A feasibility study of a novel Pulse Detonation Engine (PDE) using solid fuel (high explosives) as opposed to traditional liquid fuel/air mixtures. This study shows that the solid fuel could have a great advantage over liquid fuels in power specific mass consumption of propellants.

1. 4/24/2012
Benjamin Tincher | AE 640
ERAU SOLID FUEL HYBRID PULSE DETONATION ENGINE

2. Introduction
Aerospace and aviation is an enormous industry that is highly sensitive to variations in fuel costs
or performance efficiencies. With ever increasing fuel costs, even the smallest gain in aircraft efficiency
can have hefty returns. Engine performance has been and always will be at the forefront of research
and design. The revolutionary invention of the air breathing turbine engine has improved aeronautical
efforts tremendously by providing practical propulsion from general aviation to high performance
military air systems. Turbine research is ongoing to make quieter, more efficient, and more powerful
engines. However, the margin by which improvements are realized, although still highly valuable, is
much lower than before. Further, the turbine engine is currently not cost efficient to operate at flight
Mach numbers exceeding 2-3 and is, therefore, limited to lower velocities. Ramjets and ducted rockets
show promising research for high Mach numbers up to 4 and even past that for scramjets. But, these
systems cannot operate a low Mach numbers and require an extra system, such as rocket boosters, to
accelerate them up to operational velocities. This increases the weight, cost, and complexity of the
system. Instead of boosters, combined cycle engines such as turborockets or turboramjets have been
designed but have the same disadvantages [1]. Perhaps it is time for a new, more efficient, wide Mach
range, simpler revolutionary engine to emerge?
Many aerospace engineers and professionals believe that pulse detonation engines (PDEs) could
possibly fit that bill. In pulse detonation propulsion, heat addition producing high pressures are
achieved through repeated detonations, or supersonic explosions, to create thrust. Figure 1 shows a
conceptual illustration of a PDE [2].
Figure 1: PDE cycle concept

3. The advantages of PDEs include simplicity, scalability, greater fuel efficiency, and operational at
supersonic as well as subsonic Mach numbers [1]. Pulse Detonation propulsion can be design in a stand-
alone design where detonation tubes provide all the thrust or in a hybrid designs. Several hybrid
designs have been proposed such as replacing the high pressure compressor, combustor, and high
pressure turbine in a turbine engine with a PDE. Or, another design uses pulse detonation tubes in the
bypass regions of turbofans to create additional thrust much like an afterburner. Research in
detonation was of large interest near the beginning of the twentieth century, but the first designs for
detonation propulsion systems were not seen until the 1950s/60s [3]. Even still, it was not until 2008
that the first manned, PDE powered flight was accomplished by a dual effort between the Air Force
Research Laboratory and Innovative Scientific Solutions in an aircraft named Borealis. This aircraft used
a stand-alone PDE to power flight and marks the beginning of practical implantation of PDEs.
Discussion
Whereas turbine engines operate at a nearly constant-pressure (Brayton) cycle, PDEs operate in
a nearly constant-volume cycle modeled by the Humphrey cycle. These two thermodynamic cycles are
compared below in Figure 2 [4].
Figure 2: Thermodynamic cycle comparisons between Humphrey and Brayton cycles
It can be seen from Figure 2(a) that the Humphrey cycle includes a constant-volume portion (location 2-
3) where the addition of heat occurs due to detonation and, similarly, a constant-pressure portion
(location 2-5) with heat addition from combustion in the Brayton cycle. As it is commonly known, the
area under a P-V curve represents the work available from that process. Therefore, it can be seen
visually that the higher pressures achievable in the Humphrey cycle account for a comparable amount, if
not greater, work than the Brayton cycle. Figure 2(b) relates the fluid temperature to its entropy. It is
well known that the area enclosed by the curves of the T-s diagram represents the available work, W,
and the area under the recovery curve (Locations 4-1 in Humphrey and 6-1 in Brayton) represents the
thermal energy (or heat), QH, expended. With these values, the thermal efficiency is then calculated by
Equation 1 below.

