1. INTRODUCTION

1.1 DESCRIPTION OF PULSE COMBUSTION

Pulsating combustion is a combustion process that occurs under oscillatory

conditions. That means that the state variables, such as pressure, temperature, velocity of

combustion gases, etc., that describe the condition in the combustion zone, vary

periodically with time. Pulse combustion is a very old technology. The phenomenon of

combustion-driven oscillations was first observed in the year 1777, subsequently

explained by Lord Rayleigh in the year 1878, and used in a variety of applications around

the turn of the Century.

Fig 1.1: General Pulse Combustion Process

One of the better known examples of a pulse combustor is the German V-1

"Buzz Bomb " of World War II; Although the technology of pulse combustion has

been known for many years, devices using pulse combustion have not been implemented

widely despite their many attractive characteristics.

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Fig 1.2: Combustion chamber explosion

Compared to conventional combustion systems, their heat transfer rates are a

factor of two to five higher than normal turbulent values, their combustion intensities are

up to on order of magnitude higher, their emissions of oxides of nitrogen are a factor of

three lower, their thermal efficiencies are up to 40% higher, and they may be self-

aspirating, obviating the need for a blower. This combination of attributes can result in

favorable economic trade off with conventional combustors in many applications. Most

of the research on pulse combustors has been directed toward applied examinations of the

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engineering aspects of pulse combustors: heat transfer, efficiency, frequency of

operation, pollutant formation, etc.

There is also uncertainty over the behavior of frequency as a function of

geometry, energy input, and mass input. Zinn states that the pulse combustor can be

modeled as a Helmholtz resonator, while Dec and Keller found that the frequency of

operation is a function of the magnitude of the energy input and of the magnitude of the

mass flux. These results indicate that a Helmholtz resonator model is insufficient to

predict the frequency of operation. These fundamental questions must be answered before

the prediction of an optimum resonant condition is possible.

2. LITERATURE SURVEY

2.1 PULSE JET ENGINE

A pulse jet engine is a type of jet engine in which combustion occurs in pulses.

Pulsejet engines can be made with few or no moving parts, and are capable of running

statically. Pulse jet engines are a lightweight form of jet propulsion, but usually have a

poor compression ratio, and hence give a low specific impulse.

Pulsejet is an unsteady propulsive device with its basic components being the

inlet, combustion chamber, valve and valve head assembly and a tailpipe.

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Fig 2.1: Schematic of pulse combustion operation

2.2 TYPES OF PULSE JET ENGINES

There are two types of pulse jet engines: those with valves and those without. The

ones with valves allow air to come in through the intake valve and exit through the

exhaust valve after combustion takes place. Pulse jet engines without valves, however,

use their own design as a valve system and often allow exhaust gases to exit from both

the intake and exhaust pipes, although the engine is usually designed so that most of the

exhaust gases exit through the exhaust pipe.

A. Valved Pulsejet Engine

Valved engines use a mechanical valve to control the flow of expanding exhaust,

forcing the hot gas to go out of the back of the engine through the tailpipe only, and allow

fresh air and more fuel to enter through the intake. The valved pulsejet comprises of a

intake with a one-way valve arrangement. The valves prevent the explosive gas of the

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ignited fuel mixture in the combustion chamber from exiting and disrupting the intake

airflow, although with all practical valved pulsejets there is some 'blowback' while

running statically and at low speed as the valves cannot close fast enough to stop all the

gas from exiting the intake.

Fig 2.2: Valved Pulsejet Engine

The hot exhaust gases exit through an acoustically resonant exhaust pipe. The

valve arrangement is commonly a "daisy valve" also known as a reed valve. The daisy

valve is less effective than a rectangular valve grid, although it is easier to construct on a

small scale.

B. Valveless Pulsejet Engine

The valveless pulse jet engine operates on the same principle, but the 'valve' is the

engine's geometry. Fuel as a gas or liquid vapor is either mixed with the air in the intake

or directly injected into the combustion chamber. Starting the engine usually requires

forced air and an ignition method such as a spark plug for the fuel-air mix. With modern

manufactured engine designs, almost any design can be made to be 'self-starting' by

providing the engine with fuel and an ignition spark, starting the engine with no

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compressed air. Once running, the engine only requires input of fuel to maintain a self-

sustaining combustion cycle.

Valveless pulsejets, have no moving parts and use only their geometry to control

the flow of exhaust out of the engine. Valveless engines expel exhaust gases out of both

the intake and the exhaust, most try to have the majority of exhaust go out the longer tail

pipe, for more efficient propulsion.

Fig 2.3: Valveless pulsejet engine

Fuel is drawn into the combustion chamber through the intake valve in either as

an air-gas mixture or in liquid form. The intake valve then closes and a spark plug is used

to ignite the fuel in the combustion chamber. The fuel then expands rapidly and tries to

fill the entire chamber in order to escape. The closed intake valve forces the fuel to the

rear of the combustion chamber and allows the exhaust gases to exit through the exhaust

valve.

2.3 HISTORY OF VALVELESS PULSE JET ENGINES  

  The idea of pulsed combustion was conceived even before the use of steady state

combustion employed in gas turbine engines. Over the past hundred years various

number of valveless pulsejet designs have been invented and tested. These are classified

into three main systems

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Inline systems

U-shaped systems

Linear systems

2.3.1: Inline systems

The systems, which have an intake pipe, combustion chamber and exhaust pipe,

all on the same axis with intake and exhaust held in opposite directions are called inline

systems. The advantage of this system is that when the engine has positive forward air

velocity the intake has air rushing into it creating a ram-air effect, similar to ram jet

engines.

Moreover the fabrication and fitting of inline systems is much easier than any

other systems. The disadvantage is that these engines have lower thrust than other

systems because the hot air exiting the intake after combustion does not to contribute to

net thrust and actually creates negative trust that has to be overcome.

To overcome this many complicated and mostly infeasible aerodynamic valves

have been created to allow the ram air effect to work without allowing the air to move

back through so as to increase thrust. However none have been proven effective.

Marconnet Design

In 1909 Georges Marconnet developed the first pulsating combustor without

valves. It was the father of all valveless pulse jets. Marconnet found that a blast inside a

chamber would prefer to go through a bigger exhaust opening rather than squeezing

through a relatively narrow intake. In addition a long diffuser between the intake and the

combustion chamber would direct the charge strongly towards exhaust, the way a trumpet

directs sound.

