Daniel E. Paxson

Glenn Research Center, Cleveland, Ohio

Jack Wilson and Kevin T. Dougherty

QSS Group, Inc., Cleveland, Ohio

Unsteady Ejector Performance: An

Experimental Investigation Using

a Pulsejet Driver

NASA/TM—2002-211711

June 2002

AIAA–2002–3915
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Daniel E. Paxson

Glenn Research Center, Cleveland, Ohio

Jack Wilson and Kevin T. Dougherty

QSS Group, Inc., Cleveland, Ohio

Unsteady Ejector Performance: An

Experimental Investigation Using

a Pulsejet Driver

NASA/TM—2002-211711

June 2002

National Aeronautics and

Space Administration

Glenn Research Center

Prepared for the

38th Joint Propulsion Meeting and Exhibit

cosponsored by AIAA, ASME, SAE, and ASEE

Indianapolis, Indiana, July 7–10, 2002

AIAA–2002–3915
Available from

NASA Center for Aerospace Information

7121 Standard Drive

Hanover, MD 21076

National Technical Information Service

5285 Port Royal Road

Springfield, VA 22100

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.

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

The Aerospace Propulsion and Power Program at

NASA Glenn Research Center sponsored this work.
NASA/TM2002-211711 1 

American Institute of Aeronautics and Astronautics 

UNSTEADY EJECTOR PERFORMANCE: AN EXPERIMENTAL 

INVESTIGATION USING A PULSEJET DRIVER

Daniel E. Paxson†

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135, USA 

Phone: 216–433–8334 

FAX: 216–433–8643 

Email: Daniel.E.Paxson@grc.nasa.gov 

Jack Wilson‡

QSS Group Inc. 

Cleveland, Ohio 44135, USA 

Phone: 216–977–1204 

FAX: 216–977–1334 

Email: Jack.Wilson@qssgess.com 

Kevin T. Dougherty†

QSS Group Inc. 

Cleveland, Ohio 44135, USA 

Phone: 216–433–3546 

FAX: 216–433–2182 

Email: Kevin.T.Dougherty@grc.nasa.gov 

Abstract

An experimental investigation is described in which 

thrust augmentation and mass entrainment were 

measured for a variety of simple cylindrical ejectors 

driven by a gasoline-fueled pulsejet. The ejectors were 

of varying length, diameter, and inlet radius. 

Measurements were also taken to determine the effect 

on performance of the distance between pulsejet exit 

and ejector inlet. Limited tests were also conducted to 

determine the effect of driver cross-sectional shape. 

Optimal values were found for all three ejector 

parameters with respect to thrust augmentation. This 

was not the case with mass entrainment, which 

increased monotonically with ejector diameter. Thus, it 

was found that thrust augmentation is not necessarily 

directly related to mass entrainment, as is often 

supposed for ejectors. Peak thrust augmentation values 

of 1.8 were obtained. Peak mass entrainment values of 

30 times the driver mass flow were also observed. 

Details of the experimental setup and results are 

presented. Preliminary analysis of the results indicates 

that the enhanced performance obtained with an 

unsteady jet (primary source) over comparably sized 

ejectors driven with steady jets is due primarily to the 

structure of the starting vortex-type flow associated with 

the former. 

Introduction

Unsteady ejectors are currently under investigation for 

use in some Pulse Detonation Engine (PDE) propulsion 

systems. This is due in part to their potentially high 

performance compared to steady ejectors of the same 

size relative to the jet dimensions.1,2,3 Additionally, 

they may help to reduce noise and high levels of 

unsteadiness in the exhaust flow, both of which are 

features of PDE’s. The performance referred to here is 

the so-called thrust augmentation of the ejector, φ

defined as 

j

Total

T

T φ ≡ (1) 

where TTotal is the total thrust of the combined ejector 

and primary (i.e. driving) jet and Tj

 is the thrust due to 

the primary jet alone. In this definition, the primary jet 

thrust is often defined as being that obtained with no 

ejector present. It has been argued that the presence of 

an ejector lowers the jet exit pressure, thereby 

increasing its thrust and contributing to an increased 

total thrust. For most of the jets considered in this 

paper however, the difference between jet exit plane 

pressure and that of the ambient air is small. Thus, 

installed jet thrust measurements are sufficiently 

accurate. 

Thrust augmentation values as high as 2.0–2.4 have 

been reported using a single pulsed primary jet and 

ejectors of remarkably small, simple design.1

 While 

state-of-the-art ejectors driven by steady jets can 

† Senior Member AIAA 

‡

Associate Fellow, AIAA
NASA/TM2002-211711 2 

American Institute of Aeronautics and Astronautics 

achieve similar steady performance, they require 

multiple jets and large, long ejector bodies.3

Unfortunately, no proven theory of unsteady ejector 

performance appears to exist in the literature. Perhaps 

for this reason, neither does a consistent set of design 

criteria or scaling laws that would allow the 

construction of an effective ejector for an arbitrary 

pulsed flow. In order to provide this sort of 

information, an experimental facility has been 

constructed at the NASA Glenn Research Center. A 

commercially available pulsejet4

 design was used for 

the primary unsteady jet. This was paired with a basic, 

yet flexible ejector that allowed parametric evaluation 

of the effects that length, diameter, and inlet radius have 

on performance. 

 

The use of a pulsejet is advantageous in several ways. 

First, pulsejets are mechanically (though not fluid 

dynamically) simple, and they are inexpensive to build 

and operate, particularly when compared to the target 

ejector application, PDE’s. These features allowed for 

rapid build-up and subsequent data acquisition. 

Second, since the end goal of the investigation is in 

application to PDE’s, it is beneficial to use a primary jet 

that closely resembles them. The pulsejet does so in 

that the exiting flow has very high enthalpy compared to 

the secondary flow being entrained, the fluctuations in 

exit velocity are very large with complete flow reversal 

occurring over part of the cycle. Furthermore, the 220 

hz. frequency of the particular unit used in this 

experiment is similar those of PDE’s being considered 

for flight. Since all three of these similarities (i.e. 

primary enthalpy, jet impulse shape, and frequency) 

may influence the performance of pulsed ejectors, it 

may be possible to extrapolate the results obtained in 

this experiment to actual PDE’s. It is noted however, 

that pulsejet exhaust flows differ substantially from 

those of PDE’s in that the latter have strong associated 

gasdynamic waves that pulsejets do not. These waves 

may substantially impact the performance of ejectors. 

