Investigation of Emissivity and Junction Contacting Status of C-Type Thermocouples Using Rich Hencken Flames

Abstract

C-type thermocouples are widely used to measure rich combustions; however, the measured temperature, i.e., the thermocouple junction temperature, is not equal to the gas temperature. The junction temperature results from the junction energy balance, including radiation with environments, conduction with thermocouple wires, and convection with gas. A correction based on the junction energy conservation can derive the gas temperature from the measured temperature. Two C-type thermocouples are used to measure the core region of the standard flames with known gas velocity, composition, and temperature. By matching the CFD-simulated junction temperature with the measured temperature, the emissivity of the thermocouples is obtained. In the temperature range of 1190–1542 K, the emissivity of both thermocouples is close to 0.4. Since the junctions of the C-type thermocouple are large, the area ratios of the wire cross-section to the junction surface are small, and the wire conduction effect is minimal. CFD simulations show that the junction temperatures only decrease by 3.9 K and 8.1 K without wire conduction when the 0.5 mm and 1.0 mm thermocouples measure the Hencken flame with the temperature of 2023.5 K. With the CFD simulation of the measurement of the diffusion region of the Hencken flame, where a strong gas temperature gradient exists, the junction contacting status is judged for the 0.5 mm thermocouple. The simulated temperature of the welding point is consistent with the measured temperature, indicating no wire contact inside the junction.

1. Introduction

Temperature is a key parameter in industrial production, and accurate temperature measurement is significant for production process control, increasing production efficiency, and improving production safety [1]. Thermocouples are frequently used for gas temperature measurement because of their robustness, simplicity, and low cost. For R-, S-, B-, or K-type thermocouples, whose materials have good malleability, two thermocouple wires are welded together, forming a welding point. As shown in Figure 1, the welding point generally has a shape close to a sphere, which is called a thermocouple bead or thermocouple junction. The measured temperature of a thermocouple is the junction temperature. The junction temperature is not equal to the gas temperature, which is the result of the junction energy balance. The junction energy balance includes conduction between the junction and the wires, convection and radiation with the incoming gas, and radiation with the surroundings. The energy balance of a spherical junction in a steady flow is shown in Figure 2 and Equation (1).

Q_cond,1 is the conduction rate between the thermocouple wire 1 and the junction, while Q_cond,2 is that between the thermocouple wire 2 and the junction; Q_conv is the convection rate between the junction and the incoming gas; Q_radg is the gas radiation absorbed by the junction; and Q_rads is the radiation rate between the junction and the environment.

$$\begin{array}{l}{Q}_{cond,1}+Q_{cond,2}+Q_{radg}+Q_{rads}+Q_{conv}=0;\\ Q_{cond,1}=k_1{A}_c{\displaystyle \frac{\partial T_1}{\partial x}};Q_{cond,2}=k_2{A}_c{\displaystyle \frac{\partial T_2}{\partial x}}\\ Q_{radg}=\sigma A_b\epsilon {\epsilon }_g{T}_g^4;\\ Q_{rads}=-\sigma A_b\epsilon (T_b^4-(1-{\alpha }_g)T_{\infty }^4);\\ Q_{conv}=h_b{A}_b(T_g-T_b)\end{array}$$

(1)

Here, k₁ and k₂ are the thermal conductivity of wire 1 and wire 2; T₁ and T₂ are the temperatures of wire 1 and wire 2; A_c is the wire cross-sectional area; ε is the thermocouple emissivity; ε_g is the volumetric emissivity of the gas radiation, relating to the gas temperature, volume, and composition [2]; σ is the Stefan–Boltzmann constant; A_b is the surface area of the junction; T_g is the temperature of the gas; T_b is the temperature of the junction; α_g is the gas absorption coefficient to the environmental radiation, which is related to the gas temperature, volume, and composition, and the environmental temperature [2]; T_∞ is the surrounding temperature; and h is the junction convection coefficient. Similar energy conservation also applies to the thermocouple wires. Equation (1) can be rearranged to the following expression:

$${\displaystyle \frac{k_1{A}_c(\frac{\partial T_1}{\partial x})}{h{A}_b}}+{\displaystyle \frac{k_2{A}_c(\frac{\partial T_2}{\partial x})}{h{A}_b}}+{\displaystyle \frac{\epsilon {\epsilon }_g\sigma T_g^4}{h}}-{\displaystyle \frac{\epsilon \sigma [T_b^4-(1-{\alpha }_g)T_{\infty }^4]}{h}}=T_b-T_g$$

