Uncertainty Of Temperature Measurements Research Articles

Approaching the emissivity of CMAS at high temperatures by convenient thermocouple-based infrared thermography

It remains a grand challenge to probe the emissivity of calcium-magnesium-alumina-silicates (CMAS) at high temperatures. Herein, an innovative thermocouple-based infrared thermography (TBIT) method that combines a double hot thermocouple system and infrared (IR) camera is proposed to enable convenient measurement for CMAS emissivity at temperature >800 °C. To improve the measurement accuracy, a heat transfer model accounting for the possible uncertainty in temperature measurement is also developed to correct the real sample temperature on the hot thermocouple. On this basis, the feasibility of the TBIT method is verified by using the platinum-rhodium alloy as the benchmark. As a proof-of-principle demonstration, four different sets of CMAS samples, i.e., blast furnace (BF) slag are considered with their temperature-dependent emissivities characterized experimentally. It is found that the BF-like CMAS features an emissivity of 0.5–0.9 at 800–1500 °C. This research provides a fast, accurate and low-cost experiment effort to probe CMAS emissivity at high temperatures, which enriches the thermophysical properties of the CMAS materials.

Effective Noise Reduction Filters for Precise Temperature Measurement Using Brillouin Distributed Optical Fiber Sensors

This study explores the effectiveness of various noise reduction filters in accurately measuring temperature distributions over a 38.2 km single-mode fiber (SMF). Brillouin optical time-domain analysis (BOTDA) sensor is utilized to gather Brillouin gain spectra (BGSs), which are denoised using bilateral filter (BF), guided filter (GF), adaptive Wiener filter (AWF), non-local means filter (NLMF), average filter (AF) and disc filter (DF). The temperature distributions over the SMF are then determined by applying least-squares curve fitting (LSCF). The study assesses the efficacy of noise reduction filters considering signal-to-noise ratio (SNR), uncertainty in temperature measurement (UTM), experimental spatial resolution (ESR) and signal processing speed (SPS). Among six different filters, NLMF outperforms other filters which can provide SNR improvement of 10.22 dB for which the UTM can be improved by 58.93% without deteriorating the ESR of the sensor. The noise reduction using such filter can also provide 6.2% faster SPS. Therefore, NLMF can be considered as an effective noise reduction filter for the precise temperature measurement using BOTDA sensors. DUJASE Vol. 8 (1) 42-50, 2023 (January)

Analysis of Test Specimen Temperature Gradients Incurred in Resistive Heating System Oxidation Studies of Ultra-High Temperature Ceramics

AbstractThe need for advanced materials that can meet application requirements at ultra-high temperatures in oxidizing environments is an area of active research. One challenge facing the high temperature materials community is the ability to conduct controlled ultra-high temperature oxidation tests with minimal to no contamination or reaction with the chamber. A unique resistive heating system (RHS) capable of achieving ultra-high temperatures (> 1700 °C) to enable such experimentation is described. A concern of such a system is the potential presence of thermal gradients in directions not reflective of actual material applications, e.g., the hottest region being in the center of the sample. Experimental results from the oxidation of ZrB2 specimens at nominal temperatures of 1500°, 1700° and 1800 °C in low pO2 (0.1–1% O2 in Ar) environments are presented. Specimen thermal gradients generated during oxidation were evaluated using finite element analysis models. Thermal gradients on the order of the uncertainty in temperature measurements were calculated, confirming the RHS suitability for conducting ultra-high temperature oxidation exposures on ultra-high temperature ceramics.

Performance improvement of a distributed temperature sensor with kilometer length and centimeter spatial resolution based on polarization-sensitive OFDR

A method to improve the performance of distributed temperature sensors with kilometer sensing distance and centimeter spatial resolution is proposed based on polarization-sensitive optical frequency domain reflectometry (OFDR). This approach records the temperature change along polarization maintaining fiber (PMF) from the Rayleigh backscattering (RBS) spectral difference between two orthogonal polarization axes using the distributed autocorrelation algorithm, where PMF is used as the sensing fiber. In addition, a technique to calibrate population birefringence and local birefringence, and a method to calibrate the initial birefringence inhomogeneity of PMF are proposed to enhance the performance of the sensor. The birefringence of PMF is used for temperature sensing, which is distinct from the traditional cross-correlation method of single-mode optical fiber temperature sensing, providing us with an innovative scheme to solve real-world engineering problems. The final sensing performance is achieved, with a sensing distance of 1.5 km, a spatial resolution of 5 cm, and a temperature measurement uncertainty of ±0.2 °C, subject to environmental noise and system random noise.

