Micro-Gas Turbine Engine Ejector-Mixer Design and...

Micro-Gas Turbine Engine Ejector-MixerDesign and Testing

Final Report

16.621

Fall 2001

Author: Nathan Fitzgerald

Advisor: Prof. Alan Epstein Partner: Mark Monroe

December 11, 2001

Contents

1 Abstract 1

2 Introduction 1

2.1 Background . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

2.2 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2

3 Objectives 3

4 Technical Background 3

4.1 Ejector-Mixer Theory . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 3

4.2 Previous Research .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6

5 Experimental Approach 7

5.1 Testing Rig . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

5.2 Component Design. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5.2.1 Ejector Design . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5.2.2 Mixer Design . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 9

5.2.3 Convergent Duct Design. . . . . . . . . . . . . . . . . . . . . . . . . . . 10

5.2.4 Instrumentation . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 10

5.3 Text Matrix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

5.4 Experimental Procedure . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 13

6 Results 14

6.1 Pumping Parameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

6.2 Mixing Parameter .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16

6.3 Temperature Reduction . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 16

7 Discussion 19

7.1 Pumping Parameter. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

7.2 Mixing Parameter .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19

7.3 Temperature Reduction . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 20

i

7.4 Data Consistency .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

8 Conclusions 20

9 Future Work 22

10 Acknowledgments 22

A Uncertainty Analysis 24

A.1 Corrected Pumping Uncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . 24

A.2 Mixing Parameter Uncertainty .. . . . . . . . . . . . . . . . . . . . . . . . . . . 26

A.3 Temperature Reduction Uncertainty . . . . .. . . . . . . . . . . . . . . . . . . . 26

B Testing Procedure 29

B.1 Micro-Engine Ejector-Mixer Test Procedure .. . . . . . . . . . . . . . . . . . . . 29

B.2 Sample Data Sheet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31

C Numerical Analysis 32

C.1 performance.m . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

C.2 test1.m. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

D Technical Drawings 50

ii

List of Figures

1 Micro-Gas Turbine Engine . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 2

2 Ideal Ejector Mixer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4

3 Model Pumping Performance . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 5

4 Symmetric Mixer Lobe . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 6

5 WNEC Mixer Performance Results . . . . . .. . . . . . . . . . . . . . . . . . . . 7

6 Convoluted Mixer Lobe . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 7

7 Test Rig . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8

8 Side View of Ejector Design . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 10

9 Free Splitter and Convoluted Mixer Designs .. . . . . . . . . . . . . . . . . . . . 11

10 Convergent Duct .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11

11 Instrumentation Schematic . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 12

12 Test Matrix . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13

13 Corrected Pumping Performance. . . . . . . . . . . . . . . . . . . . . . . . . . . 15

14 Mixing Performance . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 17

15 Temperature Reduction . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 18

16 Comparison with Western New England College Data. . . . . . . . . . . . . . . . 21

17 Pumping Performance w/ Uncertainties . . .. . . . . . . . . . . . . . . . . . . . 25

18 Mixing Performance w/ Uncertainties . . . .. . . . . . . . . . . . . . . . . . . . 27

19 Temperature Reduction w/ Uncertainties . . .. . . . . . . . . . . . . . . . . . . . 28

List of Tables

1 System Measurements . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . 12

iii

1 Abstract

This study investigates the effect of low Reynolds number operation on ejector-mixers in the con-

text of their compatibility with the micro-gas turbine engine under development at MIT’s Gas

Turbine Laboratory. The high exhaust temperatures of the micro-engine inhibit its integration into

consumer devices. This research tests a possible solution to that problem, an ejector-mixer that

operates at the near-transitional Reynolds numbers experienced by the engine. A test rig was con-

structed in which a pipe directed a 350�K air stream at high and low Reynolds number through

ejector-mixers of varying geometry. The experiments show that the performance of an ejector-

mixer substantially improves at low Reynolds number and can be augmented still by forced mix-

ing. The effect could contribute substantially to the reduction of the exhaust temperature in the

micro-gas turbine engine.

2 Introduction

2.1 Background

Since the mid 1990’s, the Gas Turbine Laboratory at the Massachusetts Institute of Technol-

ogy has been developing miniature gas turbine engines using micro-electro-mechanical systems

(MEMS) technology.1 Silicon or silicon carbide wafers are etched using photo lithography into

two-dimensional layers that are then stacked and bonded together to form a three-dimensional de-

vice. The final device is just 2 cm in diameter and 3 mm thick. A schematic of the micro-engine

appears in Figure 1. At about one thousandth the linear scale of larger, conventional gas turbines,

the micro-engine is designed to produce either tens of watts of electrical power or 0.1 N of thrust

from its hydrocarbon fuel.

The uses for such a small engine are numerous and varied, from providing propulsion for

miniature aerial vehicles to controlling boundary layers of commercial aircraft. In particular, one

promising application for the device is as an alternative to conventional batteries for personal elec-

tronic devices such as cellular phones and personal GPS devices. With 20 to 30 times the energy

density of conventional lithium batteries, a hydrocarbon fueled micro-engine generator offers to

1

Figure 1: Micro-Gas Turbine Engine

expand the range and capabilities of personal electronic systems. However, the use of the micro-

gas turbine engine in such devices is hindered by the the high temperature exhaust ejected by the

engine. Under the current design, the exhaust temperature of an engine operating as a generator

will exceed 900 degrees Kelvin. This temperature makes applications that involve plastics or close

human contact impractical.

2.2 Motivation

In order for the application of micro-gas turbine engine as a power plant for personal electronic de-

vices to be realized, a method of cooling the exhaust jet must be developed. In certain commercial

and military gas turbine engines, this is done by attaching a device called an ejector-mixer at the

exit of the turbine. In addition to exhaust temperature reduction, attributes of the device include

noise reduction and thrust augmentation. The ejector uses the momentum of the exhaust to pump

in a secondary flow of ambient temperature air. The secondary and primary flows are then mixed

over a surface of complex geometry, transferring heat and momentum to the secondary flow. The

device also affects the static pressure at the exit of the turbine, thus affecting the power capabilities

of the engine.

Conventional ejector-mixers operate at very high Reynolds numbers, much higher than the

2

transition number for jet flow. An ejector mixer for the micro-engine, however, would operate very

close to the transition regime, where the viscous effects that govern the performance of the ejector-

mixer differ from those in the turbulent regime. Although theoretical models exist that allude to

the behavior of ejector-mixers at low Reynolds numbers, the existence of empirical data at such

conditions would greatly aide in design of and ejector-mixer for use with the micro-gas turbine

engine.

3 Objectives

The primary objective of this project was to characterize the performance of ejector-mixers at low

Reynolds numbers. Tests were conducted on scaled-up versions of micro-engine ejector-mixers

of varied design at both low and high Reynolds numbers. Pressure, temperature, and mass flow

obtained from those tests were used to determine the performance of each design in terms of tem-

perature reduction, secondary to primary flow pumping, and mixing metrics. Cross comparisons

were then made with regard to testing condition, device design, and ideal performance. The end

result serves as a base of knowledge useful to the design of a micro-gas turbine engine ejector-

mixer.

4 Technical Background

4.1 Ejector-Mixer Theory

As the name suggests, an ejector-mixer is composed of two parts: the ejector, and the mixer.

The ejector is the shroud in which the engine exhaust primary flow and the ambient conditioned

secondary flow meet and mix. The momentum of the primary flow pumps the secondary flow into

the ejector shroud. Once inside the shroud, viscous interaction between the two flows cause then

to mix, transferring momentum and energy between them.

