ENGINEERING RESEARCH INSTITUTE UNIVERSITY OF MICHIGAN ANN ARBOR QUARTERLY PROGRESS REPORT NO. 1 August 1, 1953 to December 31, 1953 INTERMITTENT DETONATION AS A THRUST-PRODUCING MECHANISM By J. A. NICHOLLS H. R. WILKINSON R. B. MORRISON Project 2172 WRIGHT AERONAUTICAL DIVISION CURTISS-WRIGHT CORPORATION January, 1954

ACKNOWLEDGEMENT Sincere appreciation is extended to Edward J. Schaefer, who assisted by working out the instrumentation and calibration problems associated with the accelerometer measurements. ii

FOREWORD The work reported herein was conducted under University of Michigan, Engineering Research Institute Project Number 2172, for the Wright Aeronautical Division of the Curtiss-Wright Corporation. All the work was done by personnel of the Aircraft Propulsion Laboratory. iii

TABLE OF CONTENTS Page ACKNOWLEDGEMENT ii FOREWORD iii LIST OF FIGURES v ABSTRACT vi INTRODUCTION 1 PRESSURE AND TEMPERATURE RATIOS ACROSS A DETONATION WAVE 2 THEORETICAL IMPULSE FROM A SINGLE DETONATION WAVE EXPERIMENTAL DETERMINATION OF THE IMPULSE FROM A SINGLE DETONATION WAVE 10 DEFLECTION OF A BALLISTIC PENDULUM 12 ACCELEROMETER MEASUREMENTS 15 RESULTS AND DISCUSSION 15 FUTURE PLANS 25 APPENDIX A. INSTRUMENTATION 26 APPENDIX B, CALIBRATION PROCEDURE 31 REFERENCES 34 iv

LIST OF FIGURES Figure No. Page 1, Detonation Wave in a Constant Area Duct 3 2. Pressure Distribution across a Detonation Wave 3 35 Thermodynamic Ratios across Hydrogen-Oxygen Detonations 6 4. Detonation Tube 8 5* Idealized Thrust-Time History of a Single Detonation Wave 8 6. Experimental Arrangement 11 7. Detonation Tubes 13 8, Geometry for Deflection Calculations 13 9* Curve of Impulse vs. Deflection 14 10. Block Diagram of Instrumentation 16 11 Photograph of Detonation Tube B 17 12. Photograph of Accelerometer Instrumentation 17 13. Impulse Derived from Hydrogen-Oxygen Detonations 18 14. Impulse Derived from Acetylene-Oxygen Detonations 20 15* Acceleration-Time Photograph 21 16. Comparison of Deflection and Accelerometer Method 22 17. Acceleration-Time Graphs of Acetylene-Oxygen Detonations 23 18* Linear Accelerometer 26 19. Calibration and Pre-Amplifier Circuit 28 20* Blanking Pulse Generator 30 21, Schematic of Accelerometer Calibration 32 22. Typical Accelerometer Calibration Run 33 v

ABSTRACT The feasibility of using intermittent detonation as a thrustproducing mechanism is discussed and considered theoretically. The thrust derived from a single detonation wave was measured experimentally by noting the deflection and acceleration of a ballistic pendulum. The acceleration-time traces have yielded valuable information on the pressures and wave processes. While the impulse predicted by the simplified theory is reasonably close to the experimental impulse, the force-time variation in achieving this impulse is markedly different from that postulated. vi

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN INTERMITTENT DETONATION AS A THRUST-PRODUCING MECHANISM INTRODUCTION The phenomenon of detonative combustion has been studied extensively in the past by a number of investigators. In general, these investigations were directed toward furthering the understanding of the phenomenon both from the chemical and the hydrodynamic point of view. Such knowledge is, of course, essential to minimizing the dangers of inadvertent detonation and improving the design of explosives. However, very little has been done from the standpoint of harnessing the energy associated with these highly supersonic combustion waves. In recent years some thought has been given to the possibility of stabilizing a detonation wave in a steady-flow thermodynamic cycle. More recently the idea of using intermittent detonation in the manner of a pulse jet has been advanced.* The work reported here is directed toward ascertaining the possibility of the intermittent-type cycle. On the basis of a simplified, theoretical analysis, which was made earlier, the application appears worthy of further study. These theoretical results predict very high thrusts per unit combustion-chamber area, although the specific impulse is rather low. The physical mechanism for fuel injection, heat exchange, etc., could appreciably alter these predictions in an actual engine. In this approach to the problem the philosophy has been first to establish experimentally some representative thrusts and impulses derived from a single detonation wave and then to investigate the more prominent parameters affecting these results. On the basis of these initial findings an attempt will be made to achieve cyclic detonation in a tube or series of tubes. * A literature search is currently in progress to consolidate existing information on the possibilities of detonative combustion engines. 1