Analysis of statistical uncertainties of non-contact temperature and emissivity measurements in the optical and near infrared ranges

The aim of this report is the analysis of the uncertainties of non-contact measurement of temperature and emissivity determined by the least sum of squares (LSS) method. Analytical expressions are obtained for the uncertainties of the temperature T and the emissivity ε by three methods: (1) linear regression using the Wien approximation, (2) non-linear regression with covariance matrix calculation using the Planck’s equation, and (3) hybrid method that combines linear and non-linear regression methods. It was found that the better the condition for the Wien’s approximation is fulfilled, the worse the accuracy of the emissivity measurement compared to the accuracy of the temperature measurement. The new optimal strategy is proposed to determine the T and the emissivity ε for non-contact measurements. It consists of three steps: (1) the temperature of the radiating body is found by the Wien approximation, TW; (2) the obtained value TW is used as an initial approximation for one-dimensional “hybrid” minimization. Minimization is carried out by one of the numerical methods of one-dimensional minimization. As a result, the values of ε0 and T0 are found at with the sum of the squared residuals, S0, reaches a minimum; (3) Measurement uncertainties are estimated using the covariance matrix method.

Investigations of Flow Boiling in Mini-Channels: Heat Transfer Calculations with Temperature Uncertainty Analyses

The article aims to explore boiling heat transfer in mini-channels with a rectangular cross-section using various fluids (HFE-649, HFE-7000, HFE-7100, and HFE-7200). Temperature measurements were conducted using infrared thermography for the heated wall and K-type thermocouples for the working fluid. The 2D mathematical model for heat transfer in the test section was proposed. Local heat transfer coefficients between the heated wall and the working fluid were determined from the Robin condition. The problem was solved by means of the finite element method (FEM) with Trefftz functions. The values of the heat transfer coefficient that were obtained were compared with the results calculated from Newton’s law of cooling. The average relative differences between the obtained results did not exceed 4%. The study included uncertainty analyses for temperature measurements with K- and T-type thermocouples. Expanded uncertainties were calculated using the uncertainty propagation and Monte Carlo methods. Precisely determining the uncertainties in contact temperature measurements is crucial to ensure accurate temperature data for subsequent heat transfer calculations. The results of the heat transfer investigations were compared in terms of fluid temperature, heat transfer coefficients, and boiling curves. HFE-7200 consistently exhibited the highest fluid temperature and temperature differences at boiling incipience, while HFE-7000 demonstrated the highest heat transfer coefficients. HFE-649 showed the lowest heat transfer coefficients. The boiling curves exhibited a typical shape, with a notable occurrence of ‘nucleation hysteresis phenomena’. Upon the analysis of two-phase flow patterns, bubbly and bubbly-slug structures were observed.

High-accuracy high temperature measurement based on forward Brillouin scattering of polyimide-coated optical fiber

In this paper, a novel method for high-accuracy high temperature measurement is proposed, which is based on forward Brillouin scattering (FBS) of double-coated optical fiber with polyimide outer coating. The temperature variation changes the acoustic properties of polyimide-coated fiber that is suitable for high temperature measurement in the range of 120 ∼ 220 ℃. An interesting feature is that different radial acoustic modes have different frequency responses in the polyimide-coated fiber. Another interesting phenomenon is that the temperature linearly depends on the frequency shift of FBS spectrum with high sensitivity from 120 ℃ to 220 ℃. By using one acoustic mode with a high frequency shift-temperature sensitivity, we propose a novel high temperature measurement method based on FBS with high measurement accuracy. The experimental result shows that the low temperature measurement uncertainty of 0.02 ℃ can be achieved. The proposed method is expected to be used for high-accuracy temperature measurement applications within a temperature range of 100 ∼ 200 ℃, such as underground oil layer detection, power plant monitoring and high-power electrical systems monitoring.

