Diode-laser sensor for monitoring multiple combustion parameters in pulse detonation engines

Proceedings of the Combustion Institute, Volume 28, 2000/pp. 587–594

DIODE-LASER SENSOR FOR MONITORING MULTIPLE COMBUSTION PARAMETERS IN PULSE DETONATION ENGINES SCOTT T. SANDERS, JEFFREY A. BALDWIN, THOMAS P. JENKINS, DOUGLAS S. BAER and RONALD K. HANSON High Temperature Gasdynamics Laboratory Department of Mechanical Engineering Stanford University Stanford, CA 94305, USA

Diode-laser absorption spectroscopy techniques have been adapted and applied for in situ measurements of pertinent combustion parameters in pulse detonation engines (PDEs). A sensor employing five multiplexed diode lasers operating in the 1300–1800 nm spectral region has been developed for monitoring gas temperature, H2O concentration, liquid fuel concentration, and soot volume fraction. Gas temperature is determined from the ratio of H2O absorbances at different wavelengths; water mole fraction and fuel and soot volume fractions are determined from the measured gas temperature and absorbances at selected wavelengths. The sensor’s time response (0.5 ls) and non-intrusive nature make it suitable for measurements in the hostile environment generated by PDEs. The sensor was used to monitor a 4 cm diameter PDE operating on a JP-10/oxygen aerosol. Measurements revealed charges of non-uniform equivalence ratio at ignition. Detonations processing such charges reached 95% of the Chapman-Jouget velocity and gas pressures predicted for a stoichiometric, uniform load. Gas temperature and H2O concentration, however, reached only ⬃50% of the Chapman-Jouget predictions, as a result of the decreasing fuel concentration along the length of the engine. The sensor also revealed the presence of hot H2O for a long duration (⬎100 ms) relative to the duration of the pressure pulse (⬃500 ls) in the blowdown following the detonation. The engine performance information recorded by the sensor is expected to enhance PDE modeling and optimization efforts, potentially enabling PDE combustion control.

Introduction Pulse detonation engines (PDEs) have recently received increased attention in the aeropropulsion community, owing to their high theoretical specific impulse and structural simplicity [1]. Experimental studies of PDEs have been previously founded primarily on pressure data. Sensors for other engine properties of interest have been needed but generally unavailable. The PDE is a challenging measurement environment because of its high pressures (up to 100 atm), high temperatures (up to 4000 K), and multiphase flow field (soot and liquid fuel droplets are possible). Under these conditions, absorption features are severely broadened, prohibiting traditional wavelength-tuning absorption spectroscopy techniques. In addition, reliable spectroscopic data for these conditions are sparse, creating a need for basic spectroscopic studies. Moreover, at PDE conditions, soot emits strong infrared radiation, creating an additive noise that must be removed from laser transmission signals. Soot and liquid fuel impose a wavelengthdependent extinction of the probe beams that must be distinguished from molecular absorption. Flow field density gradients induce beam-steering effects,

and stress-induced birefringence at PDE optical ports modulates transmitted laser intensities [2]. The PDE’s unsteady nature exacerbates these difficulties by demanding high-bandwidth detection. The sensor described here addresses these challenges and has demonstrated the capacity to obtain quantitative in situ measurements of gas temperature, H2O concentration, liquid fuel concentration, and soot volume fraction in PDEs. Theory The theoretical basis for determining gas temperature and species concentration in combustion flows from measured molecular absorbances at multiple wavelengths has been described previously [3– 5]. In brief, the Beer-Lambert relation [6] is used to determine gas temperature from the ratio of measured H2O absorbances at multiple wavelengths. Using an independent measurement of pressure, the water mole fraction is then determined from the measured absorption at a selected wavelength using the known absorption line strength at the measured temperature. To enable measurements at high pressures, a fixed-wavelength strategy developed previously [5,7] is used in this work.

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Fig. 1. Calculated absorption spectra for equilibrium products of stoichiometric JP-10/O2 at 3000 K and 15 atm.