SUSPENSION WIRES SPARKes $.oARK DEroNJATON rVBeI SCAL (D XTERN^AL SYNCH J Z-AX/S @ Y- AMPLITUDE (o C). I0-LOCK DIARAM OF NTRUETATCOIL | ~LTDL AOWMT 304 1 l S OSCILLO GiAPH MroDEL 3e1 _ _ ___f m j___g DFI~Ui4EA #T PUL5E ctLk o A IPL Pr FI Et, __________ _________ /16. /0- SLOCK D/A GRAM OF /NSTRUMEMTA7T/ON

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN PRESSURE AND TEMPERATURE RATIOS ACROSS A DETONATION WAVE The dynamic properties of a detonation wave are treated quite extensively in reference 2. However, for the sake of continuity, the pertinent relations will be derived here. A detonation wave in a constant-area duct may be treated as a flow discontinuity with heat addition. Assuming that the discontinuity is stationary, this system may be described by the following equations (see Fig. 1) Condition (1) refers to the unburned gases, while state (2) refers to the conditions after the heat release has been realized. Conservation of Momentum: P1 + Pi ul2 = P2 + P2 22, (1) Conservation of Mass: Pi u1 = p2 u2, (2) Equation of State: P = p T, (3) m where P = static pressure, p = density, u- = velocity, m = molecular weight, R = universal gas constant, and T = static temperature. Rearranging the momentum equation and introducing the state equation, we may write: PI [l+ ] = P2 [l+ -] RiT1 R2T2 _________________________________________ 2 ~____________________

QAS FLOW o FIG. 1 - DETONATION WAVE IN A CONSTANT-AREA DUCT a~P~~~ ~P2 P3 P1 I PRESSRE DISTRIBUTN ACOSS A TATION WAVX FICG 2 - PRESSURE DISTRIBUTION ACROSS A DETONATION WAVE

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN or P2 1_ + 71 M12 Pi 1+ 72 M22 where y = ratio of specific heats, M1 = Mach number of detonation, and M2 = Mach number of the burned gases relative to the front. In the normal case, detonation is of the Chapman-Jouguet type in which M2 is unity. The pressure ratio then becomes P2 = 1+ y? Mia. (4) P1 + 72 In the case of a flame tube, the pressure established behind the detonation wave, as indicated by equation (4), will be modified by a trailing rarefaction wave. The pressure, P2, will be reduced to a new plateau value of P3. A typical pressure distribution for a detonation wave in a flame tube is shown in Fig 2 This plateau pressure is related to the peak pressure by the relationa 2Y21(Y2 ~ 1) P = P2 [1 2- 2(- 1M2c] P1 P1 2 where Mc = Mach number of the burned gases relative to a fixed point on the flame tube, or P3S + 7Y M1a Z2 -1 M2 /(2 (6 y= Ml; i-M2c (6) P1 1+ Y2 2 In order to derive a relation for the temperature ratio, we may write from the equation of state (7) TI P1 ml P2 Equations (1) and (2) may be readily combined to give 4F

