# Solar heat gain calculation for curved facades

Hello everybody,

Within my research on adaptive facades within the SFB1244 at the University of Stuttgart, I would like to develop a state-based model of building physics adaptive facades using the example of complementary printed membrane cushion constructions. This model describes the daylight and radiation transmission through the facade and allows a life cycle cost analysis of different configurations. To do this, I would like to couple the Radiance simulation tool with the FMU of a thermal Modelica model. For the daylighting simulation, I would create a 5 phase simulation based on the tutorial by Sarith Subramaniam and evaluate the respective metrics (WPI, DGP, âŚ). The interaction to the thermal simulation is done by describing the layer absorption and direct radiation transmission in the solar and infrared range, shortly the angle dependent solar heat gain coefficient, analogous to the procedure in DIN EN ISO 52022-3 and ISO15099 respectively. For this purpose, Thierry Nouidui developed a window model within the Modelica Buildings Library and compared it with the results of WINDOW 6. As the membrane layers within the construction are printed and curved, the application of the mentioned standards and the Modelica model of Mr. Nouidui comes to its limits. Imagine that the printing is exclusively on one side. For this, I would like to compare two different methods.

1. Assume plane parallel layers and homogeneous transmission and reflection coefficients for the membrane surface. These are calculated from the averaged value between printed and non-printed areas. Otherwise the procedure is analogous to ISO15099.
2. Create a BSDF for each (curved and printed) membrane layer with Radiance genBSDF and calculate the absorbed radiation for each layer by transferring the concept of ISO15099 from a simple transmission or reflection coefficient to a coefficient matrix (e.g. Klems Basis). Can someone explain to me how this is implemented in EnergyPlus. I have not been able to find out from the EnergyPlus Reference yet.

In general, I have the following questions about my approach:

1. What do you think of the procedure? What would you improve about it? Do you know someone who has published exactly in this direction?

2. I have read that for the solar simulation with Radiance you have to take different materials and command options than for the daylight simulation. What Radiance materials would you suggest for the transparent and printed membrane (ETFE) areas? What settings other than +I need to be chosen for rfluxmtx and genBSDF specifically for solar radiation simulations?

3. Since ETFE has a non-negligible transmittance in the infrared range I wanted to ask if it is also possible to create a BSDF with genBSDF for this spectral range?

Kind regards

Simon Weber, M.Sc.
Research Associate

Pfaffenwaldring 7
70569 Stuttgart
Germany

Tel: +49 711 685 66301
E-Mail: simon.weber@iabp.uni-stuttgart.de
ORCID

Hi Simon,

âprinted membrane cushion constructionsâ you are working with?

Most parts of Radiance treat the RGB color channels as independent, and you may assign them to whatever wavelength ranges you like. As you mention, you do need to go in and make sure the RGB reflectances, etc. are consistent in all the Radiance input files. I wish I could offer you an IR materials database, but I do not know of one. Another big limitation in modeling infrared interactions is the lack of a temperature model or emission in most surfaces. You need to determine an effective reflectance and/or transmittance for each material based on the expected temperature, but I canât advise you how to do that.

Also, genBSDF will create an XML file whose data is identified as CIE-Y (photopic), and you will need to edit the file to some other wavelength range using a text editor. Cutting and pasting the relevant tags from a suitable XML with IR wavelengths should work. Remember that each surface can have up to 4 matrices per wavelength, and you must change them all.

I am hoping other people with more experience in thermal and energy modeling can offer further tips.

Best,
-Greg

Hello Greg,

I am very impressed with your years of engagement with the Radiance program and appreciate your quick personal feedback.

I plan to consider a design that is close to that in Mr. Florâs publication (Redirecting). It is a three-layer membrane cushion design, similar to the design Vector Foiltec built at Festo in 2001. On the outermost layer there is a chessboard-like pattern. The middle membrane layer also has a chessboard-like pattern printed on it, but complementary to the outer layer. Thus, no light passes through when the middle membrane is attached to the outer membrane and more light passes through when both are separated. This position can be switched in an adaptive way.

In my previous thinking, the temperature model is represented within a Modelica FMU and can then serve as an input to the radiation simulation.

I think for the solar spectrum I could do it as in Ms. Hoffmannâs publication (https://doi.org/10.1002/bapi.202100014). Here she compared the solar heat gain modeling of different blinds with the WINDOW and Radiance genBSDF tools. (Unfortunately in German). For the longwave aspect, she integrates the transmission and absorption properties over the inner and outer hemisphere.

Is there also a kind of sky vector for the longwave radiation or do you just assume here, since this radiation is usually homogeneously distributed, the same value for each sky surface propotional to the black sky temperature?

I would be very grateful for suggestions and or best practice examples.

Best regards
Simon

I think itâs reasonable to model the cushion as a single layer BSDF; consider the transmitted solar radiation through the cushion onto the glazing system; neglect the absorbed and re-radiated energy from the cushion (assuming low-e glazing); consider absorbed energy with each layer of the glazing system.

