Disassembled thermal circuits from wall description

Disassembled thermal circuits from wall description#

This notebook presents how the description of the walls is transformed into 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 (see an example):

wall types: thermo-physical properties of the materials;
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 \(b, f, y\).

import pandas as pd

import dm4bem

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

folder = "./pd/bldg_wall2TC"

Wall types#

Let’s consider two types of walls with physical properties given in the file wall_types.csv (link).

wall_types = pd.read_csv(folder + '/wall_types.csv')
wall_types

	type	Material	Conductivity	Specific heat	Density	Width	Mesh
0	0	Concrete	1.400	880.0	2300.0	0.200	1
1	0	Plaster	1.000	1000.0	1200.0	0.030	0
2	0	Insulation	0.027	1210.0	55.0	0.080	2
3	1	Glass	1.400	750.0	2500.0	0.004	1

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:
- one resistance and no capacity, if Mesh = 0;
- two resistances and a capacity. if Mesh > 0.

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.

wall_types

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

Walls data#

The models of the walls are based on the materials given in the file wall_types.csv. 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, link):

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 (link). 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.

Column	Unit	Definition	Example	_generic	_out	_in	TC
ID		Identifiant of each wall	w2	✓	✓	✓	✓
type		Type of wall given in `wall_types.csv`	1	✓	✓	✓	✓
Area	m²	Surface area of the wall	25	✓	✓	✓	✓
β	°	Tilt angle: 90° vertical; >90° upward facing	90	✓	✓
γ	°	Azimuth: 0° South, 180° North, >0° westward	90	✓	✓
albedo		Fraction of sunlight that is diffusely reflected by ground surface	0.25	✓	✓
T0	°C	Temperature source of outer surface	To	✓	✓		✓
T1	°C	Temperature source of inner surface	Ti	✓			✓
Q0	W	Flow rate source on outer surface	Qo	✓	✓	✓	✓
Q1	W	Flow rate source on inner surface	Qi	✓	✓	✓	✓
h0	W·m⁻²·K⁻¹	Convection coefficient of outer surface	25	✓	✓	✓	✓
h1	W·m⁻²·K⁻¹	Convection coefficient of inner surface	8	✓	✓	✓	✓
α0		Short-wave absorption coefficient of outer surface	0.25	✓	✓	✓
α1		Short-wave absorption coefficient of inner surface	0.30	✓	✓	✓
ε0		Long-wave hemispherical emissivity of outer surface	0.85	✓	✓	✓
ε1		Long-wave hemispherical emissivity of inner surface	0.70	✓	✓	✓
y		Output temperature nodes (by using slicing)	[0, -1]	✓	✓	✓	✓

Notes:

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).
The out walls do not need the temperature sources on the inner surfaces, T1.
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.
The column 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 (link).

walls = pd.read_csv(folder + "/walls_generic.csv")
walls

	ID	type	Area	β	γ	albedo	T0	T1	Q0	Q1	h0	h1	α0	α1	ε0	ε1	y
0	w0	1	1.0	90.0	0.0	0.25	To	NaN	Qo	Qi	20.0	10.0	0.25	0.3	0.85	0.7	[0, -1]
1	w1	1	1.0	90.0	0.0	0.25	To	Ti	Qo	Qi	20.0	10.0	0.25	0.3	0.85	0.7	1
2	w2	0	10.0	0.0	90.0	0.25	To	NaN	Qo	Qi	21.0	11.0	0.25	0.3	0.85	0.7	[1, 2, -1]
3	w3	0	20.0	NaN	NaN	0.25	NaN	NaN	Qo	Qi	22.0	12.0	0.25	0.3	0.85	0.7	[2, 1, 3]

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.

generic_wall

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 (link). The names of the walls can have a prefix.

# Thermal circuits from wall types and wall data
TCd_generic = dm4bem.wall2TC(wall_types, walls, prefix="g")

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

TCd_generic['gw0']['A']

	gw0_θ0	gw0_θ1	gw0_θ2	gw0_θ3
gw0_q0	1.0	0.0	0.0	0.0
gw0_q1	-1.0	1.0	0.0	0.0
gw0_q2	0.0	-1.0	1.0	0.0
gw0_q3	0.0	0.0	-1.0	1.0

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

dm4bem.print_TC(TCd_generic['gw0'])

A:
        gw0_θ0  gw0_θ1  gw0_θ2  gw0_θ3
gw0_q0     1.0     0.0     0.0     0.0
gw0_q1    -1.0     1.0     0.0     0.0
gw0_q2     0.0    -1.0     1.0     0.0
gw0_q3     0.0     0.0    -1.0     1.0 

G:
gw0_q0     20.0
gw0_q1    700.0
gw0_q2    700.0
gw0_q3     10.0
dtype: float64 

