Accurate measurements the thermophysical characteristics of materials and products required in almost all modern fields of technology. The presented in article methods for measuring the thermophysical and thermal radiation characteristics can be applied not only for materials but for energy-efficient glasses and thin coatings, as well as methods for determining the thermophysical parameters of concrete mixtures over a long period of time and a wide range of temperatures. Proposed unified hardware-software measuring system that combine described methods for measuring thermophysical characteristics. The main characteristics which are necessary for carrying out measurements and metrological support are defined. Methods of analysis of metrological characteristics using working standards as well as indirect method are proposed for implementation in the system. An algorithm for determining the metrological characteristics of the measuring system is proposed. Presented the metrological studies results of the measuring system. thermophysical characteristics, measuring system, thermal conductivity, emissivity, heat flux ITTAP'2021: 1nd International Workshop on Information Technologies: Theoretical and Applied Problems, November 16-18, 2021,
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Accurate measurements of the thermophysical characteristics of materials and products required in almost all modern fields of technology. Measuring information can be used in the priority areas of science and technology development such as: construction and energy, metallurgy and materials science, aviation and astronautics, electronics and mechanical engineering.
The main thermophysical characteristics are thermal conductivity, specific heat, thermal resistance. Various methods for measuring these characteristics have been developed, which can be classified according to the following general features:
by the thermal state of the sample (or stage of the thermal process): stationary, which provide for the establishment of thermodynamic equilibrium in the system [1-4], and dynamic, which study the temperature-time dependence of the thermophysical properties of the sample material [5-7]; by the method of finding the desired value: absolute (for example, by measuring the electric power consumed by the heater) [2,4] and differential (comparative);
by the nature of measurements: direct, based on the measurement of heat flux, while for the calculation it is necessary to know only the geometric parameters of the sample, and indirect, based on the measurement of temperature [1,3,5];
according to the shape of the sample (or its isothermal surfaces): flat, cylindrical and spherical.
The basic differential equations describe thermal phenomena only in the most general form, since they are derived taking into account the general laws of physics. In order to distinguish from the innumerable number of thermal processes the considered one and to give its full mathematical
2021 Copyright for this paper by its authors. description, the conditions of unambiguity (boundary conditions) are formulated, which reflect th e partial features of a concrete process. Conditions of unambiguity include: • geometric conditions that characterize the shape and linear dimensions of the body in which the process takes place; • physical conditions that characterize the properties of the environment and the body and the law of distribution of internal heat sources [8,9]; • initial (or temporal) conditions that formulate when considering non-stationary processes and characterize the distribution of temperatures in the body at the initial time; • boundary conditions characterizing the interaction of the considered body with the environment.
A wide range of new materials, different in shape and structure, requiring comprehensive studies of their thermal characteristics in accordance with the above classification and variation of boundary conditions, requires the creation of various instruments and measuring systems [10]. Measuring instruments, in turn, require the development of specific methods of calibration and verification of research results. Construction of multi-stage calibration schemes is not always technically and economically viable. This is especially true in the field of non-destructive testing, when the decisive factor is not the measured thermophysical value, but its relationship with the characteristics that reflect the quality of the material or product.
Unification of measurements the ability to determine several defining thermal characteristics using a single intelligent information-measurement system, is a promising area of development.
Considering written above the next research tasks was formulated: • Propose the methods for measuring thermophysical characteristics that can be unified in one measuring system;
• Define the main characteristics which are necessary for carrying out measurements and metrological support; • Implement hardware-software unified system; • Propose the methods for metrological support of the system.
One of the main thermophysical characteristics of modern materials is thermal conductivity or thermal resistance. The methods of thermal conductivity measuring for the particular group of materials should be chosen depending from the following criteria: • a suitable range of values of the coefficient of thermal conductivity, as for low- and highconductivity materials require different measurement methods; • range of operating temperature values; • the corresponding standard size and shape of the sample.
As a result of the analysis of schemes of measurement of thermal conductivity of the materials in the form of a plate [1,3,11], in the developed complex information-measuring system the thermometric method with use of two identical heat flux sensors. In order to ensure a uniform thermal field in the sample in the measuring cell of the system, thermal stabilization of the heater edge zones and the cooler with the help of protective peripheral heaters is applied. It is this design and thermophysical solution of the measuring cell allows not only to minimize heat loss, but also provides the fastest access to a stationary mode of measurement [11].
