4/24/2012

Benjamin Tincher | AE 640

ERAU SOLID FUEL HYBRID PULSE DETONATION ENGINE

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

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.

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

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

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].

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

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

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.

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