[American Institute of Aeronautics and Astronautics 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition - Orlando, Florida ()] 48th AIAA

American Institute of Aeronautics and Astronautics

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Stable plasma formation in non uniform flow of

Propane - air mixture:

Propagation and transition to explosion.

Vladimir Chernikov, Sergey Kamenshchikov, Evgeniy Kolesnikov.

Faculty of Physics, M.V .Lomonosov Moscow State University, Vorobjevi Gory , Moscow, 119991,

Russia, [email protected], www.plasma-flow.com.

In current paper we discuss detonation and quasi detonation combustion that is initiated in propane – air

flow with initial parameters of M0=2, v0=500 m/s. Preliminary heat of flow and its inflammation are realized

by propagation of plasma formation, generated in magnetic plasma compressor. Parameters of plasma, its

initial composition and propagation dynamics are modeled in computational and experimental way. Time

resolution of combustion waves produced by plasma trace slow down is realized by optical and

electromechanical measurements. External parametric control of regime is achieved.

1. Introduction

Possible thermo dynamical benefits of pulsed detonation engines (PDE) were proved theoretically. One cycle of

PDE working on frequency of more than 100 Hz is more effective then engine base on deflagration [1].

Investigation devoted to deflagration – detonation transitions were carried out for stable mixture without account of

flow – igniter interaction. Several types of inflammation sources were applied and most of them are spark

discharges. This work is devoted to explosive combustion of supersonic flow and its complicated interaction with

extra hot volumetric plasma. A hot nucleus of plasma provides wide continuous range of temperature in plasma

formation that provides combustion even in not premixed flow. Not uniform structure of plasma provides

preliminary heat of flow, turbulent conductivity and transition to detonation on length of one meter order.

2. Experimental installation.

In current work plasma compressor with erosive plasmatron was used as plasma generator for initiation of

combustion. Plasmodynamic discharge was realized between external cylindrical cathode and internal anode divided

by isolator of organic glass (Figure 1a). Energy was accumulated by condensers and released by discharger of Tesla.

High current in erosive plasma in the beginning of discharge is of 1 kA order for such type of plasmatron. This

process creates compression by self magnetic field, so called effect of Pinch. As a result injection of plasma has

permanent direction and plasma focus as it is displayed on Figure 1b. Momentary inlet provides strong shock wave

and high atomic excitation by ultraviolet radiation. Maximum Mach number of shock is ten for investigated

discharge type.

a) Electric scheme. b) Scheme of physical processes.

Figure 1.

1 - disc (cathode), 2 - isolator (perspex), 3 - coupling, 4 - bar (anode), 5 - constant current supply

6 - discharger, PF – plasma focus, SW – shock wave, RW – radiation wave, S – radiation flow,

j – current density, v – plasma velocity, L – typical length.

48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition4 - 7 January 2010, Orlando, Florida

AIAA 2010-267

Copyright © 2010 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.


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Equivalent scheme of plasmodynamic discharge possesses own induction and capacity and consequently qualitative

image of electric input power has form of decreasing oscillation. On Figure 2 electric power and input energy are

represented. Diagrams were achieved for initial capacity of 50 µF. Initial voltage of power supply was 3 kV while

pressure of media was 0.13 Atm. From presented dependences one can came to conclusion that most of energy is

released during 100 µs of discharge and can be divided into two stages. Typical time of investigated flow was 5 ms

and plasmodynamic discharge can be described as Dirak delta function. Efficiency of gas heat, realized by discharge

current was investigated in preliminary experiments. It was found out that output/input energy dependence is linear

with factor of 0.7 for initial energy of 220-600 J. Therefore self resistance of discharge stays constant for mentioned

range of parameters.

a) Electric power. b) Input energy.

Figure 2.

For investigation of plasma – flow interaction magnetic plasma compressor was placed in first chamber of channel

that is displayed on Figure 1a. For supersonic flow provision atmospheric air was delivered by compressor to

channel through additional system of vessels (6), collector (5) and conduit (4). Air flow was launched by electronic

valve (8). Additional vessels (6) allowed increasing work volume of camera up to 0.5 m3.

a) Flow – plasma interaction study installation. b) Scheme of plasmatron placement.

Figure 3.

a)1 – vacuum chamber, 2 – compressor, 3 – valve, 4 – air conduit, 5 – collector, 6 – vessels, 7 – manometers, 8 –

pneumatic valves, 9 – heater, 10 – heater power supply , 11 – uniform channel, 12 – pressure sensors, 13 – not

uniform channel, 14 – illuminators, 15 – fuel injectors, 16 – plasma generator placement section, 17 – fuel supply.

b)1 – coaxial electrodes, 2 – plasma, 3 – reverse stream, 4 – backward step.