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN (PI ui) - (pa U2)2 = uP _ P i 1 P2 P1 P2 / or 11 M12 (1 - P2/P,) (Pi/P - 1) Solving for P. we have P2 P2 =lM 2 + 1. (8) P2 ylH12 Introducing (4) and (8) into (7) and simplifying yields T2/T.1 = m2. + 7l M122 ml ZI Ml2" i+ Y2 A plot of the pressure, temperature, density, and molecular-weight ratios for hydrogen-oxygen detonations is. shown in Fig* 3. For these calculations the experimental Mach number of detonation as obtained in reference 2 was used. The molecular-weight ratio is based on no dissociation, while the ratio of specific heats in the burned gases was assumed to be 1i15, THEORETICAL IMPULSE FROM A SINGIE DETONATION WAVE The relatively high pressures associated with detonative combustion could conceivably be utilized in a jet propulsion device. If such an application is considered on the basis of steady flow, there will be a marked increase in entropy across the wave and the system might appear to be inefficient, However, a standing or stabilized detonation wave has never'been attained experimentally; hence the case of cyclic or intermittent detonation will be considered. 5

2.0 20 1.2 ( / CT 1.04 0 0 10 20 30 40 50 60 70 80 PERCENT HYDROGEN BY VOLUME FIG. 3- THERMODYNAMIC RATIOS ACROSS HYDROGEN-OXYGEN DETONATIONS

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Preliminary calculations on an intermittent detonation cycle have been made in reference 1. The theoretical model for those calculations will be used here in evaluating the thrust and impulse that would be expected from a single detonation wave, Figure 4 represents a detonation tube of length L and cross-sectional area A, The tube is filled with combustible gas and then spark-ignited at the closed end. The flame front will be preceded by a shock wave which is continuously strengthened by the accelerating flame front until detonation is established. At the open end of the tube a rarefaction wave will be reflected which will move through the gases at the local sonic speed. At the closed end of the tube the pressure will gradually be reduced and another rarefaction reflected. These reflections continue but, of course, are gradually damped out, These detailed processes do not lend themselves to easy quantitative evaluation. Consequently, a few simplifying assumptions will be made. First, it will be assumed that detonation is established immediately and is of the Chapman-Jouguet type. This assumption is somewhat optimistic, although the use of a long tube will tend to minimize the error. The plateau pressure will act on the closed end of.the tube until the reflected rarefaction returns, It will also be assumed that the rarefaction returns at the sonic velocity corresponding to state 2 and that it returns as a discontinuity and reduces the pressure to atmospheric. These assumptions are on the conservative side, as they tend to lower the effective time of the thrust force, The subsequent reflected waves will be neglected. Accordingly, the simplified thrust-time history of a single detonation wave is as shown in Fig. 5. In this figure td represents the time for the detonation wave to travel the distance L and tr the time for the rarefaction to return, The impulse I may then be expressed as td + tr I = T dt = T (td + tr). (10) Referring to the nomenclature in Fig. 2, the thrust can be evaluated. by the pressure differential acting on the head end of the tube, or T = (P3 -P1) A where we will assume that the tube is initially filled to the ambient pressure, PI, Then T = ( P' A=P A (1 yI Mc1 2727(721 - I ~ 7 ~

SPARK PLUG,/ - FIG.4 - DETONATION TUBE T td td btr t FIG.5 - IDEALIZED THRUST-TIME HISTORY OF A SINGLE DETONATION WAVE

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN Further td = L = L Vd V1 and tr = L L = - Vr V2 /72 Ra T2 where Vd = velocity of detonation-wave and Vr = velocity of rarefaction wave. Finally, I P\L L \y2i s2/(Y72-) r1 2 (11) I = PzAL + 1 - 72-1 M2 (l The specific impulse Is or the ratio of impulse to the weight of fuel, may be written as s. wf If oxygen is used as the oxidant rather than air, the propulsion system is penalized for the additional weight of the oxygen; hence Is = - I Wf + wo where wf = weight of fuel and o02 = weight of oxygen. Then wf = p f AL and wo0 Po2 A L (1 - f) where f = percent by volume of fuel and A L - volume of tube., 9

