NASA/TM—2006-214224 AIAA–2006–1021

Performance Assessment of a Large Scale Pulsejet-

Driven Ejector System
Daniel E. Paxson
Glenn Research Center, Cleveland, Ohio

Paul J. Litke and Frederick R. Schauer

Air Force Research Laboratory
Wright-Patterson Air Force Base
Dayton, Ohio

Royce P. Bradley and John L. Hoke

Innovative Scientific Solutions, Inc.
Dayton, Ohio

May 2006
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NASA/TM—2006-214224 AIAA–2006–1021

Performance Assessment of a Large Scale Pulsejet-

Driven Ejector System
Daniel E. Paxson
Glenn Research Center, Cleveland, Ohio

Paul J. Litke and Frederick R. Schauer

Air Force Research Laboratory
Wright-Patterson Air Force Base
Dayton, Ohio

Royce P. Bradley and John L. Hoke

Innovative Scientific Solutions, Inc.
Dayton, Ohio

Prepared for the

44th Aerospace Sciences Meeting and Exhibit
sponsored by the American Institute of Aeronautics and Astronautics
Reno, Nevada, January 9–12, 2006

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135

May 2006
 This report is a formal draft or working
paper, intended to solicit comments and
ideas from a technical peer group.

This report contains preliminary findings,

subject to revision as analysis proceeds.

This work was sponsored by the Fundamental Aeronautics Program

at the NASA Glenn Research Center.

Level of Review: This material has been technically reviewed by technical management.

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Hanover, MD 21076–1320 Springfield, VA 22161

Available electronically at http://gltrs.grc.nasa.gov

 Performance Assessment of a Large Scale Pulsejet-
Driven Ejector System

Daniel E. Paxson
National Aeronautics and Space Administration
Glenn Research Center
Cleveland, Ohio 44135

Paul J. Litke and Frederick R. Schauer

Air Force Research Laboratory
Wright-Patterson Air Force Base
Dayton, Ohio 45433

Royce P. Bradley and John L. Hoke

Innovative Scientific Solutions, Inc.
Dayton, Ohio 45440

Abstract
Unsteady thrust augmentation was measured on a large scale driver/ejector system. A 72 in. long, 6.5 in.
diameter, 100 lbf pulsejet was tested with a series of straight, cylindrical ejectors of varying length, and diameter. A
tapered ejector configuration of varying length was also tested. The objectives of the testing were to determine the
dimensions of the ejectors which maximize thrust augmentation, and to compare the dimensions and augmentation
levels so obtained with those of other, similarly maximized, but smaller scale systems on which much of the recent
unsteady ejector thrust augmentation studies have been performed. An augmentation level of 1.71 was achieved with
the cylindrical ejector configuration and 1.81 with the tapered ejector configuration. These levels are consistent
with, but slightly lower than the highest levels achieved with the smaller systems. The ejector diameter yielding
maximum augmentation was 2.46 times the diameter of the pulsejet. This ratio closely matches those of the small
scale experiments. For the straight ejector, the length yielding maximum augmentation was 10 times the diameter of
the pulsejet. This was also nearly the same as the small scale experiments. Testing procedures are described, as are
the parametric variations in ejector geometry. Results are discussed in terms of their implications for general scaling
of pulsed thrust ejector systems.

I. Introduction
In recent years there has been renewed interest in the concept of ejectors or thrust augmentors driven by
unsteady propulsion devices. The reason for this stems primarily from the interest in Pulse Detonation Engine (PDE)
based propulsion systems, which are decidedly unsteady, and which therefore seem natural candidates on which to
use an ejector. It has been suggested in the past (ref. 1), and shown convincingly in numerous recent experiments
(refs. 2 through 9) that under the proper operating conditions, and with a well designed ejector, thrust augmentation
levels approaching or even exceeding 2.0 can be achieved with unsteady thrust sources as drivers. Thrust
augmentation, φ is defined as the total time-averaged thrust provided by the ejector and driver system, Ftotal divided
by the thrust of the driver alone, Fdriver .

Ftotal
φ= (1)
Fdriver

It has further been shown that these high levels can be reached using remarkably small ejectors in comparison to
their steady state counterparts. Several studies have been conducted using actual PDE’s as drivers (refs. 5, 7, and 9);
however a number have used alternative unsteady thrust sources including simple pulsed valves (refs. 2 and 8),
Hartmann-Sprenger resonance tubes (ref. 4), synthetic jets (ref. 6), and pulsejets (ref. 3). The results from each of

