THE INFLUENCE OF WATER VAPOR ADDITION ON HYDROGEN-OXYGEN DETONATIONS B. F. Kerkam Eo Ko Dabora ORA Project 06996 under contract with U. S. Army Research Office (Durham) Contract No, DA-31-124-ARO-D-299 Durham, North Carolina Aircraft Propulsion Laboratory Department of Aeronautical and Astronautical Engineering The University of Michigan Ann Arbor, Michigan April 1965

ABSTRACT The minimum detonation Mach number, below which detonative combustion is not possible, can be predicted by Belles' explosion limit criterion for H2-02 mixtures. The criterion predicts also that the addition of water vapor increases this minimum Mach number. The experiments which are described here and which are based on the technique of slowing down an established Chapman-Jouguet detonation wave by exposing one of its sides to a compressible boundary verify this prediction. It is found that the addition of 2% water vapor to a stoichiometric H2-02 mixture increases the minimum detonation Mach number by 3% as predicted by theory. It is also found that the same amount of water vapor decreases the reaction length by approximately 50% and that the addition of 1% of water vapor to 50% hydrogen- 501% oxygen mixtures reduces the reaction length by approximately 30%. The experimental work of Kistaikowsky and Kydd is found to support the latter findings. iii

ACKNOWLEDGMENTS The work described in this report was initially started under Grant No, DA-ARO(D)-31-124-G-345 by the Uo S. Army Research Office (Durham). Its completion was made possible, however, by contract No DA-31-124ARO-D-299 from the same agency. The authors are therefore very grateful to ARO for its financial assistance, The authors wish to thank Professor Jo Ao Nicholls, Project Supervisor, for his guidance and advice during all phases of this work and to those among the staff of the Aircraft Propulsion Laboratory who assisted in many ways during this project. V

TABLE OF CONTENTS Page ABSTRACT iii ACKNOWLEDGMENTS v LIST OF FIGURES ix NOMENCLATURE xi Io INTRODUCTION 1 ILI EXPERIMENTAL ARRANGEMENTS AND PROCEDURE 5 III. EXPERIMENTAL RESULTS 11 IV. DISCUSSION 17 V. CONCLUSIONS 20 REFERENCES 21 APPENDIX I. Calibration Curves for DewProbe/Thermistor Dewpoint 31 Measurement System vii

LIST OF FIGURES Page Figure 1o Maximum Allowable Mach Number Decrement as a Function of Water Vapor Content 22 Figure 2. Model for the Interaction of a Detonation with a Compressible Inert Boundary 23 Figure 3. Schematic of Mixing and Charging System 24 Figure 4. Circuit Diagram for DewProbe Cavity Temperature 25 Measurement Figure 5. Calibration Curve for Use in Determining Water Vapor 26 Content of Explosive Mixture from Thermistor Current Flow Figure 6. Experimental Mach Number Decrement Due to the Com- 27 pressible Boundary as a Function of Channel Width. 50F% H2 + 50% 02 Mixture Figure 7. Detonation Velocity of 50% H2 + 50% 02 and 66 2/3% H2 + 28 33 1/3% 02 Mixtures as a Function of Water Vapor Content Figure 8. Experimental Mach Number Decrement Due to the Com- 29 pressible Boundary as a Function of Channel Width. 66 2/3% H2 + 33 1/3% 02 Mixture Figure 9o Density Changes in a Hydrogen-Oxygen Detonation as a 30 Function of Time. Data from Kistiakowsky and Kydd Figure a - Thermistor Calibration Temperature vs. Current Through 32 Thermistor Figure b - Dewpoint vso DewProbe Cavity Temperature 33 Figure c - Volumetric Concentration of H 0 Vapor vso Mixture Dewpoint 34 2 ix

NOMENCLATURE a b d E f ki k2 9 etc. M P R T V (X) 6* p P Subscripts a cr D e ex i th,. w 0 velocity of sound explosive channel width, inches tube diameter activation energy for chemical reaction mole fraction reaction rate constants for reactions I, II, etc, Mach number pressure universal gas constant temperature detonation velocity third body concentration reaction length ratio of specific heats displacement thickness density ambient critical detonation explosive after expansion inert theoretical water initial conditions xi

I. INTRODUCTION The purpose of this research is to investigate the effect of water vapor on the quenching of detonations in hydrogen-oxygen mixtures which are between the lean and rich limits of detonation. The explosion limit criterion proposed by Belles(1) for finding the composition limits of detonability has been shown by Dabora (2)to be an accurate description of the limits of detonability for hydrogen-oxygen mixtures. However, Belles' criterion essentially utilizes the "second explosion limit" chemical-kinetic equations while pressure and temperature conditions in the induction zone of typical hydrogenoxygen detonation are far from the second limit conditions. It is not, therefore, clear that the chemical-kinetic equations which describe the second explosion limit can be applied in general to the problem of describing the conditions at which detonation waves will quench. This research is a continuation of Dabora's work, intended to further explore the correctness of applying Belles' explosion limit criterion to the detonation quenching problem. Belles' chemical-kinetic formulation of the detonation quenching problem utilizes the following reactions:* k I OH+ H2 H20 + H I2 2 2 II H + 02- OH + O 3 III O + H2 - OH + H k6 VI H+O + X HHO2 +X Numbered according to the convention gven by Lewis and von Elbe *Numbered according to the convention given by Lewis and von Elbe3. 1