C:
gw0_θ0       0.0
gw0_θ1    7500.0
gw0_θ2       0.0
gw0_θ3       0.0
dtype: float64 

b:
gw0_q0     To
gw0_q1    0.0
gw0_q2    0.0
gw0_q3    0.0
dtype: object 

f:
gw0_θ0     Qo
gw0_θ1    0.0
gw0_θ2     Qi
gw0_θ3    0.0
dtype: object 

y:
gw0_θ0    1.0
gw0_θ1    0.0
gw0_θ2    0.0
gw0_θ3    1.0
dtype: float64 

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

print('TCd_generic')
for key in TCd_generic.keys():
    print('Wall:', key)
    dm4bem.print_TC(TCd_generic[key])

TCd_generic
Wall: gw0
A:
        gw0_θ0  gw0_θ1  gw0_θ2  gw0_θ3
gw0_q0     1.0     0.0     0.0     0.0
gw0_q1    -1.0     1.0     0.0     0.0
gw0_q2     0.0    -1.0     1.0     0.0
gw0_q3     0.0     0.0    -1.0     1.0 

G:
gw0_q0     20.0
gw0_q1    700.0
gw0_q2    700.0
gw0_q3     10.0
dtype: float64 

C:
gw0_θ0       0.0
gw0_θ1    7500.0
gw0_θ2       0.0
gw0_θ3       0.0
dtype: float64 

b:
gw0_q0     To
gw0_q1    0.0
gw0_q2    0.0
gw0_q3    0.0
dtype: object 

f:
gw0_θ0     Qo
gw0_θ1    0.0
gw0_θ2     Qi
gw0_θ3    0.0
dtype: object 

y:
gw0_θ0    1.0
gw0_θ1    0.0
gw0_θ2    0.0
gw0_θ3    1.0
dtype: float64 

Wall: gw1
A:
        gw1_θ0  gw1_θ1  gw1_θ2
gw1_q0     1.0     0.0     0.0
gw1_q1    -1.0     1.0     0.0
gw1_q2     0.0    -1.0     1.0
gw1_q3     0.0     0.0    -1.0 

G:
gw1_q0     20.0
gw1_q1    700.0
gw1_q2    700.0
gw1_q3     10.0
dtype: float64 

C:
gw1_θ0       0.0
gw1_θ1    7500.0
gw1_θ2       0.0
dtype: float64 

b:
gw1_q0     To
gw1_q1    0.0
gw1_q2    0.0
gw1_q3     Ti
dtype: object 

f:
gw1_θ0     Qo
gw1_θ1    0.0
gw1_θ2     Qi
dtype: object 

y:
gw1_θ0    0.0
gw1_θ1    1.0
gw1_θ2    0.0
dtype: float64 

Wall: gw2
A:
        gw2_θ0  gw2_θ1  gw2_θ2  gw2_θ3  gw2_θ4  gw2_θ5  gw2_θ6  gw2_θ7  gw2_θ8
gw2_q0     1.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0
gw2_q1    -1.0     1.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0
gw2_q2     0.0    -1.0     1.0     0.0     0.0     0.0     0.0     0.0     0.0
gw2_q3     0.0     0.0    -1.0     1.0     0.0     0.0     0.0     0.0     0.0
gw2_q4     0.0     0.0     0.0    -1.0     1.0     0.0     0.0     0.0     0.0
gw2_q5     0.0     0.0     0.0     0.0    -1.0     1.0     0.0     0.0     0.0
gw2_q6     0.0     0.0     0.0     0.0     0.0    -1.0     1.0     0.0     0.0
gw2_q7     0.0     0.0     0.0     0.0     0.0     0.0    -1.0     1.0     0.0
gw2_q8     0.0     0.0     0.0     0.0     0.0     0.0     0.0    -1.0     1.0 

G:
gw2_q0    210.000000
gw2_q1    140.000000
gw2_q2    140.000000
gw2_q3    333.333333
gw2_q4     13.500000
gw2_q5     13.500000
gw2_q6     13.500000
gw2_q7     13.500000
gw2_q8    110.000000
dtype: float64 

C:
gw2_θ0          0.0
gw2_θ1    4048000.0
gw2_θ2          0.0
gw2_θ3          0.0
gw2_θ4      26620.0
gw2_θ5          0.0
gw2_θ6      26620.0
gw2_θ7          0.0
gw2_θ8          0.0
dtype: float64 

b:
gw2_q0     To
gw2_q1    0.0
gw2_q2    0.0
gw2_q3    0.0
gw2_q4    0.0
gw2_q5    0.0
gw2_q6    0.0
gw2_q7    0.0
gw2_q8    0.0
dtype: object 

f:
gw2_θ0     Qo
gw2_θ1    0.0
gw2_θ2    0.0
gw2_θ3    0.0
gw2_θ4    0.0
gw2_θ5    0.0
gw2_θ6    0.0
gw2_θ7     Qi
gw2_θ8    0.0
dtype: object 

y:
gw2_θ0    0.0
gw2_θ1    1.0
gw2_θ2    1.0
gw2_θ3    0.0
gw2_θ4    0.0
gw2_θ5    0.0
gw2_θ6    0.0
gw2_θ7    0.0
gw2_θ8    1.0
dtype: float64 

