Nuclear Engineering and Design 375 (2021) 111077

Available online 2 March 20210029-5493/© 2021 The Author(s). Published by Elsevier B.V. This is an open access article under the CC BY-NC-ND license(http://creativecommons.org/licenses/by-nc-nd/4.0/).

Thermal radiation, its effect on thermocouple measurements in the PANDA facility and how to compensate it

C. Falsetti a,1,2, R. Kapulla b,*,1, S. Paranjape b, D. Paladino b

a Oxford Thermofluids Institute, University of Oxford, United Kingdom b Paul Scherrer Institute (PSI), 5232 Villigen, Switzerland

A R T I C L E I N F O

Keywords: Thermal radiation effects Thermocouples Temperature measurement Temperature compensation

A B S T R A C T

Thermocouples are one of the most widespread used sensors for temperature measurements in several appli-cations, thanks to their robustness, low cost and ease of installation. However, when used in high temperature environments or in the presence of flames or elevated hot sources, the measurement can be affected, for example, by radiative exchanges to and from the ambient. The focus of the present study is to experimentally assess the thermal radiation effect on the thermocouple measurements in a controlled environment. To do so, K-type thermocouples having different diameters (1 mm and 0.2 mm) and radiated homogeneously from all sides are used to measure the air temperature between 40 ◦C and 145 ◦C inside a black-body calibrator cavity. The experimental data are then used to implement and discuss an existing radiation correction framework, the reduced radiative error method (RRE). The results suggest to use smaller size thermocouples to reduce the errors associated with thermal radiation and improve the accuracy of the measurement. Additionally, the results show that the effect of thermal radiation is higher for larger size thermocouples, i.e. thermocouples with 1 mm diameter show an error of 1% in the range considered here. This error reduces by a factor of three when using thermocouples with 0.2 mm diameter. This benefit needs to be ultimately balanced with engineering consider-ations – smaller sized thermocouples are more likely to break during positioning or experiments.

1. Introduction

In many engineering applications, the measurement of fluid tem-peratures is a crucial but sometimes challenging task. Examples can be found in fire environments (Walker and Stocks, 1968), combustion chambers (Papaioannou et al., 2020), in the field of weather and climate prediction (Nakamura and Mahrt, 2005) and finally in experiments dedicated to nuclear safety (Kapulla et al., 2014; Kapulla et al., 2018). In nuclear safety related research, it is important to measure temperatures accurately, and thermocouples are still one of the most widespread used sensors, thanks to their low cost, simple installation and use. However, there can be significant errors in thermocouple readings when used in hot environments (Jones, 1995; Shaddix, 1999). Among these errors are catalytic reactions between the thermocouple material and the envi-ronment, thermal radiation exchange between the thermocouple and the surrounding (Pitts et al., 2002; Hennecke and Sparrow, 1970), and heat conduction (Ballantyne and Moss, 1977). All the aforementioned

errors result in differences between the real fluid/gas temperature and the thermocouple reading.

As a result, the temperature equivalent potential difference between the two junctions of a thermocouple (Wu, 2018) is not only due to the convective heat transfer at the sensing tip, but eventually a result of a combination of convection, radiation and conduction. In general, the conduction error can be minimized by using small diameter thermo-couples or by choosing an appropriate wire length. As an example, a length-to-diameter ratios larger than 200 is suggested in Heitor and Moreira (1993) to minimize this effect. Compared to the errors induced by conduction losses, the radiation errors are more difficult to evaluate. However, it is essential to consider this effect while performing a tem-perature measurement with thermocouples, since the error induced by thermal radiation can be considerably high. For example, the study performed by Attya and Whitelaw (1981) showed an error up to ~20% when measuring temperatures in a spray flame of kerosene, while the results from Luo (1997) showed that the thermocouple overestimated

* Corresponding author. E-mail address: ralf.kapulla@psi.ch (R. Kapulla).

1 These authors have contributed equally to this work. 2 Former PSI employee.

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https://doi.org/10.1016/j.nucengdes.2021.111077 Received 13 October 2020; Received in revised form 15 December 2020; Accepted 11 January 2021

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the gas temperature by more than 80 ◦C in a fire environment. Since this problem is of concern in many applications, a number of