TABLE 1 Measured refractive indices of liquid JP-10 used in computations k (lm) 1.29–1.39 1.65 1.8

Refractive Index 1.484 Ⳮ i 0.0 1.479 Ⳮ i 0.0 1.477 Ⳮ i 0.0

Calculated near-IR absorption spectra for equilibrium products of stoichiometric JP-10/O2 at representative PDE conditions of T ⳱ 3000 K and P ⳱ 15 atm are shown in Fig. 1. Based on simulated spectra such as these, the H2O-resonant wavelengths, k1 ⳱ 1343.299 nm (m1 Ⳮ m3 band), k2 ⳱ 1391.672 nm (2m1, m1 Ⳮ m3 bands), and k3 ⳱ 1799.179 nm (2m2 Ⳮ m3 ← m2 hot band), indicated in Fig. 1 were chosen for maximum sensitivity to temperature over the 900–3300 K range. Because transitions from three different vibrational bands contribute to the measured absorbances, we must assume that the H2O vibrational temperature equals the H2O rotational temperature in order to report the H2O temperature. Previous work [8] has justified this assumption by showing that the vibrational relaxation time for the H2O at our conditions is ⬍100 ns. The non-resonant wavelengths knr1 ⳱ 1290 nm and knr2 ⳱ 1643 nm were chosen to monitor extinction due to JP-10 droplets and soot. JP-10 droplets in the unburned aerosol are assigned a simplified size distribution by interpreting the ratio of extinction at multiple wavelengths using Mie scattering theory and the measured JP-10 refractive indices shown in Table 1. From the measured size distribution and the extinction at a selected wavelength, the line-of-sight averaged droplet volume fraction is determined. This process has been outlined previously [9]. When Rayleigh regime soot is present, soot volume fraction (fvol) is calculated based on non-resonant wavelength extinction and established theory [10]. Uncertainties in soot refractive index commonly cause large uncertainties in soot volume fraction measurements [11]. To calculate soot volume fraction in this work, we use the values of soot refractive index reported by Dalzell and Sarofim [12] because they are the most widely used and are thought to be among the most reliable [11]. The resulting uncertainty in the reported values of soot volume fraction is estimated at 50%. The uncertainty in soot refractive index does not introduce significant uncertainty in the reported gas temperature, H2O concentration, or fuel properties.

Spectroscopic Parameters

Fig. 2. Variation of spectral absorption coefficient at 5558.090 cmⳮ1 with temperature.

The spectroscopic parameters for the transitions near k1 and k2 have been detailed [13] and verified [5] previously. To maintain temperature sensitivity to 3300 K, an absorption feature near k3 consisting of five high-temperature H2O lines was employed. Diode-laser absorption measurements of pure H2O in a heated static cell and H2O in an ethylene/air flame were used to improve the HITRAN96/HITEMP [14] spectroscopic data available in this spectral region. The resulting updated model [15] for the spectral absorption coefficient at k3 is compared with

DIODE-LASER SENSOR FOR PDES

Fig. 3. Experimental schematic and engine timing diagram.

the HITEMP model in Fig. 2. The large discrepancy appears to be due primarily to line position errors of ⬃0.04 cmⳮ1 in the HITEMP database. Line position errors of this magnitude have been previously identified for H2O at 2.0 lm [16]. The updated model provides the desired spectral absorption coefficient to within Ⳳ2% for T ⬍ 2100 K. Agreement between the PDE gas temperature calculated using this model and the PDE soot temperature obtained by two-color pyrometry suggests that the model maintains Ⳳ10% accuracy to T ⬃ 3300 K. Experimental Method The sensor was demonstrated in the 3.8 cm diameter pulsed detonation-initiation tube at the Naval Postgraduate School in Monterey, California, shown schematically in Fig. 3 with a timing diagram. This PDE and the detonation pressure histories developed in it have been previously characterized [17]. Each cycle begins with an oxygen purge injected through the head end atomizer that lasts approximately 20 ms. Subsequently, a liquid JP-10/oxygen aerosol is injected by the atomizer for ⬃20 ms. After a further delay of ⬃20 ms, the mixture is ignited by a capacitive discharge igniter 7 cm from the head end wall. The detonation wave builds and travels toward the tail end at approximately 2 km/s. Pressure histories are recorded at several axial locations along the tube using piezoelectric transducers. Each of five distributed feedback (DFB) diode lasers in a remote control room send light via standard communications-grade optical fiber (50 lm core) to