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN Then 2y2/-(72-l) 1 r _Is -,..)1 (+-. M2c).. L. +VM.. (12) f Pf + (l-f) po2 The thrust, impulse, or specific impulse may now be evaluated from these equations. The values of Vd are available from previous experiments2. However, it is necessary to assume a value of 7y2 As with other propulsive systems, the geometry does not enter into the specific impulse. Contrary to other systems, however, the impulse is directly proportional to the length. EXPERIMENTAL DETERMINATION OF THE IMPULSE FROM A SINGLE DETONATION WAVE The theory developed is subject to modification in the real case where detonation does not ensue immediately and where unsteady fluid flow replaces the simple wave processes assumed. To gain some insight into the magnitude of these discrepancies, the impulses were determined experimentally and compared with the theory. The experimental arrangement is shown in Fig. 6. The particular combustible mixture tested was premixed in a stainless-steel reservoir. The reservoir was first evacuated to a pressure of about 0.1 inch of mercury by means of a Cenco Megavac. The fuel and oxidant were then mixed on a partial-pressure basis in which the effects of compressibility were small enough to be neglected. For each run the fuel was blown through the detonation tube. After sufficient purging the downstream end was sealed with a paper diaphragm to prevent diffusion of the test gases into the air. The pet cock was closed and the fuel line disconnected. Ordinarily, the mixture was ignited by a conventional automotivetype spark plug, although a glow plug was used on occasion. To facilitate the measurement of impulse, the detonation tube was suspended from the ceiling as a ballistic pendulum. Two pieces of 1/16-inchdiameter stainless-steel aircraft cable, 12.5 feet in length, served as the suspension. Two different detonation tubes were utilized in order to obtain reasonable deflections and accelerations for the different gaseous mixtures 10

ILiii/i///////// A IRCRAFT CABLE SPARK PLUG D IAPHRAGM RETAINER Pf, 0T COCK DETONATIONTUBE ] X~ VACUUM FUEL OX IDANT C 6XTURIBE 0 A xTAMANOMEER flG. 6 - EXPERIMENTAL ARRANGEMENT

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN used. These tubes will be designated as tube A and tube B and are shown in Figs 7The experimental measurements of impulse were made by two different methods, and will be discussed separately. DEFLECTION OF A BALLISTIC PENDULUM The first method used in evaluating the impulse of a single detonation wave was based on the impulse-momentum relation. That is, I = F dt = WV, g where W = weight of tube and V = maximum velocity of tube. As the tube is fired the thrust force causes it to swing in an arc, converting the kinetic energy into potential energy. If it is assumed that the tube achieves its kinetic energy without a change in elevation (and this assumption is well within the limits of experimental accuracy), the energy balance can be written as -w V2 = Wh = W (1 -b cot:) 2 g or I = W 2 b ct (13) /(l - b cot () where 9 = sinl b and the nomenclature is as shown in Fig. 8. 1 A plot of equation (13) is included as Fig. 9 The experimental procedure consisted simply of noting the deflection, b, for each detonation. This measurement was accomplished by superimposing a scale on the side of the tube and then noting visually the movement of the scale past a fixed vertical reference line. 12

-- O 026" I r 2.01" q~ T9ITUBE A -STAINLESS STEEL, WEIGHT = 10*.2 2,375 -I 10.7 1 153 TUBE B - BRASS, WEIGHT - 48.a FIG, 7 - DETONATION TUBES //////ii I//////ii 1111 I/I L / I l / IL h F IG. 8 - GEOMETRY FOR DEFLECT I ON CALCULATIONS