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Fig 2.4 Marconnet’s Valveless Pulsejet Engine

Schubert design

The principle of the valveless pulsating combustor was discovered by Lt.William

Schubert of the US NAVY in the early 1940s. Schubert’s design was called a “Resojet”

on the account on its dependence on resonance.

The taper less attachments of the inlet tube to the combustion chamber in

Schubert’s design creates strong turbulence for better mixing of fuel and air so that high

intensity combustion takes place. Schubert carefully calculated the geometry of the intake

so that the exhaust gas could not exit by the time the pressure inside fell below

atmospheric.

The resistance of a tube to the passage of gas depends steeply on the gas

temperature.  Thus, the same tube will offer a much greater resistance to outgoing hot gas

than to the incoming cold air.  The impedance is inversely proportional to the square root

of the gas temperature.  This degree of irreversibility seems to offer the possibility for the

cool air necessary for combustion to get in during the intake part of the cycle, but for the

hot gas to encounter too much resistance to get out of the intake during the expansion

part.

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Fig 2.5: Schubert’s valveless pulsejet engine

2.3.2: U-shaped systems

The U-shape design overcomes the shortfall of the inline design by bending the

exhaust pipe by 180 degrees, so that the exhaust and intake are aligned in the same

direction. The advantage of this design is that the thrust generated by the inlet contributes

to the net thrust of the engine as it flows in the same direction as the exhaust. The

disadvantage is that the ram-air affect is lost. Moreover fabrication is quite complex.

Lockwood-Hiller

The U-shaped Lockwood-Hiller engine was invented by Raymond Lockwood. It

is said that the Lockwood was the most effective pulse jet engine ever developed.

The air fuel mixture is generated by mixing fuel which is injected through a jet

built into the side of the combustion chamber or on a strut projecting into the chamber or

on two crossed struts spanning the front part of the chamber. The chamber is the drum

like broad part of the engine. The short straight tube attached to the combustion chamber

is the inlet. And the long U tube attached to the combustion chamber is the tail pipe. The

tailpipe is fitted with a flare at the end.

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Fig 2.6: U-shaped Lockwood Hiller engine

The Lockwood-Hiller design is the most successful example of U-shaped designs

in both performance and efficiency. Conversely it is difficult to construct because of

numerous cone sections are to be fabricated for it.

2.3.3: Linear systems

There are many designs of valveless pulsejet engines that cannot be categorized

by either U-shape or inline designs. These engines are generally variations of inline

designs with the intake moved to the side of the combustion chamber. The typical feature

of the linear engine is that the intake emanates from the side of the combustion chamber.

The advantage of this type of engine is that the physical size is smaller than an equivalent

U-shaped engine making integration into airframe more practical.

These engines are also simpler to manufacture than U-shape design. The

disadvantage of this design is the tuning difficulty for optimized performance as the

intake length is directly proportional to exhaust length. Net thrust outputs are

considerably greater than inline while performance is less than the equivalent U-shape

design as the efficiency is limited by intake position.

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Argus design

The capped tube design was first invented by the Argus Company (manufacturer

of German V-1 bombs). It consisted of combustion chamber (plenum chamber), which

formed a bottle shape design capped over with a hemispherical top. Fuel was injected

through a nozzle located on the tip of the cap and protected from the chamber with metal

grid. The grid functioned as a heat sink and prevented gas from burning at the nozzle.

Pressurized air was forced into the plenum chamber continuously using a

compressor, the combustion took place and the hot gases expanded. The continuous

supply of the compressed air into the plenum chamber prevented hot gas from getting out

of the plenum chamber and almost all of it were thrust into the exhaust. The engine did

not self-sustain or resonate due to the reasons of smaller plenum chamber and exhaust

length.

Fig 2.7: Capped tube-Argus

2.4 WHY VALVELESS PULSEJETS

A valveless pulse jet engine is a simple and ordinary engine. It is just a piece of

metal tube cut to the required dimensions. In a valveless pulsejet engine there are no

mechanical valves but they do have aerodynamic valves which for the most part resist the

flow in a single direction. They have no mechanically moving parts and so they are more

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reliable. All valveless engines have low thrust output, high fuel consumption and overall

poor performance.

Fig 2.8: A 4-Pound Valveless Pulse Jet

Pulsejets can be used on a large scale as industrial drying systems, and there has

been a new surge to study and apply these engines to applications such as high output

heating, biomass conversion, and alternative energy systems, as pulsejets can run on

almost anything that burns including particulate fuels such as sawdust or coal powder.

2.5 APPLICATION OF PULSEJET ENGINE

Pulse jet engines have been used in many functional jets; they can also be used for

a variety of other applications such as:

Ground Applications: 1) Water heating,

2) Biomass fuel conversion,

3) Heat generators and

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4) Orchard fields

Flight Applications: 1) In radio controlled aircraft and

2) Target drone aircraft and control line.

Merits

Pulse jet engines are easy to build on a small scale and can be constructed using

few or no moving parts. This means that the total cost of each pulse jet engine is much

cheaper than traditional turbine engines. Pulse jet engines do not produce torque like

turbine engines do, and have a higher thrust-to-weight ratio.

De-Merits

While pulse jet engines can be beneficial to many industries, they do have several

disadvantages. For example, pulse jet engines are very loud which only makes them

practical for military and industrial purposes. Also, pulse jet engines do not have very

good thrust specific fuel consumption levels. Likewise, pulse jet engines use acoustic

resonance rather than external compression devices to compress fuels before combustion.

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3. PRINCIPLE OF OPERATION OF PULSE JET ENGINES

3.1 RIJKE TUBE

Rijke's tube turns heat into sound, by creating a self-amplifying standing wave. It

is an entertaining phenomenon in acoustics and is an excellent example of resonance.

Fig 3.1: Rijke Tube

The Rijke tube is simply a cylindrical tube with both ends open and a heat source

placed inside it. The heat source may be a flame or an electrical heating element. It has a

wire gauze inside about one quarter the way from the bottom. Traditionally, the tube is

positioned vertically on a stand or even held in a hand and the heat source is introduced

from below into the tube. For certain ranges of position of the heat source within the tube,

the Rijke tube emits a loud sound. This phenomenon was discovered by Rijke around

1850, and is therefore called the Rijke phenomenon. Sound production in the Rijke tube

is a classic example of a thermo-acoustic phenomenon.

