Relative Temperature Error Research Articles

Multi-Spectral Radiation Temperature Measurement: A High-Precision Method Based on Inversion Using an Enhanced Particle Swarm Optimization Algorithm with Multiple Strategies.

Multi-spectral temperature measurement technology has been found to have extensive applications in engineering practice. Addressing the challenges posed by unknown emissivity in multi-spectral temperature measurement data processing, this paper adds emissivity constraints to the objective function. It proposes a multi-spectral radiation temperature measurement data processing model realized through a particle swarm optimization algorithm improved based on multiple strategies. This paper simulates six material models with distinct emissivity trends. The simulation results indicate that the algorithm calculates an average relative temperature error of less than 0.3%, with an average computation time of merely 0.24 s. When applied to the temperature testing of silicon carbide and tungsten, experimental data further confirmed its accuracy: the absolute temperature error for silicon carbide (tungsten) is less than 4 K (7 K), and the average relative error is below 0.4% (0.3%), while two materials maintain an average computation time of 0.33 s. In summary, the improved particle swarm optimization algorithm demonstrates strong performance and high accuracy in multi-spectral radiation thermometry, making it a feasible solution for addressing multi-spectral temperature measurement challenges in practical engineering applications. Additionally, it can be extended to other multi-spectral systems.

Multiparameter measurement depending on the cavity-length differentiation characteristics of a microfiber Fabry–Perot interferometer

To solve the cross-sensitivity problem affecting optical fiber sensors and realize multiparameter measurement, a microfiber Fabry–Perot interferometer (MFPI) is proposed and experimentally demonstrated. Simultaneous measurement of two distinct physical parameter (temperature and strain) is realized by monitoring wavelength and reflectivity of MFPI. In the temperature field range of 22 °C–36 °C, the maximum temperature sensitivity can reach 12 pm °C−1. The maximum strain sensitivity is up to 0.8 pm/μϵ in the strain range of 0–800 μϵ. In the simultaneous measurement experiments, the relative errors of temperature and strain were 4.0% and 0.8%, respectively. Furthermore, the sensing element used in this method was just a single fiber grating sensor without any coating layer, which demonstrated the significant advantage of the proposed method in reducing the complexity and cost of multiparameter measurement.

An improved Baldwin–Lomax algebraic wall model for high-speed canonical turbulent boundary layers using established scalings

In this work, we employ well-established relations for compressible turbulent mean flows, including the velocity transformation and algebraic temperature–velocity (TV) relation, to systematically improve the algebraic Baldwin–Lomax (BL) wall model for high-speed zero-pressure-gradient air boundary layers. Any new functions or coefficients fitted by ourselves are avoided. Twelve published direct numerical simulation (DNS) datasets are employed for a priori inspiration and a posteriori examination, with Mach numbers up to 14 under adiabatic, cold and heated walls. The baseline BL model is the widely used one with semilocal scalings. Three targeted modifications are made. First, we employ a total-stress-based transformation (Griffin et al., Proc. Natl Acad. Sci. USA, vol. 118, issue 34, 2021, e2111144118) to the inner-layer eddy viscosity for improved scaling up to the logarithmic region. Second, we utilize the van Driest transformation in the outer layer based on the compressible defect velocity scaling. Third, considering the difficulty in modelling the rapidly varying and singular turbulent Prandtl number near the temperature peak in cold-wall cases, we design a two-layer strategy and use the TV relation to formulate the inner-layer temperature. Numerical results prove that the modifications take effect as designed. The prediction accuracy for mean streamwise velocity is notably improved for diabatic cases, especially in the logarithmic region. Moreover, a significant improvement in mean temperature is realized for both adiabatic and diabatic cases. The mean relative errors of temperature to DNS for all cases are down to 0.4 % in the logarithmic wall-normal coordinate and 3.4 % in the outer coordinate, around one-third of those in the baseline model.

Accuracy analysis of RANS turbulent models on predicting thermal stratification in the SUPERCAVNA facility

The accuracy in simulating thermal stratification, a critical issue in thermohydraulic research of liquid–metal-cooled nuclear reactors, has garnered significant attention. In this study, a symmetric 3D-CFD model has been established based on the SUPERCAVNA facility to analyze the performance of four RANS turbulent models. The results indicate that the SKE is the most accurate turbulent model in predicting the temperature distribution in the SUPERCAVNA with an average relative temperature error of 2.96 % and a standard deviation of 2.7 %. A parametric study has been conducted using SKE to discuss the effect of turbulent Prandtl number, the value of which is recommended to be between 1.5 and 2.0 from the results. Moreover, the Boussinesq approximation can be regarded as an alternative method for setting the temperature-dependent variables to conduct calculations involving gravity-induced buoyancy. These results are valuable for further investigations of thermal stratification and thermohydraulic research in liquid–metal-cooled nuclear reactors.