It follows from the steady state approximation that the net rate of production of active species (0, OH, H) in the induction zone will fall to zero when: 2k2= k 6(X) (1) If this condition is obtained, it is expected that an existing detonation will cease to propagate as a detonation (i. e, quench), or that a detonation cannot be initiated. Here, X is the effective third body concentration defined (3)" by the empirical relation given by Lewis and von Elbe(3 f f + 35f + 14.3f0 + 43f + o36f 2He + Ar+ 147fC (2) x H 0 HO N HeAr c 2 Equation (2) points out the high efficiency of water vapor as a third body in the chain-breaking reaction, reaction VI. Using the appropriate reaction rates for reactions I, II, III, and VI, and using shock wave relations to determine pressure and temperature in the induction zone allowed Belles to develop a relation which can be solved for the critical, or minimum allowable Mach number of detonation. The relation given by Belles is: __ __3710 a__ _ M2 T (/3M2 +l) 30 1A1 0cr 0 cr'y log -- (3) 10 f - lO 10 1 /M2 i\ 2 (3) x T-r 3M2 + P0 cr 0 P M cr y where 7- 1 2y Solving for the critical Mach number (M ) and utilizing a theoretical Mach number (MDth) of detonation for infinite tube size and no additives, one can express the fractional maximum Mach number decrement as: 2

AM M th Mcr ~~~=........ ~~~(4) M M max MDth When the maximum decrement is reached, or exceeded, it is expected that the detonation will quencho Since water vapor is a very efficient third body, adding small amounts of water vapor to hydrogen-oxygen mixtures should have a pronounced effect on the maximum allowable Mach number decrement, and thus provide a sensitive check on the correctness of Belles9 explosion limit criteriono Figure 1 shows the results of typical calculations of the maximum allowable decrement for two hydrogen-oxygen mixtures containing from 0% to 4% (by volume) of added water vaporo The fractional decrements in this figure, and all other decrements given in this paper, are based on an M h of 5. 28 for the stoichiometric mixture and 5. 14 for the 50% H2 + 50% 02 mixture. The feasibility of checking Belles9 criterion with explosive mixtures which are not near the composition limits rests on the ability to decrease the detonation Mach number of a specified explosive composition. Specifically, the detonation must be slowed to the critical Mach number given by Eqo (3). Two effects which will result in slowing the detonation have been examined theoretically-these are the effect of a finite sized detonation tube as discussed by Fay, and the effect of a compressible boundary as (2) (5) discussed by Dabora and Sommers o Fay's analysis is based on boundary layer growth within the reaction zone, Since stream lines enter the growing boundary layer, and are concentrated near the wall of the detonation tube, the effect of the boundary layer is to cause the remaining stream lines in the reaction zone to diverge. On this basis, Fay obtains the result that AV 2. 15* V d(5) 3

where 65 = displacement thickness at C-J surface d = tube diameter Dabora developed a solution for the Mach number decrement of a detonation which is exposed to a compressible boundaryo The decrement is expressed in terms of the reaction length of the detonation (distance from the shock front to the C-J plane), the explosive channel width, and the density parameter 1/2 PeYe.i PiYi 2(Yi + 1) which gives the relative effectiveness of the inert compressible boundary in confining the detonation. Daborals analysis allows one to determine the experimental configuration (explosive channel width and inert gas) required to produce a specified Mach number decrement for a particular explosive gas, The model of the detonation-inert boundary interaction used for this analysis is shown in Fig. 2 and a detailed description of the test section used to obtain the desired experimental conditions is contained in Refo (2). Two Mach number decrements must be experimentally determined. The decrement due to the effects of finite detonation tube size and of water addition on the detonation velocity is obtained from measurements of detonation velocity in the tube section immediately proceeding the test sectiono The decrement due to the effect of the nitrogen boundary is obtained from streak photographs of the detonations as they pass through the test section. Before making the comparison with Belles' criterion, the two decrements are combinedo AM AM AM (6) M, "M,+ M cope l e 6) total tube size, compressible water addition boundary 4

