Correlation Between Immersion Profile and Measured Value of Fixed-Point Temperature

Assessment of thermal immersion effects in the melting and freezing points defined by the International Temperature Scale of 1990 is one of the vital issues of modern thermometry. In documents of the Consultative Committee for Thermometry, the deviation of the experimental immersion profile from the theoretical value of the hydrostatic effect at a height of about 3 cm to 5 cm from the thermometer well bottom is used for the estimation of the uncertainty due to unwanted thermal effects. This estimation assumes the occurrence of solely the hydrostatic effect all along the height of the well inner wall. Real distortions of the temperature gradient at the bottom and at the top part of the well caused by the change of heat-exchange conditions are not taken into account. To define more precisely the temperature gradient along the height of the well, a miniature PRT with a 30 mm sensitive element and a sheath length and diameter of about 60 mm and 6 mm, respectively, were used. Also, the measurements of fixed-points temperature at noticeably different slopes of immersion profiles due to variations of the thermometer heat exchange and phase transition realization conditions were produced by means of a standard platinum resistance thermometer (SPRT). The measurements were carried out at the tin and zinc freezing points. The immersion curves measured with a miniature thermometer demonstrated an increase of the temperature during its lifting in the first 1 cm to 3 cm above the bottom of the well. The measurement results at the zinc freezing point by means of the SPRT have not confirmed the correlation between the immersion curves, the received value of the Zn freezing temperature, and the estimation of its uncertainty.     

A New Method for the Quantification and Correction of Thermal Effects on the Realization of Fixed Points

The temperature and flatness (shape) of a fixed-point plateau depend on both the amount and nature of specific impurities and on thermal effects that are influenced by the fixed-point cell design and furnace properties. A better understanding and experimental proof of the influence of specific impurities on fixed-point realizations require the separation of impurity influences from thermal effects. In this paper the influence of heat exchange between the thermometer and furnace is quantified via a method based on changing the furnace temperature during the fixed-point measurement. It will be shown that the corresponding correction of this thermal effect has a dominant influence on the plateau shape compared to the influence of impurities. This leads to an explanation for why the maximum of an induced freeze is the most reproducible temperature. A secondary outcome is an explanation of why natural freezes have less flat plateaux compared to induced freezes, resulting in fixed-point temperatures that are too low. Furthermore, the suggested procedure is the basis of the direct and quantitative comparison of fixed-point cells and the detection of weak points within a specific design. It allows optimization of fixed-point cells and furnaces, and helps to deepen the common understanding of the phase transition in fixed-point cells.     

Coupled conduction-convection problem for a cylinder in an enclosure

The coupled heat conduction/convection problem for a solid cylinder in either a rectangular or a circular enclosure filled with air is solved by an operator-splitting pseudo-time-stepping finite element method, which automatically satisfies the continuity of the interfacial temperature and heat flux. The temperature distribution in the cylinder and in the fluid is obtained showing that the usual practice of prescribing a uniform heat flux boundary condition at the interface may not lead to an accurate solution. From the profile of the local Nusselt number, which is strongly dependent on the Rayleigh number but weakly dependent on the thermal conductivity ratio, it is concluded that most of the heat transfer takes place in the lower half of the cylinder through a convective mode.     

A homogenization technique for heat transfer in periodic granular materials

A homogenization technique is proposed to simulate the thermal conduction of periodic granular materials in vacuum. The effective thermal conductivity (ETC) and effective volumetric heat capacity (EVHC) can be obtained from the granular represent volume element (RVE) via average techniques: average heat flux and average temperature gradient can be formulated by the positions and heat flows of particles on the boundaries of the RVE as well as of the contact pairs within the RVE. With the thermal boundary condition imposed on the border region around the granular RVE, the ETC of the granular RVE can be computed from the average heat flux and average temperature gradient obtained from thermal discrete element method (DEM) simulations. The simulation results indicate that the ETC of the granular assembly consisting of simple-cubic arranged spheres coincides with the theoretical prediction. The homogenization technique is performed to obtain the ETC of the RVE consisting of random packed particles and the results exhibit the anisotropy of the thermal conduction properties of the RVE. Both the ETC and EVHC obtained are then employed to simulate the thermal conduction procedure in periodic granular materials with finite element analyses, which give the similar results of temperature profile and conduction properties as the DEM simulations.     

