INTRODUCTION
Rocket engines
that work much like an automobile engine are being developed at NASA’s Marshall
Space Flight Center in Huntsville ,
Ala.
The engine operates on pulses, so controllers
could dial in the frequency of the detonation in the "digital" engine
to determine thrust. Pulse detonation rocket engines operate by injecting
propellants into long cylinders that are open on one end and closed on the
other. When gas fills a cylinder, an igniter—such as a spark plug—is activated.
Fuel begins to burn and rapidly transitions to a detonation, or powered shock.
The shock wave travels through the cylinder at 10 times the speed of sound, so
combustion is completed before the gas has time to expand. The explosive
pressure of the detonation pushes the exhaust out the open end of the cylinder,
providing thrust to the vehicle.
A major advantage is that pulse detonation
rocket engines boost the fuel and oxidizer to extremely high pressure without a
turbo pump—an expensive part of conventional rocket engines. In a typical
rocket engine, complex turbo pumps must push fuel and oxidizer into the engine
chamber at an extremely high pressure of about 2,000 pounds per square inch or
the fuel is blown back out.
The pulse mode
of pulse detonation rocket engines allows the fuel to be injected at a low
pressure of about 200 pounds per square inch. Marshall Engineers and industry
partners United Technology Research Corp. of Tullahoma , Tenn. Seattle
NASA and its
industry partners have also proven that a pulse detonation rocket engine can
provide thrust in the vacuum of space. Technology development now focuses on
determining how to ignite the engine in space, proving that sufficient amounts
of fuel can flow through the cylinder to provide superior engine performance,
and developing computer code and standards to reliably design and predict performance
of the new breed of engines.
A developmental,
flight-like engine could be ready for demonstration by 2005 and a full-scale,
operational engine could be finished about four years later. Manufacturing
pulse detonation rocket engines is simple and inexpensive. Engine valves, for
instance, would likely be a sophisticated version of automobile fuel injectors.
Pulse detonation rocket engine technology is one of many propulsion
alternatives being developed by the Marshall
Center
DIFFERENCES COMPARED TO OTHER ENGINE TYPES
The main differences between the PDE
and the Otto engine is that in the PDE the combustion chamber is open and no piston is used to com- press
the mixture prior to ignition (and also that no shaft work is extracted).
Instead the compression is an integral part of
the detonation, and two of the main advantages of the PDE - the efficiency and
simplicity - can be explained by the fact that the combustion occurs in
detonative mode. The efficiency of the cycle can be explained by the high level
of precompression due to the strong shock wave in the detonation.
Also, the simplicity of the device
is a result of the fact that the shock wave - responsible for this compression
– is an integrated part of the detonation. Therefore, pre-compression through
mechanical devices (e.g., a piston) is not necessary. In this sense the PDE is
similar to both the pulse-jet (e.g., the engine used for propulsion of the V-1)
and the ram jet engine. But in those two cases the mechanism behind the
pre-compression is completely different:
• For the pulse-jet the
pre-compression is a result of momentum effects of the gases, and is a part of
the resonance effects of the engine. The resonance effects are influenced
strongly by the external conditions of the engine, and the thrust is
drastically reduced at higher speeds (approaching speed of sound). Furthermore,
both the specific impulse and the specific thrust are significantly lower than for turbo-jet or turbo-fan engines. This
is due to the fact that the levels of preconditioning that can be obtained
through the resonance effects are rather low.
• In the ramjet, pre-compression is obtained through the ram effects as the air is
decelerated from supersonic to subsonic. The major drawback with this concept
is that the engine is ineffective for speeds lower than around Ma=2.
PRE-COMPRESSION AND DETONATION
In the PDE the pre-compression is
instead a result of interactions between the combustion and gas dynamic
effects, i.e. the combustion is driving the shock wave, and the shock wave
(through the increase in temperature across it) is necessary for the fast combustion
to occur. In general, detonations are extremely complex phenomena, involving
forward propagating as well as transversal shock waves, connected more or less
tightly to the combustion complex during the propagation of the entity.
The biggest obstacles involved in
the realization of an air breathing PDE are the initiation of the detonation
and the high frequency by which the detonations have to be repeated. Of these
two obstacles the initiation of the detonation is believed to be of a more
fundamental character, since all physical events involved regarding the
initiation are not thorough- ly understood. The detonation can be initiated in
two ways; as a direct initiation where the detonation is initiated by a very powerful
ignitor more or less immediately or as a Deflagration to Detonation Transition
(DDT) where an ordinary flame (i.e. a deflagration) accelerates to a detonation
in a much longer time span.