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the measurement station 5 cm from the tail end of the PDE. All lasers except the laser at k2 are operated at fixed wavelength; k2 is tuned ⬃1 cmⳮ1 at a 30 kHz repetition rate over the target H2O absorption feature. The light passes through a depolarizer to mitigate the effects of stress-induced birefringence at the sapphire ports. The beam traverses the 3.8 cm path through the engine and is demultiplexed (into its component wavelengths) by a diffraction grating (830 g/mm, kb ⳱ 1.2 lm). The transmitted light is monitored by germanium detectors (2 MHz bandwidth, 3 mm diameter). The detector voltages are digitized using a 12 bit analog to digital card installed in a personal computer. In addition to demultiplexing the wavelengths, the grating rejects flow field emission. However, during the high-pressure portions of the detonation cycle, blackbody radiation from soot was still able to contaminate the laser transmission signals. Whenever this occurred, the emission was further rejected by modulating the laser intensities at ⬃1 MHz with acousto-optic modulators and applying digital lockin amplification to the recorded signals. The grating and lenses in the transmitted-beam collection path have been arranged for minimum sensitivity to flow-induced beam steering. By simulating beam steering using wedge windows, this collection system was found to be insensitive (to within 0.1%) to angular beam deflections of up to 2.6⬚. The duration of non-negligible beam steering associated with the passage of a detonation wave was found to be ⬍4 ls when this collection system was applied to the PDE at the Naval Postgraduate School.

Interpretation of Optical Results A raw transmission versus time trace recorded during the 8th of 15 consecutive engine pulses at 5 Hz is shown for two wavelengths in Fig. 4, along with a list of the information the sensor provides. The 1343 nm wavelength is resonant, absorbed by H2O and extinguished by soot and liquid fuel droplets. The 1643 nm wavelength is non-resonant, extinguished by soot and liquid fuel droplets but not absorbed by H2O. A transmission of unity corresponds to a case where the optical access windows are perfectly clean (free of soot deposits), and no soot particles, fuel droplets, or H2O are in the beam path (i.e., the condition just prior to the aerosol fill of the first pulse in the series). During region A of Fig. 4, soot and combustion gases from the previous pulse remain in the beam path and the windows are sooted, accounting for a non-unity transmission. The indicated oxygen purge is initiated at the head end and begins to displace the soot and combustion gases. By the end of region B, the oxygen purge has displaced the soot and combustion gases from the flow,

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Fig. 4. Raw transmission data at selected wavelengths for a single PDE cycle and the information provided by the sensor during each engine pulse.

Fig. 5. Properties recorded in the PDE at the Naval Postgraduate School for the first 3 of 15 consecutive engine pulses at 5 Hz.

leaving a transmission of ⬃77% due solely to the sooted windows. The transmission recorded at the end of region B is taken as the reference transmission for the upcoming fuel droplet analysis. In region C, the beam path is assumed occupied by JP-10 droplets, JP-10 vapor, and oxygen only. In this region, the wavelength dependence of the transmission loss (due to JP-10 droplets) is used to determine an approximate droplet size distribution as follows. At each instant, a log-normal droplet size distribution is assumed as an initial guess. The transmission ratios R1 ⬅ T1643/T1343 and R2 ⬅ T1799/T1343 based on this assumed distribution are compared with the measured ratios R1meas and R2meas. A bestfit log-normal size distribution is then found using a