This paper describes the experimental setup, operation, 

and data acquisition methods of the Glenn facility. 

Results obtained to date are also presented. Analysis of 

these results, and comparison with other experiments3,5

indicates that the particular shape (i.e. time history) of 

the exiting jet flow, along with its associated starting 

vortex is primarily responsible for the enhanced 

performance over steady ejectors observed here and 

elsewhere.1–5 The manner in which this jet entrains 

secondary flow determines thrust augmentation. This 

indication suggests that, in the absence of a well-defined 

theory, predictions of unsteady ejector performance 

should have a correlation parameter that characterizes 

the exiting jet flow. Such a parameter is discussed 

herein. 

Experimental Setup

Two configurations were used in the experiment. One 

was used for measuring thrust augmentation. The other 

was used to measure ejector mass entrainment. They 

are shown schematically in Figs. 1 and 2, respectively 

and are described below. 

Thrust Augmentation Rig

The open rig used ambient air to supply the pulsejet and 

ejector. The pulsejet and ejector(s) were each mounted 

on stands that were in turn clamped to a fixed rail. This 

configuration allowed variations of the distance 

between the pulsejet and the ejector as well as between 

the ejector and the thrust plate. Of course, it was also 

possible to remove the ejector entirely and measure the 

thrust of the pulsejet alone. 

 Thrust Plate

The thrust plate was 2.0 ft. square in dimensions. It was 

attached to a frame and ultimately suspended from a 

beam in the ceiling of the test cell by four chains as 

shown in Fig. 1. A load cell was attached to a fixed 

mount and placed at the center of the thrust plate. The 

axial position of the load cell was adjusted so as to 

Pulsejet

Thrust plate

Fuel line

Ignition wire

Starting air line

Load Cell

Ejector Plug

Fig. 1 Experimental setup for measuring thrust

augmentation. 

Metered supply air

Pulsejet

Fuel line

Ignition wire

Starting air

Ejector

Sealed

Containment

Box

Thrust plate

Flaps

∆P transducer

Fig. 2 Experimental setup for measuring 

entrainment. 
NASA/TM2002-211711 3 

American Institute of Aeronautics and Astronautics 

create a small amount of preload (i.e. it pushed the 

thrust plate forward from the neutral hanging position). 

A small pad of silicone was placed between the load 

cell and the thrust plate in order to reduce vibrations. 

Furthermore, stiffeners were added to the thrust plate 

and the load cell mount. Nevertheless, the signal from 

the load cell was far from steady. The frequency 

content was dominated by the 220 hz. signal of the 

pulsejet and an approximately 14 hz. natural frequency 

of the plate. It was therefore coupled to a 1 hz. lowpass filter. Furthermore, the filtered signal was read 

from an averaging circuit on an oscilloscope with a 

sweep period of 5.0 seconds. 

The distance between the thrust plate and either the 

pulsejet or ejector was found to make little difference to 

the readings obtained. This was an expected result and 

held true provided the plate was not so close as to alter 

the back pressure of the jet (approximately one 

diameter), or so far as to become smaller in dimension 

than the jet plume. In the present tests, the distance 

varied between 15 diameters for the pulsejet alone, to 

2.5 for the largest ejector. 

Mass Entrainment Rig

In the entrainment rig, the pulsejet and ejector were 

placed within a sealed containment box. Originally, the 

only openings in the box were those made for the 

ejector exhaust and for a metered supply line. It was 

found however that the pulsejet, which has a Venturi 

fuel feed system, and which was installed with the fuel 

reservoir outside the containment box, was 

operationally sensitive to the pressure in the box. If 

significant air flow was established through the 

containment box prior to starting the pulsejet, the 

pressure inside would rise relative to the ambient 

pressure. This, in turn, would starve the pulsejet of fuel 

(i.e. the venturi system could not overcome the pressure 

differential). On the other hand, if the pulsejet was 

started prior to flowing air through the box, the ejector 

would immediately begin acting as a pump. This would 

quickly lower the pressure in the containment box 

relative to ambient pressure and essentially flood the 

pulsejet. The solution to the problem was to install a set 

of four flap valves in back of the containment box. The 

valves were simply 3.0 in. diameter holes covered on 

the outside with a piece of hinged plastic sheet. The 

hinge (actually tape) was placed at the top of the sheet. 

Thus, if the pressure in the box rose above ambient, 

they would open. At ambient pressure, or below, they 

would close. 

With this arrangement, it was possible to establish 

airflow through the box first, and subsequently start the 

pulsejet. Due to thermal considerations, the pulsejet 

was only operated for 15 sec. per run. During this time, 

a highly sensitive (i.e. ±7.5 in. H2O) differential 

pressure transducer in the containment box was 

monitored. If the reading was below ambient, then the 

mass flow to the box was increased for the next run. If 

it was above ambient, mass flow was decreased. In this 

trial and error manner, airflow into the box was adjusted 

until the pressure in the box was equal to the ambient 

pressure. 

Ejectors

The series of ejectors examined were essentially of a 

straight, cylindrical form, although a small divergence 

was added at the exhaust ends.5

 An example is shown 

in Fig. 3, along with the parametric designations used 

elsewhere in the paper. The variable parameters were 

the length, L, the diameter, D and the rounding radius 

on the inlet, R. It was also possible to measure the 

effect of the spacing between pulsejet exhaust and 

ejector inlet, δ. For all of the ejectors tested, the length 

of the divergent section was the same (2.625 in.). The 

pulsejet diameter dj was 1.25 in. 

Pulsejet Primary Source

As described earlier, the unsteady flow source was a 

gasoline-fueled pulsejet shown in Fig. 4. The 

operational theory of these resonant devices can be 

found in numerous sources and will not be presented 

here.1,4 The design was that of the commercially 

available Dynajet model. In fact, the valve body and 

valve were obtained directly from a Dynajet pulsejet. 