In the case of the Rijke tube air can move in and out of both ends. A heated metal

mesh placed a quarter of the way up from the bottom heats the air flowing past it. This

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flow of air is a combination of the convection current caused by the transfer of heat from

the metal mesh and the sound wave that is set up for the condition of two open ends.

For half of the oscillation cycle of the sound wave air moves in from both ends as

it flows towards the center generating a pressure antinode (displacement node) there.

Even though some of the air moving past the hot metal mesh has already been heated

during the cycle prior to this, some additional cool air flows in, passing through it and

acquiring thermal energy and further increasing the pressure, thus reinforcing the

oscillation. For the remaining half cycle air passing by the metal mesh while flowing

outward from the center of the tube is already heated and therefore energy transfer is

minimal.

The sound comes from a standing wave whose wavelength is about twice the

length of the tube, giving the fundamental frequency. Lord Rayleigh, in his book, gave

the correct explanation of how the sound is stimulated. The flow of air past the gauze is a

combination of two motions. There is a uniform upwards motion of the air due to

a convection current resulting from the gauze heating up the air. Superimposed on this is

the motion due to the sound wave. For half the vibration cycle, the air flows into the tube

from both ends until the pressure reaches a maximum. During the other half cycle, the

flow of air is outwards until the minimum pressure is reached. All air flowing past the

gauze is heated to the temperature of the gauze and any transfer of heat to the air will

increase its pressure according to the gas law.

As the air flows upwards past the gauze most of it will already be hot because it

has just come downwards past the gauze during the previous half cycle. However, just

before the pressure maximum, a small quantity of cool air comes into contact with the

gauze and its pressure is suddenly increased. This increases the pressure maximum, so

reinforcing the vibration. During the other half cycle, when the pressure is decreasing, the

air above the gauze is forced downwards past the gauze again. Since it is already hot, no

pressure change due to the gauze takes place, since there is no transfer of heat. The sound

wave is therefore reinforced once every vibration cycle and it quickly builds up to very

large amplitude. This explains why there is no sound when the flame is heating the gauze.

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All air flowing through the tube is heated by the flame, so when it reaches the gauze, it is

already hot and no pressure increase takes place.

Fig 3.2: Working of a Rijke Tube

When the gauze is in the upper half of the tube, there is no sound. In this case, the

cool air brought in from the bottom by the convection current reaches the gauze towards

the end of the outward vibration movement. This is immediately before the pressure

minimum, so a sudden increase in pressure due to the heat transfer tends to cancel out the

sound wave instead of reinforcing it.

The position of the gauze in the tube is not critical as long as it is in the lower

half. To work out its best position, there are two things to consider. Most heat will be

transferred to the air where the displacement of the wave is a maximum, i.e. at the end of

the tube. However, the effect of increasing the pressure is greatest where there is the

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greatest pressure variation, i.e. in the middle of the tube. Placing the gauze midway

between these two positions (one quarter of the way in from the bottom end) is a simple

way to come close to the optimal placement.

The Rijke tube is considered to be a standing wave form of thermo

acoustic devices known as "heat engines" or "prime movers".

3.2 THE HELMHOLTZ RESONATOR

Helmholtz resonance is the phenomenon of air resonance in a cavity, such as

when one blows across the top of an empty bottle. The name comes from a device created

in the 1850s by Hermann von Helmholtz. The "Helmholtz resonator", which he, the

author of the classic study of acoustic science, is used to identify the

various frequencies or musical pitches present in music and other complex sounds. The

Helmholtz resonator can best be demonstrated by taking a normal soft drink bottle and

blowing over the mouth of the bottle. When air is forced into a cavity, the pressure inside

it increases. When the external force pushing the air into the cavity is removed, the

higher-pressure air inside will flow out. The cavity will be left at a pressure slightly lower

than the outside, causing air to be drawn back in. This process repeats with the magnitude

of the pressure changes decreasing each time.

The air in the port (the neck of the chamber) has mass. Since it is in motion, it

possesses some momentum. A longer port would make for a larger mass, and vice-versa.

The diameter of the port is related to the mass of air and the volume of the chamber. A

port that is too small in area for the chamber volume will "choke" the flow while one that

is too large in area for the chamber volume tends to reduce the momentum of the air in

the port.

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Fig 3.3: Helmholtz Resonator

An important type of resonator with very different acoustic characteristics is the

Helmholtz resonator. Essentially a hollow sphere with a short, small-diameter neck, a

Helmholtz resonator has a single isolated resonant frequency and no other resonances

below about 10 times that frequency.

The resonant frequency (f) of a classical Helmholtz resonator, shown in Figure, is

determined by its volume (V) and by the length (L) and area (A) of its neck:

Here, f = ( S2π )√ A

LV

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Figure 3.4: A Classic Helmholtz Resonator

where S is the speed of sound in air. As with the tubes discussed above, the value of the

length of the neck should be given as the effective length, which depends on its radius.

The isolated resonance of a Helmholtz resonator made it useful for the study of

musical tones in the mid-19th century, before electronic analyzers had been invented.

When a resonator is held near the source of a sound, the air in it will begin to resonate if

the tone being analyzed has a spectral component at the frequency of the resonator. By

listening carefully to the tone of a musical instrument with such a resonator, it is possible

to identify the spectral components of a complex sound wave such as those generated by

musical instruments.

Helmholtz Resonator Analogy in Pulse Jet Engines

The simplest analytical model of the valveless pulsejet is that of a Helmholtz

resonator in a combination with a quarter wave oscillator. While their analogy is one of

the simplest forms, it allows for a wealth of understanding of the fundamental operation

of a valveless pulsejet. The model assumes that the combustion chamber and inlet can be

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modeled as a Helmholtz resonator and the exhaust as a matched, or tuned, quarter wave

oscillator (the familiar pipe organ)

It is a classic element in the study of acoustics. The pressure of the gas within the

cavity of the resonator changes as it is alternately compressed and expanded by the influx

and efflux of the gas through the opening and thus provide the stiffness element. At the

opening, there is a radiation of sound into the surrounding medium, which leads to the

dissipation of acoustic energy and thus provides a resistance element.