simplex search method to minimize X2 ⬅ (R1 ⳮ R1meas)2 Ⳮ (R2 ⳮ R2meas)2. This process is repeated at each instant, yielding an approximate droplet size distribution versus time during the fill; using the assumed distribution and the extinction at a selected wavelength, the droplet volume fraction versus time during the fill is readily obtained. Region D begins with the passage of the detonation wave through the aerosol. The droplets are expected to shatter, vaporize, and combust within the first microsecond following wave passage [18]. JP-10 droplets are therefore assumed absent in region D and until the next fuel fill, leaving flow field H2O, flow field soot (assumed to be in the Rayleigh scattering regime [19]), and window soot deposits (assumed to be in the geometric scattering regime [20]) as the possible absorbers. As has been demonstrated in sooted-foil studies of detonation structures [21], the detonation wave has the ability to clean the access windows, so the window transmission established in region B is no longer applicable. The flow field soot volume fraction and the window transmission are calculated versus time using the absorption at the two non-resonant wavelengths and a previous measurement of the refractive index of soot [12]. The absorbance due to H2O for each of the resonant wavelengths is calculated as (recorded absorbance at resonant wavelength) ⳮ (theoretical absorbance at resonant wavelength due to measured soot volume fraction and window transmission). The gas temperature is then calculated from the ratio of absorbances at k1 and k3. Finally, the H2O concentration is calculated from the absorbance at k1, using the calculated temperature and the pressure measured by the piezoelectric gauge at the test station. Region E begins when the test section pressure is between 0.9 and 1.1 atm and the flow properties begin to change slowly enough that they can be faithfully monitored by the 30 kHz scans of k2. A scanwavelength spectroscopy technique is used to obtain

DIODE-LASER SENSOR FOR PDES TABLE 2 Chapman-Jouget properties for stoichiometric JP-10/ oxygen detonation Vwave

2.3 km/s

Ta Pa XH2Oa

3900 K 40 atm 0.20

a

Burned gas properties.

Fig. 6. High-resolution record of results from pulse 1 in Fig. 5. Temperature plummets at ⬃77.05 ms when a tailto-head traveling rarefaction wave passes the test plane.

the absorbance at k2 in this region. Because the H2O feature is spectrally narrow at these pressures (⬃0.3 cmⳮ1), the laser is able to scan over the entire line shape in each of its 1 cmⳮ1 scans, making these measurements immune to interference from flow field or window soot; while the extinction due to soot in the PDE and on the access windows can in general vary with wavelength in an unknown way, it does not vary appreciably over 1 cmⳮ1. This advantage is critical, since the assumption of Rayleigh-regime soot may become inappropriate in region E, prohibiting the soot interference subtraction scheme used in region D. The absorbance at k1 can be obtained, however, using a modified soot subtraction scheme: the transmission near k2 but at the far wing of the H2O feature and the transmission at knr1 are interpolated to obtain the appropriate absorbance due to soot at k1. The absorbance due to H2O at k1 is then readily obtained, and gas temperature and H2O concentration are determined as in region D, this time using the absorbances at k1 and k2. Results and Discussion Typical pressure, gas temperature, and H2O concentration results are shown versus time for the first

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3 of 15 consecutive engine pulses at 5 Hz in Fig. 5. The indicated wave speeds were determined from the pressure pulse arrival times at transducers a and b labeled in Fig. 3. Calculated Chapman-Jouget detonation properties for stoichiometric JP-10/oxygen detonation are shown in Table 2. As was typical for this engine, the test-section wave speed is much lower for the first pulse than for subsequent pulses. High-pressure gases exist at the test plane for approximately 500 ls following each detonation. Hightemperature H2O typically remains at the test plane for a much longer time (⬎100 ms), due to combustion occurring in the blowdown following each detonation. Blowdown combustion interferes with a subsequent pulse’s aerosol loading, limiting the maximum pulse rate for this PDE to approximately 10 Hz. When the temperature drops below 900 K or the water mole fraction below 0.01, results become inaccurate and are not presented. For the gas temperature and H2O concentration results presented in this work, the uncertainty is estimated at Ⳳ10%, typically limited by the variation in optical fiber transmission as it vibrates in the acoustic output of the PDE. The uncertainty in the soot fvol measurements is estimated at Ⳳ50%, limited by the assumption of soot refractive index as explained above. The uncertainty in the JP-10 droplet volume fraction measurements is estimated at Ⳳ25%, limited by the degree to which the measured best-fit droplet size distribution represents the actual line-of-sight averaged droplet size distribution. Properties measured during pulse 1 of Fig. 5 are presented in Fig. 6 with high time resolution. Gas temperature remains near 2500 K (64% of TCJ) as the pressure decreases to near atmospheric. The temperature decreases rapidly to near 1000 K approximately 650 ls after the detonation wave passes the test plane. This is very near the calculated time of 600 ls required for the detonation wave to exit the tube and allow a rarefaction wave to propagate back to the test plane against the output flow; this rarefaction wave is likely responsible for the rapid gas cooling. Conventional two-color pyrometry results were recorded at the same test plane using a system described previously [11]; the agreement provides confidence in the sensor’s accuracy. Soot volume fraction ( fvol) and H2O concentration results indicate the presence of combustion products within 4 ls of wave passage. The JP-10 droplet volume fraction recorded during the fill just prior to pulse 1 is presented in Fig. 7, with a typical best-fit droplet size distribution inset. This distribution was approximately constant during each fill and agrees well with the Sauter mean diameter of 5.9 lm measured in a previous characterization of this atomizer [17]. The peak volume fraction of 2.0 ⳯ 10ⳮ5 would correspond to an equivalence ratio of 0.047 if the contiguous phase were pure oxygen. Given this very lean mixture, the