Typically, hundreds of joules are
required to obtain a direct initiation of a detonation in a mixture of the most
sensitive hydrocarbons and air, which prevents this method to be used in a PDE
(if oxygen is used instead of air, these levels are drastically reduced). On
the other hand, to ignite an ordinary flame requires reasonable amounts of energy,
but the DDT requires lengths on the order of several meters to be completed,
making also this method impractical to use in a PDE.
It is important to point out that there are
additional difficulties when liquid fuels are used which generally make them substantially
more difficult to detonate. A common method to circumvent these difficulties is
to use a pre-detonator - a small tube or a fraction of the main chamber filled
with a highly detonable mixture (typically the fuel and oxygen instead of air)
- in which the detonation can be easily initiated.
The detonation from the
pre-detonator is then supposed to be transmitted to the main chamber and
initiate the detonation there. The extra component carried on board (e.g.
oxygen) for use in the pre-detonator will lower the specific impulse of the
engine, and it is essential to minimize the amount of this extra component.
PRINCIPLE OF THE ENGINE
As the name implies the engine
operates in pulsating mode, and each pulse can be broken down to a series of events.
The time it takes to complete each of these events puts a limit to the performance
of the engine, and the thrust can be shown to be proportional to the frequency and
volume of the engine. The events in one cycle are shown schematically in Fig 2,
where p0 is the ambient pressure, p1 represents the pressure of the fuel and
air mixture, p2 is the peak pressure of the detonation and p3 is the plateau pressure
acting on the front plate. As stated above, the thrust of the engine is
proportional to the frequency of the engine, and in order to reach acceptable performance
levels the indicated cycle has to be repeated at least 50 times per second
(depending on the application and the size of the engine).
STATUS
The first experiments on the PDE
were done in the beginning of the 1940s, and since then several experiments and
numerical calculations have been done. No flying applications have been
reported in the open literature, and doubts have been expressed regarding the
claimed success of some of the earlier experiments. However, in recent years
the PDE has received a renewed interest, and especially in the US
One of the most promising efforts is pursued
at the Air Force Research Lab (AFRL) at Wright Patterson's Air Force Base headed by Dr. Fred Schauer In that group
successful operation of a PDE using hydrogen and air at frequencies at least up
to 40 Hz has been demonstrated. In a series of experiments, the proportions between
air and hydrogen have been varied from stoichiometric (i.e., where in an ideal
combustion process all fuel is burned completely) to lean mixtures. Even at
rather lean mixtures the engine is reported to operate in detonative mode and
to deliver the expected performance.
This is an indication that the
engine could operate on liquid hydrocarbon fuels since those fuels (in a
stoichiometric mixture with air) and lean hydrogenair mixtures have similar
properties regarding the initiation of the
detonation. The PDE at FOI described earlier, did not produce clean
detonations propagating over the whole length of the engine. In an effort to
improve the situation several parameters were varied: • The length of the
mixture chamber. • The shape of the “contraction section” connecting the air
supply to the rest of the engine. • The separation between the contraction
section and the beginning of the tube. • The position where hydrogen is
introduced. • The position of the spark plug. • In four of the geometries a reed valve was also used, in an
attempt to uncouple the engine from the supply systems during the initiation of
the detonation.
In these cases hydrogen was introduced either
upstream or downstream relative to the valve. These changes did not result in a
successful, detonative operation of the engine. However, localized peak
pressures well above those obtained in detonations, and valuable insight
regarding detonations were obtained.
For example, it was concluded that a valve
controlling the inflow of hydrogen and air is a critical component in the
engine. This is also the most significant difference between the engine at FOI
and the successful one at AFRL described above. This issue is addressed in the
ongoing research at FOI, whose goal is to obtain better understanding of the physical
processes involved, and thereby providing efficient design strategies for the
PDE.
COMBUSTION ANALYSIS
While real gas effects are important
considerations to the prediction of real PDE performance, it is instructive to
examine thermodynamic cycle performance using perfect gas assumptions. Such an
examination provides three benefits. First, the simplified relations provide an
opportunity to understand the fundamental processes inherent in the production
of thrust bythe PDE. Second, such an analysis provides the basis for evaluating
the potential of the PDE relative to other cycles, most notably the Brayton
cycle. Finally, a perfect gas analysis provides the 0framework for developing a
thermodynamic cycle analysis for the prediction of realistic PDE performance.
The present work undertakes such a perfect gas
analysis using a standard closed thermodynamic cycle. In the first sections, a
thermodynamic cycle description is presented which allows prediction of PDE
thrust performance. This cycle description is then modified to include the
effects of inlet, combustor and nozzle efficiencies. The efinition of these
efficiencies is based on standard component performance.