The combustion chamber and tailpiece were machined 

from Inconel according to Dynajet specified 

dimensions. The exception to this was the wall 

thickness, which was approximately doubled. Since the 

pulsejet was run statically in the experiment, there was 

no convective cooling available. This meant that the 

material became particularly hot, and was the reason 

L

D

R (inlet radius)

δ

Pulsejet

Tailpipe 5.0 deg.

Front View

Side View

D

dj

Fig. 3 Ejector design and parametric variables. 
NASA/TM2002-211711 4 

American Institute of Aeronautics and Astronautics 

that test durations were limited to 15 sec. The 

commercially produced Dynajet was made from thin 

(0.015 in.) stainless steel and was constructed from two 

half-shells requiring two full-length seam-welds. Even 

with the short tests, the welded seam tended to rupture 

after only a few runs. The use of high temperature 

materials (Inconel) and machining to create a pulsejet 

with only one circumferential seam resulted in an 

almost indefinite operational life. 

The pulsejet was instrumented with two static pressure 

transducers. One was a low frequency, remotely 

located type, connected to the pulsejet by several feet of 

0.0625 in. OD tubing. The other was a high frequency, 

high temperature (750 °F) transducer mounted to a 

0.125 in. ID standoff tube, 2.5 in. in length. Figure 5 

shows a sample trace from the high frequency 

transducer during operation. The ambient pressure has 

been subtracted. Also shown in the figure are the 

average value of the trace (over the 0.2 sec. interval) 

and the average value of the low frequency transducer 

read from an averaging circuit on an oscilloscope with a 

5.0 second sweep. The nominal 220 hz. operating 

frequency can be observed in the oscillating pressure 

signal. It can also be seen that the average values of the 

high and low frequency transducers differed slightly 

(3.3 vs. 3.8 psig, respectively). This difference was not 

observed in steady-state pressure tests of the 

combustion chamber and is believed to be due to 

flowfield asymmetries during operation. 

It is noted that if the mean of these two averaged 

pressure differences is multiplied by the area of the 

pulsejet tailpipe (1.227 in.2

), the resulting thrust 

estimate is 4.36 lbf. The value measured from the thrust 

plate for this particular run was 4.33 lbf. This is an 

expected result and proved true over the very limited 

throttling range of the pulsejet. However, for unknown 

reasons it also proved to have significant run-to-run 

scatter. That is to say, on any given run, the two 

measurements could differ by as much as ±5%. If an 

average of three runs was used, the maximum difference 

was only ±3% with a standard deviation for all of the 

runs of only 1.4%. Thus, for all results to be shown a 

three runs averaging technique was applied. Using a 

three run average also reduced the relatively large 

scatter due to natural variations in pulsejet thrust. 

By calculating thrust from the combustion chamber 

pressures, it was possible to measure the pulsejet thrust 

while it was coupled with an ejector. This capability is 

important since, as will be shown hence, some ejector 

configurations had a rather large effect on pulsejet 

operation and therefore on the thrust produced. Since 

this effect is not likely to occur with other unsteady 

sources, such as PDE’s, it has been eliminated from the 

most of the results presented (i.e. by using in-situ 

primary thrust). 

 Tailpieces

For the majority of tests conducted, the final 

approximately three inches of the pulsejet were as 

shown in Fig. 4. That is, the tailpipe was flared and a 

collar was permanently attached for installation in the 

containment box without ejectors (i.e. for measuring 

mass flow through the pulsejet alone). This section will 

be designated as the tailpiece, and the particular 

arrangement in Fig. 4 will be designated ORIGINAL. 

In an effort to examine the effect of the jet shape, the 

pulsejet was actually constructed such that different 

tailpieces could be threaded on to the same tailpipe. 

Limited tests were conducted on three other 

configurations. These are shown in Fig. 6 along with 

their designations. It is noted that the STAR tailpiece 

-10

-5

0

5

10

15

20

25

0.00 0.05 0.10 0.15 0.20

Time (sec.)

p-pam bient (psi)

high frequency low freq.-5.0 sec. avg.

high freq.-0.2 sec. avg.

Fig. 5 Pressure trace and average pressures in the

pulsejet combustion chamber during operation. Front View

(valve body removed)

High frequency pressure transducer

Line to low frequency pressure transducer

Valve body

Spark plug

Combustion chamber

Tailpipe

pressure tap

Valve

Starting 

air line

Fuel line

Side View

seam

Collar

Fig. 4 Pulsejet primary unsteady jet source. 
NASA/TM2002-211711 5 

American Institute of Aeronautics and Astronautics 

had the same cross sectional area as the STRAIGHT 

tailpiece along its entire length. 

Results: Thrust Augmentation

Ejector Length

The effects of ejector length on thrust augmentation are 

shown in Fig. 7 for various ejector diameters. For all 

of the data in this figure the spacing between pulsejet 

exit and ejector inlet was maintained at a constant value 

of δ/dj=2.0. The figure shows thrust augmentation 

plotted two ways. The first is in the conventional 

manner, with the pulsejet thrust being defined as that 

obtained without an ejector present. The second 

method, designated ‘insitu’ uses the pulsejet thrust 

measured with the ejector present, using the pressure in 

the combustion chamber as described earlier in the 

paper. For both methods the total thrust is the same 

value, obtained from the thrust plate. Although the two 

methods do not differ substantially in their resultant 

values at this particular δ/dj location, they do at others 

(see Fig. 8). More importantly however, they differ in 

terms of trends. Both show clear maxima for the D=3.0 

and 4.0 in. ejectors; however, for the ‘insitu’ 

measurements, both the D=2.2 and 6.0 in. ejectors show 

continuously increasing augmentation with larger L, 

while the conventional measurements show weak 

maxima. 

