Narrow Angle Radiometer Instrument Model

Paper from the AFRC 2017 conference titled Narrow Angle Radiometer Instrument Model

Narrow-angle radiometers based on the International Flame Research Foundation design have been; used to measure the incident radiative heat flux in a coal-fired combustion furnace located at the University; of Utah. This method of heat flux measurement uses a probe that limits the field of view, allowing; radiation measurements of relatively precise locations. The probe contains a Wheatstone bridge with; two thermistors, one that is irradiated and one that is not. The measured voltage difference between the; two thermistors is used to determine the heat flux based on calibration curves obtained in a blackbody; furnace. This calibration produces a curve of measured voltage vs. blackbody temperature. The heat; flux is calculated from the blackbody temperature and corrected for the view angle.; Using the concept of an instrument model, we have conducted an extensive analysis of the errors; associated with using this radiometer design to measure incident heat flux. The purpose of an instrument; model is to identify how the measured signal (in this case mV) is converted to the variable of interest; (incident heat flux) and what possible sources of uncertainty might contribute to the calculated heat; flux. We have identified many sources of uncertainty in the construction, operation, and calibration of; the radiometers, including transient ambient temperature effects on the Wheatstone bridge, view angle; variation, lens refractive index variation, blackbody temperature, and target size. We discuss how each; source of uncertainty is managed (determined to be negligible, eliminated, or included in the analysis).; The major contributor to the total uncertainty is the use of the thermistor in the Wheatstone bridge.; There is also unexplained drift in the calibration curves. We present new maximum and minimum; calibration curves that account for all identified uncertainties. The overall uncertainty could be greatly; reduced by modifying the construction of the radiometers for future tests. Specific changes for future; radiometer design are suggested.

Narrow Angle Radiometer Instrument Model Kaitlyn Scheib, Jennifer Spinti, Andrew Fry, Stan Harding, Igancio Preciado University of Utah, Salt Lake City, UT August 1, 2017 Abstract Narrow-angle radiometers based on the International Flame Research Foundation design have been used to measure the incident radiative heat flux in a coal-fired combustion furnace located at the University of Utah. This method of heat flux measurement uses a probe that limits the field of view, allowing radiation measurements of relatively precise locations. The probe contains a Wheatstone bridge with two thermistors, one that is irradiated and one that is not. The measured voltage difference between the two thermistors is used to determine the heat flux based on calibration curves obtained in a blackbody furnace. This calibration produces a curve of measured voltage vs. blackbody temperature. The heat flux is calculated from the blackbody temperature and corrected for the view angle. Using the concept of an instrument model, we have conducted an extensive analysis of the errors associated with using this radiometer design to measure incident heat flux. The purpose of an instrument model is to identify how the measured signal (in this case mV) is converted to the variable of interest (incident heat flux) and what possible sources of uncertainty might contribute to the calculated heat flux. We have identified many sources of uncertainty in the construction, operation, and calibration of the radiometers, including transient ambient temperature effects on the Wheatstone bridge, view angle variation, lens refractive index variation, blackbody temperature, and target size. We discuss how each source of uncertainty is managed (determined to be negligible, eliminated, or included in the analysis). The major contributor to the total uncertainty is the use of the thermistor in the Wheatstone bridge. There is also unexplained drift in the calibration curves. We present new maximum and minimum calibration curves that account for all identified uncertainties. The overall uncertainty could be greatly reduced by modifying the construction of the radiometers for future tests. Specific changes for future radiometer design are suggested. 1 Purpose This paper evaluates the uncertainties associated with a narrow-angle method for measuring incident radiative flux in combustion environments. The method uses a probe that limits the field of view, allowing radiation measurements at relatively precise locations [1, 2]. Measurement uncertainty is introduced in both the construction of the radiometer and in the calibration. We exanmine both types of uncertainties in this document and provide a sample data analysis based on these uncertainties. 