The following model can be used to anticipate the performance of an ejector-mixer operating

under incompressible conditions. The primary and secondary mass flows are assumed to travel

isentropically from their sources, the engine exhaust pipe and the ambient air respectively, to the

3

Figure 2: Ideal Ejector Mixer

inlet of the ejector shroud. The primary and secondary flows enter the ejector at their own re-

spective uniform velocities and exit the shroud at a single uniform velocity, corresponding to the

complete mixing of the two streams. The pressure at the plane of the primary flow exit and the

pressure at the exit of the ejector are both assumed to be uniform. A schematic of this model

ejector appears in Figure 2.

Under these assumptions, the performance of the ejector is simply a function of its geometry

and ambient conditions. In particular, the ratio of primary mass flow to secondary mass flow,

_ms= _mp is a function of the primary to secondary area ratio,As=Ap, and the stagnation temperature

ratio of the two flows,Tts=Ttp:

TtsT(tp)

(_ms

_mp

)2((Ap

As

)2 + 1) +

sTtsTtp

_ms

_mp

� 4� 2(Ap

As

) = 0: (1)

The parameter_ms

_mp

qTtsTtp

allows the pumping performance to be investigated independently of

temperature, allowing researchers to conduct ejector pumping tests at convenient primary and sec-

ondary total temperatures.3 Figure 3 displays this parameter as a function of area ratio.

In a real device, the temperature, pressure, and velocity profiles will not be uniform. Therefore,

it is useful to define a mixing parameter to quantify the degree of uniformity in the exit stream.

The parameter chosen in this study is defined as follows:

� =

RT 22 dA2

A2 � �T22 (2)

4

0 1 2 3 4 5 6 7 8 9 100

0.5

1

1.5

2

2.5

3

Area Ratio

Cor

rect

ed P

umpi

ng R

atio

Figure 3: Model Pumping Performance

whereT2 is a discrete temperature at the exit of the ejector,�T2 is the average temperature at the

exit, andA2 is the exit area. A� of unity signifies complete mixing and uniform temperature and

velocity distributions.� increases from unity with increasingly non-uniform exit flow.

The mixer is a device that controls the interaction of the primary and secondary flows. At its

simplest, a mixer is a pipe from which the primary flow exits to meet with the secondary flow. This

is called a free splitter. More complicated designs, such as the mixer seen in Figure 4, augment

the mixing process by increasing the effective surface contact area between the two flows. This is

done in two ways. First, the curved shape of the mixer increases the surface area over which the

primary and secondary flow meet. Secondly, many geometries generate off-axis vorticity which

even further increases the effective contact area. Forced mixing has been proven to decrease the

ejector length needed for complete mixing and to increase the pumping ratio of a given ejector

geometry.9

5

Figure 4: Symmetric Mixer Lobe

4.2 Previous Research

Ejector-mixers have been given a good deal of attention in the last few decades, especially with

regards to their application as a solution to the high order problem of jet aircraft noise. The work of

Walter M. Presz at Western New England College has shown that forced mixing increases pumping

rates and shortens required ejector lengths. Presz also conducted parameter studies on various types

of mixers, characterizing and classifying their performance.9 Figure 5 displays the results from one

such study, showing pumping as a function of the mixer geometry parameters of lobe angle and

penetration. Penetration refers to the depth through which the mixer protrudes in to the primary

and secondary flows. A mixer with zero penetration is essentially a free-splitter. The lobe angle

basically describes how steeply that penetration is achieve. Again, a lobe angle of zero means

that the mixer is essentially a free-splitter. For the conditions conducted in Presz’s experiments,

asymmetric and high penetration mixers produced the most ideal performance. These two types of

mixers employ strong off-axis vorticity to enhance mixing.

At high Reynolds numbers, the work of David Tew at MIT’s Gas Turbine Laboratory confirmed

that of Presz, that off-axis vorticity increases pumping efficiencies.7 However Tew notes that the

effect of that vorticity diminishes as shear layer growth rate increases. At low Reynolds numbers,

viscous effects are quite strong and unforced mixing occurs rapidly between two flows. Therefore,

the additional surface contact area obtained by the swirling of the primary and secondary flows

has less of an effect on the pumping ratio in comparison with the negative effects of the off-axis

vorticity, like decreased thrust in a propulsion system. One alternative to vorticity inducing forced

6

Figure 5: WNEC Mixer Performance Results

mixers is a convoluted mixer, seen in Figure 6. This mixer increases the surface contact area of the

primary and secondary flows, but doesn’t induce large amounts of off-axis vorticity.

5 Experimental Approach

In order to characterize the performance of ejector-mixers at low Reynolds numbers, tests were

conducted on a number of ejector and mixer geometries for both transitional and fully turbulent

primary flows. To approximate the running conditions of a micro-gas turbine engine, the cross sec-

Figure 6: Convoluted Mixer Lobe

7

Figure 7: Test Rig

tional area of the primary flow was designed represent a five times linear scaling from the projected

jet area of the micro-engine. The increase in size eased the difficultly of test component construc-

tion and allowed for better spatial resolution with the instrumentation. Test were conducted in lab

space in the Gas Turbine Laboratory at MIT.

5.1 Testing Rig

A photograph of the test set-up appears in Figure 7. Air entered the setup from an oil free com-

pressor then passed though a rotameter. The flow was heated to 350�K by a ceramic heater and

then passed thorough a conditioning screen, after which it entered a convergent duct to reduce the

area of the flow to the scale of the experiment. On the low Reynolds number tests, additional heat-

ing tape was wrapped around the piping to prevent heat conduction loss to the piping. From the

convergent duct, it passed thorough the primary flow pipe, which terminated at the opening of the

test ejector. The test mixer was attached to the end of primary flow pipe. The primary flow then

entered the ejector shroud, drawing in a secondary mass flow. The mixed primary and secondary

flows left the rig at the exit of the ejector.

8

5.2 Component Design

Most of the test rig was constructed of standard copper piping, coupling, and mounts, but parts of

three sections needed to be specially designed to function in the experiment. This section contains

a summary of the design choices for those components. Engineering drawings of all manufactured

components appear in Appendix D.

5.2.1 Ejector Design

There are a total of four ejector designs tested in this experiment. The ejector designs were chosen

such that correlations may be drawn between low Reynolds number performance and well under-

stood high Reynolds number performance. A schematic of one of the designs appears in Figure 8.

The work of Presz4 shows that although ideally pumping increases indefinitely with area ratio,

empirically pumping begins to diminish for area ratios greater than 3. Therefore the four ejectors

were constructed with secondary to primary area ratios of 1 and 3. Ejector length to diameter ratios

of 1 and 4 reflect the scope of experiments made at macro scale, and thus have been incorporated

into the scope of this experiment as a basis for comparison.

The last main design consideration with the ejectors was that the secondary flow must enter

them smoothly. An elliptical inlet was therefore designed to prevent separation. It was confirmed

that the geometry prevented separation by a computational fluid dynamics code. All ejectors were

machined from aluminum alloy.

5.2.2 Mixer Design

Two mixer designs were chosen to investigate low Reynolds number effects on ejector perfor-

mance. The first was a free splitter, seen on the left of Figure 9. This design offers no forced

mixing and can be used to determine the baseline effect of low Reynolds number. It was machined

out of aluminum alloy.