4. Equation 1
Visual inspection of Figure 2(b) shows how the Humphrey cycle is more efficient than the Brayton cycle
for comparable values of work. Thermal efficiency then directly relates to fuel consumption. The more
efficient thermal cycle of the PDE, operating at a similar performance level to a typical turbine engine,
will burn less fuel. Further, since a PDE relies on detonation waves to create high pressures, unlike
ramjets that rely on high dynamic pressures at the inlet during supersonic flight to create compression,
they are operable at low speeds and even standstill.
To describe the thermodynamic occurrences during detonation, Chapman-Jouguet theory
considers two states of flow surrounding the shock, one in front of the shock wave and one behind [5].
Gas properties are governed by equations for the conservation of mass, momentum, and energy as seen
in Equations 2, 3, and 4 respectively.
Equation 2
Equation 3
⁄ ⁄ Equation 4
Where m is mass flux, q is the heat of reaction, p is pressure, u is gas velocity, cp is the heat capacity, and
T is temperature. The heat of reaction addition to the energy equation is given as the change in
standard state enthalpy, h0
, as follows:
Equation 5
These relationships must remain true throughout combustion, and, therefore, combining specific
equations yields characteristic relationships for properties within a particular gas mixture. Combining
Equations 1 and 2 yields what is commonly known as the Rayleigh equation given below.
⁄ ⁄ Equation 6
Since m is a constant, this relationship represents a linear relationship between pressure and specific
volume, ν (1/ρ = ν), known as Rayleigh Lines. Further, combining Equations 2-5 yields a similar looking
equation named the Rankine-Hugoniot equation as follows:
( ⁄ ⁄ )
Equation 7

5. For a specific enthalpy change, h2-h1, this relationship between pressure and specific volume is known as
the Hugoniot curve. These two relationships are often plotted together to characterize a combustion
reaction. Figure 3 shows an example of this plot [6].
Figure 3: Example Hugoniot curve with Rayleigh lines
The location where the Rayleigh lines become tangent to the Hugoniot curve originating at the point of
p1 and ρ1 designated (1,1) represents the CJ detonation point and sets the limits for deflagration and
detonation. Detonation occurs at pressures exceeding the CJ detonation point and is the area of
interest. For estimation purposes, the CJ detonation point is often used for detonation characteristics
[7].
Design Proposal
Figure 4: Proposed Engine Design
Solid Fuel
Detonation tubes Turbine
Drive Shaft
p
1/ρ

6. A novel PDE, shown in Figure 4, is proposed such that solid fuel in the form of high explosive RDX
(the explosive used to create the common military explosive c-4) is used to create detonation inside
multiple detonation tubes. The high pressure and temperature shock wave produced then moves the
gaseous products into a turbine thus creating power to drive a fan or propeller. Having both detonation
tubes and a turbine, this is a hybrid design. But, unlike other hybrid PDE designs, the engine proposed
will be non-airbreathing save purge air and will require no mechanical compressor. RDX offers higher
detonation energy than those of liquid fuel/air mixtures and do not require fuel mixing.
Detonation Initiation and Sustainability
Whereas liquid fuels can possess difficulties creating detonation with sensitive fuel/air mixtures
and flow properties, RDX and other solid fuels would need only a blasting cap or electric spark to initiate
detonation. Two solutions are proposed for maintaining repeated detonations. First, the reflection
wave created when the shock wave exits the detonation tube travels back up the tube and provides
enough pressure to detonate the next charge of fuel. Or, secondly, as the pressure wave travels the
length of the tube, the sudden pressure spike triggers an electric pulse through a piezoelectric device
sending its electrical energy into the next charge for detonation.
Fuel Storage and Delivery
For practical purposes, fuel must be stable in storage. RDX is often combined with a
polymeric/binder composition to form a stable, putty like substance. This material is resistant to large
changes in temperature, even under open flame, and reasonable impact or static loading. Small
portions can be easily separated from by mechanical means to create individual detonation charges.
The delivery system will be mechanical operating in timed sequence with detonation cycles.
Multi-Tube Design
Implementing multiple detonation tubes instead of a larger single tube has three immediate
design advantages. First, the frequency of detonations can be reduced for a single tube thereby
allowing better control of the system. Secondly, due to the high energy of detonation, firing tubes
oppositely located simultaneously will help maintain body forces which translates to engine and aircraft
stability. And, thirdly, with tubes set to fire on intervals, a more constant flow can be realized in the
turbine as opposed to a single cycle.
Power Comparison to Typical Turboprop Engine
Detonation in a constant area tube exhibits several key characteristic flow properties as it
travels down the tube. Figure 5 conceptualizes the phenomena occurring within a general detonation
tube utilizing liquid fuel/air mixture [7].