previous studies suggested different methods to either reduce or to consider and finally compensate the radiative exchange for the ther-mocouple measurement. The dependence of the radiation error on the sensor size and on the air velocity was demonstrated in the literature. For example, in the field of meteorology a common rule is that the radiative error depends on the square root of the diameter of the sensor and inversely on the square root of the air speed past the sensor (de Podesta et al., 2018; Harrison, 2015). The most generally accepted methods, as reducing i) the size and ii) the sensor surface emissivity, partially reduce the error in air temperature measurements. The use of small size sensor is limited in some applications due to their fragility. Other proposed solutions are the use of suction pyrometers (Blevins, 1999; Luo, 1997), or single- and double- shielded thermocouples (Roberts et al., 2011). Nevertheless, the presence of a suction pyrometer might disturb the hydraulic conditions of the tests, whilst the use of a sheath tube leads to a slower sensor response time. Thus, several radi-ation correction methods were developed. The four most common are the electrical compensation (EC), the reduced radiative error (RRE) – which is the subject of the present paper –, the extrapolation method and the multi-element method. In the electrical compensation, the radiation losses are calibrated by comparing the temperature measurements per-formed under vacuum, where only radiation exists, to the combustion/ flame conditions (Brohez et al., 2004). The extrapolation method, that was presented for the first time by Daniels (1968), starts from the assumption that an ideal zero-surface TC undergoes no radiation losses and extrapolates the results of two TCs having different diameter by performing a fit of 2-degree. The multi-element method uses two or three TCs with different diameters and quantifies the radiation losses from the energy balance on each probe, as presented by De (1981). These method, except for the EC, are based on the use two (or more) thermocouples with different diameter (Blevins and Pitts, 1999; Brohez et al., 2004; Kim et al., 2010) or different surface emissivities by applying a coating (Menshikov, 1976), since the absorption (and emis-sion) of radiation will be lower if the sensor emissivity is reduced.

The RRE method was developed by Brohez et al. (2004) to estimate radiation errors based on the heat transfer model of a bare-bead ther-mocouple developed by Blevins and Pitts (1999) in the field of compartment fire. The method employed two thermocouples with the same material, but different bead diameters of 0.25 mm and 1 mm, respectively, in order to generate a radiative-sensitive relevant differ-ence for the probing elements. The thermocouples were placed side-by- side such that they experience the same ambient conditions (tempera-ture and velocity). The measurements were done in the range of tem-peratures from 77 ◦C to 927 degrC and gas velocities from 0.5 m/s to 2 m/s. Starting from the heat transfer balance on a thermocouple bead, they defined a radiation correction parameter (RRE) as a function of the thermocouples readings and gas temperature. The RRE values were found to be almost constant for the range of conditions tested with RRE = 1.8. They proposed to multiply the RRE-factor by the tempera-ture difference measured by the two thermocouples, and adding the result to the measurement of the thermocouple with the larger diameter. Experiments were carried out to validate this simple method, and a good agreement was found. Subsequently, the RRE method was successfully applied by Kim et al. (2010) to correct for the radiation error on ther-mocouple measurements in the High Temperature Gas-cooled Reactor (HTGR).

The radiation errors were also estimated by Luo (1997) by using the multi-element method. They solved the energy balance for the ther-mocouple bead assuming steady-state conditions and neglecting the conduction term. To test for their approach, a suction pyrometer, a thermocouple with a radiation shield and a bare thermocouple of 1.5 mm diameter were placed in the burning chamber. The results indicated that the shielding of thermocouple is not the most suitable solution since this increases the thermocouple response time. A CFD model was used to

simulate the gas burner fire and validate the radiation correction of the bare thermocouple, showing good agreement.

A study to estimate the thermocouple errors for measuring the flame temperature was performed in Hindasageri et al. (2013). Three B-type thermocouples, having diameters of 0.15 mm,0.3 mm, and 0.6 mm, respectively, were used to measure the flame temperature and the temperature data were corrected by using a developed numerical pro-cedure, namely, the multi-element and the extrapolation methods. Their results showed that the flame temperatures estimated by the multi- element method and the extrapolation method deviated from their nu-merical results by 2.5% and 4%, respectively.

More recently, an interesting comparison between the four methods introduced above (EC, RRE, multi-element and the extrapolation method) was conducted in a fully characterized lab-scale flat flame reactor and is presented in Lemaire and Menanteau (2017). Their study showed that the EC and the RRE methods lead to converging trends, the latter being the easiest method to be implemented, so the most efficient.

Another comparison of the compensation methods was presented by Zhou et al. (2018) in the context of fire temperature measurement. They performed turbulent pool fire temperature measurements to assess and compare three methods to compensate for the radiation errors: the double- and triple-thermocouple corrections, also called multi-element method, and the extrapolation method. Four Type-K (chromel–alumel) thermocouples having different bead diameters (0.23 mm, 0.62 mm,

0.85 mm and 1.77 mm) were installed 5 mm apart. Among the compensation methods tested, the extrapolation method gave a reasonable correction temperature, whilst the double and triple- corrections were largely under- and over-estimating the temperatures as they neglected the thermocouple transient heating response.

The literature review presented above emphasizes that the number of studies on the radiation error on thermocouple measurements in the context of nuclear safety research is very limited. Consequently, the present study is intended as a first step towards assessing the magnitude of radiation errors on thermocouple measurements in a range of tem-perature similar to those typically found during experiments conducted in the PANDA facility in the course of the OECD/NEA HYMERES-2 project (Kapulla et al., 2014, 2018; Paranjape et al., 2017). In fact, it is essential to obtain accurate measurements, not only to understand the physical phenomena occurring inside the vessels, but also to validate numerical results and help the development of predictive models.