2 Principle of Operation The narrow-angle (NA) radiometer is a long, water-cooled probe with a sensing element at the receiving end (see Figure 1). Radiation enters the probe along a field of view established by the inner tube of a water-cooled jacket. The long probe collimates the radiant light in the field of view, which is then focused by a lens onto a thermistor, inducing a change in resistance as the thermistor's temperature changes. Figure 2 shows a schematic of the focusing lens used in the radiometer. This lens focuses the incoming radiation onto the irradiated thermistor located at focal distance f. 1 Figure 1: Schematic of NA Radiometer [2] Figure 2: Plano-Convex Lens Schematic [3] 2.1 Wheatstone Bridge A Wheatstone bridge circuit with a second, non-irradiated thermistor is intended to account for changes in ambient conditions between the calibration and the actual measurement. A schematic of a Wheatstone bridge is given in Figure 3. As the irradiated thermistor temperature changes, its resistance changes and the voltage drop across the bridge is measured using Equation (1) [2]: Rnon Rirr Vmeas = Vapp − (1) Rnon + R1 Rirr + R2 Here, Rnon is the resistance of the non-irradiated thermistor, Rirr is the resistance of the irradiated thermistor, R1 and R2 are the resistors in Figure 3, Vapp is the voltage applied to the source, and Vmeas is the voltage drop across the bridge. The measured voltage is calibrated against a blackbody furnace and provides the basis for the measurement [2]. Figure 3: Wheatstone Bridge Circuit [2] 2 Figure 4: Voltage Divider Schematic We placed a voltage divider into the Wheatstone bridge to measure the voltages across each thermistor. A diagram of the voltage divider is shown in Figure 4, where Vout is the measured voltage across one thermistor. We had a voltage divider across each set of resistors and thermistors. From these measured voltages, we calculated the resistance of the thermistors (Rnon and Rirr ) using Equation 2. These thermistor resistances can then be used in the Equation 1 and are used in the uncertainty analysis discussed in Section 6. R1 = 2.2 Vout Rirr Vapp − Vout (2) Field of View The theoretical field of view of the NA radiometer is the angle of divergence resulting from the radiometer geometry. The divergence angle, αf v , is given by Equations (3), (4), and (5) [2]: (3) αf v = 2θ αf v = tan −1 D1 /2 Lp1 = tan Lp = Lp1 + Lp2 −1 D2 /2 Lp2 (4) (5) In these equations, Lp1 is the length from the lens to the blue star in Figure 1 and Lp2 is the length from the blue star to the probe orifice [2]. For the radiometers used in the this study, Lp = 65 cm, D1 = 1.14 cm, and D2 = 1.97 cm. Given these values, the following were obtained: Lp1 = 23.8 cm, Lp2 = 41.2 cm, and αf v = 2.74˚. Based on this divergence angle, the view angle θ is 1.37˚ and the theoretical diameter of the target area, where the distance across the furnace is 1 m, is 6.75 cm. 3 3.1 3.1.1 Design and Construction Description of NA Radiometers Body The NA radiometer probes are divided into two sections. The front section consists of a long, narrow, water-cooled jacket that collimates the light and defines the field of view. The back section consists of the focusing lens, Wheatstone bridge, and lens mounting ring. 3 (a) Wavelength vs. refractive index (b) Wavelength vs. power at different blackbody temperatures Figure 5: Refractive index vs. wavelength plots for CaF2 lens [4] 3.1.2 Lens The lens is a plano-convex, uncoated, CaF2 lens [3]. The diameter is 12.7 mm (0.5 in.) and the focal length is 20 mm (Thorlabs Part No. LA5315) at a refractive index of 1.435. The refractive index varies from 1.35 to 1.51 within its transmittance range of 180 nm to 8.0 μm; see Figure 5 [4]. This range in refractive index results in a range of possible focal lengths from 17-25 mm. The relationship between refractive index and focal length is given in Equation 6, where f is the focal point, n is the refractive index, and R is the radius of curvature (8.7 mm). R (6) n−1 Figure 5a shows that refractive index also changes as a function of wavelength. Figure 5b shows the Planck distribution of wavelength vs. refractive index at different blackbody temperatures. The yellow shaded region shows the range of wavelengths transmitted by the CaF2 lens. The wavelength where the maximum emissive power occurs changes with temperature. Thus, the lens refractive index will vary depending on the temperature of the incident radiation being measured. The lens reflectivity lowers the measured heat flux by 2-4%. The reflectivity is a function of the refractive index of both the lens and the purge gas as shown in the Fresnel Equation, Equation 7. Here n1 is the refractive index of air (the purge gas) and n2 is the refractive index range of the lens (1.35-1.51). The resulting lens reflectivity ranges from 0.022 to 0.041. For example, using a focal length of 20 mm, the corresponding refractive index (n1 ) and reflectivity (ρ) are 1.435 and 0.032, respectively. f= n1 − n2 2 ρ= n1 + n2 3.1.3 (7) Resistors/Thermistors The Wheatstone bridge circuit uses a 5V regulated DC power source, 250 ohm (Ω) resistors for R1 and R2 (WHA250FET from Ohmite [5]) and 450 Ω (at 70°F) thermistors (NTCLE100E3 from Vishay [6]). The measured output voltage is between -100 to 100 mV DC. The relationship between temperature and resistance for the NTC thermistors is shown graphically in Figure 6 and in Equation 8, where A, B, C, and D are constants specific to the thermistors. In this case, A = -13.0723, B = 4190.574 K, C = -47158.4 K2 , and D = -1.199256 × 107 K3 [6]. In Equation 8, Rref is the thermistor resistance at 25˚C (450 Ω), Tt is the thermistor temperature and R is the thermistor resistance. C D B R = Rref exp A + + 2+ 3 (8) Tt