Based on the measurements results of the heat flux passed through the sample and the temperature difference on its working surfaces, the thermal resistance is calculated , m2·K/W, and thermal conductivity (W/(m∙K)) based on dependences presented in Table 1. The measurement range of the thermal conductivity from 0,02 up to 3 W/(m∙K) in the temperature range from 240 up to 400 K, sample sizes from 100 × 100 to 300 × 300 mm with thickness up to 120 mm.
The Heat module of the measuring system during installing the sample for thermal conductivity measurements is shown in Fig. 1.
A special place among modern thermal insulators is occupied by thin-layer coatings, such as paints and mastics based on acrylic binders containing hollow ceramic or glass microspheres. Determination of their thermal resistance is usually carried out by the calculation method, based on data for ordinary paints, which is incorrect for complex inhomogeneous compositions. To objectively assess the effectiveness of such thermal insulation materials, a method for measuring the thermal resistance and thermal conductivity of thin coatings has been developed. A uniform layer of the studied paint is thickness ℎcoat = 1. . .2 mm applied to a substrate of rigid sheet dielectric material (for example glass), whose thermal resistance gl (m2·K/W) determined in advance. The coated sample is placed in the measuring cell of the system, and in the centers of the working surfaces of the sample are placed the joints of the tape differential thermocouple thickness 0,05 ... 0,07 mm and provide their pressing to the surface of the sample with thin elastic silicone gaskets, which eliminates possible micro-irregularities of the coating surface. Based on measurements of the heat flux and temperature the calculation of the thermal conductivity value for the investigated coating performed.
Heat-protective properties of thin coatings are characterized not only by the thermal conductivity, but also the thermal radiation characteristics. The emissivity which is determined using a specialized expensive device - Fourier spectrophotometer [13]. For unify the measurements, an experimental and computational method for measuring the emissivity of energy-saving glass and other coatings proposed calorimetric method. This method requires two identical samples of glass or coated material are collected in a package having a layer of air of known thickness between the two test surfaces. This package is placed in the measuring cell of the system and determine its thermal resistance, which depends on the conductive-convective and radiative heat transfer in the package. Based on the obtained results the emission of the coatings is determined by calculation (see Table 1) [11, 14].
The scheme of the study and calculation formulas presented in Table 1.
Table 1
measurement scheme
Emissivity sp of thin coating Volumetric and integral heat release of thermolabile materials = ℎ ∙ ̅⁄ =
⁄ ̅ c =
ℎcoat coat − gl coat =
⁄ ̅ sp =
⁄4 ̅ 3 =
1 − 2 gl
− =
⁄ ̅ = ⁄ℎ = ∫ 0 ̅ = ( 1 + 2)/2 – average heat flux recorded by HFM1, 2
= 1 − 2 – temperature difference on the sample surfaces ℎ – sample thickness
– coating thickness coat, gl,
– thermal resistance of coating, glass and
air layer ̅ – average sample temperature – Stefan
= | 1 + 2| – heat flux recorded by HFM1, 2
Particular interest for modern technologies of monolithic frame construction is the study of the process of hydration of concrete mixtures and forecasting the strength and durability of building structures. Design of the information-measuring system, as well as technical characteristics allows to study the thermophysical parameters of thermolabile substances during long-time range (up to several days). In one experiment, it is possible to measure the current values of heat output during hydration of binders or concrete and their thermal conductivity for 72 hours, as required by the relevant standards, a prepared sample of concrete mixture is inserted into the measuring cell of the system and the intensity of its heat release during hydration is recorded according to the signals of heat flux sensors (see Table 1) [11]. The result of calorimetric analysis is to obtain thermokinetic information, which allows to give recommendations on the composition of concrete and conclude the need to adjust the composition in a certain direction, the favorable modes of hardening of concrete, taking into account the influence of technological factors. From the analysis Table. 1, the main information parameters when measuring several thermophysical characteristics are the values of heat flux and temperature, as well as the geometric parameters of the sample.
The metrological characteristics analysis unit can be used for verification of the calibration. For this task unit able work with methods based on using reference materials and working standards as well as an indirect method.
In practice, working standards act as a means of maintaining the uniformity of measurements of product properties. One of the most important advantages of their use is the ability to calibrate the working device in conditions close to operational ones, and to verify it directly at the operation site [3]. The working standard acts as a material carrier of the corresponding units, its main metrological characteristics are the values of the physical quantity and its error.