Three-dimensional numerical simulation and experiment of moisture condensation mechanism inside high voltage switchgear

High voltage switchgear is prone to moisture and condensation in environments with high humidity and large temperature difference, which seriously affects its safe and reliable operation. This paper uses three-dimensional numerical simulation, experimental verification, and mechanism analysis to examine the moisture condensation problem inside high voltage switchgear. First, a three-dimensional electromagnetic-fluid-thermal-humidity coupling field simulation model of full-size 40.5 kV switchgear is established, and the temperature distribution and humidity diffusion process are calculated. Then, a refined measurement is performed on the temporal and spatial distribution of temperature and humidity inside the switchgear to validate the simulation results. Finally, the condensation development sequence of each room and insulating component is revealed for the first time by combining the natural penetration test and simulation results. The results show that the relative errors of temperature and humidity data between the simulation and experimental results are within ±6%, which verifies the three-dimensional numerical simulation. Condensation is easy to occur on insulating components, including the current transformer and contact box in the cable room, where the humid air first accumulates. Furthermore, the condensation formation time decreases with the increase of relative humidity or temperature difference. The research results can provide reference for the anti-condensation measures for high voltage switchgear.

Predictions of the P1 approximation for radiative heat transfer in heterogeneous granular media

The P1 approximation is a computationally efficient model for thermal radiation. Here, we present a P1 formulation in the context of the combined computational fluid dynamics and discrete element method (CFD-DEM), including closures for dependent scattering and coarse-graining. Using available analytical and semi-analytical solutions, we find agreement for steady-state and transient quantities in size-disperse systems. Heat flux is identified as the most sensitive quantity to predict, displaying unphysical spatial oscillations. These oscillations are due to a temperature slip at the locations of abrupt change in solid fraction. We propose two techniques that mitigate this effect: smoothing of the radiative properties, and pseudo-scattering. Furthermore, using up to a million times enlarged particles, we demonstrate practically limitless compatibility with coarse-graining. Finally, we compare predictions made with our code to experimental data for a pebble bed under vacuum conditions, and in presence of nitrogen. We find that a carefully calibrated simulation can replicate trends observed in experiments, with relative temperature error of less than 10%.

Single Spectral Line Method for TDLAS Imaging of Temperature and Water Vapor Concentration

A single spectral line method for gas temperature as well as concentration extraction was proposed by using iterations with a fuzzy proportional–integral-derivative (PID) controller in tunable diode laser absorption spectroscopy (TDLAS). Usually, two or more spectral lines are essential to extract temperatures from coupled gas concentration and pressure. The proposed method utilized the line shape of a single absorption spectrum to decouple gas parameters along the laser path simultaneously and simplified the optical implementations. Differential equations of the Voigt profile were introduced at multiple wavenumbers to extract gas parameters from a single spectral line. A fuzzy PID controller was utilized to iteratively achieve the single spectral line from widely existed overlapping spectra. A relative temperature error within 2.5% at reference temperatures ranged from 300 to 2300 K was achieved by using the spectral line of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7444.35\,\,{\mathrm {cm}}^{-1}$ </tex-math></inline-formula> from noise free data. At low temperatures below 350 K, the proposed method using the single spectral line of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7181.14\,\,{\mathrm {cm}}^{-1}$ </tex-math></inline-formula> yielded smaller errors in noisy cases, and the temperature errors were verified within 5 °C on the water-based thermostat below 100 °C using the single spectral line. Experiments of axisymmetric counterflow flames at different heights were also implemented. The proposed method effectively reconstructed distributions of flame temperature and water vapor concentration inside, by only using a single spectral line of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$7444.35\,\,{\mathrm {cm}}^{-1}$ </tex-math></inline-formula> .