Il, EXPERIMENTAL PROCEDURE The procedure and equipment used are essentially those developed by (2) Dabora) with two exceptions —the addition of a humidifier to the balloonfilling circuit, and the use of a dewpoint measurement system at the entrance of the test sectiono A schematic of the system used is given in Figo 3. Two methods of adding water vapor to the combustible mixture were used for the series of preliminary experiments, The first method, which shall be called the "moisturizer, P makes use of a piece of 1 1/2 ino diameter cost iron pipe filled with sponges and provided with appropriate connections at the two endso Cellulose sponges were cut to fit the interior diameter and were then tightly packed into the pipe, Water was added through a removable pipe pluge, The exterior of the moisturizer was heated with a 200 watt infrared bulb placed approximately 6 ino from the moisturizer, and premixed hydrogen-oxygen was then slowly flowed from the mixing chamber through 3 the moisturizer and into the balloon. Typical fill times for a 0. 1 ft balloon were on the order of 30 seCo Using room-temperature dry nitrogen gas, this device produced a dewpoint, as measured by an Alnor Dewpointer of 55-58 Fo But since the H2-02 mixing chamber is located outside the Propulsion Labora2 2 tory, and the preliminary tests were made in March, the hydrogen-oxygen mixtures admitted to the moisturizer had a temperature of 35-50 Fo Although the hydrogen-oxygen mixtures were heated by contact with the moisturizer, the dewpoint produced by the moisturizer was reduced to 40-50 Fo A drawback of the moisturizer, due to its design, was that the moisture content of the sponges could not be readily determined or controlledo The seond metd of adding waer vapor nsisted o flowig the eer combustible mixture through a DeVilbiss No, 40 Nebulizer, The Nebulizer was used on- all but the first few preliminary experiments, This device is essentially a glass-enclosed atomizer, with the interior of the glass enclosure 5

serving as a reservoir for the water. Due to the relatively low temperature of the entering gas, it was necessary to preheat the gas prior to its entry into the Nebulizero The pre-heating was accomplished in a 6 ft long piece of 1/4 ino copper tubing which was wound in a spiraL The exterior of the tubing was heated with a 200 watt infrared bulb placed about 6 in. from the tubing, which produced a temperature rise of 50-600F at a flow rate of 0. 1 to 0O 2 ft /min. Initial measurements made with the Alnor Dewpointer showed that the Nebulizer plus heat exchanger was capable of producing a dewpoint of 67-71~F at a room temperature of 81 Fo The humidity measurements made prior to, and during, the series of preliminary experiments were made with an Alnor Type 7300 DEWPOINTER (Illinois Testing Laboratories9 Chicago, Illinois). This instrument is operated by compressing with a hand pump a small sample of the gas in a lighted observation chambero When the chamber is rapidly vented to atmospheric pressure, the chamber temperature drops, and the presence or absence of condensed vapor (fog) is notedo A trial and error procedure is followed to find the pressure P09 necessary to cause condensation when the gas is expandedo For an initial temperature TO of the pressurized gas and ambient pressure Pa the gas temperature after expansion, Tex which will be equivalent to the dewpoint temperature, can be calculated from the adiabatic relation~ P (? - 1)/y T TOPO (7) ex ^o The Dewpointer gives repeatable, accurate (+ 1 F) results, but the procedure is time consuming, and is not well suited to monitoring the changing dewpoints which occur during post-run purges, and during prerun charging with the combustible mixture. For these reasons a system consisting of a Honeywell SSP-129A DewProbe and a thermistor temperature sensor was built to allow continuous readout of the dewpoint, The 6

operation of the DewProbe is based on two unique characteristics of lithium chloride- it is hygroscopic, and at a relative humidity of 11% or greater, lithium chloride will absorb enough water to become electrically conductiveo The DewProbe humidity sensing element consists of a lithium chloride impregnated cloth sleeve which is wound with a two-wire element and is slipped over a metal tube, or bobbin. The two wires are wound next to each other, but are not connected, so that an electric potential placed on the two wires will result in a current flow only when the lithium chloride is conductiveo The electric current flow heats the cloth sleeve and metal bobbin until the relative humidity of the moist atmosphere is 11% at that temperature, at which point the lithium chloride becomes nonconductive. The DewProbe element thus maintains itself at the temperature which corresponds to a relative humidity of 1%o Measurement of the bobbin cavity temperature gives the temperature for which the relative temperature is 11%9 from which the dewpoint of the moist atmosphere can be determinedo The cavity temperature readout was accomplished by connecting a Fenwell 6A45JI thermistor (selected for its high temperature sensitivity) in series with a 1o 34 volt mercury battery power supply and a 0-100 pamp Simpson Model 1329 meter as shown in Figo 4. Temperature readout is made in terms of Iamps of current through the variable resistance of the thermistor9 from which the temperature of the thermistor and the DewProbe cavity can be obtained. The thermistor-meter-battery system was calibrated against a mercury thermometer (WOODCO M-1100) and against copperconstantin thermocouples and the results are shown in the Appendix, Figo ao Since the maximum difference between the two calibrations is 1o 5 0F the accuracy of the resulting temperature vso current calibration is estimated to be + 0. 8 Fo The cavity temperature readout is converted to dewpoint by 7