NASA/TM—2006-214224 1
these varied experiments have helped identify the factors which contribute to the superiority of unsteady ejector
systems in general (and therefore how they can be optimized), and which factors are unique to the particular driver.
For example, it is now generally agreed that the frequency, unsteadiness level (the standard deviation of the exhaust
velocity for example), and exhaust gas temperature of the thrust source play a significant role in the maximum thrust
augmentation that can be achieved (ref. 6). These and other parameters (ref. 10) characterize the emitted vortex
associated with each pulse of any unsteady thrust device. This vortex plays a critical role in determining thrust
augmentation, though the physical mechanism is not understood. It has been shown through experimental
measurements for example that vortex diameter is closely matched to the diameter of the ejector yielding maximum
thrust augmentation (refs. 5, 6, 10, and 11). On the other hand, it is believed that the strong emitted shock, uniquely
associated with the PDE pulse, has a large, though currently not well understood, influence on the maximum
attainable thrust augmentation.
Despite the many unsteady ejector experiments performed to date, and the growing body of understanding
associated with them, generalization of some results is not yet possible because the experiments have shared a
common scale, which is to say, small. The thrust levels have been low (less than 15 lbf), and the driver diameters
have been between 1 and 2 in. Rules have been suggested relating the optimal diameter of the ejector as a fixed ratio
relative to that of the driver; however, they are not definitive because all the drivers tested are nearly the same size.
The experiment described in this paper was developed to at least partially address this issue.
A large pulsejet, approximately an order of magnitude larger in exhaust cross-sectional area and thrust than
most recent tests, was operated with a series of ejectors of varying diameter, length, and shape (cylindrical and
tapered). The geometric ejector parameters, along with the spacing between the pulsejet tailpipe and ejector inlet
were systematically varied in order to determine the configuration yielding the highest thrust augmentation, as
measured by the thrust stand to which the system was mounted. The results were then compared to previous
experiments both in terms of augmentation achieved, and in terms of optimized ejector dimensions. This paper will
describe the experiment including the major components (pulsejet, ejector sets, and thrust stand), construction,
testing procedures, and parametric variations of ejector dimensions. Results will then be presented, and a discussion
of findings will follow.

II. Experimental Setup

The experimental setup is shown in figure 1 with the major components labeled. These are the ejector (1 of 4
tested), the pulsejet, and the thrust stand. Each will be described.

Starting Air
Ejector
Pulsejet

Fuel

Thrust Stand

Figure 1.—Experimental setup.

NASA/TM—2006-214224 2
 d=6.5 in

Figure 2.—Pulsejet schematic.

120

100

80
Thrust, lbf

60
Previous Measurements
40 Present Baseline
Cubic Fit-All Data
20 +2 St. Dev.
-2 St. Dev.
0
2 3 4 5
Fuel Flow Rate, lbm/min.

Figure 3.—Pulsejet thrust as a function of fuel flow.

A. Pulsejet Driver
The pulsejet tested and discussed in this paper is a Solar PJ32, originally developed and manufactured by the
Solar Aircraft Company for the Globe Corporation Aircraft Division in 1951. Details of the device and performance
characteristics are described in reference 13. Relevant dimensions are shown in the schematic of figure 2. In brief, it
is a self-aspirating, valved, unit which operates on liquid fuel (Avgas in this experiment) that is fed directly into the
combustion chamber via a pressurized fuel line. Like most pulsejets it requires forced air directed at the inlet and a
high frequency sparking system in the combustion chamber in order to initiate operation. However, once operation
has commenced, the resonant nature of the device does not require forced air or spark. The fact that that fuel supply
is pressurized (as opposed to a venturi-based arrangement found in small scale units (ref. 3) allows the pulsejet to be
throttled in a reasonably predictable fashion. Figure 3 shows the relationship between measured thrust and fuel flow
rate. Fuel flow rate is measured using an in-line turbine-type flow meter. Data is shown both from previous testing
done to characterize the pulsejet (ref. 13), and from baseline testing done in the present experiment without an
ejector installed. Also shown are a cubic fit to the data, and the bounds representing two standard deviations above
and below the fit. It can be seen that a certain amount of scatter is present, which appears to be typical for pulsejets.
For the present experiment, the pulsejet was operated near the maximum thrust point during all testing. The scatter
in this operating region results in a maximum uncertainty of ±7 percent. For the present baseline data shown, the
root-mean-square error between measured and curve-fit thrust was 3.7 percent. The maximum error was 6 percent.
The thrust stand can only measure total system thrust (pulsejet and ejector combined); however, thrust
augmentation can only be determined if the thrust of the jet alone is known. One way to determine this is to simply
run the pulsejet on the thrust stand without an ejector and use that thrust value as the baseline for all subsequent
ejector tests. However, it is prohibitively time consuming to do this for each of the many ejector configurations
tested. Instead, this measurement was made on average of once every sixteen operational runs of the engine. This
method of determining jet-alone thrust will be referred to as Method I in subsequent sections of the paper where
results are presented. If the rate of fuel flow could be accurately controlled, this method would suffice, save for the
run-to-run uncertainty already described. The fuel flow rate through the system varied over time however, possibly
due to clogging at the injectors. As a result, the same pressure in the fuel system did not always yield precisely the
same flow rate. To account for this, the jet-alone thrust was also determined using the curve-fit presented above and

NASA/TM—2006-214224 3
the measured fuel flow rate from each run. This estimation method, referred to later as Method II, could be made
each run, with or without an ejector present.
The frequency of operation of this pulsejet was 69 Hz, with a standard deviation of 2 Hz for all of the testing
performed. The operational frequency is weakly, and inversely related to the fuel flow rate. The observed frequency
of the present tests was, like the thrust values, consistent with that observed in previous tests. It is interesting to note
in passing that the product of operational frequency and length on this pulsejet is 15 percent higher than that for the
small scale unit used in reference 3. Pulsejets are often thought of as gasdynamic devices with a frequency that is
determined by the end-to-end transit time of a fixed set of dominant waves. All other things being equal, this
conception implies that the product of frequency and length should be a constant. The observed difference therefore
either indicates that the average temperature of the combustion products is 30 percent higher in the large unit (which
would probably melt the steel), or that there are other elements contributing to the resonance than simply wave
reflections (e.g., Helmholtz-like behavior, heat release rate, etc.).