(2)

The temperature difference between the measurement temperature and the gas temperature is due to the thermocouple surface radiation (radiation loss) and the conduction between the junction and the wires (conduction loss or gain). Gas radiation reduces the difference between the measurement temperature and the gas temperature. As the incoming gas velocity increases or the junction size decreases, the junction convection coefficient increases, and the junction temperature has less of a difference with the gas temperature. Theoretically, when the convection coefficient approaches infinity (infinite velocity or zero junction diameter), the junction temperature equals the gas temperature [3,4,5]. Reducing thermocouple size is always a good way to decrease the measurement error, i.e., the junction and gas temperature difference. The effect of conduction between the wires and the junction depends on the temperature gradients of the wires and the area ratio of the thermocouple wire cross-section to the junction surface.

Based on the energy conservation analysis of the thermocouple, the gas temperature can be derived according to the measured temperature, i.e., the junction temperature. For example, Shaddix [6,7] considered the conduction effect between the junction and the wires, including the convection and radiation effects of the junction, to obtain a correction equation for thermocouples. As evaluated by Li et al. [8], the correction accuracy is not bad, but for the large thermocouples, the equation underestimates the loss of the junction conduction and increases the correction errors. Accurate wire temperature profiles are needed to calculate the accurate conduction loss of the junction. The one-dimensional (1D) numerical program developed by Sato et al. [9] was used to solve the energy conservation equations of the thermocouple, including the wires and junction. Considering all heat transfer forms, the energy conservation equations for the wires and junction are established, which are discretized along the wire direction. The input is the gas temperature, and the output is the junction temperature and the wire temperature profiles. If the measured temperature is known, the input of the gas temperature can be adjusted until the predicted junction temperature is equal to the measured temperature. This inverse process is called the correction process. Li et al. [8] also used this method to simulate the temperature measurement of the standard Hencken flames. Compared with the experimental data, the predicted junction temperature has errors of less than 35 K. The correction is also carried out with this method, and the difference between the real and corrected temperatures is less than 29.6 K. In the 1D simulations, the convection coefficients of the bead and the wires calculated with the correlations from the literature, whose error is normally about ±20%, cause simulation errors. To better calculate the convection of the thermocouple, direct CFD simulations of the measurement process can be used. Li et al. [8] predicted the junction temperature of the thermocouple measuring the standard Hencken flames with a maximum error of 13 K (compared with experimental values), which is much less than the error of 35 K with the 1D simulation. Of course, CFD simulations can also be used for correction; the incoming gas temperature can be adjusted to match predicted junction temperatures with measured temperatures. Skovorodko et al. [10] have demonstrated the disturbance of thermocouples on the flow field with strong temperature gradients, which in turn influences the energy balance and reading of thermocouples. Since the existence of flow field disturbance, the CFD simulation method should be better than the traditional correction methods, including the 1D simulation method, because the disturbance effect is automatically included in CFD simulations.

For the correction of thermocouple measurement, emissivity is the most important parameter since surface radiation is the major cause of the temperature difference between the gas and the thermocouple junction. The accuracy of the emissivity, in fact, determines the correction accuracy. S-type thermocouples are widely used for the temperature measurement of lean flames since they only work in neutral and oxidizing atmospheres. Li et al. [8] reported the emissivity of five S-type thermocouples of different sizes from the same manufacturer by matching the simulated junction temperature with the measured temperature of standard Hencken flames. Some important conclusions for the tested S-type thermocouples are given: (1) different thermocouples have different emissivity values; (2) emissivity decreases with temperature, which is different from previous reports in the literature; and (3) emissivity is much larger than the reported values in the literature because of the rough surface condition and possible surface oxidation of the thermocouples.