Fig 3.5: Valveless Pulse Jet during operation

3.3 OPERATION OF A VALVELESS PULSE JET ENGINE

The operation of valveless pulsejet requires a fundamental knowledge about

mixing ignition, combustion and wave initiation, wave propagation and wave reflection.

Any disturbance in the fluid medium creates a wave pattern. If the propagation of the

wave is parallel to the motion of the fluid, then it is termed as longitudinal waves e.g.

sound waves. This is the mode of wave propagation that occurs in a valveless pulsejet.

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When the deflagration begins, a zone of significantly elevated pressure travels outward

through both air masses as a "compression wave". This wave moves at the speed of sound

through both the intake and tailpipe air masses.

(Because these air masses are significantly elevated in temperature as a result of

earlier cycles, the speed of sound in them is much higher than it would be in normal

outdoor air.) When a compression wave reaches the open end of either tube, a low

pressure rarefaction wave starts back in the opposite direction, as if "reflected" by the

open end. This low pressure region returning to the combustion zone is, in fact, the

internal mechanism of the Kadenacy effect. There will be no "breathing" of fresh air into

the combustion zone until the arrival of the rarefaction wave.

Mixing of air and fuel in a Valveless Pulsejet

In the combustion chamber fuel is injected into the flow of fresh air entering the

engine. At the beginning of the charging cycle the mixture is very rich, then it gets leaned

and at the end of the cycle it gets richer again but this mixing of fuel and air in a flow

stream are affected by the parameters of molecular size, concentration, temperature, flow

velocity in the vicinity of the injector and evaporation rate, vary within wide bounds, the

mixture is very non-homogeneous. The combustion chamber consists of two distinct

layers: a highly enriched layer with fuel and combustion products from the previous cycle

and a cold layer arising at the end of the suction cycle. This mixture in-homogeneously

causes a noticeable drop in its combustible properties. The proper engine operation could

be achieved with a mixture composition of air/fuel ratio 1.1 - 1.4.

Ignition in a Valveless Pulsejet

Initially the fuel-air ignition is done manually with the help of blower and a spark

plug. Since the pressure inside the combustion chamber is above atmospheric pressure,

the combustion products along with the air flow towards the exhaust and continue so long

as the pressure in the chamber falls below atmospheric pressure. Now the gases will

retrace its path back into the combustion chamber since the atmospheric pressure is

greater than the combustion pressure. Because of the momentum or the turbulence of the

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hot gas rushing back in, the pressure and temperature inside the combustion chamber will

increase drastically. Once the chamber temperature is above the ignition temperature of

the fuel the next ignition takes place and this cycle continues.

Combustion process in a Valveless Pulsejet

The combustion process likely exists in two phases: an initial ignition which

gradually takes over the entire combustion chamber and this increases pressure and

temperature in the chamber and thereby facilitating the evaporation of the remaining

unburned mixture, and a main combustion process occurring almost instantaneously in

the entire chamber and lasting about 25% of the entire cycle. The combustion chamber

can reach up to a maximum approximate temperature of 2000K.

Since the pressure difference between the combustion chamber and exhaust is

oscillating, there will only be intermittent flow of air to the chamber to support

combustion. A pulse jet engine is an ideal example for an unsteady combustion process.

Here the combustion process is pulsating. The potential coupling between the unsteady

components of pressure and heat release can lead to sustained, large amplitude acoustic

oscillations which being driven by heat release is referred to as a thermo-acoustic

instability. Rayleigh was the first to hypothesize the onset of the instability and define a

criterion for positive coupling.

According to Rayleigh criteria “if heat be periodically communicated to and

abstracted from a mass of air vibrating in a cylinder, the effect produced will depend on

the phase of vibration at which heat transfer takes place. If the heat be given to air at

moment of greatest compression or taken at the moment of greatest rarefaction the

vibration is encouraged. On the other hand heat is given moment of greatest rarefaction

or abstracted at the moment of greatest condensation, the vibration is discouraged.”

Expansion of gases

Due to pressure being setup only at a certain region of engine, the gases at high

pressure migrate to low pressure regions in the engine and eventually out of the engine

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(atmosphere). This happens at a very high velocity since the potential difference in static

pressure between atmosphere and the combustion chamber is very high.

This phenomenon occurs at the cost of losing the achieved high static pressure in

combustion chamber, a very high migration velocity implies a very high volume flow rate

of the engine, hence a very quick and drastic drop in static pressure

Suction of gases

Owing to the exit of the exhaust gases at very high velocities, the static pressure

in the combustion chamber drops drastically, the drop is to such an extent that a negative

gauge pressure (partial vacuum) is setup in the combustion chamber, which forces to

cease any further exit to the combustion gases, instead the combusted products still

dwelling in the engine is sucked back into the combustion chamber along with the fresh

atmospheric air. This leads to the fresh mixing of air and fuel inside the combustion

chamber for subsequent combustions. The cyclic process is shown in the fig (3.3-1)

Fig 3.6: Working of Valveless Pulsejet Engine

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3.4 WORKING OF A VALVELESS PULSE JET ENGINE

The figure below shows a layout of a valveless pulsejet engine.  It has a chamber

with two tubular ports of unequal length and diameter.  The port on the right,

curved backwards, is the intake pipe.  The bigger, flared one on the left is the exhaust, or

tailpipe.  In some other engines, it is the exhaust pipe that is bent into the U-shape, but

the important thing is that the ends of both ports point in the same direction. When the

fuel-air mixture combusts in the chamber, the process generates a great amount of hot gas

very quickly. This happens so fast that it resembles, an explosion.

Fig 3.7: Layout of a Valveless Pulse Jet Engine

The immediate, explosive rise in internal pressure first compresses the gas inside

and then pushes it forcefully out of the chamber, two powerful spurts of hot expanding

gas are created – a big one that blows through the tailpipe and a smaller one blowing

through the intake.  Leaving the engine, the two jets exert a pulse of thrust – they push

the engine in the opposite direction. As the gas expands and the combustion chamber

empties, the pressure inside the engine drops.  Due to inertia of the moving gas, this drop

continues for some time even after the pressure falls back to atmospheric. The expansion

stops only when the momentum of the gas pulse is completely spent. At that point, there

is a partial vacuum inside the engine. The process now reverses itself.  The outside

(atmospheric) pressure is now higher than the pressure inside the engine and fresh air

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starts rushing into the ends of the two ports.  At the intake side, it quickly passes through

the short tube, enters the chamber and mixes with the fuel. The tailpipe, however, is

rather longer, so that the incoming air does not even get as far as the chamber before the

engine is refilled and the pressure peaks. 