B. Ejectors
Four ejectors were constructed from mild-steel sheet ranging in gage from 18 to 20. Scaled drawings of each are
shown in figure 4, which also shows symbolic nomenclature for the relevant dimensions. Those dimensions are
listed in table 1. The commercially available bellmouth inlets were seamless, and terminated with a 1.0 in. long
straight section. The main body of each cylindrical ejector was composed of a single rolled piece with a welded
seam along the length. It was joined to the bellmouth with a circumferential weld. The main body of the tapered
ejector was composed of two symmetric halves. The conical shape was achieved through a process called
“bumping” whereby a small bend is applied approximately every inch along the circumference. This actually creates
a many-sided polygon rather than a pure circular cross-section. The two halves were welded together along the
entire length. The finished body was then attached to the inlet with a circumferential weld.

L
R
D

Figure 4.—Ejector schematics and symbols for relevant dimensions.

NASA/TM—2006-214224 4
 TABLE 1.—EJECTOR DIMENSIONS (AS-BUILT)
R L D
(in.) (in.) (in.)
Straight, cylindrical
3 64 13
4 65 16
4 65 20
Tapered, conical
4 69 16

The dimensions of the ejectors were chosen by a geometrical scaling of the small scale ejectors tested in the
pulsejet-based experiments of reference 3. The length and diameter of the reference 3 ejector yielding the highest
thrust augmentation was normalized by the diameter of the pulsejet driver (1.25 in.). Those ratios were then
multiplied by the pulsejet diameter in the present work (6.5 in.) to obtain the length and diameter of the central
ejector. The other two diameters were then selected as 20 percent smaller and 25 percent larger than the central
value with the supposition that this span would be sufficient to bound the value of the optimal diameter. The inlet
radius, R was not variable because the bellmouth inlets were commercially available stock-items, and the radius was
pre-determined based on the selected diameter, D. However, it has been shown that while inlet rounding is necessary
(a sharp-edged inlet will produced almost no augmentation), rounding beyond values of R/D = 0.15 shows little
benefit. The ejectors used in this experiment had R/D≥0.20.

C. Thrust Stand
Details of the thrust stand have been presented elsewhere in the literature (ref. 9 and 14). As such only a brief
description will be given here. It consists of a cart with linear bearings which ride along a pair of fixed, low-friction
rails. The test article (pulsejet or pulsejet and ejector combination) is rigidly attached to the cart. The cart pushes
against a damped, calibrated spring, one end of which is fixed. Thrust is ultimately determined by measuring the cart
displacement with a positional sensor which is low-pass filtered with a cut-off frequency of 0.5 Hz. A time trace of
measured thrust during a typical test run is shown in figure 5. The damping and filtering system is evidently quite
effective, as there are no oscillations in the measured thrust. It is noted that there is a small positive thrust measured
prior to engine ignition. This is the result of a preload applied to the spring at the zero point of the positional sensor.

D. Test Procedure
Each test run was approximately 30 sec in duration and consisted of the following sequence. Fuel pressure was
set. Starting air was then turned on as was the spark. Shortly thereafter the fuel flow valve was opened, and engine
operation commenced. The starting air and spark were then shut off. After approximately 15 sec, the thrust reading
would level off and for the next 15 sec thrust was measured at approximately 1.0 sec intervals. After the thrust
measurement was acquired the fuel valve was closed, and the starting air was re-activated in order to provide
cooling. The thrust data to be presented represents a simple time-average over the 15 sec sampling period. This basic
sequence is illustrated in figure 5 which shows actual test data from a typical run.
For each ejector tested, the baseline thrust of the pulsejet was first measured without the ejector present. A
straight-sided ejector was then mounted on the thrust stand, with its axis of symmetry aligned with that of the
pulsejet. Thrust measurements were made with the ejector inlet placed at various axial positions relative to the
exhaust plane, as shown in figure 6. For each ejector, an optimal spacing value was found which yielded the highest
thrust augmentation. This procedure was followed for each of the three straight ejector diameters.
The diameter yielding the highest thrust augmentation was then selected for length variation testing. It was first
lengthened by welding a 19.5 in. extension to the cylindrical section, at the exhaust end. This modified ejector was
then tested according to the procedure just described. The length of the ejector was then reduced by simply cutting
off a portion of the exhaust end. The length reduction was done in increments of one pulsejet diameter (6.5 in.).
Due to resource limitations, it was possible to test only one tapered ejector. The minimum diameter of this
ejector was chosen to be the same as that of the cylindrical ejector yielding the highest thrust augmentation. A
tapered ejector made the same way was tested on several small scale rigs and found to yield very high thrust
augmentation levels (refs. 1, 5, and 15). The spacing and length of this ejector were varied in the manner described
above; however, no extension was made to the initial 70 in. length.

NASA/TM—2006-214224 5
 Thrust Fuel Flow Rate Starting Air Flow Rate X 0.05

180 4.5
160 4.0
140 3.5

Flow Rate, lbm/min.

Spark
120 Acquisition Time 3.0

Thrust, lbf
100 2.5
80 2.0
60 1.5
40 1.0
20 0.5
0 0.0
0 10 20 30 40 50
Time, sec.
Figure 5.—Measured thrust as a function of time for a
typical pulsejet and ejector combination. Fuel and starting
air flow rates are also shown.

