Temperature oscillations in the wall of a cooled multi

pulsejet propeller for aeronautic propulsion

TRANCOSSI, Michele <http://orcid.org/0000-0002-7916-6278>, PASCOA,
Jose <http://orcid.org/0000-0001-7019-3766> and CARLOS, Xisto
<http://orcid.org/0000-0002-7106-391X>
Available from Sheffield Hallam University Research Archive (SHURA) at:
https://shura.shu.ac.uk/13964/

This document is the Published Version [VoR]

Citation:
TRANCOSSI, Michele, PASCOA, Jose and CARLOS, Xisto (2016). Temperature
oscillations in the wall of a cooled multi pulsejet propeller for aeronautic propulsion.
SAE Technical Papers, 2016 (1-1998), 1-8. [Article]

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Temperature Oscillations in the Wall of a Cooled Multi 2016-01-1998

Pulsejet Propeller for Aeronautic Propulsion Published 09/20/2016

Michele Trancossi
Sheffield Hallam University

Jose Pascoa
Universidade Da Beira Interior

Carlos Xisto
Chalmers University of Technology

CITATION: Trancossi, M., Pascoa, J., and Xisto , C., "Temperature Oscillations in the Wall of a Cooled Multi Pulsejet Propeller for
Aeronautic Propulsion," SAE Technical Paper 2016-01-1998, 2016, doi:10.4271/2016-01-1998.
Copyright © 2016 SAE International

