Accounting for Transient Temperature Measurement Error
with a High Fidelity Thermocouple and Application to Metal/Mold Interfacial
Heat Flux Estimation
The University of Alabama
Department of Mechanical Engineering
August 2008
Abstract of Dissertation
A high fidelity three-dimensional
sensor model is developed to account for bias errors in solid-embedded
thermocouples. The model yields unprecedented bias estimates. The detail
of the model permits the representation of the three compositional regions of
the thermocouple: the two wires and the weld. The improvement in the error
estimates is demonstrated by contrasting the results with axisymmetric model
results. A theory is developed to relate the sensed temperature within a
thermocouple to the modeling of the thermocouple’s sensed temperature.
The kernel method for correcting
thermocouple measurements is derived. This derivation yields a convolution
which contains a kernel function. The kernel function can be expressed in terms
of discrete numerical data in Laplace transform space. Methods for obtaining
the values of the kernel in the time domain are introduced and evaluated. An adaptation
of Beck’s sequential function specification method is shown to be the most
reliable technique for obtaining the kernel values.
The technique is applied to the
problem of evaluating heat transfer at the cast metal/mold interface. The most
expansive review ever published of metal/mold interfacial heat transfer
literature is included. The methodology is demonstrated with a numerical
aluminum sand casting experiment. Thermocouples configured parallel and
perpendicular to the mold surface are considered. For both configurations, the RMS
errors for the temperature histories improved by 93%. The RMS errors for
the heat fluxes improved by 72% for the perpendicular case and by 57% for the
parallel case.
The methods are applied to
experimental data obtained from thermocouples installed perpendicular and
parallel to the surface of aluminum sand castings. The temperature data was
used to estimate the surface heat flux. The heat flux estimates increased by up
to 85% for the perpendicular data and by up to 48% for the parallel data.
For the perpendicular thermocouples, the RMS difference between the heat
fluxes estimated with measured and corrected temperatures was 30.3 kW/m2
for the mold bottom and 56.6 kW/m2 for the top. For the parallel
thermocouples, the RMS difference between the heat fluxes estimated with
measured and corrected temperatures was 27.3 kW/m2 for the bottom
and 18.8 kW/m2 for the top.
Acknowledgments