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Work pressure of compressor was controlled by manometers (7) and could reach 6 Atm. Preliminary heat of air

could be reached by hollow spiral (9). After that it was delivered to channel (11) through Laval nozzle of M=2.

Pressure gradient necessary for organization of flow was created by compressor (2) and vacuum camera (1) with 3

m3 work volume. Fuel (propane) was injected from vessels (15) with pressure of 5 Atm directly in first division and

in the beginning of forming section (15) from four points in each section. Channel and corrugated tube (13) were

placed between system of fuel-air supply and work camera of low pressure. Triangular ledges of corrugated tube had

dimension of 1 cm for triangular perpendicular and basis. Speed camera, photo multiplier, refraction and pressure

sensors were used for experimental investigation of mechanism. For optical investigation two quartz illuminators

were placed in divisions walls. For determination of plasma temperature emission spectrum measurements were

realized through mentioned illuminators. On Figure 1b scheme of plasmatron placement is displayed. Degree

between plasma jet and flow vectors was 150°; plasma was injected in area of reverse stream. All dimensions on

Figure 1b correspond to centimeters.

3. Results of investigations.

For determination of plasma ability to ignite high speed mixture it is necessary to know its thermodynamic,

kinetic parameters and their time evolution. During this series of experiments emission spectrum of plasma was

measured. Previous experiments1 have shown that for initial stage of discharge with duration of 1-4 µs plasma is

composed from products of erosion and has electron concentration of 1016

cm3. Therefore one can make assumption

that during initial stage plasma exists in equilibrium state and radiation of certain lines occurs only during this stage.

It is close to truth for lines of ablation material of electrodes – copper2. In this case we may apply plasma model of

local thermodynamic equilibrium and determine plasma temperature by comparison of two copper lines with

wavelength of 521.8 and 578.2 nm. Average gas temperature that was determined for equilibrium stage of erosive

plasma is 10 000 K. Basing on this assumption numerical modeling of plasma composition was realized using GRI

Mech 3.0 library (325 reactions and 53 species). Below mass and energy balance equations are displayed.

D(ci·Vr)/Dt==Vr·Ri; Vr·Σ(ci·Cp,i·(D(T)/Dt))=ωs+Q+Qext+Vr·D(p)/Dt; Q= - Vr· ΣHjrj

Here ci is molar concentration of species, Vr - reactor volume, Ri - species rate, ci – molar concentrations of

components, Cp,i - molar capacity of components, T – temperature of mixture, ωs – additional work, Q - chemical

reactions heat, Qext - external heat, p – pressure of mixture, t – time, Hi – enthalpy of reactions, ri – reactions

velocity. Uniform composition of mixture and direct heat of gas were assumed. Term for external heat consists of

two summands: Joule heating and negative heat flow caused by thermal conductivity. Overall electric power is input

in magnetic field compression and heat of gas. It was assumed that magnetic field power in input only in

acceleration of jet in longitudinal direction and 0 v02

= B 2

/(20) (0 – initial density, v0 – velocity of plasma

jet, B - density of magnetic field induction). Therefore expression for pure heating of gas by electric power can

be written in following way: Qext=W0-W1-W2. Here W0 is overall electric power input, W1 – heat loss term, W2 –

magnetic field work. Expressions for these terms are given:

W0=U0·exp (-α·t) ·cos (ω·t) ·J0·exp (-α·t) ·cos (ω·t)

W1=λ· (T-T0); W2=D{Bφ·Vr (t)/ (4·μ0)}/Dt

Here U0 and J0 are amplitudes of current and voltage, α – relaxation coefficient that was determined

experimentally as well as frequency of oscillations in contour, B is induction of magnetic field that could be

expressed as

B= I·0/(2·r0) where r0 is plasmatron radius. For summands expressions D is differentiation

operator, T0 – initial temperature of mixture (temperature of flow) and λ is heat loss factor. Expression for heat

loss [3] was written above with account of uniform mixing. Therefore temperature, molar concentrations got in this

model correspond to average magnitude. Expression for heat loss factor3 can be displayed in following way:

λ=3.51·(Δ·q·E·k0·R·exp(-E/T0)·(2·R·T02)

-1)