Optimizing Contact Thermometry High-Temperature Fixed-Point Cells ( > 1,100 °C) Using Finite-Element Analysis

The advent of high-temperature (i.e., metal–carbon eutectic) fixed points (HTFP) has placed high demands on the equipment needed to implement them. In particular, the HTFP performance is sensitive to the thermal environment. The temperature gradient in the crucible volume determines the duration and form of the melting plateau, and a gradient in the wrong direction along the crucible can result in mechanical damage. With an emphasis on crucibles for contact thermometry, a transient thermal model, which employs the finite element method is described. The aim is to optimize the HTFP environment, and to evaluate the relationship between the temperature of the liquid–solid interface (the actual fixed-point temperature) and the temperature measured by the contact thermometer (the measured fixed-point temperature). A simple mechanism to minimize temperature gradients along the HTFP cell axis is also presented. Importantly, the model shows that the actual temperature of the liquid–solid interface during melting is given by the indicated temperature at the end of the plateau, i.e., the liquidus point, not the point of inflection of the plateau, as is currently the convention. This does not significantly affect the conventional pure metal fixed points of the ITS-90, but could have ramifications for the new generation of high-temperature fixed points where the melt takes place over a temperature range and the liquidus temperature has yet to be identified.     

The effect of thermal boundary conditions on local features of low-intensity natural convection in a square enclosure

Local features are investigated of heat transfer and thermal stratification under conditions of weakened natural convection in a square enclosure. The dependence of local effects on the type of thermal conditions on horizontal boundaries is studied. Conditions of two types are employed, namely, a uniform heat flux (or efflux) and the general condition of heat transfer. Estimates are given of the limits of modes of convection, and the dependences of temperature fields and heat fluxes on criterional numbers are obtained.     

Optimization of a Graphite Tube Blackbody Heater for a Thermogage Furnace

Design modifications are presented for a 289-mm long, 25.4-mm inner diameter blackbody heater element of a 48 kW Thermogage blackbody furnace, based on (i) cutting a small “heater zone” into the ends of the tube and (ii) using a mixture of He and Ar or N₂ to “tune” the heat losses and, hence, gradients in the furnace. A simple numerical model for the heater tube is used to model and optimize these design changes, and experimental measurements of the modified temperature profile are presented. The convenience of the Thermogage graphite-tube furnace, commonly used in many NMIs as a blackbody source for radiation–thermometer calibration and as a spectral irradiance standard, is limited by its effective emissivity, typically between 99.5% and 99.9%. The design simplicity of the furnace is that the blackbody cavity, heater, and electrical and mechanical connections are achieved through a single piece of machined graphite. As the heater also performs a mechanical function, the required material thickness leads to significant axial heat flux and resulting temperature gradients. For operation at a single temperature, changes to the tube profile could be used to optimize the gradient. However, it is desired to use the furnace over a wide temperature range (1,000–2,900°C), and the temperature-dependence of the electrical conductivity and thermal conductivity, and that of the insulation, makes this approach much more complex; for example, insulation losses are proportional to T ⁴, whereas conduction losses are proportional to T. In the results presented here, a slightly thinner graphite region near each end of the tube was used to “inject heat” to compensate for the axial conduction losses, and the depth, width, and position of this region was adjusted to achieve a compromise in performance over a wide temperature range. To assist with this optimization, the insulation purging gas was changed from N₂ to He at the lower temperatures to change the thermal conductivity of the felt insulation, and the effectiveness of this approach has been experimentally confirmed.     

Improved Thermal Model for the Realization of the Triple Points of Cryogenic Gases as Temperature Fixed Points

The realization of the triple points of the cryogenic gases hydrogen, neon, oxygen, and argon as temperature fixed points at the highest level of accuracy requires consideration of the special properties of these fixed-point substances, as done in a general measurement protocol published elsewhere. The protocol is applied to the apparatus and methodology used for an international star intercomparison of sealed fixed-point cells. A generalized thermal model is developed to include the coexistence of different solid?Cliquid interfaces and various thermal resistances. This results in further components in the detailed uncertainty budget for the correction of the measuring power of the thermometer and for the extrapolation to the liquidus point. As a basis for an optimum fixed-point realization, especially an explanation is given why extremely long time periods may be necessary for the thermal recovery after pulses of the intermittent heating used for the calorimetric method.     

车室内热环境的计算模型与数值模拟

用计算流体力学与计算传热学的方法对车室内的非均匀热环境进行了模拟与数值计算。文中首先对车室内的热环境建立了相应的计算模型,然后进行了相应的数值计算。计算中不仅考虑了空气温度、空气流速、空气湿度、太阳辐射和车室内热辐射的影响,而且还考虑了车窗玻璃表面的几何形状、周围物体的物理特性和热特性对车室内热环境的影响。因此该模型可以用于预测车室内不均匀热环境的特性,以便为人体局部热舒适性的评价提供必要的计算数据。     

Spectral and Total Effective Emissivity of a High-Temperature Fixed-Point Radiator Considered in Relation to the Temperature Drop Across its Back Wall