Rich combustions are popular in industry, where C-type thermocouples (measuring a temperature of up to 2320 °C), only working in neutral and reducing atmospheres, are frequently used to measure their temperatures [11,12,13]. Of course, the measured temperature should be corrected to obtain the gas temperature, and the emissivity is critical for the correction. However, there is no report on the emissivity of C-type thermocouples yet. The wires of the C-type thermocouples are made of tungsten–5%rhenium (W5%Re) and tungsten–26%rhenium (W26%Re). There are some emissivity data for the materials close to the wire materials. Moraga et al. [14] measured the emissivity of the sintered W3%Re and W25%Re plates. For the W3%Re plate, the emissivity increases from 0.296 to 0.365 when the temperature increases from 1600 K to 2500 K. Logunov et al. [15] measured the emissivity of W5%Re (the C-type thermocouple material), which is about 20% lower than the W3%Re values reported by Moraga et al. [14]. Vertogradskii [16] measured the emissivity of the W5%Re material, which is about 25% lower than the values of the W3%Re material reported by Moraga et al. [14]. The emissivity of the W25%Re plate increases from 0.25 to 0.341 when the temperature increases from 1600 K to 2500 K [14], while the emissivity of the W27%Re material reported by Peletskii et al. [17] is about 15% lower. Since the emissivity of a surface depends on the surface conditions, even the emissivity reported for the same materials should be used cautiously. It is important to measure the emissivity of thermocouples directly instead of using the values from the literature.

It is well known that the thermocouple wires should be clearly separated. If the wires contact before the junction as shown in Figure 3, the thermocouple reading, i.e., the measurement temperature, is the temperature of the contacting point instead of the junction. This location is not where the thermocouple is supposed to carry out its measurements. However, the wire contacting situation seems to be unavoidable for C-type thermocouples. W5%Re and W26%Re materials are very brittle and hard. A spherical bead, i.e., the welding point, is not strong enough to hold the wires together for a long time. General C-type thermocouple junctions are shown in Figure 4 (thermocouple A with a wire diameter of 0.5 mm and thermocouple B with a wire diameter of 1.0 mm). One wire is wrapped several turns around another one, and the ends of the two wires are welded together, forming a welding point with a shape close to a hemisphere. The thermocouple configurations in Figure 4 are typical, and most commercial C-type thermocouples look like them [18]. It is hard to judge the contacting situation of the wires of the junction. The outer wire could contact the central wire anywhere. If the temperature difference within the junction (the welding point and the wrapping region) is minimal, e.g., when the thermocouple is measuring a uniform flow field, the temperature of the contacting point and the average temperature of the junction have little difference. It is not necessary to identify the contacting point, and the average temperature of the junction can be considered as the measurement temperature. However, when the thermocouple is measuring the flow field with strong temperature gradients, the temperature difference within the junction could be very large; it is important to differentiate the temperature of where the thermocouple reading is indicating. This is very important when 1D simulations or 3D simulations are used to correct the measurement temperature to obtain the real gas temperature.

Since emissivity depends on surface conditions, the thermocouple emissivity might not be consistent with literature values. Two C-type thermocouples, as shown in Figure 4, are used to measure the core region of Hencken flames, where the velocity, gas composition, and temperature are accurately known. With known gas parameters and the measured temperatures, the emissivity of the thermocouples is derived. Since the junctions of the C-type thermocouples are much larger than those of regular thermocouples with only spherical welding points, whether the conduction has a negligible effect on the junction temperature is investigated by comparing the junction temperatures with and without wires using CFD simulations. The junction contacting situations of the C-type thermocouples are also investigated via the comparison of CFD simulation and experimental measurement of the diffusion region of standard Hencken flames.