7. Figure 5: Detonation wave in a constant area tube
If the shock wave is held in place and the reactants move through the shock wave, the flow will
experience the properties of temperature, pressure, velocity, and density as shown. Unlike a liquid
fuel/air mixture detonation, solid fuel detonation includes mass addition to the gaseous flow in the form
of RDX detonation products. This causes difficulty in calculating flow properties of the gaseous
products. The necessary assumptions and theory to characterize the flow within solid fuel detonations
is beyond the scope of this work; therefore a comparison of fuel consumption and power output will be
used to qualify the efficiency of the proposed engine.
A modern turboprop engine, such as the one found in the example given by Farokhi on page 210
[9], has a total turbine power output around 4.5 MW. Using this value as a baseline for design of the
PDE system, the necessary masses of fuel can be obtained to generate the same amount of power.
Across a turbine the power is calculated from the equation
Equation 10
where P is power, m is mass flow rate, and h is total enthalpy. Station 4 represents the region just
following the detonation tubes before flowing into the turbine, and station 5 is located just following the
exit of the turbine. The enthalpy at station 5 is given by
Equation 11
The enthalpy at station 4 is found using an energy balance across the detonation tubes by the relation
Equation 12
where mair is the mass flow rate of the air flowing through the engine, mfuel is the mass flow rate of the
fuel, mtotal is the sum of mfuel and mair, T1 is the initial temperature of the air, and QD is the heat of
detonation value for the fuel. Since the mass flow rate of the air through the tube is much smaller than
that of the fuel in the tube considering the relative density, the first term of Equation 12 can be

8. neglected. The total mass flow rate, then, is simply the mass flow rate of fuel through the detonation
tube. Therefore, Equation 12 reduces to
Equation 13
For RDX, QD has been shown to be around 2100 kJ/mol, which will be underestimated as 2000 kJ/mol for
the purposes of these calculations [10]. Equation 10 now becomes
Equation 14
For a detonation of RDX, the products are assumed to be in equal mole fractions of CO, N2, and H2O [5].
From this mixture, the molecular weight of the mixture is calculated to be 24.64 g/mol. QD can then be
calculated as 85.23 MJ/kg. Not having values of heat capacity for RDX products are temperatures typical
for the exit of a turbine have made difficult finding a reasonable value for h5. But, comparing the
magnitude of QD with that of h5, typically ~107
J/kg, it is a safe assumption to take h5 to be less than 5%
of QD. Therefore the value (QD-h5) is estimated as 0.95*QD. Equation 13 is now
Equation 15
Substituting the desired power output allows the mass flow rate of fuel necessary to be discovered.
Equation 16
Equation 17
Equation 18
Comparing this result to the fuel mass flow rate, 1015 kg/hour, of the typical turboprop engine from the
example, it can be seen that there is a significant decrease in the mass of fuel consumed. This result
shows that, for a certain power output, a solid fuel pulse detonation hybrid engine has the possibility to
achieve considerable lower mass fuel consumption. The power specific fuel consumption, PSFC, is
calculated by Equation 19 and Table 1 summarizes the results of these two engine systems.
Equation 19
Table 1: Fuel Consumption comparison of a typical turboprop and proposed PDE hybrid engine having
the same power output
Engine Fuel Mass Flow Rate
(kg/hour)
PSFC (mg/s/KW)
Turboprop 1015 62.65
PDE Hybrid 200.1 12.35