Tt Tt 4 Figure 6: Resistance vs. temperature for an NTC thermistor Figure 7: Thermistor Resistance Error vs. Temperature The operating temperature range of the resistors is -55 to 150°C and for the thermistors is -40 to 125°C continuously and to 150°C for short periods. In theory, the resistors/thermistors are stable over these temperature ranges [5, 6] within ±1%. The resistors can drift up to 2% over 1000 hours [5]. The thermistor resistance uncertainty varies with temperature as shown in Figure 7. The minimum resistance uncertainty between individual thermistors is 5% at 25˚C. 3.2 Sources of Uncertainty: Design and Construction There are several sources of uncertainty in the design and construction of the radiometers. Each of the identified uncertainties are discussed in this section 3.2.1 Transient Temperature Effects in Wheatstone Bridge We measured transient temperature effects on the voltage by applying a heater to the Wheatstone bridge of the radiometer. We placed one thermocouple near the non-irradiated thermistor inside the radiometer and a second thermocouple on the outside of the pipe that holds the electronics. We then applied a heat source as shown by the rapid increase in surface temperature in Figure 8a. Because of transient heating effects, the thermistor temperature inside the radiometer increases more slowly. This large temperature difference between the thermistor and the surface of the radiometer results in a decrease in the voltage signal. The voltage signal returns to its original value once the temperature difference decreases to ~2˚C as seen in Figure 8b, indicating that the system has reached a thermal steady state with the heat source applied. To minimize the effect of the ambient temperature transients on the measured voltage, we needed to maintain a constant temperature between the surface of the radiometer and the non-irradiated thermistor. We accomplished this by wrapping ¼ in. copper coils, attatched to a recirculating water chiller, around the section of pipe that holds the electronics as shown in Figure 9. We then wrapped insulation around the 5 (a) Voltage vs. time (b) Voltage gradient vs. time Figure 8: Effect of ambient temperature on radiometer voltage (a) Radiometer cooling coils (b) Insulation around radiometer cooling coils (c) Recirculating chiller water Figure 9: Radiometer cooling coils and recirculating chiller copper cooling coils and the entire lens mounting section of the radiometer. With these changes, the chiller was able to maintain a constant temperature of 20°C and we thus eliminated transient temperature effects as a source of error in our measurements. 3.2.2 Irradiated Thermistor Temperature We determined the temperature range experienced by the irradiated thermistor by placing a thermocouple inside the radiometers close to the non-irradiated thermistor. During testing in a coal-fired furnace, the temperature measured by this thermocouple remained within 1˚C of the chiller set point temperature of 20˚C. Assuming that the non-irradiated thermistor temperature is close to this measured thermocouple temperature (20˚C), Rnon is 572.9 Ω (from Equation 8). At a maximum temperature of 125˚C for the irradiated thermistor, Rirr would be 22.6 Ω (from Equation 8). Given these resistances, we use Equation 1 to compute a maximum voltage of 3V. Since the actual measured voltages during the furnace tests were <100mV, we concluded that the temperature of the irradiated thermistor was within 1-2˚C of the nonirradiated thermistor, ruling out high thermistor temperatures as a source of thermistor drift over time. 3.2.3 View Angle Because the radiometer is made from stainless steel, the inside is reflective. Ideally, the inner tube of the front end is roughened to prevent stray light that enters the probe from reflecting back to the thermistor 6 Figure 10: View angle experimental setup (a) Radiometer 1 view angle (b) Radiometer 3 view angle Figure 11: Radiometer view angle vs. percent of max mV reading and to ensure effective beam collimation. Unfortunately, this was not the case for the radiometers we used and some reflection did occur, resulting in view angles that were different than the theoretical view angle. We measured the radiometer view angle with a heated rod that we set at a prescribed distance from the radiometer and then moved in small increments along a ruler perpendicular to the radiometer (see Figure 10). At each location, we noted the change in mV reading from the radiometer and calculated the angle from the rod to the end of the radiometer. The resulting view angle curves are shown in Figure 11. As expected, the amount of radiation seen by the radiometer changes with angle. We defined two limits for the view angle: the locations where the signal decreased to 2% and to 0% of the maximum signal. We chose these values arbitrarily to provide a range of measurements close to the maximum view angle. This range is shaded in orange in Figures 11a and 11b. The view angle needs to be corrected for the area under the curve since only a percentage of the incoming radiation is seen. We found an area correction factor (α) by computing the area under the curve and dividing by the area of the rectangle containing the curve (shaded in grey in Figures 11a and 11b). We can find a more accurate view angle correction factor by