DESIGN AND CONTROL OF A VARIABLE GEOMETRY TURBOFAN WITH AN INDEPENDENTLY MODULATED THIRD STREAM DISSERTATION Presented in Partial Fulfillment of the Requirements for the Degree Doctor of Philosophy in the Graduate School of The Ohio State University By Ronald J. Simmons, M.S. * * * * * The Ohio State University 2009 Dissertation Committee: Professor Meyer Benzakein, Adviser Professor Richard Bodonyi Approved by Professor Jeffrey Bons Professor Jen-Ping Chen Adviser Professor Nicholas J. Kuprowicz Aerospace Engineering Graduate Program
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DESIGN AND CONTROL OF A VARIABLE GEOMETRY TURBOFAN WITH AN
INDEPENDENTLY MODULATED THIRD STREAM
DISSERTATION
Presented in Partial Fulfillment of the Requirements for
the Degree Doctor of Philosophy in the Graduate
School of The Ohio State University
By
Ronald J. Simmons, M.S.
* * * * *
The Ohio State University
2009
Dissertation Committee:
Professor Meyer Benzakein, Adviser
Professor Richard Bodonyi
Approved by
Professor Jeffrey Bons
Professor Jen-Ping Chen
Adviser
Professor Nicholas J. Kuprowicz Aerospace Engineering Graduate Program
Distribution Statement A: Unlimited Distribution.
Cleared for Public Release by AFRL/WS Public Affairs
Case Number 88ABW-2009-1697
The views expressed in this article are those of the author and do not reflect the official policy or position
of the United States Air Force, Department of Defense, or the U.S. Government.
ii
ABSTRACT
Abstract
Emerging 21st century military missions task engines to deliver the fuel efficiency of a high bypass
turbofan while retaining the ability to produce the high specific thrust of a low bypass turbofan. This study
explores the possibility of satisfying such competing demands by adding a second independently modulated
bypass stream to the basic turbofan architecture. This third stream can be used for a variety of purposes
including: providing a cool heat sink for dissipating aircraft heat loads, cooling turbine cooling air, and
providing a readily available stream of constant pressure ratio air for lift augmentation. Furthermore, by
modulating airflow to the second and third streams, it is possible to continuously match the engine‟s
airflow demand to the inlet‟s airflow supply thereby reducing spillage and increasing propulsive efficiency.
This research begins with a historical perspective of variable cycle engines and shows a logical
progression to proposed architectures. Then a novel method for investigating optimal performance is
presented which determines most favorable on design variable geometry settings, most beneficial moment
to terminate flow holding, and an optimal scheduling of variable features for fuel efficient off design
operation. Mission analysis conducted across the three candidate missions verifies that these three stream
variable cycles can deliver fuel savings in excess of 30% relative to a year 2000 reference turbofan.
This research concludes by evaluating the relative impact of each variable technology on the
performance of adaptive engine architectures. The most promising technologies include modulated turbine
cooling air, variable high pressure turbine inlet area and variable third stream nozzle throat area. With just
these few features it is possible to obtain nearly optimal performance, including 90% or more of the
potential fuel savings, with far fewer variable features than are available in the study engine. It is
abundantly clear that three stream variable architectures can significantly outperform existing two stream
turbofans in both fuel efficiency and at the vehicle system level with only a modest increase in complexity
and weight. Such engine architectures should be strongly considered for future military applications.
iii
Dedication
Dedicated to my beloved bride Bonnie.
iv
ACKNOWLEDGMENTS
Acknowledgments
I wish to express thanks to my adviser, Professor Meyer Benzakein, and the entire dissertation
committee for creating plentiful intellectual challenges, providing emotional support, and offering an
almost inexhaustible supply of patience. You recognized potential in this aging student long before I did
and cultivated a desire to live up to your expectations.
Furthermore, I would like to acknowledge a number of consummate professionals at the Air Force
Research Laboratory (AFRL). Mr. Jeffrey Stricker, Mr. Tim Lewis, Mr. Chris Norden, Mr. Jed Cox, and
Mr. Greg Bruening for their insight into variable cycle engine operation and research guidance. It is likely
that this research would have been helplessly adrift without your steadfast direction.
Additionally, I would like to recognize Dr. Tom Curran of Universal Technology Corporation for
his research into the history of variable cycle engines. To Mr. Jim Felder, Mr. Scott Jones, Mr. Tom
Lavelle, and Mr. Scott Townsend of the NPSS support group at NASA Glenn research center, you have my
most sincere thanks; without your tireless efforts this research would not have been possible.
