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Understanding the origin of uncertainty in thermometer calibration

01 April 2015

Researchers at the UK's National Physical Laboratory are using simulation software to improve the calibration of temperature sensors. Jennifer Hand reports.

Thermometers have widespread application, ranging from their role in measuring temperature in common consumer goods to integration in sophisticated medical and industrial technology or processes. Like any measurement device, they must be calibrated against the International Temperature Scale of 1990 (ITS-90).

ITS-90 is based on fixed-points at which a pure metal changes its phase by melting or freezing. During the phase change process, heat is either absorbed or released by the metal without changing its temperature. At a fixed point, a thermometer immersed in it observes a temperature plateau that can be used as a practical reference.

As Jonathan Pearce, who leads contact thermometry at the National Physical Laboratory, explains, the ITS-90 is disseminated to users with the standard platinum resistance thermometer - a very sensitive device capable of measuring temperatures with a precision of the order of a microkelvin.

The platinum resistance thermometer calibrates using a fixed-point cell. This is typically a graphite crucible, which is a container with a well running through its centre for insertion of the thermometer. In the container is a material of very high purity - typically 99.9999 percent. The central well allows a thermometer to be inserted so that the sensing element at its bottom is completely immersed in the fixed-point metal. The container is then placed in a furnace to allow controlled melting and freezing of the metal.

Despite the high-performance device, the uncertainty of temperature during calibration can still be of the order of 1 millikelvin. To better understand the microscopic behaviour, Pearce, working with Surrey University student Matthew Large, turned to COMSOL Multiphysics simulation software.

Simulating morphological instability
Freezing or solidification is much less well-behaved than melting. For example, some areas will solidify before others, thus influencing the freezing temperature. The simulation utilising the phase-field method implemented in COMSOL Multiphysics provided the researches with fascinating insights: under certain conditions the liquid-solid interface is not planar at all; as freezing progresses, ripples become apparent at the interface. These become cells that begin to protrude outwards (see illustration) with their tips being at a significantly lower temperature than their roots. 

“This positive feedback loop is very interesting,” says Pearce. “Although such an effect was predicted by Mullins and Sekerka in the 1960s, this is the first time we have observed its manifestation in this context. Our main objective was to simulate freezing behaviour by investigating the effect of furnace settings on the process and identifying what the actual sensor used was measuring. The working model we ended up with is a very powerful means of understanding the influence of heat and mass flow on the evolution of the liquid-solid interface.”

Through simulation, it is possible to identify specific behaviour in a system that is difficult to observe experimentally and yet contributes to the overall uncertainty in a measurement. The information gained through simulation can be applied to a thoughtful re-design of the device, ultimately improving measurement precision.

Simulation in measurement validation
NPL continues to demonstrate its commitment to multiphysics modelling with additional licences ordered of COMSOL Multiphysics and a selection of its add-on products. The software will be used by research teams across the technical areas covered by NPL to support their work developing and validating measurement techniques. 

“NPL is pleased to be able to expand its relationship with COMSOL,” says Louise Wright, Principal Research Scientist, Mathematics & Modelling Group at NPL. “COMSOL Multiphysics has already supported the development and analysis of equipment and experiments in areas ranging from improving the realisation of the international temperature scale of 1990 [ITS-90], to designing microfabricated ion traps for applications in quantum information processing, quantum metrology, and optical clocks.

"The new licensing agreement will help us to quickly respond to measurement challenges in new applications, and be confident in the knowledge that we are using a reliable software for our multiphysics simulations.”

With the new purchase, NPL now uses COMSOL to integrate with CAD software and to simulate systems involving acoustics, heat transfer, chemical reactions, MEMS and microfluidic devices, CFD, optics and photonics, high and low frequency electromagnetics, and other physics within the electrical, mechanical, fluid, and chemical disciplines.

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