TEMPERATURE CORRECTION METHOD OF RADIATION THERMOMETER BASED ON THE NONLINEAR MODEL FITTED FROM SPECTRAL EMISSIVITY MEASUREMENTS OF Ni-BASED ALLOY

Accurate temperature monitoring of heat transfer tube is crucial for safe and efficient operation of nuclear power plants, and radiation thermometer is a common method used for this purpose. This paper thoroughly introduces the measurement principle of the radiation thermometer with an operation wavelength range of 8-14 μm. The spectral emissivity of Ni-based alloy DD6 under argon condition is measured using an emissivity measurement setup equipped with a Fourier-transform infrared (FTIR) spectrometer. By integrating the spectral emissivity in the working wavelength range, the spectral band emissivity can be calculated to enhance the accuracy of calculation results obtained by radiation thermometer. And curve of the spectral band emissivity with temperature can be accurately described by the nonlinear model. The radiation and corrected temperatures are compared with the temperatures obtained by a K-type thermocouple to verify the availability of the spectral band emissivity obtained by fitting the nonlinear model. The temperature comparison results demonstrate that the corrected temperatures are closer to the true temperature than the radiation temperature, with a maximum temperature deviation of only 4.38°C. The combined relative uncertainty of true temperature measurement by the radiation thermometer at temperatures of 200, 300, 400, and 500°C is less than 3.60%.

Fast Brillouin optical time domain sensing based on two-dimension sparse sampling and deep learning recovery

Brillouin optical time domain sensing (BOTDS) is a technique for acquiring the Brillouin scattering spectrum (BSS) of a fiber under test (FUT) by utilizing multiple frequency scans. However, the time-consuming nature of this process limits its applicability in scenarios that require rapid measurements. In order to enhance measurement efficiency and decrease storage capacity, without compromising measurement accuracy or spatial resolution, we propose a novel fast BOTDS method based on two-dimensional (2D) sparse sampling and residual channel attention network (RCAN). The proposed method employs sparse sampling to measure the BSS signal, which is then accurately restored to the BSS with normal frequency sampling intervals by using deep learning techniques. Temperature and strain information is extracted from the restored BSS, facilitating rapid and precise measurements. The effectiveness of the proposed method has been verified through simulation and experiments. In a proof-of-concept experiment, we employed a 3000 m bend-insensitive fiber as the sensing fiber and reduced the sampling frequency by a factor of 10. Our proposed method successfully recovered the Brillouin scattering spectrum signal, resulting in a temperature measurement uncertainty of 0.25 °C. Moreover, the measurement accuracy and spatial resolution almost remained unaffected, surpassing that of interpolation-based approaches.

A two-step in situ measurement method for temperature and thermal stress of power device based on a single Raman peak

Temperature and thermal stress are primary factors leading to the performance failure of power devices. Thus, simultaneously determining the temperature and stress variation of the working devices has become the premise of revealing the failure mechanism. However, the existing methods are still unsatisfactory for in-situ temperature-stress decoupling measurement. To solve this problem, a two-step decoupling method based on a single Raman peak is proposed. In the calibration step, the effective temperature - Raman shift coefficients at different positions of the power devices were measured in the OFF state, and the contribution ratio of temperature and thermal stress to the single peak shift can be determined by analyzing the difference of effective temperature - Raman shift coefficients with intrinsic temperature - Raman shift coefficient. In the in-situ measurement step, the temperature rise and thermal stress variation can be calculated based on the Raman peak shift of the target semiconductor layer and the calibrated contribution ratio. A measurement of the GaN high electron mobility transistor was used to further illustrate the advantages of the proposed method. Compared with the previous multi-peak decoupling method, the temperature and thermal stress distributions of the working device obtained by the two-step decoupling method make more physical sense, and the measurement uncertainty of temperature and stress can be reduced to 1/4 and 1/3 of the previous method respectively. The consistency with the thermo-stress simulation further verifies the reliability and accuracy of the proposed method.