9. The real determination of savings, then, is the comparable cost of using RDX fuels as opposed to
jet fuel. No credible information about the current cost of RDX could be found, but this would be highly
important to the feasibility of this engine. If RDX is much more expensive than common jet fuel, another
solid explosive might be substitutable.
Funding and Collaboration
Contact has been made for possible funding and research collaboration with multiple
organizations. The largest funding opportunity is from the Turbine Engine Division of the Air Force
Research Laboratory who developed the Borealis aircraft and has increasing research in PDEs. Two
universities stand out in the United States for pulse detonation research. The California Institute of
Technology is home to the Explosion Dynamics Laboratory under the direction of Professor Joseph
Shepherd. The researchers involved with this lab have done much work in the past in PDE research and
have an excellent knowledge to support the proposed research. Not only the personnel, but also, the
laboratory contains necessary systems to properly test detonation systems including shock tubes and
explosion test cells. Attempts have been made to contact Professor Shepherd directly, but no response
has been given to date. Also, the University of Texas at Arlington (UTA) has been completing research in
pulse detonation at its Aerodynamics Research Center. This center also is well equipped for testing, and
the work being completed there included hybrid designs where the PDE flows directly into a turbine just
like the proposed design. The contact attempted at UTA is Professor Donald Wilson who is leading pulse
detonation research at UTA. Lastly, an industry past participant in PDE research, Universal Technology
Corporation (UTC), was contacted about collaboration and funding. Mr. Dick Hill responded with the
following excerpt about solid fuel detonation, “All of our prior work has been on liquid fueled systems,
and we are not aware of any solid fuel efforts. We would assume that if it is desired to use solid
propellants they would be used in a gas generator arrangement and that would involve quite complex
issues of detonation initiation.” Mr. Warren also informed that UTC is no longer active in PDE research
but offered the suggestion to contact the Air Force Research Laboratory. Hopefully, the Air Force will
respond soon to the previous sent inquiry.

10. References
1. G.D. Roy, S.M. Frolov, A.A. Borisov, D.W. Netzer, Pulse detonation propulsion: challenges,
current status, and future perspective, Progress in Energy and Combustion Science, Volume 30,
Issue 6, 2004, Pages 545-672
2. http://propulsiontech.files.wordpress.com/2010/07/pde4stroke-gif.gif, accessed April 2012
3. W. Bollay, PULSE DETONATION JET PROPULSION, US Patent 2942412, 1952
4. Sivarai, Amith, “Parametric and Performance Analysis of a Hybrid Pulse Detonation/Turbofan
Engine,” Master’s Thesis, Department of Mechanical and Aerospace Engineering, The University
of Texas at Arlington, Arlington, TX, 2011.
5. Naminosuke Kubota, “Propellants and Explosives: Thermochemical Aspects of Combustion,”
Wiley-VCH; KGaA, Weinheim, 2007
6. http://upload.wikimedia.org/4ikipedia/commons/3/31/CJ_detonation_and_deflagration_points
.jpg
7. Panicker, Philip K., “The Development and Testing of Pulsed Detonation Engine Ground
Demonstrators,” Doctoral Dissertation, Department of Mechanical and Aerospace Engineering,
The University of Texas at Arlington, Arlington, TX, 2008.
8. Kuznetsov, N. M., Shvedov, K. K., “Equation of state of the detonation products of RDX,”
Combustion, Explosion, and Shock Waves, 1966, pp. 52-58, vol. 2, 4
9. Farokhi, Saeed; “Aircraft Propulsion,” John Wiley and Sons, INC.; 2009
10. NIST Chemistry Webbok,
http://webbook.nist.gov/cgi/cbook.cgi?ID=C121824&Units=SI&Mask=2#Thermo-Condensed