# Mapping of the Indoor Conditions by Infrared Thermography

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Theoretical Fundamentals of the Sensor

#### 2.1. The Measurement Grid

#### 2.2. Thermal Model of the Sensor

#### 2.3. Estimation of the Ambient Parameters

## 3. Experimental Performance of the Sensor

#### 3.1. Validation of the Thermal Model of the Sensor

#### 3.2. Validation of the Measurement of Air Speed

#### 3.3. Validation of the Measurement of Air Temperature and Mean Radiant Temperature

## 4. 3D Reconstruction of the Measurement Grid

#### 4.1. Scanning of the Measurement Grid

#### 4.2. Detection of Sensors in the Images

#### 4.3. Corresponding Points between Images

#### 4.4. Geometric Calibration of A Camera

#### 4.5. Triangulation by Stereoscopic Vision

#### 4.6. Rotation and Translation between Two Positions of the Camera

## 5. Mapping of the Indoor Parameters

#### 5.1. Acquisition System

#### 5.2. Example of 2D Mapping of Air Speed and Air Temperature above A Fan-Coil Unit

#### 5.2.1. 2D Mapping of the Air Speed

#### 5.2.2. Air Thermal Stratification

#### 5.2.3. 2D Mapping of the Air Temperature

#### 5.3. Example of 3D Mapping of Air Speed and Air Temperature above a Fan-Coil Unit

## 6. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 1.**Measurement grid [21]. Reprinted with permission from Rev. Sci. Instrum., 84, 084906 (2013). Copyright 2013 American Institute of Physics.

**Figure 2.**Thermal model of the sensor [21]. Reprinted with permission from Rev. Sci. Instrum., 84, 084906 (2013). Copyright 2013 American Institute of Physics.

**Figure 3.**Performance of the sensor. (

**a**) Sensor without (

**left**) and with (

**right**) the high-emissivity paint; (

**b**) synoptic of the experimental setup; and (

**c**) the experimental setup.

**Figure 4.**Typical curves; (

**a**) experimental and estimated curves; and (

**b**) difference between both curves.

**Figure 5.**CHTC versus air speed. (

**a**) Experimental results; and (

**b**) comparison with other correlations.

**Figure 6.**Measurement error on air temperature versus the ratio ${h}_{2}/{h}_{1}$. (

**a**) ${h}_{1}=8.77\text{W}/{\mathrm{m}}^{2}/\mathrm{K}$; (

**b**) ${h}_{1}=14.00\text{W}/{\mathrm{m}}^{2}/\mathrm{K}$; and (

**c**) ${h}_{1}=18.74\mathrm{W}/{\mathrm{m}}^{2}/\mathrm{K}$.

**Figure 7.**MRT measured versus the ratio ${h}_{2}/{h}_{1}$. (

**a**) ${h}_{1}=8.77\text{W}/{\mathrm{m}}^{2}/\mathrm{K}$; (

**b**) ${h}_{1}=14.00\text{W}/{\mathrm{m}}^{2}/\mathrm{K}$; and (

**c**) ${h}_{1}=18.74\text{W}/{\mathrm{m}}^{2}/\mathrm{K}$.

**Figure 9.**Scanning of the measurement grid. (

**1**) to (

**6**): partial views of the measurement grid corresponding to the successive positions of the stereoscopic cameras.

**Figure 10.**Sensors detection in an IR image. (

**a**) Original image; (

**b**) edge points image; and (

**c**) detected sensors.

**Figure 17.**Data retrieved during the scanning. (

**1**) to (

**6**): partial views of the measurement grid corresponding to the successive positions of the cameras.

**Figure 18.**2D mapping above a fan-coil. (

**a**) Fan-coil position in the room; and (

**b**) scheme of the experimental setup.

**Figure 19.**2D mapping of the air speed above a fan-coil. (

**a**) Inlet air speed ${v}_{air1}=1.25\text{m}/\mathrm{s}$; (

**b**) inlet air speed ${v}_{air2}=1.95\text{m}/\mathrm{s}$; and (

**c**) inlet air speed ${v}_{air3}=2.80\text{m}/\mathrm{s}$.

**Figure 20.**2D mapping of the air speed above a fan-coil, horizontal profiles. (

**a**) Height of $10\text{cm}$; (

**b**) height of $50\text{cm}$; and (

**c**) height of $90\text{cm}$.

**Figure 22.**Air stratification. (

**a**) Air temperature spatial distribution; (

**b**) horizontal profiles; and (

**c**) vertical profile at the center axis.

**Figure 23.**2D mapping of the air temperature above a fan-coil. (

**a**) Inlet air speed ${v}_{air1}=1.25\text{m}/\mathrm{s}$; (

**b**) inlet air speed ${v}_{air2}=1.95\text{m}/\mathrm{s}$; and (

**c**) inlet air speed ${v}_{air3}=2.80\text{m}/\mathrm{s}$.

**Figure 24.**3D mapping above a fan-coil. (

**a**) Experimental setup; and (

**b**) successive positions of the measurement grid.

**Figure 25.**3D coordinates of the sensors. (

**a**) Raw data of the triangulation; (

**b**) filtered data; and (

**c**) the reconstructed measurement grid for the four positions.

Quantity | Class C (Comfort) | Class S (Thermal Stress) | ||
---|---|---|---|---|