The second is a version of the convoluted mixer described in Section 4.2. An isometric drawing

of this mixer appears on the right in Figure 9. The viscous effects of the low Reynolds number were

expected to nullify the effect of induced vorticity in the flow, and testing of a convoluted mixer gave

the opportunity to investigate that claim. In accordance with successful practices at macro scale,

9

Figure 8: Side View of Ejector Design

the mixer was designed to cover 75% of the ejector area. Due to the complex geometry of the

mixer, it couldn’t easily be manufactured using standard machining techniques. Instead, C Ideas,

Inc. was contracted to construct the mixer using photo lithography techniques.

5.2.3 Convergent Duct Design

A convergent duct was required to reduce the area of the flow to the size of the primary jet pipe.

An isometric view of this component appears in Figure 10. The primary concern with this com-

ponent was that the flow remain attached throughout the contraction. Flowing the model of Morel

on axisymmetric wind tunnel contractions,8 this is accomplished using a matched pair of cubic

polynomials. These equations appear in the engineering drawings in Appendix D.

5.2.4 Instrumentation

This experiment required information in the form of temperature, pressure, volume flow, and po-

sition data. All of the pressure readings were made using a single Setra digital pressure transducer

connected to various parts of the test rig using a manifold. All of the temperature readings were

10

Figure 9: Free Splitter and Convoluted Mixer Designs

Figure 10: Convergent Duct

11

Figure 11: Instrumentation Schematic

Table 1: System MeasurementsLocation Measurements Numberatmospheric pressure, temperature 2system inlet pressure, temperature, mass flow 3after heater pressure, temperature 2primary flow exit pressure 1ejector exit temperature 11TOTAL 19

made using thermocouples, which were connected to a ten-channel thermocouple reader. Volume

flow was read with a rotameter; a different rotameter was used for the high and low Reynolds

number tests since the two tests differed in volume flow by two orders of magnitude.

A schematic including the locations of the instrumentation appears in Figure 11. Total pressure

and temperature were measured just as the air entered the rig. Next, the volume flow was measured

in the rotameter. Before the flow entered the convergent duct, another set of total pressure and

temperature measurements were taken. On the ejector shroud, at the exit of the primary jet pipe, a

static pressure measurement was taken. At the exit of the ejector shroud, a thermocouple mounted

on a translation stage monitored the temperature field in eleven locations across the diameter of the

exit. A dial caliper mounted above the translation stage to monitor its position. In total, nineteen

measurements were made per test. Those measurements are outlined in Table 1.

12

Figure 12: Test Matrix

5.3 Text Matrix

The test matrix appears in Figure 12. A total of twelve tests were run, six at a turbulent Reynolds

number of 70,000, and six at a more transitional value of 3,000. Combining length to diameter

ratios of 1 and 4 and primary to secondary area ratios of 1 and 3 created four different geometries of

ejector shrouds. All shrouds were tested at both Reynolds numbers. Two mixer types were tested:

a free splitter and a convoluted mixer. The free splitter was tested with all of the ejector shrouds.

Designed for optimal performance in the shrouds with an area ratio of three, the convoluted mixer

did not geometrically fit inside the shrouds with an area ratio of one. Therefore, the convoluted

mixer was only tested with shrouds with an area ratio of three.

5.4 Experimental Procedure

To run a test, first the valves to the oil free compressor were opened and adjusted until the proper

volume of air flowed through the test set up, as indicated by the rotameter. Then the heating

element would be engaged, including the additional heating tape wrapped around the pipes during

the low Reynolds number tests. The voltages on the heaters would be adjusted with variac power

supplies until the thermocouple monitoring the primary flow between the heater and the convergent

duct was steady near 350�K. Then pressures, temperatures, and mass flows would systematically

13

be observed from upstream in the system to downstream. The percentage power on the variacs

would and other notable observations would also be recorded. A more detailed version of the

experimental procedure as well as a sample data sheet appears in Appendix B.

6 Results

The data from the ejector-mixer tests in this experiment been compiled in terms of the performance

metrics described in Section 4.1. This section contains plots of those metrics. The Matlab code

used for the analysis appears in Appendix C. The legend for the plots is as follows: squares

represent a low Reynolds number test with a free-splitter mixer, circles are a high Reynolds number

test with a free-splitter, plus-signs represent a low Reynolds number test with a convoluted mixer,

and X’s are high Reynolds number tests with a convoluted mixer. Error bars have been omitted

from the plots for clarity, but the average uncertainty for the points in the figure are shown on

the bottom chart, along with a sample error bar for sizing. Plots of the performance metrics that

include the error bars appear in Appendix A.

6.1 Pumping Parameter

Figure 13 presents the corrected pumping parameter as a function of the area ratio of the ejector

shroud. It is plotted separately for each length to diameter ratio in the test matrix. Also plotted

is the curve for the model ejector-mixer described in Section 4.1. The average uncertainty for

the two plots was�.0252. Corrected pumping is shown to increase with decreasing Reynolds

number between 37% and 144%. The effect of the convoluted mixer compared to the free splitter

is generally to further augment pumping. Most of the comparable tests saw an increase between

12% and 23% over the free splitter. One set of tests contradicted this trend; the low Reynolds

number tests at an area ratio of 3 experienced a 17% decrease in pump from the free splitter to the

convoluted mixer.

14

Figure 13: Corrected Pumping Performance

15

6.2 Mixing Parameter

Figure 14 displays the mixing parameter as a function of length to diameter ratio for both of the

area ratios in the test matrix. Also appearing are the ideal, uniform mixing parameter of unity

and the worse case scenario under the test conditions. The worst case scenario was calculate by

assuming that the conditions at the exit of the ejector were identical to those at the inlet, i.e. that

no mixing had occurred. Specifically, for radii less than the radius of the primary jet pipe, the flow

temperature was assumed to be that of the primary, about 350�K. For radii outside the radius of

the jet pipe, the temperature was assumed to be ambient, about 300�K. The average uncertainty for

this parameter was�.002.

The mixing improved with increasing length to diameter ratio. An improvement of between

200% and 400% is observed from a length to diameter ratio of 1, to a ratio of 4. The convoluted

mixer contributed a consistent but less substantial improvement on the mixing. One striking feature

of the data is the reversal of the Reynolds number effect between tests at the two area ratios. At

an area ratio of one, the high Reynolds number tests had better mixing than their low Reynolds

number counterparts. However, at the area ratio of 3, that situation was reversed.

6.3 Temperature Reduction

Figure 15 shows the percent temperature reduction as a function of the area ratio for the two

ejector length to diameter ratios. Also plotted is the ideal curve, calculated by assuming that the

primary flow was cooled entirely to the ambient temperature, i.e. assuming infinite secondary flow

pumping. The average uncertainty is�.143. The data shows between 13% and 89% increases in

pumping from high Reynolds number to low. In most comparisons, convoluted mixer consistently

increased the temperature reduction an average of 8% above the free splitter. The low Reynolds

number length to diameter ratio of 1, area ratio of 3 test was again an exception. There the convo-

luted mixer decreased the temperature reduction by 6%.

16

Figure 14: Mixing Performance

17

Figure 15: Temperature Reduction

18

7 Discussion

7.1 Pumping Parameter

The corrected pumping parameter essentially followed the trends suggested by theory. Viscous

effects increase with decreasing Reynolds numbers, so greater momentum transfer would be ex-

pected to occur at lower Reynolds numbers. The momentum transfer contributes to secondary flow

pumping. In this sense, the data strengthens the theory.

Similarly, one would expect a the convoluted mixer, a device which increases the surface con-

tact area over which viscous momentum transfer can occur, to improve secondary flow pumping.