This study will focus on the radiation effect on thermocouple mea-surements only. Other effects, like conduction through the wire, are neglected. The basic idea is to measure the air temperature at the same location with K-type sheathed thermocouples having different proper-ties with respect to radiation, i.e. the thermocouple diameter was varied. The possible influence of conduction is considered negligible since the length-to-diameter ratios of the thermocouple wires is beyond 200 as suggested by Heitor and Moreira (1993). The radiation errors are eval-uated for a range of temperatures varying from 40 ◦C to 145 ◦C. In addition, the correction method based on two different diameter ther-mocouples (RRE method), which was initially developed by Brohez et al. (2004), was implemented to estimate the correct gas temperature.

This paper is structured as follows. The experimental setup and procedure, including the calibration method for the thermocouples, will be described in the next section. In Section 3 we present the results of the temperature measurements and the implemented radiation correction model will be explained and discussed. The conclusions are summarized in Section 4.

2. Experimental setup and procedure

2.1. Thermocouple calibration

The thermocouples used for the temperature measurements in the PANDA facility are class 1 thermocouples, i.e. they have an error of ∊ =

±1.5 ◦C (Wu, 2018). If we assume a nominal temperature of T = 20 ◦C,

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hypothetical temperature readings of TTC1 = 18.5 ◦C and TTC2 = 21.5 ◦C from two thermocouples, both would be valid temperature signals within the specification of the thermocouples. Since the temperature errors caused by the radiation affects are expected to be of the same magnitude, a careful calibration of the individual sensors is required to reach higher acuracies. This was done with a dry block temperature calibrator ATC-650 B from AMETEK. In total four thermocouples were calibrated; two thermocouples with a diameter of 0.2 mm and two thermocouples with a diameter of 1 mm. The thermocouples were inserted into the dry block of the calibrator which was filled with sand blasting powder consisting of Al2O3 (Biloxit 50) to homogenize the heat transfer and to avoid possible convection loops in the dry block cavity, Fig. 1.

The temperature of the calibrator was varied in the range from 25 to 300 ◦C with an automatic step function and with a stability of ±0.03 ◦C. For each calibration point the temperature was kept constant for 15 min and the data were time averaged. The steps are selected as set points in the calibrator and for this study we used the following steps: [25, 45, 65, 85, 120, 150, 180, 210, 250, 300] ◦C. Since the maximum possible temperature in the PANDA facility is 200 ◦C, the final calibration of the thermocouples was done for the temperature range from 25 ◦C to 180 ◦C

Since the maximum possible temperature in the PANDA facility is 200 ◦C, the final calibration of the thermocouples was done for the temperature range from 25 to 180 ◦C. The reference or nominal tem-perature, Tref , was directly read from the calibrator display. In order to test for an hysteresis effect resulting either from the calibration device or the thermocouples, calibration runs were performed with increasing and decreasing temperature steps, but no hysteresis was found. A 4th order polynomial function was fitted to each of the raw temperature readings, Traw, of the four thermocouples to obtain individual calibration co-efficients a0 to a4, as expressed below:

Tfit(raw) = a0 + a1Tref + a2T2ref + a3T3

ref + a4T4ref (1)

Three calibration runs spanning the entire temperature range were performed and the final calibration coefficients were obtained by averaging the results of the three calibrations. The three data sets differ by 0.1 ◦C on average over the tested temperatures.

The temperature differences between the reference temperature and

the thermocouple readings before (Tref − Traw) and after applying the calibration (Tref − Tcal) with

Tcal = Traw −{

Tref − Tfit(raw)}

(2)

are shown in Fig. 3. The raw signals of the thermocouples, Traw, expe-rience maximum differences with respect to the reference temperature Tref up to − 1 ◦C within the temperature range 25⩽Tref ≤ 180 ◦C and up to − 2 ◦C for 25⩽Tref ≤ 300 ◦C, for small and large bead sizes, respec-tively (Fig. 3a). Applying the calibration, the remaining maximum de-viation reduces to ±0.06 ◦C for all thermocouples (Fig. 3b).

The performance of the selected 4th order polynomial according to Eq. (1) to minimize the remaining deviations with respect to the refer-ence temperature after calibrating the thermocouple signals was bench- marked against lower and higher order polynomials in the range from 1st

(linear function) to 7th order. That is, the raw temperatures were fitted with the corresponding polynomials according to the method described above and the remaining deviations after applying the calibrations (see Fig. 3b) were combined into a single rms-number Tcal,rms to quantify the resultant remaining spread. The corresponding results are presented in Fig. 2 as a function of the order of the polynomial used for the calibra-tion. It is found that the selection of a 4th order polynomial is well chosen. It represents a good compromise between accuracy and the required efforts to finally compensate hundreds of thermocouples in the PANDA facility, for which a 4th order polynomial is used. Decreasing the errors in the temperature measurements leads to lower errors – using error propagation – required for the calculation of other quantities such as the density in conjunction with Mass Spectrometer measurements.