Abstract Introduction
Environmental and economic issues related to the aeronautic
transport, with particular reference to the high-speed one are opening
Generalities
new perspectives to pulsejets and derived pulse detonation engines. A pulsejet engine is a jet engine with combustion occurring in pulses.
Their importance relates to high thrust to weight ratio and low cost of It is made with no moving parts [1] or a simple moving valve [2]. It is
manufacturing with very low energy efficiency. This papers presents capable of running statically (i.e. it does not need to have air forced
a preliminary evaluation in the direction of a new family of pulsejets into its inlet typically by forward motion). Pulsejet engines are a
which can be coupled with both an air compression system which is lightweight and cheap jet propulsion, but the usually suffer of both
currently in pre-patenting study and a more efficient and enduring poor compression ratio and low specific impulse. Pulsejets operate
valve systems with respect to today ones. This new pulsejet has bee according to Lenoir cycle [3], which has not any compression process
specifically studied to reach three objectives: a better thermodynamic and leads to lower thermal efficiency than Otto and Diesel cycle [4].
efficiency, a substantial reduction of vibrations by a multi-chamber
cooled architecture, a much longer operative life by more affordable Historic Background
valves. Another objective of this research connects directly to the
Pulsejet is probably the oldest jet propulsion system. Early attempts
possibility of feeding the pulsejet with hydrogen. This paper after a
to utilize the power from explosions for propulsive applications date
preliminary analysis of the pulsejet takes into account two necessary
back to late 17th-early 18th centuries and the contributions of
stages of this activity with the initial definition of the starting point of
Huygens and Allen are note worthy. In 1729, Allen proposed a
this activity, which aim to define an initial thermodynamic balance of
jet-propelled ship by explosion of gunpowder in a proper engine [4].
a Lenoir cycle and a preliminary but effective estimation of the
Berthelot and Vieille, and Mallard and Le Chatelier moved their
thermal problem. It analyses the heat transfer process through the
attention to gaseous explosions and combustion modes. They
wall of the combustion chamber of a pulsejet for aeronautic
discovered [5] a combustion mode propagating at a velocity ranging
propulsion. The inside wall is exposed to burning gases with an
from 1.5 to 2.5 km/s. They obtained this result by igniting gas with a
average temperature of 1500 K, which oscillates with an amplitude
high-explosive charge. Similar effects have been produced in long
500 k and a frequency of 50 Hz. It has been considered the possibility
tubes even when gas was ignited by non-explosive means (spark or
of using Hydrogen injection to reduce the environmental impacts at
open flame). Flame acceleration along the tube, often accompanied
the price of introducing a cooling water envelope at an average
with flame speed oscillations, was detected prior to onset of
temperature of 80 °c. The water mass flow to ensure this condition
detonation. It has been also discovered that detonation velocity is
has been evaluated and it has been evaluated both the average
independent of the ignition source and tube diameter. It is primarily a
temperature profile within the wall and the effects of the oscillations
function of the composition of the explosive mixture, with severe
of gas temperature inside the combustion chamber. Obtained results
mechanical effect implying the development of high pressure in the
have allowed starting an effective activity through a radically new
propagating wave, which is governed by adiabatic compression of the
pulsejet architecture, which is expected to outclass any former
explosive mixture rather than by molecular diffusion of heat [6].
pulsejet in term of operative life and of compression ratio with a
Initially, the interest in detonation was associated only with
consequent step increase in terms of thermodynamic efficiency.
preventing explosions in coalmines. Mikhelson (1890), Chapman
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(1899), and Jouguet (1904) estimated the detonation parameters by Derived concepts such as ramjets and scramjets achieved a higher
considering one-dimensional (1D) flow, mass, momentum and energy success level because of higher performances.
conservation laws according to the shock wave theory of Rankine and
Hugoniot. This model describes the detonation wave as a pressure
discontinuity coupled with the reaction front (instantaneous reaction) Pulsejet Potential and Limits
and presents a good agreement with observed detonation velocities. The key advantage of pulsejets lays on its simplicity with respect to
any other propulsion system. The construction of pulsejets is cheap
During the first decades of the 20th century, a fundamental and not sophisticated. It is a fundamental advantage in the field of
advancement has produced by experimentation and analysis of miniature propulsion. Thermodynamic cycle of a pulsejet can be
detonations, which deal with the development of reciprocating approximated by the Lenoir cycle, because unsteady pulsating
internal combustion engines [7]. Lorin (1913) designed the first combustion does not happen at constant pressure such as in most jet
subsonic pulsejet, which has never achieved high enough speed for propulsion systems. Pulsejets burn fuel intermittently in a quick
operating. Fonó (1915) studied a ramjet propulsion unit to launch succession of detonating pulses. The consequent pressure shocks and
heavy projectiles with long range and low initial velocity from formation of gaseous product of combustion produces the thrust of
lightweight guns. the system with a net pressure gain between the air intake and outlet.
The absence of a compression stage reduces the thermodynamic
The historic milestone for pulsejet development has been the German efficiency, but also eliminates the energy consumption by the
Fieseler Fi 103 (V1 middle range bomb) [8, 9], which was propelled by compressor. The gain by pulsating combustion is difficult to be
Argus As 014 pulsejet. The research activity that produces such an utilized for propulsion. It can be stated that pulsation is both the
engine was based on the design of a pulsejet engine by Paul Schmidt. central problem and the main benefit of this propulsion system. Some
Schmidt and Madelung (1934) proposed a "flying bomb" powered by historic realizations demonstrate that the efficiency of a pulsejet can
his pulsejet. In 1938, they demonstrated that a pulse jet-powered be increased when it is used as a combustor of a turbine engine. If the
unmanned bomber could be realized even if the prototype lacked range air is preliminary compressed the pressure gain is multiplied by the
and accuracy and was expensive. Further developments of this project high-pressure environment. The architecture of British centrifugal
leaded to the Argus engine [10], which equipped the V1 bombs. turbojets such as Rolls Royce Derwent (Figure 3) is a demonstration
of this statement.

Figure 3. Rolls Royce Derwent

Figure 1. Fieseler Fi 103 - V1 Bomb

Figure 2. Schema of Argus As 014 pulsejet engine of V1 bomb.

Argus As 014 has been probably the valved pulsejet with the longer
operative life (around 40 minutes). Figure 4. Detail of combustion chamber of Rolls Royce Derwent

It is evident that the combustion chamber of Derwent (Figure 4) has

After WW II, the pulsejet has been nearly abandoned. Other
the same architecture of a valueless pulsejet.
architectures had preferred because of vibration-induced problems,
acoustic impacts, low operative life, low thrust and specific fuel
consumption.
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If compared to traditional constant pressure combustors, pulsejets

have smaller mechanical losses and lower fuel consumption or higher
fuel efficiency. The system irregularity produces problems with axial
turbine blades. Radial turbines are more solid on this point of view
but they have lower efficiency especially with intermittent flows.

The effects of pulsation and high temperatures are also evident on the
pulsejets with petal valve, which have a very low operative life. They
generate evident accelerated fatigue stresses, which appears the main
cause of these failures. “Wedge” Shape Holes Circular Drill Holes

Figure 5. Small pulsejets’ valve designs

Today Valved Pulsejet Architecture
Today, pulsejets seem promising as a low cost solution for alternative
propulsion purposes in the subsonic velocity range. The main
problem is that valved pulsejets, which are the more viable for high
thrusts, suffers of a very low operative life of the valves There are
three basic types of valve systems used in the average pulsejet
engine. The calculator generates the dimensions of all three types
regardless of how much thrust you want from the engine.