Any thermodynamic cycle analysis of the PDE
must begin by examining the influence of detonative combustion relative to
conventional deflagrative combustion. The classical approach to the detonative
combustion analysis is to assume Chapman-Jouget detonation conditions after
combustion.
The Chapman-Jouget condition is
merely the Rayleigh line analysis limited to sonic velocity as the outlet
condition, Shapiro4. Detonation is the supersonic solution of the
Chapman-Jouget limited Raleigh
A comparison of the ideal gas
Rayleigh process loss was made for deflagration and Chapman-Jouget detonation
combustion, Figure 2. The comparison was made for a range of heat additions,
represented here by the ratio of the increase in total temperature to the
initial static temperature. Four different entrance Mach numbers were also
considered. The figure of merit for the comparison is the ratio of the increase
in entropy to specific heat at constant pressure. The results show that at the
same heat addition and entrance Mach number, detonation is consistently a more
efficient combustion process, as evidenced by the lower increase in entropy.
This combustion process efficiency is one of the basic thermodynamic advantages
of the PDE.
LOSSES
INLET LOSSES
To understand the relative
importance of each component efficiency to the ideal cycle analysis, component
efficiencies were added one at a time. The first component efficiency added was
inlet total pressure recovery. For the inlet component efficiency model, MIL
STD 5007D total pressure recoveries were used. To use total pressure recovery
as an efficiency index, ideal gas relationships were used to transform the total
pressure recovery into its associated process temperatures. These process
temperatures were then used to compute a compression efficiency for use in the
cycle analysis. The resultant fuel consumption comparison is shown in Figure 7.
As both the ramjet and the PDE are experiencing the same component efficiency
through the same compression process, no change occurred to the relationship
between the cycles. The PDE still exhibits reduced fuel consumption at all Mach numbers.
COMBUSTOR LOSSES
The next step in the cycle
comparison is to introduce degraded combustor component
efficiencies. In this step, a
nominal 90% heat release efficiency was used. The results, Figure 8, are
similar to the inlet degraded results in that the PDE still exhibits reduced
fuel consumption. As before, both the ramjet and PDE are experiencing similar
component losses, so no significant relative change in performance occurs.
NOZZLE LOSSES
For nozzle loss modeling, the
generally accepted nozzle gross thrust coefficient, CV, is used. Gross
thrust is obtained from the equation:
Where VY is the ideal
velocity of the flow expanded to ambient pressure with no losses. To use nozzle
gross thrust coefficient, the energy based thrust equation ( 5 ) must be
combined with the basic thrust equation ( 4 ). Substituting the definition of
the gross thrust coefficient ( 6 ) results in an expression of the actual exit
velocity including losses:
In this formulation, the
thermodynamic efficiency must not include any nozzle thermodynamic losses as
they are included in the CV. Using the above formulation for thrust, the
fuel consumption for a “real” engine was computed, as shown in Figure 9, using
a CV of 95%. Once again, the PDE sustains its performance advantage at
all Mach numbers. This result differs from the previous work of Heiser and
Pratt3.
To understand the apparent
discrepancy with previous results, an examination of the momentum and energy
forms of the nozzle efficiency (CV and ηe respectively) is
necessary. The two nozzle efficiencies are directly related, equation ( 10 ).
The state indicated by subscript Y, represents the isentropic expansion
from state 4 to ambient pressure. Expansion losses result in the actual nozzle
exit velocity, V10, being lower than that possible with isentropic
expansion, VY. The lower exit velocity equates to lower kinetic energy
and higher temperature in the exhaust stream. The 95% value of CV used
for this study equates to an ηe of 90%.
The momentum form of the nozzle
efficiency, CV, operates only on the ideal thrust.
The ideal thrust, in turn, is solely
dependent on the post-combustion fluid entropy, state 4, and ambient pressure,
which together define the ideal, isentropic expansion to state Y, Figure
10.
Therefore, the momentum form, CV,
is only dependent on the post-combustion entropy state of the fluid, and
independent of the postcombustion fluid energy level, state 4. On the other
hand, the energy form of the nozzle efficiency, ηe , operates directly
on the energy of state 4, as can be seen by comparing Figure 4 with Figure 10.
Expanding from state 4 incurs a significant loss. However, as previously
explained, state 4 includes the kinetic energy of the detonation wave which is
paid back when the gases expand back to static conditions. Therefore, a state
reflective of the actual available energy is required. The state reflective of
the actual energy available to the system can be determined by considering the
instant the detonation arrives at the end of the chamber. At this instant, the
entropy of the system is known to be the same as the CJ entropy because the
gases expand to rest isentropically.
The known CJ entropy, combined with
the known system enthalpy (h0 + qadd), defines state 4’. In this way, energy conservation is assured.
This analysis assumes a thin detonation wave.