2.2. Radiation experiments

The experimental set-up used to estimate the radiation effect con-sisted of a temperature calibrator Sika TPM 165S-U with a black body cavity, used for the present study as a thermal radiation source, and two K-type (Chromel-Alumel) thermocouples having different diameters, Fig. 4. The tested thermocouples are sheathed, i.e. the two thermocouple wires (Chromel and Alumel) are embedded in a stainless steel capillary and are electrically and thermally insulated with an Aluminum oxide powder. The Sika calibrator was used to create an gas environment at

Fig. 1. Calibrator ATC-650 B from AMETEK used for the thermocouples calibration. The dry block of the calibrator was filled with sand blasting powder to avoid convection currents which might deteriorate the calibration.

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different elevated temperatures by heating its cavity walls with a controlled temperature.

A black body with an internal diameter of 30 mm was embedded in the Sika calibrator (see black body in Fig. 4) and it was coated with black paint in order to achieve an emissivity as close as possible to one. The two thermocouples are located inside the black body, around its center- line. A layer of insulation material covered the cavity at the top to maintain a constant temperature inside and reduce convection heat transfer with the ambient. The thermocouples are clamped above the calibrator. An additional K-type thermocouple was mounted in the

largest hole in the black body wall to double-check the temperature read by the Sika calibrator. Its location is indicated in Fig. 4. To maximize the effect of the radiation onto the thermocouple reading we have chosen to use one thermocouple with a diameter of 0.2 mm and one with of 1 mm. For the radiation experiments, the temperature of the calibrator was varied in steps between 45 ◦C and 145 ◦C to cover approximately the range of temperatures typical for the tests in PANDA. After the tem-perature in the cavity stabilized, the temperatures measured by the two thermocouples were recorded with an analog-to-digital input module NI 9113 from National Instruments in an ASCII file for further processing. In order to check for the repeatability, we repeat each experiment twice, and we obtain a difference of ±0.04◦C between repeated tests. The re-sults will be presented and discussed in the following section.

3. Results

To investigate the effect of thermal radiation on the thermocouple readings, the selected temperatures were varied with the radiation fa-cility Sika TPM 165S-Uin steps between 45 ◦C and 145 ◦C, i.e. we have performed measurements for nominal or reference temperatures 45 ◦C, 65 ◦C, 85 ◦C, 100 ◦C, and 130 ◦C, respectively. We intentionally depict these temperatures as nominal since it is expected that the temperatures inside the cavity are slightly below these values. When the temperature recordings inside the cavity was stable and did not vary anymore in time, the thermocouple signals were recorded for 20 min with a fre-quency of 1 Hz. The representative time-averages subsequently pre-sented cover this window, even though we present selected shorter time traces for the benefit of highlighting fluctuating details.

3.1. Thermocouple characteristics

An example of the resultant air temperature measurement inside the black body cavity by the two thermocouples having different diameters at Tref = 85 ◦C – after applying the calibration described in the previous section – is shown in Fig. 5. The temperature traces are complemented by the average value (solid line on the left-hand side) and the corre-sponding probability density functions (PDF) of the data (Bendat and

Fig. 2. Remaining rms scatter Tcal,rms (see also Fig. 3b) after applying different polynomials in the range from 1st (linear function) to 7th order to calibrate the raw data of the thermocouple signals.

Fig. 3. Temperature difference between the reference Tref and the four thermocouples (Traw) before a) and after the calibration (Tcal) b). Only the temperature range 25⩽Tref ≤ 180 ◦C is considered for the calibration.

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Piersol, 1986). The most prominent and obvious difference between the two thermocouples is found in the much larger temperature fluctuations recorded through the smaller sized thermocouple T0.2. This is an ex-pected result, since the smaller thermocouple has a much lower thermal inertia usually characterized by the time constant of the sensor which depicts the ability to follow imposed temperature fluctuations up to a certain frequency without damping and delay. Additionally, it is found that the probability density function for the smaller sized thermocouple is non-Gaussian which is usually depicted and labeled as ‘skew’, i.e. we find repeated temperature drops down to ΔT ≈ 2 ◦C with respect to the mean value in the absence of corresponding temperature spikes of a similar magnitude towards higher temperatures. Even though the details of the PDF might highlight certain flow structures inside the cavity and introduce a possible challenge worth considering for more advanced radiation compensations methods, we rely here solely on time averaged signals completely neglecting the details of the PDF for the present study. More relevant for the proposed radiation correction methods is the observation that the larger size sensor shows a higher time averaged temperature (80.5 ◦C) compared with the smaller thermocouple (79.9 ◦C). This is in agreement with previous studies based on the use of two different sized thermocouples (Brohez et al., 2004; Kim et al., 2010). If we decompose the temperature reading, Tcal, into a component which depicts the pure gas temperature – approximating this temperature is the scope of present article – in the absence of any radiation effects depicted by Tgas and a component representing the effective temperature equiv-alence, Trad, of the radiation intake into the thermocouple signal, it follows:

Tcal = Tgas +Trad (3)

For fluctuating velocities, Trad is a function of the surface area A of the sensing tip of the thermocouple (see Eq. (5)), i.e. the larger sized ther-mocouple is more prone to an radiation intake Trad with an accordingly higher average temperature Tcal. Conversely, the reading of the smaller sized thermocouple is expected to be closer – but not identical – to Tgas. Only in the approximate mathematical limit d→0, a thermocouple with a zero sized diameter would not at all be affected by radiation contri-butions to the recorded signal and would represent in fact Tgas.