0.5. Here Δ is thermal conductivity factor, q – specific heat (per

initial mass unit), E – activation energy for propane – air mixture, R – universal gas constant. Further calculations

will be made without taking into account of interaction between flow and plasma and until time of upper wall of

channel reaching. According to photo measurement of plasma – flow interaction in first division of channel plasma

propagation takes 45 μs for parameters used in all further experiments (Figure 4). On presented shots exposition of

camera was varied. In calculations of model determining plasma composition after upper wall reaching flow

influence on penetration of plasma jet was neglected. Estimation of square power for plasma jet and flow gives us:

η·C· (U0) 2/ (2· (τ·d

2)) = 10

10 for plasma jet and ρυ

3/2 = 10

7 for flow. Here η is part of accumulated energy

released in plasma, C – capacity of condensers, U0 – initial condenser voltage, τ – half period of current and

voltage, d – diameter of plasma jet, ρ – typical density of flow and υ is typical velocity of flow.


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Figure 4. Plasma jet propagation in first division of channel.

Video measurements verify this estimation. On Figure 5 velocity of plasma jet longitudinal front is represented

as well as left front of plasma formation. One can see that average velocity of plasma jet propagation is 1.5 km/s

while flow typical velocity in undisturbed flow is 0.5 km/s (three times less). Left part of Figure 5 gives hint that by

upper wall reaching left plasma goes under flow influence and its left boundary velocity slows down to zero and

turns. Relative mass consumption used in represented experimental figures was 0.03 for φ=0.5 where φ=

(mpropane/mair) ·14.5. Composition of fuel mixture therefore was supposed to be constant in area of plasma injection.

Results of computational model have shown that process of chemical and thermodynamics evaluation of plasma can

be divided into two phases. First – is partial combustion and radical generation. Second one is thermal

decomposition of radicals and molecules into ions and atoms.

Figure 5. Velocity of front and left boundary evaluation.

As it was mentioned above we get equilibrium stage of plasma as initial time of calculation. Nevertheless further

propagation of plasma can pass stages of non equilibrium state. That’s why to make model more complete we

should take plasma effects into account. This is the material of future investigations. Still model is calculated

without taking into account of ionization and recombination processes in plasma. On Figure 6 one can see plasma

reactions with duration of 40 μs. Combustion stage occurs during 2-4 μs. From 10 μs and till end of process

dissociation takes place with partial association of nitrogen from 25 to 40 μs caused by decrease of power input

oscillations. Last are indirectly reflected by temperature evaluation. Determination of average parameters of mixture

has shown that by reach of upper wall plasma formation has temperature of 10 000 K. In fact formation is not

uniform and has relatively cold boundaries and hot nucleus. Nevertheless estimation of temperature permits to state

that deflagration may takes place on boundaries of plasma formation and may be strengthened by turbulent thermal

conductivity. Final composition of mixture represented on Figure 7 shows that by moment of upper wall reaching

plasma jet is mostly dissociated gas with small amount of nitrogen. Plasma nucleus therefore is inactive from the

point of view of combustion reaction in its volume in this moment. Only cooling down of formation may change its

ability to be ignited; at first stage of plasma propagation boundaries combustion is possible.


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Figure 6a. Partial combustion of propane during 2-4 μs after discharge start.

Figure 6b. Dynamics of dissociation of molecules, radicals; partial association of nitrogen at 20-40 μs.

Figure 7. Final composition of mixture.


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Measurements were made by photoelectron multiplier (PEM) with slit located near channel first division illuminator

(Figure 8). First sharp peak taken by PEM corresponded to electric noise of high voltage contour. Second peak

corresponds to propagation of illuminating areas. Experimental data shows that additional of propane in flow causes

extension of signal in time. Half width was enlarged from 250 to 500 μs; signal magnitude increased in 1.7 times.

Last is to due to large heat capacity of propane while increasing of illuminating area corresponds to combustion on

left and right boundary of plasma.

a) Air flow b) Propane – air flow.

Figure 8. Photoelectron multiplier signal for illumination in first division.

Further propagation of plasma in channel is followed by destruction of initial geometric consistency and quasi

spherical composition is transformed into two hot plasma formation divided by hot products of combustion.

Illumination of this complicated structure was fixed by photomultiplier located in front of forth channel division

illuminator. Two intensive peaks of signal corresponding to plasma illumination are divided by less “bright” area of

deflagration. Experiments with application of refraction sensor verified this version. Density perturbs were detected

by deviation of laser beam focused on photomultiplier split.

Figure 9. Photoelectron multiplier signal for illumination in forth division.