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Fig. 7. Record of fuel fill just prior to pulses 1 and 3 shown in Fig. 5.

Fig. 8. High-resolution record of results for pulse 3.

3.5% H2O measured 4 ls after the wave passage (see Fig. 6) is impossible. JP-10 vapor is therefore playing a significant role in the combustion shown in Fig. 6. If the contiguous phase were composed of oxygen plus JP-10 vapor at its room temperature vapor pressure (rather than pure oxygen), the line-of-sight averaged equivalence ratio would become 0.09 and the measured H2O concentration would become possible. Since this detonation is the first in a series of 15, the assumption of a room temperature charge is appropriate; in subsequent engine pulses, the charge may be heated by remaining combustion gases or PDE walls, generating a greater vapor concentration.

Although the PDE was loaded with an overall equivalence ratio near 1.0 for the detonations shown in Fig. 5, the low droplet volume fraction measured at the test section indicates that the engine is loaded rich at the head end and very lean at the tail end at the time of ignition. Furthermore, the correlated unsteadiness in the H2O concentration and soot fvol records (see Fig. 6) suggests that the fuel distribution varies irregularly from head to tail end or that collection of fuel on the engine walls during the fill is significant. While the charge may not be ideal, the ignition timing for the current fuel injector configuration is approximately optimized in the sense that very little fuel is loaded past the tail end of the engine (into the atmosphere) before the detonation wave passes. Several techniques may be used to create a more uniform fuel distribution in the engine at the time of ignition (i.e., adding injectors at several axial locations). However, numerical simulations have shown that a perfectly uniform fuel distribution is not the optimum load (in terms of specific impulse) for this particular engine geometry [22]. Results from pulse 3 of Fig. 5 are shown in Fig. 8 with high time resolution. The JP-10 droplet volume fraction for this pulse’s charge again remains below 2.0 ⳯ 10ⳮ5 (see Fig. 7), yet the peak pressure, wave speed, gas temperature, and H2O concentration are significantly higher. An increased JP-10 vapor concentration in the charge, due to higher charge temperature (and thus increased droplet evaporation) or leftover fuel vapor from the previous pulse, is believed responsible for this improved performance. This wave exhibits a speed and peak pressure within 5% of Table 2 predictions, even though it arrives at the test plane processing a mixture of rapidly decreasing equivalence ratio that prevents it from reaching the predicted temperature and H2O concentration. The 700 Hz temperature oscillations in the blowdown following this pulse are driven by flow direction oscillations at the test plane. Numerical studies of PDEs predict such oscillations [23]. The measured frequency is in agreement with a calculated frequency of 750 Hz based on a one-dimensional acoustic analysis. Sensor Applications Combustion occurring during each pulse’s blowdown can limit the maximum PDE cycle frequency by interfering with the loading of a subsequent charge. Because this sensor clearly reveals this combustion, it should prove useful in maximizing PDE cycle frequency (and thus maximizing thrust). Monitoring the arrival of fuel at a PDE’s exit plane enables a more precise scheduling of each pulse’s ignition. Optimized ignition scheduling should enhance engine performance. The equivalence ratio at the time of PDE ignition can be a strong function of location, especially for

