Towards an Ultra-High-Speed Combustion Pyrometer "2279

International Journal of Turbomachinery Propulsion and Power

Article † Towards an Ultra-High-Speed Combustion Pyrometer

Alberto Sposito, Dave Lowe and Gavin Sutton * National Physical Laboratory (NPL), Hampton Road, Teddington TW11 0LW, UK; [email protected] (A.S.); [email protected] (D.L.) * Correspondence: [email protected] This paper was presented at the 9th EVI-GTI International Gas Turbine Instrumentation Conference, Graz, † Austria on 20–21 November 2019. Received: 2 March 2020; Accepted: 10 December 2020; Published: 15 December 2020

Abstract: Measuring reliably the correct temperature of a sooty flame in an internal combustion engine is important to optimise its efficiency; however, conventional contact thermometers, such as thermocouples, are not adequate in this context, due to drift, temperature limitation ( 2100 K) and ≤ slow response time (~10 ms). In this paper, we report on the progress towards the development of a novel ultra-high-speed combustion pyrometer, based on collection of thermal radiation via an optical fibre, traceably calibrated to the International Temperature Scale of 1990 (ITS-90) over the temperature range T = (1073–2873) K, with residuals <1%, and capable of measuring at a sampling rate of 250 kHz.

Keywords: combustion; temperature; pyrometer; optical sensor

1. Introduction Traceable, reliable measurement of combustion temperature is important because it can improve the understanding of the combustion process and provide a mechanism for the optimisation of engine power, fuel consumption and emissions [1]. These measurements are performed under highly dynamic conditions, with temperature changes of up to ~3300 K occurring on a millisecond timescale. Conventional temperature sensors based on contact thermometry (e.g., thermocouples) are inadequate in this context, due to their slow response time (~10 ms), temperature limitation ( 2100 K), drift and ≤ perturbation of the combustion process. To address this challenge, with particular reference to internal combustion and diesel engines, we are developing a novel ultra-high-speed combustion pyrometer, within the framework of the European joint research project DynPT—Development of measurement and calibration techniques for dynamic pressures and temperatures, part of the European Metrology Programme for Innovation and Research (EMPIR) [2].

2. System Design and Theoretical Model A schematic of the thermometer system design is shown in Figure1. It consists of:

A sensor: a 2 m long gold-coated multi-mode (MM) step-index fibre, with 400 µm core diameter, • numerical aperture NA = 0.22, stainless-steel monocoil sheathing, a sub-miniature (SMA) connector on one end (hot front end) and a fibre-channel (FC) connector on the other end (cold back end)—for testing purposes, this was placed inside a ~1.7 m long stainless-steel tube (outer diameter: 20 mm, inner diameter: 16 mm), with the SMA connector protected by a recessed sapphire window; sensor and packaging can be tailored to the final application and installation requirements (e.g., addition of a collimating lens). An extension lead fibre: a lightly-armoured 10 m long MM step-index fibre patch-cord, with 600 µm • core diameter, NA = 0.22, dual acrylate coating, 3 mm diameter polyvinyl chloride (PVC) sleeve and FC connectors on both ends—this connects the sensor (on the FC connector) to the interrogator.

Int. J. Turbomach. Propuls. Power 2020, 5, 31; doi:10.3390/ijtpp5040031 www.mdpi.com/journal/ijtpp Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 2 of 15

Int.• J. Turbomach.An extension Propuls. lead Power fibre:2020 a, 5lightly-armoured, 31 10 m long MM step-index fibre patch-cord, with2 of600 16 µm core diameter, NA = 0.22, dual acrylate coating, 3 mm diameter polyvinyl chloride (PVC) sleeve and FC connectors on both ends—this connects the sensor (on the FC connector) to the A passive optoelectronic interrogator, assembled in-house and consisting mainly of: • interrogator. • A passive optoelectronic interrogator, assembled in-house and consisting mainly of: a custom-made 1 3 mm2 step-index fibre coupler/splitter with 600 µm core diameter, × #o a custom-madeNA = 0.22 and 1 FC× 3 connectors mm2 step-index on all fibre ports; coupler/splitter with 600 µm core diameter, NA = 0.22three and photodetector FC connectors assemblies, on all ports; using off-the-shelf components, for measuring optical #o threethermal photodetector radiation at assemblies, 3 different wavelengths: using off-the-shelfλ1 = 850 components, nm, λ2 = 1050 for nm measuring and λ3 = 1300 optical nm; thermala power radiation supply at unit 3 different to power wavelengths: the photodetectors. λ1 = 850 nm, λ2 = 1050 nm and λ3 = 1300 nm; o a power supply unit to power the photodetectors. A# National Instrument (NI) data acquisition (DAQ) system, with maximum sampling rate • fAMAX National= 1 MHz, Instrument connected (NI) to data the optoelectronicacquisition (DAQ) interrogator system, with via BNC maximum cables sampling and to a Personalrate fMAX Computer= 1 MHz, (PC)connected via a USB to cable.the optoelectronic interrogator via BNC cables and to a Personal Computer (PC) via a USB cable.

Figure 1. Schematic of the system.