using a Honeywell supplied cavity temperature vso dewpoint calibration shown in Appendix Figo bo Accuracy of the DewProbe in the range of interest is stated by Honeywell to be + 0, 25 F in dewpoint, so the resulting accuracy in dewpoint is taken to be + lo 0 Fo The mercury battery power supply (two Mallory RM-4RT in parallel) has a very flat voltage vso time characteristic, but continuing checks on the condition of the batteries were made by switching a known, fixed resistor into the circuit in place of the thermistor-any deviation from the current reading (65 Camps) taken at the time of the original calibration would indicate a change in battery voltage, Since no change in this reading occurred during these experiments, the original calibration was assumed to remain valido Figure 5 obtained from Appendix Fig. a-c gives the conversion from the meter reading to volumetric concentration of water vaporo Operationally, the DewProbe proved to be superior to the Alnor Dewpointer due to the ease with which the dewpoint of the system could be monitoredo However9 it had two disadvantages, the first of which is poor response to large, fast changes in dewpointo It is believed that this was due to the absorbtion of a large amount of water vapor by the DewProbe bobbin, which caused a virtual short circuit of the heating element. This overloaded the DewProbe transformer, and caused a reduced potential (0o 5 volts vso a nominal 28. 0 volts) across the heating element, which resulted in a substantial delay before the DewProbe bobbin reached an equilibrium temperature and evaporated the excess moisture. To avoid this difficulty, the system was purged to an intermediate dewpoint (about 40 F) after each run, and then slowly brought up to the equilibrium dewpoint with moist H2 + 02 mixture prior to the next runo 2 2 8

The other disadvantage of the DewProbe is that it cannot measure very low dewpoints-for an ambient temperature in the 78-82~F range, the lowest dewpoint which can be measured is in the 19-23 F range. This limitation affected only those runs made with a "dry'v mixture, io e., once the minimum dewpoint reading was obtained, it could only be assumed that continued flowing with a dry mixture would lower the dewpoint of the system, Until the DewProbe system was installed, it was not realized that the detonation tube and the plumbing used to charge the system with moist H2 + 02 mixture were absorbing water, This absorbtion of water was first noted when 3 it was found that approximately 0. 5 ft of moist mixture were required to produce an indication of increased dewpoint at the DewProbe if the system had been purged out after the preceeding runo (The DewProbe itself required 0, 1 or at most 0. 2 ft3 of gas to reach an equilibrium reading. ) It was this situation which first resulted in doubt as to the dewpoint actually obtained during the preliminary tests, since these tests were made by flowing only 3 0, 2 ft of moist H2 + 02 through the system after it had been purged for approximately 20 minutes with dry N2o Run Procedure~ (Refer to Figo 3) 1. Connect DewProbe to the detonation tube, by removing ionization probe No, 3, inserting an adapter in its place, and connecting the DewProbe tubingo 2. Purge the system with dry N2 by opening V-17, to a dewpoint of 30-40 Fo Progress of purge is monitored with an EICO Model 221 VTVM connected to the DewProbe thermistor leads, 3. Install balloon at the adaptor downstream of valve V-8. 4o Close V-17, V-14, and V-9, and evacuate this part of the system. 5o Open V-14o Then open V-5 until a pressure of 5 psig is indicated on pressure gage P-lo This operation fills the balloonewith moist H2 + 02 mixtureo 2L 2 9

60 Close V-14 and open V-9 one turn to flow the mixture through the detonation tube and DewProbe. Monitor system dewpoint with the EICO VTVMo 7o Repeat step 6 until a steady dewpoint reading is obtained. 80 Refill the balloon with moist mixture, and open V-9 three turns (runs are made with V-9 opened three turns). Monitor system humidity with the Simpson microammetero If any changes occur during this balloonful, repeat this step until a stable reading is obtained. Record the microammeter reading obtained before the balloon is empty. 9o Remove the DewProbe tubing, adapter, and insert ion probe No. 3 into the detonation tube, while the balloon is maintaining a positive pressure on the system. 10. Load the rotating drum camera with film (note, this step is usually accomplished during the pre-run purge), 11o Insert the nitrocellulose film, on its holder, into the test section. 12o Refill the balloon with moist H2 + 02 mixture. 2 2 13. Close V-8 and V-14, and evacuate the closed-off part of the system. This is a safety feature designed to reduce the possibility of the detonation propagating back into the Nebulizer/moisturizer and the mixing chamber. 14. Open V-9 three turns, maintaining an equal pressure on both sides of the nitrocellulose film by opening and closing V-1 as required. 15. Bring the rotating drum camera up to full speed. 16. When the balloon is almost empty, initiate the detonation. 17. Record data: 1) T-13detonation time from time-interval counter. 2) Manometer (P-2) reading. 3) Temperature at level of test section and flooro 10