In this article, calculations of the spectral and total cavity emissivity of a high-temperature fixed-point radiator by means of the Monte–Carlo technique in conjunction with calculations of the temperature drop across its back wall using the finite-element approach are presented. The temperature drop across the back wall of a fixed-point cavity radiator is influenced by the heat exchange within the cavity and between the cavity and the front end of the associated furnace. The special effects of these influences were virtually neglected in earlier estimates of the temperature drop for high-temperature fixed-point radiators, resulting in an overestimation of the value of this parameter. These same effects have a non-negligible influence on the cavity emissivity. Even though the heat exchange between the furnace and cavity enhances the temperature uniformity within the cavity, it appears that the cavity cannot be assumed to be isothermal for the case considered, as is usually taken for granted when dealing with fixed-point cavity radiators. Since the temperature drop and total emissivity are affected by the same thermophysical processes, there exists a correlation between these parameters, which might find practical application. To provide experimental evidence to the findings inferred from the calculations, results of measurements of the cavity radiance-temperature of two high-temperature fixed-point cells are presented, enclosing an ingot of eutectic Re-C, for which the cavities are provided with different apertures. For λ = 650 nm, the measured differences in cavity radiance-temperature are shown to be compatible with the differences in radiance temperature calculated for these cavities.     

基于微型镓固定点的精密铂电阻温度计原位校准的研究

基于固定点温标传递技术,设计可在镓熔点原位校准的精密铂电阻温度计,并对微型固定点相变温坪特性进行实验分析.实验结果表明:微型镓固定点温坪可持续最大时长为1.2h,温坪在20 min内稳定性优于2.8 mK,复现性优于2.3 mK;微型固定点温坪值与加热温度之间存在线性关系,并且随着加热温度的升高,固定点温坪值越高,通过...     

Thermal behavior and energy storage of a suspension of nano-encapsulated phase change materials in an enclosure

The energy storage capability of a suspension of Nano-Encapsulated Phase Change Material (NEPCM) nanoparticles was addressed in an enclosure during the charging and discharging process. The nanoparticles contain a Phase Change Material (PCM) core, which are capable to absorb a notable quantity of thermal energy on melting. There is a heat pipe in the cavity at the bottom corner, which is enhanced by a layer of metallic matrix. The natural convection flow occurs due to a temperature gradient during the charging or discharging process. The particles of NEPCM move with the natural convection flow and contribute to heat transfer & storage of thermal energy. The regulating equations for the heat transfer & flow of the NEPCM suspension were established & converted in the non-dimensional type. The finite element method (FEM) was utilized in resolving the equations. The results show that there was a rise in the rate of heat transfer & storage of total energy with a rise in nanoparticles volume fraction. The decrease of the Stefan number from 0.2 to 0.6 increases the total stored energy by 25%. The fusion temperature is another important parameter in which its behavior depends on the charging or discharging process.     

热管恒温槽校准工业用短型温度计的可行性研究

在(200~500)℃范围内,热管恒温槽是一种替代油槽和盐槽的清洁恒温源。受传热效率的限制,热管恒温槽在校准短型温度计时会产生较大的偏差。本文从传热学角度分析了短型温度计校准中偏差产生的原因。分析证明,在校准过程中,通过增大接触面积,提高换热系数的方式可以有效强化传热,减小因传热造成的偏差。实验表明,通过增加辅助金属环的方式能够有效提高传热效率,提高测量准确度,降低对被测温度计浸没深度的要求,完成工业用短型温度计的校准。     

梯度复合材料热传导分析的梯度单元法

给出了一种适用于梯度复合材料热传导分析的梯度单元, 采用细观力学方法描述材料变化的热物理属性, 通过线性插值和高阶插值温度场分别给出了4节点和8节点梯度单元随空间位置变化的热传导刚度矩阵。推导了在温度梯度载荷和热流密度载荷作用下, 矩形梯度板的稳态温度场和热通量场精确解。基于该精确解对比了连续梯度模型和传统的离散梯度模型的热传导有限元计算结果, 验证了梯度单元的有效性, 并讨论了相关参数对梯度单元的影响。结果表明, 梯度单元和均匀单元得到的温度场基本一致; 当热载荷垂直于材料梯度方向时, 梯度单元能够给出更加精确的局部热通量场; 当热载荷平行于材料梯度方向时, 4节点梯度单元性能恶化, 8节点梯度单元和均匀单元的计算结果与精确解吻合很好。     

An optimum spacing problem for five chips on a horizontal substrate in a vertically insulated enclosure

The optimum spacing problem for five heated chips rested on a conductive substrate in a vertically insulated enclosure filled with air is solved by an operator-splitting pseudo-time-stepping finite element method, which automatically satisfies the continuity of the interfacial temperature and heat flux. It is found that the conventional equi-spaced arrangement is not an optimum option. An optimum thermal performance can be obtained when the center-to-center distances between the chips follow a geometric series. The maximum relative temperature drop in the optimum configuration can be as much as 20% of the equi-spaced arrangement. Received 28 April 1999     