Finally, I would like to express my most sincere gratitude to my family for their support
throughout this process. To my wife Bonnie, may God richly bless you for cups of late night coffee and
inspirational words after a demoralizing test. To my children who have been a continuous motivation to
me, I pray that God fill your heart with dreams and the faith to achieve each of them. Most of all, I wish to
thank the Lord for seeing me through this course of study and working every hindrance for good (Romans
8:28); to God be all praise, honor and glory forever.
This work was supported by the Air Force Research Laboratory, Propulsion Directorate, Turbine
Engine Division, Engine Integration and Assessment Branch, Wright-Patterson AFB, OH. The U.S.
Government is authorized to reproduce and distribute reprints for Governmental purposes notwithstanding
any copyright notation thereon.
v
VITA
August 16, 1965 ............................ Born – Harvey, Illinois
1988 ............................................... B.S. Aeronautical Engineering, US Air Force Academy
B.S. Astronautical Engineering, US Air Force Academy
1990 ............................................... M.S. Aeronautical and Astronautical Engineering, MIT
1991-1994 ..................................... Assistant Professor of Astronautics, US Air Force Academy
2006-Present .................................. Doctoral Student, The Ohio State University
PUBLICATIONS
Research Publication
1. R. J. Simmons, J.E. Cox, N.J. Kuprowicz “System level benefits of a turbofan propulsion system
equipped with an independently modulated auxiliary stream.” 56th
JANNAF Propulsion Meeting, Boston
MA, (2008).
FIELD OF STUDY
Major Field: Aerospace Engineering
vi
TABLE OF CONTENTS
Page
Abstract .......................................................................................................................................................... ii Dedication ..................................................................................................................................................... iii Acknowledgments ..........................................................................................................................................iv VITA ............................................................................................................................................................... v List of tables ................................................................................................................................................. vii List of figures .............................................................................................................................................. viii Nomenclature .................................................................................................................................................. x
Point of Interest (POI) Optimization Read in off design parameters from GA
Rerun POIs (in parallel NPSS instances)
Each POI estimates objective function; see calculation details below
(NOTE - TSFCinst for other POI assumed)
Off Design Optimization Loop
GA selects new Fan, LPC, HPT, LPT Is Genetic Yes inlet guide vanes (IGV) & Fan A8 settings Algorithm Generation (NOTE - settings different for each POI)
< Max allowed? Optimization progresses subject to limits
on vane & nozzle displacements as well as max generations without improvement
No
Calculate overall objective function If POI failed to converge or a constraint
violated, set objective function = 5 * 108
Guess fuel load required for mission
Find fuel reserve with Breguet range eq.
using the TSFCinst calculated at each POI
If fuel reserve ≠ 10%, modify fuel load & iterate until a 10% reserve is obtained
Objective Function = Mission Fuel Load + penalties for undesirable behavior
If fuel load does not equal max fuel load, find max standoff range and loiter time
Print optimal off design settings and performance data for this design point
On Design Optimization Loop
GA selects new IGV settings, Op lines, Is Genetic Yes corrected speeds & 3rd stream bypass ratio
Algorithm Generation Optimization progresses subject to limits
< Max allowed? on vane displacements, corrected speeds,
minimum third stream bypass ratio, and max generations without improvement
No
Optimization Complete
Figure 23. Computation of objective function within nested optimization
32
Finally, there are many engine designs that are simply incapable of performing stated missions
with the available fuel load. As mentioned in the assumptions above, required fuel load is always
calculated without increasing the aircraft size to accommodate fuel loads greater than the predetermined
max takeoff fuel. This approach is consistent with an aircraft re-engining program, and required fuel loads
greater than max takeoff fuel are simply understood to represent unacceptable engine designs.
Furthermore, maximum achievable high altitude cruise leg (standoff range) and loiter time, if applicable, is
calculated for each engine; similarly, ranges and loiter times less than those stated in the mission represent
unacceptable engine designs. These range and loiter figures of merit will be discussed further in chapter 3.
2.8 Searching a discontinuous design space with numerous local minima
The search methodology outlined in section 2.7 describes a nested genetic algorithm structure used
to determine the most optimal variable cycle engine for a given mission. The reason for this search
architecture is quite simple; if one has an engine capable of varying internal geometries, and hence internal
flows, it is highly probable that the variable feature settings would vary from the design point to each cruise
point of interest. Furthermore, the amount of flow variation from the core to the second and third streams
is a strong function of the design point selected. Therefore to be effective, engine optimization must
simultaneously investigate both the on design search space and the associated off design search space at
each cruise point of interest.
