INFLUENCE OF AIR GAP BETWEEN THE TRANSFORMER OF RESISTANCE AND OBJECT OF MONITORING ON TEMPERATURE MEASUREMENT ERROR

In operation the description of the developed heattransfer model in thermotransformers of resistance (RTD) in the conditions of air gap between surfaces of the sensor and object of measurement is provided. Research of influence of thickness of air gap on the relative error of temperature measurement by platinum, copper and nickel thermotransformers of resistance in the ranges of temperatures corresponding to each type is executed. Dependences of minimum necessary duration of heating up of sensors on the taken temperatures are received.


Introduction
Monitoring systems and regulations of temperature on production play an important role.Quality of operation of such systems directly depends on reliability of the measuring information received from sensors of the bottom level of systems therefore the accuracy of gages should pay special attention.At the bottom level measurement of technological parameters is performed by the sensors set directly on control objects.In a production activity one of the parameters of technological processes which are most often measured by such sensors is temperature.This parameter defines quality of course of technological processes, an equipment status, safety of production in general.
For temperature measurement and a signal transmission on distance in industrial conditions the wide circulation along with thermoconjugate sensors (thermocouple) was received by thermotransformers of resistance (RTD) [1,2].The principle of their action is based on dependence of electrical resistance of metal on temperature [1][2][3][4].Often temperature is not only an index of efficiency of course of technological process, but also a safe criterion of operation of the equipment.Not full thermal contact with a work environment or a surface of object of measurement, namely air gaps [5,6] can be one of temperature measurement error origins contact sensors.In this case increase of accuracy can be promoted by correction of conditions of execution of measurements or determination of optimum duration of execution of measurements which will be enough for receiving authentic results [5,6].
The purpose of the real operation is development of model of a sensitive element of the thermotransformer of resistance and numerical research of a measurement error in different conditions of thermal contact of the sensor with object of measurement or a work environment.

Physical model of heat transfer
Is considered 1 diagram of area of the solution of the task of heat conduction which is representing the non-uniform system and including a metal sensitive element (copper, platinum or nickel), aluminum oxide powder, a protective cover and air gap given on fig.In case of the solution of the task the assumptions which aren't superimposing essential restrictions on a problem definition community are accepted: 1) heatphysical characteristics of elements of area of the decision don't depend on temperature; 2) the sensitive element has the correct cylindrical form.The initial temperature of system "a sensitive element -the powder Al 2 O 3 -a protective coverair" corresponds to reference conditions and makes 20 °C.The model assumes process of temperature measurement of the surface of object separated from RTD by air gap.
As an index of the end of process of heating up an achievement moment by a sensitive element of temperature other than temperature on decision area boundary on the value which isn't exceeding the allowed measurement error which values are given in table 1 is chosen.
Boundary conditions on inner and outline borders are given in the table 2.

Tr T (r=R).
The solution of the task is executed by method of finite differences on the basis of the four-dot implicit difference diagram [8].The area of the solution of the task represents a grid 200×200 nodes with steps of 2,5•10-2 mm on axial and radial coordinates, a step on dt time = 0,001 sec [8].

Results and discussion
Mathematical modelling were carried out at parameters [9,10]: sensitive element RTD (type Pt):     The analysis of fig. 2 allows to draw a conclusion that with increase in duration of heating up the error of measurements non-linearly decreases.So, for RTD Pt type at a thickness of air gap of 0,5 mm of 50 seconds of heating up of the sensor will be enough for receiving results with a margin error, not exceeding the permissible deviations defined according to [7].Researches showed that the increase in thickness of air gap between RTD and object of measurement causes increase of necessary time of heating: on 1 mm, on average, -by 1,6 times, on 1,5 mm -twice, and on 2 mm -by 2,5 times.
Similar dependences are received for copper and nickel thermotransformers of resistance.So, for copper RTD in the conditions of air gap 0,5 mm thick for receiving results within blundered the sufficient duration of execution of measurement makes 45 seconds, and for nickel RTD -55 seconds.
During research dependence of duration of heating up of the RTD sensitive element on the taken temperature was also defined at the fixed thickness of air gap -1 mm (tab.3).From table 3 it is visible that dependence of sufficient duration of heating up of RTD non-linearly increases with increase in temperature.On average, the greatest time of heating is required for platinum RTD, the smallest -for copper that is caused by heatphysical characteristics of materials of the sensor.Thermophysical Basis of Energy Technologies 2015 01041-p.5

Conclusion
The developed heattransfer models in the RTD sensitive element allow to predict sufficient measurement execution duration.Results of numerical researches show that temperature measurement error non-linearly decreases with increase in time of heating up of the sensor and can be lowered to the required level.It is set that the increase in thickness of air gap between the sensor and the controlled environment can lead to the multiple increase of a measurement error which can be lowered by increase in duration of execution of measurements.

Figure 1 .
Figure 1.The diagram of area of the solution of the task of heattransfer in the RTD sensitive element: on outline borders boundary conditions of the II sort 1 -the RTD sensitive element are set; 2 -aluminum oxide powder; 3protective cover; 4 -air.

Figure 2 .
Figure 2. The dependences of a measurement error of temperature on time of heating up of the Pt type RTD sensitive element corresponding to values of thickness of air gap: 1 -2 mm; 2 -1,5 mm; 3 -1 mm; 4 -0,5 mm; 5 -admissible error.

Figure 3 .
Figure 3.The dependences of a measurement error of temperature on time of heating up of the Cu type RTD sensitive element corresponding to values of thickness of air gap: 1 -2 mm; 2 -1,5 mm; 3 -1 mm; 4 -0,5 mm; 5 -admissible error.

Figure 4 .
Figure 4.The dependences of a measurement error of temperature on time of heating up of the Ni type RTD sensitive element corresponding to values of thickness of air gap: 1 -2 mm; 2 -1,5 mm; 3 -1 mm; 4 -0,5 mm; 5 -admissible error.

Table 2 .
Boundary conditions of the task of heattransfer with the given external heat flux and boundary heat exchange.

Table 3 .
Dependences of necessary duration of operation of TPS in case of temperature measurement.