Figure 6.—Schematic of ejector spacing variation. The schematic is to scale.

III. Results and Discussion

A. Straight, Cylindrical Ejectors

1. Driver-to-ejector spacing variations.—Although spacing variation testing was performed on every ejector
configuration, the results tended to be similar in trend. As such, results from only one configuration will be shown.
Figure 7 displays the thrust augmentation as a function of driver-to-ejector spacing for the 16 in. diameter ejector, of
65 in. length. The spacing has been normalized by the driver diameter, d. Results are presented using both Methods I
(baseline measured pulsejet thrust) and II (pulsejet thrust estimated from the fuel flow rate curve-fit of figure 3) to
compute thrust augmentation. Also shown are the results from the small scale pulsejet experiment of reference 3.
Negative values of ejector spacing indicate that the exhaust plane of the pulsejet was actually inside the ejector. In
the reference 3 experiment, such measurements were not possible as the pulsejet would cease to operate at low
spacing values. The same phenomenon occurred in the present experiment, but at much smaller, even negative
values. It is interesting to note that the augmentation reaches a peak as the ejector and driver are brought closer
together. It then decreases to a minimum, and begins to rise again as the driver is brought into the ejector interior. It
is not known whether a second peak exists because, as mentioned, the pulsejet stopped operating. Such ‘twin peak’
behavior was observed in the PDE driven experiment of reference 5. The spacing yielding peak performance is
approximately 2.0 pulsejet diameters. This value is similar to, but slightly larger than, the value found in the small
scale experiment. Comparison with other experimental results (refs. 4 and 5) indicates that the value varies between
1 and 2.5 driver diameters. It therefore appears to be a somewhat experiment specific parameter, perhaps depending
on both the physical geometry of the driver and the characteristic of the unsteady pulse.
Optimal ejector spacing was found to be invariant with changing ejector length. However, it should be kept in
mind that only one diameter ejector was varied in this manner.

NASA/TM—2006-214224 6
 2.0
Present Experiment-

Thrust Augmentation
Method I, L/d=10.0,
1.8 R/d=0.62, D/d=2.46
Present Experiment-
Method II, L/d=10.0,
1.6 R/d=0.62, D/d=2.46
Small Scale Experiment,
1.4 L/d=10.1, R/d=0.60,
D/d=2.4
1.2

1.0
-2.0 -1.0 0.0 1.0 2.0 3.0
Ejector Spacing, δ∠/d
Figure 7.—Thrust augmentation as a function of
driver-to-ejector spacing for the D/d = 2.46,
L/d = 10.0 ejector.

For variations in diameter using a fixed length, the optimal spacing followed a nearly perfect linear relationship
described by

⎛δ ⎞ ⎛D⎞
⎜ ⎟ = 0.90⎜ ⎟ − 0.27 (2)
⎝ d ⎠ optimal ⎝d⎠

The general increase in optimal spacing as ejector diameter increases is consistent with the results of references 3
through 5.

2. Ejector diameter variations.—Thrust augmentation levels obtained with optimally spaced, fixed length
ejectors are shown as a function of ejector diameter in figure 8. The ejector diameter has been normalized by the
driver diameter. Once again, results using both Methods I and II to obtain pulsejet thrust are shown. For comparison,
results from the reference 3 small scale pulsejet experiment also appear. There is a clear optimal ejector diameter,
and for both the large and small scale experimental results it appears to be very nearly 2.5 driver diameters. This
result is remarkably consistent over a range of drivers. Table 2 lists the ejector to driver diameter ratios at which
peak augmentation levels were found in a number of experiments using cylindrical or nearly cylindrical ejectors.
The values all fall between 2.4 and 3.0, indicating that the optimal ejector diameter is a near constant multiple of the
driver diameter, probably having a weaker secondary dependence on other, as yet unknown parameters. This result
supports the notion that the vortex emitted with each pulse of the driver plays a key role in unsteady thrust
augmentation since, as was pointed out in references 5 and 6, its size (bounding diameter) appears to follow the
same ratio when divided by the driver diameter.
It is noted that although the optimal value of D/d is nearly the same for all of these ejectors, the thrust
augmentation obtained is not. Part of the reason for this may be that while all of the unsteady drivers emit a vortex,
the amount of vorticity present, its velocity, the balance between fluid trapped in the vortex and that which follows
behind, and the interaction between vortex bound fluid and trailing jet fluid may be vastly different. These features
may play a key role in the entrainment of and momentum transfer to the secondary fluid in the ejector; although the
mechanism isn’t clear (refs. 6 and 16).
It was suggested in reference 6 (and based on the observations of reference 17) that a characterizing feature of
the emitted pulse, essentially a type of inverted Strouhal Number, may be a correlating parameter to the peak thrust
augmentation achievable with an ejector that has been optimized for length and diameter. In that paper, the
parameter, heretofore referred to as the non-dimensional formation time, was defined as

u′2
τf = (3)
2 fd

NASA/TM—2006-214224 7
 2.0

Thrust Augmentation
1.8

1.6

1.4 Present Experiment-Method I, L/d=9.8-10.0,

R/d=0.62-0.76
1.2 Present Experiment-Method II, L/d=9.8-10.0,
R/d=0.62-0.76
Small Scale Experiment, L/d=10.1, R/d=0.60
1.0
1.0 2.0 3.0 4.0 5.0
Ejector Diameter, D/d
Figure 8.—Thrust augmentation as a function of ejector
diameter for the L/d=10.0 ejectors. The ejectors are
optimally spaced for each point. Data from the
reference 3 small scale experiment is also shown.