Fibres with large core diameterdiameter and large NANA werewere chosenchosen toto maximisemaximise collectioncollection of optical thermal radiation; the gold (Au) co coatingating allows the fibre fibre to withstand high temperatures, up to ~1000 K, although the core diameter ofof Au-coatedAu-coated fibresfibres isis limitedlimited toto 400400 µµm.m. The wavelengths of of the the photodetector photodetector assemblies assemblies were were chosen chosen based based on on previous previous experience experience to toavoid avoid spectral spectral features features (emission (emission and and absorption absorption lines) lines) from from the the combustion combustion by-products by-products and the components ofof the the pyrotechnic pyrotechnic charges charges (see figures (see below,figures taken below, from taken earlier from spectroscopic earlier spectroscopic experiments), asexperiments), well as to test as well the assumptionas to test the thatassumption the measured that the combustion measured combustion process behaves process like behaves a blackbody like a (emissivityblackbody (emissivityε = 1.0)—good ε = agreement1.0)—good amongstagreement the amongst temperatures the te estimatedmperatures at diestimatedfferent wavelengths at different canwavelengths be used to can confirm be used that to theconfirm blackbody that the condition blackbody is met. condition is met. Figure2 2aa showsshows thethe emissionemission spectrumspectrum capturedcaptured withwith aa SiSi spectrometer,spectrometer,where wherethe thefollowing following features werewere identified:identified:

A. 589589 nm—Sodium nm—Sodium (Na) (Na) emission emission lines; lines; B. 619619 nm—CaOH nm—CaOH emission emission lines; lines; C. 693 nm—Potassium (K) emission lines; C. 693 nm—Potassium (K) emission lines; D. 767 nm—K emission and absorption lines; D. 767 nm—K emission and absorption lines; E. 960 nm—Uncertain of assignment.

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Int.Int. J. Turbomach. J. Turbomach. Propuls. Propuls. Power Power 20202020, 5, 5x, FOR 31 PEER REVIEW 3 of3 of15 16 E. 960 nm—Uncertain of assignment. E. 960 nm—Uncertain of assignment.

Figure 2. Pyrotechnic emission spectrum from (a) Si spectrometer, (b) InGaAs spectrometer, ~36 ms after ignition. The coloured vertical lines identify the chosen wavelength: 850 (blue line in (a)), 1050 FigureFigure 2. 2.PyrotechnicPyrotechnic emission emission spectrum spectrum from ((aa)) SiSi spectrometer, spectrometer, (b ()b InGaAs) InGaAs spectrometer, spectrometer, ~36 ~36 ms ms after (green line in (b)) and 1300 nm (red line in (b)). afterignition. ignition. The The coloured coloured vertical vertical lines lines identify iden thetify chosenthe chosen wavelength: wavelength: 850 (blue850 (blue line inline (a )),in 1050(a)), (green1050 (green line in (b)) and 1300 nm (red line in (b)). Figureline in (b2a)) andalso 1300 shows nm (redthe line blackbody in (b)). spectrum from a tungsten calibration lamp (with a temperatureFigureFigure 2a2 ofa also also3165 shows showsK) overlapped the the blackbody blackbody to the spectrum measur spectrum fromed spectrum. afrom tungsten a Thetungsten calibration agreement calibration lamp between (with lamp a the temperature (withshape ofa temperaturetheof 3165two spectra K) overlapped of 3165 suggests K) tooverlapped that the measuredthe blackbody to the spectrum. measur assumptioned The spectrum. agreement for a fireball The between agreement is a valid the shapebetween hypothesis. of the the two shape spectra of thesuggests twoFigure spectra that 2b the suggestsshows blackbody the that emission the assumption blackbody spectrum for assu a fireballcaptmptionured is for awith valid a fireball an hypothesis. InGaAs is a valid spectrometer, hypothesis. where the followingFigureFigure features 2b2b shows shows were the the identified: emission emission spectrum spectrum capt capturedured with with an an InGaAs InGaAs spectrometer, spectrometer, where where the the following features were identified: A.following 1104 nm—K features emission were identified: lines; A.B.A. 110411691104 nm—K nm—K nm—K emission emission emission lines; lines; lines; B.C.B. 1169Broad1169 nm—K OH nm—K absorption emission emission lines; in lines;the fibre; C. Broad OH absorption in the fibre; C.D. Broad1243 and OH 1252absorption nm—K in emission the fibre; lines; D. 1243 and 1252 nm—K emission lines; D.E. 1243Broad and OH 1252 absorption nm—K emissionin the fibre; lines; E. Broad OH absorption in the fibre; E.F.F. Broad15171517 nm—K OH nm—K absorption emission emission in lines. the lines. fibre; F. 1517As photodetectors nm—K emission with lines. variable gain G were used, a simple theoretical model was developed to As photodetectors with variable gain G were used, a simple theoretical model was developed to estimate the optical power measured by each photodetector and how their voltage signals change estimateAs photodetectors the optical power with measuredvariable gain by each G were photodetector used, a simple and theoretical how their voltage model signalswas developed change with to with G. Their bandwidth B also decreases with increasing G, adjustable in 10 dB steps from 0 to 70 estimateG. Their the bandwidth optical powerB also measured decreases withby each increasing photodetectorG, adjustable and how in 10 their dB stepsvoltage from signals 0 to 70 change dB. dB. with GFirst. Their of all,bandwidth the blackbody B also radiationdecreases power with increasing coupled into G, theadjustable core ofthe in 10 optical dB steps fibre from (see geometry 0 to 70 First of all, the blackbody radiation power coupled into the core of the optical fibre (see geometry dB.sketched in Figure3) was calculated, assuming an emissivity ε = 1 and optical transmission of the fibre sketched in Figure 3) was calculated, assuming an emissivity ε = 1 and optical transmission of the overFirst the of range all, theλ = blackbody(0.3–2.4) µ radiationm as specified power in coupled the Au-coated into the fibrecore datasheet.of the optical fibre (see geometry sketchedfibre over in the Figure range 3) λ was = (0.3–2.4) calculated, µm as assuming specified an in emissivitythe Au-coatedε = 1fibre and datasheet. optical transmission of the fibre over the range λ = (0.3–2.4) µm as specified in the Au-coated fibre datasheet.