To better quantify the experimentally determined average temper-

ature difference ΔT21 between the two thermocouples – which is the basis of the discussed compensation methods in this paper – with diameter 0.2 mm (index 2) and 1.0 mm (index 1) we calculate:

ΔT21 = Tcal,0.2 − Tcal,1.0 (4)

and the corresponding results can be found in Fig. 6a as a function of the reference temperature Tref . Without violating the principal arguments, it is worth noting that the temperature Tref has absolutely no physical relevance – except that it depicts (eventually) the surface temperature of the black body – in the context of the discussion and it was simply chosen for convenience as a basis to present the results.

It is found that ΔT21 decays with increasing Tref , i.e. the contribution of the radiation to the recorded temperature becomes increasingly more important for the larger sized thermocouple (Tcal,1.0) when the temper-ature is increased compare with the smaller sized sensor (Tcal,0.2), see Eq. (4). This observation lead to the development of several radiation compensation methods based on the time averaged temperatures as outlined in Brohez et al. (2004), Kim et al. (2010) and Lemaire and Menanteau (2017). Additionally, the calculated values for ΔT21 provide an important order of magnitude argument for the necessary correction required to compensate the temperature readings to approach the pure gas temperature Tgas, see Eq. (3), i.e. for the temperature range consid-ered representative for the PANDA facility, this upper maximum correction limit is Tcorr≈ 1 ◦C. Finally, to check the repeatability, each radiation experiment was repeated twice. An enveloping accuracy margin of ±0.04◦C was obtained for successive tests, showing an excellent repeatability as presented in Fig. 6b with the inaccuracy magnitude being almost identical to the resultant accuracy of the tem-perature readings after applying the calibration, see Fig. 3b.

3.2. RRE method

The results of the different temperature readings as shown in Fig. 6 will be used to implement the reduced radiative error (RRE) method as outlined in Brohez et al. (2004). The corresponding experimental implementation is straightforward since it solely requires two thermo-couples having different diameters d manufactured from the same ma-terial and with the same surface treatment to ensure identical emissivity

Fig. 4. Temperature calibrator Sika TPM 165S-U (left) which was used for the present study as a thermal radiation source to exposed two K-type (Chromel-Alumel) thermocouples to elevated gas temperatures while the black body cavity (right) acts a the radiative source. Dimensions in mm.

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∊. The general – time dependent – energy balance around the sensing tip of a thermocouple neglecting any conduction losses can be written as:

mcpdTdt

= ∊⋅σ⋅A⋅F(

T4∞ − T4

cal

)

− h⋅A(

Tcal − Tgas

)

(5)

which reduces for steady state conditions, dT/dt ≈ 0, to:

σε(T4

cal − T4∞

)= h

(Tgas − Tcal

)(6)

where the radiative heat transfer from/to the thermocouple to/from the surrounding balances the natural convection heat transfer around the thermocouple sensing tip. It is interesting to note that the energy bal-ance for steady state conditions becomes independent from the ther-mocouple surface area A. The temperatures in Eq. (6) depict the surface temperature of the radiative relevant surrounding, T∞, which is for the present experiments the black body cavity surface temperature, the gas temperature, Tgas (see also Eq. (3)), and the thermocouple signal cali-brated, Tcal (Fig. 3). Please note that for the required calculations the temperature unit is in Kelvin. The parameter σ represents the Ste-fan–Boltzmann constant, ε the emissivity of the thermocouple surface (which is taken as 0.3 for an unmodified metal surface) and h the heat

transfer coefficient. The latter was calculated for the present study via the Nusselt number correlation for external flow over a sphere as out-lined in Whitaker (1972). Since the implementation of the Nusselt number calculation with a more advanced approach around a cylinder according to Kramers (1946) did not show any remarkable effect on the results, we have decided to follow the original method outlined in Brohez et al. (2004) by using the Nusselt number around a sphere. In principal the gas velocity approaching the thermocouple might have an impact onto the Nusselt number calculation and therefore also onto the radiation errors prediction, but it was shown in Lemaire and Menanteau (2017) that a velocity variation in the range from 0.5 m/s to 2.0 m/s can be neglected. The non-dimensional view factor F in Eq. (5) quantifies possible in–homogeneous radiation conditions, i.e. the radiating source influences only a part of the thermocouple surface. For the present experimental setup, the thermocouples are located inside the black body cavity expected to be exposed to a homogeneous surface temperature within 360 degr, therefore it is reasonable to assume that F = 1.