The first type is a petal valve system, and is the most common type
used in small pulsejet engines. The petal valve system has two key Figure 6. Image of failed valve (left) and the valve head (right) [13]
elements: a surface with drilled holes, a disk with valve petals that
covers the holes. This system is simple, economic, easy to
manufacture, but presents different problems: low affordability and
large reduction of valve area. It is not used for larger engines, but it
gives optimal performances in small pulsejets. If the thrust of your
engine falls in the range of thrust between 1 to 5 kg. Some
applications up to 50 kg of static thrust have been produced but they
look inefficient and have a very low operative life. Today valved
pulsejets uses petal valves, which have a very short life span. When
subject to the extreme temperatures, pressures and very high
frequency, tests performed at NASA Glenn [13] demonstrated that the
valves last approximately fifty seconds. This is detrimental to pulsejet
performance and hinders research efforts. Figure 6 presents two Figure 7. Architecture and valve detail of a high thrust pulsejet based on Argus
images depicting a failed valve (left) and the valve head (right). 0.14 design.

High efficiency petal valve system is similar to the regular petal valve
system in that it is a circular array of valve holes, but uses valve plate
area by adopting optimized and shaped valve holes. The optimized
shape of the inlet holes increases the efficiency of the pulsejet and
requires a smaller diameter combustion chamber for the same amount
of thrust. In particular, this solution has reduced drag and better
airflow through the engine. On the other side, it has higher costs
because each valve hole must be machined to the correct shape and
size, instead of simply drilling the hole. The applications range
spaces from 1 to 50 kg.
Figure 8. High temperatures during a Lockwood-Hiller experiment
Larger pulsejet engines (Figure 7) adopt the valve grid system, which
is directly derived from the original design of the Argus engine of the The must have limited dimensions in order to seal correctly the
V1 bomb. A valve grid is a rectangular array of valved holes. Unlike combustion chamber. This architecture allows a more optimized fluid
the previous two types, the valved holes are not perpendicular to the dynamic of the inlet section and a larger area of openings. Thus, they
axis of the combustion chamber. Valves are still reed valves, which further reduce the fluiddynamic losses and have a smaller diameter of
are constituted by a set of thin plates and are placed on inclined the combustion chamber and less aerodynamic drag. Usually this
planes. They open when the pressure in the combustion chamber architecture is used for engines with a thrust above 20 kg and
decreases allowing the airflow through the holes, and closes when increases it competitiveness with increasing thrust.
pressure increases.
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A New Pulsejet Development Hypothesis Constant Volume Heat Addition (1-2)

This paper is a preliminary step of an independent research project The heat addition phase (combustion) of a Lenoir cycle is an
with the aim of increasing both the performances and the robustness isochoric (constant volume) transformation. In the ideal gas version
of pulsejet related propulsion. The first step relates to an effective of the traditional Lenoir cycle, the first stage (1-2) involves the
preliminary analysis of the thermodynamic cycle of a pulsejet. This addition of heat in a constant volume manner. This results in the
analysis will be the reference for the design activity of pulsejets with following for the first law of thermodynamics:
a preliminary air compression stage. The second stage focuses on the
possibility of using more robust valve systems which use requires an
effective reduction of the temperatures on the envelop of the and from the definition of constant volume specific heats for an ideal
combustion chamber and an increased thermal stability of the system. gas:
In particular, to reach this goal a cooling system has been taken into
account and analysed.