According to a standardized technique [1-3], the process is carried out by comparing the thermal conductivity measured value of the reference standard with the value indicated in its certificate or corresponding regulatory document. As thermal conductivity reference materials Polymethyl methacrylate, optical glasses LK5 and KV6, High Density Expanded Polystyrene are used. Error of the thermal conductivity working standard have to be no more than ± 3%, which must be confirmed by the appropriate certificate.
Thermal conductivity measurement range of the system is determined in experimental studies of the basic relative error at one fixed sample temperature from the values range close to room temperature using standard thermal conductivity measures and a control sample from granite.
To determine the basic relative error of the thermal conductivity measuring and establish its boundaries, experiments are performed at three temperature points of the working temperature range corresponding to its beginning, middle and end using one thermal conductivity working standard – optical glass LK5, because its thermal conductivity lies in the middle part measuring range. The list of
, K includes the thermal conductivity working standards error ± 3% [11].
So, the metrological characteristics of the system evaluation by the comparison method need to have several working standards, their characteristics have to cover the range of the desired thermophysical quantity and be confirmed by studies on the standard device. In this case, the error value of the working measuring instruments certified with their help includes the error of the working standard and, based on the example of the thermal conductivity study devices, it is twice the normalized in [1, 3]. To eliminate these inconsistencies and simplify research, a technique for determining the metrological characteristics of a measuring system by an indirect method has been developed.
4.2.
The measurement system calibration is carried out according to the technique [20]. The individual static transfer functions each of two HFM are determined by the method of two measurements using a special certification electric heater. Individual calibration of primary thermocouples is carried out using a reference resistive temperature transducer Pt100 – a 3rd category working standard in the temperature range from 220 K to 430 K.
The information-measuring system metrological characteristics determination is reduced to the evaluation the range and the main relative measurement error of the desired value and the range of the operating temperature.
Taking into account that = ( , ), = ( , , 1 … ),
= ( , , 1 … ), where 1 … are geometric parameters of the sample, this procedure can be implemented according to the indirect measurements method by evaluating the measurement error components of the parameters used in determining the thermophysical characteristics: heat flux density , temperature values T, as well as geometric parameters of the sample 1 … .
As a basis the definition of thermal conductivity metrological characteristics can be accepted [18, 19]. In this case, according to ISO [1, 3], are determined: • • • the standard deviation of the measurement result error (RMSD); non-excluded systematic error (NSE); standard measurement uncertainties.
The total error of measuring the thermal conductivity in the developed system characterized by the RMSD and NSE was determined by the computational and experimental method for studying individual errors in measuring basic physical quantities. Components of the error in measuring the heat flux density and the temperature values difference were determined experimentally using a special certification electric heater and a reference resistive temperature transducer, respectively [20]. Standard measuring instruments, such as digital multimeters Picotest M3500A and Fluke 8845A, reference electrical resistance coil, DC voltage regulator and a digital caliper, are also used [22–25].
The measuring system metrological characteristics determination is carried out according to the developed algorithm (Figure 3).
The experiments are performed in 10 consecutive thermal regimes in the process of investigating the components of the error in measuring the heat flux density. The first five modes are carried out at one constant temperature value, but at different total heat flux values set by the calibration heater, which correspond to 5%, 25%, 50%, 75% and 95% of the heat flux density measurement range. The following five modes are carried out at five points of the measuring system operating temperature range corresponding to 5%, 25%, 50%, 75% and 95% of its value, but at one constant heat flux density value equal to the middle of its operating range. In each mode, the temperature of the heater, cooler and lateral isolation is set identical by the appropriate regulators.
In each n-mode after reaching a thermal steady state the system software records and averages data from the heat flux sensors and the electric heater during 20 minutes minimum. The NSE component of the heat flux density measurement is taken equal to the value of the series of measurements relative error : were − the relative error of the series of measurements in 10 modes, calculated by formula:
NSE boundaries of the thermal conductivity measurement result are determined as a positive square root of the sum of squares of all components of the systematic error, in measuring the heat flux density and temperature difference, as well as the errors of all measuring devices calculated based on data taken from manufacturer's specifications and calibration certificates, by formula: were k =1,96 − а coverage factor, which is chosen depending on the effective degrees of freedom at the level of confidence р = 0,95 (see Table G.1 in Annex G [17]).
RMSD of the thermal conductivity measuring is estimated based on the results obtained as the square root:
The components of the temperature difference measurement error are investigated in seven consecutive temperature modes of the operating temperature range. In each m-mode, the heater, cooler and lateral isolation regulators are simultaneously set to the same beginning and ending temperatures, wherein ∆ = 10 ± 2 К.