rotating the curve about the vertical axis to create a 3D representation of the view angle. These surface plots are shown in Figure 12. The correction factor is the ratio of the measured view angle volume to the volume of the box containing the view angle volume. The correction factors calculated from both the 2D and 3D plots are shown in Table 1. As discussed in Section 5.4.1, the radiometer calibrations are corrected using these view angles. Another parameter related to the reflectivity inside the tube (and thus view angle) is the particle buildup. During the course of the combustion tests, some ash was deposited inside the first few inches of the radiometers. However, the radiometers were not cleaned during any of the tests. This desposition would decrease the 7 (a) Radiometer 1 3D plot (b) Radiometer 3 3D plot Figure 12: Radiometer view angle surface plots Table 1: Radiometer view angles Radiometer Percent of max signal View Angle Correction (α) 2D plot Correction (α) 3D plot 1 2% 5.67˚ 0.286 0.303 1 0% 6.7˚ 0.244 0.238 3 2% 3.7˚ 0.356 0.552 3 0% 4.16˚ 0.318 0.474 reflectivity and impact radiation arriving at the lens. This uncertainty is not accounted for in this analysis. 3.2.4 Image Size Relative to Thermistor Size If the radiation entering the lens is focused onto an image that is larger than the thermistor, the thermistor will not detect all incoming radiation. The thermistor diameter is 3 mm at its widest. If we assume the object distance during the tests was 1 m, the view angle was 5˚ (theoretical value is 1.37˚), and the refractive index represents mid-range for the lens (for n = 1.435, f = 20 mm), we compute an image diameter of 3 mm from the lens optics equations (the thin lens approximation and the magnification equation) shown in Equations 9 and 10. In Equation 9, ri and ro are the image and object radii, di and do are the image and object distances from the lens. In Equation 10, f is the focal distance. Since this maximum image diameter is the same as the thermistor diameter, we conclude that all incoming radiation is focused by the lens onto the thermistor, and that this is not a source of error. ri = di = 3.2.5 di ro do (9) 1 − (10) 1 f 1 do Focal Point Uncertainty Since the theoretical focal point may be different than the actual focal point, we eliminated this source of uncertainty by adjusting the electronics until the maximum mV reading was obtained. 3.2.6 Other Sources of Error Other sources of error that have not yet been accounted for include: 1. Non-irradiated thermistor placement - This thermistor may not be completely isolated from the irradiated thermistor. 8 2. Lens mounting - If the lens is crooked in the mounting, the light beam may not be focused completely onto the thermistor. We reduced this potential error source by tightly screwing the lens mounting ring into the threaded lens mount. 3. Measuring the induced voltage - The wires from the Wheatstone circuit are connected to an OPTO module and the voltage difference is measured and recorded by OPTO. Uncertainty is introduced if the signal is outside the range of the OPTO module. In all the tests performed, the mV signal was not outside this range, so we discount this as a source of uncertainty. 4 Operation The NA radiometer requires three inputs [1]. These inputs and the sources of uncertainty associated with them are listed below: 1. Cooling water supply: Cooling water prevents probe damage from the hot furnace environment. The cooling water enters the inside of the probe jacket and exits on the outside of the probe. This arrangement provides a constant temperature on the inside surface of the probe, minimizing error associated with radiation from the water jacket tube. Water flow is controlled with a ball valve and metered with a paddle wheel transmitter that is recorded by OPTO. The flow rates are relatively stable. Damstedt [2] states that changing the cooling water flowrate may alter the calibration. During calibrations we tested this effect at four flow rates (0.5, 6, 8 and 10 L/min). With a 0.5 L/min water flow rate, the radiometer got warm and changes in mV readings were observed. At the high water flow rates (6, 8 and 10 L/min), the radiometer remained cold and changes in mV readings were not significant. Since we use a water flow rate of 30 L/min for all tests, this error was insignificant. 2. Gas purge: The gas purge prevents buildup from obscuring the field of view. Gas flow rate and type of purge gas used can be a significant source of uncertainty. If the purge gas flow rate is too low, particles will build up on the lens of the radiometer. If the purge gas is CO2 , changes in flow rate have a large impact on the calibration because CO2 absorbs and emits radiation. We used air flowing at 20 SCFH as the purge gas for these calibrations and tests. After the tests, we observed a deposit film on the lenses, suggesting that the chosen purge flow rate was not high enough. This introduces a potential significant source of uncertainty as the film will prevent some radiation from passing though the lens and alter the refractive index and focal length. 3. Power supply for the bridge circuit: We used a regulated power supply with a 5V output (Grainger Item No. 5JV98); its output voltage fluctuated ± 3 mV [7]. These small fluctuations were included in the uncertainty analysis for the calibration curves. 