i 3 II I ar I -I I I i U 2 0 0 5 1o 15 20 25 30 35 DEFLECTION - INCHES FIG. 9 - CURVE OF IMPULSE VS. DEFLECTION

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN ACCETLEROMETER MEASUREMENTS Although the deflection method afforded a convenient means of measuring the impulse, it yielded no information as to the variation of thrust with time, Such information would be extremely pertinent to the design of an intermittent detonating device, Accordingly, an accelerometer was mounted at the center of the tube so that the variation of tube acceleration (and hence thrust and pressure) with time could be obtained, The schematic arrangement for making these measurements is shown in Fig, 10, The instrumentation and calibration equipment associated with the accelerometer traces are described in the appendix, Figure 11 is a photograph of the brass detonation tube, while Fig, 12 is a photograph of the instrumentation, RESULTS AND DISCUSSION A series of runs were made with hydrogen-oxygen mixtures in tube A., For these runs the impulse was obtained by the deflection method and is plotted in Fig. 13 as a function of the mixture ratio., The specific impulse, or the impulse divided by the weight of the hydrogen and oxygen, is also shown. on this curve and is compared with the theoretical values. As may be seen, the agreement is quite good with richer mixtures, but there is a radical departure as the mixture is leaned below 45 percent. This mixture ratio checks very well with spark-schlieren photographs of hydrogenoxygen detonations3, where two regimes of detonation might be indicated. With mixtures below about 45 percent, the initial shock front of the detonation is followed by an array of oblique shock waves and then the lagging combustion. The burning phase lags more and more as the mixture becomes leaner. However, in the case of mixture ratios greater than 45 percent, the detonation is relatively clean, with the combustion evidently initiated right in the shock front. It appears reasonable that the leaner unstable mixtures (possibly subject to spinning detonation) are less prone to detonate, which would account for the defect in the impulse, The specific impulse of the hydrogen-oxygen mixtures is quite low and is seen to increase with the richer mixtures even though the impulse is falling off, The low values are, of course, attributable to the oxygen, which is included in the specific impulse; but the increase in hydrogen decreases the weight of the fuel-oxygen mixture sufficiently to overbalance 15

AXE*.]v~~wo Photograph ofW 1X..........t...i. jj_:jl _::_::_:: lj-.......... -...'..... ^" ~ -:- - -: ~ iii-'^ ~ f i Big^II ~Photograph of" letonati-ion^ Tube B. ----- - --—:~:: _ l:ig, 12. Photograph of Accelerometer liIstrumen-ba..o., ii.7:. FiS. Phntoprnr-na of Ace-elroi-tiete Tnstrmenttion

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN the decreasing impulse. In the case of hydrogen-air mixtures, the specific impulse should be materially improved, In Fig, 14 is shown the impulse and specific impulse of acetyleneoxygen mixtures in which the deflection was also measured. The detonations were initiated by a glow plug. There was appreciable scatter in the experimental points for the lean and rich mixtures, but the results were quite consistent for mixtures in the neighborhood of 50 percent. It is felt that the glow plug has some effect on this scatter, as it does represent a minimum energy input for the initiation. The maximum impulse was noted at 50 percent, which corresponds to the point of the maximum Mach number of detonation, In the past this mixture ratio has been noted to be one of the easiest to detonate. The specific impulse has been plotted on the basis of the arithmetic average of the points for the impulse curve. The discrepancy between experiment and theory is now appreciable for the lean and rich mixtures. The reasons for this discrepancy will be considered shortly. The chemical considerations involved in the theoretical curve are discussed in reference 4, in which the authors evaluated the equilibrium temperatures and compositions behind acetylene-oxygen detonations. In another series of runs, made with acetylene-oxygen mixtures in tube B, both the deflection and acceleration were noted. For these runs a conventional spark plug was used, A typical acceleration-time photograph is shown in Fig. 15, The superimposed horizontal lines are calibration lines, while the zero axis is the second line from the top. Time increases to the right and acceleration increases positively downward. The horizontal sweep of the oscillograph was triggered by the spark plug, so that the time lag before establishment of detonation is indicated. Each blanked spot on the zero trace represents 1 millisecond, The fluctuations in the trace are due to longitudinal vibrations set up in the wall of the detonation tube, With the accelerometer mounted at the center of the tube, the frequency detected is the second harmonic of the fundamental frequency of about 450 cps. The natural frequency of the accelerometer used for Fig. 15 is 250 cps., which is too low to follow the tube vibrations correctly.. However, comparison with traces of a higher-response accelerometer(800 cps) indicates that the first accelerometer is recording the overall acceleration of the tube correctly, If the accelerometer were mounted at either end of the tube, the fundamental frequency would be predominant and the amplitude of the undesirable vibrations would be much more pronounced, More detailed information on the instrumentation appears in the appendix, The areas under the accelerometer-time traces were integrated by means of a planimeter so that the impulse obtained in this manner could be compared with that by the deflection method. The results of this comparison are shown in Fig, 16, The agreement is quite good, the average difference 19