Because the pulsejet is a resonant device, its 

performance is quite sensitive to, among other things, 

exit pressure. Thus, the presence of ejectors can 

strongly influence the thrust delivered. As mentioned 

earlier, this behavior is believed to be unique to 

pulsejets (and possibly other resonant, unsteady thrust 

sources5

) and therefore not applicable to forced 

unsteady devices such as PDE’s. Furthermore, it is the 

performance of the ejector that is of interest here, and 

not the thrust source. Thus, unless otherwise stated, the 

‘insitu’ thrust augmentation measurement will be used. 

 

Examination of Fig. 7 reveals two interesting trends. 

The first is that the maxima for the D=3.0 and 4.0 in., 

and arguably, at least a ‘knee’ in the D=2.2 and 6.0 in. 

ejectors all occur at the same length. This suggests that 

scaling for optimal length should not be based on some 

number of ejector diameters, as is typically done with 

steady ejectors, but instead should be based on some 

parameter of the unsteady jet flow. This argument is 

further substantiated by the observation that Refs. 1, 2 

and 5 all showed different values of L/D for which peak 

performance occurred. The second evident trend in Fig. 

7 is the presence of a clear ejector diameter at which 

peak performance occurs. The D=3.0 ejector shows 

superior performance at all lengths over the other 

diameters. Taking the ratio of this diameter to the 

pulsejet (driver) diameter gives a value of D/dj=2.4. 

This is similar to the peak values observed in Refs. 1 

and 5 of 3.3 and 3.0 respectively. This was also near 

the value used in Ref. 2, although it is not certain that 

this was optimal. It is noted that the jet driver in Ref. 5 

is annular, and dj was taken to be the hydraulic 

diameter. These results suggest that for unsteady 

ejectors of the cylindrical type, scaling diameters for 

peak performance may be geometrically related to the 

primary jet source diameter. 

dj =1.25 in. D=1.45 in.

dj=1.25 in.

0.50 in.

dj =1.25 in.

STRAIGHT

Flared No Collar (FNC)

STAR

Fig. 6 Various tested tailpiece configurations for 

the final approximately 3.0 inches of the pulsejet 

tailpipe. 

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

5.0 10.0 15.0 20.0

Ejector Length (in.)

Thrust Augmentation, φ

D=2.2" D=2.2" insitu

D=3.0" D=3.0" insitu

D=4.0" D=4.0" insitu

D=6.0" D=6.0" insitu

Fig. 7 Thrust augmentation as a function of ejector 

length for various ejector diameters, with fixed 

δ/dj=2.0 and R=0.75 in. 
NASA/TM2002-211711 6 

American Institute of Aeronautics and Astronautics 

Ejector Proximity

The effect of spacing between primary jet and ejector 

inlet is shown in Fig. 8 for several different values of D. 

For each diameter shown, the ejector length was that 

which gave the best performance at δ/dj=2.0. In the 

present experiment, the 3.0 in. diameter ejector yielded 

the best performance for any of the lengths tested. 

Unfortunately, for the optimal length at this diameter 

(L=12.6 in.) proximity data was only obtained with the 

STAR tailpiece shown in Fig. 6. The other proximity 

data was obtained with the ORIGINAL tailpiece; 

however, it is not expected that the tailpiece shape will 

alter the trends shown in Fig. 8. For all of the data 

shown in this figure the inlet radius was R=0.75 in. The 

figure also shows both conventional and insitu 

augmentation results in order to underscore the 

substantial effect of the ejector on pulsejet performance. 

Examining the conventionally measured augmentation 

data, it can be seen that for the D=3.0 in. ejector peak 

performance occurs at approximately 1.8 jet diameters. 

For the D=6.0 in. ejector, the peak appears to occur at 

δ/dj=2.0; however, this is no definitive. Similarly, for 

D=2.2 in., the peak must be estimated, and appears to 

occur near δ/dj=0.0. This trend (δ/dj decreasing with D) 

is consistent with the results of Ref. 5. If insitu thrust 

augmentation is examined however, the results are quite 

different. Here it is seen that, although the D=6.0 in. 

ejector shows a peak, both the D=3.0 and 2.2 in. 

ejectors show increased augmentation as the primary jet 

moves toward the ejector. It is not known whether a 

peak occurs somewhere inside the ejector. 

Unfortunately, the leftmost points of Fig. 8 (for D=3.0 

and 2.2 in.) were the smallest values of δ/dj for which 

the pulsejet could successfully be started. Noting again 

that PDE’s will not likely suffer the same performance 

effects as pulsejets due to ejector proximity, Fig. 8 

suggests that improved performance can be gained by 

placing the primary jet inside the ejector inlet. 

Ejector Inlet Rounding

Figure 9 illustrates the dependence of thrust 

augmentation on the inlet rounding, R for several 

ejector diameters. The ejector length was only optimal 

for the D=3.0 in. ejector (an unfortunate mistake); 

however, since this was clearly the diameter yielding 

the best performance, the results are still useful. For the 

results in this figure the value of δ/dj was 2.0. Data at 

R/D=0.0 was obtained, for the D=3.0 in. case, using 

3.25 in. diameter sheet metal tubing (stove pipe). Thus, 

the specified ejector diameter should be interpreted as 

nominal. For the D=2.2 in. case, data at R/D=0.0 was 

obtained by reversing the ejector and removing the 

rounded inlet. Obviously, for different values of R the 

length of the ejectors changes. The change is small 

however, and insignificant to the results. 

The effects of inlet rounding are quite striking for the 

D=3.0 in. ejector, particularly in contrast to the Ref. 5 

experiment which, using the same ejectors, showed 

virtually no effect on performance. It is not clear why 

this would be so; however, it may suggest that it is 

related to the nature of the jet, which differed markedly 

between the two experiments. It may also suggest that 

the effect of lip rounding depends on the overall 

performance of the ejector. It can be seen that the 

effects were quite small for the D=6.0 in. ejector, but so 

was the augmentation level. The Ref. 5 experiment also 

had fairly low levels of augmentation. It does not 

appear that ejector diameter is the proper length scale 

for the inlet rounding since, at different diameters the 

peak performance in Fig. 9 occurred at different values 

of R/D. The appropriate length scale is not clear at this 

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

0.0 1.0 2.0 3.0 4.0

δ /dj

Thrust Augm entation, φ

D=6.0" L=17.0" insitu

D=3.0" L=12.6" insitu

D=2.2" L=17.0" insitu

STAR tailpiece

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

0.0 1.0 2.0 3.0 4.0

δ /dj

Thrust Augm entation, φ

D=6.0" L=17.0" insitu

D=3.0" L=12.6" insitu

D=2.2" L=17.0" insitu

STAR tailpiece

Fig. 8 Thrust augmentation as a function of

distance between pulsejet exhaust and ejector inlet

for several ejector diameters, with R=0.75 in. 