FigureFigure 3. 3. GeometryGeometry of of the the end end of of the the sensor sensor (Au-coated (Au-coated fibre): fibre): dd == fibrefibre core core diameter; diameter; θθ == maximummaximum Figureacceptanceacceptance 3. Geometry half-angle. half-angle. of the end of the sensor (Au-coated fibre): d = fibre core diameter; θ = maximum acceptance half-angle. NeglectingNeglecting the the Fresnel Fresnel reflection reflection losses losses from from th thee end-facet end-facet of of the the fibre fibre and and from from the the sapphire sapphire window,window,Neglecting the the total total the blackbodyFresnel blackbody reflection radiation radiation losses power power from coupl coupled theed end-facet into into the the of fibre fibrethe fibrecore core overand over fromthe the full fullthe blackbody blackbodysapphire window,radiationradiation the spectrum spectrum total blackbody (i.e., (i.e., all all wavelengths) wavelengths) radiation power is: is: coupled into the fibre core over the full blackbody radiation spectrum (i.e., all wavelengths)P is:in, TOT (T) = ΩAεσT4/π

where: Pin, TOT(T) = ΩAεσT4/π where: Int. J. Turbomach. Propuls. Power 2020, 5, 31 4 of 16

4 Pin, TOT(T) = ΩAεσT /π where:

T is the blackbody temperature in K; • σ = 5.67 10 8 W m 2 K 4 is the Stefan–Boltzmann constant; • × − · − · − A = πd2/4 = 1.25664 10 7 m2 is the fibre core area; • × − Ω = πtan2(θ) is the maximum solid acceptance angle of the Au-coated fibre, with θ the • maximum acceptance half-angle of the Au-coated fibre, which is related to the NA of the fibre as: NA = nsin(θ) = 0.22

As the refractive index of air is n 1, the maximum solid acceptance angle can be re-written as: ≈ Ω = πtan2(arcsin(NA)) 0.16 sr ≈ Hence, the total blackbody radiation power coupled into the optical ﬁbre is:

16 4 P (T) 3.624 10− T W in, TOT ≈ × The fractional power coupled into the optical ﬁbre over the wavelength range λ = (0.3–2.4) µm, Pin(T), can be calculated numerically or through tabulated values, considering the wavelength-temperature products. With such a model, approximately 10 mW of optical thermal radiation is coupled into the optical ﬁbre for T 2500 K; however, for T = 300 K: P (T) < 10 pW. ≈ in To calculate the optical power measured by each photodetector and the associated voltage signals, the losses in the optical transmission line from the sensor head to the detectors need to be considered. To estimate the signals accurately, the following contributions need to be taken into account:

1. The transmission factor of the sapphire window placed in front of the fibre end-facet, due to Fresnel reflection losses (7% at each interface/surface): t = 0.93 0.93 = 0.8649. 0 × 2. The transmission factor at the end-facet of the Au-coated fibre, due to Fresnel reflection losses: t1 = 0.96. 3. Transmission losses of 12 m of fibre (2 m sensor + 10 m of extension lead fibre)—considering that typical losses for large-core multi-mode fibre are of the order of 10 dB/km or less at λ = (0.6–1.6) µm: t = 0.12 dB 0.973. fibre − ≈ 4. Losses due to optical connectors (3), typically of the order of 0.3 dB each—i.e., a transmission factor tconnector = 0.933 5. The splitting ratio of the 1 3 optical coupler/splitter: t 0.333. × splitter ≈ 6. The optical transmission (tfilter) of the bandpass filters in the photodetector assemblies—it is worth noting that the filters used have different values of optical transmission peak and Full-Width-at-Half Maximum (FWHM):

t850 nm = 70%; # t1050 nm = 45%; # t1300 nm = 40%; # FWHM = 40 nm 8 nm; 850 nm ± # FWHM = 10 nm 2 nm; 1050 nm ± # FWHM = 30 nm 6 nm. 1300 nm ± # Hence, the optical power incident on the photodetectors can be calculated as: Int. J. Turbomach. Propuls. Power 2020, 5, 31 5 of 16