Measuring Range | Accuracy | Measuring Range | Accuracy | |

Air speed | [0.05; 1] m/s | Required:±(0.05 + 0.05v _{air}) m/s^{a}Desirable: ±(0.02 + 0.07v _{air}) m/s^{a} | [0.2; 20] m/s | Required:±(0.1 + 0.05v _{air}) m/s^{a}Desirable: ±(0.05 + 0.05v _{air}) m/s^{a} |

Air temperature | [10; 40] °C | Required: ±0.5 °C ^{b}Desirable: ±0.2 °C ^{b} | [−40; 120] °C | Required:[−40; 0]°C: ±(0.5 + 0.01|T _{air}|) °C^{c}[0; 50] °C: ±0.5 °C ^{c}[50; 120] °C: ±(0.5+0.04(T _{air} − 50)) °C^{c}Desirable: required/2 ^{c} |

Mean radiant temperature | [10; 40] °C | Required: ±2 °CDesirable: ±0.2 °CWhen the levels cannot be achieved, indicate the actual measuring precision. | [−40; 150] °C | Required:[−40; 0] °C: ±(5 + 0.02|T_{air}|) °C[0; 50] °C: ±5 °C[50; 150] °C: ±(5+0.08(T_{rad} − 50))°CDesirable: [−40; 0] °C: ±(0.5 + 0.01|T_{rad}|)°C[0; 50] °C: ±5 °C[50; 150] °C: ±(0.5 + 0.04(T_{rad} − 50)) °C |

_{air}− T

_{rad}| ≤ 10 °C; c: these levels shall be guaranteed at least for |T

_{air}− T

_{rad}| ≤ 20 °C.

Trial | Air Temperature (°C) | Lamp Power | Air Speed (m/s) CHTC (W/m ^{2}/K) | $\mathbf{\Delta}{\mathit{v}}_{\mathit{a}\mathit{i}\mathit{r}}$ (m/s) | ||||||
---|---|---|---|---|---|---|---|---|---|---|

1 | 2 | 3 | 4 | 5 | 6 | 7 | ||||

1 | 25.5 ± 0.5 | P_{1} | 0 8.77 | 0.15 14.00 | 0.30 18.74 | 0.45 23.03 | 0.75 30.41 | 1.30 40.60 | 2.00 49.81 | 0.2 |

2 | P_{2} | |||||||||

3 | P_{3} | |||||||||

4 | P_{4} = 0 |

Trial | ${\mathit{h}}_{\mathbf{2}}\mathbf{/}{\mathit{h}}_{\mathbf{1}}\mathbf{>}\mathbf{2.63}$ ${\mathit{h}}_{\mathbf{1}}\mathbf{=}\mathbf{8.77}W\mathbf{/}{m}^{\mathbf{2}}\mathbf{/}K$ | ${\mathit{h}}_{\mathbf{2}}\mathbf{/}{\mathit{h}}_{\mathbf{1}}\mathbf{>}\mathbf{1.60}$ ${\mathit{h}}_{\mathbf{1}}\mathbf{=}\mathbf{8.77}W\mathbf{/}{m}^{\mathbf{2}}\mathbf{/}K$ | ${\mathit{h}}_{\mathbf{2}}\mathbf{/}{\mathit{h}}_{\mathbf{1}}\mathbf{>}\mathbf{1.60}$ ${\mathit{h}}_{\mathbf{1}}\mathbf{=}\mathbf{14.00}W\mathbf{/}{m}^{\mathbf{2}}\mathbf{/}K$ | |||
---|---|---|---|---|---|---|

Mean Value | Standard Deviation | Mean Value | Standard Deviation | Mean Value | Standard Deviation | |

1 | 67.91 °C | 0.75 °C | 67.00 °C | 1.67 °C | 74.55 °C | 1.72 °C |

2 | 53.32 °C | 0.69 °C | 52.53 °C | 1.42 °C | 57.98 °C | 1.22 °C |

3 | 37.29 °C | 0.42 °C | 36.88 °C | 0.73 °C | 40.38 °C | 1.26 °C |

4 | 23.73 °C | 0.22 °C | 23.80 °C | 0.22 °C | 22.84 °C | 0.52 °C |

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**MDPI and ACS Style**

Djupkep Dizeu, F.B.; Maldague, X.; Bendada, A.
Mapping of the Indoor Conditions by Infrared Thermography. *J. Imaging* **2016**, *2*, 10.
https://doi.org/10.3390/jimaging2020010

**AMA Style**

Djupkep Dizeu FB, Maldague X, Bendada A.
Mapping of the Indoor Conditions by Infrared Thermography. *Journal of Imaging*. 2016; 2(2):10.
https://doi.org/10.3390/jimaging2020010

**Chicago/Turabian Style**

Djupkep Dizeu, Frank Billy, Xavier Maldague, and Abdelhakim Bendada.
2016. "Mapping of the Indoor Conditions by Infrared Thermography" *Journal of Imaging* 2, no. 2: 10.
https://doi.org/10.3390/jimaging2020010