Thrust Characteristics of an Airbreathing Pulse Detonation Engine …frolovs.ru/pdf/2016-1-eng.pdf · [5–7] and three-dimensional [8, 9] numerical simula-tions of the cyclic operation

272

ISSN 1990-7931, Russian Journal of Physical Chemistry B, 2016, Vol. 10, No. 2, pp. 272–283. © Pleiades Publishing, Ltd., 2016.Original Russian Text © A.E. Zangiev, V.S. Ivanov, S.M. Frolov, 2016, published in Khimicheskaya Fizika, 2016, Vol. 35, No. 3, pp. 65–76.

Thrust Characteristics of an Airbreathing Pulse Detonation Engine in Flight at Mach Numbers of 0.4 to 5.0

A. E. Zangiev, V. S. Ivanov, and S. M. Frolov*Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow, Russia

Center of Pulse Detonation Combustion, Moscow, RussiaNational Nuclear Research University “MEPhI,” Moscow, Russia

*e-mail: [email protected] December 8, 2014

Abstract—Multidimensional calculations are performed to demonstrate that, by its characteristics, the pulsedetonation engine (PDE) is a unique type of ramjet propulsion system, which can be used in both subsonicand supersonic aircraft. By a number of examples, it is shown that, in various thrust characteristics, such asthe specific impulse, specific fuel consumption, and specific thrust, the PDE substantially exceeds ramjetengines.

Keywords: deflagration to detonation transition, pulse detonation engine, ideal ramjet engine, thrust charac-teristicsDOI: 10.1134/S1990793116020135

INTRODUCTIONThe thrust characteristics of air-breathing ramjet

engines can be enhanced by using pulse detonationcombustion chambers [1]. The cyclic operation pro-cess of such chambers comprises the following stages:(1) filling of the chamber with a combustible mixture,(2) initiation of detonation, and (3) burning of themixture in a traveling detonation wave, and (4) empty-ing of the chamber of the combustion and detonationproducts. The thermodynamic cycle of this process isclose to the Humphrey cycle, a cycle with combustionat constant volume; ramjet engines with such cham-bers are called pulse detonation engines (PDEs).

The specific impulse of PDEs was estimated in [2,3]. It is believed that fuel-based specific impulse of aPDE operating on hydrogen or hydrocarbon fuels canbe very high, over 5500 and 2500 s in a wide range offlight Mach numbers, from 0 to 4–5, respectively.However, these estimates have been obtained based ona number of simplifications: for a single-cycle, on theassumptions of instantaneous detonation initiation,absence of the incoming f low, applicability of one-dimensional approximation, and conditions charac-teristic of sea level. In most theoretical studies, deto-nation initiation in PDEs, one of the key processes ofthe operation cycle, received insufficient attention: asa rule (see, e.g., [4]), the calculations postulate thedirect initiation of detonation, implying that, for deto-nation to occur in the combustion chamber, it sufficesto have an ignition device. However, it should be keptin mind that, detonation can be somehow initiated

only within a limited range of compositions, pressures,and temperatures of the fuel–air mixture (FAM) inthe combustion chamber and that its onset depends, inaddition, on the type of fuel and the characteristicdimensions the combustion chamber.

In our previous works, we carried two-dimensional[5–7] and three-dimensional [8, 9] numerical simula-tions of the cyclic operation process in a PDE with amechanical valve under conditions of supersonicflight at a Mach number of M = 3 and different alti-tudes (8 to 28 km above sea level), with considerationgiven to the finite time of deflagration-to-detonationtransition (DDT) and the integration of the pulse det-onation combustion chamber with the air intakedevice and exhaust nozzle of the engine. It was shownthat, under these conditions, the PDE can operate ina high-frequency cyclic mode (~50–80 Hz), withignition with a weak source (~0.1 J) and subsequentDDT. The specific impulse and specific fuel con-sumption for a PDE operating on a stoichiometricpropane–air mixture under conditions of f light at alti-tudes of up to 26 km were found to be 1700–1800 s and0.19–0.21 kg/(N h), respectively, which is very close tothe relevant characteristics of an ideal ramjet enginewith conventional combustion [10, 11], operating,however, on a lean FAM, with a fuel-to-oxidizerequivalence ratio of φ = 0.7. As regards the specificthrust of the PDE, its estimated value under theseconditions turned out to be 18–38% higher than thatof the ideal conventional-combustion ramjet. Notethat, in order to achieve a positive effective thrust of