Thermal Conductivity of Ternary Aqueous H2O + Li2SO4 + Zn(NO3)2 Solutions at High Temperatures and Pressures

The thermal conductivity of ternary aqueous H2O + Li2SO4 + Zn(NO3)2 solutions at high temperatures (from 298 to 573 K) and at two isobars of 10 and 30 MPa is reported in the present work. The measurements were made for five solutions with concentration ratios of Li2SO4/Zn(NO3)2 of 1:1, 2:1, 1:2, 1.75:2.00, and 0.7:0.3 (mol·kg–1) using a concentric cylinder (steady) method. The combined expanded relative uncertainties of thermal conductivity, pressure, concentration, and the absolute uncertainty of temperature measurements (at 0.95 confidence level, a coverage factor of k = 2) were estimated to be less than 0.02, 0.0005, 0.0002, and 20 mK, respectively. The measured data were used to confirm the reliability, accuracy, and predictive capability of the existing correlation methods for multicomponent aqueous electrolyte solutions. It was shown that the temperature and pressure behavior of the aqueous solutions is controlled by the water. The effect of Li2SO4 and Zn(NO3)2 concentrations on the thermal conductivity of H2O + Li2SO4 + Zn(NO3)2 solutions at various temperatures and pressures has been studied.

Fast and Accurate Brillouin Optical Time-Domain Sensing by Sparse Frequency Sampling and ANN-Based Recover Method

We propose a novel sparse frequency sampling and Brillouin scattering spectrum (BSS) recover method to greatly reduce the acquisition time of the frequency-sweep based Brillouin optical time domain sensor (BOTDS) without increasing hardware complexity. In the proposed method, the acquired BSSs only contain a few frequency points and thus show low resolution due to the sparse frequency sampling strategy. Then an artificial neural network (ANN) is used to accurately recover the BSSs with sparse frequency sampling to that with normal frequency sampling, and thus achieve fast and accurate temperature/strain measurement. In a proof-of-concept experiment, we measured the BSS of a 3 km sensing fiber and achieved 3 m spatial resolution by using a Brillouin optical time domain reflectometry (BOTDR) sensor. Through sparse frequency sampling, the data acquisition time is 5.5% with respect to that of the normal sampling. When the average (AVG) times of BSS is higher than 1000, the temperature measurement uncertainty is 0.2 °C.

Magnetic particle based MRI thermometry at 0.2 T and 3 T

This study provides insight into the advantages and disadvantages of using ferrite particles embedded in agar gel phantoms as MRI temperature indicators for low-magnetic field scanners. We compare the temperature-dependent intensity of MR images at low-field (0.2 T) to those at high-field (3.0 T). Due to a shorter T1 relaxation time at low-fields, MRI scanners operating at 0.2 T can use shorter repetition times and achieve a significant T2⁎ weighting, resulting in strong temperature-dependent changes of MR image brightness in short acquisition times. Although the signal-to-noise ratio for MR images at 0.2 T MR is much lower than at 3.0 T, it is sufficient to achieve a temperature measurement uncertainty of about ±1.0 °C at 37 °C for a 90 μg/mL concentration of magnetic particles.

Heat Transfer Calculations during Flow in Mini-Channels with Estimation of Temperature Uncertainty Measurements

The main aim of this work was to provide heat transfer calculations of flow boiling in mini-channels with an application for the Trefftz functions. The test section comprised five parallel mini-channels with a depth of 1 mm, with a common heated wall. For the estimation of the temperature uncertainty, during the experiment the temperature measurement was performed with the use of K-type thermoelements and an infrared camera in two mini-channels simultaneously. According to the Guide to the Expression of Uncertainty in Measurement, the Monte Carlo method is a practical alternative to the GUM uncertainty framework. Since the uncertainty components are not approximately the same magnitude, the Monte Carlo method was indicated to estimate the uncertainty of the surface temperature measurement. The results obtained from this simulation method were compared with the results of the computation related to the uncertainty propagation method. The results of both methods of temperature measurement were found to be consistent. The results of the statistical analysis were used to describe heat transfer calculations. The heat transfer investigations concerning the subcooled boiling region were performed during the other experiment. The local heat transfer coefficients on the contact surface between the working fluid and the heated wall were calculated from the Robin boundary condition. The mathematical model described by the heat equation in the mini-channel wall and by the Fourier-Kirchhoff equation in a flowing fluid leads to an inverse heat transfer problem. This problem was solved using the FEM with the Trefftz-type basis functions. The estimation of temperature uncertainty measurements due to the Monte Carlo method was included in the final results of the heat transfer coefficient.