Investigation of the scavenging process in two-stroke uniflow scavenging marine engines by a real-time multi-stage model

The increasing demand of digital twin marine engine requires real-time physical models for prediction. In two-stroke uniflow scavenging marine engines, a real-time physical model for the scavenging process is rarely found since it is difficult to describe the complex in-cylinder air motion. Without an accurate prediction of the fresh air loss and residual burned gas in the cylinder, the precision of combustion and emission simulation cannot be guaranteed as well. In a marine engine digital twin system, the scavenging ratio and fresh air skip are the vital for the further simulation of combustion and emission. To predict them in real-time, a novel zero-dimensional (0D) multi-stage scavenging model is proposed in this article. In the cylinder zone, the complex gas motion is ideally divided to four stages: exhaust gas blowdown, perfect displacement, displacement-mixing, and perfect mixing. The duration of each stage is determined by the engine design and control parameters. Then, the thermodynamic conditions at each stage are simulated to obtain the mass of residual burned gas, fresh air inlet, and outlet. The results of the 0D model agree well with the results of the CFD simulation, and the mean relative errors of temperature, pressure, and total mass do not exceed 3%, 4%, and 2%, respectively, which indicates the potential for the two-stroke marine engine digital twin system. It could also be applied in a control-oriental engine model or engine diagnostics in the future.

Ga-modified YAG:Pr3+ dual-mode tunable luminescence thermometers

• Dual-mode thermometry is executed in YAG:Pr 3+ -YGG:Pr 3+ systems. • Bandgap engineering allows enhancing the performance of the thermometers. • YAG:Pr-YGG:Pr present manageable high relative sensitivity and high accuracy. • Garnet-based luminescence thermometers work effectively in the range 17–700 K. • Relative temperature errors are calculated and compared for all the garnets. The temperature determination using luminescent materials is nowadays considered the perspective remote technique for temperature gauging, despite the few examples reported so far combining wide operating temperature range with satisfying relative thermal sensitivity and temperature uncertainty values. In this paper, we study the Y 3 (Al,Ga) 5 O 12 :0.1%Pr phosphors with controlled Ga:Al composition to deliberately affect their luminescent properties. We demonstrate that the energy barrier for thermal quenching of the 5d-4f luminescence can be effectively tailored, yielding the fine tune of the thermometric parameters of these phosphors. By exploiting time-resolved and time-integrated approaches we show that the thermometers can cover the 17–700 K temperature range with a maximum relative sensitivity up to 3.6%·K −1 and a temperature uncertainty as lower as 0.02 K. For each sample, the temperature readout of the distinct thermometric parameters is compared illustrating that the performance of the thermometers should also consider the relative temperature error between the calculated and the measured temperatures, besides relative thermal sensitivity and temperature uncertainty.

Estimation of moving heat source for an instantaneous three-dimensional heat transfer system based on step-renewed Kalman filter

Inverse estimation of moving heat source is a common issue in many fields. A real-time method based on Kalman filter is proposed and further developed to identify the moving heat source in a three-dimensional heat transfer system. Firstly, a step-renewed state space model considering the source position is established according to principle of source contribution. Using this model, a technique coupling fuzzy adaptive Kalman filter with weight recursive least squares algorithm is implemented to realize the simultaneous estimation of moving heat source and temperature field. Different spatiotemporal changes of heat source and measurement noises are assumed to validate the feasibility and test its performances of this technique. Results illustrates that this method can be used to inversely estimate moving heat source with different changes rates and directions. When the moving velocity varies as 0.25, 0.50, 1.00 mm/s and the time period is employed as 100, 200, 400, 800 s, the estimated heat source can accurately agree with exact one while the reconstructed temperature field is of low deviation. The mean relative errors of estimated heat source are no more than 3.25% and mean relative errors of temperature are smaller than 1.37% while standard deviation of measurement noises increases from 0.01 to 5.00, which demonstrates that this method is of high robustness and can be used under a deteriorated condition.

Numerical analysis of heat and mass transfer in kiwifruit slices during combined radio frequency and vacuum drying

Kiwifruit slices subjected to combined radio frequency (RF) and vacuum drying undergo a complicated process, including electromagnetic heating, heat and mass transfer along with a phase change of evaporation and shrinkage under a low pressure. The aim of this paper was to obtain an in-depth understanding of this complicated drying process. A 3D multiphase porous model was established to describe heat and mass transfer within the kiwifruit slices in a 3 kW, 27.12 MHz RF-vacuum drying system using COMSOL Multiphysics software. The validation results showed that the established model could be applied to describe the RF-vacuum drying process of kiwifruit slices since the maximum relative errors of temperature, moisture content, and drying rate between simulation and experiment were less than 10%. The temperature distribution of kiwifruit slices both from simulation and experiment indicated that the sample temperature at corners and edges were higher than that at the center of the container, and the sample temperature at the center was the lowest for a single kiwifruit slice. But the distribution of moisture content was opposite to that of temperature. Evaporation rate constant was found to be sensitive to moisture content of treated samples compared with temperature. The influences of sample thickness, electrode gap, and vacuum pressure of the RF-vacuum drying system on temperature and moisture content-time histories were determined during the RF-vacuum drying process. The findings of this research may help to gain a comprehensive understanding of RF-vacuum drying and optimize treatment parameters for drying processes.