200 1.0 Xo 160 0o.8 ~/ X / | EXPER I MENTAL IMPULSE I ILh 120 o0.6 ^ I THEORETICAL SPEC I F I C I MPULSE 8o 0.2 10 20 30 40 50 60 70 80 PERCENT HYDROGEN BY VOLUME FIG. 13 - IMPULSE DERIVED FROM HY DROGEN - OXYGEN DETONATIONS FIG. 13-" IMPULSE DER IVED FROMI HYDROGN - OXYGEN DETONAT IONS

THEORET I CAL EXPER I MENTAL SPECIFIC IMPULSE SPECIFIC IMPULSE 0200 I 2 U o 6o o 20 )o 60 8o PERCENT ACETYLENE BY VOLUME FI G 14 - IMULSE DERIVED FROM ACETYLENE-OXYGEN DETONATIONS

ENGINEERING RESEARCH INSTrII"I' UNIVERSITY OF MICHIGAN Fig. 5A........-' ai. Fig, 15,.... A:cl; totn-TI. me PhoIto:graph, being less than 2 percent,. It miighot be t te Impulse for this series of runs is somewhat higher than'that shown In Fig. ]t.l The only plausible explanation would seem to lie:in the d:l.ff erenee of spark plugs. The higherintensity conventional spark plug undoubtedly initiates detonation sooner than in the case of the glow plug. The acceleration-t LtMe curves for four acetylene -oxygen mixtures are shown in Fig, 1T.7 also included on these c.nrves is the simplified theory. It is interesting that while'the theoretical and experrirmenta)l impulses agree reasonably well., there is a marked di. fference in the manner of achieving this impulse, As is evident from the traces,'the detonat:i.on wave Is not established instantaneously: rather there i.s a transient phaset, which was described earlier. This transient phase is longer for mxtlures near the detona'tion limits. The shock wave gives rise -to a steady increase ohf pr essure on the head end of the tube until the shock strength is sufficient to initi.ate detonation, The gradual decrease in acceleration (or pressure) is due to the returning rarefaction wave, which is not a discontinuity as was as,'sumed hfo:r" simpli.:city. This effect materially lengthens the cycle time, which should be advantageous in the design of a cyclic engine, The acceleration traces:i.ndi.cat' e t ha't Lthe'tube pressurIe is reduced to approximately 1./2 atmosphere for a sho:;rt ti.,me. This was observed experimental.ly, iX ~ ~ 1

3.0 2*0 W~M qh 0 ^^ DErLCCT ION MCTHOD ~ A\ ACCELERONETER METHOD I-0........___________ 10 20 30 4 50 60 PERCENT ACETYLENE BY VOLUME FIG. 16 - COMPARISON OF DEFLECTION AND ACCELEROMETER METHOD

16.. - 16- l l THEORETICAL 12 8 1 12d I t o 8~- 8~---- HEORETICAL z ^I I I4..,0 i i..I. I - 1 O 16 2 0 16 TIME - MILLISECONDS TIME - MILLISECONDS 10% ACETYLENE 30% ACETYLENE FIG. 17 ACCELERATION - TIME GRAPHS OF ACETYLENE-OXYGEN DETONATIONS

I i6 ~ Ii6~si - I I THEORETICAL THEORET ICAL 12 -___ 12___________ I, 0 0I 0 IM MILLIECOND TIM - EXPERIMENTALD I 17 EXPERIMENTAL I G O \ W, h 11 & h )~ I/\w~ ~J I f ~ \________^ ____ I ____ LJ T ^I \ I ~ I \) U) II I U 44: 1 I I 0 l 0 _ _ _ \ TIME - MILLISECONDS TIME - MILLISECONDS 50% ACETYLENE 60% ACETYLENE FIG. 17 (Cowr~uuEo) - ACCELERATION - TIME GRAPHS OF ACETYLENE-OXYGEN DETONATIONS

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN as fragments of the diaphragm were repeatedly found distributed throughout the tube. Conceivably, the reduced pressure could be utilized to induce a fresh charge of fuel. In operating the detonation tube an appreciable ejector effe-ct was noted at the discharge end. As the exhaust gases were discharged a secondary flow was induced which, in an actual engine, might be worthy of investigation as a device to induce a fresh charge, FUTURE PLANS A few more gaseous mixtures will be tested in the detonation tube, especially air mixtures. It is also planned to investigate end effects, that is,the effects of a tail nozzle and different diaphragms. A literature search is in progress to assimilate existing information on the possibility of utilizing detonation combustion in an engine. Concurrent with the above studies, thought and effort will be directed toward the design of an intermittent detonative device., 25