DIODE-LASER SENSOR FOR PDES

liquid-fueled PDEs, as was the case in the PDE at the Naval Postgraduate School. The sensor will enable studies of this effect on engine performance. Such studies will be critical for PDE optimization guided by accurate PDE models. For example, by using the sensor to optimize the fuel distribution at ignition, blowdown combustion measured by the sensor should be simultaneously minimized, thus maximizing thrust. The sensor will be upgraded to allow measurements at several axial locations to facilitate such studies. The addition of a JP-10 vapor sensor based on 3.39 lm He-Ne laser absorption is also planned. Conclusions A first-generation diode-laser–based sensor has been developed for and applied to PDE flows. The sensor has demonstrated the capacity to obtain quantitative, in situ measurements of gas temperature, H2O concentration, liquid fuel concentration, and soot volume fraction in a liquid-fueled detonation tube. The sensor reveals information that should prove useful in PDE modeling, optimization, and control strategies. Acknowledgments This work was sponsored by the Office of Naval Research (ONR), with Dr. Gabriel Roy as technical monitor, under the ONR MURI on PDEs. The authors gratefully acknowledge Professors C. M. Brophy and D. W. Netzer at the Naval Postgraduate School, Monterey, California, for valuable discussions on PDE performance and for hosting our visit to demonstrate this sensor in the Rocket Propulsion and Combustion Laboratory.

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5. Baer, D. S., Nagali, V., Furlong, E. R., Hanson, R. K., and Newfield, M. E., AIAA J. 34:489–493 (1996). 6. Arroyo, M. P., and Hanson, R. K., Appl. Opt. 32:6104– 6116 (1993). 7. Nagali, V., and Hanson, R. K., Appl. Opt. 36:9518– 9527 (1997). 8. Kung, R. T. V., and Center, R. E., J. Chem. Phys. 62:2187–2194 (1975). 9. Swanson, N. L., Billard, B. D., and Gennaro, T. L., Appl. Opt. 38:5887–5893 (1999). 10. Hottel, H. C., and Sarofim, A. F., Radiative Transfer, McGraw-Hill, New York, 1967. 11. Jenkins, T. P., and Hanson, R. K., “A Soot Temperature Diagnostic Combining Flame Emission and Modulated Laser Absorption,” AIAA paper 2000-0953, Thirty-Eighth AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan 10–13, 2000. 12. Dalzell, W. H., and Sarofim, A. F., J. Heat Transfer 91:100–104 (1969). 13. Toth, R. A., Appl. Opt. 33:4851–4867 (1994). 14. Rothman, L. S. et al., J. Quant. Spectrosc. Radiat. Transfer 60:665–710 (1998). 15. Sanders, S. T., Baer, D. S., and Hanson, R. K., AIAA paper 2000-0358, “Diode-Laser Absorption Sensor for Measurements in Pulse Detonation Engines,” ThirtyEighth AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan 10–13, 2000. 16. Mihalcea, R. M., Baer, D. S., and Hanson, R. K., Proc. Combust. Inst. 27:95–101 (1998). 17. Brophy, C. M., and Netzer, D. W., “Effects of Ignition Characteristics and Geometry on the Performance of a JP-10/O2 Fueled Pulse Detonation,” AIAA paper 992635, Thirty-Fifth AIAA Joint Propulsion Conference, Los Angeles, CA, June 20–24, 1999. 18. Sanders, S. T., unpublished results, 1999. 19. Bohm, H., Feldermann, C., Heidermann, T., Jander, H., Luers, B., and Wagner, H. G., Proc. Combust. Inst. 24:991–998 (1992). 20. Brugman, T. M., Stoffels, G. G. M., Dam, N., Meerts, W. L., and ter Meulen, J. J., Appl. Phys. B 64:717–724 (1997). 21. Auffret, Y., Desbordes, D., and Presles, H. N., Shock Waves 9:107–111 (1999). 22. Li, C., Kailasanath, K., and Patnaik, G., “A Numerical Study of Flow-Field Evolution in a Pulsed Detonation Engine,” AIAA Paper 2000-0314, Thirty-Eighth AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, Jan 10–13, 2000. 23. Kailasanath, K., Patnaik, G., and Li, C., “Computational Studies of Pulse Detonation Engines: A Status Report,” AIAA paper 99-2634, AIAA Joint Propulsion Conference, Los Angeles, CA, June 20–24, 1999.