COMBUSTION, EXPLOSION,AND SHOCK WAVES

RUSSIAN JOURNAL OF PHYSICAL CHEMISTRY B Vol. 10 No. 2 2016

THRUST CHARACTERISTICS OF AN AIRBREATHING PULSE DETONATION ENGINE 273

the PDE during a supersonic f light at M = 3 at thesealtitudes, the authors of [5–9] adjusted the shape ofthe air intake device and exhaust nozzle, as well as thesize and placement of the annular obstacles. Due to anoptimal shape of the air intake device, the combustionchamber provided the desired temperature, velocity,and turbulence of the fuel–air mixture, an optimalshape and placement of the obstacles provided a “fast”DDT (in the terminology of [12]), whereas an optimalshape of the exhaust nozzle provided the pressure inthe combustion chamber required for fast DDT. Inother words, the configuration of the PDE in the [5–9]was determined by the selected f light conditions at aconstant supersonic viscosity. A f light at a subsonic ortransonic velocity with this engine is impossible.

The problems solved in the present work is a proofof the feasibility of the cyclic pulse detonation opera-tion of a PDE in arrangement with an air intake deviceand an exhaust nozzle during a subsonic f light atMach numbers from 0.4 to 0.8 at low altitudes and alti-tudes up to 10 km and during a supersonic f light atM = 5.0 and an altitude of 28 km with taking intoaccount all the physicochemical characteristics of theoxidation and combustion of hydrocarbon fuel, as wellas the finite time of turbulent f lame acceleration andDDT. The work is a continuation of studies performedin [5–9, 13].

STATEMENT OF THE PROBLEM

The study examines two variants of PDE: for a sub-sonic f light at Mach numbers of 0.4 to 0.8 (Fig. 1) andfor a supersonic f light at M = 5.0 (Fig. 2). The axisym-metric PDEs for subsonic and supersonic f lights con-sist of air intake device 1, mechanical valve 2, fuel sup-ply manifold 3, ignition source 4, annular bypasschannel 5, pulse detonation combustion chamber 6with obstacles 7, and exhaust nozzle 8.

In the engine for subsonic f light (Fig. 1), the airintake device is an internal compression diffuser,whereas the outlet device is a Laval nozzle. As in [13],the engine is equipped with an annular bypass chan-nel, which provides a continuous f low of air throughthe air intake device when the airf low into the com-bustion chamber is shut off with a mechanical valve.The combustion chamber is equipped with a fuel sup-ply manifold (propane gas), an ignition source (withan ignition energy of 0.1 J), and turbulizing obstaclesfor providing fast DDT. The PDE was assumed tooperate on a propane–air mixture. The supply of fuelwas simulated by placing a source of mass in all gridcells of fuel supply manifold 3 (Fig. 1). The character-istics of the source of mass were selected so that, on theaverage, the combustion chamber was filled with amixture with an fuel-to-oxidizer equivalence ratio ofφ ≈ 1, i.e., with a nearly stoichiometric mixture. Thefill factor of the combustion chamber was taken to beχ = 0.9. The fill factor was defined as the ratio of theweight of the fuel supplied to the combustion chamberof the PDE, to the weight of the fuel when the cham-ber was completely filled (in Fig. 1, from the valve tothe beginning of the nozzle) with a mixture of thesame composition, ceteris paribus. The total length ofengine was 1.3 m, whereas the combustion chamberdiameter was 82 mm.

The air intake device in the engine for supersonicflight (Fig. 2) is a conical supersonic diffuser, whichprovides the maximum pressure recovery at zero angleof attack, whereas the outlet device is a Laval nozzle[5–9]. The engine is also equipped with an annularbypass channel and a mechanical valve, whereas thecombustion chamber has a fuel (propane gas) supplymanifold, an ignition source (with an energy of 0.1 J),and obstacles to provide fast DDT. The coefficients φand χ were the same φ ≈ 1 and χ = 0.9. The total lengthof the engine was 2.2 m, and the combustion chamberdiameter was 82 mm.