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN APPENDIX A. INSTRUMENTATION This section is devoted to a brief description of the equipment shown in block diagram (Fig. 10) with which the acceleration-time history of the impulse detonation tube was obtained. The acceleration pickup device selected was the Schaevitz type AB accelerometer shown schematically in Fig. 18. The seismic system of this accelerometer consists of a mass suspended by two parallel beryllium-copper Shell ZZ/////////////// / // PRI tQQ-, ~~~ ^Spring Core Mass Sensitive Axis Secondaries Fig, 18. Linear Accelerometer. cantilever springs. The mass, in the form of an iron core, moves in proportionally to the applied acceleration within. a cylindrical form on which are would three adjacent coils, The entire system is 60 to 70 percent critically damped by immersion in a damping fluid of proper viscosity. Displacement of the mass is detected by the change in electromagnetic coupling of the coils. The primary coil located at the center, is excited by approximately 2.5 volts RMS at 22,5 RC. The secondaries, on either side, are connected in phase opposition, so that the net output is zero when the core is perfectly centered. Motion of the core increases the voltage induced in the secondary in the direction of motion and reduces the voltage induced in the other secondary. The net output is a voltage which is a linear function of the displacement of the core (within the design range of the instrument); phase depends on the direction of motion, changing 1800 as the core passes through the equilibrium position. 26