5 5.1 5.1.1 Calibration Blackbodies Description To quantitatively measure heat flux, the NA radiometers must be calibrated with a blackbody furnace. Manufactured blackbodies usually consist of a sphere or tube with a small aperture as shown in Figure 13. This causes any radiation entering the cavity to be reflected enough times that it is eventually absorbed within the chamber. The aperture then radiates energy at the same rate as a blackbody of the same size and temperature [8]. Blackbody emissivities are typically in the 0.98-0.99 range. 5.1.2 Alignment Because there is some reflectivity inside the tube or sphere, only the aperture is considered to be a blackbody. This means that acurate alignment is important when calibrating using a blackbody source. Emissive power depends on the angle of the radiation source as shown in Equation 11. Here, θ is the angle 9 (a) θ = 0˚ (b) θ = 3˚ Figure 13: Radiometer alignment to blackbody between the blackbody and the radiometer, Ib is the blackbody intensity (Ib = σT 4 ) and Eb is the blackbody emissive power. Figure 13 represents the radiometer and blackbody when the radiometer is perfectly aligned, θ = 0˚, and when the radiometer is misaligned by θ = 3˚. The higher the misalignment, the less emissive power the radiometer will see from the blackbody. Eb = Ib cosθ 5.2 (11) Low Temperature Range Blackbody We used the LANDCAL blackbody furnace type R1200P [9] for this calibration. It was designed to create a target of uniform temperature with a high emissivity (approximately 0.98) at short wavelengths. The target is a conical cavity at one end of a 55.9 mm diameter hollow cylinder, and the radiometer views the target along the axis of the cylinder. The cone plays an important part in establishing uniformity of radiation emitted by the target. When calibrating radiometers, the target size requirements must be met by the cone. If the radiometer target size is so big that the walls of the cylindrical block are viewed, a less accurate calibration will result. The R1200P provides a temperature source up to 1200°C, although the recommended temperature range is 350°C to 1150°C. The source is fitted with a three-term temperature controller which allows it to heat up to 1150°C within 25 minutes and holds it to within ±1°C over a 60-minute period. In reality, the maximum temperature reached during calibration was 871˚C . The target temperature is measured by a thermocouple embedded into the target wall located in the back of the blackbody's cylindrical chamber. A second thermocouple, situated close to the heating elements, is used to control the furnace temperature. As a result, the control thermocouple is hotter than the target temperature. Both the control thermocouple and indicator thermocouple are Type N, mineral insulated, 3mm OD with Nicrobell B sheaths. The calibration was performed by recording the output signal (mV) from the radiometer for a range of target temperatures in the blackbody. We then computed the emissive power of the blackbody source from Equation 12. Here, qb is the blackbody emissive power, σv is the Stefan-Boltzmann constant, ε is the emissivity of the blackbody (0.98), and T is the target temperature. qb = εσT 4 5.2.1 (12) Calibration Procedure for Low-Range Blackbody We used the following procedure for radiometer calibration [2]. 1. Place the probe on the calibration mount. 2. Visually align tip of radiometer with the blackbody aperture. 3. Turn on the cooling water. Set flow rate of 30 L/min to eliminate uncertainty related to low water flow rates. 4. Turn on the purge gas (air). Set flow rate to 20 SCFH for air. The flow rate of purge gas does not have an effect on calibration, but the type of purge gas does. 5. Record an ambient "baseline" measurement with the blackbody at room temperature. 10 6. Change the blackbody temperature and allow system to come to steady state (when the blackbody temperature and radiometer mV signal stop changing). It takes around 30 minutes for the furnace to increase 200˚C. 7. Record the radiometer mV output and "Target" temperature. The specific mV reading for a given heat flux depends on the radiometer. 8. Repeat steps 6-7 to generate a calibration curve. 5.2.2 Sources of Error in the Low-Range Blackbody The following are potential sources of error when calibrating in the low-temperature blackbody. These sources are assumed to be accounted for by the calibration curves. 1. Non-uniform temperature - The temperature gradients across the middle 40 mm of the 55 mm blackbody cavity are within ±1°C over the temperature range 400-1150°C. The measurement uncertainty is ±3˚C. 2. Target size - The measured voltage will change depending on the relative sizes of the target and aperture. Assuming the radiometer is flush with the blackbody aperture, the target size is equal to the radiometer tube diameter. Because the target size is 1.96 cm and the aperture size is 5.6 cm. the radiometer only sees radiation from the blackbody. Thus, this is not a significant source of uncertainty. 3. Target temperature - The target temperature was displayed on a digital indicator having ±1°C resolution. If traceability to national standards is not required, the target temperature is given by the 'target' indication temperature. According to the manufacturer [9], the target indication temperature agrees with the radiance temperature to within ±10°C at short wavelengths. Other methods of calibration are available if higher accuracy is required. This uncertainty of ±10˚C in the measured blackbody temperature is included in the calibration curve uncertainty. 