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

0.0 0.1 0.2 0.3 0.4 0.5

Ejector R/D

Thrust Augmentation, φ

D=2.2" L=12.6"

D=3.0" L=12.6"

D=6.0" L=7.6"

Fig. 9 Thrust augmentation as a function of ejector 

inlet rounding for various ejector diameters and 

lengths, with fixed δ/dj=2.0. 
NASA/TM2002-211711 7 

American Institute of Aeronautics and Astronautics 

time. It can also be seen that there is a point at which 

further increases in rounding do not yield improved 

performance. 

Jet Tailpiece Profiles

Limited testing was performed with the different 

tailpieces shown in Fig. 6. The results are summarized 

in Fig. 10 which shows thrust augmentation for each 

tailpiece using the D=3.0, L=12.6, R/D=0.25 ejector 

(the configuration producing the highest thrust 

augmentation) at δ/dj=2.0. A significant performance 

difference was observed only with the STRAIGHT 

configuration. It is noted however that both the STAR 

and STRAIGHT configurations resulted in reduced 

pulsejet thrust compared to the ORIGINAL, even with 

no ejector present. This was accompanied by a slight 

rise in operating frequency from 220 to 238 hz. Thus, it 

is not clear whether improved augmentation resulted 

from a change in the tailpiece geometry, or a change in 

the nature of pulsed jet. 

Results: Entrainment

Four different ejector diameters were tested in the 

entrainment rig shown in Fig. 2. All four had L=12.6 

in., R=0.75 in., and δ/dj=2.0. Since insitu mass flow 

rates could not be measured in the pulsejet, the value of 

δ/dj was chosen so that the performance of the pulsejet 

was largely unaffected by the presence of the ejector. 

Thus, mass flow rates were measured with the pulsejet 

alone and with ejectors in place. From these 

measurements the entrainment ratio could calculated. 

This is defined as 

pulsejet

ejector

m

m

!

! β = (2) 

where mejector ! is the secondary air mass flow rate 

through the ejector, and mpulsejet ! is the mass flow rate 

through the pulsejet alone. The value of mejector ! is found 

by subtracting pulsejet flow from the total flow. For the 

tests conducted, the mean value of the pulsejet mass 

flow rate was mpulsejet ! =0.057 lbm/s. Unless otherwise 

noted, all quantities are time-averaged. 

The test results are shown in Fig. 11 where thrust 

augmentation is plotted as a function of entrainment 

ratio. The value of D/dj is shown next to each point. 

Also shown in the figure are the measured results from 

Ref. 5 (where jet hydraulic diameter has again been 

used in D/dj). A curve defined by 

( ) 1 γ−1

γ

φ = + β (3) 

has also been plotted. This is an empirical curve-fit for 

steady ejectors representing an observed limit to ejector 

performance;3

 however, it is similar in form to the ideal 

limit,6

 in which the exponent γ/(γ-1) is replaced by 1/2. 

Thus, the exponent may be thought of as containing an 

efficiency of the form ηm/2.

The results of steady, constant area mixing calculations7

are also shown in Fig. 11. It may be shown that for 

subsonic primary jets, these calculations yield thrust 

augmentation and entrainment ratio that depend only on 

the total temperature ratio and area ratio. The total 

temperature ratio is defined as 

0

secondary

0

jet TR

θ

θ = (4) 

1.6

1.7

1.8

1.9

2.0

2.1

ORIGINAL FNC STAR STRAIGHT

Tailpiece Configuration

Thrust Augmentation, φ

δ/dj

=2.0

D=3.0”

L=12.6”

R/D=0.25

1.6

1.7

1.8

1.9

2.0

2.1

ORIGINAL FNC STAR STRAIGHT

Tailpiece Configuration

Thrust Augmentation, φ

δ/dj

=2.0

D=3.0”

L=12.6”

R/D=0.25

Fig. 10 Thrust augmentation for various tailpiece

configurations using the D=3.0, L=12.6, R/D=0.25

ejector at δ/dj=2.0. 

1.0

1.1

1.2

1.3

1.4

1.5

1.6

1.7

1.8

1.9

2.0

0 5 10 15 20 25 30 35

Entrainment Ratio, β

Thrust Augmentation, φ

Pulsejet

Ref. 5

Eqn. 3

Steady mixing

TR=4.5

TR=9.0

TR=1.0

( ) 1 γ−1

γ

φ = +β

D/dj=4.8

D/dj

=3

D/dj

=6

D/dj

=9

D/dj

=11

1.8

2.4

3.2

3.0

2.2

Fig. 11 Thrust augmentation as a function of

entrainment ratio for various ejector diameters, 

with fixed L=12.6 in., R=0.75 in., and δ/dj=2.0. 
NASA/TM2002-211711 8 

American Institute of Aeronautics and Astronautics 

where θ has been used to denote temperature. Mixing 

calculations yield thrust augmentation values that agree 

very well with steady, single nozzle ejector 

measurements2,3 provided the ejectors are sufficiently 

long such that complete mixing can occur. 

Examination of Fig. 11 reveals several interesting 

trends. First, the performance of the pulsejet-driven 

ejector is not monotonically related to entrainment ratio, 

an assumption often made (or implied) by other 

researchers.8,9 In fact, the ejector with the lowest thrust 

augmentation yielded the highest entrainment ratio.*

 

Second, though the pulsejet primary produced much 

higher thrust augmentation levels, with the same 

ejectors, than the resonance-tube primary of Ref. 5, the 

efficiency of the process was, apparently much lower. 