According to Brohez et al. (2004), the RRE parameter was defined as the ratio between the time averaged radiation error influencing the thermocouple with the larger diameter T1 (compared to the gas tem-perature Tgas) and the temperature difference measured by the two

Fig. 5. Typical temperature signals of the two thermocouples having a diameter of 0.2 a) and 1.0 mm b) during 1600 s. The measurements were conducted at the reference temperature Tref = 85 ◦C. Additionally, the corresponding probability density functions (PDF) are given.

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thermocouples having different sizes, ΔT21 = T2 − T1 (see Fig. 6) and it follows:

RRE =Tgas − T1

T2 − T1(7)

In introducing Eq. (6) for the two thermocouples with different diameter into Eq. (7), the radiating surface temperature T∞ of the surrounding and therefore the radiative cause for the different temperature readings can be eliminated and it follows for the calculation of the RRE coefficient:

RRE =σε(

T22 + T2

1

)(T2 + T1

)+ h2

h2 − h1(8)

which is the rational for the RRE based temperature correction method.

The definition of the coefficient RRE according to Eq. (8) underlines how advantageous this method is, since it does not require a precise knowl-edge of the surrounding radiation relevant temperature T∞. In fact, the RRE coefficient depends only on the recorded time averaged (radiation influenced) temperatures through thermocouples T1 and T2 having different sizes and the heat transfer coefficients h1 and h2 of the two sensors, see Eq. (8). The heat transfer coefficients, calculated using the Nusselt number correlation for external flow over a sphere and a gas velocity of 0.5 m/s, were slightly varying around the values of 115 W/

m2K and 400 W/m2K,depending on the thermophysical properties calculated at each gas temperature.

The calculated RRE coefficient was found to be almost constant over the entire range of test conditions considered here, showing a mean value equal to RRE = 1.42 ± 0.005, Fig. 7.

With the known constant coefficient RRE calculated from Eq. (8), Eq. (7) can be re-arranged to obtain the estimate for the corrected gas

Fig. 6. Temperature difference ΔT21 between the two thermocouples – Eq. (5) – with diameter 0.2 mm (index 2) and 1.0 mm (index 1) as a function of the reference temperature Tref a). The repetition measurement of ΔT21 is depicted by and is accurate within the limits ±0.04 ◦C for the temperature range considered here b).

Fig. 7. Reduced radiation error coefficient (RRE) calculated with Eq. (8) as a function of the reference temperature Tref a) and the resulting temperature correction according Eq. (9) required to minimize the radiation affected temperature readings for the thermocouples T1 and T2 having different diameters b). The error bars represent an accuracy based on a significance level of ±1σ with respect to the uncertainty calculation exemplified in the text.

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temperature, Tgas, i.e. the targeted temperature with minimized radia-tion effects imposed, according to:

Tgas = T1 +RRE(

T2 − T1

)(9)

Even though the numerical magnitude of the present result for the co-efficient RRE (RRE = 1.42) is not identical to the findings in Brohez et al. (2004), our result is in accordance with this study where the parameter RRE was also almost constant and in the average equal to RRE = 1.8 over a wide range of gas temperatures (up to 1000 ◦C). For our study we find an uncertainty of ±0.005 for the mean RRE coefficient within the temperature range considered, Fig. 7a. Additionally, it was also shown in Brohez et al. (2004) that the coefficient RRE was almost insensitive to the gas velocities from 0.5 to 2 m/s around the thermo-couple tip. An important observation since the gas velocity could in principal affect the thermocouple readings through the influence of the corresponding heat transfer coefficients h1 and h2 characterized by the Nusselt number, see also Eq. (8).

The difference ΔTcg=Tcal − Tgas (Fig. 7) provides a solid estimate of the upper bound of the expected maximum radiation effect Trad, influ-encing the thermocouple reading, Eq. (3), i.e. this number well repre-sents an upper limit for the radiation induced error magnitude required to finally minimize the thermocouple measurements in the PANDA fa-cility. Consistent with the expectations, it is found that the radiation error increases with the reference temperature irrespective of the ther-mocouple diameter, with the larger sized thermocouples requiring a larger compensation, see Fig. 7. In fact, the difference between the measured temperature and the approximated gas temperatures (Tcal − Tgas in Fig. 7b) is larger for the thermocouple with a diameter of 1.0 mm, showing a relative maximum difference of 1over the range of tested air temperatures when using the nominal temperature Tref as a basis. As an example, there is a required temperature compensation of ≈1.3 ◦C at Tref = 145 ◦C for a thermocouple with a diameter of 1 mm (Fig. 7). Conversely, the radiation influences the thermocouple with smaller size to a lesser extent, resulting in a more accurate temperature measurement with respect to Tgas. These results are in agreement with the experimental tests presented by de Podesta et al. (2018).

