (Is=0) = U DeltaT
   
3. DeltaT = T_interior - T_exterior
   
4. qout = U DeltaT - SHGC*Is
5. all of the above at NFRC100-2010 Summer condition except when specified otherwise
   

[D. Charlie Curcija]

Daniel,

Depending how you define qout. If qout would include Tsol, then 1. from your list would be correct. The way we defined it in WINDOW, equation 5-19 is correct. Also, qout is still U*Delta T+SHGC*Is, since both SHGC and Is are by definition positive quantities.

Charlie

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[Daniel Kuang Chen Liu]

Hi Charlie,

Really appreciate your patience and time in helping me understand this.

So here I'm purely rearranging Eqn 5-106 on page 5-19 after rename qin as qout

Negative sign is present because Is is positive INWARDS, while qout and U DeltaT are both positive OUTWARDS.

RHS is consistent with U*Delta T+SHGC*Is (if we redefine Delta T = T_ext - T_int and look at positive qin)

LHS is consistent with qout not containing the effect of Tsol, so this is what you mean when you say item (1) from my list is correct with a redefinition of qout.

I had thought that qout contained the effect of direct solar radiation (Is) given that we are contrasting it with qout(Is=0), but now that I look over chapter 5 again, I see that Is does not appear any where in Eqns 5-87 - 5-98.

Presumably there are whole sections missing that deals with:

1. how overall Tsol is calculated,
   
2. how Si are dealt with when Is=/=0?

[Daniel Kuang Chen Liu]

Sorry I posted too soon.

Method for calculating overall Tsol is detailed in Section 7.6.

I guess Si is calculated using the technique in section 7.6.2.

[D. Charlie Curcija]

Hi Daniel,

Thanks again for going over equations. As defined, qout=qout(Is=0) - Is(SHGC-Tsol) is correct. In the Summer qout is negative (by convention as the heat flux into the room), qout(Is=0) is also negative (into the room), and the inward flowing fraction is negative, since SHGC is larger than Tsol, so it adds to the qout. One thing that I don't like about this form of equations is that q is heat flux and that normally includes everything that goes through, Is*Tsol included. In our notation that is not the case, which is why I said that this should be updated to agree with the guiding ISO 15099 document. Perhaps, define some new notation that distinguishes total q from heat flux absent direct solar transmitted radiation. This is especially concerning given that another important reference, ASHRAE Handbook of Fundamentals gives total heat flow equation as:

where Et is Is in our notation, so q (or Q when q*A) is clearly defined as total heat flow. Perhaps we can use notation like q' for heat flux without directly transmitted solar irradiance, or some fancy looking q (e.g., ꝗ, ꝙ, ؏, etc.) to distinguish from total q.

Tsol, Rsol and Asol are detailed in section 7. However, I am realizing that there is really no explicit definition that Si=Ai*Is. It is implied from one of the Figures, but it should be defined explicitly.

Charlie

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