Wall: gw3
A:
        gw3_θ0  gw3_θ1  gw3_θ2  gw3_θ3  gw3_θ4  gw3_θ5  gw3_θ6  gw3_θ7  \
gw3_q0    -1.0     1.0     0.0     0.0     0.0     0.0     0.0     0.0   
gw3_q1     0.0    -1.0     1.0     0.0     0.0     0.0     0.0     0.0   
gw3_q2     0.0     0.0    -1.0     1.0     0.0     0.0     0.0     0.0   
gw3_q3     0.0     0.0     0.0    -1.0     1.0     0.0     0.0     0.0   
gw3_q4     0.0     0.0     0.0     0.0    -1.0     1.0     0.0     0.0   
gw3_q5     0.0     0.0     0.0     0.0     0.0    -1.0     1.0     0.0   
gw3_q6     0.0     0.0     0.0     0.0     0.0     0.0    -1.0     1.0   
gw3_q7     0.0     0.0     0.0     0.0     0.0     0.0     0.0    -1.0   
gw3_q8     0.0     0.0     0.0     0.0     0.0     0.0     0.0     0.0   

        gw3_θ8  gw3_θ9  
gw3_q0     0.0     0.0  
gw3_q1     0.0     0.0  
gw3_q2     0.0     0.0  
gw3_q3     0.0     0.0  
gw3_q4     0.0     0.0  
gw3_q5     0.0     0.0  
gw3_q6     0.0     0.0  
gw3_q7     1.0     0.0  
gw3_q8    -1.0     1.0   

G:
gw3_q0    440.000000
gw3_q1    280.000000
gw3_q2    280.000000
gw3_q3    666.666667
gw3_q4     27.000000
gw3_q5     27.000000
gw3_q6     27.000000
gw3_q7     27.000000
gw3_q8    240.000000
dtype: float64 

C:
gw3_θ0          0.0
gw3_θ1          0.0
gw3_θ2    8096000.0
gw3_θ3          0.0
gw3_θ4          0.0
gw3_θ5      53240.0
gw3_θ6          0.0
gw3_θ7      53240.0
gw3_θ8          0.0
gw3_θ9          0.0
dtype: float64 

b:
gw3_q0    0.0
gw3_q1    0.0
gw3_q2    0.0
gw3_q3    0.0
gw3_q4    0.0
gw3_q5    0.0
gw3_q6    0.0
gw3_q7    0.0
gw3_q8    0.0
dtype: object 

f:
gw3_θ0    0.0
gw3_θ1     Qo
gw3_θ2    0.0
gw3_θ3    0.0
gw3_θ4    0.0
gw3_θ5    0.0
gw3_θ6    0.0
gw3_θ7    0.0
gw3_θ8     Qi
gw3_θ9    0.0
dtype: object 

y:
gw3_θ0    0.0
gw3_θ1    1.0
gw3_θ2    1.0
gw3_θ3    1.0
gw3_θ4    0.0
gw3_θ5    0.0
gw3_θ6    0.0
gw3_θ7    0.0
gw3_θ8    0.0
gw3_θ9    0.0
dtype: float64 

Outdoor walls#

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

Figure 3a shows 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).

in_wall

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

walls = pd.read_csv(folder + '/walls_out.csv')
walls

	ID	type	Area	β	γ	albedo	T0	Q0	Q1	h0	h1	α0	α1	ε0	ε1	y
0	w0	1	1	90	0	0.25	To	Qo	Qi	20	10	0.25	0.3	0.85	0.7	[0, -1]
1	w1	1	1	90	0	0.25	To	Qo	Qi	20	10	0.25	0.3	0.85	0.7	1
2	w2	0	10	0	90	0.25	To	Qo	Qi	21	11	0.25	0.3	0.85	0.7	[1, 2, -1]
3	w3	0	20	0	90	0.25	Tsoil	Qo	Qi	22	12	0.25	0.3	0.85	0.7	[2, 1, 3]

# Thermal circuits from data & type files of walls
TCd_out = dm4bem.wall2TC(wall_types, walls, prefix="o")

# Uncomment below to print all thermal circuits
# print('TCd_out')
# for key in TCd_out.keys():
#    print('Wall:', key)
#    pd_dm4bem.print_TC(TCd_out[key])

Indoor walls#

Indoor walls do not have temperature sources on surfaces (Figure 4, link). 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.