Fig. 1. Schematic diagram of a subsonic PDE.

1 2 3 4 5 6 7 8

Fig. 2. Schematic diagram of a supersonic PDE.

1 2 3 4 6 5 7 8

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As in [5–9, 13], the operation of the PDE wasnumerically simulated in the two-dimensional axiallysymmetric approximation. The mathematical modelof the f low consisted of the Reynolds averaged con-servation equations of mass, momentum, and energyfor an unsteady compressible turbulent reacting f low.The turbulent f luxes of mass, momentum, andenergy were simulated using the k–ε turbulencemodel (k is the kinetic energy of turbulence and ε isits dissipation rate). Simulation of chemical sourcesfor turbulent combustion and DDT required takinginto account the contributions from both frontalcombustion and bulk pref lame reactions. To deter-mine these quantities, we used an algorithm ofexplicit f lame tracking (FT), whereas the contribu-tions from the bulk reactions were determined usingthe particle method (PM).

The system of governing equations supplementedby the k–ε turbulence model and the coupled FT–PMmodel was closed by the caloric and thermal equationsof state of an ideal gas with variable specific heat andprovided with initial and boundary conditions. All thethermophysical parameters of the gas were consideredvariable. The system of equations was solved using thefinite-volume discretization method with first-orderapproximation in space and time. To avoid excessivemesh refinement near solid surfaces with no-slip con-ditions, we used the standard wall functions method.

To determine the thrust characteristics of the PDE,calculations were performed for four to five operationcycles (until a fully reproducible periodic operationmode was reached), with consideration given to theexternal f low over the engine. This involved calculat-ing the pressure force (integral of the absolute pressureover the surface) and the viscous drag (integral viscousshear stresses over the surface) acting on all solid sur-faces of the PDE both in internal and external f lows.That the grid cell size has only a slight influence on thestructure of the f low and the resulting thrust charac-teristics was checked by special calculations on muchfiner grids [7].

CALCULATION RESULTS

The most important result of the work is the proofof the potential feasibility of realization of a cyclicPDE operating at a frequency of 55–75 Hz for sub-sonic f light at Mach 0.4 to 0.8 and for supersonicflight at M = 5.0 with positive effective thrust. As anexample, Fig. 3 shows the calculated fields of pressure,temperature, and propane mass fraction (from top tobottom) at different times, illustrating the operationcycle of the PDE during f light at M = 0.8 and an alti-tude of 1 km. The duration of the operation cycle was14.5 ms; i.e., the frequency of operation of the PDEwas 69 Hz.

The beginning of the first stage of the operationcycle, the filling of the combustion chamber with

combustible mixture, corresponds to a time of111.50 ms. At a time of 112.00 ms, the valve opens andthe combustion chamber is filled with air through theintake device, whereas fuel is supplied through the fuelsupply manifold (see time points 113, 114, and 118 ms).The stage of filling ends at a time of 120 ms.

At the time of 120.01 ms, the valve rapidly closes,and the second stage of the operation process, detona-tion initiation, begins. At this stage, the mixture isignited with a weak source located behind the first tur-bulizing obstacle (at 120.3 ms), and then, after a shortperiod of accelerated propagation of the turbulentflame (see time instants 120.5, 120.7, and 120.8 ms),DDT occurs (see times 120.82, 120.84, 120.86, 120.88,and 120.90 ms). A key event in the DDT process is“explosion in the explosion” (according to the termi-nology accepted in [14]), which takes place betweentimes 120.82 and 120.84 ms within a small regionbehind the penultimate turbulizing obstacle, at a dis-tance of 0.35 m from the ignition source. The calcu-lated fields of pressure and temperature at a time of120.84 ms clearly show a visible “bubble” of secondaryexplosion at the leading edge of the accelerating f lamenear the outer wall of the combustion chamber. At thistime, the visible f lame velocity reaches ~1000 m/s. Inthe “bubble,” a change in the mechanism of propaga-tion of the reaction takes place: a small amount ofshock-compressed fresh mixture, instead of burning inthe turbulent f lame, ignites spontaneously to form asecondary blast wave. Within 60–80 microseconds,the “bubble” spreads throughout the entire cross sec-tion of the combustion chamber and forms therein anoverdriven detonation wave that propagates into thesmooth section (without turbulizing obstacles) of thetube (120.90 ms).