IIL EXPERIMENTAL RESULTS Ao Preliminary Experiments A series of preliminary experiments was made with 50% H2 + 50% 02 (by volume) mixtures in order to determine if the addition of water vapor did have an effect on the characteristics of detonation wave propagation, The 50% H2 mixture was selected because it emphasizes the effect of water addition on the effective third body concentration given by Eqo (2)o It was apparent from analysis of the rotating drum camera photographs that the addition of small amounts of water vapor did have an effect on the Mach number decrement due to a compressible boundary. The Mach number decrements obtained from these experiments are summarized on Fig. 6. Dewpoint measurements made with the Alnor DEWPOINTER prior to and during the preliminary experiments showed the mixtures were approximately 25% saturated, corresponding to approximately 1% by volume of water vaporo As a result of the preliminary experiments, the Honeywell DewProbe dewpoint measurement system was installed, and a more extensive series of experiments on stoichiometric hydrogen-oxygen mixtures was madeo B. Detonation Velocity Measurements In the absence of appropriate detonation velocity data for hydrogenoxygen mixtures with small amounts of water added, a series of tests were run on the 50% H2 + 50% 02 and 66 2/3% H2 + 33 1/3% 02 mixtureso The experimental data are presented in Fig. 7 along with the theoretical velocity predictions from Gordon for the stoichiometric H2-02 mixtures. The Mach number decrement due to finite tube size and water addition is calculated from the experimental data for use in Eqo (6)0 11

Scatter in the velocity data is attributed principally to small variations in the hydrogen-oxygen ratio due to the mixture preparation technique, The velocity error represents approximately + 0. 5% variation in the percentage of hydrogen in the mixtures. For this reason, the curve for the stoichiometric mixture was drawn to follow the trend of the data from a particular filling of the mixing chamber, and was then shifted so as to represent the average of the datao It should also be noted that the water content of the data plotted at 0. 0% H20 could be as high as 0. 3% H20 since the minimum 2 2 measurable dewpoint corresponded to 0. 3%o However, the moisture content was considered to be closer to 0O 0%, since purging with commercially dry N2 was continued for 20 minutes after the minimum readable dewpoint was obtained, and the detonation tube was then charged with dry H2-O2 mixture. The curve for the 50% H2 + 50% 02 mixtures was drawn as a straight line between the average velocities of the two groups of data shown as no experiments were performed at the intermediate pointso Co Compressible Boundary Effects Streak photographs were obtained with a rotating drum camera for several test section channel widthso These photographs give a distance vso time trace of the detonation wave as it travels through the test section, so that the change of slope of the trace will give the velocity decrement, AV/V, suffered by the detonation when it is exposed to the compressible (nitrogen) boundaryo Since Belles' criterion is based on the calculation of a critical Mach number9 it is necessary to assess the effect of water addition on conversion of the velocity decrement data to a Mach number decrement, The experimental data gives AV /V from which it is desired to obtain AM /M )th Then AM AM M AM V a w w w w w th h MDth MDth M a VDth Dth w Dth w w Dth 12

where AV /Vw AM /M and the ratio Vw/YDth is.evaluated from the w w w w w Dth experimental velocity data by considering only the effect of water vapor, io e.,9 by excluding the effect of finite tube sizeo Evaluated at a 2% (by volume) concentration of water vapor in stoichiometric H2-O2, the ratio Vw/VDth ath/aw = ( 984)(1. 006) = 990 which may be considered unityo To this approximation, AM AV rw _ w (9) MDth Vw A summary of the data obtained on the Mach number decrements due to the effect of the compressible nitrogen boundary is presented in Figo 6 and 8, and on Table 1, Daborals equation for AM/M (Eqo (2. 27) of Refo 2) was utilized to draw the curves on Fig. 6 and 8 by determining the reaction lengths x required to produce agreement with the experimental datao These lengths are shown in Table IIo Examination of Fig. 6 and 8 reveals three significant features-(a) the decrease in Mach number decrement for a given channel width when water vapor is added to the explosive mixture, (b) the agreement between the predicted and experimental level of the maximum Mach number decrement, and (c) the indicated decrease in Mach number decrement for mixtures with and without water added as the quenching limit is approachedo The significant decrease in Mach number decrement when water vapor is added is most plausibly explained by assuming that the reaction length (the distance from the shock wave to the Chapman-Jouguet plane) is decreased by the addition of small amounts of water vapor, The Mach number decrement data are fitted to the theoretical prediction of (AM/M)c of Dabora when the reaction lengths in Table 2. are usedcomp of Dabora when the reaction lengths in Table 2. are usedo 13