Third, the entrainment ratio for all of the ejectors tested 

was well above that estimated for comparably sized 

steady ejectors. For comparison, it is noted that the 

measured pulsejet temperature ratio, TR was 

approximately 4.6 based on simple time averaging. 

This compares favorably with values found in the 

literature.10 The mass averaged temperature ratio is 

expected to be considerably higher, near 6.0.†

Discussion

In order to interpret some of the results presented, it 

may be worthwhile to consider the pulsejet thrust source 

as composed of two components, one steady and the 

other unsteady. For subsonic jets, the average thrust 

may be written approximately as 

∫

τ

ρ

τ =

0

2

c

j u dt

g

A T (5) 

 

*

 The entrainment ratio for D/dj=4.8 was actually an 

extrapolated value because the facility could not supply 

a sufficient mass flow of air for this ejector. The 

extrapolation has a high level of confidence however, 

and is described in Appendix 1. 

†

 This value was obtained by simulating the pulsejet 

cycle with a Q-1-D code11 and matching mass flow, 

thrust and time averaged exit temperature. 

where τ is the cycle period, A is the cross sectional area 

and gc is the Newton constant. Although density is 

clearly not constant in a pulsejet, for algebraic 

simplicity, it will be assumed so here. Thus, denoting 

steady (time-averaged) and unsteady velocity components such that u = u + u′ , Eq. 5 may be written as 

 2

c

2

c

j u

g

A

u

g

A T ′ 













 ρ + 













 ρ = (6) 

where ∫

τ

′ τ ′ =

0

2 2 u dt 1 u . The terms on the right of Eq. 6 

will be denoted j Tss , and j Tus respectively. Thus, the 

steady and unsteady thrust components are clearly 

delineated. If it is now supposed that the total thrust has 

similar steady and unsteady components, the following 

relationship may be written 

2

2

2 us

2

ss

u

u 1

u

u

′ +

φ ′ φ +

φ = (7) 

where j

ss

Total

ss

ss T

T φ = and j

us

Total

us

us T

T φ = . Equation 7 clearly 

shows that the ‘shape’ of the unsteady primary jet, 

which is characterized by 2 2 u′ u , plays a large role in 

performance. 

The entrainment may also be divided into components 

ss us j

ejector

us

j

ejector

ss

m

m

m

m β = + ≡ β + β !

!

!

! (8) 

Experimentally, the rms velocity fluctuations may be 

found by assuming a mean density and rearranging Eqn. 

6 to read 

 

2

1

2j

j c

2

1

m

Ag T

u

u















 −













 ρ = ′

! (9) 

Table 1 lists these values for the present and Ref. 5 

experiments. The mean density used for the present 

experiment in Eq. (9) was 0.0126 lbm/ft3

. This value 

was obtained by dividing the density of standard air 

by the estimated mass-averaged pulsejet exhaust 

temperature ratio of 6.0. The result agreed well 

with measured rms velocity values obtained 

experimentally.12 For the Ref. 5 ex periment the 

Table 1 RMS velocity values for the present and 

Ref. 5 experiments. 

 Pulsejet Ref. 5 

(Resonance Tube) 

u u 2

′ 1.89 0.94 
NASA/TM2002-211711 9 

American Institute of Aeronautics and Astronautics 

standard air density of 0.076 lbm/ft3

 was used. 

Evidently, the unsteady thrust component of the pulsejet 

experiment is over three times larger than the steady 

component. In the resonance tube, the unsteady 

component is slightly less than the steady component. 

Assuming that the steady-state behavior of the ejector 

flowfield can be modeled using the mixing calculation 

described earlier (though it is clear that several of the 

ejectors tested are far too short when scaled by the 

diameter), the unsteady quantities can be obtained. 

These are listed in Table 2. For the Ref. 5 data, the 

values of L and R used are those yielding the highest 

thrust augmentation ratios. The hydraulic diameter was 

used for dj. 

Figure 12 shows the unsteady thrust augmentation from 

the two experiments plotted as a function of ejector to 

jet diameter ratio. It is evident that there is a strong 

maximum in the vicinity of D/dj=3 for both 

experiments, as mentioned earlier. It is well known that 

an impulsively started flow emitted from a pipe forms a 

starting vortex. It has been shown that the features of 

this flow change radically based on the so-called 

Formation number13 

j d

U F τ = (10) 

where U is some characteristic velocity of the pulse and 

τ is a characteristic time over which the pulse occurs. 

Remarkably however, the maximum size of the vortex 

seems to scale with the dimensions of the jet. This 

observation is consistent with the findings here. It 

suggests that, for unsteady thrust augmentation, the 

dimensions of the ejector yielding peak performance are 

related to the size of the starting vortex, which in turn is 

related to the size of the jet source but not the particular 

structure of the jet. 

Since Formation number seems to affect the features of 

a starting vortex, it may be supposed that it could be 

used as a parameter to explain the performance 

differences between the present and Ref. 5 experiments. 

The Formation number (which is essentially an inverse 

Strouhal number) may be written as follows. 

j

2

2fd

u F ′ = (11) 

where f is the frequency of the primary source. Table 3 

shows the values obtained for the two experiments. 

Also listed in the table are values of efficiency derived 

from the equation 

( ) 2 us us

m

1 η

φ = + β (12) 

using the nominal diameter ejector to jet diameter ratios 

yielding the highest performance in Fig. 12. These 

quantities are also shown plotted in Fig. 13. It is clear 

that efficiencies greater than 1.0 are inconsistent; 

however, it is striking that the high efficiency occurs 

Table 2 Steady and unsteady augmentation and 

entrainment ratio components for the present and 

Ref. 5 experiments 

D/dj φss βss φus βus

Pulsejet Driven Ejector 

1.8 1.05 1.34 1.50 6.83 

2.4 1.16 3.24 1.99 13.00 

3.2 1.26 5.62 1.84 15.57 

4.8 1.40 10.38 1.43 20.09 

Ref. 5 Resonance Tube Driven Experiment 

2.2 1.01 0.13 1.33 0.77 

3.0 1.12 0.73 1.56 1.16 

4.0 1.22 ----- 1.32 ------ 

6.0 1.36 ----- 1.13 ------ 

1.0

1.2

1.4

1.6

1.8

2.0

1.0 2.0 3.0 4.0 5.0 6.0 7.0

D/dj

Unsteady Thrust Augmentation, φ us

Pulsejet

Ref. 5

Fig. 12 Unsteady thrust augmentation as a function

ejector to jet ratio for the pulsejet and Ref. 5

experiment. 