Vapor concentration and temperature field measurement of an evaporating sessile drop by tomographic laser absorption spectroscopy

Drop evaporation is a ubiquitous phenomenon that has been studied for over a century. However, the surrounding gas-phase field including the temperature and vapor concentration distribution is not sufficiently studied experimentally. In this paper, a sensor based on tunable laser absorption spectroscopy is designed to study the vapor-phase temperature and concentration distribution of evaporating sessile drops, and data processing method involving data pre-processing and tomographic reconstruction is proposed to realize high-precision, spatially resolved measurement, which was realized by scanning the mechanical galvanometer in the horizontal direction. With free-knot splines smoothing and “denucleated” onion-peeling algorithm, temperature and H2O concentration distributions surrounding the evaporated drop at three different substrate plate temperatures are observed. The concentration and temperature in close vicinity to the gas–liquid interface are reconstructed accurately despite the high-gradient changes. A spatial resolution of under 100 μm with a temporal resolution of 10 s has been realized. Quantitative depiction of the temperature and concentration fields shows evidence of convection and indicates that while the concentration level sharply peaks at the interface, temperature in the close vicinity to the drop shows flattening or even dipping trends. The in situ laser measurement results are validated against contact measurement, theoretical prediction with saturated vapor pressure, and model simulation of COMSOL. Uncertainties have been evaluated based on both repeated measurements and model prediction of input uncertainty propagation. Temperature and concentration measurement uncertainties are estimated to be <1.5% and <3.5%, respectively, even though all experiments were performed in open air with non-negligible buoyancy-induced convection.

Measurement of critical parameters for the binary mixture of R744 (carbon dioxide) + R1234yf (2,3,3,3-tetrafluoropro-1-ene)

The critical parameters including critical temperature, critical pressure, critical densities, and mole fraction for the binary mixture of R744 (carbon dioxide) + R1234yf (2,3,3,3-tetrafluoropro-1-ene) mixture were measured using a metal-bellows variable volumeter. The critical point was determined by visually observing the critical opalescence and reappearance of the meniscus. The expanded combined uncertainties of the critical temperature, critical pressure, critical density, and composition measurements were assessed to be less than 50 mK, 21 kPa, 0.006, and 0.015 (k = 2, 0.95 level of confidence), respectively. The experimental critical properties for the mixture correlated by Redlich-Kister equations were 0.15 % for critical temperature, 0.46 % for critical pressure, 0.10 % for critical density, and 0.08 % for critical molar volume. The mixture formed by mixing about 0.15 M fraction of R1234yf can increase the critical temperature by about 20 K and reduce the critical pressure by about 0.4 MPa compared with the pure material of CO2.

Evaluation of the relationships and uncertainties of airborne and ground-based sea ice surface temperature measurements against remotely sensed temperature records

ABSTRACT Sea ice surface temperature (IST) is an important indicator of environmental changes in the Arctic Ocean. In this study, the relative performance of four mainstream IST records, i.e. airborne IST, infrared radiometer measured IST (IR IST), longwave radiation derived IST (LWR IST), and snow and ice mass balance array buoy derived IST (Buoy IST), were evaluated against the MODIS IST product. Bias, standard deviation (STD), and root mean square error (RMSE) were used to evaluate the data quality. Results revealed that airborne IST had the best accuracy, which was 0.21 K colder than MODIS IST, with STD of 1.46 K and RMSE of 1.47 K. Ground-based ISTs were biased with each other but all warmer than the MODIS IST. The IR IST had the best overall accuracy (bias = 0.55 K; STD = 1.52 K; RMSE = 1.61 K), while the LWR IST was the noisiest measurement with the largest outlier data percent. Besides, co-located IR and LWR ISTs were more consistent than any type of evaluated IST against MODIS IST (correlation coefficient = 0.99). Airborne and IR ISTs are thus the premier choice for monitoring the rapidly changing Arctic sea ice, together with satellite observations.