3 P (λ, T) = t t t t (tconnector) t (λ)P (λ, T) 0.22t (λ)P (λ, T) (1) i 0 1 fibre splitter filter in ≈ filter in Finally, to calculate the voltage signal, we also need to consider the photodetector transimpedance gain Gi [V/A] and responsivity R(λi) [A/W], which is a function of wavelength; hence: Z Z Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 5 of 15 Vi = GiRi(λ)Pi(λ, T)dλ = 0.22Gi tfilter(λ)Ri(λ)Pin(λ, T)dλ (2) where: 𝑃(𝜆, 𝑇) = 𝐴𝛺𝐿(𝜆, 𝑇) ( ) = ( ) with: Pin λ, T AΩLb λ, T with: 2𝑐 1 2𝑐 𝐿 (𝜆, 𝑇) = 2c 1 ≈ 2c 𝑒⁄ 1 ⁄ 1 c2/λT Lb(λ, T) = 𝜆 𝑒 −1 𝜆 e− λ5 ec2/λT 1 ≈ λ5 where c1 and c2 are the first and second radiation constants− equal to 0.59552197 × 10−16 W·m−2·sr−1 and c c 16 2 1 where 1 and −2 are the first and second radiation constants equal to 0.59552197 10− W m− sr− and 1.438769 × 10 2 m·K, respectively, and the expression after the ≈ symbol is the× Wien approximation· · 1.438769 10− m K, respectively, and the expression after the symbol is the Wien approximation valid for ×c2 >> λT. · ≈ valid for c >> λT. Equations2 (1) and (2) were evaluated at different temperatures, with the results compared with Equations (1) and (2) were evaluated at different temperatures, with the results compared with preliminary experimental data. These showed a lower signal than expected (by a factor of ~2), likely preliminary experimental data. These showed a lower signal than expected (by a factor of ~2), likely due due to extra connection losses. This was fed back into the model, which gave the results shown in to extra connection losses. This was fed back into the model, which gave the results shown in Figure4 Figure 4 in terms of optical power incident onto the photodetectors—noise floors are shown only for: in terms of optical power incident onto the photodetectors—noise floors are shown only for: G = 0 dB, G = 0 dB, B = 12 MHz (highest noise floor); G = 20 dB, B = 1 MHz and G = 70 dB, B = 3 kHz (lowest B = 12 MHz (highest noise floor); G = 20 dB, B = 1 MHz and G = 70 dB, B = 3 kHz (lowest noise floor). noise floor).

Figure 4.4.Blackbody Blackbody radiation radiation power power incident incident onto photodetectorsonto photodetectors as a function as a of function blackbody of temperature. blackbody temperature. Noise ﬂoor was estimated for each photodetector as: Noise floor was estimated for each photodetector as: 1/2 Pn, i = NEP B / RMAX/R(λi) 𝑃, =𝑁𝐸𝑃𝐵× ×𝑅/𝑅(𝜆) where NEP isis thethe NoiseNoise EquivalentEquivalent PowerPower andand RRMAXMAX isis the the peak peak responsivity—both responsivity—both provided in the photodetector datasheets. Figure 44 showsshows that,that, in any case, the instrument instrument should should be be capable capable of of measuring measuring temperatures temperatures T T> >16001600 K Kat atall all wavelengths, wavelengths, with with photodetectors photodetectors set set at at GG == 00 dB dB and and B = 12 MHz.MHz. However, However, considering that the maximum sampling sampling rate rate of of the the DAQ DAQ system system is is ffMAXMAX = =1 MHz,1 MHz, a gain a gain setting setting of ofG = 20 dB (B = 1 MHz) would allow measurement of temperatures as low as ~1000 K with the 1300 nm photodetector (but not at λ1 = 850 nm and λ2 = 1050 nm), with no penalty in terms of speed. The minimum and maximum temperatures measurable by the instrument are dictated, respectively, by the noise level (experimentally measured as ~1 mV for most values of G) and the saturation level (~10 V) of the photodetectors. To find the photodetector settings that optimise the measurable temperature range, Equation (2) was evaluated at different temperatures for different G and B settings of the photodetectors. Voltage signals generated by the three photodetectors were plotted versus temperature for all values of G and B. Figure 5 shows two of these plots for representative values of G and B.

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•G = 20With dB (aB gain= 1 MHz) of G would= 20 dB allow (B = measurement 1 MHz—Figure of temperatures 5a), the instrument as low as can ~1000 measure K with a the minimum 1300 nm photodetectortemperature (but of not ~1150 at λ K1 at= 850a single nm andwavelengthλ2 = 1050 (λ nm),3 = 1300 with nm) no or penalty ~1400 K in at terms all three of speed. wavelengths. • WithThe minimum a gain of andG = maximum30 dB (B = temperatures 260 kHz), the measurable minimum by measurab the instrumentle temperature are dictated, can respectively,be brought by thedown noise to level ~1025 (experimentally K for single-wavelength measured asmeasurement ~1 mV for most (λ3 = values 1300 nm) of G )and and ~1275 the saturation K at all three level (~10wavelengths, V) of the photodetectors. but at cost of Toreduced find the sampling photodetector speed ( settingsf ≤ B = 260 that kHz), optimise while the still measurable avoiding temperaturesaturation range, at 3300 Equation K, our (2) ma wasximum evaluated temperature at different of interest. temperatures for different G and B settings •of theWith photodetectors. a gain of G ≥ Voltage40 dB (Bsignals = 90 kHz—Figure generated by5b), the the three photodetectors photodetectors would were start plotted saturating versus at temperatureTMAX < 3300 for all K valuesand their of G bandwidthand B. Figure would5 shows decrease two ofsignificantly, these plots fordown representative to B = 3 kHz values at G of= 70G and BdB..

Figure 5. Modelled signals from photodetectors vers versusus blackbody blackbody temperature temperature at at different diﬀerent G and B settings: ( (aa)) GG == 2020 dB dB and and BB == 11 MHz, MHz, (b (b) )GG == 4040 dB dB and and BB = =9090 kHz. kHz.