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Additional collimating splits were used in this experiment (Figure 10a). Increase of PEM signal (with relation to

average level) corresponds to inlet of not uniform area, decrease of signal corresponds to its outlet. On Figure 10b

results for propagation of disturbances through forth division of channel are represented.

a) Refraction scheme b) Measurement in forth division.

Figure 10. Photoelectron multiplier signal for illumination in forth division.

Time distance between two disturbances is 2000 μs while for half width of illumination we have 2500 μs. Two

independent methods give good correlation and verify hypothesis of two plasma fronts with combustion products

between them. PEM measurements in first and forth divisions allow to determine average velocity in channel. It is

270 m/s and conclusion of partial chocking of flow can be made therefore. Besides longitudinal not uniform

composition of plasma its cross distribution of parameters is not uniform as well. Photo shots made with variable

expositions (Figure 11) show that plasma has more intensive illumination in the direction of lower wall. This fact is

caused by influence of backward step in first division of channel that provides more intensive compression and

disturbance for upper layers of gas than for lower ones lying in the area of gas dynamic shadow.

Figure 11. Video in forth division for different exposition times. Shutter opening time is discharge start.

Detection of further processes occurring in channel was realized by combination of tens metric static pressure

sensors and photoelectron multipliers located in front of forth division illuminator and camera entrance illuminator.

Both diagnostic instruments have fixed slowing down of plasma propagation in corrugated tube and appearance of

detonation and fast combustion waves propagating along flow direction and in opposite direction correspondingly.


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On Figure 12 one can see propagation of pressure waves along the channel in time. Small disturbances caused by

plasma slow down have constant velocity of 135 m/s – depression wave propagating in opposite direction of general

flow. Slow down of plasma formation is caused by turbulent friction in corrugated tube. Strong disturbance

following plasma injection propagates with velocity of 681 m/s in mixture, 654 m/s in air flow and 577 m/s in still

air. Higher magnitude of disturbance in flow can be explained by additional rate of disturbance relaxation in still

flow relatively to one in pressure asymmetry case.

As it was mentioned above adding of propane with high heat capacity leads to more efficient power input with

relation to air case and to higher magnitude of wave consequently. Initially connected with plasma pressure

disturbances are carried away during propagation in channel due to difference in velocities (270 m/s for plasma

propagation and 731 m/s for pressure wave that is initiated by plasma). Nevertheless application of pressure sensors

allowed fixing quality of processes taking place in tube. Pressure disturbance caused by plasma propagation was

marked as “plasma” wave. Pressure waves caused by combustion and detonation are marked like explosive wave

due to strong blow sound producing by overall process during experiment. Actually two signals in opposite direction

were fixed in camera entrance and inside channel divisions. Pressure magnitude of direct detonation wave was

determined by expression for strong shock in one dimensional approximation:

v= {(c2· ((γ-1) + (γ+1) · (p2/p1))/ (2·γ))

0.5}

Here v – velocity of shock propagation, c – local sound velocity, γ – adiabatic factor, p1 – undisturbed flow pressure,

p2 – amplitude of shock. Calculation of this expression for wave with amplitude of 17 Atm gave 2.18 km/s velocity

and Mach number of eight – hypersonic detonation wave. Determination of Chapmen – Jug velocity of detonation

for the same parameters with adiabatic heat release can be made through following expression:

D= (γ· p1·V1 – (2· (γ-1) ·q) 0.5

)/ (2· (γ2-1) ·q· (γ+1))

0.5

V1 is reciprocal to undisturbed flow density, q – specific heat of mixture (per mass unit). Mentioned expression

gives 1.228 km/s for detonation velocity. Therefore hypersonic wave is over pressed detonation or transmission to

stable detonation of Chapmen – Jug after following of corrugated tube where it is formed.

Figure 12. Propagation of pressure waves in time.


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Figure a) corresponds to dependence taken from sensor of camera entrance while b) – to one located in the end of

forth division. Represented diagrams are consequence of well known concentration limits for combustion processes.

In case of detonation wave gates of process are wider and this is consequence of intense turbulent mixing in

corrugated tube. Therefore on Figure 13 a) only left branch of dependence is displayed while Figure b) corresponds

to classic concentration curve of normal combustion. In order to obtain additional information about chemistry of

direct and reverse wave’s illumination measurement was realized by photoelectron multipliers located in front of

forth division illuminator and in front of camera entrance (Figure 14). It was detected that delay between shock and

luminosity appearance on second PEM is 2 ms that corresponds to theoretical induction time3 for mixture with

average temperature of 283 °K. Induction time here is estimated through adiabatic approximation:

Τind=(R·T02·exp (E/(R·T0)))/ (k0·a0· (Tb-T0));

Tb= (1+ (1-8·θ/E) 0.5

) ·E/4;

θ= (E· (1-(1-4·R·T0/E) 0.5

))/ (2·R) In displayed expression Tind is induction time, R is universal gas constant, T0 – initial temperature of mixture, k0 –

first order reaction velocity, a0 – weight concentration of mixture, Tb – adiabatic temperature of combustion, E –

activation energy.

a) Camera entrance b) Forth division

Figure 13. Propagation of pressure waves in time.