TABLE 2.—OPTIMAL D/d VALUES

Reference Driver type φmax Optimal d
D/d (in.)
Present Large pulsejet 1.71 2.4 6.50
2 Chopped pulse 1.45 3.0 3.14
3 Small pulsejet 1.83 2.5 1.25
4 Resonance tube 1.38 2.7* 1.50
5 PDE 2.00 3.0 1.00
6 Synthetic jet 1.67 2.4+ 0.93
7 PDE 2.10 3.0 1.93
*
Using the hydraulic diameter of the driver 275 Hz. driver.
+
Using ‘effective diameter’ measured w/PIV.

where f is the frequency of operation, and u′2 is the root mean square of the periodic velocity fluctuations in the
exit plane of the driver. This velocity can be estimate from measured thrust, mean flow rate and temperature of the
driving jet. It was argued that peak thrust augmentation should rise with formation time up to some critical value,
τ crit
f . Beyond this value, peak thrust augmentation should slowly fall. Figure 9 shows the peak thrust augmentation
obtained as a function of formation time for the present experiment and several others for which sufficient data was
available*. A simple parabolic fit through the data is also shown. The data seems to follow the expected trend,
indicating a value of τ crit
f near 40; however, the data is admittedly sparse and much more is needed. Furthermore, it
was noted in reference 6 that other experimental results don’t fall on this same curve. This implies that other factors
such as the exhaust gas temperature (relative to the entrained secondary flow) may play a significant role in
determining peak thrust augmentation. The experiments represented in figure 9 have vastly different exhaust
temperatures for which no accounting has been made other than the effect on u ′ 2 . Beyond this, the use of
formation time as is done here provides no insight into the physical mechanism of unsteady thrust augmentation. It
only provides a potentially predictive correlating parameter, albeit one that is fairly compelling.

*
For the reference 5 PDE experiment the rms velocity was obtained from a numerical simulation matching flow rate
and thrust. Because the thrust producing period of a typical PDE is only a small fraction of the operating period,
only the thrust producing period was used in the rms velocity calculation. The inverse of this period was used for f in
equation (3).

NASA/TM—2006-214224 8
 2.2

Thrust Augmentation
2.0
1.8
Resonace Tube, Ref. 4
1.6 Synthetic Jet, Ref. 6
Large Pulsejet, present
1.4 Small Pulsejet, Ref. 3
PDE, Ref. 5
1.2
1.0
20 0 30 10
40 50
Formation time,τ f
Figure 9.—Peak thrust augmentation as a function of
formation time for the present, and several other
experiments.

3. Ejector length variation.—As stated earlier, length variation tests were only performed on a single
cylindrical ejector. The 16 in. diameter ejector was chosen (D/d = 2.46) since it had yielded the highest performance
at the as-built 65 in. length. The variation in thrust augmentation as a function of ejector length is shown in
figure 10. The length has been normalized by the driver diameter. Results from the small pulsejet experiment of
reference 3 are also shown. The trends of the two experiments are somewhat different; however, it is noted that the
peak value of thrust augmentation occurs at the same value of L/d = 10 for both. This turned out to be the as-built
length in the present experiment.
This ratio does not hold for the other unsteady experiments; however, it is not clear that it should. There are
several conceptual models for the mechanism by which fluid is entrained and energized in the ejector. One posits a
sort of piston-like behavior of the driver flow which delivers momentum to the secondary flow via direct pressure
exchange as the two flows collide within the ejector. A second notion suggests that the mechanism of entrainment
and momentum exchange is the same as that for a steady ejector, namely shear flow and mixing (most likely driven
by turbulence). Secondary fluid is literally dragged into the ejector and accelerated. In this concept, the emitted
vortex serves the function of vastly increasing the shearing surface area (compared to a steady jet) due both to its
initial structure and to its observed disintegration†.
If the latter mechanism is correct, it might be expected that the emitted vortex would decelerate (even as it
broke apart) at a rate proportional to its surface area and to the square of the difference between its velocity and that
of the secondary flow. That is

dU v ⎛ρ ⎞⎛ S ⎞
Uv ≈ −α ⎜⎜ s ⎟⎜ ⎟( U v − U s ) 2
⎟⎝ V ⎠ (4)
dx ⎝ ρv ⎠

where ρv is the density of the vortex, V is the vortex volume, S is the surface area, Uv is the velocity of the vortex, Us
is the average velocity of the secondary flow (assumed constant), α is a constant, and ρs is the density of the
secondary flow. Assuming that the vortex volume and surface area are proportional to the cube and square of its
diameter respectively, and assuming further that its diameter is proportional to the diameter of the driver, the ratio
(S/V) in equation (4) simply becomes proportional to (1/d), i.e.,

d(U v − U s ) ⎛ρ ⎞
Uv ≈ −κ ⎜⎜ s ⎟( U v − U s ) 2
⎟ (5)
d( x / d ) ⎝ ρv ⎠

With κ a constant, equation (5) can be solved numerically to yield x/d as a function of (Uv-Us), for any given
ρs ρ v and U vinitial U s , which is the initial vortex velocity as it enters the ejector divided by the average secondary

†
Observations of vorticity in the ejector exit region of the references 11 and 12 indicate no coherent vortical flow
structure at radial distances less than the ejector diameter.