While the basic search architecture appears self evident, the selection of an appropriate
optimization method is a bit more difficult. To begin this process one must first understand the nature of
the on and off design search spaces. Both of these are replete with locations that violate either explicitly
stated design constraints such as minimum surge margin, maximum shaft speed, or maximum fan diameter,
or simply will not satisfy the most basic physical cycle requirements including shaft balance, mixing plane
pressure balance or maintaining subsonic flow in all ducts. While intelligently limiting the design variable
search range can mitigate some of these effects, there still exists a myriad of locations throughout the
search space for which no converged solution is possible. Unfortunately, the objective function response
surface not only has a number of unacceptable locations with essentially infinite cost, but it also abounds
33
with local minima (Millhouse, 2002). Therefore, the selection of a suitable search algorithm is absolutely
essential to making a reasonable exploration of this objective function and to drawing rational conclusions.
Each of the algorithms considered here begins with a specified range on each design variable.
Then this search space is discretized or seeded with a reasonable number of initial points. How one
proceeds from this initial state determines the character, efficiency, and reliability of the search method.
For example, a purely random search would arbitrarily sample the design space within the specified range.
With sufficient sampling locations this unstructured search would provide a reasonable understanding of
the space but would likely not return the global minimum of the cost function. Such a search would require
a large number of sample points, especially as the number of design variables increased, and therefore a
greater computational time than its structured counterpart; however, random searches do not typically fail
even in a completely random design space.
Although the objective function is remarkably complex in this problem, it is not random; for this
reason one might be compelled to explore a more structured search algorithm. The simplest such structured
algorithm is known as an enumerative or grid based search in which the search space in a divided into an
evenly spaced grid across the user defined range space. The cost function is then evaluated at each of the
intersections and a relative minimum is located among these initial points. At the lowest objective function
location, the grid is refined by reducing the spacing between grid points and the cost function is again
evaluated at each intersection. The process continues until a specified number of refinements has been
accomplished or until the grid size reaches a predetermined minimum, see figure 24.
Figure 24. Grid based search algorithm with one grid refinement
34
This rudimentary enumerative search is capable of finding a minimum value using a comparable
number of objective function evaluations as used in a random search. However if a cost function has many
local minima, the value returned by this method is not likely to be the global minimum. The easiest way to
mitigate this problem would be to increase the number of points in the original gridding thereby increasing
the probability that the global minimum is located. Unfortunately a finely gridded search significantly
increases the computation time required for even a modest sized multidimensional problem, thereby
rendering this methodology unacceptable for this study.
In an effort to avoid computationally intensive enumerative searches, researchers have developed
a family of algorithms known as calculus or gradient based optimizers. In their simplest form, these
methods begin from a seed point and attempt to find the minimum of an objective function by continuously
moving in the most favorable, or maximum gradient, direction. It is important to note that such methods
need not evaluate the partial derivatives of the cost function with respect to each design variable to be
successful; therefore, they can be used effectively on discontinuous objective functions. A rudimentary
gradient based search is illustrated in Figure 25. This search begins at point A and evaluates the objective
at each of the surrounding grid points x using a fixed step size. The search progresses to the lowest of these
objective evaluations B. This movement in the direction of the maximum gradient continues until a relative
minimum is located, here point D. The grid is then refined further and the process continues until a user
defined minimum step size is reached.
Figure 25. Gradient based search algorithm with one grid refinement
35
Gradient based methods require far fewer objective evaluations than random or grid based
searches described above and yield very good results for functions with a single minimum. However, these
methods often fail to return optimal solutions in functions with multiple local minima or when the initial
point is selected far from the global minimum (Goldberg, 1989). There are a number of modifications to
this basic architecture that can be employed to improve the probability that a more global minimum is
located in functions with several local minima. For example, one could begin with multiple initial points
and find local minima associated with each. Additionally, one could modify the gradient method to
incorporate random step directions, random step sizes or even the occasional movement in a direction with
a higher objective function (often called simulated annealing). These three modifications attempt to help
the algorithm move out of flat regions or local minima in which the search algorithm is currently „stuck‟.