Preliminary investigation of undisturbed mixture temperature gave 200 °K. Sensitivity of induction time to initial

temperature doesn’t allow speaking about good correlation between estimated and experimental data, but order of

induction time is in typical range corresponding to combustion of propane – air mixture. Illumination character of

direct and reverse waves allow to state that for detonation wave it is relaxation layer with sharp boundary, while for

reverse wave volumetric inflammation takes place. It is typical for combustion that is formed in corrugated tubes.

Overall display of direct – reverse combustion and plasma propagation is represented on Figure 15. Here 1 - plasma

propagation process, 2 – reverse combustion wave propagation, 3 - direct combustion wave propagation. PEM

corresponding to lower channel at picture was placed in front of camera entrance illuminator. It can be seen from

represented diagram that in plasma volume illumination is stronger in 2.5 times as for combustion waves. Sensitivity

of described combustion regime to initial parameters variation was investigated as well. In this series of experiments

we were able to vary condensers voltage in certain range. Other parameters stayed constant because of firm

requirements of discharge existence. For plasmodynamic discharges of erosive type two basic processes take place

and are in competition: heat of gas and compression – acceleration of plasma. This processes define further

phenomena that are started by plasma influence.


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a) Camera entrance b) Forth division

Figure 14. PEM measurement of illumination of combustion waves.

On Figure 16 a) normalized velocity of plasma left boundary propagation is represented. Due to competition of

mentioned processes it has local maximum corresponding to condensers initial voltage of 3.6 kV. It can be explained

from qualitative point of view.

Figure 15. PEM measurement of combustion waves illumination.

Primary expansion of plasma is caused by energy of jet propagation and its interaction with upper wall.

Intensity of this interaction is determined by initial velocity of jet that is defined like 0 v02

= B 2

/ (20) (0 –

initial density, v0 – velocity of plasma jet, B - density of magnetic field induction). Therefore increase of

initial condenses voltage leads to current increase and plasma propagation intensification. At the same time

generator power is input at gas heat. Described character of plasma expansion dependence allows explaining

combustion intensity increase and consequently combustion products illumination. As it was mentioned plasma

interacts with mixture during its propagation (it doesn’t occupy entire cross section of channel) and realizes its

preliminary heat.


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a) Normalized propagation velocity of plasma b) Illumination of combustion in forth division

Figure 16.

Higher initial temperature of flow produces more advantageous conditions for intensity of reverse combustion wave

due to reactions acceleration by Arrhenius law. At the same time it slows down transition to detonation. Therefore

detonation wave is firmed faster in direction of flow then in opposite direction and reverse wave is process of

transition to detonation.

4. Conclusion.

Inflammation of high speed (M0=2, v0=500 m/s) propane – air mixture has been achieved by application of

plasmodynamic discharge of magnet plasma compressor. Propagation of plasma through channel and its slow

down in corrugated tube led to detonation and quasi detonation waves propagating from plasma trace in

opposite directions. Not uniform structure of plasma formation allowed making preliminary heat of mixture

by its propagation in channel and turbulent conductivity. Volumetric inflammation of mixture was realized

and external control of regime has been got by variation of initial condensers voltage. Most effective work

point of initial conditions has been found and its influence on further processes has been explained.

Acknowledgement

The work is performed with the financial support of EOARD (CRDF # RUP-1514-MO-06). Author express deep

gratitude to AIAA for online versions of articles devoted to plasma assisted combustion.

References

1S.M.Frolov. “Reactive engine based on detonation inflammation of fuel”. Fundamental and applied problems of

forcer engines improvement. 05-01-038, 2005. 2U.S.Protasov. “Radiation plasma dynamics”, 1981, p.58

3J.B.Zeldovisch, G.I.Barenblatt, V.B.Librovich, G.M.Maxviladze. “Mathematical theory of combustion and

explosion”, 1980, p. 128.

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[American Institute of Aeronautics and Astronautics 48th AIAA Aerospace Sciences Meeting Including the New Horizons Forum and Aerospace Exposition - Orlando, Florida ()] 48th AIAA