With a gain of G = 20 dB (B = 1 MHz—Figure5a), the instrument can measure a minimum • Hence, the optimum photodetector gain is G = 30 dB, which allows temperatures above 1025 K temperature of ~1150 K at a single wavelength (λ3 = 1300 nm) or ~1400 K at all three wavelengths. to be measured for λ3 = 1300 nm, or temperatures above 1275 K to be measured for all wavelengths, With a gain of G = 30 dB (B = 260 kHz), the minimum measurable temperature can be brought with• a maximum sampling rate f ≤ B = 260 kHz. down to ~1025 K for single-wavelength measurement (λ = 1300 nm) and ~1275 K at all three 3

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wavelengths, but at cost of reduced sampling speed (f B = 260 kHz), while still avoiding ≤ saturation at 3300 K, our maximum temperature of interest. With a gain of G 40 dB (B = 90 kHz—Figure5b), the photodetectors would start saturating at • ≥ TMAX < 3300 K and their bandwidth would decrease signiﬁcantly, down to B = 3 kHz at G = 70 dB.

Hence, the optimum photodetector gain is G = 30 dB, which allows temperatures above 1025 K to be measured for λ3 = 1300 nm, or temperatures above 1275 K to be measured for all wavelengths, with a maximum sampling rate f B = 260 kHz. Int. J. Turbomach. Propuls. Power 2020, 5, x FOR≤ PEER REVIEW 7 of 15 3. Instrument Calibration 3.1. Test Rig 3.1. Test Rig The instrument was calibrated using a Thermo Gauge blackbody radiation furnace and a The instrument was calibrated using a Thermo Gauge blackbody radiation furnace and a KE- KE-Technologie GmbH LP3 linear pyrometer calibrated traceably to the ITS-90 [3], with the Technologie GmbH LP3 linear pyrometer calibrated traceably to the ITS-90 [3], with the stainless- stainless-steel tube of the packaged sensor ﬁlled with sand to avoid overheating the Au-coated steel tube of the packaged sensor filled with sand to avoid overheating the Au-coated fibre that could ﬁbre that could be irreversibly damaged. A photograph of part of the test rig is shown in Figure6: be irreversibly damaged. A photograph of part of the test rig is shown in Figure 6: the hot Thermo the hot Thermo Gauge blackbody furnace and temperature sensor are visible in the background and Gauge blackbody furnace and temperature sensor are visible in the background and foreground, foreground, respectively. The latter is placed on a stainless-steel V-groove mounted on an optical respectively. The latter is placed on a stainless-steel V-groove mounted on an optical breadboard and breadboard and safely held in place by removable brackets bolted to the breadboard. This breadboard is safely held in place by removable brackets bolted to the breadboard. This breadboard is installed on installed on a motorised stage, controlled by a computer, for horizontal and vertical alignment. The LP3 a motorised stage, controlled by a computer, for horizontal and vertical alignment. The LP3 (not (not visible in Figure6) is mounted on the same framework, so that it can be easily moved in front of visible in Figure 6) is mounted on the same framework, so that it can be easily moved in front of the the blackbody, in place of the sensor, to measure the temperature at each setpoint of the calibration. blackbody, in place of the sensor, to measure the temperature at each setpoint of the calibration.

Figure 6. PhotographPhotograph of the the calibration calibration furnace: the the instru instrumentment sensor, housed in a steel tube, is sitting on the V-grooveV-groove placedplaced inin front front of of blackbody blackbody furnace, furnace, ready ready to to be be manually manually moved moved in andin and out out of itof for it dynamicfor dynamic calibration calibration at a at set a temperature.set temperature.

Data from the instrument were acquired using a NI LabVIEW program written in-house and executed on the PC that is part of the system, whereas the blackbody furnace was controlled with a separate desktop computer that also controls thethe motorisedmotorised framework.framework.

3.2. Test Method The instrument was configured with the photodetectors set with optimum gain G = 30 dB (B = 260 kHz) and the sampling rate set at f = 250 kHz. At the beginning of the calibration, the voltage offset from the three photodetectors was measured once, to zero the photodetectors. The instrument was calibrated in the temperature range T = (1073–2873) K, in steps of ∆T = 200 K, according to the following procedure:

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3.2. Test Method The instrument was conﬁgured with the photodetectors set with optimum gain G = 30 dB (B = 260 kHz) and the sampling rate set at f = 250 kHz. At the beginning of the calibration, the voltage oﬀset from the three photodetectors was measured once, to zero the photodetectors. The instrument was calibrated in the temperature range T = (1073–2873) K, in steps of ∆T = 200 K, according to the following procedure:

1. The blackbody furnace was set at the required temperature set-point. 2. The temperature of the blackbody cavity was monitored using the LP3. 3. Once the blackbody temperature reached stability, a measurement was taken from the LP3, by measuring the average and standard deviation over ~30 s (the LP3 is sampled at 1 Hz). 4. The LP3 was moved out of the way and the sensor moved into place, so that it was in line with and parallel to the long axis of the blackbody, as shown in Figure6. 5. Data acquisition and logging were started on the instrument. 6. Manually, the sensor was quickly moved into and out of the blackbody (within a few seconds). 7. Two measurements were made at each set-point temperature.