When the energy form of nozzle
efficiency is applied to the cycle, the difference between state 4 and 4’
becomes important, Figure 10. Counter intuitively, use of the higher energy
state, 4, results in lower performance. This occurs because the expansion from
the higher energy state leads to higher entropy generation and lower
performance. Use of energy state 4’, rather than state 4, is a more
representative cycle point for accurate PDE analysis, as it more appropriately
represents the available energy:
CRUISE POWER COMPARISONS
To complete this study of PDE
performance, reduced power levels meant to represent cruise conditions were
evaluated. The cruise fuel-to-air ratios of Figure 3 were used. The resulting
fuel consumption is presented in Figure 12. The energy conserved PDE maintained
its fuel consumption improvement over the ramjet, although its margins of
improvement have diminished. These diminished margins are a direct result of
the diminished heat addition. Since the heat addition, i.e. combustion, phase
of the cycle provides the PDE its efficiency advantage, its advantage reduces
as the heat addition reduces.
This effect is illustrated in more
detail in Figure 13, where the fuel consumption at Mach 3 is examined over a
range of heat additions. At the higher heat additions, represented here by the
higher levels of specific thrust, the PDE enjoys its highest fuel consumption
benefit. As heat addition and specific thrust are reduced, the PDE advantage is
reduced until at the low power settings the ramjet enjoys the better fuel
efficiency. It should be noted, however, that these power settings are not
representative of sustained flight, as vehicle drag will far exceed engine
thrust.
DYNAMIC
CONSIDERATIONS
In order to make a first order
comparison between the PDE and ramjet cycles, the present analysis conserved
global enthalpy and tracked the entropy generated by the detonation and by
process inefficiencies. However, in order to gain further insight into the
detailed operation of the PDE cycle and to apply more suitable component
efficiencies, the different phases of PDE operation must be carefully
described.
Such a thermodynamic description will
carefully apply conservation of energy and conservation of enthalpy
respectively to the imbedded constant mass and steady flow processes which
occur during the PDE cycle. For example, the preceding discussions have used
global enthalpy considerations to examine the most appropriate state against
which to levy nozzle losses.
A similar result can be reached through
consideration of the wave dynamics in the chamber: After being processed by the
detonation wave, each fluid element is brought to rest relative to the closed
end of the detonation tube by an isentropic expansion. The coupled expansion is
an inherent part of the detonation which burns the mixture in the chamber in a
constant mass process. In contrast, the subsequent blow-down of the detonated
gas from the chamber is a quasisteady flow process. It is the blow-down process
which generates thrust and is directly related to the classical nozzle flow.
Thus, again, it is appropriate to
keep the detonation-coupled expansion process (4 - 4’) separate from the flow
expansion through the nozzle (4’ - 10’) and to assess nozzle losses against
this last expansion. The simplified
analysis given in the previous sections made use of constant nozzle thrust
coefficients. Real systems, however, have fixed nozzles, and their performance
is a function of nozzle pressure ratio. Nozzle pressure ratio can vary an order
of magnitude during the dynamic chamber blow-down process. Detailed
integrations of the blowdown process show that energy is conserved.
To correctly enter the dynamic
blowdown calculation, the system energy, rather than enthalpy, must be evaluated.
A state 4” is defined to be the conserved energy and post-CJ entropy, Figure
10. In the dynamic calculation the energy exiting the PDE can be shown to
conserve global enthalpy exactly as state 4’. However, since impulse is a
function of velocity and kinetic energy is a function of velocity squared, the
dynamically calculated impulse is slightly lower than the effective steady
state computation.
CONCLUSION
A first principals comparison was made between the performance of
the ramjet and PDE cycles. The PDE was found to out perform the ramjet through
Mach 5 for the ideal cycle and for representative component efficiencies.
Component efficiencies were applied as inlet recovery, combustion heat release efficiency,
and nozzle velocity coefficient. It was shown that conserving global energy
provided a more representative basis for the assessment of nozzle loss.
Application of the energy form of nozzle performance coefficient to the local
CJ state resulted in over prediction of entropy generation during the nozzle
expansion process. Finally, the effect of throttle setting was examined. It was
shown that at high flight speeds and very low throttle settings, the
thermodynamic advantage of the PDE is lost.
Shadowgraph visualizations of a pulse detonation engine exhaust
flowfield were performed using a new 10
nanosecond duration light source. The complete blowdown cycle was reconstructed
by synchronizing the shadowgraph system with the detonation event. Images of
the highest quality were obtained with this new visualization system due to the
short pulse of light produced by the source. No smear or distortion of the
detonation front and shock waves was observed. The experimental visualizations
were then compared to preliminary computational modeling results obtained from
a newly developed code at the University
of Cincinnati
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