The third stage of the operation cycle of the PDE isthe combustion of the mixture in the propagating det-onation wave (see time instants 120.96, 121.00, 121.06,and 121.12 ms). Although wave front in the scale ofFig. 3 appears f lat, it actually has a structure similar tothat of multifront detonation (Fig. 4) with a character-istic distance between transverse waves in the frontclose to 13 mm. This size is considerably smaller thanthe size of the multifront detonation cell for a stoichio-metric propane–air mixture under normal conditions(~40–50 mm). The difference is explained by the factthat, firstly, the detonation wave in this area remainssomewhat overdriven, and secondly, the conditions inthe chamber are different from normal: the tempera-ture and pressure ahead of the wave front are 330 Kand 0.088 MPa, respectively. Further, the detonationwave propagates through a movable gas (at an averagespeed of ~90 m/s) with a high degree of turbulence(~22%). At a time of 121.18 ms, the detonation waveenters the end portion of the fuel–air mixture charge,the composition of which is gradually depleted in fuel,and at a time of 121.30 ms, it passes through the nozzleinto the surrounding atmosphere as a shock wave.



Fig. 3. Calculated fields of temperature, pressure, and propane mass fraction at different times, illustrating the PDE operationcycle for subsonic f light at M = 0.8 and an altitude of 1 km.

Absolute pressure, Pa

111.50 ms

112.00 ms

113.00 ms

114.00 ms

118.00 ms

120.00 ms

120.01 ms

15 000

200

0 0.006 0.012 0.018 0.024 0.030 0.036 0.042 0.048 0.054 0.060

500 800 1100 1400 1700 2000 2300 2600 2900 3200

78 5001.42e+05 2.69e+05 3.96e+05 5.23e+05

3.325e+05 4.595e+05 5.865e+056.5e+05

2.055e+05Temperature, К

Propane mass fraction

120.30 ms

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ZANGIEV et al.

Fig. 3. (Contd.)

120.96 ms

120.50 ms

120.70 ms

120.80 ms

120.82 ms

120.84 ms

120.86 ms

120.88 ms

120.90 ms



Fig. 3. (Contd.)

123.00 ms

121.00 ms

121.06 ms

121.12 ms

121.18 ms

121.24 ms

121.30 ms

121.50 ms

121.70 ms

122.00 ms

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ZANGIEV et al.

Fig. 3. (Contd.)

125.00 ms

126.00 ms

124.00 ms

Fig. 4. Structure of the detonation wave front: (a) staticpressure and (b) temperature.

Absolute pressure, Pa(a)

(b)Temperature, К

2800

2е+06

2760272026802640260025602520248024402400

1.87e+06

1.74e+06

1.61e+06

1.48e+06

1.35e+06

1.22e+06

1.09e+06

9.6e+05

8.3e+05

7e+05

At 121.30 ms, the fourth stage of the operationcycle, emptying the chamber from the products ofcombustion and detonation, begins. At this stage,wave processes still occur in the combustion chamber,related mainly to the reflection of shock waves fromthe closed valve and the convergent portion of thenozzle. The pressure and temperature of the residualgas reduce gradually, with the pressure and tempera-ture fields at 126.50 ms becoming almost the same asthose at 112 ms. From this point of time, the valveopens and a new cycle begins.