3.3. Test Data Analysis Method The raw voltage signals from the three photodetectors of the optoelectronic interrogator were analysed to find the optimum calibration point in each signal. This is explained in Figure7, showing typical measurement traces—the signal from the 1050 nm photodetector was the lowest, because of the combined effect of the responsivity of the photodetector and the transmission and the bandwidth of the optical bandpass filter. Considering Figure7b:

t < 1.3 s: the blackbody cavity had a temperature gradient along the cavity wall and across its rear • surface, it was hotter to the outside, and this was seen as the sensor approached: the radiance signal increased as the field of view of the sensor was initially filled. t (1.3–1.6) s: the signal fell as the sensor progressively saw more of the cooler central section of • ≈ the back wall. t (1.6–1.77) s: there was a period when the blackbody temperature fell due to heat lost to the • ≈ cold sensor. t (1.77–1.92) s: as the sensor was withdrawn, the hotter regions of the blackbody cavity were • ≈ seen again, so that the signal increased. t > 1.92 s: the signal decreased, as the sensor was withdrawn from the blackbody cavity. • The maximum in the signal during sensor removal was lower than during insertion. This is • consistent with the cooling of the blackbody cavity. The voltages recorded for calibration were chosen at the inflection point of each signal, • highlighted by the blue circle, as it corresponds to the point when the field of view of the fibre is filled with thermal radiation from the back wall, before any further cooling caused by the sensor. Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 8 of 15

5. Data acquisition and logging were started on the instrument. 6. Manually, the sensor was quickly moved into and out of the blackbody (within a few seconds). 7. Two measurements were made at each set-point temperature.

3.3. Test Data Analysis Method The raw voltage signals from the three photodetectors of the optoelectronic interrogator were analysed to find the optimum calibration point in each signal. This is explained in Figure 7, showing Int. J. Turbomach.typical measurement Propuls. Power traces—the2020, 5, 31 signal from the 1050 nm photodetector was the lowest, because of9 of 16 the combined effect of the responsivity of the photodetector and the transmission and the bandwidth of the optical bandpass filter.

FigureFigure 7. Typical 7. Typical calibration calibration measurement measurement traces: traces: the the black blackline line inin thethe middlemiddle of chart ( (aa) )identifies identiﬁes the pointsthe used points for used calibration; for calibration; (b) is a(b close-up) is a close-up on the on 1300the 1300 nm nm signal signal and and its its calibration calibration point.point.

CalibrationConsidering was Figure performed 7b: by ﬁtting experimental data to the Planckian version of the Sakuma–Hattori• t < 1.3 s: equationthe blackbody with cavity three adjustablehad a temperature parameters gradientAi, alongBi and theci forcavity each wall wavelength and across λitsi [4]: rear surface, it was hotter to the outside, and this was seen as the sensor approached: the radiance signal increased as the field of view ofA thei sensor was initially filled. Vi = (3) eci/(λi T+Bi) 1 · − At each calibration point, the two voltage measurements for each wavelength/photodetector were averaged; each average was then converted into temperature using the inverse function of Equation (3):

c 1 T = i (4) i A λi ln i + 1 Vi

Optimum values of the adjustable parameters were found using the Generalized Reduced Gradient (GRG) solving method for smooth non-linear problems, to minimise the sum of the squares of temperature diﬀerences with the LP3. Int. J. Turbomach. Propuls. Power 2020, 5, 31 10 of 16

3.4. Calibration Test Results The average signal at each setpoint was measured for each wavelength/photodetector and plotted versus the set-point temperature measured from the LP3 linear pyrometer. Figure8 shows good agreement between experimental data and the theoretical model at G = 30 dB, as used for the calibration, with the signal from the 1300 nm photodetector higher than predicted, most likely due to overestimated losses, as a single ﬁgure was used for all three wavelengths. Figure8 also shows that the instrument can measure a temperature as low as 1073 K at λ3 = 1300 nm or 1273 K at all three wavelengths—these minimum temperatures match with those expected from the theoretical model. Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 10 of 15

Figure 8. Experimental data compared with theoretical model.

Using the inverse PlanckPlanck function—i.e.function—i.e. Equation (4)—average voltage measurements for each wavelength at each set-point were converted into temperatures and the adjustable parameters were optimised to minimise the sumsum ofof thethe squaressquares ofof calibrationcalibration residuals.residuals. The optimum calibration i coecoefficientsfficients areare shown inin Table1 1( (Bi coefficientscoefficients are not included, because they were found to be equal to zero)zero) andand thethe residuals residuals are are shown shown in in Figure Figure9, showing 9, showing relative relative temperature temperature di fferences differences within within1% ± (absolute±1% (absolute differences differences are within are within15 K). ±15 K). ± Table 1.1. Optimum values of the adjustable calibration coecoefficients,fficients, minimising sum of squares of relative errors.

λi [nm] λi [nm] AAi [V]i [V] ci [µm K]c i [µm K] 850850 527.6 527.6 14,082.2 14,082.2 10501050 53.0 53.0 14,431.8 14,431.8 13001300 91.7 91.7 14,307.3 14,307.3

Figure 9. Calibration residuals.

Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 10 of 15

Figure 8. Experimental data compared with theoretical model.

Using the inverse Planck function—i.e. Equation (4)—average voltage measurements for each wavelength at each set-point were converted into temperatures and the adjustable parameters were optimised to minimise the sum of the squares of calibration residuals. The optimum calibration coefficients are shown in Table 1 (Bi coefficients are not included, because they were found to be equal to zero) and the residuals are shown in Figure 9, showing relative temperature differences within ±1% (absolute differences are within ±15 K).

Table 1. Optimum values of the adjustable calibration coefficients, minimising sum of squares of relative errors.

λi [nm] Ai [V] ci [µm K] 850 527.6 14,082.2 Int. J. Turbomach. Propuls. Power 2020, 5, 31 11 of 16 1050 53.0 14,431.8 1300 91.7 14,307.3

Figure 9. Calibration residuals.