The calculated uncertainty of the gas temperature Tgas considers Eqs. (8) and (9) according to the uncertainty propagation method presented in Kline and Mcclintock (1953). To numerically apply this method, the uncertainty of the thermocouple signals after the calibration was considered to be equal to ±0.06 ◦C (see Fig. 3), whilst the propagated uncertainty of the RRE parameter was calculated by assuming the un-certainties of the heat transfer coefficients, h, and of the emissivity, ε, to be equal to 15 % and 1 %, with respect to the nominal value, respec-tively. The resulting uncertainty of the approximated gas temperature, Tgas, varied from 0.089 ◦C to 0.133 ◦C when increasing the black-body cavity temperature from 45 ◦C to 145 ◦C, Fig. 7.

In summary, the RRE coefficient correction method represents a decent solution to estimate and minimize, via Eq. (9), the errors in the thermocouple measurements induced by thermal radiation. This method only requires two thermocouples with the same material and the same surface emissivity ∊ having different diameters provided that both sen-sors are placed at the same distance from the radiating source. It is worth mentioning that when applying this method to real world applications, such as in the PANDA facility, the view factor F (Eq. (5)) should be considered and becomes important for the analysis. The view factor can considerably lower the required reported corrections by approximately a factor of 2 (and eventually below) when off-axis placed thermocouples ‘see’ an in-axis radiating jet at elevated temperatures T∞, which is typical for the case of a stratification erosion experiment as reported in Kapulla et al. (2014).

4. Conclusions

A study to estimate the radiation effect on the thermocouple readings in a range of temperature between 45 ◦C and 145 ◦C was performed to obtain accurate experimental data in the context of nuclear reactor safety in larger experimental facility. In general, the temperature read by a thermocouple is a function of the gas temperature and gas composition, conduction to and from the sensor, and thermal radiation. The latter effect is the subject of the present study. The experiments were done in a small size facility, comprising a calibrator, a reference radi-ating black body, five thermocouples and a data acquisition system. The thermocouples under investigation had different sizes of 0.2 mm and 1.0 mm, respectively.

The results showed that the contribution of radiation increases with temperature, and it affects the larger size sensor to a higher extent. In addition, the data were used to validate the reduced radiation error method (RRE) to minimize the radiation influence to the thermocouple reading. Based on the results of the RRE method, thermocouples with a diameter of 1 mm showed an error of about 1% of the temperatures with respect to the corrected temperature (when measured in ◦C) for the temperature range considered here. In line with the expectations, it was highlighted that thermocouples with a smaller diameter (0.2 mm) are less influenced by thermal radiation. The difference between the smaller sized thermocouples readings and the (approximated) corrected gas temperature was found to be at maximum 0.4 ◦C at Tref = 145 ◦C (compared with the required maximum correction of 1.38 ◦C obtained with the thermocouples having a diameter of 1 mm at the same tem-perature). For these concluding considerations it is important to finally also account for the radiation relevant view factor F when using the RRE based correction method, as the view factor depends on the detailed geometrical setup. The resultant view factor F for a given experiment might be much lower than the appropriately chosen value of F = 1 used through this exercise with thermocouples exposed equally to radiation in a black body from all sides. The view factor for typical thermocouples is expected to be considerably below F = 1 for experiments in the PANDA facility with a central jet at elevated temperatures eroding a helium stratification monitored by off-axis placed thermocouples (Kapulla et al., 2014). In view of this, smaller sized and lower emissivity thermocouples are preferred without no doubt to use with respect to reduce the errors associated with thermal radiation. But this has to be finally balanced with practical engineering considerations: smaller sized thermocouples are more sensitive to break and fail.

CRediT authorship contribution statement

C. Falsetti: Investigation, Formal analysis, Visualization, Data curation. R. Kapulla: Investigation, Formal analysis, Writing - review & editing, Data curation. S. Paranjape: Investigation, Formal analysis, Writing - review & editing. D. Paladino: Conceptualization, Supervi-sion, Project administration, Funding acquisition.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgment

The authors would like to thank the staff member Wilhelm-Martin Bissels for his engaged support in conducting these experiments. The generous support from the PRG PSI and MB of the HYMERES-2 project is gratefully acknowledged.

C. Falsetti et al.

Nuclear Engineering and Design 375 (2021) 111077

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References

Attya, A.M., Whitelaw, J.H., 1981. Velocity, temperature and species concentrations in unconfined kerosene spray flames. Am. Soc. Mech. Eng., (Pap.); (United States) 81- WA/HT-47.

Ballantyne, A., Moss, J.B., 1977. Fine wire thermocouple measurements of fluctuating temperature. Combustion Science and Technology 17, 63–72.

Bendat, J., Piersol, A., 1986. Random Data – Analysis and Measurement Procedures. Wiley-Interscience Publication, New York, Chichester, Brisbane, Toronto, Singapore.

Blevins, L., 1999. Behavior of bare and aspirated thermocouples in compartment fires. In: Proceedings of the 33rd National Heat Transfer Conference, Albuquerque, New Mexico.