TABLE 1. SUMMARY OF DATA %2 in H2-2 50 b inch No. of runs % H20 by Vol...4 4 est. <.3 6 est. 1. 0+.5 4 est <.3 6 est. 1. 0 ~. 5 3 est. <.3 4 est. I. 0 +. 5 3 est. <. 3 V ft/sec + 160 - 168 + 299 7416 -139 7476+ 71 -- 27 7449+ 98 37 7339+ 42 - 36 74 76+ 210 - 234 7407 + 16 16 AM/M 062 +. 023 - o 017 0 + + 020 - 023 077 + 026 -.033. 044 + 011O - 0 010 n + O 13 068 - o 012 quench quench.35 035 66 2/3 4 1 88 +. 15 -. 30 + 48 +. 007 9068 48.027+.007 - 47 - 0 008.35 4 4.25. 20. 15 4 200 + 15 2.00 _ ~-30 1. 74 + - o34.+ 0 20 -. 15 1. 94 + 24 lo'94 - 026 2. 00 +. 30 - 042 9 + 136 9052 - 70 9076 + 186 9076 71 9044+ 48 - 31 9037+ 15 16 8997 + 24 - 38 0 024 + 016 - 0 011Oil. 045 + o 008 045 + 0 022 018 0 020 +. 006 - 009 quench 5 3 *Measured by ionization probes 14

TABLE 2. REACTION LENGTH ~~Mixture,Reaction Length Mixture.. inches (66 2/3% H2 + 33 1/3% 02), 2% water vapor added 058 66 2/3% H2 + 33 1/3% 029 dry 128 (50% H2 + 50% 02), 1% water vapor added 108 50% H2 + 50% O2 dry.160 The comparison between experimental data and Belles' predicted explosion limit was hampered by the existence of an unsteady phenomenon (spin) which appear near the limits of detonability and by practical considerations which limit the increments in channel width to 0. 05 inches. Therefore, the exact value of the maximum Mach number decrement could not be experimentally determined. Of the two, the unsteady behavior of the detonation is more fundamental obstacle to an exact determination of the quenching imi The unsteadiness which is observed near the limit is apparently the spin phenomenon described by a number of investigators, including Dove (8) and Wagner It is interesting to note that the onset of pronounced unsteadiness results in a decrease in the measured velocity decrement, iL e, the points for b =. 3 ino with H20, b = 35 in. without H20 on Figo 6 and for b = o 2 ino with and without H20 on Fig. 8. The reduction in velocity 2 decrement is probably due to the way in which the decrements were measured-that is, the average slope of the peaks of the detonation trace were used. The decrement obtained in this way may not be representative of the true time average of the propagation velocity since the shape of the position vso time trace is quite complex and not at all regular. Nevertheless, the peaks of the waves do appear to travel at a "steady" average velocity, and the detonation shows no signs of definitely quenching within the observable length of the test section. 15

From Fig. 6 and 8, it is apparent that the extrapolated experimental Mach number decrement curves intersect Belles' explosion limit in the region between the channel width which experimentally results in pronounced unsteadiness (spin), and the channel width which produces definite quenching of the detonation wave within the test section'The (AM/M) lines labeled "Belles' Explosion Limit" on Fig. 6 and 8 represent the theoretical maximum decrement which the compressible boundary alone can induce before quenching occurs. They are obtained by subtracting the experimentally determined values of the Mach number decrement due to finite tube size and water vapor addition from the appropriate values in Fig.o 1 The observed agreement between the predicted and experimental level of the maximum Mach number decrement supports Belles' formulation of the limits of detonabilityo Specifically, the strong influence of water vapor on the second explosion limit, through its effect on the effective third body concentration, is seen to have a similar effect on the quenching limit of detonative combustion. 16

IV. DISCUSSION Belles' formulation of the limits of detonability utilizes two chemicalkinetic assumptions which are not obviously valid: (a) that the concentration of H29 029 and H20 do not change in the induction zone, and (b) that the HO2 radicals produced by reaction VI are inert in the induction zone. The constancy of (H2) and (02) can be inferred from the extremely small concentrations of H, OH, and 0 produced in the induction zone, and from the fact that the dissociation of H and 02 in the induction zone is (9) negligible, as shown by Nicholls(9 The approximation (H0) = consto in 2 the induction zone rests on the fact that very little H20 is produced initially 2 by the H2, 02 reaction, and so in the induction zone only the dissociation of H 0 need be considered. For the dissociation of H 0, Bauer, Schott 2 2 and Duff prefer either of the two decomposition reactions H 0+ OH -HOOH + H (10a) 2 H2O + OH -HO2 + H2 (lb) as a path to dissociation in the temperature range of 2400~-3200~Ko However even though these reactions have lower activation energies (~ 45 Kcal/mole) than that of the direct dissociation (- 70 Kcal/mole) the temperature behind the shock in our case is low enough to preclude appreciable amount of dissociation. Assumption (b) is more difficult to rationalize. Specifically, the gas phase reaction of HO2 has been stated by Lewis and von Elbe(3) to be: 2IHO2+ H XI HO +H -HO +H 2 2 2 2 17