Having calibrated the sensor, the maximum measurable temperatures can be estimated by extrapolation of the Planck function in Equation (3), until the photodetector saturation level (VMAX = 10 V) is reached or, more accurately, by replacing this value in the inverse Planck function—i.e., Equation (4). In a similar way, minimum measurable temperatures were estimated by replacing the noise level (V 1 mV) in the inverse Planck function. Table2 shows minimum and noise ≈ maximum measurable temperatures.

Table 2. Minimum and maximum measurable temperatures.

λi [nm] TMIN [K] TMAX [K] 850 1260 4160 1050 1260 7470 1300 960 4740

4. Dynamic Tests

4.1. Test Rig To demonstrate the speed of the instrument, dynamic tests were performed using theatrical flash charges [5] in the pyrotechnic facility at NPL (National Physical Laboratory). This consists of a vented enclosure where pyrotechnic charges, placed on a stage, are remotely triggered with a controller that is connected and synchronised with the instrument. The sensor is mounted such that its front end protrudes into the enclosure with its tip ~15 cm above and ~5 cm away from the centre of the charge. The optimum position of the sensor is based on experience from previous tests, when we also conducted absorption/transmission experiments, from which no optical transmission was observed during the explosion, thus suggesting that the fireball is opaque and supporting our blackbody assumption, and an initial absorption coefficient α = 0.25 cm 1 was estimated at λ 850 nm. 0 − ≈ 4.2. Test Method Two sets of explosion tests were performed: a preliminary set of 3 tests with medium pyrotechnic charges and another set of 3 tests with large pyrotechnic charges. In all cases, the photodetector gain was set at G = 30 dB, as the instrument was calibrated only with this setting. Sampling rate and number Int. J. Turbomach. Propuls. Power 2020, 5, 31 12 of 16 of samples were set, respectively, at f = 50 kHz and N = 50,000 (giving an acquisition time t = N/f = 1 s) for the first 4 tests and then at f = 250 kHz and N = 25,000 (giving an acquisition time t = N/f = 0.1 s) for the last 2 tests. Sampling rate f and number of samples N were initially chosen based on experience from previous explosion tests, to collect enough data at a high speed but without having to record excessive data. N and f were changed in the last two tests, based on observations from the previous test, again to avoid recording data where no signal was present, but also to capture finer details and test the maximum sampling speed.

4.3. Test Results The preliminary set of tests with medium pyrotechnic charges (shown in Figure 10) demonstrated that f = 50 kHz was sufficient to measure the rapid temperature rise and decay and identify signal structure in between. Variability in temperature evolution was observed from test to test—this was to be expected as no two charges are the same. Nevertheless, there was a good correlation among all traces for a given test, although the temperature agreement was poor—in particular, the temperature estimated from the signal at λ3 = 1300 nm was significantly lower than the other two, by up to ~600 K. This suggested that the effective emissivity at the longest wavelength was significantly less than unity—i.e., the blackbody condition necessary for successful thermometry is not met. On the contrary, the set of tests with large pyrotechnic charges shown in Figure 11 produced more consistent results and better agreement among temperatures measured at different wavelengths, meaning that the blackbody Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 12 of 15 condition (ε = 1) is more closely met than with medium charges. In explosion tests with large charges, thecharges. maximum In explosion temperatures tests with estimated large charges, at different the wavelengths maximum temperatures agree with each estimated other within at different up to ~137wavelengths K or ~4.5%. agree with each other within up to ~137 K or ~4.5%.

Figure 10. Time trend of temperaturestemperatures for pyrotechnic tests with medium charges—temporal ooffsetﬀset introduced forfor clarity.clarity.

Figure 11 shows again that a sampling rate of f = 50 kHz was still fast enough to capture events from large charges, despite shorter pulse duration (<20 ms versus ~200 ms), sharper rise time (<1 ms versus ~10 ms) and faster decay times (~10 ms versus ~100 ms) than medium charges. The sampling rate was increased to f = 250 kHz in the last two trials to test the maximum sampling frequency allowed by the gain set in the photodetectors (G = 30 dB). A temperature rise of up to ~3.25 K/µs was estimated for explosions of large charges.

Figure 11. Time trend of temperatures for pyrotechnic tests with large charges—temporal offset introduced for clarity.

Figure 12 shows that large pyrotechnic charges produced not only more consistent results, but also higher peak temperatures than medium charges, by ~700 K. It is also worth observing that the

Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 12 of 15

charges. In explosion tests with large charges, the maximum temperatures estimated at different wavelengths agree with each other within up to ~137 K or ~4.5%.

Figure 10. Time trend of temperatures for pyrotechnic tests with medium charges—temporal offset introduced for clarity.

Figure 11 shows again that a sampling rate of f = 50 kHz was still fast enough to capture events from large charges, despite shorter pulse duration (<20 ms versus ~200 ms), sharper rise time (<1 ms versus ~10 ms) and faster decay times (~10 ms versus ~100 ms) than medium charges. The sampling Int.rate J. Turbomach. was increased Propuls. Powerto f =2020 250, 5 ,kHz 31 in the last two trials to test the maximum sampling frequency13 of 16 allowed by the gain set in the photodetectors (G = 30 dB). A temperature rise of up to ~3.25 K/µs was estimated for explosions of large charges.

FigureFigure 11. 11.Time Time trend trend ofof temperaturestemperatures forfor pyrotechnic tests tests with with large large charges—temporal charges—temporal offset oﬀset introducedintroduced for for clarity. clarity.

