3.4 Summary
157
An objective function S is introduced as an error norm to present the error
between calculated and experimental interior temperatures. Depending on the minimum objective function S obtained by the Levenberg-Marquardt (LM) method,
the thermal diffusivity can be estimated. However, since the LM method is a local
optimization algorithm, the objective function S may stop at an optimal local value
rather than an optimal global value, generating an incorrect result with an arbitrary
initial value. An integration equivalence principle is also proposed by considering
the intrinsic physical effect of the thermal diffusivity. This principle is allowed for
determining a proper initial value and avoiding the value falling into inauthentic local
results, by which the ill-posed problem of the inverse method can be solved.
The calculated results have proven that it is a practical algorithm for data processing, and the analyses of sensitivity and uncertainty also illustrate its desirable
characteristics on robustness and uncertainty. The uncertainty analysis indicates that
statistical errors of thermocouples make a little influence in the inverse method, while
a constant system error should be treated carefully.
Four heating tests have been conducted up to 1200
◦ C, of which two are under vacuum condition, and the others are helium tests. Repeatable results have been verified
in both experiments with different heating processes. The less time consumption in
helium tests implies that the effective thermal diffusivity in the helium condition is
higher than that in the vacuum condition. The comparison with HTTU and SANA
also proves the availability of this facility and the methodology.
Despite this, some temperature differences in the same radial position are observed
due to the errors of thermocouple installation and random packing structure in the
radial position. And this experiment finds the wall effect that also exists in the independent experiment of HTTU. By retrieving the proper positions and using the highorder spline function in the improved inverse method, the primary experimental
errors from installation positions of thermocouples, random packing effect, as well
as temperature variation produced by the wall effect can be eliminated or alleviated.
The improved inverse method not only reduces the disparities of diffusivities and
conductivities of different azimuthal sets. It also identifies the interesting decrease
of diffusivity of the helium test within low or moderate temperatures.
References
1. Li, C., C. Ren, X. Yang, S. Jiang, and Y. Sun. 2014. Thermal conductivity measurement of
carbon felt used in high temperature gas-cooled reactor and inverse problem calculation. Atomic
Energy Science and Technology 48: 1976–1984.
2. Jarny, Y., M.N. Ozisik, and J.P. Bardon. 1991. A general optimization method using adjoint
equation for solving multidimensional inverse heat conduction. International Journal of Heat
and Mass Transfer 34 (11): 2911–2919.
3. Beygi, K. Darya. 2002. Heat transfer in high-temperature fibrous insulation 17 (1): 10–20.
4. Huang, C., and Y. Zhang. 2014. Calculation of high-temperature insulation parameters and
heat transfer behaviors of multilayer insulation by inverse problems method. Chinese Journal
of Aeronautics 27: 791–796.
157
An objective function S is introduced as an error norm to present the error
between calculated and experimental interior temperatures. Depending on the minimum objective function S obtained by the Levenberg-Marquardt (LM) method,
the thermal diffusivity can be estimated. However, since the LM method is a local
optimization algorithm, the objective function S may stop at an optimal local value
rather than an optimal global value, generating an incorrect result with an arbitrary
initial value. An integration equivalence principle is also proposed by considering
the intrinsic physical effect of the thermal diffusivity. This principle is allowed for
determining a proper initial value and avoiding the value falling into inauthentic local
results, by which the ill-posed problem of the inverse method can be solved.
The calculated results have proven that it is a practical algorithm for data processing, and the analyses of sensitivity and uncertainty also illustrate its desirable
characteristics on robustness and uncertainty. The uncertainty analysis indicates that
statistical errors of thermocouples make a little influence in the inverse method, while
a constant system error should be treated carefully.
Four heating tests have been conducted up to 1200
◦ C, of which two are under vacuum condition, and the others are helium tests. Repeatable results have been verified
in both experiments with different heating processes. The less time consumption in
helium tests implies that the effective thermal diffusivity in the helium condition is
higher than that in the vacuum condition. The comparison with HTTU and SANA
also proves the availability of this facility and the methodology.
Despite this, some temperature differences in the same radial position are observed
due to the errors of thermocouple installation and random packing structure in the
radial position. And this experiment finds the wall effect that also exists in the independent experiment of HTTU. By retrieving the proper positions and using the highorder spline function in the improved inverse method, the primary experimental
errors from installation positions of thermocouples, random packing effect, as well
as temperature variation produced by the wall effect can be eliminated or alleviated.
The improved inverse method not only reduces the disparities of diffusivities and
conductivities of different azimuthal sets. It also identifies the interesting decrease
of diffusivity of the helium test within low or moderate temperatures.
References
1. Li, C., C. Ren, X. Yang, S. Jiang, and Y. Sun. 2014. Thermal conductivity measurement of
carbon felt used in high temperature gas-cooled reactor and inverse problem calculation. Atomic
Energy Science and Technology 48: 1976–1984.
2. Jarny, Y., M.N. Ozisik, and J.P. Bardon. 1991. A general optimization method using adjoint
equation for solving multidimensional inverse heat conduction. International Journal of Heat
and Mass Transfer 34 (11): 2911–2919.
3. Beygi, K. Darya. 2002. Heat transfer in high-temperature fibrous insulation 17 (1): 10–20.
4. Huang, C., and Y. Zhang. 2014. Calculation of high-temperature insulation parameters and
heat transfer behaviors of multilayer insulation by inverse problems method. Chinese Journal
of Aeronautics 27: 791–796.