Itâs tricky to setup genBSDF to capture the periodic pattern of the system (cushion + checker board) to get both front and back properties, e.g. the repeating pattern of the ETFE cushion, the location and size of the ray-spawning area. Depending on the geometry of the cushion system, you might want to send rays across the window height (and width if cushion repeating horizontally), with the entire multi-story facade modeled.

You can consider the absorbed energy of the cushion by estimating the mass of the system and so on, using WINDOW/pyWinCalc to obtain the absorption matrix of the system. Here both front and back transmission has to be modeled properly. The methodology was derived from the original Klems publication, I think.

Here is a relevant pub where Radiance and Modelica is used to model MPC controlled EC glass.

1 Like

Hello Taoning,

Thank you for your rapid feedback. I am aware of your mentioned publication and that recent review by you, Greg, Bruno and others. I will build my work on these publications.

However, it is still not clear to me how you describe the long wavelength part.

Do you also use a matrix based method for this? How would you determine a sky vector for the long wavelength region? Is there an isotropic or anisotropic model? The inner hemisphere would be easier to assume as isotropic.
I realize that in the long wavelength region you need different transmission and reflection parameters. However, what Radiance materials do you use for this region?

First of all I will move along your suggestions and then see how good the results are.

Best regards
Simon Weber

Youâll be relying on Modelica FMU or EnergyPlus to compute long wave. For example, window heat balance module in Modelica takes absorbed short wave radiation at each layer of a glazing system and compute how that energy gets transferred elsewhere. Similar can be done in EnergyPlus. Similar mechanism can occur at each interior surface.

Yes, we use the matrix-based method to compute the angle dependent absorbed energy at each layer. You can derived such layer-by-layer absorption matrices from WINDOW, and most, if not all, of the window pane will be isotropic.

I think sky temperature is handled in EnergyPlus/Modelica, but not familiar with it.

Hi all, just realised that my reply by mail did never get through, so just pasting it:

Hi Simon,

maybe the two papers listed below are helpful. They describe the heat flux modelling in Modelica that was used by my colleague Thomas WĂźest in the development of a facade module with integrated thermal storage:

WĂźest, Luible (2018). Solar Energy Balanced FaĂ§ade. In: Facade 2018, Lucerne, Switzerland, pp. 183-194. (PDF) Solar Energy Balanced FaĂ§ade [accessed 29 March 2022].

WĂźest, Grobe, Luible (2020). An Innovative FaĂ§ade Element with Controlled Solar-Thermal Collector and Storage. Sustainability, 12. Sustainability | Free Full-Text | An Innovative FaĂ§ade Element with Controlled Solar-Thermal Collector and Storage

We have been discussing to couple that model with Radiance before, but did not do so yet.

Best, Lars.

Hello Mr. Grobe,

Kind regards
Simon

Hello Tiaoning, and every helpful community member,

regarding the layer-by-layer method with pyWinCalc. Can I do this for the short wavelength region as follows, for the long wavelength region I would start with isotropic condition:

1.1. construction of the first layer: entire frame, only the first layer, this is placed at the outer boundary
1.2. construction of the second layer: entire frame, only the second layer, this is placed in the middle of the frame.
1.3. construction of the third layer: entire frame, only the third layer, this is placed completely inwards
2. create the BSDF of each membrane layer construction with Radiance genBSDF
3. calculation of the layer absorption with pyWinCalc
4. integration and interpolation of the (layer absorptance against klems patch) tabular values in Modelica RC model.

Questions:

• Could this approach work?
• Does the division of the total into the subconstructions work?
• As can be seen from MCNeelâs tutorial, a frame around the construction is needed. Should this frame always be completely contained in the construction?
• What genBSDF commands are needed to create the BSDF for the entire solar domain?
• Can I use pyWinCalc to set up a window model where each pane consists of a BSDF description, not just the outer shading layer?
• Does Klemâs matrix method / pyWinCalc also take into account the spacing between the layers? This can be over 20cm for membrane cushion constructions. Or is a matrix needed, which describes the transition between the air gaps?

Simon

Hi Simon,

• Could this approach work?

The approach make sense in general, but canât say for sure.

• Does the division of the total into the subconstructions work?

My intuition is to model it as a single layer but there might be some other factors at play that require this approach.

• As can be seen from MCNeelâs tutorial, a frame around the construction is needed. Should this frame always be completely contained in the construction?

As suggested above, I think you might want to model the entire facade, or 2/3 stories, using the entire window of interest as the âray spawning areaâ for genBSDF.

• What genBSDF commands are needed to create the BSDF for the entire solar domain?

Youâll need to specify you material in the solar spectrum.

• Can I use pyWinCalc to set up a window model where each pane consists of a BSDF description, not just the outer shading layer?

I think so.

• Does Klemâs matrix method / pyWinCalc also take into account the spacing between the layers? This can be over 20cm for membrane cushion constructions. Or is a matrix needed, which describes the transition between the air gaps?

If computing thermal conductance, Yes. For optical I donât think so.