One of the prime reasons for the extra length of the tailpipe is to retain enough of

the hot exhaust gas within the engine at the moment the suction starts.  This gas is greatly

rarified by the expansion, but the outside pressure will push it back and increase its

density again.  Back in the chamber, the gases of the previous combustion mix vigorously

with the fresh fuel/air mixture that enters from the other side. The heat of the chamber

and the free radicals in the retained gas will cause ignition and the process repeats.

The spark plug shown on the picture is needed only at start-up. The retained hot

gas provides self-ignition and the spark plug becomes unnecessary. Indeed, if spark

ignition is left on, it can interfere with the normal functioning of the engine. In the J-

shaped and U-shaped valveless engines, gas spews out of two ports.  Some valveless

pulsejet designers have developed engines that are not bent backwards, but

employ various tricks that work in a similar fashion to valves -- i.e. they allow fresh air to

come in but prevent the hot gas from getting out through the intake. A gentler, more

gradual entry would not generate the necessary swirling of gases.  In addition,

turbulence increases the intensity of combustion and the rate of the heat release.

Fig 3.8: A U-shaped Pulse Jet

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3.5 THERMODYNAMIC CYCLE FOR A PULSEJET ENGINE

The thermodynamic working principle of a pulsejet engine does not have an exact

explanation; hence a popular and commonly accepted thermodynamic model is a Lenoir

cycle.

Lenoir Cycle

The Lenoir Cycle is an idealized thermodynamic cycle, where the ideal gas undergoes

basically 3 processes to produce work. The most interesting part of this cycle is that the

output work is obtained with no energy spent on compressing the working fluid. The

cyclic process are as follows,

(1) Constant volume (isochoric) heat addition and then

(2) Adiabatic expansion and

(3) Constant pressure (isobaric) heat rejection.

As Pulsejets typically have a very small compression ratio that reaches a maximum at

around (1.7). The Lenoir three cycle process can be seen below in:

Fig 3.9: Lenoir Cycle

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As the expansion process is isentropic and hence involves no heat interaction.

Energy is absorbed as heat during the constant volume process and rejected as heat

during the constant pressure process. Hence the (P-V) diagram from fig (3.5-1) represents

the thermodynamic process of the Lenoir cycle.

Due to the finite time of combustion and incomplete filling of the chamber with

the fresh charge, the pressure at the end of the heat supply process depends on both the

fuel-air composition and on the relative volume of the fresh mixture entering through the

inlet valve. In this case the heat supply process is not isochoric. This deviation from the

ideal process demands for implementation of modifications to the existing ideal process.

3.6 DESIGNING OF A VALVELESS PULSE JET ENGINE

Valveless Pulse jets are much simpler in design than the valved engines, but with

simplicity you have to sacrifice kgs of thrust and loose the ram air effect. The following

section breaks a valveless pulsejet engine into major components and investigates design

approaches used in other designs for each component. The most important components

are the combustion chamber, the exhaust and intake pipes, the fuel injection system, the

spark ignition system and the air assist starting system. For each of the components,

various solutions are considered to guide in designing a suitable pulsejet engine.

Combustion Chamber

The combustion chamber is arguably the most important component of a

valveless pulsejet design. For a valveless pulsejet engine, the combustion chamber

geometry is critical as any flow inconsistency can disrupt the pulsating combustion cycle,

as pressure waves may be reflected at sudden area changes. The most suitable solution

depends heavily on the selected configuration but there are several design parameters that

apply to all cases. The most significant attribute of a combustion chamber is the circular

cross section. This is because the pressure inside the combustion chamber, positive or

27

negative depending on the cycle, causes stress within the wall. This stress is more evenly

distributed by a circular cross-section design.

Fig 3.10: Comparison of conical sections

Combustion chambers also have conical sections leading into the intake and

exhaust pipes. These sections maintain smooth gas flow throughout the engine. The

above figure depicts the gas flow after combustion in both a conical section and a stepped

transition. The example on the left has a higher pressure increase because the post

ignition confinement is improved, but produces lower thrust because the gas suffers

choking due to entrance effects upon entering the exhaust, limiting the exiting velocity.

Conversely, a tapered cone that is too shallow has poor levels of post ignition

confinement, meaning thrust is also low. A good compromise is required in order to have

a practical engine.

Fig 3.11: Lockwood Hiller Combustion Chamber

28

Fig 3.12:

Logan

Combustion Chamber Section

The Logan combustion chamber section shows the implementation of the cone

sections on two different design solutions. Notably, the Lockwood-Hiller design has

steep cones while the Logan design features shallower tapers. This is because the

Lockwood- Hiller design has much larger intake and exhaust openings that allow the

flow to move relatively smoothly so post ignition confinement is the most critical

component of that design. Conversely, the Logan design has smaller openings and

requires unimpeded air flow exiting and entering the engine thus the conical section is

much shallower. From Simpson (2005), the optimum cone angle for an inline or linear

valveless configuration is approximately 30 degrees, depending on the size of the engine.

The cone section is a critical compromise between the flow of the gases and post ignition

confinement and as such, is a relatively critical consideration for our design.

Exhaust and Intake

The exhaust and intake pipes of a valveless pulsejet engine are generally straight,

circular cross-section tubes with a critical length. The length is critical as it must promote

the acoustic resonance necessary to sustain engine operation. The diameter of the pipe is

also an important consideration as it needs to allow sufficient flow to produce the

required thrust; however, some degree of pressure must be retained to aid in combustion

chamber pressure increase.

29

Fig 3.13: Standard Exhaust Runner Design

The fig shows an arbitrary exhaust pipe section. The length to diameter ratio is

not as critical as the length is the critical dimension. Generally, however, the length to

diameter ratio is 7 to 10 percent of the length (Simpson 2005) to give sufficient volume

for gas flow. This is similar for intake pipes to allow a sufficient fresh air charge into the

combustion chamber. Standard exhaust runner design also depicts the diffuser on the end

of the pipe. This is the same for both intake and exhaust and is necessary to control the

flow of gas exiting and entering the engine.