With each modification, the computational time increases along with the probability that a more global
optimum would be located. Unfortunately even with the modifications outlined above, gradient based
searches are incapable of adequately searching the vast, discontinuous and noisy search space of this study.
Fortunately there is a search algorithm that is able to locate a global optimum with the regularity
of a fine mesh grid while requiring significantly fewer objective function calls. These search methods,
called genetic algorithms, begin by discretizing the search space between the allowable minimum and
maximum values. Then this space is seeded with a set of representative designs, called a population,
throughout this space. It is important to note that although this initial population is generally much smaller
than its traditional grid search counterpart, the very nature of a genetic algorithm yields a much higher
resolution than a grid search with the same gridding.
This increased resolution is accomplished by the unique nature by which subsequent points are
selected in a genetic algorithm. First each individual design in a population is described by a chromosome,
which is a series of ones and zeros that represents the design variable selection for that individual. The
objective function is evaluated for this and every individual in the initial generation. The most promising
designs are then chosen to reproduce in this generation; this process is called selection and determines not
only those who will reproduce but also the rate at which they will do so. During this reproduction,
elements of the parent chromosomes will pair together to form children with characteristics similar to the
parents. Finally, occasional random changes to the child chromosomes will be made in a process known as
36
mutation in an effort to recover genetic material lost in the selection or crossover processes. This process is
summarized for a notional two variable system in figure 26.
Figure 26. Creation of new generation via a genetic algorithm
While not as efficient as calculus based algorithms at solving problems whose objective has a
single minima, genetic algorithms have proven remarkably robust across a broad spectrum of problems. It
accomplishes this first by working with a population of points rather than a single point; this population,
which becomes increasingly well adapted with each generation, reduces the probability of reaching a false
minima. Second, the genetic algorithm uses objective function information only and not its derivatives nor
any other auxiliary information; this eliminates any susceptibility to discontinuities in the cost function and
makes them applicable to virtually any problem. Finally, genetic algorithms make use of probabilistic
transition rules to guide the search to more promising regions of the search space (Goldberg, 1989). These
unique features make a genetic algorithm well suited to search the immense, noisy, and discontinuous
search space presented in this study.
37
CHAPTER 3
RESULTS
3.0 Results
During the course of this research several million variable cycle engine designs were evaluated
using the optimization method outlined above. Through analysis of this data a great deal of insight into the
nature and potential of the double bypass engine was garnered. This chapter begins by summarizing some
of the major design, control, and computational lessons learned. Then an optimal variable cycle is
presented for each vision mission along with a schedule of variable features at each point of interest.
Finally, a study of the variable features with greatest performance enhancement is conducted and a sub-
optimal variable cycle is recommended for each mission which achieves superior performance with the
fewest variable features.
3.1 Termination of flow holding
Early in the research it became apparent that the double bypass VCE examined in this study was
remarkably adept at holding corrected airflow to very low power settings. While this is traditionally touted
as a significant benefit of variable cycles, one begins to wonder if indefinite flow holding truly yields the
minimum fuel use. Furthermore, prolonged flow holding could cause even more troubling aerodynamic or
mechanical problems. For these reasons some effort was expended in determining the most advantageous
time to terminate flow holding.
The following discussion is based on a notional tactical mobility engine operating at the high
cruise point of interest. The control of this engine has been modified to hold airflow until one or more of
the following physical limits is reached: compressor pressure ratio of one, no airflow in a duct approaching
a mixing plane, or supersonic flow in a duct. Therefore, the illustrations that follow do not represent the
optimal control of a variable cycle engine, but rather a depiction of the changes in internal flow and the
38
associated costs of indefinitely holding engine airflow constant. At the termination of this analysis, a more
appropriate time for termination of flow holding will be offered along with the associated enhancements in
cycle performance.
Figures 27 and 28 further illustrate the basic concepts of flow holding first introduced in Table 2.
Notice in Figure 27 that the overall engine airflow remains constant even though power is reduced. This is
primarily accomplished by closing the LPC inlet, HPT inlet, and primary nozzle throat areas while
simultaneously increasing the fan nozzle throat area (detailed optimal engine control is presented in
sections 3.5 thru 3.7) This discourages flow to the engine core and the second stream while promoting flow
to the third stream. Therefore, both the bypass ratio to the third stream and the overall bypass ratio increase
as power is reduced (see Figure 28). If there were no associated costs associated with these flow changes,
one would gladly accept the associated decrease in spillage drag and increase in propulsive efficiency.