Blevins, L.G., Pitts, W.M., 1999. Modeling of bare and aspirated thermocouples in compartment fires. Fire Safety Journal 33, 239–259.

Brohez, S., Delvosalle, C., Marlair, G., 2004. A two-thermocouples probe for radiation corrections of measured temperatures in compartment fires. Fire Safety Journal 39, 399–411.

Daniels, G.E., 1968. Measurement of gas temperature and the radiation compensating thermocouple. Journal of Applied Meteorology 7, 1026–1036.

De, D.S., 1981. Measurement of flame temperature with a multielement thermocouple. Journal of the Institute of Energy 54, 113–116.

de Podesta, M., Bell, S., Underwood, R., 2018. Air temperature sensors: dependence of radiative errors on sensor diameter in precision metrology and meteorology. Metrologia 55, 229–244.

Harrison, R.G., 2015. Meteorological Measurements and Instrumentation. Heitor, M., Moreira, A., 1993. Thermocouples and sample probes for combustion studies.

Progress in Energy and Combustion Science 19, 259–278. Hennecke, D., Sparrow, E., 1970. Local heat sink on a convectively cooled

surface–application to temperature measurement error. International Journal of Heat and Mass Transfer 13, 287–304.

Hindasageri, V., Vedula, R.P., Prabhu, S.V., 2013. Thermocouple error correction for measuring the flame temperature with determination of emissivity and heat transfer coefficient. Review of Scientific Instruments 84, 024902.

Jones, J., 1995. On the use of metal sheathed thermocouples in a hot gas layer originating from a room fire. Journal of Fire Science 257–260.

Kapulla, R., Mignot, G., Paranjape, S., Ryan, L., Paladino, D., 2014. Large scale gas stratification erosion by a vertical helium-air jet. Science and Technology of Nuclear Installations 2014, 1–16.

Kapulla, R., Mignot, G., Paranjape, S., Andreani, M., Paladino, D., 2018. Large scale experiments representing a containment natural circulation loop during an accident scenario. Science and Technology of Nuclear Installations 2018, 1–12.

Kim, C.S., Hong, S.-D., Seo, D.-U., Kim, Y.-W., 2010. Temperature measurement with radiation correction for very high temperature gas. In: 2010 14th International Heat Transfer Conference, Volume 4, ASMEDC.

Kline, S., Mcclintock, F., 1953. Describing uncertainties in single-sample experiments. Mechanical Engineering 75, 3–8.

Kramers, H., 1946. Heat transfer from spheres to flowing media. Physica 12, 61–80. Lemaire, R., Menanteau, S., 2017. Assessment of radiation correction methods for bare

bead thermocouples in a combustion environment. International Journal of Thermal Sciences 122, 186–200.

Luo, M., 1997. Effects of radiation on temperature measurement in fire environments. Journal of Fire Science 443–461.

Menshikov, V.I., 1976. Measurement of gas-flow temperatures by two thermocouples. Journal of Engineering Physics 31, 1269–1273.

Nakamura, R., Mahrt, L., 2005. Air temperature measurement errors in naturally ventilated radiation shields. Journal of Atmospheric and Oceanic Technology 22, 1046–1058.

Papaioannou, N., Leach, F., Davy, M., 2020. Improving the uncertainty of exhaust gas temperature measurements in internal combustion engines. Journal of Engineering for Gas Turbines and Power 142.

Paranjape, S., Kapulla, R., Mignot, G., Paladino, D., 2017. Parametric study on density stratification erosion caused by a horizontal steam jet interacting with a vertical plate obstruction. Nuclear Engineering and Design 312, 351–360.

Pitts, W., Braun, M., Peacock, E., Mitler, R.D., Johnsson, E.L., Reneke, P.A., Blevins, L., 2002. Temperature uncertainties for bare-bead and aspirated thermocouple measurements in fire environment, ASTM STP 1427, West Conshocken.

Roberts, I., Coney, J., Gibbs, B., 2011. Estimation of radiation losses from sheathed thermocouples. Applied Thermal Engineering 31, 2262–2270.

Shaddix, C., 1999. Correcting thermocouple measurements for radiation loss: A critical review. Sandia National Labs., Livermore, CA, Report No.CONF-990805-TRN: IM200002672.

Walker, J., Stocks, B., 1968. Thermocouple errors in forest fire research. Fire Technology 4, 59–62.

Whitaker, S., 1972. Forced convection heat transfer correlations for flow in pipes, past flat plates, single cylinders, single spheres, and for flow in packed beds and tube bundles. AIChE Journal 18, 361–371.

Wu, 2018. A basic guide to thermocouple measurements, Technical Report, Texas Instruments.

Zhou, K., Qian, J., Liu, N., Zhang, S., 2018. Validity evaluation on temperature correction methods by thermocouples with different bead diameters and application of corrected temperature. International Journal of Thermal Sciences 125, 305–312.

C. Falsetti et al.