Calculation Assumptions There is no work during the process because the volume is held
constant:
It has been assumed that the combustion chamber is exposed to
burning gases with an average temperature of 1500 K, oscillating 500
K at 30 Hz. Inside the chamber it has been assumed a convective
coefficient in line with values of ICE (Internal Combustion Engine):
U = 1000 W/(m2·K) including radiation transfer [11, 12]. The pressure after the heat addition can be calculated from the ideal
gas law:
The outside is exposed to cooling water at 353 K, with a heat transfer
coefficient including convection and radiation of 5000 W/ (m2·K)
[12, 13]. In addition, this case is in line with the values assumed for
ICE. The wall is supposed made of stainless steel 2 mm thick with Isentropic Expansion (2-3)
the following values of conductivity: The second stage involves a reversible adiabatic expansion (in the
ideal case) or an isentropic expansion of the fluid back to the original
pressure. For an isentropic process, the second law of
thermodynamics can be expressed by the following expression:

Dimension of combustion chamber have been evaluated to be a

cylinder with diameter 0.25 m and length 0.8 m.
Where p3 = p1 for this specific cycle. The first law of thermodynamics
Lenoir Cycle results in the following for this expansion process:

The thermodynamic cycle that best describes the pulsejet behaviour

is the Lenoir cycle. It is composed by four main phases:

1-2. Constant volume (isochoric) heat addition; because for an adiabatic process: Q23 = 0
2-3. Isentropic expansion with no heat interaction and production of
work; Constant Pressure Heat Rejection (3-1)
3-1. Constant pressure (isobaric) heat rejection with consume of The final stage (3-1) involves a constant pressure heat rejection back
some work. to the original state and according to the first law of thermodynamics
it can be described by

From the definition of work assumes the following expression:

And the amount of heat rejected during this process is:

Figure 9. PV and TS Diagram of Lenoir cycle.

where
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Efficiency
The overall efficiency of the cycle is determined by the total work
over the heat input,

Note that pulsejets gain work during the expansion process but lose
some during the heat rejection process.

Figure 10. Temperature profile across the walls of the combustion chamber in
Numerical Results a pulsejet.
The volume V of the combustion chamber is 39 dm3, and the
frequency f is 50 Hz. According to the above ideal model, a total The planar approximation allows simplifying the average temperature
work of 490 KJ can be evaluated with about 25 kN at the specified profile within the wall, 0<x<L by a linear function
frequency.

Assuming that the fuel is gasoline with a LHV of 43.4 MJ/kg the fuel
consumption can be evaluated according to [14] and [15]. Mass of air The end values, and the unitary heat flux, are:
is about 0.04 kg and requires about 0.0032 kg of fuel/explosion. It
means 0.16 kg fuel/s. It means that the energy introduced by mean of
fuel is around 6.9 MJ/s with fuel efficiency around 7.1%.

Assuming that the combustible is Hydrogen it is necessary 0.00115

kg fuel/explosion with a unitary consumption of 0.046 Kg fuel/s.

Those results show clearly that a serious improvement is necessary to from which
make the pulsejet energetically competitive against other propulsion
systems. But on the other side very low cost very high simplicity and
large improvement potential opens large spaces for the research on
new and more efficient architectures of controlled pulsejets.
and
Reducing Thermal Stresses
This paper is a preliminary part through an effective definition of a
new pulsejet architecture. This architecture is designed to take
Transient Analysis
advantage of traditional spring actuated valves. Those valves will
Transient analysis of the specific case is a complex problem also by
problems in the range of temperatures at which the combustion
mean of numerical simulation by mean of CFD or other codes
chamber of a pulsejet operates.
because of its transient periodic nature. The simplest solution seems
to be the analytical one, by integrating the heat equation considering
It has been then assumed the possibility of analyzing the opportunity
a periodic boundary condition in a semi-infinite slab.
of cooling the combustion chamber of a pulsejet by modelling the
heat transfer through the walls. It can be then possible to evaluate the
average state of the temperature profile within the wall and the effect
of the oscillations of gas temperature.
A solution can be reached assuming that the thickness of the pipe is
adequate and that the high-frequency excitation produces only a small
Steady State Solution
penetration depth of the oscillations. This paper in particular does not
The geometry and nomenclature are graphically presented in Fig. 10, look at the initial transient condition when the engine starts started. It
together with the expected solution. Notice that a planar geometry is focuses on the periodic solution when the system has reached the
assumed because the wall thickness is assumed much smaller than the operating regime.
diameter of the cylinder.
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The following solution gives the If we try a solution to the heat

equation within the solid wall. The period is assumed τ=1/30 s, and
decays exponentially with a penetration xc. Those conditions lead to
the following law of temperature:

By substituting this expression into heat equation, it results:

and then
Figure 11. Temperature oscillations in the wall (they are only noticeable near
the internal surface of the combustion chamber).

and assuming t>>τ it results It means that the surface temperature oscillates only 500·0.0052=2.6 K
(to be superposed to the mean temperature value of 582 K, previously
found), and the phase shift relative to the imposed gas oscillations

where T0,mean and T0,max are the average and peak values of the
temperature oscillation on the solid surface.
Some temperature profiles have been presented are in Fig. 11.