Integrated optic-fiber sensor based on enclosed EFPI and structural phase-shift for discriminating measurement of temperature, pressure and RI

An optic-fiber sensor based on integration of extrinsic Fabry–Pérot interferometer (EFPI) and phase-shifted fiber Bragg grating (PS-FBG) is depicted and demonstrated. The proposed sensor structure mainly consists of an enclosed EFPI fabricated with photosensitive adhesive between two end-faces of a halved FBG. Since the periodic refractive index (RI) distribution of FBG is interrupted and resulted in a structural PS-FBG in the middle of FBG. Consequently, the enclosed EFPI is capable of measuring the variations of temperature, pressure and RI due to optical cavity length changes, whereas the notch wavelength of introduced structural phase-shift spectrum is only sensitive to temperature, and the intensity of structural phase-shift spectrum is only insensitive to pressure. Therefore, the discriminating measurement of temperature, pressure and RI can be realized, due to using the methods of wavelength modulation and intensity modulation. The relative errors of temperature, pressure and RI, between the analysis results and measurement values, are 1.4%, 4.1% and 0.1%. The proposed integrated sensor with cost-effective merit has a promising research prospect in the field of the multiple parameters distinguish measurement.

An annular thermoelectric couple analytical model by considering temperature-dependent material properties and Thomson effect

In this paper, an annular thermoelectric couple (ATEC) analytical model is proposed with simultaneous consideration of temperature-dependent thermoelectric (TE) material properties and Thomson effect. To obtain a more precise analytical solution, this model is analyzed with two different approximate assumptions and then applied in skutterudites (SKU) and half-Heusler TE materials. The reliability and accuracy of this model are validated by comparing with numerical results. The results show that the proposed analytical model with a parabolic assumption is especially appropriate to be applied in the obvious temperature-dependent TE materials, such as SKU. When this analytical model is applied in SKU material, the calculated relative errors of temperature, derivative of temperature, output power, and conversion efficiency are less than 0.14%, 0.9%, 0.6% and 1.52%, respectively. Besides, it is emphasized that the Thomson effect and temperature-dependent material properties should be taken into account simultaneously for precise performance analyses of an ATEC. The proposed analytical model could be applied for convenient calculation of the output power and conversion efficiency of ATECs. It also could be an approach of investigation and determination for the best parameter estimation if this model is applied for optimal design of ATECs.

Turbine blade temperature error as measured with an optical pyrometer under different wavelengths and blade TBC thickness.

The optical pyrometer is a widely used instrument for measuring the temperature of gas turbine blade targets. However, one of the limitations of this instrument is the measurement error caused by reflected radiation from the high-temperature surrounding environment. This paper presents an analysis of such measurement error with consideration of a wavelength detection range of 2.5 to 22μm with blade thermal barrier coatings (TBCs) ranging from 18 to 279μm. Surface temperature distributions were simulated using the software ANSYS CFX. Radiation heat transfer was calculated based on discretized triangular surface elements. The variation characteristics of relative temperature error under different wavelengths and TBC thicknesses were obtained. The results obtained are well suited to provide theoretical guidance for choosing the wavelength of a pyrometer when measuring blade temperature with different TBC thickness, and can also be used to provide a method for estimating and correcting the temperature error.

Effect of pyrometer type and wavelength selection on temperature measurement errors for turbine blades

Turbine blade temperature measurements are important for monitoring the working state of the blades. However, the reflected radiation from the high temperature surrounding environment leads to significant error in the optical pyrometer measurements. This study calculates and compares temperature error of single wavelength pyrometer, ratio pyrometer and multicolor pyrometer in measuring turbine rotor blade temperature. Emissivity of the blade was measured in the wavelength range of 1.2 μm to 2.5 μm. Temperature distribution of the rotor blade and the guide vane was simulated by CFD software. Additionally, temperature error was calculated based on - discretization of a three-dimensional blade model. The results show that from the leading edge to the trailing edge of the rotor blade pressure side, the variation trend of the three kinds of pyrometer temperature error is the same, first decreasing, then increasing before decreasing again. The maximum relative temperature error was found to be 7.5%, 4.9% and 2.6% when the wavelength of the pyrometer was 1.3 μm, 1.6 μm, 2.2 μm, respectively. The study also shows that wavelength selection has great influence on the ratio pyrometer. It was found that the maximum relative temperature error ranged from 2.6% to 15.7% based on the choice of the various wavelengths. On the other hand, the maximum relative temperature error of the multicolor pyrometer was 3.8%. The analysis presented in this work will be of importance in providing guidelines for choosing the optimum measurement wavelengths for optical pyrometers. Furthermore, the finding will also useful in the calculation and correction of the optical pyrometer error.