In addition, Miyama, and Takeyama used reaction XI in an analysis of the reactions in shocked argon, hydrogen and oxygen mixtures, and found an activation energy of 14. 8 + 2. 2 Kcal/mole, which is of the same order of magnitude as the controlling reaction, reaction IL From this point of view, the approximation that HO2 is an inert molecule in the induction is not particularly goodo Furthermore, if reaction XI for H02 is included in the reaction scheme, and the time rate-of-change of active radicals is calculated, it is found that there is no simple requirement, like 2k2 = k(X), for which the time rate-of-change of active radicals is ~~~2 6 p12) zero, However, Brokaw 2) has included reaction XI in an analysis of induction times, and concludes that if the "explosion limit" condition 2k2 = k6(X) is invoked, the induction time increases by approximately two orders of magnitude as the lean limit of detonability is approached. This means that the time rate-of-change of active radicals becomes very small, but not zero, when the condition 2k2 = k6(X) is invokedo In an experimental situation, nonsteady phenomena become pronounced as the limit of detonability is approached and the determination of the exact limit is difficult and therefore it is not possible to distinguish between Belles' and Brokaw s statements on the limit of detonability. Hence, within experimental limits, the assumption that HO2 is an inert molecule in the 2 induction zone results in a correct limit of detonabilityo Although the effect of water vapor on the induction zone can be theoretically determined, its effect on the remainder of the reaction zone is still not definedo At present there is no theoretical justification for postulating that the addition of water vapor shortens the reaction length in hydrogen-oxygen detonations. However, the experimental work of Kistiakowsky and Kydd( seems to lend support to this conclusion. These authors studied the density variation with time behind shocked mixtures 18

of xenon, hydrogen, oxygen and various additives including water vapor, and concluded in part that water vapor has no retarding effect on the reactiono However, the part of their data which is pertinent to this work was re-examined and their data for mixtures containing 2H2 + 02 + 1/2 Xe, 2 2 2H2 + 0 + 1/2 Xe + 1/4 H20, and 2H2 + 02 + 1/2 Xe + 1/2 H20 are plotted in Fig. 9. It is seen that adding water vapor results in a faster rise to a higher peak density and a faster decay to the equilibrium density, (the C-J density), Although the data for the mixture containing 1/2 H20 shows a 2 slight increase in reaction time compared to the mixture containing 1/4 H 0, 2 it is apparent that either of these mixtures has a reaction length lower than that of the dry mixture. Thus these data can be considered to confirm our findings regarding the reaction lengtho 19

V. CONCLUSIONS It has been experimentally verified that, for 50% H2 + 50% 02 and 66 2/3% H2 + 33 1/3% 02 mixtures, the addition of water vapor increases the minimum required Mach number of propagation. This finding is in agreement with the explosion limit criterion given by Belles. Specifically, the high efficiency of water vapor as a third body in the chain breaking reaction, has been verified for detonative combustion. In addition, it was found that the addition of water vapor to both the 50% H2 and 66 2/3% H2 mixtures acted to reduce the Mach number decrement due to the compressible boundary when the same channel width and boundary gas are usedo This reduction in Mach number decrement is explained by postulating a reduction in reaction length. The experimental work of Kistiakowsky and Kydd was found to give further support to this conclusion. 20

REFERENCES 1. Belles, Fo Eo, "Detonability and Chemical Kinetics, Prediction of Limits of Detonability of Hydrogen, " Seventh Symposium (International) on Combustion, 745-751, Butterworths, London, 1959o 2o Dabora, Eo Ko 9 The Influence of a Compressible Boundary on the Propagation of Gaseous Detonations, Pho D. Thesis, The University of Michigan, December 1963. See also Proceedings of Tenth Symposium (International) on Combustion, to be publishedo 3o Lewis, Bo and von Elbe, Go Combustion, Flames, and Explosions of Gases9 2nd edo, Chapt. 1, Academic Press, New York, 1961. 4o Fay, J. A, "Two-Dimensional Gaseous Detonations- Velocity Deficit9,T The Phys. of Fluids, Volo 2, No 3, 283-289, May-June 1959. 5o Sommers, W. P. The Interaction of a Detonation Wave with an Inert Boundary, IP-501, The University of Michigan Industry Program of the College of Engineering, Ann Arbor, March 1961, 60 Gordon, S. private communicationo 7o Kistiakowsky, G. Bo and Kydd, P. Ho, "Gaseous Detonationso IXo A Study of the Reaction Zone by Gas Density Measurements, 9 J, Chemo Phys, 25,824-835, 1956. 80 Dove, Jo Eo and Wagner, Ho Ggo, "A Photographic Investigation of the Mechanism of Spinning Detonation, " Eighth Symposium (International) on Combustion, 589-600, Williams and Wilkins, Baltimore (1962)o 9. Nicholls9 Jo Ao, Stabilization of Gaseous Detonation Waves with Emphasis on the Ignition Delay Zone, Report No, IP-421, Industry Program of the College of Engineering, The University of Michigan (1960)o 10 Bauer, So Ho, Schott, Go L, and Duff, Ro Eo " Kinetic Studies of Hydroxyl Radicals in Shock Waves, Io The Decomposition of Water Between 24000 and 32000K, " Jo Chemo Phys., 28, No. 6, 10891096 (1958)o 11. Miyama, Ho and Takeyama, To 9 "Kinetics of Hydrogen-Oxygen in Shock Waves, " J Chemo Phys,, 41, No 8, 2287-2290 (1964)o 12o Brokaw, Ro So Analytic Solutions to the Ignition Kinetics of the Hydrogen-Oxygen Reaction9 NASA TMX 52003 (1964)o See also Tenth Symposium (International) on Combustion, to be publishedo 21