4. Oxide layer formation - An oxide layer may form inside the cavity, resulting in decreasing emissivity as a function of wavelength. A spectrometer could be used to verify the magnitude of this effect by measuring the intensity versus the wavelength of the blackbody. This effect was not evaluated during these tests. 5. Calibration alignment - Because the alignment procedure was not precise, there is some uncertainty in the calculated heat flux due to misalignment. However, the magnitude of this uncertainty is unknown. 5.3 Mid Temperature Range Blackbody Because the operating temperatures of the combustion furnace exceeded the temperature range of the low temperature blackbody, we needed a blackbody with a higher temperature range for calibration. We created a pseudo-blackbody using a Thermolyne muffle furnace (maximum temperature of 2100˚C) into which we inserted a graphite slab (7.62 cm by 10.16 cm); we directed the radiometer tip at the graphite slab. We roughed up the graphite surface to decrease its reflectivity and purged the furnace with a small flow rate of Ar (5-10 SCFH) to prevent the graphite from burning. Nevertheless, the size of the graphite decreased over time, indicating either an air leak into the furnace during operation or at the end of the day when the Ar gas was shut off (and the graphite was still hot). After a few calibrations, we replaced the graphite slab. This muffle furnace and calibration setup can be seen in Figure 14. We measured the furnace temperature with a type K thermocouple placed in front of the graphite slab (not shown) in the top left corner. This thermocouple is coming in from the ceiling in Figure 14a. We embedded a second type K thermocouple in the back of the furnace (visible in Figure 14a) and connected it to the temperature controller. The thermocouple at the back of the furnace consistently measured around 10˚C higher than the thermocouple in front of the graphite slab. 11 (a) View inside muffle furnace. The "furnace face" indicates the plane where the end of the radiometer is placed. (b) Radiometer calibration setup in muffle furnace. We secured a piece of Insboard to the furnace opening with aluminum tape. We then placed the radiometer tube through a hole in the middle of the insboard and aligned the end of the radiometer with the inside face of the furnace. Figure 14: Calibration setup in muffle furnace 5.3.1 Calibration procedure for Mid Temperature Range blackbody We used the following procedure for calibration [2]. 1. Place the probe on the calibration mount. 2. Turn on the cooling water. Set flow rate to 30 L/min to eliminate uncertainty related to low water flow rates. 3. No purge is necessary as long as the probes are full of stagnant air. 4. Turn on Ar purge gas for the blackbody to 5 SCFH. 5. Place graphite slab in the furnace at a specified distance from the furnace face (5 cm to 20 cm). 6. Place type K thermocouple in front of the graphite slab and connect to a temperature reader. 7. Record an ambient "baseline" measurement with the furnace at room temperature. 8. Change the furnace temperature and allow it to come to steady state (when the furance temperature and radiometer mV reading stop changing). It takes approximately 30 minutes for the furnace to increase 200˚C. 9. Record the mV output from the radiometer and the thermocouple temperature. The specific mV reading for a given heat flux depends on the radiometer. 10. Repeat steps 8-9 to generate a calibration curve. 5.3.2 Sources of Error in the Mid Temperature Range Blackbody 1. Target temperature - The thermocouple manufacturer states a standard error of 0.75%, but the measured temperature uncertainty is significantly higher. We assume the same uncertainty range as the low-temperature black body, ±10˚C. 2. Graphite slab - The graphite slab needed to be replaced every few calibrations. The decreasing graphite surface area could affect the target the radiometer was seeing. Also, each graphite slab may not be identical or roughened up the same amount, which might affect its emissivity. 12 3. Non-uniform temperature - Since the heating elements are on the sides of the furnace, the temperature in the blackbody may not be uniform. Only two thermocouples were in the furnace during calibrations: one in the back of the furnace and one in the top left corner in front of the graphite slab. The temperature difference between these was ~10˚C. For our analysis, we assume a uniform blackbody temperature using the temperature provided by the thermocouple placed in front of the graphite slab. However, this non-uniformity in temperature is an unaccounted for source of uncertainty. 4. Target size -The mV signal from the radiometer changes with changing distance from the radiometer tip to the graphite slab. We account for this uncertainty in the calibration curves. 