2. Experiments

The experimental setup was used in Li et al. [8], and it is briefed here. The one-inch Hencken burner (RD1X1) produces rich H₂/air diffusion flames. Figure 5 shows the top surface picture and the burner schematic. The oxidizer and fuel flow out of the main flow exit, and the main flow exit is surrounded by an inert coflow exit, which is used to isolate the flame from the atmosphere. The fuel tubes are evenly distributed and nested in the honeycomb structure.

After flowing out of the fuel tubes and the honeycomb, the fuel and oxidizer mix and burn within 6 mm above the burner surface, forming multiple tiny flamelets (the overall flame is a plane flame) [19]. As shown in Figure 5b, above the combustion zone is the combustion product zone. While the combustion product flows upward, it transfers mass and heat with the coflow. There is a pyramid core region in which this transfer effect is negligible. In this core region, the temperature is uniform horizontally, and the gas radiation decreases the product temperature linearly with height [19].

Outside is the cold atmosphere and coflow, and the diffusion region is between the cold region and the core region. The diffusion region of a Hencken flame is where the hot combustion product and the cold gas (coflow and air) exchange momentum, energy, and species, where it has a strong temperature gradient (over 1000 K temperature drop within several millimeters). The measurements in the core region and the diffusion region are carried out here.

The oxidizer is the bottled dry air, H₂ is the fuel, and N₂ is used as the coflow gas. The TELEDYNE HFM-203 meters (Teledyne Hastings Instruments, Hampton, VA, USA) are used for mass flow rate measurement of H₂ and air. The uncertainty of mass flow rate is ±1% of the full scale. In some test cases, extra N₂ is used as a diluent to reduce flame temperature, and it is blended in the air stream before entering the burner. The flow rate of the blended N₂ is measured with the TELEDYNE HFM-D-300B flow meter (Teledyne Hastings Instruments, Hampton, VA, USA), whose uncertainty of mass flow rate is ±0.5% of full scale. The mass flow rate uncertainty causes the equivalence ratio uncertainty, and the corresponding uncertainty of adiabatic equilibrium temperature is about ±20 K. Since C-type thermocouples can only work in neutral or reducing environments, the rich flames are used in the tests covering the equivalence ratio of 2.08–3.68.

Table 1. Experimental flow rate and real gas temperature at measurement point.

	Equivalence Ratio	H2 (SLPM)	Air (SLPM)	DiluentN2 (SLPM)	CoflowN2 (SLPM)	Species Mole Fraction H2:H2O:N2	Velocity of Measurement Point (m/s)	Adiabatic Equilibrium Temperature (K)	Real Gas Temperature of Measurement Point (K)
1	2.08	17.73	20.32	/	14.7	0.27:0.253:0.477	6.94	2033.4	2023.5
2	2.48	21.18	20.36	/	14.7	0338:0.23:0.432	7.18	1909.8	1902.1
3	2.90	24.84	20.39	/	14.7	0.398:0.209:0.393	7.42	1795.0	1789.2
4	3.30	28.29	20.43	/	14.7	0.443:0.193:0.364	7.63	1701.8	1697.4
5	3.68	31.69	20.48	10.25	14.7	0.396:0.149:0.455	8.26	1414.3	1412.5
6	2.55	21.34	19.93	/	15.7	0.35:0.226:0.424	7.07	1887.7	1880.5
7	2.45	21.05	20.47	/	16.2	0.335:0.231:0.434	7.21	1918.7	1911.2

presents the experimental data and the adiabatic equilibrium temperature. The real temperature, velocity, and species mole fraction of the gas in the plane of 15 mm above the main flow exit of the core region are also calculated and presented in the table. Subtracting the gas-radiation temperature drop from the equilibrium temperature gives the real gas temperature [19]. The thermocouples are in the plane 15 mm above the main flow exit. For the case with the highest temperature (flame 1), the temperature drop from the equilibrium temperature by gas radiation in the core region is only 9.9 K.

