1. Hot wire measurement method based on inverse method
Presented by
Matthieu THOMAS
PhD thesis: Airbus/LTN
Hot wire measurement method based on inverse method
SFT – Airbus meeting
Monolithic composites thermal characterisation
Round Robin Test
May 19, Toulouse

2. Hot wire measurement technique
First part
Hot wire measurement technique
Mai 2005 Round Robin test

3. 4 Coupons of polymer reinforced with fibres aligned along x-direction
General description
4 Coupons of polymer reinforced with fibres aligned along x-direction x y z
hot wire
Heating step
Thermocouples z x
Insulation
Thermo-regulated plate
Temperature response measurement
Instrumented sample
Time
120mm
Temperature

4. General description x z ρcp Power dissipated by the hot wire (U,I) +
Temperature rises in the plane (x,z) x z
ρcp
Identification process
Advantages
Estimation simultaneously of 3 parameters
Alternative method for Cp measurement
Effective power dissipated in the sample is known and controlled
Drawbacks
Restricted to materials with low thermal conductivity
Instrumentation of the sample

5. Identification process
Initial parameters (x0, z0, ρCp0)
Criteria of calculations ending
Conductances (h1, h2)
Semi-infinite time (Tmax)
Exactness location of the thermocouples
Insulation, Grease
Measurement temperature q0 …
Comparison
Experimental data
Measured
temperatures
Numerical solver
Analytical solver
Calculated
temperatures
xi
zi
ρCpi
Inverse method
(Nelder Mead)
RMS x z
ρCp

6. Practical case  Mean of the residuals  zero
Residuals (°C)
Thermo n°2
Thermo n°3
Thermo n°1
Thermo n°5
Measurement noise: °C
RMS of residuals: °C
 Mean of the residuals  zero
 Systematic error / Bias
 Uncertainty on the thermocouples locations?

7. Measurement discrepancy - Future improvements
Repeatability test campaign
Dispersion dues to experimental conditions < 3%
Uncertainty on the thermocouples locations < 2%
Improvements
Realise a sensitivity analysis
Take into account the thermocouples location uncertainty
Measure the heat losses  Better known of limit conditions

8. Second part
Experimental results
Mai 2005 Round Robin test

9. Measurements realised
x, z, ρCp
25°, 40°, 60°, 95°C
Sample dimension: 120mm*120mm
Temperature imposed by thermo-regulated plates
Hot wire technique
5 measurements per temperature
REPEATABILITY
Dispersion of the measurement method

10. Thermal conductivity along fibres direction : x
Mean value 5%
Temperature (°C)
x (W/mK)
Mean value 25
4,67 40
4,89 60
5,23 80
5,62 90
5,92
Dispersion  5%

11. Transverse thermal conductivity : z
Mean value 5%
Temperature (°C)
z (W/mK)
Mean value 25
0.670 40
0.680 60
0.715 80
0.734 90
0.753

12. Specific heat Cp Cp (J/Kg.K) Mean value 5% Temperature (°C)25
945 40
1006 60
1089 80
1186 90
1221

13. Conclusion - Comments
Hot wire measurement method provides two thermal conductivities and the specific heat
Measurement dispersion  5%
Temperature (°C)
x (W/mK)
Mean value
z (W/mK)
Cp (J/Kg.K) 25
4,67
0.670
945 90
5,92
0.753
1221