NASA/TM—2006-214224 9
 2.0

Thrust Augmentation
1.8

1.6

1.4 Present Experiment-Method I, D/d=2.46, R/d=0.62

Present Experiment-Method II, D/d=2.46, R/d=0.62
1.2 Small Scale Experiment, D/d=2.40, R/d=0.60

1.0
5.0
9.0 11.07.0 13.0 15.0
Ejector Length, L/d
Figure 10.—Thrust augmentation as a function of ejector
length for the D/d = 2.46 ejector. The ejectors are
optimally spaced for each point. Data from the
reference 3 small scale experiment is also shown.
3.0

2.5
Ref. 3 Small Pulsejet
ρ s ρ d = 3.0, U initial
v U s = 1.52
2.0
Ref. 4 Resonance Tube
Uv /U s-1

1.5 ρ s ρ d = 1.0, U initial

v U s = 1.12
Ref. 5 PDE
1.0 ρ s ρ d = 3.0, U initial
v U s = 6.96

0.5

0.0
0 5 10 15
x/d
Figure 11.—Numerical solution to equation (5) for
several relevant parameters of density ratio and
vortex velocity ratio. The value of κ in equation (5) is
0.32.
flow velocity. If the optimal ejector length, Lopt is defined as that value of x for which (Uv/Us-1) is less than some
specified small value such as 0.1, and if estimates of U vinitial U s and ρ s ρ v are available, then equation (5) can be
used to obtain Lopt/d. This is illustrated in figure 11 which shows the numerical solution to equation (5) for different
values of the parameters U vinitial U s and ρ s ρ v .
Estimates for U vinitial and Us were obtained for the references. 3, 4, and 5 experiments using PIV data from
references 11, 16, and 12‡. They are listed in table 3. Values of ρ s ρ v were not available. For the reference 4
resonance tube, this ratio should be near 1.0 since the driver gas was at near ambient temperature. For the references
3 and 5 pulsejet and PDE driven experiments, the ratio was estimated at approximately 3.0. This estimate assumes
that the very hot, low density gas from each driver entrains a certain amount of cooler air as it forms the emitted
vortex.
TABLE 3.—VORTEX AND SECONDARY FLOW VELOCITIES,
AND OPTIMAL L/D VALUES.
Reference Driver type Uv Us ρs Lopt/d
(ft/s) (ft/s) ρ v
3 Small Pulsejet 460 303 3.0 10.1
4 Resonance Tube 275 245 1.0 6.5
5 PDE 800 115 3.0 14.6

‡
For the reference 4 experiment, Us was obtained from hotwire measurements taken in the exit plane of the ejector.

NASA/TM—2006-214224 10
 When these values of U vinitial , Us, and ρ s ρ v were used in the numerical solution of equation (5), together with
an ending criterion (Uv/Us-1) = 0.1, it was found that for a single value of κ = 0.32, the values for Lopt/d calculated
were almost exactly the values found experimentally, and listed in table 3. This result is by no means proof of the
shear mechanism for ejector entrainment and thrust augmentation, particularly given the scarcity of data and the
density estimates used. It is nevertheless suggestive that this mechanism predominates.

Note that equation (5) may be rewritten as an ordinary differential equation in time as

d(U v − U s ) κ ⎛ ρs ⎞
≈− ⎜ ⎟( U v − U s ) 2 (6)
dt d ⎜ρ ⎟
⎝ v ⎠

Integrating this equation using the parameters listed above presumably gives the time required for the emitted
vortex to travel down the ejector, decelerate, degenerate, and accelerate the secondary fluid. The inverse of this time
provides an estimate for the optimal operational frequency from the perspective of shear-driven momentum transfer.
For the references 3, 4, and 5 experiments, these frequencies are listed in table 4, along with the actual operational
frequencies of the devices. All other things being equal, it would be intuitively expected that the closer together the
optimal and operational frequencies, the higher the thrust augmentation. If this is true, it suggests that PDE’s which
for a given length ideally operate at a much higher frequency than that listed in table 3, could obtain even higher
augmentations levels than have been reported to date. It would also suggest that the present experiment, while
generally exhibiting lower overall thrust augmentation values compared to those of the small scale pulsejet
experiment of reference 3, is actually better matched in terms of this optimal frequency criterion. The reason for this
is as follows. The value of Lopt/d found in the present experiment is identical to that of reference 3. It is expected that
the values of ρ s ρ v , U vinitial , Us are therefore quite similar. These can be used to integrate equation (6) but with
the larger diameter of the present experiment. The resulting optimal frequency is found to be 67 Hz, which is very
close, and therefore better matched, to the actual operating frequency of 69 Hz.

