Study on Thermal Conductivity Methane Sensor Constant Temperature Detection Method

The thermal conductivity methane sensor can detect methane concentration that measures the thermal conductivity coefficient of the measured methane different from the background gas. This sensor has advantages of detection of a variety of gases, large measuring range, stability, long working life, but also has defects, such as poor detection accuracy, sensitivity affected by ambient temperature and sensor temperature, the defect limits a wide applications of the sensor. This paper analyzes the theory of thermal conductivity methane sensor and method of measurement, proposes thermal conductivity methane sensor constant temperature detection method, and experimentally validates the feasibility of ambient temperature compensation. Experimental results show that the method effectively reduces the effect of ambient temperature on measuring accuracy.


Introduction
Each of the molecular structure and molecular weight of the gas is not the same; therefore, the thermal conductivity will change with the change of gas concentration.For the multi-component gas, heat capacity of the mixed gas will vary due to the different components [1][2][3] .The thermal conductivity sensor is based on the principle that it can achieve the gas composition analysis according to the heat capacity difference of mixed gas.Thermal conductivity sensor is an earlier gas sensors for gas detection, thermal conductivity of gas sensors are typically used for high concentrations of gas measurement, it has the following advantages: 1) The sensor has a large measuring range; 2) The sensor can detect a variety of gases, it not only detects flammable gas, but also detects inert gas; 3) The measured environment is unrestricted, the sensor can achieve gas detection in the aerobic or anaerobic conditions; 4) The sensor has a strong resistance against poisoning.
Many gas sensors do not have these excellent characteristics.But the thermal conductivity gas sensor has defects of low sensitivity and large temperature drift in application of gas detection that limits the applications of the sensor [4][5][6].This paper proposes thermal

The thermal conductivity gas sensor thermodynamic theory analysis
The working mechanism of thermal conductivity sensor needs going on the theoretical analysis to complete the method and the application research about thermal conductivity gas detection.Build static characteristic equation of thermal conductivity sensor based on basic theory of heat transfer, namely thermal balance equation.
Sensor operating current is set as I, the resistance set as r, the heat of sensor only comes from operating current heating power, that is r I Qin

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.Based on theory of heat transfer, there are three basic modes: heat transfer, heat radiation and heat convection [7][8][9].On the technology craftsmanship of sensor, in order to reduce heat transfer of resistance wire axial, draw ratio of resistance wire is usually above 2  10 3 ~3 10 3 , so the influence of heat transfer of sensor axial can be ignored [10].When thermal conductivity sensor is working, the loss of heat convection caused by air flow also can be ignored because of the effective defense of sensor.So the main heat loss is heat transfer Q out1 and heat radiation Q out2 that can be expressed as: Q out1 is the loss heat of heat transfer, expressed as: In the formula above: λ is the gas thermal coefficient; t is the temperature; r is the radius of the sphere; S is the heat transfer area.The thermal conductivity type gas sensor used in this article is sensitive balls as shown in Figure 1, according to the structure of the ball; the following formula about heat losses of heat conduction can be obtained.
The above equation can be deformed as follows: Both sides of the equation are integrated at the same time, we can get: Where C is a constant of integration, determined by the boundary conditions.In Figure 1, the radius of the sensitive ball is r a , and T is its temperature; the distance between the center of the sensitive ball to the outer wall of the sensor is r b , and T 0 is its temperature.So, we can get: , K is a constant determined by the structure of the sensor, we can get: Q out2 is the loss heat of heat radiation, based on Stefan-Boltzmann's law, expressed as: In the formula above: A is radiation coefficien; σ is Stefan-Boltzmann constant, when meets thermal equilibrium condition: Ideal operating temperature of thermal conductivity sensor is at 400-500℃.In this paper, we adopt the constant temperature detection method; therefor the loss heat of heat radiation Q out2 is constant and far less than the loss heat of heat transfer Q out1 , that means Q out2 can be ignored.So heat-balance equation can be simplified to: Suppose that test gas is simple gas, and background gas is air.Volumetric concentrations of test gas and air in the gas mixture are C m and C c separately, thermal conductivities of test gas and air are m λ and c λ separately, thermal conductivity of gas mixture , thermal coefficient of gas mixture can be achieved: According to Figure 2, Heat-balance condition of the reference component and sensitive component is followed: In the formula above: c λ is thermal conductivity of air; x λ is thermal conductivity of gas mixture; R c is resistance of the reference component; R m is resistance of the sensitive component;  is the temperature difference between the reference component and environment ℃ ; 2 t  is the temperature difference between the sensor component and environment ℃.So bring formula (13) into (14), we can get: In the formula above, C is the relative coefficient of variation of gas mixture thermal conductivity: The relation between resistance of the reference component and resistance of the sensor component with temperature: Output of the bridge V  is: According to formula ( 14), ( 15), ( 18) and ( 19), it can derive: Bring formula(16) into the formula above, the expression between volume with concentration about methane gas is: We can see from formula (21), the concentration of measured gas and the output of the bridge is in direct ratio, the concentration and the voltage of the reference component is in inverse ratio, and it also has direct relation with temperature coefficient of platinum resistance wire inside the sensor, environment temperature and the temperature of the sensitive component.