Figure 5 shows the evolution of the calculated pro-files of static overpressure and total pressure along theaxis of the combustion chamber from the time of igni-tion to the time of exit of the detonation wave throughthe nozzle into the surrounding space. The profilescorrespond to the times (in ms) indicated over thepressure peaks. At times of 120.9 and 121.0 ms, thepeak overpressure in the detonation wave is very closeto the Chapman–Jouguet theoretical value for a stoi-chiometric propane–air mixture (1.73 MPa). Whenthe detonation wave enters the end portion of the fuel-air mixture charge, the maximum overpressure thereindecreases gradually (at 121.1 and 121.2 ms), but thereflection of the wave from the convergent portion ofthe nozzle again increases it to ~1.5 MPa (at 121.3 ms).The maximum total pressure in the combustion cham-ber of the PDE reaches 3.7–3.9 MPa at the stage ofcombustion of the mixture in the running detonationwave. The most important conclusion from Fig. 5 isthat the process of combustion of the fuel charge isaccompanied by increases in the static (Fig. 5a), andtotal (Fig. 5b) pressures, which distinguishes the PDEfrom the ramjet engine, wherein the combustion of thecharge occurs at constant or decreasing static and totalpressures.

Despite a significant increase in the static pressurein the combustion chamber of the PDE and a subsonicspeed of air in the air intake device, air continuouslyflows into the engine through the air intake device, at



both the open and closed valve. The solid curve inFig. 6a shows the calculated time dependence of themass f low rate of air through the inlet section of theintake device for two consecutive cycles at the stagewhen the PDE operates in a reproducible periodic

mode. Despite some fluctuations in the mass f lowrate, caused by opening and closing of the mechanicalvalve, it generally remains steady (~0.39 kg/s on theaverage) due to the presence of a bypass channel in thePDE scheme. The curve in Fig. 6b represents the cal-

Fig. 5. Evolution of the calculated profiles of static overpressure and total pressure along the combustion chamber axis from thetime of mixture ignition to the time of exit of the detonation wave through the nozzle into the environment for a subsonic f lightof the PDE at M = 0.8 and an altitude of 1 km. The numbers at the peaks are instants of time in ms.

0

0.5

1.0

3.0

4.0

2.0

1.5

2.5

3.5

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3

0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3

120.7

120.7

120.8

120.8

120.9(a)

(b)120.9

121.0

121.0

121.1

121.1

121.2

121.2

Distance from the ignition source, m

121.3

121.3

Tota

l pre

ssur

e, M

Pa

Sta

tic o

verp

ress

ure,

MPa

280


ZANGIEV et al.

culated time dependence of the mass f low rate of gasthrough the outlet section of the nozzle for the sametwo cycles. The average f low rate through the nozzle isless than that through the inlet section (~0.25 kg/s),since during the second, third, and fourth stages of theoperation cycle (when the valve is closed), no airenters the combustion chamber, f lowing into theatmosphere through the bypass channel.

The table shows the calculation results for f light atM = 0.4, 0.6, 0.8, and 5.0 and, as well as (for complete-ness) some calculation results for M = 3.0, taken from[7]. Note that, in [7], the absolute values of the thrustcharacteristics are indicated for a sector with an apex angleof 5°, whereas in the present work (as in the [8, 9, 13]),they are specified for the entire cross section of thePDE. The table uses the following notations: Z is alti-tude, Pa is the atmospheric pressure, Ta is the ambientair temperature, f is the frequency of the operationcycle (obtained from calculations), R is the thrustforce (the sum of the effective thrust and the aerody-namic drag force), Isp is the fuel-based specificimpulse, Rsp is the specific thrust (engine thrust

divided by the air mass flow rate), Csp is the specific fuelconsumption (hourly fuel consumption per 1 N thrust),and is the fuel consumption rate. To determine thethrust force R created by the PDE, it is necessary to cal-culate the in-flight aerodynamic drag force.

The aerodynamic drag force acting on the PDE inflight was determined in the last cycle after the estab-lishment of reproducible periodic operation. Since theaerodynamic drag is created only by the air f lowingaround the walls, then when the valve is closed (at thestages of combustion and expiration), the inner wallsof the combustion chamber practically do not contrib-ute to this effect, in contrast to the periods when thevalve is open (during purging and filling), so that thewalls contribute to this force. Taking into account thiscircumstance and calculating the average aerody-namic drag force acting on the engine during onecycle, it is easy to determine the thrust. Note that thismethod for determining the aerodynamic drag forceyields results that are very close to the results obtainedin [7]. This fact is discussed in detail in [8, 9].