In each m-mode, the stationary state is monitored according to HFM data, the parameters for regulating the heat flux density are not more than 2 W/m2, the set temperature values permissible fluctuations have to be no more than ±0,5 К.
After reaching a thermal steady state the system software records and averages data from the temperature sensors and reference resistive temperature transducer during 20 minutes minimum. The NSE component of the temperature difference measurement is taken equal to the value of the series of measurements relative error :
The root-mean-square deviation (RMSD) of the heat flux density measuring results is estimated according to the measurement data in 10 modes by formula:
Assessment of measurement uncertainties (type A, B, total and extended) is carried out according to the standard technique [17]. The results are presented in Table 3.
= 1 = , ∑ , 1 = √∑
2 = √ 2 + 2 .
= , = ∑ =1 , = √
1 − 1
=1 ∑ ( − ) 2 were
− the relative error of the series of measurements in 7 modes, calculated by formula: measurement data in 7 modes by formula:
RMSD of the temperature difference measuring results is estimated according to the (1) (2) (3) (4) (5) (6) (7) (8) ̂ ̂В ̂С ̂ 0,32 0,06 1,25 0,72 0,63 0,96 0,96 0,72 1,20 2,35
These results demonstrate the validity of the developed technique with the requirements of modern standards [1, 3]. This technique allows to pass the measurements range of the desired value with the appropriate step in a wide range of temperatures. The software allows to set the required temperature parameters, assess the stationarity of a stable thermal regime, record the readings of all measuring sensors in a series of measurements, form a data bank, process information and switch to the next temperature regime.
Analyzed methods for measuring thermophysical and thermal radiation characteristics of materials, energy-efficient glass and thin coatings. Proposed method for measuring thermophysical characteristics of concrete mixtures in a long-time interval and a wide temperature range. The main characteristics which are necessary for carrying out measurements and metrological support are defined.
The hardware-software module of unified system for research of thermophysical characteristics based on proposed methods is suggested and implemented. The proposed software allows to set the required temperature parameters, assess the thermal regime, record the readings of all measuring sensors in a series of measurements, form a data bank, process information. Also, the proposed construction of heat module system meets requirements of the standard ISO 8301 [1].
Methods of analysis the metrological characteristics using working standards as well as indirect method are implemented in system. An algorithm for determining the metrological characteristics of a measuring system is proposed. Presented the metrological studies results of the measuring system.
The results of this study can be used to simplification measurements of thermal characteristics using a single intelligent information- measurement system. Also, the results of this study improve the data processing and exclude subjective factor during measurements.
These researches have been performed within the project № 19 1.7.1.902 «Information-measuring system for thermophysical characteristics of materials and products studying».
[1] International Organization for Standardization (1991). Thermal Insulation—Determination of Steady-State Thermal Resistance and Related Properties—Heat Flow Meter Apparatus (ISO [2] International Organization for Standardization (1991). Thermal insulation-Determination of steady-state thermal resistance and related properties-Guarded Hot Plate Apparatus (ISO Standard No. 8302:1991). [3] European Committee for Standardization (2001). Thermal Performance of Building Materials and Products—Determination of Thermal Resistance by Means of Guarded Hot Plate and Heat Flow Meter Methods—Products of High and Medium Thermal Resistance. (EN Standard No. 12667:2001). [4] American Society for Testing and Materials (2013). Standard Test Method for Steady-State Heat Flux Measurements and Thermal Transmission Properties by Means of the Guarded-Hot-Plate Apparatus. (ASTM Standard No. C177–13). [5] American Society for Testing and Materials. (2010). Standard Test Method for Tensile Properties of Plastics. (ASTM Standard No. C518-10). [6] T. Ruuska, J. Vinha, and H. Kivioja. Measuring thermal conductivity and specific heat capacity values of inhomogeneous materials with a heat flow meter apparatus. J. Build. Eng. 9 (2017): 135– 141. https://doi.org/10.1016/j.jobe.2016.11.011. [7] Y. Li, C. Shi, J. Liu, E. Liu, J. Shao, Z. Chen, D.J. Dorantes-Gonzalez, and X. Hu. Improving the accuracy of the transient plane source method by correcting probe heat capacity and resistance influences. Meas. Sci. Technol. 25 (2014) doi:10.1088/0957-0233/25/1/015006. [8] Z. Pásztory, and D.H. Anh Le. An overview of factors influencing thermal conductivity of building insulation materials. J. Build. Eng. 44 (2021): 1–16. https://doi.org/10.1016/j.jobe.2021.102604. [9] Á. Lakatos, and F. Kalmár. Investigation of thickness and density dependence of thermal conductivity of expanded polystyrene insulation materials. Mater. Struct. 46 (2013): 1101–1105. doi:10.1617/s11527-012-9956-5. [10] N. Mathis. Transient thermal conductivity measurements: Comparison of destructive and nondestructive techniques. High Temp. High Press 32 (2000): 321–327. Available online: https://www.ctherm.com/files/Transient_Thermal_Conductivity_Measurements.pdf [11] T. Grischenko (Ed.), Heatmetry: theory, metrology, practice. Book 3: Thermometric equipment for solving applied problems: in 2 volumes. Vol. 1. Institute of Engineering Thermophysics of National Academy of Sciences of Ukraine, Kyiv, 2018. (In Russian) [12] International Organization for Standardization (2003). Glass in building. Determination of light transmittance, solar direct transmittance, total solar energy transmittance, ultraviolet transmittance and related glazing factors (ISO Standard No. 9050:2003). [13] V. Babak, L. Vorobiov, L. Dekusha, V. Volkov, Z. Burova, O. Dekusha, and S. Kovtun.