Fig 3.14: Sudden Expansion Exit Conditions

For the exit condition, this fig shows that when a sharp expansion occurs, the flow

creates turbulent eddies as it separates from these edges. This separation causes the flow

to lose energy, thus reducing the overall thrust developed by the engine. By making this

transition conical or bell-shaped these effects are negated keeping the flow smooth and

30

directing more of the energy of the flow into generating thrust from the engine.

Conversely, for the intake condition, the fig shows that the flow separates from the

surface at the sharp corner creating a vena contractor that effectively limits the cross-

sectional area through which the air can flow.

This limits the effectiveness of the intake to draw in the fresh air charge and the

exhaust to ingest the cool dense air required to confine the combustion event. Conical or

bell-shaped diffusers limit flow separation allowing smooth transition of the air into the

engine.

Fig 3.15: Entrance Flow Conditions

Fuel Injection System

Injector position and design is an important parameter in the pulsejet design. Poor

fuel delivery and injection can limit the effectiveness of combustion and in some cases,

can render the engine inoperable. Propane gas is the fuel of choice for a large majority of

pulsejets as its gaseous form does not require a nozzle for fuel atomization. Liquid fuel

systems are generally not used due to the complexity and difficulty of atomizing the fuel,

although, in the past they have been used with varying degrees of success.

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4. OBJECT AND APPROACH

Although not all waves have a speed that is independent of the shape of the wave,

and this property therefore is an evidence that sound is a wave phenomenon, sound does

nevertheless have this property .For instance, the music in a large concert hall or stadium

may take on the order of a second to reach someone seated in the nosebleed section, but

we do not notice or care, because the delay is the same for every sound. Bass, drums, and

vocals all head outward from the stage at 340 m/s, regardless of their differing wave

shapes. The speed of sound in a gas is related to the gas's physical properties. It is a series

of compressions and expansions of the air.

Fig 4.1: Propagation of Sound during the Operation of Pulse Jet

Even for a very loud sound, the increase or decrease compared to normal

atmospheric pressure is no more than a part per million, so our ears are apparently very

sensitive instruments. In a vacuum, there is no medium for the sound waves, and so they

cannot exist. The roars and whooshes of space ships in Hollywood movies are fun, but

scientifically wrong.

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Kadenacy Effect

Fig 4.2: Kadenacy Effect

In the explanation of the working cycle, inertia keeps driving the expanding gas

out of the engine all the way until the pressure in the chamber falls below atmospheric.

The opposite thing happens in the next part of the cycle, when the outside air pushes its

way in to fill the vacuum.  The combined momentum of the gases rushing in through the

two opposed ports causes the chamber briefly to be pressurized above atmospheric before

ignition. There is thus an oscillation of pressure in the engine caused by inertia.  

The gases involved in the process (air and gaseous products of combustion) are

stretched and compressed between the inside and outside pressures.  In effect, those

fluids behave like an elastic medium, like a piece of rubber.  This is called the “Kadenacy

Effect”.

The elastic character of gas is used to store some of the energy created in one

combustion cycle and use it in the next.  

The energy stored in the pressure differential (partial vacuum) makes the

aspiration (replacement of the burned gas with fresh fuel-air mixture) possible. Without

it, pulsejets would not work.

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4.1 PROPAGATION OF SOUND IN PULSE JETS

The phenomenon of sound is easily found to have all the characteristics we expect

from a wave phenomenon Sound waves obey superposition. Sounds do not knock other

sounds out of the way when they collide, and we can hear more than one sound at once if

they both reach our ear simultaneously. The medium does not move with the sound. Even

standing in front of a titanic speaker playing earsplitting music, we do not feel the

slightest breeze. The velocity of sound depends on the medium. Sound travels faster in

helium than in air, and faster in water than in helium. Putting more energy into the wave

makes it more intense, not faster.

Acoustic Theory

The pressure wave travels up and down the tube. When the wave front reaches an

end of the tube, part of it reflects back.  Reflections from opposed ends meet and form the

so-called ‘standing wave’.

Fig 4.3: Standing Wave

34

A standing wave in a transmission line is a wave in which the distribution of

current, voltage, or field strength is formed by the superposition of two waves of the

same frequency propagating in opposite directions. The effect is a series of nodes (zero

displacement) and anti-nodes (maximum displacement) at fixed points along the

transmission line. Such a standing wave may be formed when a wave is transmitted into

one end of a transmission line and is reflected from the other end by an impedance

mismatch, i.e., discontinuity, such as an open circuit or a short. The failure of the line to

transfer power at the standing wave frequency will usually result in attenuation distortion.

In practice, losses in the transmission line and other components mean that a

perfect reflection and a pure standing wave are never achieved. The result is a partial

standing wave, which is a superposition of a standing wave and a traveling wave. The

degree to which the wave resembles either a pure standing wave or a pure traveling wave

is measured by the standing wave ratio.

Fig 4.4: Wave Formation at the Exhaust

Another example is standing waves in the open ocean formed by waves with the

same wave period moving in opposite directions. These may form near storm centers, or

35

from reflection of a swell at the shore, and are the source of microbaroms and

microseisms. Graphically, the standing wave is best represented by a double sine curve.

The same is true for the pulsejet cycle.  The undulations of a single sine curve depict the

changes of gas pressure and gas speed inside a pulsejet engine very well. The doubling of

the curve – the addition of a mirror image, so to say – shows that the places where the

pressure and speed are the highest in one part of the cycle will be the places where they

are the lowest in the opposite part.

The changes of pressure and the changes of gas speed do not coincide. They follow

the same curve but are offset from each other.  One trails (or leads) the other by a quarter

of the cycle.  If the whole cycle is depicted as a circle – 360 degrees – the speed curve

will be offset from the pressure curve by 90 degrees. The resonance establishes a pattern

of gas pressures and speeds in the engine duct that is peculiar to the pulsejet and not

found in the other jet engines.

In some ways it resembles a 2-stroke piston engine resonant exhaust system more

than in does a conventional jet engine. Understanding this pattern is very important, for it

helps determine the way the events in the engine unfold. When considering a pulsejet

design, it is always good to remember that those machines are governed by a complex

interaction of fluid thermodynamics and acoustics.