.14.12 -4-) 0) E a) Q) c4 k 0) I Ct W B o cz 4 C I Q) *r —l I:9.10.08.06.04.02 2 1 |_ \% 66%H2+ 333%O2 50% H2+ 50% 02,I I I I L I 0 0 I 2 3 4 5 Water Vapor Content -- % by Volume Figure 1. Maximum Allowable Mach Number Decrement as a Function of Water Vapor Content 22

ks% CO EXI/ EXPLANION C-J PLANE COMPF (NITRO VD D tESSIBLE INERT BOUNDARY )GEN) I I I I I I I I T1 HYDROGEN-OXYGEN P EXPLOSIVE MIXTURE -INDUCTION ZONE -SHOCK PLANE -I / //// I x. —ON i' / ///// Figure 2. Model for the Interaction of a Detonation With a Compressible Inert Boundary

IION PROBES (4) PLUG Figure 3. Schematic of Mixing and Charging System

Mll1or 4400N 13 Mallory RM-4T Simpson No. 1329 Mallory RM- 4T - 100 0-100 jpamps Batteries (1. 34V) Fenwall GA45JI Thermistor Figure 4. Circuit Diagram for DewProbe Cavity Temperature Measurement 25

I I I I I I / 4 3 0 0 a). 1 2 0.E o-r ct CD 0 <u I L -LL —LL/ 1 I I I I l I l l I I I 2( D 30 40 50 60 70 80 Thermistor Current Flow - Liamps Figure 5. Curve for Use in Determining Water Vapor Content of Explosive Mixture from Thermistor Current Flow 90 26

.10.08 1 -i I r. 0 Q, CD X..06.04.02 0 0 I 2 3 4 5 Inverse of Channel Width - 1/b Figure 6. Experimental Mach Number Decrement Due to the Compressible Boundary as a Function of Channel Width. 50% H2 + 50% 02 Mixture. 27

c) 0.&4 0 Q) 7600 7400 7200 0 Symbols Indicate Different Fillings of Mixing Chamber +-~ I I 50% H2 + 50% 02I -I l_ I, _ 7000 0 2 3 4 5 Water Vapor Content, % by Volume. Figure 7. Detonation Velocity of 50% H + 50% 02 and 66 2/3% H2 + 33 1/3% 02 Mixtures as a Function of Water Vapor Content 28

.12.10 I2z 0 f1 0 C) Q, (1) i QS 1:: C; a) k O 4r\ z Cd.08.06.04.02 0 0 I 2 3 4 5 6 7 Figure 8. Inverse of Channel Width - 1/b Experimental Mach Number Decrement Due to the Compressible Boundary as a Function of Channel Width. 66 2/3% H2 + 33 1/3% 02 Mixture.

0 Mixture 3 2H2 + 2 + 1/2Xe E Mixture 10 2H2 + 02 + 1/2 Xe + 1/4 H20 4. 3. Mixture 11 2H2 + 02 + 1/2 Xe + 1/2 H20 Q. II b H H 1 2. 1. Microseconds From Zero Time Figure 9. Density Changes in a Hydrogen-Oxygen Detonation as a Function of Time. Data from Kistiakowsky and Kydd(7). 30

Appendix I CALIBRATION CURVES FOR DEWPROBE/THERMISTOR DEWPOINT MEASUREMENT SYSTEM 31

170 160/ 150 - 140 o4 130 - -- 0 10 - - I00, <u / /3 9070 1 - | - I 20 30 40 50 60 70 80 90 100 Thermistor Current ~ /amps Figure a - Thermistor Calibration Temperature vs. Current Through Thermistor 32

70 50 0 40 0 30 20 10 70 80 90 100 110 120 130 140 15C DewProbe Cavity Temperature ~ OF Figure b - Dewpoint vs. DewProbe Cavity Temperature ) (Data from Honeywell Special Sensor Products Div. )

3.0 2.5 ~2.0 O 0 C) o 1.5 r-4 C).5 0 0 0 a -L I I I -1 - - I I I I I 10 20 30 40 Mixture Dewpoint OF 50 60 Figure c - Volumetric Concentration of H20 Vapor vs. Mixture Dewpoint (Data from Handbook of Chemistry and Physics, 36th Edition) 15. 0 psia Ambient Pressure

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