Two C-type thermocouples connected to the Omega CL3515R meter (Omega Engineering Inc., Norwalk, CT, USA) are used for the temperature measurement. The picture of the thermocouples is shown in Figure 4. The smaller thermocouple has a wire diameter of 0.5 mm, and one wire wraps about 6 turns around another, making the junction relatively large. The junction is about 1.52 mm in diameter and 4.35 mm in length. For the thermocouple with a wire diameter of 1 mm, one wire wraps about 2 turns around another one, and the diameter and length of the junction are 3.07 mm and 3.9 mm, respectively. These two thermocouples are frequently used in industry. Smaller thermocouples are not strong enough to bear the harsh conditions of industrial environments, e.g., large gas velocities and possible particles. For the combination of the meter and thermocouple, the measurement uncertainty is ±(0.05% reading + 2) °C, and it is less than 3 K even for a 1600 K reading. The double-hole Omega TRM-04018 ceramic protector (Omega Engineering Inc., Norwalk, CT, USA) is used to insulate the thermocouple wires, and the junction projects beyond the insulator about 15 mm. The wire length is 300 mm, which is long enough to ensure that the cold end temperature is consistent with the environmental temperature.

The coordinate is defined in Figure 6a, while the origin is at the center of the main flow exit. Thermocouples A and B are first used to measure flames 1–5 with the center of the junction consistent with the origin (x_jc = 0 mm). The whole junction and about 8 mm of the thermocouple wires are in a uniform temperature field (core region). The measured temperature is reported in

Table 2. Comparison of measured temperature and gas temperature (K).

Flame	1	2	3	4	5
Real gas temperature	2023.5	1902.1	1789.2	1697.4	1412.5
Thermocouple A reading	1542.15	1506.15	1463.15	1422.15	1236.15
Thermocouple A error	481.35	395.95	326.05	275.25	176.35
Thermocouple B reading	1474.15	1448.15	1410.15	1371.15	1191.15
Thermocouple B error	549.35	453.95	379.05	326.25	221.35

.

Due to the junction radiation loss, the measured temperatures (junction temperatures) are much less than the gas temperatures. When the gas temperature is higher, the gas and junction temperature difference is greater. When the 0.5 mm thermocouple measures flame 5, the junction temperature is 176.35 K lower than the gas temperature, while the measured temperature is 481.35 K lower than the gas temperature for flame 1. Also, the larger the junction diameter (lower junction convection coefficient), the larger the junction and gas temperature difference. For flame 1, the measured temperature of thermocouple A is 481.35 K below the gas temperature, and thermocouple B has a measured temperature of 549.35 K below the gas temperature. Li et al. [8] measured a Hencken flame with an equivalence ratio of 0.6 and a flame temperature of 1832 K using an S-type thermocouple (spherical bead diameter of 1.05 mm and wire diameter of 0.5 mm); the measurement temperature (1486 K) is 346 K lower than the gas temperature. Obviously, since thermocouple A (junction length of 4.35 mm, junction diameter of 1.52 mm, and wire diameter of 0.5 mm) has a much larger junction, it has a smaller convection coefficient, resulting in a larger measurement error (the emissivity of the two thermocouples is very close).

Thermocouple A measured flame 6 at x_jc = 14.5 mm to study the performance of a thermocouple measuring the flow field with a large temperature gradient (diffusion region). The whole thermocouple junction is 15 mm above the coflow inlet as shown in Figure 6b, and the measured temperature is 1281.15 K. Thermocouple B measured flame 7 at x_jc = −12 mm, and half of the thermocouple junction is 15 mm above the coflow inlet as shown in Figure 6c. The thermocouple reading is 1414.15 K.