Heat transfer model and design method for geothermal heat exchange tubes in diaphragm walls

The technology of embedding heat exchange tubes in diaphragm walls is a new direction for Ground-coupled Heat Pumps (GCHP). This paper examines the heat transfer model and design method for geothermal heat exchangers in diaphragm walls, which are seldom investigated in the world. Two-dimensional (2D) heat transfer models for diaphragm wall heat exchangers (DWHE) are established. A design method for DWHE is further developed to calculate the hourly heat exchange capacity of DWHE and to get the reasonable design parameter of DWHE. The DWHE model over the excavation line has the same changing trend with numerical solutions, and the relative errors between them are less than 2%. The relative errors of calculated heat exchange rate per meter using DWHE model and measured data are less than 6% after running 10h. The relative errors of temperature between DWHE model under the excavation line and the measured data at different positions are no more than 9%, whereas the relative error between the tradition models in GCHP (line source model and finite-line source model) and the measured data may reach as much as 40%.

High-Temperature Sensor Based on Neutron-Irradiated 6H-SiC

Nitrogen-doped 6H-SiC single crystals irradiated with neutrons up to a fluence of 5.74×1018 n/cm2 at the temperature of 60-80°C were investigated by means of X-ray diffractometer and metallurgical microscope. The experimental results showed the X-ray diffraction peak (0006) was broadened due to the lattice distortion resulting from irradiation-induced defects, and then narrowed linearly when isochronally annealed over the temperature of 700°C. Meanwhile, from the chemical etching photomicrographs, the characteristic was accompanied by the changes of the dislocation density after the process of irradiation and post-irradiation annealing. According to this characteristic of irradiated 6H-SiC crystals, a novel temperature sensor suitable for the temperature range of 700-1300°C or more is developed, which depends on the linear relationship between XRD FWHM (the full width at the half maximum of X-ray diffraction peak) and isochronal annealing temperature over about 700°C. The subsequent application test demonstrated that the sensor remained no damage in the very harsh conditions as well as possessed a less than +5% of the relative temperature error. Therefore, the neutron-irradiated 6H-SiC can be employed as a kind of non-invasive temperature measurement sensor to determine the temperature of closed, high-speed rotating and difficult-to-access parts on a running machine such as internal-combustion engine pistons, turbine blades and so on.

Cooling process of iron ore pellets in an annular cooler

A 3-D mathematical model was presented for the cooling process of iron ore pellets based on the laws of mass, momentum, and heat transfer. The flow, pressure, and temperature fields were obtained by numerical simulation with the commercial software FLUENT. In order to verify the model, a mass and energy balance field test was systematically carried out on an annular cooler in Shougang Mining Company. The maximum relative errors of temperature, pressure, and velocity between computational and testing results are 2.87%, −8.11%, and 7.14%, respectively, indicating the validity of the model. Further, the effects of process parameters, such as pellet diameter, bed thickness, air velocity, and temperature, on the pellet bed temperature profiles were studied.

The Immersion Characteristics of Industrial PRTs

Immersion effects are one of the most significant sources of error in the use of industrial platinum resistance thermometers (IPRTs). This article combines the development of a mathematical model of immersion error and experimental measurements of the immersion characteristics of a range of IPRTs immersed in different fluids at different temperatures. The mathematical model relates the relative temperature error in the thermometer indication to two exponential terms, with one of the 1/e decay lengths three times the other. The experimental results show that both of the exponential terms are important for shallow immersion, but one is sufficient for long immersion. The decay length for the thermometers depends on the diameter of the probe and on the thermal environment into which it is immersed. For the thermometers evaluated here in mineral oil, silicon oil, and molten salt, the 1/e decay length is about three to four times the diameter of the thermometers. A simple rule of thumb for ensuring adequate immersion in calibration baths is developed.