ENGINEERING RESEARCH INSTITUTE * UNIVERSITY OF MICHIGAN Damping is employed to reduce "ringing" of the system after the applied acceleration is removed. Quantitatively it has been shown that 60 to 70 percent of critical damping extends the range of usefulness of the accelerometer to nearly 75 percent of its natural frequency and produces an almost linear phase-lag relation in this range, thereby eliminating phase distortion, It can also be shown that the response of such a damped system to a step function input is within 1 percent of the true value within 5/8 of its natural period* The ensuing oscillations about the true value never exceed 1-1/2 percent and damp out rapidly. Thus, for the type AB-3 accelerometer which was used, the natural period of which is 4 milliseconds (250 cycles/sec), the response to a suddenly applied acceleration of constant magnitude is within 1 percent of the true value in 2.5 milliseconds. The response to accelerations which require some time to reach peak amplitude is closer to the true values, To separate the intelligence from the 22o5-kc carrier requires a phase discriminator and detector. These functions are performed in the S. Sterling Model 301 Differential Transformer Amplifier. In addition, the driving voltage is obtained from this instrument. Briefly, the excitation voltage is derived from a conventional oscillator-driven amplifier transformer coupled to the accelerometer primary. The secondary outputs are amplified and then applied to a phase-discriminator amplitude detector stage. The output of this stage is a voltage, the amplitude of which is proportional to the acceleration and the polarity of which depends on the direction of acceleration. A four-stage RC low-pass filter is utilized in the output to attenuate the 22.5-kc carrier. The output of the differential transformer amplifier is applied to the d-c y-axis amplifier of a Du Mont Type 304- H oscillograph through the calibration and pre-amplifier circuit shown schematically in Fig.. 19. Here provision is made for selecting the accelerometer signal or an accurately known calibration voltage in the form of a step function. The circuit also permits the insertion of a single-stage resistance-coupled triode pre-amplifier when necessary. The high-frequency response of this pre-amplifier is intentionally attenuated to reduce the 22,5 kc carrier output further without materially affecting the low-frequency components up to approximately 1000 cycles. The d-c response of the entire system is sacrificed in the interest of simplicity by the use of the 1-mf coupling condenser in -the output of this circuit. The time constant of this condenser and the 2-megohm input impedance of the oscillograph is 2 seconds.- It can easily be shown that the response of such a system to a step function at the end of 0.02 second (a typical sweep time) is only 1 percent below the true value (note the calibration traces, Fig, 15). Response to any other signal will be more accurate, In obtaining data, a single driven sweep of the oscillograph is employed, and the trace is photographed by a DuMont Type 297 oscillographrecord camera operating on the Polaroid-Land principle. The sweep is triggered 27

~~~ O^ ri 0 C ^~ ~~~~~~~~~~~~~ i A _ 3 (3 i i~ (3 ~ c.'i~~~~~~~a I~~~I'00 GI 0,~~ b ~ (no b (FC~__. r3'I( >~~~~~~ ss "0 I N P 0 ^ o o o o o ^I:b ^ Q 0 ~^^ u, " _____,: - o~______ H-)~^ ^~1'~~

ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN by a signal obtained by opening the switch which generates the spark for igniting the mixture in the tube. The entire spark system is shielded to eliminate the interference which would otherwise mask the desired signal. Time calibrations of each trace are obtained by blanking the oscillograph beam with pulses spaced at known time intervals, To produce these pulses, the circuit of Fig. 20 was employed. This circuit is variously known as a cathode-coupled clipper or a slicer. It is essentially an overdriven two-stage RC coupled amplifier with positive feedback introduced by the common cathode resistor. Driven by a calibrated oscillator, its output is a rectangular wave of steep slope synchronized at the oscillator frequency, Differentiating the output produces a series of pulses of alternate polarity, The positive pulses are attenuated by the crystal rectifier across the output. The remaining negative pulses, spaced by the oscillator period, are applied to the z-axis oscillograph input, thereby blanking the beam at a known frequency. To eliminate the extraneous signals due to microphonics, the entire instrumentation with the exception of the accelerometer, is located about 30 feet from the blast tube. Thus all the events of interest are recorded before the sound waves of the blast reach the equipment to generate microphonic signals, 29

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ENGINEERING RESEARCH INSTITUTE ~ UNIVERSITY OF MICHIGAN APPENDIX B. CALIBRATION PROCEDURE To obtain quantitative data from the accelerometer signals, it was necessary to calibrate the output of the differential transformer amplifier in terms of millivolts as a function of the acceleration experienced by the accelerometer, Known accelerations were obtained by the spring-mass system shown schematically in Fig. 21. Here the accelerometer is a portion of a mass suspended on a spring. The entire system is stressed by a known force composed of weight suspended from the accelerometer by means of a fusible link of 0.016-inch piano wire. Electrically melting the link releases the weight, whereupon the mass is accelerated upward by a known force equal to the released weight. The effect of the distributed mass of the spring is taken into account by adding 1/3 of its total mass to that of the suspended mass5. This empirical correction is accurate to within 1.5 percent for the case when the suspended mass and that of the spring are equal and the error is reduced for the larger suspended masses employed. The output of the accelerometer and associated instrumentation is recorded by photographing the single driven sweep of the oscillograph. Triggering of the sweep is accomplished by a signal obtained from the same switch which closes the electric circuit to melt the fusible link, Following each recording of an accelerometer signal, a calibration grid composed of step-function voltages of known values is superimposed on the picture. Thus a calibration in terms of millivolts per g acceleration is obtained (see Fig, 22), By superimposing a similar calibration grid on subsequent detonation tube records, quantitative information of the values of recorded accelerations is obtained. 31

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REFERENCES 1. Morrison R. B., Nicholls, J. A., and Ong. R., "Preliminary Calculations on the Thrust and Impulse Characteristics of Intermittent Detonations" University of Michigan Engineering Research Institute, not yet published. 2. Morrison, R, B,, "A Shock Tube Investigation of Detonative Combustion," Report UMMJ97, University of Michigan, Engineering Research Institute, January, 1952. 3. Nicholls, J. A., Morrison, R. B., Reid., F. A., and Ong. R., "Final Report on Detonative CombustiOn," Project M898, University of Michigan, Engineering Research Institute, August, 1953 4* Weir, A. Jr., and Morrison, R. B., "Equilibrium Temperatures and Compositions behind a Detonation Wave," Paper presented before Division of Gas and Fuel Chemistry, 124th Meeting, ACS, Chicago, Ill*, September, 1953. 5, Myklestad, N. O., Vibration Analysis, McGraw-Hill, New York, 1944. 34