For both the high and low Reynolds number flows, the data follows this trend with one exception.

As noted in Section 6.1, the mixer degraded the pumping performance for the area ratio of 3, length

to diameter ratio of 1, low Reynolds number test. This may be due to a peculiar interaction at low

Reynolds numbers with the shortened ejector shroud. However, comparing those points with the

relative distances between other tests, one may notice that the free-splitter, area ratio of 3, length

to diameter of 1 test is abnormally high compared to the rest. This seems to indicate that the data

point may be an error.

7.2 Mixing Parameter

A typical free jet will completely mix with the free stream about ten jet diameters away from

the source. With that in mind, the observation in the data that the mixing parameter improved

as the length to diameter ratio increased is not surprising. The effect of the convoluted mixer

on the mixing parameter was also as expected. The increased surface contact area of the two

streams allowed for greater viscous interaction and thus contributed to complete mixing. The

effect was similar for both low and high Reynolds number flows. The observation that the effect

of Reynolds number on the mixing changed with the area ratio was not expected. The change

is within the uncertainty in the measurements; however, the trend is graphically quite consistent

despite the numerical uncertainty. That consistency suggests that the correlation may still have

merit. However, the phenomenon has not yet been explained.

19

7.3 Temperature Reduction

The temperature reduction was expected to follow the same trends as the pumping performance.

In general, the pumping governs how much low enthalpy can be drawn away from the hot primary

flow. The experimental data follows the pumping trend, as expected.

Assuming that the micro-engine could expect ejector-mixer performance similar to these tests,

a convoluted mixer with an area ratio of three and a length to diameter ratio of one would produce a

corrected pumping ratio of about 1.5. This translates to a pumping ratio of 2.6, assuming a primary

flow temperature of 900�K and a secondary flow temperature of 300�K. This would cool the flow

to around 470�K, corresponding to a temperature reduction of 430�K.

7.4 Data Consistency

The data from this experiment was compared to work by Presz at Western New England College

to ensure its consistency. In Figure 16, the data from this experiment is plotted with that from

Western New England College as a function of mixer geometry. For mixers of similar geometries

operating at high Reynolds numbers and similar area ratios, the data from this experiment matched

Western New England College’s data by an average of 11%. This suggests good consistency in the

experiment.

8 Conclusions

Due to the greater viscous effect, the lower Reynolds number tests experienced a larger corrected

pumping ratio. The difference was about 75% greater than the high Reynolds number case. The

convoluted mixer was shown to augment the pumping ratio even further when compared to the free

splitter, and the effect was similar for both high and low Reynolds number conditions. The mixing

parameter did not display as strong a Reynolds number dependence as the corrected pumping; the

effect changed at different secondary primary flow area ratios. The effect of the convoluted mixer

was similar at both high and low Reynolds numbers in that the convoluted mixer contributed to

more complete mixing than with a free-splitter.

Given the corrected pumping ratios attained in this experiment, the designer of a micro-gas

20

Figure 16: Comparison with Western New England College Data

21

turbine ejector-mixer could expect a temperature as high as 430�K. This makes an ejector-mixer a

promising solution for cooling the exhaust of the micro-engine.

9 Future Work

Due to the scope of this project, a limited number of mixers were tested for comparison. The mixer

that was tested was designed specifically for low Reynolds number flows. A suitable follow up to

this study would be the investigation of other more common mixer types at low Reynolds numbers

to provide an even deeper comparison with the existing high Reynolds number data.

One issue left unexplained in this project was the nature of area ratio dependence on the mixing

parameter at high and low Reynolds number. To follow up on this, a study could be performed

where area ratio was varied on a more fine scale to determine the nature of the changing Reynolds

number dependence on mixing.

A key issue to a designer of a micro-gas turbine ejector-mixer will be the performance impact

the device will have on the engine. It’s likely that the performance detriment will come in the form

of a total pressure loss in the exhaust. A future study could categorize the total pressure loss for a

number of ejector-mixer designs in an attempt to correlate engine performance with ejector-mixer

performance.

10 Acknowledgments

The author would like to thank his partner, Mark Monroe; his project advisor, Prof. Alan Epstein;

as well as Dr. Richard Perdichizzi, Carl Dietrich, Dr. Gerald Guenette, Don Weiner, Andrea

McKenzie, James Letendre, and Jerry Wentworth for their invaluable assistance during this project.

References

[1] Epstein, Alan et al. “Shirtbutton-Sized Gas Turbines: The Engineering Challenges of Micro

High Speed Rotating Machinery.” ISROMAC-8. Hawaii, March 2000.

22

[2] Pennathur, Sumita. “Flow Analysis of Integrated Micro Air Vehicle and Micro Gas Turbine

Engine.” 16.62x Project Notebook, 1999.

[3] Presz, W., Gousy, R., and Morin, B. “Forced Mixer Lobes in Ejector Designs.” AIAA 86-1614,

June 1986.

[4] Presz, Walter M., Skebe, Stanley A., and McCormick, Duane C. “Parameter Effects on Mixer-

Ejector Pumping Performance.” AIAA 88-0188, June 1988.

[5] Doebelin,Measurement Systems: Application and Design. 3rd ed. New York:McGraw-Hill,

1983.

[6] Omega Temperature Handbook (Vol. 29) and Omega Flow and Lever Handbook (Vol. 27)

[7] Tew, D., Temple, B., and Waitz, I. “Mixer-Ejector Noise-Suppressor Model.” Journal of

Propulsion and Power. Vol. 14, No. 6, Nov.-Dec. 1998.

[8] Morel, T. “Comprehensive Design of Axisymmetric Wind Tunnel Contractions.” Journal of

Fluids Engineering. June 1995.

[9] Presz, Morin, and Blinn. “Short Efficient Ejector Systems.” AIAA 87-1837, June 1987.

23

A Uncertainty Analysis

Given the uncertainty in the measuring instruments, the uncertainty of the calculated design metrics

can be determined by weighting their sensitivities to measured inputs. The thermocouples used in

the testing were assumed to be accurate to within 1%. The thermocouple used for the temperature

field at the exit of the ejector is the exception. That particular device was a precision calibrated

thermocouple mounted in a pitot tube designed specifically for flow measurements. Its uncertainty

was much less that 1%.

A.1 Corrected Pumping Uncertainty

The pumping metric is a function of the primary and secondary flow temperatures (Tp andTs) and

the average temperature at the exit of the ejector (T2).

f =_ms

_mp

=Tp � �T2�T2 � Ts

(3)

The root mean square uncertainty in the uncorrected pumping is:

�_ms

_mp

=

vuut(j�Ts@f

@Tsj)2 + (j�Tp

@f

@Tpj)2 + (j� �T2

@f

@ �T2j)2: (4)

Corrected pumping is a function for the primary to secondary temperature ratios and the pump-

ing:

g =_ms

_mp

sTsTp

: (5)

The root mean square uncertainty in the metric is:

�g =

vuut(� _ms

_mp

j@ @g

_ms_mp

j)2 + (�Tpj

@g

@Tpj)2(�Tsj

@g

@Tsj)2: (6)

This gives an average uncertainty of�0.0252 for the conditions of the test.