3. CFD Simulations

As in Li et al. [8], the whole flow simulation is used, which only considers the flow above the burner surface. The adiabatic equilibrium gas flows out of the main flow exit without modeling fuel/oxidizer mixing and reacting. Ignoring the mixing and reaction slightly overestimates the gas temperature drop by gas radiation since the temperature and H₂O concentration in the mixing and combustion zone are lower than those of the combustion product. For the extreme condition of the tested flames (flame 1), the gas temperature error caused by this overestimation at the thermocouple location is less than 6/15 × 9.9 = 3.96 K. As shown in Figure 7, the simulation domain is 120 mm × 70 mm × 70 mm. The main flow inlet and the coflow inlet constitute the velocity inlet boundary, the wall between the main flow and the coflow is the adiabatic wall boundary, and other fluid surfaces constitute the environmental pressure boundary. Both the right ceramic tube end and the right thermocouple end are set to be adiabatic. The position of the thermocouple is set to be consistent with the experiment.

The flow is a laminar, steady, and multi-species (N₂, H₂O, and H₂) flow with surface radiation and conjugate heat transfer. The buoyancy effect is also considered. The flames are very small, so the absorption effect of gas radiation by thermocouples is negligible. In the flames, the radiation beam lengths are in the order of one inch; the optical thicknesses are in the order of 0.01 [8]; and the optically thin criteria are satisfied. The radiation loss of H₂O is treated as a heat sink in the enthalpy equation and calculated by a field function. The Planck mean absorption coefficient comes from Ju et al. [20]. The gas mixture is considered an incompressible ideal gas, i.e., the density is calculated by the ideal gas law with a constant atmospheric pressure. The NASA 14 coefficient polynomials are used to calculate enthalpy and specific heat. Accurate transport simulation uses mixture averaging rules to calculate mixture properties, polynomials of temperature to calculate viscosity and conductivity for each species, and kinetic theory to calculate binary mass diffusivity, and the mixture-averaged mass diffusion model is used for species diffusion. The thermal conductivity and emissivity of the ceramic insulator are set to 2.3 W/m/K and 0.65, respectively [21].

The thermal conductivity of the wires is correlated based on the data of Refs. [22,23,24], and the correlations are shown in the following equations. The property of the welding point is the average value of the two wires.

$$\begin{array}{l}{k}_{W5\%Re}=-0.0116T+88.417\\ k_{W26\%Re}=-2.355\times {10}^{-12}{T}^4+1.924\times {10}^{-8}{T}^3-5.721\times {10}^{-5}{T}^2+0.07397T+14.876\end{array}$$

(3)

The polygon and extruded mesh are used (around 5.76 million fluid cells, 0.31 million ceramic tube cells, and 0.71 million thermocouple cells) as shown in Figure 8, and the mesh independence was tested. The current flow is a laminar flow; the solved Navier–Stokes equation by the CFD software represents the real physics without any simplification and approximation. With enough mesh and proper physical properties and boundary conditions, the simulation results are accurate.

Figure 9 shows the simulated temperature contours of thermocouple A measuring flame 1 (x_jc = 0 mm). The surface emissivity of the thermocouple surfaces is set to 0.46 in the simulation. Figure 9a presents the gas temperature contour in the plane of z = 0 mm, which demonstrates the heat transfer between the coflow and the main flow. Figure 9b,c present the thermocouple temperature contour and the junction temperature contour, respectively. The temperature difference within the junction is only 6.8 K. When the whole junction is in the uniform flow field, the junction temperature is quite uniform; in this situation, the volumetric average temperature of the junction can be considered as the numerical thermocouple reading. The highest temperature is on the W26%Re wire (5.5 mm from the junction center), which is 43.8 K more than the average junction temperature, since the wire convection coefficients are higher than the junction convection coefficient (smaller size and larger convection coefficient), and the thermal conductivity of the W26%Re wire is lower than that of the W5%Re wire.