Elements of Resonance

In acoustic terms, the combustion chamber is the place of the greatest impedance,

meaning that the movement of gas is the most restricted.  However, the pressure swings

are the greatest.  The chamber is thus a speed node but a pressure antinode. The outer

ends of the intake and exhaust ports are the places of the lowest impedance.  They are the

places where the gas movement is at the maximum and the speed changes are the greatest

– in other words, they are speed antinodes.  The pressure swings are minimal, so that the

port ends are pressure nodes. The pressure outside the engine is constant (atmospheric).  

The pressure in the combustion chamber seesaws regularly above and below

atmospheric.  The pressure changes make the gases accelerate through the ports in one

36

direction or another, depending on whether the pressure in the chamber is above or below

atmospheric. The distance between a node and an antinode is a quarter of the wavelength.

This is the smallest section of a standing wave that a resonating vessel can accommodate.

In a valveless pulsejet, this is the distance between the combustion chamber (pressure

antinode) and the end of the tailpipe (pressure node).  This length will determine the

fundamental wavelength of the standing wave that will govern the engine operation. The

distance between the chamber and the end of the intake is rather shorter.  It will

accommodate a quarter of a wave of a shorter wavelength.  This secondary wavelength

must be an odd harmonic of the fundamental.

5. PROCEDURE ADOPTED

5.1 MATERIAL EMPLOYED

The material used in the manufacturing process is Mild Steel. Mild steel is a type of

steel that only contains a small amount of carbon and other elements. It is softer and more

easily shaped than higher carbon steels. It also bends a long way instead of breaking

because it is ductile. It is used in nails and some types of wire, it can be used to make

bottle openers, chairs, staplers, staples, railings and most common metal products. Its

name comes from the fact it only has less carbon than steel.

Some mild steel properties and uses:

Mild steel has a maximum limit of 0.2% carbon. The proportions of manganese

(1.65%), copper (0.6%) and silicon (0.6%) are approximately fixed, while the

proportions of cobalt, chromium, niobium, molybdenum, titanium, nickel,

tungsten, vanadium and zirconium are not.

37

A higher amount of carbon makes steels different from low carbon mild-type

steels. A greater amount of carbon makes steel stronger, harder and very slightly

stiffer than a low carbon steel. However, the strength and hardness comes at the

price of a decrease in the ductility of this alloy. Carbon atoms get trapped in the

interstitial sites of the iron lattice and make it stronger.

What is known as mildest grade of carbon steel or 'mild steel' is typically low

carbon steel with a comparatively low amount of carbon (0.16% to 0.2%). It has

ferromagnetic properties, which make it ideal for manufacture of many products.

The calculated average industry grade mild steel density is 7.85 gm/cm3. Its

Young's modulus, which is a measure of its stiffness is around 210,000 MPa.

Mild steel is the cheapest and most versatile form of steel and serves every

application which requires a bulk amount of steel.

The thickness of 2mm for both the pulsejets is maintained.

5.2 COMPONENTS OF THE PULSE JET

A Valve less Pulse Jet Engine has three major components,

1. Inlet

2. Combustion chamber

3. Exhaust tail pipe

Inlet

Inlet is the smallest component in a pulsejet engine designed for air intake. The

inlet is a 100mm long open cylinder with 38mm inner diameter and 42mm outer

diameter, maintaining 2mm thickness.

38

Photo 5.1: Air Inlet

Combustion Chamber

The combustion chamber is a combination of cylindrical section and tapered section.

Fig 5.1: Combustion chamber

Combustion chamber is equipped with 4 sockets for fuel injectors and spark plug

to inject the fuel and to initially ignite it to start the combustion process. The air drawn

inside is combusted to high pressures and temperatures.

39

Photo 5.2: Combustion Chamber undergoing Turning Operation

Exhaust Tail Pipe

The exhaust tail pipe is the largest part of a pulsejet engine. The length of the tail

pipe determines the resonant characteristics of Pulse Jet. The higher the tail length, the

greater the hot gases retained in it and the temperature increase is high in the combustion

chamber.

As the pulse combustion is the consequence of a combustion instability that is

driven into resonance via this resonance pipe. Hence the exhaust pipe is also called as

“Resonance Pipe”.

Photo 5.3: Exhaust Pipe before Machining

40

The diameter of the pipe should be somewhat larger 8% than that of the inlet pipe

and the tube length needed to be able to be adjusted for frequency manipulation so that

the flow of combusted air moves with a certain velocity. These are the main important

factors to design the exhaust pipe.

The cause of designing the exhaust pipe with a larger diameter than that of the

inlet pipe gives the pulse jet the ability to pump out most of the combustion products

while re-inhaling the fresh charge of air from the inlet portion

Fig 5.2: Exhaust

Fuel Injectors

We have produced three fuel injectors of varying injection holes, one of 0.8mm, the

other with 1mm and finally with 1.2mm holes drilled at equidistant positions from the injector

head which has been brazed to lock the fuel and create the injection effect.

41

Photo 5.4: Fuel Injectors

Fuel

Propane is a three-carbon alkane with the molecular formula C3H8, normally a

gas, but compressible to a transportable liquid. A by-product of natural gas processing

and petroleum refining, it is commonly used as a fuel for engines, oxy-gas torches,

barbecues, portable stoves, and residential central heating. Propane is one of a group of

liquefied petroleum gases.

Propane undergoes combustion reactions in a similar fashion to other alkanes. In

the presence of excess oxygen, propane burns to form water and carbon dioxide.

C3H8 + 5 O2 → 3 CO2 + 4 H2O + Heat

Propane + Oxygen → Carbon dioxide + Water

When not enough oxygen is present for complete combustion, incomplete

combustion occurs when propane burns and forms water, carbon monoxide, and carbon

dioxide.

C3H8 + 4.5 O2 → 2 CO2 + CO + 4 H2O + Heat

Propane + Oxygen → Carbon dioxide + Carbon monoxide + Water

42

5.3 DIMENSIONS

Name of the section Length

(in mm)

Inner diameter

(in mm)

Cross Sectional

Areas (mm2)

Flow Volume

(mm3)

Inlet 100 38 4534.16 453416

Combustion chamber 100 80 20096 2009600

Tapered section 72 80 Variable

Exhaust tail pipe 400 42 5538.96 2215584

Table 5.1: Dimensions of a single pulsejet engine

Fig 5.3: Pulse Jet Exploded Diagram

43

Photo 5.5: Finished Pulse Jet undergoing TIG Welding

44

6. RESULTS

In this section, the Experimental setup and procedure along with the results are

given. A schematic diagram for each experimental setup is given. The procedure for

starting and operating the engine is presented at the beginning and the procedures for

measuring variables like mass flow, noise levels etc. in different operations are given

after the schematic diagram of setup for their measurement. The results are given in a

tabular form for each operation.