24

Figure 17: Pumping Performance w/ Uncertainties

25

A.2 Mixing Parameter Uncertainty

The mixing parameter is a function of the individual temperature readings at the exit of the ejector

(T) as well as the position of the translation stage (r):

� =

RT 22 dA2

A2 � �T22 (7)

which, for the discrete measurements at the end of the ejector, can be approximated as:

� =�

A2�T22

10Xi=1

0:5(T 2i+1jri+1j+ T 2

i jrij)�r (8)

for which the root mean square uncertainty is:

�� =

s(j��T

@�

@ �Tj)2 + (j�T1

@�

@T1j)2 + (j�T2

@�

@T2j)2 + : : :+ (j�T11

@�

@T11j)2 + (j�r

@�

@rj)2: (9)

This gives an uncertainty of around�0.00128.

A.3 Temperature Reduction Uncertainty

The percent temperature reduction is a function of the average, primary, and secondary tempera-

tures:

T% =Tp � �T

Ts(10)

So the uncertainty in the temperature reduction is:

�T% =

vuut(j�Tp@T%

@Tpj)2 + (j�Ts

@T%

@Tsj)2 + (j��T

@T%

@ �Tj)2 (11)

which gives an average uncertainty of�0.143 over the testing conditions.

26

Figure 18: Mixing Performance w/ Uncertainties

27

Figure 19: Temperature Reduction w/ Uncertainties

28

B Testing Procedure

B.1 Micro-Engine Ejector-Mixer Test Procedure

1. Mount and align test pieces to be tested

2. Align station 3 thermocouple and determine temperature field z-locations

3. On a cold start, record pressures and temperatures at all locations

4. Check pipe seals and heater continuity

5. Turn on air

� Close regulator and hose valve

� Turn on oil free compressor

� Open two supply valves to regulator

� Open regulator to 50 psig

6. Slowly open hose valve to achieve desired volume flow

� For high volume flow tests, want 1.878 PPM @ standard conditions

� For low volume flow tests, want 64.701 SCFH @ standard conditions

7. Turn on heater (and heating tape for low Reynolds number tests) and adjust voltage until

thermocouple at station 2 reads 76.9�C

8. Record data

� Test date and time.

� Ambient pressure and temperature

� Pressure and temperature at stations 1 and 2

� Pressure at stage 3

� Rotameter volume flow reading

29

� 11 temperature measurements along diameter of ejector exit from bottom to top (station

3)

� Variac percentage(s) of max voltage

� Pressure at station 1 and temperature at station 2 (again)

� Notes

9. Turn off heater

10. Close regulator and hose valve. Prepare for next test or turn off compressor

30

B.2 Sample Data Sheet

31

C Numerical Analysis

This appendix contains samples of the source code for the data analysis used in the project.

C.1 performance.m

% Matlab script to reduce ejector-mixer test data and output% performance metrics%% Authors: Mark Monroe & Nathan Fitzgerald% Created: 11=19=01% Modified: 12=3=01

% Clear workspace and prompt user for name of file to use

clear all 10

close allfilename = ['test1 ''test2 ''test3 ''test4 ''test5 ''test6 ''test7 ''test8 ''test9 ' 20

'test10''test11''test12''test00'];

AR3r = linspace(�0.986=2, 0.986=2, 11);AR1r = linspace(�0.698=2, 0.698=2, 11);

for i2=1:length(filename)30

eval(filename(i2,:))

% Calibrate data to initial cold start values

for i = 1:4error = Temps(1,1) � Temps(i,1);TempsMod(i) = Temps(i,2) + error + 273.15;if i == 3

32

Tpi = Temps(i,2) + error + 273.15;Tpf = Final(2) + error + 273.15; 40

endendTempsMod(5:14) = Temps(5:14,2) + error + 273.15;

PressuresMod = Pressures(:,2).�6.894757361e3;

% Determine radii vector

if Parameters(2) == 1radius = AR1r; 50

elseradius = AR3r;

endarea =pi � (radius(11))ˆ2;

% Define instrument errors

if Parameters(4) == 1TCerr = 0.1;

else 60

TCerr = 0.5;endPerr = 2.0265e3;Rerr = 0.001 = 39.37007874;%Rerr = 0;

% Find average exit temperature

TempsExit = TempsMod(4:14);Integrand = TempsExit .� abs(radius); 70

Tbar = pi�trapz(radius,Integrand)=area;

Integrand = TempsExit.̂2.�abs(radius);mixing = pi�trapz(radius,Integrand)=area=Tbar̂ 2;

dr = radius(11) � radius(10);

% Mixing Error BarsDmixing = (Rerr � abs(pi � (abs(radius(1)) � TempsExit(1)ˆ2 + . . .

abs(radius(11)) � TempsExit(11)ˆ2 + . . . 80

sum(abs(radius(2:10)) .� TempsExit(2:10).ˆ2)) = 2 = Tbar̂ 2 = area))̂ 2Dmixing = Dmixing + (TCerr � abs(dr � pi � (abs(radius(1)) � TempsExit(1)ˆ2 + . . .

33

abs(radius(11)) � TempsExit(11)ˆ2 + . . .sum(abs(radius(2:10)) .� TempsExit(2:10).ˆ2)) = Tbar̂ 3 = area))̂ 2

Dmixing = Dmixing + (TCerr � abs(pi � dr � radius(1) � TempsExit(1) . . .= Tbar̂ 2 = area))̂ 2

Dmixing = Dmixing + (TCerr � abs(pi � dr � radius(11) � TempsExit(11) . . .= Tbar̂ 2 = area))̂ 2

for j = 2:10Dmixing = Dmixing + (TCerr � abs(2 � pi � dr � radius(j) � . . . 90

TempsExit(j) = Tbar̂ 2 = area))̂ 2endDmixing = sqrt(Dmixing);

% Pumping Error Bars% Corrected Pumping Error Bars% Tempurature reduction error bars% Pressure reduction error bars

100

% Performance MetricsTp = (Tpi + Tpf) = 2;pumping = (Tp�Tbar)=(Tbar�TempsMod(1));Dpumping = (TCerr� abs(1 = (Tbar � TempsMod(1))))ˆ2Dpumping = Dpumping + (TCerr�abs((Tp�TempsMod(1))=(Tbar�TempsMod(1))ˆ2))ˆ2

%Dpumping = Dpumping + (TCerr � abs((Tp - Tbar)=(Tbar - Temps Mod(1))ˆ2%Dpumping = Dpumping + 1= (Tbar - Temps Mod(1))))ˆ2Dpumping = Dpumping +(TCerr� abs((Tp � Tbar)=(Tbar � TempsMod(1))ˆ2))ˆ2; 110

Dpumping = sqrt(Dpumping)

corr pumping = pumping�sqrt(TempsMod(1)=Tp);Dcorr pumping = (Dpumping�sqrt(TempsMod(1)=Tp))̂ 2Dcorr pumping = Dcorrpumping + (TCerr�(.5�pumping=sqrt(Tp�TempsMod(1))))ˆ2Dcorr pumping = Dcorrpumping + (TCerr�(.5�pumping�sqrt(TempsMod(1)=Tpˆ3)))ˆ2Dcorr pumping = sqrt(Dcorr pumping)

Temp redux = (Tp�Tbar)=Tp; 120

DTemp redux = (TCerr=TempsMod(1))ˆ2DTemp redux = DTempredux + (TCerr=TempsMod(1))ˆ2DTemp redux = DTempredux + (TCerr�(Tp�Tbar)=TempsMod(1)ˆ2)ˆ2DTemp redux = sqrt(DTemp redux)pressureredux = (PressuresMod(1)�PressuresMod(4))=PressuresMod(1);DPressureredux = (Perr=PressuresMod(1))ˆ2

34

DPressureredux = DPressureredux + (Perr�PressuresMod(4)=PressuresMod(1)ˆ2)ˆ2DPressureredux = sqrt(DPressureredux)

130

correctedvol = Volume(2)�sqrt(TempsMod(2)�101325=294.26=PressuresMod(2));if Parameters(4) == 1

massflow = correctedvol � 1.2 � (28.3168e�3)=3600;else

massflow = correctedvol = 60 = 2.2046226;end

Reynolds =4�massflow=pi=(2.07e�5)=.0125;140

Analysis(i2,:) = [ Parameters, Tbar, mixing, pumping, corrpumping, . . .Temp redux�100, pressureredux�100, massflow, Reynolds, TempsExit, radius, . . .

