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Hello. I am trying to check Type 1b. In principle, in efficiency mode 2, the efficiency of the solar collector is:
Eff1 = a0 -a1*(Tm – Tamb)/Radiation – a2*((Tm-Tamb)^2)/Radiation
I expect to obtain the same value while doing the following:
Eff2 = Useful_energy / (Radiation * Collector Area)
I have entered the values of a0, a1 and a2 for parameters 6,7 and 8
Tested flow rate: the same as the one I use as constant input (I divided the constant flowrate by the Collector area).
For IAM, I have set both the 1st and 2nd order IAM to zero, to avoid influence of IAM in the equation.
So, when I got the simulation, results, I have checked calculated in Excel Eff1 and Eff2, using the following outputs:
Radiation = Total tilted surface radiation for surface
Tm = (Tin + Tout)/2
Tamb = Dry bulb temperature
For the units, I make sure everything is fine.
1/ Why I do not get Eff1 = Eff2? Most of the time, ABS (Eff1 – Eff2) is about 0,05 (that is 5% in efficiency point) and one hour after sunrise (or before sunset), the difference may reach 0,6, that i.e. 60% in efficiency point.
2/ Does the value of “Tested flow rate” actually influence the result? I have changed in another simulation the values and obtained the same results.
Thanks
Hi Ken,
I applaud your efforts and understand your confusion. I think you did everything right, there are just a couple of details missing from the documentation of Type 1 that affect Type 1b specifically (using 2nd order IAMs) that I suspect explain the discrepancy you're seeing.
When you set the 2nd order IAM in Type 1b to 0, the code for Type 1 reverts to a split-linear version of the IAM equation; it behaves exactly as advertised for incidence angles <= 60 degrees, then proportionally decreases the IAM for incidence angles between 60 and 90 degrees such that the IAM at 90 degrees is 0. I just ran the algorithm using 1st order IAM = 0 at various incidence angles and got the following results:
Incidence Angle IAM 0 1 5 1 10 1 15 1 20 1 25 1 30 1 35 1 40 1 45 1 50 1 55 1 60 1 65 0.833333333 70 0.666666667 75 0.5 80 0.333333333 85 0.166666667 90 0
That would certainly explain why the efficiency doesn't match what you calculated for the hour following sunrise or just before sunset. As for the remaining hours, that is probably because Type 1 calculates three different IAMs, one each for the beam radiation, diffuse sky radiation, and diffuse ground-reflected radiation, and the latter two solve by integrating over the entire sky dome / ground surface visible to the collector, including diffusions and reflections from incidence angles > 60 ... so, even at mid-day, the IAMs for sky diffuse and ground-reflected diffuse radiation are probably slightly less than 1.0.
I would recommend using a different optical mode for Type 1, such as Type 1a (no IAMs) or Type 1c (reads in IAMs from a data file, which can be all 1's down to 90 degrees or whatever you like), and see if you're still not getting the efficiency results you expect.