改进型封装固定点黑体在辐射测温中的应用

为了延长固定点黑体容器使用寿命和简化使用流程,依据热管黑体和传统石墨坩埚黑体的设计使用经验,研制了改进型封装固定点黑体。针对所研制的锡固定点黑体分别用二等标准铂电阻和传递辐射温度计开展复现测试。改进型封装固定点黑体在经历20余次熔凝循环后,没有出现破裂和金属泄露现象。用标准铂电阻复现多次的平均值为231.909℃,扩展不确定度为0.015℃(k=2);而用固定点黑体校准传递辐射温度计的多次平均值为231.85℃,扩展不确定度为0.096℃(k=2)。     

Construction and Characterization of a Large Aperture Blackbody for Infrared Radiometer Calibration

A large aperture blackbody (LABB) with a diameter of 1 m has been successfully constructed for calibrating radiation thermometers and infrared radiometers with a wide field of view in the temperature range between 10 °C and 90 °C. The blackbody is a 1 m long cylindro-conical cavity with a diameter of 1.1 m. Its conical bottom has an apex angle of 120°. To achieve good temperature stability and uniformity, the cavity is integrated to a water-bath to which the pressurized water is supplied from a reservoir. To reduce the convection heat loss from the cavity to the ambient, the cavity is purged of the dried air that passes through a coiled tube immersed in the reservoir. For an uncertainty evaluation of the LABB, its temperature stability was measured by using a reference radiation thermometer (RRT) and a platinum resistance thermometer (PRT), and its radiance temperature distributions on the aperture plane were measured by using a thermal camera. Measuring the spectral emissivity of the coating material, the effective emissivity of the blackbody was calculated to be 0.9955 from 1 ??m to 15 ??m. The expanded uncertainty of the radiance temperature scale was evaluated based on the PRT readings, which vary from 0.3 °C to 0.5 °C (k = 2) in the temperature range. The temperature scale is validated by comparing with the RRT of which the temperature scale is realized by a multiple fixed-point calibration.     

Study of standard thermometers and their reproduction of the λ point in liquid helium

Self-calibrated resistance thermometers to be used as standards have been investigated. The heat exchange of the sensor coil with liquid helium per unit coil surface area at 0.3 K is 12 times better than that of a conventional gas-filled thermometer. The exchange is due to Kapitza surface thermal resistance. The λ point in liquid helium filling of the thermometer is reproducible to within 0.1 mK. Translated from Izmeritel’naya Tekhnika, No. 7, pp. 50–52, July, 1999     

900 nm照度辐射温度计的研制

介绍了中国计量科学研究院基于黑体辐射原理研制的波长为900 nm、测温范围为600～1 500 ℃的照度辐射温度计。该辐射温度计测量探测器接收的光谱辐射照度,采用单点分度法,结合有效波长测量技术,直接依据普朗克辐射定律计算被测温度,具有结构简单、测温稳定性好的特点。单点分度法以Cu点为固定点在Al点测温偏差为-0.04 ℃,而在800 ℃和900 ℃两个点,与RT9032辐射温度计测量结果偏差分别为0.09 ℃和0.11 ℃。     

Experimental and Numerical Investigation of the Temperature Field of a Fixed-Point Cavity

The temperature field non-uniformity of a blackbody cavity is one of the components of uncertainty of fixed-point realization. Here a study of the design and opportunities of the temperature furnace used in VNIIM is described. The dependence of the uniformity of a temperature field on various factors is shown by results of numerical calculations of a temperature field of VNIIM??s copper and gold fixed-point cells, realized with the software packages Elcut 5.3 and Ansys 11.0. A thermophysical model of the phase transition considered as steady state with convection and radiation heat exchange to an environment is applied. The basic focus is made on calculation of the radiation heat exchange between crucible elements and the environment and a furnace cavity, as a dominating component of the heat transfer. Results using analytically and numerically calculated angular factors of radiation of heat exchange are discussed. The data obtained in measurements of a temperature field of a cavity fixed point during phase transitions of copper and gold by a spectrocomparator with high sensitivity, are also shown here. Both theoretical calculation and experiment were realized at various distributions of temperature along an external surface of a crucible. Good agreement of results between steady-state calculation of a temperature field and the measured data with the best entry conditions is observed. The average value of non-uniformity of a temperature field along a cavity for points of phase transition of copper and gold for an 88?mm long graphite crucible with a 54?mm deep, 8?mm diameter cavity was 40?mK, and the temperature drop across the graphite wall was 20 mK. In this paper the reasons for occurrence of large gradients inside a fixed-point cavity during the phase transition, received during some experimental research, are also discussed.