� fm

Fig. 6. Calculated time dependences of the air mass f low rate through the (a) air intake and (b) exhaust nozzle for two consecutivecycles for the PDE operating in the reproducible periodic mode during subsonic f light at M = 0.8 and an altitude of 1 km.

0

1

2

3

4

5

95 100 105 115 125110 120 130

0.15

0.25

0.35

0.45

0.20

0.30

0.40

0.50

95 100 105 115 125110 120 130

Mas

s flow

rate

, kg/

s

Time, ms

(a)

(b)



The specific impulse of the PDE at subsonic f lightat low altitudes reaches 1470 s, which is approximatelytwo times higher than the specific impulse of the pul-sating engine of the V-1 rocket (~700 s [15]) fromWorld War II operating on slow combustion (deflagra-tion), whereas for supersonic f light at M = 5.0 and alti-tude of 28 km, 1680 s. Although these values are lowerthan the specific impulse of the PDE in supersonicflight at M = 3.0 (1600–1700 s [5–9]), they demon-strated advantages over ramjet engines. In contrast toramjet engines, the effectiveness of which in subsonicflight is extremely low, the PDE in such a f light at lowaltitudes can operate quite effectively. The sameapplies to supersonic f light at M = 5.0 and an altitudeof 28 km: in the conditions of such a f light, the ramjetengine has a relatively low specific impulse, 900–1200 s [10, 11]. Moreover, for a supersonic f light atM = 5.0, the PDE exceeds the ramjet engine in spe-cific thrust Rsp as well: 1.03 instead of ~0.5 kN/(kg s),

when the latter operates on a lean fuel–air mixture,φ = 0.7 [11], despite the fact that a significant portionof the air is not involved in the combustion process(flows through the bypass channel. At the same time,such indicators as the values of the specific fuel con-sumption Csp for a PDE operating on a φ ≈ 1 mixtureand a ramjet engine operating on a φ = 0.7 mixture aresimilar: ~ 0.22 (0.23) and 0.21 kg/(N h) [11].

Figure 7 shows the time dependences of the effec-tive thrust (instantaneous total force) acting on all thesolid surfaces of the engine for four to five operationcycles for a PDE in f light at M = 0.8 and an altitude of500 m (Fig. 7a) and at M = 5.0 and an altitude of 28 km(Fig. 7b). As can be seen, for subsonic f light, the aver-age effective thrust (the average integral value of thetotal force acting on the PDE during one cycle) isessentially positive and significant; i.e., the PDEshould move with acceleration. For f light at M = 5.0,

The results of calculations for the f light Mach number M = 0.4, 0.6, 0.8, 3.0 [7] and 5.0

Z, km Pa, MPa Ta, К f, Hz R, N Isp, s Rsp,kN/(kg s)

Сsp,kg/(N h)

g/s

М = 0.4

0 0.101 288.2 39 161 1490 0.92 0.25 11

1 0.090 281.7 38 156 1590 0.95 0.24 10

2 0.080 275.2 40 138 1560 0.93 0.25 9

М = 0.6

0 0.101 288.2 57 225 1530 0.99 0.23 15

1 0.090 281.7 54 197 1540 0.94 0.24 13

2 0.080 275.2 56 171 1450 0.92 0.25 12

М = 0.8

0 0.101 288.2 75 263 1460 0.91 0.25 18

1 0.090 281.7 70 230 1460 0.92 0.25 15

2 0.079 275.2 70 205 1450 0.91 0.25 14

3 0.070 268.7 70 185 1460 0.91 0.25 13

5 0.054 255.7 70 144 1460 0.91 0.25 10

8 0.036 236.2 70 104 1520 0.95 0.24 7

10 0.027 223.3 65 79 1520 0.95 0.24 5

М = 3.0 [7]

16 0.010 216.7 50 297 1700 1.05 0.22 15

20 0.0055 216.7 50 143 1650 1.05 0.22 9

24 0.003 220.6 50 75 1650 1.03 0.22 4

М = 5.0

28 0.0016 224.5 55 33 1680 1.03 0.22 2

� ,fm

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ZANGIEV et al.

the effective thrust is close to zero; i.e., the PDE has tomove with a nearly constant speed.