4. Results and Discussion

4.1. Thermocouple Emissivity

A solid surface’s emissivity depends on its material and surface condition, especially its surface roughness related to the manufacturing process, i.e., different thermocouples could have different emissivity values. Since the gas conditions of Hencken flames and measured temperatures are known, the thermocouple emissivity can be obtained through CFD simulations. During the simulations, the emissivity of the thermocouple can be continuously adjusted to match the measured and simulated temperatures [8]. The Hencken flames 1–5 in Table 1 are measured with the thermocouples A and B, and the surface emissivity of the thermocouples under different temperatures is obtained by adjusting the thermocouple emissivity of the simulation until the average junction temperature is consistent with the experimental reading. The emissivity under different temperatures is shown in

Table 3. Surface emissivity under different temperatures.

Flame	1	2	3	4	5
Thermocouple A temperature (K)	1542.15	1506.15	1463.15	1422.15	1236.15
Thermocouple A emissivity	0.46	0.42	0.39	0.37	0.4
Thermocouple B temperature (K)	1474.15	1448.15	1410.15	1371.15	1191.15
Thermocouple B emissivity	0.45	0.4	0.37	0.35	0.37

and Figure 10. The emissivity of the two thermocouples has the same trend and similar values. Between temperatures of 1200 K and 1500 K, their emissivity values fluctuate around 0.4. The emissivity of an S-type thermocouple with a 0.5 mm wire diameter from Li et al. [8] is also presented in the figure. Their study demonstrates a monotonically decreasing trend with temperature. From 1200 K to 1500 K, the value decreases from 0.46 to 0.4. The emissivity of the two C-type thermocouples is fitted to the polynomials of Equation (4), which are used in the following CFD simulations. For the wire with a temperature less than the lower limit of the equation, the emissivity at the lower limit is used.

Since the wrapping wire is the W26%Re wire for both thermocouples, the emissivity of the junction is mainly determined by this wire. So, the data here are compared with the W25%Re data in Moraga et al. [14]. They showed that the emissivity monotonically increases from 0.25 to 0.341 when the temperature increases from 1600 K to 2500 K. Their data indicate that the emissivity of the W25%Re plate below 1600 K should be less than 0.25. Our emissivity is at least 40% more than 0.25, which is attributed to surface roughness and partial surface oxidation. The surface could be partially oxidized during the welding process or the cooling process in the air after the hot experiments.

$$\begin{array}{l}\mathrm{Thermocouple} \mathrm{A}:\epsilon =3.554117\times {10}^{-9}{T}^3-1.19831\times {10}^{-5}{T}^2+0.01282883T-3.860837, 1236\mathrm{K}<T<1542\mathrm{K}\\ \mathrm{Thermocouple} \mathrm{B}: \epsilon =2.37267\times {10}^{-8}{T}^3-9.208883\times {10}^{-5}{T}^2+0.1188333T-50.6184, 1191\mathrm{K}<T<1474\mathrm{K}\end{array}$$

(4)

4.2. Effect of Wire Conduction

As shown in Equation (2), the influence of the wire conduction on the junction temperature is proportional to A_c/A_b, the ratio of the wire cross-section area to the junction surface area. Different from S-type thermocouples, a C-type thermocouple has a very large junction, resulting in a very small area ratio. For example, thermocouple A has an A_c/A_b (the junction surface area is output directly from the CAD software) of about 0.01, while thermocouple B has an A_c/A_b of about 0.02. As a comparison, for a regular thermocouple with a spherical bead, the typical ratio of bead diameter to wire diameter is about 2, resulting in a much larger A_c/A_b of 0.071. So, the wire conduction effect on the junction temperature of a C-type thermocouple should be minimal. CFD simulations are carried out for the thermocouples measuring flame 1 with and without wires (only junction). The simulated junction temperatures with the wires for thermocouples A and B are 1543.0 K and 1479.1 K, while those without wires report temperatures of 1546.9 K and 1487.2 K. The existence of wires only increases the junction temperature by 3.9 K and 8.1 K for thermocouples A and B, respectively, demonstrating that the wire conduction effect is almost negligible for C-type thermocouples when the whole junction is in a uniform flow field.