5. Calibration alignment - See Section 5.1.2. The radiometer was not perfectly aligned with the blackbody furnace. This would result in a lower measured heat flux. 5.4 5.4.1 Calibration Results Calibration Curve Correction We corrected the heat fluxes obtained from the calibration for the solid angle seen by the NA radiometer [10]. The expression for the solid angle is shown in Equation 13 with ψ = 2π; θ1 is the radiometer view angle. We determined the incident flux to the radiometer from Equation 14 where θ2 is the angle of the radiometer with respect to the blackbody furnace radiation. ˆ ψ ˆ θ1 sinθ1 dθ1 dψ = (1 − cosθ1 )ψ Ω= ψ=0 (13) θ1 =0 ˆ q"i = Icosθ2 dΩ (14) We then substitute the expressions for the intensity, I = q"πb , qb" = σTb4 , and the solid angle Ω = 2π (1 − cosθ1 ) into Equation 14. Assuming that θ2 ∼ = 0 (the radiometer is perfectly aligned), we then have the heat flux corrected for the narrow angle, qi" : q"b (1 − cosθ1 ) 2π = 2q"b (1 − cosθ1 ) (15) π Adding in corrections for the reflectivity of the lens (Equation (7)) and the view angle area correction (α) from Table 1 and substituting in the equation for qb (Equation (12)), the corrected NA flux equation is: q"i = q"cal = qi" (1 − ρ)α 5.4.2 (16) Heat Flux Calibration Curves Heat flux calibration curves for the low- and mid-range blackbodies are shown in Figure 15. We originally fabricated three radiometers, but Radiometer 2 stopped working prior to being calibrated in the mid-range blackbody furnace. With the mid-range blackbody, the distance from the radiometer tip to the graphite sheet was varied from 5.1 to 20.8 cm. The fluxes for these curves were calculated using Equation 16. Since the measured mV signal is a result of the voltage difference between the two thermistors, thermistor resistance uncertainty could cause a negative mV reading which we see in Figure 15b. Radiometer 1 calibrations show that there were shifts between the various low-range and mid-range calibrations. The specific causes of these shifts are still unknown. The radiometers were used in the University of Utah's coal-fired combustion furnace for 2 weeks in the end of June and 1 week in October. Possible sources of the calibration shifts include (1) the use of different OPTO modules to record data, (2) particle deposition in the probe and on the lens (which may be related to radiometer location), (3) and radiometer cleaning. Radiometer 1 was placed 27.95 cm from the burner face, Radiometer 2 was 60.97 cm, and Radiometer 3 was 94 cm. Radiometer 1 may have experienced more deposits and heat than the other radiometers which would explain its larger shift in calibrations. The radiometers were not cleaned during testing but they were taken apart and cleaned prior to the calibrations done in December. 13 (a) Radiometer 1 calibration curves with low and mid-range blackbodies (b) Radiometer 2 calibration curves with low-range blackbody (c) Radiometer 3 calibration curves with low and mid-range blackbodies Figure 15: Radiometer calibration curves with heat flux vs. mV signal. We varied date calibrated, distance from tip of radiometer to graphite sheet, and blackbody furnace 14 (a) Radiometer 3 mV uncertainty with ±1% thermistor uncertainty (b) Radiometer 3 mV uncertainty with no thermistor uncertainty Figure 16: Radiometer 3 with mV uncertainty Table 2: Radiometer 3 thermistor data Tbb (˚C) 600 800 1000 1190 6 U1 (V) 3.516 3.491 3.4656 3.443 U2 (V) 3.4886 3.4576 3.4294 3.3824 Rnon (Ω) 592.318 578.363 564.651 552.826 Rirr (Ω) 577.0478 560.425 545.874 522.750 Tnon (K) 319.168 305.213 291.501 279.676 Tirr (K) 303.898 287.275 272.724 249.600 Instrument Uncertainty There are several sources of error that need to be accounted for in the final uncertainty calculations of the heat flux. As shown in the previous section, there are uncertainties associated with the design, operation, and calibration of the NA radiometers that contribute to the calibration curve uncertainties. The effects of both the mV and heat flux uncertainty will be discussed in this section. 6.1 Uncertainty in mV Reading First, we calculated the error in the mV signal using the Wheatstone bridge equation with uncertainty included as shown in Equation 17. This equation includes the applied voltage from the regulated power supply and the thermistor and resistor resistances with their accompanying uncertainties. We then computed the maximum and minimum possible values for Vmeas from Equation 17 for each point on the calibration curves. The results are shown in Figure 16 and in Table 2for Radiometer 3. The U1 and U2 values in the table are from the voltage divider discussed in Section 2.1. We computed Rnon and Rirr values using Equation 1 and the Tnon and Tirr values using Equation 8. For this example calibration for Radiometer 3, the average calculated mV uncertainty is ±58.5%. This is the maximum uncertainty assuming the maximum amount the thermistor and resistors resistances drift over time. The calculated mV uncertainty is most sensitive to the thermstor uncertainty. For instance, if we remove the ±1% thermistor drift and assume they are perfectly stable, the mV uncertainty decreases to ±0.41%. This impact of mV uncertainty is shown in Figure 16. Rnon ± 1% Rirr ± 1% Vmeas = (Vapp ± 3mV ) − (17) (Rnon ± 1%) + (R ± 1%) (Rirr ± 1%) + (R ± 1%) 6.2 Uncertainty in Heat Flux Table 3 lists several parameters that impacted the calibration curves through the calculated heat flux that we include in our uncertainty analysis. Parameters that did not affect the calibration curves included the purge gas flow rate and