6.1 PROCEDURE FOR STARTING AND OPERATING THE ENGINE

Gaseous Propane from the cylinder as fuel is supplied to the combustion chamber

(directly or using injectors) using fuel pipes through fuel regulating valve(s). The

pressure of the gas from the cylinder is maintained using pressure regulator. Fuel is

ignited either manually or using spark plug and pressurized air is provided i.e. air is

blown in through inlet initially till the engine attains self-sustaining combustion.

The minimum fuel flow for self-sustaining combustion is maintained using fuel

regulating valve. Once the engine is self-sustained and resonating, the required variables

can be measured using the specific instruments. At first experiments were done on single

pulsejet engine to tune the engine and freeze the dimensions and also to determine the

minimum fuel flow required for self-sustained resonating combustion and the range of

flow for which the engine operates with ease and smooth.

With the fixed dimensions, the noise levels and temperatures in the combustion

chamber were measured for single engine in a single operation. Simultaneously fuel mass

flow rate is also measured from micro motion mass flow meter.

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6.2 EXPERIMENTAL SETUP - 1

In this setup the engine is tested and the length of the inlet is fixed to 160mm and

different fuel flow ranges for engine operation are determined. The fuel is injected

directly into the combustion chamber perpendicular to the air flow through an injector of

5x1mm holes. The schematic diagram of the test setup is shown in the following figure.

The mass flow readings were noted from micro motion mass flow meter.

Fig 6.1: Experimental Setup - 1

Table 6.1: Fuel Flow Rate Range for Engine Direct fuel Injector 1mm

46

Trial No.

Inlet Length

(mm)

Tail Pipe length

(mm)

Cylinder Pressure

(psi)

Mass Flow

(kg/min)

1. 100 400 90 0.056-0.063

2. 100 400 90 0.042-0.049

3. 100 400 90 0.061-0.0673

4. 100 400 90 0.0605-0.067

It is very clear from the above table that the engine has a wide range of fuel flow

rate ranging between 0.042 kg/min and 0.0673 kg/min at a cylinder pressure of 90psi.

6.3 EXPERIMENTAL SETUP - 2

In this setup again single engine was operated with the same dimensions and a

fuel injector with 5x2 holes of 0.8mm diameter was used to inject the gaseous hydrogen

into combustion chamber perpendicular to the air flow. The engine was operated twice

and the range of fuel flow rate was determined at a cylinder pressure of 90psi. The below

figure is the schematic diagram of the test setup with the fuel injector.

Fig 6.2: Experimental Setup - 2

47Trial No.

Inlet Length

(mm)

Tail Pipe length

(mm)

Cylinder Pressure

(psi)

Mass Flow

(kg/min)

1. 100 400 90 0.034-0.044

2. 100 400 90 0.0338-0.0446

Table 6.2: Fuel Flow Rate range for Engine with Fuel Injector 0.8mm

It was observed that the usage of fuel injectors has reduced the minimum fuel

flow rate required for engine operation. It was also observed that the engine starts at the

flow rate of 0.034 kg/min.

Trail no. Pressure

(psi)

Noise levels For

engine run (dB)

1 100 89.7

2 100 82.8

3 100 80.3

4 100 86.8

5 100 88.9

Table 6.3: Noise levels for Pulsejet

Table 6.4: Temperatures in the Combustion Chamber during Engine Operation

The temperatures are manually determined using multi point temperature meter.

48

Trail no. Pressure

(psi)

Fuel mass

Rate(kg/min)

Temperature in

Combustion Chamber

(oC)

Noise level for

Pulsejet

(dB)

1 90 0.0525 – 0.0545 1096 84.6

2 90 0.0525 – 0.0545 1112 85.1

3 90 0.0525 – 0.0545 1136 84.9

4 90 0.0525 – 0.0545 1152 84.2

5 90 0.0525 – 0.0545 1184 83.8

7. CONCLUSIONS AND FUTURE STUDY

As we knew that valveless pulsejet engines are easy to build and operate but they

produce a lot of noise during its operation, we identified the need to reduce the noise

levels.

In order to further improve on the pulsejet research, several things can be done

during the testing phase that would enhance the results. A pressure transducer that

measures a pressure differential of 30 psi which would be compared with theoretical

results to see how close to optimum the pulsejet is performing.

Additionally, further research in the effects of optimum fuel to air ratios and

maximizing flow into the inlets could potentially show improvements in thrust and

efficiency within the engine. Potentially something such as gasoline or Jet A fuel could

be an alternate fuel source to the pulse jet and with acceptable fuel injection, these fuels

could allow for greater thrust from the engine and overall lighter setup that could be used

on a unmanned air vehicle or RC plane.

FUTURE STUDY

In Future they might be used in any of the ground applications efficiently so they

are non-pollutant and eco-friendly engines. The fuels which are used for the operation of

these engines are also cheap and can be helpful in all the needs.

The design of the plenum chambers can also be changed into elliptical shape

design in where we can expect to yield good results in reducing the sound

49

8. REFERENCES

[1] Anderson, R., LukacsT., ‘Design and Build of a Pulsejet’

[2] Bruce Simpson, ‘Enthusiasts Guide To Design, Construction and Operation of

valveless Pulse jets.’

[3] Cottrill, L., “First Principles: The Kadenacy Effect,”

[4] Franco Marcenaro, Advanced Pulsejet Theory.

[5] Ogorelec, B., “Valveless Pulsejet Engines 1.5,” http://www.pulse-jets.com/valveless/

[6] Sulprizio, C., “Lockwood Valveless Pulsejet,” Senior Project, Cal Poly Univ.,

WEBSITES

[a] pulsecombustion.com

[b] aardvark.com

[c] xjets.com

[d] wikipedia.org

[e] aiaa.org

[f] pulsejetengines.com

[g] pulse-jets.com

[h] jetzilla.com

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APPENDIX

.

51