TABLE 4.—OPTIMAL EJECTOR AND ACTUAL

DRIVER OPERATIONAL FREQUENCIES
Reference Driver type fopt fdriver
(Hz) (Hz)
3 Small pulsejet 350 220
4 Resonance tube 335 275
5 PDE 135 20

B. Tapered, Conical Ejector

As mentioned earlier, only one diameter of tapered, conical ejector was tested. The length was varied using the
same technique as that for the cylindrical ejector. Similarly, at each length the driver-to-ejector spacing was varied
until the highest augmentation was achieved. As with the straight ejectors, this optimal spacing was very nearly 2
driver diameters for every length. The results of the length variation tests are shown in figure 12, along with those
from the small scale pulsejet experiment of reference 3. Like the small scale experiment, the maximum
augmentation achieved was higher with the tapered ejector than with the best of the straight type. Both experiments
also show much more sensitivity at the shorter lengths than was seen with the straight ejectors. However, the small
scale experiment has a clear length at which peak augmentation is observed, whereas the present experiment exhibits
nearly flat region where the augmentation is high and insensitive to length. The start of this region and the peak
performance point of the small experiment both appear to occur between 8<Lopt/d<8.5. The peak augmentation
obtained in the present experiment was 1.83, while the small scale experiment yielded a value of 1.98. The same
trend was seen with the straight ejectors. As mentioned earlier, part of the reason for this may be due to the
somewhat different vortex parameters associated with the two drivers (despite their both being valved pulsejets).
Some of the difference may also be attributed to the slightly different nature of the ejectors used in the two
experiments; however, these are fairly subtle. Figure 13 shows a profile of the best performing straight and tapered
ejectors used in the reference 3 work. The straight ejector is seen to actually have a short diffusing section at the
exhaust end, and both have a half circle inlet profile as opposed to the quarter round profile of the present work.

NASA/TM—2006-214224 11
 2.0

Thrust Augmentation
1.8

1.6

1.4 Present Experiment-Method I, D/d=2.46, R/d=0.62

Present Experiment-Method II, D/d=2.46, R/d=0.62
1.2 Small Scale Experiment, D/d=2.40, R/d=0.60

1.0
5.0 7.0 9.0 11.0 13.0 15.0
Ejector Length, L/d
Figure 12.—Thrust augmentation as a function of ejector
length for the D/d = 2.46 tapered ejectors. The ejectors
are optimally spaced for each point. Data from the
reference 3 small scale experiment is also shown.

Figure 13.—Straight and tapered ejector profiles used in

the small scale pulsejet experiment of reference 3.

Another possible explanation for the comparatively lower peak augmentation in the large system may lie in the
scale of the turbulence which is involved in the exchange of momentum between the driver and the secondary flow.
There are numerous potential turbulence length scales in a pulsejet. Some are governed by the physical size of the
unit, but others are not. It is possible that the scales from say, combustion, and the exhaust plane shear layer coincide
in the small unit and thus, being encased in the emitted vortex, efficiently transfer the large scale vortex rotational
energy to the secondary flow. In the large unit, this matching of scales may not hold. Of course, there is no proof yet
for this (rather intuitive) explanation other than the observation that the measured turbulence levels in the emitted
vortex of several unsteady thrust experiments are quite high (refs. 6, 11, and 12). Clearly, much more investigation
is needed into the issue of peak thrust augmentation in unsteady thrust systems in general, and in large versus small
systems in particular.

NASA/TM—2006-214224 12
 IV. Conclusion
A large scale pulsejet-driven ejector system was tested with the objective of obtaining ejector dimensions which
maximize thrust augmentation. Tests were conducted using ejectors of various length, diameter, and cross sectional
profile. The spacing between the pulsejet exit and ejector inlet was also examined for its influence on performance.
Comparisons with other unsteady ejector experiments were also made both in the level of augmentation achieved
and in the dimensions of the optimized ejectors. A peak thrust augmentation value of 1.71 was obtained with straight
ejectors. The optimized ejector diameter was found to be 2.46 times the pulsejet driver diameter of 6.5 in. This ratio
was observed to be nearly constant over numerous experiments and may therefore be a sizing rule. The optimal
length was found to be 10 times the driver diameter. This result was found to be the same as another, small scale
pulsejet experiment, but somewhat different from those where another driving source was used. It was found that the
tapered profile ejector yielded a higher thrust augmentation than the best of the straight profile series. The value
obtained was 1.81. This result was consistent with numerous other unsteady thrust augmentation experiments.
Additional research is needed to determine if there is an optimal ejector taper angle, and if that angle can be related
to parameters of the driver.
References
1. Lockwood, R.M. “Interim Summary Report on Investigation of the Process of Energy Transfer from an
Intermittent Jet to Secondary Fluid in an Ejector-Type Thrust Augmenter,” Hiller Aircraft Report No. ARD-
286, March, 1961.
2. Binder, G. and Didelle, H, “Improvement of Ejector Thrust Augmentation by pulsating or flapping Jets,” Paper
E3 of Proc. 2nd Symposium on Jet Pumps & Ejectors and Gas Lift Techniques, Cambridge, England, March
1975.
3. Paxson, D.E., Wilson, J., and Dougherty, K.T., “Unsteady Ejector Performance: An Experimental Investigation
Using a Pulsejet Driver,” AIAA paper 2002–3915, July, 2002.
4. Wilson, J., and Paxson, D.E., “Unsteady Ejector Performance: An Experimental Investigation Using a
Resonance Tube Driver,” AIAA paper 2002–3632, July, 2002.
5. Wilson, J., Sgondea, A., Paxson, D.E., Rosenthal, R., “Parametric Investigation of Thrust Augmentation by
Ejectors on a Pulsed Detonation Tube,” AIAA paper 2005–4208, July, 2005.
6. Paxson, D.E. Wernet, M.P., John, W.T., “An Experimental Investigation of Unsteady Thrust Augmentation
Using a Speaker-Driven Jet,” AIAA–2004–0092, January, 2004.
7. Landry, K., Shehadeh, R., Bouvet, N., Lee, S.-Y, Pal, S., and Santoro, R.J., “Effect of Operating Frequency on
PDE Driven Ejector Thrust Performance,” AIAA paper 2005–3832, July, 2005.
8. Choutapalli, I.M., Alkislar, M.B., Krothapalli, A. Lourenco, L.M., “An Experimental Study of Pulsed Jet
Ejector,” AIAA paper 2005–1208, January, 2005.
9. Allgood, D. Gutmark, E. Hoke, J. Bradley, R., Schauer, F., “Performance Measurements of Pulse Detonation
Engine Ejectors,” AIAA paper 2005–223, January, 2005.
10. Wilson, J. “Effect of Pulse Length and Ejector Radius on Unsteady Ejector Performance,” AIAA paper 2005–
3829, July, 2005.
11. John, W.T., Paxson, D.E., Wernet, M.P., “Conditionally Sampled Pulsejet Driven Ejector Flow Field Using
DPIV,” AIAA paper 2002–3231, June, 2002.
12. Opalski, A.B., Paxson, D.E., Wernet, M.P., “Detonation Driven Ejector Exhaust Flow Characterization Using
Planar DPIV,” AIAA paper 2005–4379, July, 2005.
13. Litke, P.J., Schauer, F.R., Paxson, D.E., Bradley, R.P., Hoke, J.L., “Assessment of the Performance of a
Pulsejet and Comparison with a Pulsed-Detonation Engine,” AIAA paper 2005–0228, January, 2005.
14. Schauer, F.R., Stutrud, J., and Bradley, R.P., “Detonation Initiation Studies and Performance Results for Pulsed
Detonation Engine Applications,” AIAA Paper 2001–1129, January 2001.
15. Paxson, D.E., “2003 Pulse Detonation Engine Project: University/Government Spring Ejector Meeting,”
unpublished presentation, 2003.
16. Wilson, J. “Vortex Rings Generated by a Shrouded Hartmann-Sprenger Tube,” AIAA paper 2005–5163, June
2005.
17. Gharib, M., Rambod, E., Shariff, K., “A universal time scale for vortex ring formation,” Journal of Fluid
Mechanics, vol. 360, pp. 121–140, 1998.