4.3. Junction Contacting Status

In the above analysis of thermocouples measuring the core region of the standard flames, the temperature difference inside the junction is small, and the average temperature of the whole junction is used to indicate the thermocouple reading of the CFD simulations. As stated in Section 1, the temperature of the first contacting point of the junction should be the thermocouple reading. When measuring the flow field with a strong temperature gradient, the temperature difference inside the junction might be large; it is important to identify the wire contacting status of the junction. In Section 2, the two thermocouples measured the temperature in the diffusion region of the Hencken flames. The measurement case of thermocouple A with x_jc = −14.5 mm is CFD-simulated, and the simulated junction temperature contour is shown in Figure 11. As shown in the figure, D represents the welding point, E represents the first possible contacting point of the junction (the wires contact here by visual judgment at room condition), and F represents the whole junction. As can be seen, the temperature difference inside the junction is as much as 69.4 K. The simulated temperature of the D region is 1282.49 K, the temperature of the E region is 1325.7 K, and the temperature of the F region is 1300.1 K. The experimental reading of this case is 1281.15K, which is consistent with the temperature of the D region, indicating no wire contact within the junction. Since the wire contact is visually observed at room conditions, it is believed that the wires of the junction do not contact each other before the welding point because of the thermal expansion of wires during the measurement.

Similar simulations and comparisons are also carried out for thermocouple B measuring flame 7 with x_jc = −12 mm. However, the temperature difference within the whole junction is only 7 K; considering the measurement error of about 3 K and the gas temperature uncertainty of ±20 K, this small temperature difference is not enough to judge the contacting status of the junction, even though the simulated average temperature of the junction (1416.5 K) is only 2 K away from the experimental reading (1414.15 K). The match of the simulated and experimental temperature also validates the simulation accuracy. The good thing is that it is not necessary to identify where the thermocouple reading corresponds to when the temperature difference within the junction is small.

5. Conclusions

The core region of five Hencken flames is measured by two C-type thermocouples with different wire diameters. The C-type thermocouples have relatively large junctions, resulting in significantly lower readings than the real gas temperature. For the thermocouple with the 0.5 mm wire diameter, the thermocouple reading is 176.35 to 481.35 K lower than the gas temperature (1412.5–2023.5 K). For the thermocouple with the 1.0 mm wire diameter, the thermocouple reading is 221.35–549.35 K lower than the gas temperature. The measurements are CFD-simulated to obtain the emissivity of the thermocouples by adjusting the emissivity to match the average junction temperatures and the experimental readings. For both thermocouples, the emissivity fluctuates around 0.4 in the temperature range of 1191–1542 K. The simulation results also indicate that the temperature difference within the junction is minimal when the junctions are in the core region of the flames and there are 8 mm thermocouple wires in the core region.

The diffusion region of two flames is measured by the two thermocouples, and the results are used for comparison with the CFD simulations. When the junction is completely above the coflow zone, the simulation temperature difference within the junction of the 0.5 mm thermocouple is as large as 69.4 K. The temperature of the welding point is consistent with the experimental reading, indicating no wire contact in the junction, even though the wires are observed to contact each other at the end of the junction at room conditions. It is believed that thermal expansion eliminates the wire contacting of the junction in hot flows. The junction temperature difference of the 1.0 mm thermocouple is not large enough to judge the wire contacting status of the junction.

Different from other types of thermocouples, C-type thermocouples have relatively larger junctions, and ignoring the conduction with the wires only introduces slight errors. During steady measurements with C-type thermocouples, ignoring the wire conduction can simplify the correction significantly. The emissivity reported here is for typical C-type thermocouples, which can be used in thermocouple corrections. During the correction of thermocouple measurements in flow fields with strong temperature gradients, the junctions of C-type thermocouples demonstrate large temperature differences; it is crucial to identify the wire contact status of C-type thermocouple junctions.