Pyroreflectometry as a technique for the accurate measurement of very high temperatures in molten materials.

Experimental research into severe nuclear accidents often requires the accurate measurement of high temperatures of molten materials. Measurements of very high temperatures (1500-2500 °C) in liquid materials using standard pyrometry can entail uncertainties in the order of 5%-10%. Pyroreflectometry is a powerful technique with the potential to significantly reduce these uncertainties. A method is proposed to optimize pyroreflectometry temperature measurements in the 1500-2500 °C range and to allow more easily the detection of the solid-liquid phase transition. The originality of this research essentially relies on the use of pyroreflectometry based on two wavelengths (1.3 and 1.55μm) and its application to liquid materials at high temperature, which implies to adapt technological elements and metrological procedures. The proposed procedure first requires temperature calibration, which is undertaken using three eutectic fixed-point cells, reducing temperature uncertainty. Second, precise settings are adopted to enable reflectivity measurements on specular surfaces, such as the surfaces of molten metals. Pyroreflectometry measurements on liquid surfaces have been validated on an iron sample. Subsequently, the application of pyroreflectometry at very high temperatures was validated on various materials: metal (iron and 18MND5 steel), oxide (alumina), and carbide (rhenium-carbon eutectic). For each of these samples, the uncertainties of temperature measurements in the 1500-2500 °C range were estimated in the range of 1%-2%, performing well against standard pyrometry measurements. The principal difficulties encountered during the pyroreflectometry characterization were the fine-tuning of parameters (optical head orientation and lens focusing) to enable measurements on highly specular surfaces and ensuring inert interactions between the samples and the crucible.

Upgrade of the helically symmetric experiment Thomson scattering diagnostic suite.

The Helically Symmetric eXperiment (HSX) Thomson Scattering (TS) diagnostic is being upgraded to decrease uncertainty in electron temperature and density measurements. Upgrades to the HSX TS diagnostic will consist of a novel redesign of polychromator electronics and digitization of the TS output signal. Here, we also present a study of the benefits of an additional spectral channel that will sample the red-shifted band of the scattered spectrum. To maximize system bandwidth (BW) and gain, while minimizing noise, the existing low-BW polychromator electronics on HSX will be replaced by high-BW, high gain circuitry designed in-house.

A Bayesian model to solve a two-dimensional inverse heat transfer problem of gas turbine discs

Blade tip clearances in gas turbine engines are strongly affected by heat transfer on rotating disc surfaces as it determines the temperature and in turn the radial growth of rotating discs. In experiments, disc heat transfer is often calculated from disc temperature measurements. This creates a typical ill-posed inverse problem where small uncertainties of temperature measurements can cause large uncertainties of the calculated heat fluxes. In this paper, a Bayesian method is built to calculate heat transfer on both the upstream and downstream surfaces of discs from simulated temperature measurements, reducing the ill-posedness of the problem. A Matérn covariance matrix is employed in the Gaussian prior distribution, and parametric studies are conducted to investigate the accuracy, stability and robustness of the Bayesian method. It is shown that, compared to traditional curve-fitting methods, the Bayesian method offers better accuracy, robustness, and stability. With a temperature uncertainty of 5e-3, the relative errors of the calculated Biot number from the Bayesian method are less than 10%, whereas those from the curve-fitting methods are in the range of 40–90%. Using different initial guesses of the Biot number, the variations of the relative errors are less than 0.8%. The accuracy of the Bayesian method depends on the selection of the standard deviation in the prior distribution, and the best accuracy is obtained when it is twice the maximum Biot number. This study provides guidelines for subsequent experimental research on gas turbine disc heat transfer and data processing.