Disassembled thermal circuits from walls description¶

This notebook presents how the description of the walls is transformed in a set of disassembled thermal networks implemented in the function wall2TC() of dm4bem module.

The description of the walls is given in a folder that contains two types of files:

• wall types: thermo-physical properties;
• walls data: regarding the area, temperature & flow-rate sources, coefficients for convection and radiation of the wall surfaces.

The thermal network is a data structure (dictionary) containing the matrices A, G, C and the vectors b, f, y.

The input data needed for the thermal model of the building is in a folder.

Wall types¶

Let's consider two types of walls with physical properties given in the file wall_types.csv.

The file wall_types.csv contains:

• the physical properties of the materials given in SI units: conductivity in W·m⁻¹·K⁻¹, specific heat in J·kg⁻¹·K⁻¹, density in kg·m⁻³;
• the width of the layers in m;
• the number of meshes in which each layer is numerically discretized; each mesh has two resistances and a capacity.

There are two types of walls in the file wall_types.csv (Figure 1):

• The wall of type 0 has two layers: Concrete and Insulation. Concrete layer has one mesh (two resistances and a capacity) and Insulation layer has two meshes (i.e., four resistances and two capacities).
• The wall of type 1 has one layer: Glass, discretized in one mesh.

Figure 1. The two types of wall described in the file wall_types.csv

Walls data¶

The models of walls are based on the materials given in the file wall_types.cvs. For each specific wall, data related to surfaces is given (area, orientation, convection coefficients, radiative properties, temperature and flow-rate sources).

There are three kinds of walls (Table 1):

• generic (e.g., file walls_generic.csv),
• outdoor (e.g., file walls_out.csv),
• indoor (e.g., file walls_in.csv).

Table 1. Columns of walls_generic.csv, walls_out.csv, and walls_in.csv files. The columns that are present in the file are maked by ✓ for _generic, _out and _in walls. The columns needed to define the thermal circuit are marked by ✓ in TC.

Notes:

1. The generic walls may define out or in walls by not specifying temperature sources (see wall_generic.csv, wall_out.csv, and wall_in.csv files for examples).

2. The out walls do not need the temperature sources on the inner surfaces, T1.

3. The in walls do not need tilt (β) and azimuth (γ) angles, the albedo of the ground, and the temperature sources on the outer (T0) and the inner (T1) surfaces.

4. The colums TC shows the information needed to obtain the thermal circuit. The data related to radiative exchange is used in the calculation of flow-rate sources in short-wave and for conductances in long-wave radiative exchange.

Generic wall¶

Generic walls contain all the information listed in Table 1. For example, wall_generic.csv file describes the walls shown in Figure 2.

The file walls_generic.csv describes four walls (Figure 2):

• according to the types of walls:
  • w0 and w1 are of type 1, i.e., concrete and insulation;
  • w2 and w3 are of type 0, i.e., glass.
• according to the temperature sources:
  • w0 and w1 are outdoor walls that have as boundary condition the outdoor temperature T0; the temperature on the inner surface is a room temperature, which is an output of the model.
  • w1 is a wall that has temperature sources on both sides.
  • w3 is an inner wall that separates two rooms. It does not need information for solar direct radiation (tilt and azimuth angles and the albedo of the ground surface in front of the wall).

Outdoor walls, such as gw0 (generic wall w0) and gw2 (generic wall w2) in Figure 2, can be obtained from the generic walls by not considering a temperature source T1 on inner surface, which is indicated by NaN in rows w0 and w2 for column T1.

Likewise, indoor walls, such as gw3 (generic wall 3) in Figure 2, can be obtained from the generic walls by indicating that there are no temperature sources in T0 and T1, i.e. T0 = NaN and T1 = NaN.

The outputs y are indicated in a list using slicing. For example, the outputs of wall w0 are temperature nodes 0 and -1 (i.e., the last node which is node 3) in Figure 2.

The numbering convention of the elements of the circuits is:

• the nodes (i.e., temperatures) are numbered from left to right and from up to down;
• the oriented branches (i.e., flows) are numbered from the node with a lower index to the node with a higher index;
• the reference temperature node is not numbered.

Figure 2. Four examples of generic walls described in the file wall_generic.csv. Walls gw0 and gw1 are of type 1 (glass), described in wall_type.csv. Walls gw2 and gw3 are of type 0 (concrete and insulation), described in wall_type.csv.

The files describing the types (wall_types.csv) and the data (walls_generic.csv) of the walls contain the information needed to obtain the disassembled thermal circuits. The names of the walls can have a prefix.

Each matrix (A, G, C) of vector (b, f, y) of the thermal circuit can be accessed as Pandas dataframes.

All matrices (A, G, C) and vectors (b, f, y) of each thermal circuit can be printed.

All thermal circuits read from the file walls_generic.csv can be printed.

Outdoor walls¶

Outdoor walls do not have temperature sources on indoor surfaces (Figure 3). They can be obtained from generic walls by not indicating the temperature source T1 (on the indoor surface), or they can be described by specific files, such as walls_in.csv.

Figure 3a shows a walls w0 and w1 of type 1 (described in wall_types.csv) with only one layer which has one mesh.

Figure 3b shows walls w2 and w3 of type 0 (described in wall_types.csv) with two layers (concrete and insulation).

Figure 3. Outdoor walls: a) of type 1 b) of type 0. The type is indicated in the file wall_types.csv.

Indoor walls¶

Indoor walls do not have temperature sources on surfaces (Figure 4). They can be obtained from generic walls by not indicating temperature sources T0 and T1, or they can be described by specific files, such as walls_in.csv.

Figure 4a shows walls w0 and w1 of type 1 (described in wall_types.csv) with only one layer which has one mesh.

Figure 4b shows wall w2 and w3 of type 0 (described in wall_types.csv) with two layers (concrete and insulation); the insulation layer is discretized in two meshes.

Figure 4. Indoor walls: a) of type 1 b) of type 0. The type is indicated in the file wall_types.csv.