NASA/TM—2006-214224 13
 Form Approved
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May 2006 Technical Memorandum
4. TITLE AND SUBTITLE 5. FUNDING NUMBERS

Performance Assessment of a Large Scale Pulsejet-Driven Ejector System

WBS 599489.02.07.03
6. AUTHOR(S)

Daniel E. Paxson, Paul J. Litke, Frederick R. Schauer, Royce P. Bradley,

and John L. Hoke
7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION
REPORT NUMBER
National Aeronautics and Space Administration
John H. Glenn Research Center at Lewis Field E–15472
Cleveland, Ohio 44135 – 3191

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING/MONITORING

AGENCY REPORT NUMBER
National Aeronautics and Space Administration
Washington, DC 20546– 0001 NASA TM—2006-214224
AIAA–2006–1021

11. SUPPLEMENTARY NOTES

Prepared for the 44th Aerospace Sciences Meeting and Exhibit sponsored by the American Institute of Aeronautics and
Astronautics, Reno, Nevada, January 9–12, 2006. Daniel E. Paxson, NASA Glenn Research Center; Paul J. Litke and
Frederick R.Schauer, Air Force Research Laboratory, Wright-Patterson Air Force Base, Dayton, Ohio 45433;
Royce P. Bradley and John L. Hoke, Innovative Scientific Solutions, Inc., Dayton, Ohio 45440. Responsible person,
Daniel E. Paxson, organization code RIC, 216–433–8334.
12a. DISTRIBUTION/AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE

Unclassified - Unlimited
Subject Category: 07
Available electronically at http://gltrs.grc.nasa.gov
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.
13. ABSTRACT (Maximum 200 words)

Unsteady thrust augmentation was measured on a large scale driver/ejector system. A 72 in. long, 6.5 in. diameter, 100 lbf
pulsejet was tested with a series of straight, cylindrical ejectors of varying length, and diameter. A tapered ejector
configuration of varying length was also tested. The objectives of the testing were to determine the dimensions of the
ejectors which maximize thrust augmentation, and to compare the dimensions and augmentation levels so obtained with
those of other, similarly maximized, but smaller scale systems on which much of the recent unsteady ejector thrust
augmentation studies have been performed. An augmentation level of 1.71 was achieved with the cylindrical ejector
configuration and 1.81 with the tapered ejector configuration. These levels are consistent with, but slightly lower than the
highest levels achieved with the smaller systems. The ejector diameter yielding maximum augmentation was 2.46 times
the diameter of the pulsejet. This ratio closely matches those of the small scale experiments. For the straight ejector, the
length yielding maximum augmentation was 10 times the diameter of the pulsejet. This was also nearly the same as the
small scale experiments. Testing procedures are described, as are the parametric variations in ejector geometry. Results are
discussed in terms of their implications for general scaling of pulsed thrust ejector systems.

14. SUBJECT TERMS 15. NUMBER OF PAGES

19
Pulse detonation engines; Combustion; Thermodynamic cycles 16. PRICE CODE

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