Table 3 RMS velocity values for the present and 

Ref. 5 experiments. 

 Pulsejet Ref. 5 

(Resonance Tube) 

Formation No. 21.9 3.6 

ηm (D/dj≈3.1) 0.43 1.15 

ηm(D/dj≈2.3) 0.52 1.00 
NASA/TM2002-211711 10 

American Institute of Aeronautics and Astronautics 

precisely at the critical Formation number identified in 

Ref. 13 as marking the transition from starting vortices 

without to those with ‘trailing jets’. 

Figure 13 also shows some simple curves representing 

proposed behavior of ηm and βus over the range of 

Formation numbers. These have no theoretical basis 

(though arguments can be made for the shape) and are 

obviously based on extremely limited data. 

Furthermore, there is no accounting for the temperature 

of the unsteady flow, which is clearly influential for 

steady ejectors. Nevertheless, it may be instructive to 

use these curves in order to obtain unsteady thrust 

augmentation as a function of Formation number. This 

is shown in Fig. 14. Also shown are the data from the 

present and Ref. 5 experiments, from which the curve 

was constructed, and a single datum from the Ref. 2 

experiment. Though the uncertainty in the F is large for 

this latter point, the agreement with the present curve 

seems at least encouraging. 

It is interesting to consider some of the other results of 

the present experiment in light of Fig. 14. In particular, 

it was noted that the pulsejet with the STRAIGHT 

tailpiece yielded higher thrust augmentation than that 

with the ORIGINAL flared tailpiece. It was also noted 

that the STRAIGHT pulsejet had a higher frequency. 

It has been observed that for the ORIGINAL tailpiece 

u u 2

′ is nearly identical to cc

2

cc ∆p′ ∆p , where 

cc ∆p is the difference between the combustion chamber 

and ambient pressures. The quantity u u 2

′ was not 

measured for the STRAIGHT tailpiece, nor was the 

mass flow rate; however, the thrust was measured, as 

was cc

2

cc ∆p′ ∆p . Assuming the same relationship 

exists between rms quantities in the STRAIGHT 

pulsejet as those in the ORIGINAL, Eq. 9 can be used 

(after rearranging) to yield the mass flow rate. This 

can, in turn be used to find u , and ultimately F. The 

value of φus can also be found allowing an estimated 

data point to be plotted in Fig. 14 for the STRAIGHT 

configuration. It can be seen that this point is consistent 

with predictions made using the model described above. 

It is also interesting to consider the implications of the 

present model with respect to PDE’s. It is noted that, in 

principle, PDE’s have a significant thrust component 

due to unsteady pressure forces. Thus, Eqs. 5, and 6 are 

no longer valid. Furthermore, the powerful emitted 

shock from a PDE cycle may have profound effects on 

ejector performance. Nevertheless, Table 4 shows 

values of rms velocity and Formation number for an 

ideal PDE cycle11 and two ex isting PDE 

experiments.14,15 For the ideal cycle, an assumed 

L/dj=10 has been used. These results were obtained 

from 1-D CFD simulations; however, the simulation 

results agree well with experimental data in terms of 

thrust produced. 

It can be seen from Table 4 that results obtained from 

current PDE experiments may not be applicable to one 

that is optimized (e.g. self-aspirating at the maximum 

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 5 10 15 20 25

Formation Number

Augmentation Efficiency, η m

0

2

4

6

8

10

12

14

16

18

20

Entrainment Ratio, β us

D/dj=3.1

D/dj=2.3

D/dj=3.1

D/dj=2.3

ηm

βus

Fig. 13 Unsteady augmentation efficiency and 

entrainment ratio as functions of Formation

number. 

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

0 5 10 15 20 25

Formation Number

Thrust Augmentation , φ us

Pulsejet

Ref. 5

Ref. 2

Pulsejet-NF (estimated)

Fig. 14 Unsteady thrust augmentation as a function 

of Formation number. 

Table 4 RMS velocity and Formation number for 

ideal and experimental PDE’s. 

 RMS Velocity 

u u 2

′

Formation No. 

j

2

2fd

u′

Ideal 1.21 21.0 

Ref. 14 3.04 110 

Ref. 15 0.82 53 
NASA/TM2002-211711 11 

American Institute of Aeronautics and Astronautics 

theoretical frequency). The Ref. 14 experiment would 

apparently exhibit a strong unsteady component of 

thrust augmentation; however, due to the high 

Formation number (and extremely high temperature), 

the unsteady augmentation would be poor. The Ref. 15 

experiment would have a relatively weak unsteady 

augmentation component which would also be poor. 

Summary

Thrust augmentation and mass entrainment 

measurements were presented from an experiment using 

a series of cylindrical ejectors driven by a pulsejet. 

Several jet shapes were tested as well. Significant 

augmentation and entrainment values were obtained 

compared to similarly sized steady ejectors. Significant 

observations included the following: 

• Optimal ejector length does not scale with ejector 

diameter. 

• The size of the ejector inlet radius can have a 

strong effect on augmentation. 

• For the ejector geometry yielding the highest thrust 

augmentation, peak values were found when the 

primary source was in close proximity to the 

ejector inlet face. Higher values may be possible 

with the source placed some distance inside the 

ejector. 

• Mass entrainment and thrust augmentation are not 

monotonically related. 

The results were compared to those from an experiment 

using the same ejectors, but with a primary jet driven by 

a resonance-tube. A modeling approach that separates 

the augmentation into steady and unsteady components, 

weights the components using rms velocity, then 

determines the unsteady entrainment and augmentation 

efficiency as functions of Formation number appears to 

reconcile the observed differences between the 

experiments. Although far from complete, the modeling 

approach at least demonstrates the importance of rms 

velocity and Formation number in determining unsteady 

ejector performance, and shows how these numbers may 

be determined from readily obtainable experimental 

data. 