Measurement of Thermo-Radiation Characteristics of Spectral-Selective Materials for Space Structures Designs. Path of Science 4(6) (2018): 1009–1019. http://dx.doi.org/10.22178/pos.35-2 [14] V.P. Babak, S.V. Babak, M.V. Myslovych, A.O. Zaporozhets, and V.M. Zvaritch. Principles of construction of systems for diagnosing the energy equipment, in: V.P. Babak (Ed.), Studies in Systems, Decision and Control, 2020, pp. 1–22. https://doi.org/10.1007/978-3-030-44443-3_1. [15] V.P. Babak, S.V. Babak, M.V. Myslovych, A.O. Zaporozhets, and V.M. Zvaritch. Methods and models for information data analysis, in: V.P. Babak (Ed.), Studies in Systems, Decision and Control, 2021, pp. 23–70. https://doi.org/10.1007/978-3-030-44443-3_2. [16] V.P. Babak, S.V. Babak, M.V. Myslovych, A.O. Zaporozhets, and V.M. Zvaritch. Simulation and software for diagnostic systems, in: V.P. Babak (Ed.), Studies in Systems, Decision and Control, 2021, pp. 71–90. https://doi.org/10.1007/978-3-030-44443-3_3. [17] Joint Committee for Guides in Metrology (2008) Evaluation of measurement data — Guide to the expression of uncertainty in measurement: First edition (JCGM 100:2008). [18] X. Meng, B. Yan, Y. Gao, J. Wang, W. Zhang, and E. Long. Factors affecting the in-situ measurement accuracy of the wall heat transfer coefficient using the heat flow meter method.
Energy and Buildings 86 (2015): 754–765. https://doi.org/10.1016/j.enbuild.2014.11.005. [19] R. Zarr, S. Carvajal, and J. Filliben. Sensitivity Analysis of Factors Affecting the Calibration of Heat-Flow-Meter Apparatus. Journal of Testing and Evaluation 47, no. 4 (2019): 2979–3002. https://doi.org/10.1520/JTE20170588. [20] O. Dekusha, Z. Burova, S. Kovtun, H. Dekusha, and S. Ivanov. Information-Measuring Technologies in the Metrological Support of Thermal Conductivity Determination by Heat Flow Meter Apparatus, in: V.P. Babak (Ed.), Systems, Decision and Control in Energy, 2020, pp. 217– 230. https://doi.org/10.1007/978-3-030-48583-2_14. [21] V. Babak, S. Kovtun, and O. Dekusha. Information-measuring technologies in the metrological support of heat flux measurements, in: CEUR Workshop Proceedings, vol. 2608, 2020, pp. 379– 393. URL: http://ceur-ws.org/Vol-2608/ [22] UTP3305 DC Power Supply. URL: https://www.uni-trend.com/html/product/gongye/thi/
UTP3300_Series/UTP3305.html. [23] M3510A Digital Multimeter. URL: https://www.picotest.com/products_M3510A.html. [24] Fluke 8845A 6.5 Digit Precision Multimeter. URL: https://www.fluke.com/enus/product/precision-measurement/bench-instruments/fluke-8845a-8846a. [25] Topex Digital caliper 150 mm. URL: https://www.toolmach.eu/hand-tools/measuring/topexdigital-caliper-150mm.html.