Instead of the solid-surface temperature, the far-field temperature in a

fluid in contact with that surface is imposed, Analysis of the Results and Future Directions
The presented results are a preliminary milestone through the design
of a new pulsejets' family that can overcome the well-known
This equation can be solved by introducing a damping in surface- limitations of today ones. In particular, they can be analysed
temperature amplitude and a phase-shift in the time response. They separately with specific reference to the specific aspects, which have
can be computed from the convective heat-transfer equation: been analysed in this paper.

The thermodynamic analysis shows clearly that an increase of the air

pressure at the inlet can produce a major increase of thermodynamic
and fuel efficiency. In particular, inlet pressures around 2 bars can
The temperature field within the solid can be expressed as a function
almost double the efficiency of the system. Further increases are
of Biot number in line with Dumas and Trancossi [16, 17] former
possible by much higher pressures. Another important aspect relates
solution to a crossflow heat exchanger.
to the fact that an increase of pressure could allow a reduction of the
dimensions of the combustion chamber. The known problems related
to the use of axial turbines forces to take into consideration different
architectures such as a centrifugal turbine similar to the one of Rolls
Royce Derwent. In addition, pass-through fans will be considered
together with other breakthrough configurations.

The preliminary heat exchange analysis shows that some cooling of

the combustion chamber could be possible. This result is fundamental
for an effective design of more efficient and enduring valve systems,
which can be an effective element of the preliminary compression
with T1,mean=1500 K the mean temperature of the combustion gases, system. The pulsating nature of combustion authorizes to explore also
T1,max=1500+500=2000 K is maximum value (i.e. the gas temperature the hypothesis of a pulsejet with a double chamber; a compression
oscillates from 1000 K to 2000 K sinusoidally at 50 Hz). one and combustion one. When the valves are closed, air is
compressed in one chamber and combustion is produced in the other.
The characteristic penetration depth is 0.37 and Biot number: 0.0074. At the end of the combustion pressure decreases in the combustion
chamber and compressed air pressure opens the valves and produces
The value for the amplitude damping at the surface-temperature is air inlet into the combustion chamber.
 Downloaded from SAE International by Michele Trancossi, Monday, November 07, 2016

Conclusions 14. Moeckel, M., "Computational Fluid Dynamic (CFD) Analysis

of a Six Cylinder Diesel Engine Cooling System with
This paper has analyzed pro and contra of pulsejet propulsion
Experimental Correlations," SAE Technical Paper 941081,
focusing on valved pulsejets. In particular, after presenting the nature
1994, doi:10.4271/941081.
of the thermodynamic cycle it has focused on the definition of the
guidelines for future improvements analysing also pro and contra of 15. O’Brien, J. G., “The pulsejet engine a review of its development
pulsejet propulsion. The intrinsic weakness related to valves allows potential”, US Naval Postgraduate School, Monterey, California,
taking into considerations new architectures. In particular, to verify USA, 1974
the feasibility of a new configuration, which is currently under study 16. Chaurasia, S. R.. Gupta R., and Sarviya, R. M., “Performance
it has been, analyzed the efficacy of possible cooling system Analysis of a Pulsejet Engine”, International Journal of
considering both steady values and transient ones. This analysis has Engineering Research and Applications (IJERA), Vol. 3, Issue 4,
verified that water-cooling can be effective authorizing the pp.605-609, 2013, ISSN: 2248-9622.
continuation of the investigation through new pulsejet architecture 17. Winter Berger E., “Application of Steady and Unsteady Detona-
with much longer life-cycle and much higher thermodynamic tion Waves To Propulsion”, California Institute for Technology,
performances. 2004.
18. Torda, P., et al., “Compressible Flow Through Reed Valves for
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Contact Information
potential”, Naval Postgraduate School, Monterey, CA, USA,
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m.trancossi@shu.ac.uk
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 Downloaded from SAE International by Michele Trancossi, Monday, November 07, 2016

xc - Penetration [m]
Q - Heat [J]
R - Universal gas constant [8.31446 JK-1 mol-1]
T - Temperature [K]
U - Overal heat transfer coefficient (including radiation) [W/(m2·K)]
V - Volume [m3]
W - Work [J]

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