FigureFigure 11 12 shows shows again that large that a pyrotechnic sampling rate charges of f =produced50 kHz wasnot only still fastmore enough consistent to capture results, eventsbut fromalso large higher charges, peak temperatures despite shorter than pulse medium duration charges, (<20 by ms ~700 versus K. It ~200 is also ms), worth sharper observing rise time that (

FigureFigure 12. 12.Plot Plot of of maximum maximum temperatures temperatures versusversus test nu number.mber. The The inset inset on on the the upper upper left left shows shows some some statistics: Mean TMAX and σ (TMAX) are, respectively, the average and the standard deviation of peak statistics: Mean TMAX and σ (TMAX) are, respectively, the average and the standard deviation of peak temperatures measured at different λ. temperatures measured at diﬀerent λ.

In any case, having calibrated our instrument with a blackbody cavity, it is possible to state that the fireball will have reached at least the highest measured temperature, regardless of the emissivity and of the blackbody assumption. In fact, if the blackbody assumption is made (ε = 1), but the true emissivity is ε < 1 and constant with wavelength (i.e., the fireball is not a blackbody, but a grey body), then the difference between the true temperature T and the measured temperature, also called colour temperature, Tc, can be written as: 1 1 𝜆 = + ln (𝜀) 𝑇 𝑇 𝑐 From this expression, an error in emissivity of Δ𝜀 will lead to an error in the inferred temperature: 𝜆𝑇 Δ𝑇 = − Δ𝜀 𝑐

where: Δ𝑇 = 𝑇 −𝑇 and Δ𝜀 = 1 − ε. From the expression above, it is clear that the temperature error is temperature- and wavelength- dependent and that a grey body would not provide identical temperature readings at different wavelengths (as in the blackbody case), as shown also in Figure 13, where temperature error is plotted versus wavelength at three given emissivities at T = 3000 K, and in Figure 14, where temperature error is plotted versus true temperature at the three wavelengths used for ε = 0.8. It is worth observing that, for a given emissivity, the error is smaller for shorter wavelength, which agrees with the experimental findings (see Figure 12).

Int. J. Turbomach. Propuls. Power 2020, 5, 31 14 of 16

In any case, having calibrated our instrument with a blackbody cavity, it is possible to state that the fireball will have reached at least the highest measured temperature, regardless of the emissivity and of the blackbody assumption. In fact, if the blackbody assumption is made (ε = 1), but the true emissivity is ε < 1 and constant with wavelength (i.e., the fireball is not a blackbody, but a grey body), then the difference between the true temperature T and the measured temperature, also called colour temperature, Tc, can be written as: 1 1 λ = + ln(ε) T Tc c2 From this expression, an error in emissivity of ∆ε will lead to an error in the inferred temperature:

λT2 ∆T = ∆ε − c2

where: ∆T = Tc T and ∆ε = 1 ε. − − From the expression above, it is clear that the temperature error is temperature- and wavelength-dependent and that a grey body would not provide identical temperature readings at diﬀerent wavelengths (as in the blackbody case), as shown also in Figure 13, where temperature error is plotted versus wavelength at three given emissivities at T = 3000 K, and in Figure 14, where temperature error is plotted versus true temperature at the three wavelengths used for ε = 0.8. It is worth observing that, for a given emissivity, the error is smaller for shorter wavelength, which

Int. J. agreesTurbomach. with Propuls. the experimental Power 2020, 5,ﬁndings x FOR PEER (see REVIEW Figure 12). 14 of 15

FigureFigure 13. Plot 13. Plotof temperature of temperature erro errorr versus versus wavelength wavelength atatT T= = 30003000 K K for for di differentﬀerent values values of emissivity.of emissivity.

Figure 14. Plot of temperature error versus temperature for ε = 0.8 and for the three chosen wavelengths.

5. Conclusions In summary, a novel ultra-high-speed combustion pyrometer, based on collection of thermal radiation via an optical fibre, was successfully designed, developed and tested. The instrument was traceably calibrated to the ITS-90 over the temperature range T = (1073–2873) K with residuals <1%. Dynamic tests with pyrotechnic charges demonstrated that the instrument can measure rapid (sub- ms) events, due to its high sampling rate (up to 250 kHz): a temperature rise of up to ~3.25 K/µs was estimated for explosions of large pyrotechnic charges. The accuracy of the temperature measurements can be assessed by considering the extent of agreement between readings at the three wavelengths—a self-diagnostic feature that is a critical strength of the technique. However, even when agreement between temperatures is poor, we can say, with a high level of confidence, that the fireball temperature is at least that reported by the reading at 850 nm. In future, the instrument will be tested in a maritime test engine.

Int. J. Turbomach. Propuls. Power 2020, 5, x FOR PEER REVIEW 14 of 15

Int. J. Turbomach. Propuls. Power 2020, 5, 31 15 of 16 Figure 13. Plot of temperature error versus wavelength at T = 3000 K for different values of emissivity.

Figure 14.14. PlotPlot of of temperature temperature error error versus versus temperature temperature for ε = 0.8for andε = for 0.8 the and three for chosen the three wavelengths. chosen wavelengths. 5. Conclusions 5. Conclusions In summary, a novel ultra-high-speed combustion pyrometer, based on collection of thermal radiationIn summary, via an optical a novel ﬁbre, ultra-high-speed was successfully combustion designed, pyrometer, developed based and on tested. collection The instrumentof thermal wasradiation traceably via an calibrated optical fibre, to the was ITS-90 successfully over the de temperaturesigned, developed range T and= (1073–2873) tested. The K instrument with residuals was

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