The thermal conductivity gas sensor constant temperature detection technology
Through the above theory analysis, the concentration of measured gas has relations with the temperature of the sensitive component.Conventional constant-current detection method supplies power for platinum resistance wire of the sensor by using of a constant-current source [11], when the ambient temperature changes or gas concentration changes, the temperature of the sensor can not guarantee constant, so that the temperature of sensitive component is unknown, unpredictable, this paper presents a constant temperature detection method.Figure 2 is the schematic diagram of thermal conductivity gas sensor constant temperature detection.In Figure 2, resistance R4, R5, Rm and Rc compose measuring bridge, the sensor is composed of R m and R c , Rm is sensitive component of the sensor, Rc is reference component of the sensor, which is used for environment compensation.R4 and R5 are the resistances of the other side of the bridge, the bridge picks up the measurement signal.
The key to achieve thermal conductivity sensor for temperature detection is how to ensure that the sensor is always working at predetermined temperature in the case of variety of environmental temperature and the detected gas concentration changes.This paper uses the variable current source technology to achieve constant temperature detection, by adjusting the current change heating power to ensure the temperature of sensor constant.
In the formula above, the relationship between sensitive component resistance R m and the temperature of sensitive component t m is: When the concentration of measured gas is zero, the bridge is made to keep balance by adjusting the resistance value of the bridge arm, and so that the sensor is working at a predetermined temperature.The measured gases is detected , assuming that the thermal conductivity of the measured gas is greater than the thermal conductivity of air which make thermal conductivity of gas mixture increase and enhance heat transfer of gas, then the temperature of the sensor t m becomes low, sensitive element resistance t m reduces , bridge is unbalanced, current is coordinately regulated through the feedback link control amplifiers and transistor, making it increase ,so sensor temperature t m and sensitive element resistance R m increase, until the bridge rebuilt to a new equilibrium point.
As the bridge finally remains in equilibrium, the sensor resistance R m is not changed, the sensor working temperature t m is unchanged, the system is constant, and this is the most notable feature of the constant temperature detection [12].
Based on the theory of constant temperature measurement, sensor is set in a desired operating temperature by matching of resistances, and then the temperature sensors measure the current ambient temperature according to type (21) to compensate temperature, eliminating the effect of temperature on measuring sensitivity.

The application of the test results analysis
In order to verify the theoretical analysis and experimental results, a test experiment for sensor temperature compensation and sensor sensitivity experiment of wide range concentration are conducted.Thermal conductivity sensor takes at 450℃ constant temperature through the constant temperature control circuit, 20% methane standard gas at 25 ℃ ambient temperature is used for sensor calibration.When operating ambient temperature is 0, 10, 20, 30 and 40℃, after calibration, the sensor takes a measurement without temperature compensation experiment by using 20% methane gas.Data without compensation is processed by the formula (20) for temperature compensation to obtain the experimental data shown in Table 1 The above table can be drawn that when ambient temperature reached 40℃, the maximum effect of ambient temperature is 3.1% methane equivalent without compensation, after the temperature compensation the residual value falls below 0.4%,this shows that the thermal conductivity gas sensor constant temperature detection method can effectively reduce the impact of temperature on the measurement accuracy.
Thermal conductivity sensor takes at 450℃ constant temperature through the constant temperature control circuit, after the temperature compensation, experiments are conducted at 25℃ ambient temperature.Dry air and concentration of 99.9% methane configures the following concentration methane standard gas: 0%, 50%, and 70%, the sensor is calibrated by using 50% concentration methane gas, measuring experiment with the configuration gas of each concentration.Experimental data are shown in Table 2.By the data in the above table, within a wide range, output of the sensor is a linear relationship, within the range of 0% to 90%, maximum non-linearity error is 2.4%, so that the thermal conductivity gas detection method based on the constant temperature detection technology has high linearity, the reason is that the thermal conductivity of single-component gas is constant when the sensor operates in a constant-temperature state, the relationship between the thermal conductivity of mixed gas and gas concentration is linear.
In this paper, the gas detection method of thermal conductivity based on constant temperature detection technology effectively improves the detection accuracy of the system, solves the problem that the sensitivity of the sensor is affected by ambient temperature and creates conditions for achieving full scale measurement of gas concentration by using single thermal conductivity sensor.

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ISSN: 1693-6930 TELKOMNIKA Vol.11, No. 4, December 2013 : 725 -732 726 gas-detection methods based on constant temperature detection, in order to reduce the effects of temperature drift and improve the sensitivity of the sensor.

Figure 1 .
Figure 1.Schematic diagram of sensor sensitive ball and shell structure

ISSN: 1693- 6930 TELKOMNIKA
Vol. 11, No. 4, December 2013 : 725 -732 728 Study on Thermal Conductivity Methane Sensor Constant Temperature ... (Ding Xibo) 729 In the formula above:R 0 is the resistance of reference component when temperature is 0℃; t is environment temperature ℃; αis temperature coefficient of platinum resistance wire inside the sensor.Voltage of the reference component and voltage of the sensitive component:

Figure 2 .
Figure 2. schematic diagram of thermal conductivity gas sensor constant temperature detection

Table 1 .
. Thermal conductivity gas sensor temperature compensation experimental data

Table 2 .
Gas sensor sensitivity experimental data