 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. Porter, J.L., and Squyers, R.A., “A 

Summary/Overview of Ejector Augmentor Theory 

and Performance Phase IITechnical Report,” 

ATC Report No. R–91100/9CR–47A, Sept., 1979. 

4. Kentfield, J.A.C, Nonsteady, One-Dimensional, 

Internal, Compressible Flows, Oxford University 

Press, 1993. 

5. Wilson, J, and Paxson, D.E., “Unsteady Ejector 

Performance: an Experimental Investigation Using 

a Resonance Tube Driver,” AIAA paper # 2002–

3632. 

6. Heiser, W.H., “Thrust Augmentation,” ASME 

paper 66–GT–116, March, 1966. 

7. Foa, J.V. Elements of Flight Propulsion, John 

Wiley and Sons, 1960. 

8. Johnson, W.S. and Yang, T. “A Mathematical 

Model for the Prediction of the induced Flow in a 

Pulsejet Ejector with Experimental Verification,” 

ASME Paper 68–WA/FE–33, 1968. 

9. Marzouk, E.M., and Abdel Wahab, A.F., “A 

Numerical Model for Prediction of the Induced 

Flow in Pulse Jet Ejector with Experimental 

Verification,” AIAA–97–1016, 1997. 

10. Lockwood, R.M. “Investigation of the Process of 

Energy Transfer from an Intermittent Jet to 

Secondary Fluid in an Ejector-Type Thrust 

Augmenter,” Hiller Aircraft Report No. APR–64–

4, March, 1964. 

11. Paxson, D.E., “A Performance Map for Ideal Air 

Breathing Pulse Detonation Engines,” AIAA paper 

2001–3465, July, 2001. 

12. Wentworth, T.J, Paxson, D.E., Wernet, M.P., 

“Conditionally Sampled Pulsejet Driven Ejector 

Flow Field Using DPIV,” AIAA paper 2002–3231, 

June, 2002. 

13. Gharib, M., Rambod, E., Shariff, K., “A universal 

time scale for vortex ring formation,” Journal of 

Fluid Mechanics, Vol. 360, pp. 121–140, 1998. 

14. Schauer, F., Stutrud, J., Bradley, R., “Detonation 

Initiation Studies and Performance Results for 

Pulsed Detonation Engine Applications” AIAA 

Paper 2001–1129, January, 2001. 

15. Wolter, J., NASA GRC PDE Rig Data, personal 

consultations, results unpublished. 
NASA/TM2002-211711 12 

American Institute of Aeronautics and Astronautics 

Appendix 1 Mass Entrainment Extrapolation

Although the description of the entrainment rig given 

earlier mentions a sealed containment box, in actuality 

the box contained a small, fixed opening in the side 

through which ambient air could flow. The purpose of 

this opening was to prevent excessive vaccum 

conditions from occurring (which ultimately prevent the 

pulsejet from operating) when insufficient air is 

supplied to the box during ejector tests. With this 

opening it was possible to run entrainment tests with 

either too much or too little supply air, thus arriving at 

the appropriate amount more quickly. 

Figure A1 shows the supplied mass flow rate as a 

function of the square root of the box differential 

pressure (measured relative to the ambient pressure) 

∆PBox = Pambient − PBox (13) 

for the four ejectors tested. The ejector diameters are 

shown in the legend. The data for each ejector is well 

fit with a linear regression, the y-intercept of which is 

the correct mass flow rate. For all of the ejectors except 

D=6.0 in. it is seen that there are data points 

representing both excess and insufficient air. The 

supply system could not provide enough air for this 

ejector; however, the trend in the data is clear and 

consistent with the other ejectors tested. Therefore, 

extrapolation is warranted and the result may be 

obtained with confidence. 

0.0

0.5

1.0

1.5

2.0

2.5

-1.0 -0.5 0.0 0.5 1.0 1.5 2.0

(∆ PBox)

1/2 (in. H2O)1/2

Mass Flow Rate (lbm/s)

D=6.0"

D=4.0"

D=3.0"

D=2.2"

Fig. A1 Containment box mass flow rate as a 

function of the square root of the box differential

pressure for the four ejectors tested. 
This publication is available from the NASA Center for AeroSpace Information, 301–621–0390.

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19

Unsteady Ejector Performance: An Experimental Investigation Using

a Pulsejet Driver

Daniel E. Paxson, Jack Wilson, and Kevin T. Dougherty

Pulsejet engines; Thrust augmentation; Ejectors

Unclassified -Unlimited

Subject Category: 07 Distribution: Nonstandard

Prepared for the 38th Joint Propulsion Meeting and Exhibit cosponsored by AIAA, ASME, SAE, and ASEE, Indianapolis,

Indiana, July 7–10, 2002. Daniel E. Paxson, NASA Glenn Research Center; Jack Wilson and Kevin T. Dougherty,

QSS Group, Inc., Cleveland, Ohio 44135. Responsible person, Daniel E. Paxson, organization code 5530, 216–433–8334.

An experimental investigation is described in which thrust augmentation and mass entrainment were measured for a

variety of simple cylindrical ejectors driven by a gasoline-fueled pulsejet. The ejectors were of varying length, diameter,

and inlet radius. Measurements were also taken to determine the effect on performance of the distance between pulsejet

exit and ejector inlet. Limited tests were also conducted to determine the effect of driver cross-sectional shape. Optimal

values were found for all three ejector parameters with respect to thrust augmentation. This was not the case with mass

entrainment, which increased monotonically with ejector diameter. Thus, it was found that thrust augmentation is not

necessarily directly related to mass entrainment, as is often supposed for ejectors. Peak thrust augmentation values of 1.8

were obtained. Peak mass entrainment values of 30 times the driver mass flow were also observed. Details of the experimental setup and results are presented. Preliminary analysis of the results indicates that the enhanced performance

obtained with an unsteady jet (primary source) over comparably sized ejectors driven with steady jets is due primarily to

the structure of the starting vortex-type flow associated with the former.