the cooling water flow rate (if maintained at a level of 6 L/min or higher). Other potential sources of calibration uncertainty 15 Table 3: Heat flux uncertainty parameters Input parameters View angle View angle area correction (α) Blackbody furnace temperature Lens refractive index Range 3.7˚ - 4.16˚ 0.356 - 0.318 ±10˚C 1.35 - 1.51 Figure 17: Radiometer 3 with heat flux uncertainty including lens material, thermistor wire radius and temperature, thermistor bead radius, connecting wire length, and the number and type of connections. We did not account for these potential sources of error in this analysis and they are assumed to be negligible [1]. We calculated the heat flux uncertainty using Equation 16 and the uncertainties in the view angle, blackbody temperature, and refractive index (the reflectivity is a function of refractive index) shown in Table 3. From this analysis we obtained the maximum and minimum value of incident flux, qi , at each point on the calibration curves. These results are shown in Figure 17 and in Table 4. For this Radiometer 3 calibration, the average calculated uncertainty in the heat flux is ±10.6%. This uncertainty in heat flux could be reduced using a more accurate blackbody and a smaller range for the view angle. However, this heat flux uncertainty is still small compared with the uncertainty due to the mV signal. 6.3 Total Uncertainty Figure 18 and Table 5 show the uncertainty range with both voltage and heat flux uncertainty applied. Figure 18a and 5a show the results when using ±1% drift in thermistor resistance. Figure 18b and 5b show the results using no drift in thermistor resistance. The total calculated uncertainty with some thermistor drift results in an average uncertainty of ±64.2% at a constant heat flux. With no thermistor drift, this value is ±5.02%. These results tell us that the total radiometer uncertainty is mostly dependent on the thermistor drift. When there is no thermistor drift, the uncertainty in the calculated heat flux becomes the dominant uncertainty. If this is the case, the view angle uncertainty becomes most important followed by Table 4: Radiometer 3 calibration data Tbb (˚C) 600 800 1000 1190 mV 27.61 34.03 44.71 60.57 qrad min 8.358E-05 0.00019 0.00038 0.00067 qrad max 0.00028 0.00063 0.00124 0.00215 16 qrad avg 0.000182 0.00041 0.00081 0.00141 qi min 43.883 101.003 201.268 352.531 qi max 55.38 125.314 246.81 428.778 qi avg 49.632 113.159 224.039 390.655 (a) Radiometer 3 calibration with mV and heat flux uncertainty using ±1% thermistor uncertainty (b) Radiometer 3 calibration with mV and heat flux uncertainty with no thermistor uncertainty Figure 18: Radiometer 3 with heat flux and mV uncertainty Table 5: Total calculated uncertainty range in mV signal (a) Total uncertainty range with ±1% thermistor uncertainty Tbb (˚C) 600 800 1000 1190 mV min 3.067 8.891 19.056 34.33 mV max 46.284 53.515 66.137 85.101 (b) Total uncertainty range with no thermistor drift Tbb (˚C) 600 800 1000 1190 ±% 87.57% 71.51% 55.26% 42.51% mV min 24.008 29.887 40.149 55.569 mV max 25.516 32.637 45.067 63.744 ±% 3.05% 4.40% 5.77% 6.85% the blackbody temperature. 7 Conclusions and Recommendations With the current radiometers, there are many sources of uncertainty. This document identifies these sources and how they were managed. We have eliminated some of these sources of error by changing the calibration procedure and experimental setup. The largest source of error comes from the use of the Wheatstone bridge. The thermistor resistances have the potential to drift ±1% over their lifetime. This change of ±1% in the thermistor resistance changes the total calculated uncertainty from ±5.02% to ±64.2%. We have also not yet identified the source of the shift in calibrations seen in Figure 15. The largest shift occured in Radiometer 1 with a mV signal varying ±35% at a constant heat flux. Because the radiometers were used for testing in a coal-fired furnace, a potential source of error could be film deposits on the lens and probe. This uncertainty has not yet been quantified. In the future, we need a heat flux measurement that is accurate to within 5%. Since most of the radiometer uncertainty comes from the sensitivity of the Wheatstone bridge, we recommend eliminating the circuit and using a thermopile rather than the thermistors. Other changes that would reduce the measurement uncertainty would be to minimize the view angle and reflectivity inside the tube and to determine the cause of the operational shift. We recommend that the radiometers be redesigned to implement theses changes. References [1] N. Fricker. Ifrf online combustion handbook. Web, 2001. [2] Brad Damstedt. Heat flux probes operation summary. Technical report, Praxair, 2008. [3] ThorLabs. Calcium fluoride plano-convex lenses, uncoated. Web, 2017. 17 [4] Crystran. Calcium fluoride (caf2). Web, 2012. [5] Ohmite. Wh/wn series: Miniature molded wirewound, 2017. [6] Vishay. Ntc thermistors, radial leaded, standard precision, 2017. [7] SOLA/HEVI-DUTY. Linear Open Frame DC Power Supplies Silver Line Instruction Manual Model: SLD-12-1010-12T. [8] LumaSense Technologies. Ir calibration. Web. [9] Landcal Blackbody Source, Type R1200P. [10] Frank P. Incropera, David P. Dewitt, Theodore L. Bergman, and Adrienne S. Lavine. Fundamentals of Heat and Mass Transfer. John Wiley, 2007. 18