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COMMENTS In-Seuck Jeung, Seoul National University, Korea. Please discuss the performance of the measurement technique when it is applied on the repetitive multishot PDE experiment. Author’s Reply. The sensor has worked well in both single-shot and multishot PDE experiments. At high PDE pulse rates, sequential pulses can interface with each other, changing PDE performance. By monitoring the temperature and composition continuously, and the concentration of unburned fuel droplets between pulses, the sensor provides key data needed to characterize pulse-to-pulse interference. The sensor data can be used to understand and minimize these interferences, enabling higher pulse rates, and thus higher thrust. ● Jay Gore, Purdue University, USA. Can you describe the fuel balance (for example, 5% was picked up by the probe; where was the remaining 95% of it?) in the liquid-fueled PDE? Author’s Reply. Low fuel droplet volume fractions of approximately 1 ⳯ 10ⳮ5 (corresponding to an equivalence ratio ␾ of approximately 0.05) were measured at the optical test plane just before the detonation wave arrival. This information, coupled with knowledge of the total fuel input to the PDE for each pulse, confirms the existence of a fuelrich mixture between the optical test plane and the head end of the tube. ● K. M. Isaac, University of Missouri-Rolla, USA. Because the JP-10 combustor is horizontally configured, have you observed fuel drops settling on the lower combustor wall? Author’s Reply. Although we did not attempt to visualize the progress of the spray as it filled the tube, we did observe pools of liquid fuel on the lower wall following PDE misfires. Even in a healthy detonation cycle, however, it is likely that some fuel accumulates on the wall surfaces during fuel injection. This accumulation of fuel on the walls may be partly responsible for the non-uniform distribution of fuel (rich head end, lean tail end) revealed by the sensor. ● Mark Jermy, Cranfield University, UK. Obtaining information on the droplet size distribution is achieved by the

use of attenuation measurements at three wavelengths. The ratio of any two attenuation coefficients is a function of droplet size distribution. This function is not unique, as for example, a large number of small droplets and a small number of large droplets can give the same attenuation. First, how do you get around this non-uniqueness to measure droplet volume fraction? Second, how do you choose the wavelengths so that the two attenuation-coefficient ratios give you sufficiently different information to do a twoindependent-parameter fit? Are the radiation/droplet interactions significantly different for the different wavelengths? Author’s Reply. We assume a log-normal form with two free parameters for the droplet size distribution function. We then find the best-fit values of these two parameters: the values that cause the theoretical attenuations to best match our measured attenuations. Using a Malvern system, we verified that our sensor was providing accurate measurements. To obtain sufficiently different information from the two attenuation-coefficient ratio, the wavelengths must be chosen carefully, and the proper choice depends heavily on the specifics of the spray (size distribution as well as fuel index of refraction n-ik). Simulations were performed to determine the sensitivity of the measurements to the wavelengths chosen. For the JP-10 aerosol on the PDE at NPS, three wavelengths separated by approximately 300 nm typically provided ratios that were sufficiently different to enable meaningful measurements. Some cases, however, required information from more than three wavelengths (more than two ratios) to remove ambiguities during the fitting. ● Eremin Alexander, Moscow Institute for High Energy Density, Russia. It is known that the serious problem for PDE is overheating of the walls. Is it possible to use your sensors for direct measurements of the heat flux to the walls? Author’s Reply. The sensor measures only the gas (and liquid) properties, not wall heat flux. However, measurements of the burned gas temperature in the PDE are certainly useful for understanding the heat flux to PDE walls. Although exterior wall temperatures may be easily monitored using thermocouples, diode-laser sensors may prove to be critical for understanding and reducing heat transfer to PDE walls.