Dmixing, TempsMod(1), TempsMod(3), Dpumping, Dcorrpumping, . . .DTemp redux�100, DPressureredux�100];

end

area o = linspace(0,5,100);temp o = 1; 150

[area p, temp p] = meshgrid(area o, temp o);

a = tempp.�((1.=areap.̂ 2)+1);b = 2�(temp p+1);c= �2�area p;pumping p = (�b.=(2�a))+((((b.̂ 2)�4.�a.�c).̂ .5).=(2�a));

160

%% Plots w= Error bars

% pumping ratio as a function of area ratio% for each of the 2 LD’s separatelyfiguresubplot(2,1,1) % LD of 1hold onplot(area p, pumpingp) 170

35

% Free - lowplot([Analysis(7,2),Analysis(9,2)],. . .

[Analysis(7,8),Analysis(9,8)], 'ob')% Free - highplot([Analysis(1,2), Analysis(5,2)], . . .

[Analysis(1,8), Analysis(5,8)], 'or')% Conv - lowplot([Analysis(12,2)], [Analysis(12,8)], 'xb')% Conv - highplot([Analysis(4,2)], [Analysis(4,8)], 'xr') 180

% Free - lowerrorbar([Analysis(7,2),Analysis(9,2)],. . .

[Analysis(7,8),Analysis(9,8)], . . .[Analysis(7,39), Analysis(9,39)],'ob')

% Free - higherrorbar([Analysis(1,2), Analysis(5,2)], . . .

[Analysis(1,8), Analysis(5,8)], . . .[Analysis(1,39), Analysis(5,39)],'or')

% Conv - lowerrorbar([Analysis(12,2)], [Analysis(12,8)], [Analysis(12,39)], 'xb') 190

% Conv - higherrorbar([Analysis(4,2)], [Analysis(4,8)], Analysis(4,39), 'xr')xlabel('Area Ratio')ylabel('Corrected Pumping')title('L/D =1')legend('Model','Free, Re-low','Free, Re-high', . . .

'Conv, Re-low','Conv, Re-high')

subplot(2,1,2) % LD of 4 200

hold onplot(area p, pumpingp)% Free - lowplot([Analysis(8,2),Analysis(10,2)],. . .


[Analysis(2,8), Analysis(6,8)], 'or')% Conv - lowplot([Analysis(11,2)], [Analysis(11,8)], 'xb') 210

% Conv - highplot([Analysis(3,2)], [Analysis(3,8)], 'xr')errorbar([Analysis(8,2),Analysis(10,2)],. . .

[Analysis(8,8),Analysis(10,8)], . . .

36

[Analysis(8,39), Analysis(10,39)],'ob')% Free - higherrorbar([Analysis(2,2), Analysis(6,2)], . . .


% Conv - low 220

errorbar([Analysis(11,2)], [Analysis(11,8)], [Analysis(11,39)], 'xb')% Conv - higherrorbar([Analysis(3,2)], [Analysis(3,8)], [Analysis(3,39)], 'xr')

xlabel('Area Ratio')ylabel('Corrected Pumping')title('L/D =4')legend('Model','Free, Re-low','Free, Re-high', . . .

'Conv, Re-low','Conv, Re-high')230

% mixing parameter as a function of L=D% for each of the 2 AR’s separatelyfigurerange = linspace(.5,5,10);idealmixing = ones(1,length(range));subplot(2,1,1) % Area Ratio of 1hold onplot(range, idealmixing)plot(range, Analysis(13,6)�ones(1,length(range)),'--k') 240


[Analysis(8,6),Analysis(9,6)],'ob')% Free - highplot([Analysis(5,3), Analysis(6,3)], . . .

[Analysis(5,6), Analysis(6,6)],'or')% Free - lowerrorbar([Analysis(8,3),Analysis(9,3)],. . .

[Analysis(8,6),Analysis(9,6)],. . .[Analysis(8,35),Analysis(9,35)],'ob') 250


[Analysis(5,6), Analysis(6,6)],. . .[Analysis(5,35),Analysis(6,35)],'or')

xlabel('Length / Diameter Ratio')ylabel('Mixing Parameter')title('AR = 1')legend('Ideal','Worst','Free, Re-low','Free, Re-high')

37

subplot(2,1,2) % Area Ration of 3 260

hold onplot(range, idealmixing)plot(range, Analysis(13,6)�ones(1,length(range)),'--k')% Free - lowplot([Analysis(7,3),Analysis(10,3)],. . .


[Analysis(1,6), Analysis(2,6)], 'or')% Conv - low 270

plot([Analysis(11,3),Analysis(12,3)],. . .[Analysis(11,6),Analysis(12,6)], 'xb')

% Conv - highplot([Analysis(3,3), Analysis(4,3)], . . .

[Analysis(3,6), Analysis(4,6)], 'xr')


[Analysis(7,6),Analysis(10,6)],. . .[Analysis(7,35),Analysis(10,35)],'ob') 280




[Analysis(11,6),Analysis(12,6)],. . .[Analysis(11,35),Analysis(12,35)],'ob')

% Free - higherrorbar([Analysis(3,3), Analysis(4,3)], . . . 290


xlabel('Length / Diameter Ratio')ylabel('Mixing Parameter')title('AR = 3')legend('Ideal','Worst','Free, Re-low','Free, Re-high', . . .


% temperature reduction as a function of area ratio 300

% for each of the 2 LD’s separatelyfigure

38

subplot(2,1,1) % LD of 1hold on%idealplot(area p,(54=300)�ones(1,length(area p))�100)% Free - lowplot([Analysis(7,2),Analysis(9,2)],. . .

[Analysis(7,9),Analysis(9,9)], 'ob')% Free - high 310

plot([Analysis(1,2), Analysis(5,2)], . . .[Analysis(1,9), Analysis(5,9)], 'or')

% Conv - lowplot([Analysis(12,2)], [Analysis(12,9)], 'xb')% Conv - highplot([Analysis(4,2)], [Analysis(4,9)], 'xr')% Free - lowerrorbar([Analysis(7,2),Analysis(9,2)],. . .