CONCLUSIONSThus, our calculations for the first time showed

that, by its characteristics, the PDE is a unique type oframjet propulsion system, which can potentially beused in both subsonic and supersonic aircraft. Partic-ular examples of subsonic f light at M = 0.4, 0.6, and0.8 show that, in various thrust characteristics, such asthe specific impulse, specific fuel consumption, andspecific thrust, the PDE substantially exceeds the

ramjet engine, the effectiveness of which in subsonicflight is extremely low. For f light at M = 5.0 andan altitude of 28 km, the PDE is also superior to theramjet engine in specific impulse (~1600 s instead of900–1200 s) and specific thrust (1.03 versus~0.5 kN/(kg s)); on the one hand, in fuel consump-tion, the PDE and ramjet engine are similar, ~0.22and 0.21 kg/(N h).

ACKNOWLEDGMENTSThe authors are grateful to V.V. Vlasenko (TsAGI)

for help in the design of the intake devices and for

Fig. 7. Calculated time dependences of the effective thrust (instantaneous total force) acting on all the solid surfaces of the enginefor four operation cycles of the PDE in f light at (a) M = 0.8 and an altitude of 500 m and (b) M = 5.0 and 28 km.

–15

–10

–5

0

5

10

40 60 80 100 120 140

–4

–3

–2

–1

0

1

2

3

4

40 60 80 100 120

Cycle 1

Cycle 1 Cycle 2 Cycle 3 Cycle 4

Time, ms

Cycle 2 Cycle 3 Cycle 4 Cycle 5

Effe

ctiv

e th

rust

, NE

ffect

ive

thru

st, k

N

(a)

(b)



fruitful discussions. This work was supported by theRussian Science Foundation (grant no. 14-13-00082).

REFERENCES

1. Pulse Detonation Engines, Ed. by S. M. Frolov (TorusPress, Moscow, 2006), p. 19 [in Russian].

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6. A. E. Zangiev, V. S. Ivanov, and S. M. Frolov, in Com-bustion and Explosion, Ed. by S. M. Frolov (TorusPress, Moscow, 2012), No. 5, p. 136 [in Russian].

7. A. E. Zangiev, V. S. Ivanov, and S. M. Frolov, Russ. J.Phys. Chem. B 7, 276 (2013).

8. A. E. Zangiev, V. S. Ivanov, and S. M. Frolov, in Com-bustion and Explosion, Ed. by S. M. Frolov (TorusPress, Moscow, 2014), No. 7, p. 113 [in Russian].

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10. J.-L. Moerel, W. Halswijk, RTO-AVT-VKI Lectureseries 2010-AVT 185 (Von Karman Inst. Fluid Dynam-ics, Belgium, 2010), Paper 6, p. 6.1.

11. J. Kurzke, RTO-AVT-VKI Lecture series 2010-AVT 185(Von Karman Inst. Fluid Dynamics, Belgium, 2010),Paper 2, p. 2.1.

12. S. M. Frolov, Russ. J. Phys. Chem. B 2, 442 (2008).13. A. E. Zangiev, S. M. Frolov, and V. S. Ivanov, in Tran-

sient Combustion and Detonation Phenomena: Funda-mentals and Applications, Ed. by G. D. Roy and S. M.Frolov (Torus Press, Moscow, 2014), p. 414.

14. A. K. Oppenheim, Introduction to Gasdynamics ofExplosions (Springer, Wien, New York, 1972).

15. K. V. Migalin, A. V. Ambrozhevich, V. A. Sereda, et al.,Pulsating Air-Reactive Engines (Tolyat. Gos. Univ.,Tolyatti, 2014) [in Russian].

Translated by V. Smirnov

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Thrust Characteristics of an Airbreathing Pulse Detonation Engine …frolovs.ru/pdf/2016-1-eng.pdf · [5–7] and three-dimensional [8, 9] numerical simula-tions of the cyclic operation