[Analysis(7,9),Analysis(9,9)], . . .[Analysis(7,40),Analysis(9,40)], 'ob') 320


[Analysis(1,9), Analysis(5,9)], . . .[Analysis(1,40), Analysis(5,40)], 'or')

% Conv - lowerrorbar([Analysis(12,2)], [Analysis(12,9)], [Analysis(12,40)], 'xb')% Conv - higherrorbar([Analysis(4,2)], [Analysis(4,9)],[Analysis(4,40)], 'xr')

xlabel('Area Ratio') 330

ylabel('Temperature Reduction (%)')title('L/D =1')legend('ideal','Free, Re-low','Free, Re-high', . . .


subplot(2,1,2) % LD of 4hold on%idealplot(area p,(54=300)�ones(1,length(area p))�100) 340



[Analysis(2,9), Analysis(6,9)], 'or')

39

% Conv - lowplot([Analysis(11,2)], [Analysis(11,9)], 'xb')% Conv - highplot([Analysis(3,2)], [Analysis(3,9)], 'xr') 350


[Analysis(8,9),Analysis(10,9)], . . .[Analysis(8,40),Analysis(10,40)],'ob')



% Conv - lowerrorbar([Analysis(11,2)], [Analysis(11,9)], [Analysis(11,40)], 'xb') 360

% Conv - higherrorbar([Analysis(3,2)], [Analysis(3,9)],[Analysis(3,40)], 'xr')

xlabel('Area Ratio')ylabel('Temperature Reduction (%)')title('L/D =4')legend('ideal','Free, Re-low','Free, Re-high', . . .


% % pressure reduction as a function of area ratio 370

% % for each of the 2 LD’s separately% %figure% %subplot(2,1,1) % LD of 1% hold on% % Free - low% plot([Analysis(7,2),Analysis(9,2)],. . .% [Analysis(7,10),Analysis(9,10)], ’ob’)% % Free - high% plot([Analysis(1,2), Analysis(5,2)], . . .% [Analysis(1,10), Analysis(5,10)], ’or’) 380

% % Conv - low% plot([Analysis(12,2)], [Analysis(12,10)], ’xb’)% % Conv - high% plot([Analysis(4,2)], [Analysis(4,10)], ’xr’)% errorbar([Analysis(7,2),Analysis(9,2)],. . .% [Analysis(7,10),Analysis(9,10)], . . .% [Analysis(7,41),Analysis(9,41)],’ob’)% % Free - high% errorbar([Analysis(1,2), Analysis(5,2)], . . .% [Analysis(1,10), Analysis(5,10)], . . . 390

40

% [Analysis(1,41),Analysis(5,41)], ’or’)% % Conv - low% errorbar([Analysis(12,2)], [Analysis(12,10)],[Analysis(12,41)],’xb’)% % Conv - high% errorbar([Analysis(4,2)], [Analysis(4,10)], [Analysis(4,41)], ’xr’)% xlabel(’Area Ratio’)% ylabel(’Pressure Reduction (%)’)% ax = axis;% axis([0 5 ax(3:4)])% title(’L=D =1’) 400

% legend(’Free, Re-low’,’Free, Re-high’, . . .% ’Conv, Re-low’,’Conv, Re-high’)%%% subplot(2,1,2) % LD of 4% hold on% % Free - low% plot([Analysis(8,2),Analysis(10,2)],. . .% [Analysis(8,10),Analysis(10,10)],’ob’)% % Free - high 410

% plot([Analysis(2,2), Analysis(6,2)], . . .% [Analysis(2,10), Analysis(6,10)], ’or’)% % Conv - low% plot([Analysis(11,2)], [Analysis(11,10)], ’xb’)% % Conv - high% plot([Analysis(3,2)], [Analysis(3,10)], ’xr’)% errorbar([Analysis(8,2),Analysis(10,2)],. . .% [Analysis(8,10),Analysis(10,10)], . . .% [Analysis(8,41), Analysis(10,41)], ’ob’)% % Free - high 420

% errorbar([Analysis(2,2), Analysis(6,2)], . . .% [Analysis(2,10), Analysis(6,10)], . . .% [Analysis(2,41), Analysis(6,41)], ’or’)% % Conv - low% errorbar([Analysis(11,2)], [Analysis(11,10)], [Analysis(11,41)], ’xb’)% % Conv - high% errorbar([Analysis(3,2)], [Analysis(3,10)], [Analysis(3,41)], ’xr’)% ax = axis;% axis([0 5 ax(3:4)])% xlabel(’Area Ratio’) 430

% ylabel(’Pressure Reduction (%)’)% title(’L=D =4’)% legend(’Free, Re-low’,’Free, Re-high’, . . .% ’Conv, Re-low’,’Conv, Re-high’)

41

% Data from “Short Efficient Ejector Systems”, Presz%

% Note: The penetration of our mixer is about 60% 440

% AR = 0.52, LD = 1, Penetration = 44%, Diffuser Angle = 6 deg, Re High

LobeAngle = [0 15 20 25];K1 = [0.48 0.87 0.98 0.92];OurLobe = [20,0];Tratio = [Analysis(4,36)=Analysis(4,37), Analysis(5,36)=Analysis(5,37)];Aratio = [3, 1];OurPumping = [Analysis(4,7),Analysis(5,7)];OurIdeal = sqrt(1.=Tratio).�(�2+2.�(1+0.5.�(Aratio + 1.=Aratio)).̂ 0.5).=(1+. . . 450

(1.=Aratio).̂ 2);OurK =OurPumping.=OurIdeal;figuresubplot(2,1,1)plot(LobeAngle,K1,'rx',OurLobe,OurK,'bo')xlabel('Lobe Angle (deg)')ylabel('Pumping Ratio / Model Pumping Ratio')title('Ejector-Mixer Data Comparison')legend('WNEC Data','16.622 Data',2);

460

% AR = 0.52, LD = 1, Diffuser Angle = 0 deg, Lobe Angle = 25 deg, Re High

K2 = [0.57 0.81 0.93 1.08];Penetration = [0 28 44 57];OurPen = [60, 0];subplot(2,1,2)plot(Penetration,K2,'rx',OurPen,OurK,'bo')xlabel('Penetration (%)')ylabel('Pumping Ratio / Model Pumping Ratio') 470

legend('WNEC Data','16.622 Data',2);

%% Plots w=o Error bars

% pumping ratio as a function of area ratio

42

% for each of the 2 LD’s separatelyfigure 480

subplot(2,1,1) % LD of 1hold offplot(area p, pumpingp)hold on% Free - lowplot([Analysis(7,2),Analysis(9,2)],. . .


[Analysis(1,8), Analysis(5,8)], 'or') 490

% Conv - lowplot([Analysis(12,2)], [Analysis(12,8)], 'xb')% Conv - highplot([Analysis(4,2)], [Analysis(4,8)], 'xr')xlabel('Area Ratio')ylabel('Corrected Pumping')title('L/D =1')legend('Model','Free, Re-low','Free, Re-high', . . .

'Conv, Re-low','Conv, Re-high')500

subplot(2,1,2) % LD of 4hold offplot(area p, pumpingp)hold on% Free - lowplot([Analysis(8,2),Analysis(10,2)],. . .

[Analysis(8,8),Analysis(10,8)], 'ob')% Free - highplot([Analysis(2,2), Analysis(6,2)], . . . 510

[Analysis(2,8), Analysis(6,8)], 'or')% Conv - lowplot([Analysis(11,2)], [Analysis(11,8)], 'xb')% Conv - highplot([Analysis(3,2)], [Analysis(3,8)], 'xr')avg error = mean(Analysis(1:12,39));ax = axis;errorbar([(ax(2)�ax(1))�0.98+ax(1)], [(ax(4)�ax(3))�0.2+ax(3)], [avg error],'k')text((ax(2)�ax(1))�0.65+ax(1),(ax(4)�ax(3))�0.2+ax(3),. . .

strcat('Avg. Uncertainty = \pm',num2str(avg error,3))) 520

xlabel('Area Ratio')

43

ylabel('Corrected Pumping')title('L/D =4')legend('Model','Free, Re-low','Free, Re-high', . . .


% mixing parameter as a function of L=D% for each of the 2 AR’s separately 530

figurerange = linspace(.5,5,10);idealmixing = ones(1,length(range));subplot(2,1,1) % Area Ratio of 1hold onplot(range, idealmixing)plot(range, Analysis(13,6)�ones(1,length(range)),'--k')% Free - lowplot([Analysis(8,3),Analysis(9,3)],. . .

[Analysis(8,6),Analysis(9,6)],'ob') 540

% Free - highplot([Analysis(5,3), Analysis(6,3)], . . .

[Analysis(5,6), Analysis(6,6)],'or')

xlabel('Length / Diameter Ratio')ylabel('Mixing Parameter')title('AR = 1')legend('Ideal','Worst','Free, Re-low','Free, Re-high')

subplot(2,1,2) % Area Ration of 3 550

hold onplot(range, idealmixing)plot(range, Analysis(13,6)�ones(1,length(range)),'--k')% Free - lowplot([Analysis(7,3),Analysis(10,3)],. . .


[Analysis(1,6), Analysis(2,6)], 'or')% Conv - low 560

plot([Analysis(11,3),Analysis(12,3)],. . .[Analysis(11,6),Analysis(12,6)], 'xb')

% Conv - highplot([Analysis(3,3), Analysis(4,3)], . . .

[Analysis(3,6), Analysis(4,6)], 'xr')

44

avg error = mean(Analysis(1:12,35));ax = axis;text((ax(2)�ax(1))�0.65+ax(1),(ax(4)�ax(3))�0.2+ax(3),. . .

strcat('Avg. Uncertainty = \pm',num2str(avg error,3))) 570

errorbar((ax(2)�ax(1))�0.98+ax(1),(ax(4)�ax(3))�0.2+ax(3),avg error,'k')xlabel('Length / Diameter Ratio')ylabel('Mixing Parameter')title('AR = 3')legend('Ideal','Worst','Free, Re-low','Free, Re-high', . . .


% temperature reduction as a function of area ratio% for each of the 2 LD’s separatelyfigure 580



[Analysis(1,9), Analysis(5,9)], 'or') 590

% Conv - lowplot([Analysis(12,2)], [Analysis(12,9)], 'xb')% Conv - highplot([Analysis(4,2)], [Analysis(4,9)], 'xr')

xlabel('Area Ratio')ylabel('Temperature Reduction (%)')title('L/D =1')legend('ideal','Free, Re-low','Free, Re-high', . . .

'Conv, Re-low','Conv, Re-high') 600


[Analysis(8,9),Analysis(10,9)], 'ob')% Free - high 610

45

plot([Analysis(2,2), Analysis(6,2)], . . .[Analysis(2,9), Analysis(6,9)], 'or')

% Conv - lowplot([Analysis(11,2)], [Analysis(11,9)], 'xb')% Conv - highplot([Analysis(3,2)], [Analysis(3,9)], 'xr')% Free - low

avg error = mean(Analysis(1:12,40));ax = axis; 620

text((ax(2)�ax(1))�0.65+ax(1),(ax(4)�ax(3))�0.2+ax(3),. . .strcat('Avg. Uncertainty = \pm',num2str(avg error,3),'%'))

errorbar((ax(2)�ax(1))�0.98+ax(1),(ax(4)�ax(3))�0.2+ax(3),avg error,'k')xlabel('Area Ratio')ylabel('Temperature Reduction (%)')title('L/D =4')legend('ideal','Free, Re-low','Free, Re-high', . . .


print �f1 �djpeg PumpingNoError 630

print �f2 �djpeg MixingNoErrorprint �f3 �djpeg TempNoErrorprint �f4 �djpeg Compprint �f5 �djpeg PumpingErrorprint �f6 �djpeg MixingErrorprint �f7 �djpeg TempError

% % pressure reduction as a function of area ratio% % for each of the 2 LD’s separately% figure 640

% subplot(2,1,1) % LD of 1% hold on% % Free - low% plot([Analysis(7,2),Analysis(9,2)],. . .% [Analysis(7,10),Analysis(9,10)], ’ob’)% % Free - high% plot([Analysis(1,2), Analysis(5,2)], . . .% [Analysis(1,10), Analysis(5,10)], ’or’)% % Conv - low% plot([Analysis(12,2)], [Analysis(12,10)], ’xb’) 650

% % Conv - high% plot([Analysis(4,2)], [Analysis(4,10)], ’xr’)%% xlabel(’Area Ratio’)

46

% ylabel(’Pressure Reduction (%)’)% ax = axis;% axis([0 5 ax(3:4)])% title(’L=D =1’)% legend(’Free, Re-low’,’Free, Re-high’, . . .% ’Conv, Re-low’,’Conv, Re-high’) 660

%%% subplot(2,1,2) % LD of 4% hold on% % Free - low% plot([Analysis(8,2),Analysis(10,2)],. . .% [Analysis(8,10),Analysis(10,10)],’ob’)% % Free - high% plot([Analysis(2,2), Analysis(6,2)], . . .% [Analysis(2,10), Analysis(6,10)], ’or’) 670

% % Conv - low% plot([Analysis(11,2)], [Analysis(11,10)], ’xb’)% % Conv - high% plot([Analysis(3,2)], [Analysis(3,10)], ’xr’)%% ax = axis;% axis([0 5 ax(3:4)])% avg error = mean(Analysis(1:12,41));% ax = axis;% text((ax(2)-ax(1))�0.65+ax(1),(ax(4)-ax(3))�0.2+ax(3),. . . 680

% strcat(’Avg. Uncertainty = npm’,num2str(avg error,3),’%’))% xlabel(’Area Ratio’)% ylabel(’Pressure Reduction (%)’)% title(’L=D =4’)% legend(’Free, Re-low’,’Free, Re-high’, . . .% ’Conv, Re-low’,’Conv, Re-high’)

query = [ ];for i=1:12 690

test req = [1 1 4]if (Analysis(i,1:3)==test req)

query = [query ,Analysis(i,8)];end

end

percentinc = (query(2)�query(1))=query(1)

47

700

C.2 test1.m

%% Micro�Gas Turbine Engine Ejector�Mixer Testing Data

Parameters= [ 1 3 1 2 ]% Freesplitter=1 , Convoluted=2% area ratio% L to D ratio% low Re = 1 , high Re =2

10

Volume = [ 2 , 1.89 ];% SCFH =1 , PPM =2

Pressures= [14.788 14.78814.788 20.49014.788 16.18014.788 14.782]

% Column: 1�initial 2�test% Row:% 1�ambient 20

% 2�station 1% 3�station 2% 4�station 3

Temps= [22.7 23.223.2 22.923.2 77.022.9 26.60 37.6 30

0 55.50 73.60 76.60 77.10 77.00 73.10 54.30 38.0

48

0 26.8]% same convention as pressures with additional rowsfor temp 40

% feild at station3.

Final = [20.464 77.3]% 1�final pressure2�final temperature

49

D Technical Drawings

1. Ejector Shrouds

(a) Area ratio = 1, Length/Diameter = 1

(b) Area ratio = 1, Length/Diameter = 4

(c) Area ratio = 3, Length/Diameter = 1

(d) Area ratio = 3, Length/Diameter = 4

2. Base Plate

3. Convergent Duct Connector

4. Convergent Duct

5. Convoluted Mixer

6. Primary Jet Pipe

7. Primary Jet Pipe (adapted for convoluted mixer)

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Micro-Gas Turbine Engine Ejector-Mixer Design and...

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Transcript of Micro-Gas Turbine Engine Ejector-Mixer Design and...