Unfortunately, indiscriminately varying these internal engine flows does come at a price. As will soon be
evident, the performance costs associated with excessively changing internal flows will ultimately exceed
any propulsive benefit realized.
Figure 27. Internal airflow variations with unrestricted flow holding
0
50
100
150
200
250
60 65 70 75 80 85 90 95 100
Mas
s Fl
ow (l
b m)
% Military Thrust
Unrestricted Flow Holding, Airflow vs. Installed Thrust
Overall Airflow
Third Stream Airflow
Second Stream Airflow
Core Airflow
39
Figure 28. Bypass ratio changes with unrestricted flow holding
A dramatic rise in duct losses associated with prolonged flow holding became evident in the
earliest days of this study. Figure 29 plots the losses in the third stream duct just aft of the fan exit plane
(labeled fan duct in figure 15) against percent military thrust. Remember that as power is reduced, airflow
is increased in the third stream and, therefore, the Mach number in this stream increases for a fixed duct
size. As total pressure loss in a duct is modeled as a function of Mach number squared,
Where: p is the total pressure in the duct
even a modest change in duct Mach number can have a significant impact on total pressure. Figure 29
shows that as fan duct Mach increases from 0.25 to 0.56, the pressure loss increases fivefold and reaches
nearly 16%.
While this duct pressure drop is a very real effect, it can be mitigated in two ways. First, the third
stream duct can be slightly oversized at the design point. In other words the Mach number in this duct
could be chosen to be 0.15 rather than the 0.25 as depicted in this illustration. By doing so, this duct is
sized to the desired airflow and Mach number at the cruise points of interest where the bypass ratio is much
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
4.5
60 65 70 75 80 85 90 95 100
Byp
ass
Rat
io
% Military Thrust
Unrestricted Flow Holding, Bypass Ratio vs. Installed Thrust
Overall BPR
BPR1
BPR2
40
greater. Second, flow holding can be terminated when the propulsive benefit of increased bypass ratio is
surpassed by the duct pressure drop and other losses. This second option will be developed further below.
Figure 29. Fan duct Mach number & pressure drop with unrestricted flow holding
The next problem noted with indefinite flow holding was that the excessive variations in inlet
areas can have undesirable effects on component performance. Figure 30 provides an example of this
degradation in performance on the low pressure compressor. Notice that as the power is reduced the inlet
area is also reduced (depicted in the figure by an increase in IGV setting). While this does encourage flow
to the third stream, inlet area variations continuously reduce the pressure ratio and ultimately the
component efficiency.
There is a clear physical limit on LPC inlet area defined by the minimum allowable component
pressure ratio of 1.0; this limit occurs at roughly 60% power in this example. However, a more stringent
LPC minimum pressure ratio of 1.2 is enforced in this study to minimize the potential for flutter and any
associated component damage; this limit occurs at approximately 70% power in this example. A closer
examination of figure 30 reveals that there may be a point prior to either of these two pressure ratio limits
where reductions in inlet area, and hence flow holding, should be ceased. Notice that below 90% thrust the
LPC efficiency begins to drop at an ever accelerating rate. In fact by 70% power, or 1.2 LPC pressure
0%
2%
4%
6%
8%
10%
12%
14%
16%
18%
0.0
0.1
0.2
0.3
0.4
0.5
0.6
60 65 70 75 80 85 90 95 100
Th
ird
Str
ea
m D
uct
Pre
ssu
re L
oss
(%
)
Th
ird
Str
ea
m D
uct
Ma
ch N
um
be
r
% Military Thrust
Unrestricted Flow Holding, Duct Losses vs. Installed Thrust
Fan Duct Mn
Fan Duct Loss
41
ratio, the adiabatic efficiency is just 54%. As this drop in efficiency is also noted in other variable
components, one can easily understand how reductions in thermal efficiency will eventually offset the
benefits of improved propulsive efficiency associated with flow holding.
Figure 30. LPC efficiency and pressure ratio changes with unrestricted flow holding
The final concern with indefinite flow holding is excessive variations in nozzle throat area.
Figures 27 showed that as power is reduced, flow is moved from the core and second streams to the third
stream. In order to maintain the operating lines of the fan and LPC, the fan and primary nozzle throat are
changed accordingly (see Figure 31). While the variations depicted here are not beyond the capabilities of
current technology, smaller variations or even fixed nozzles are desirable from a cost and survivability
standpoint. The strategy for flow hold termination outlined below ensures that nozzle areas vary by less
than 100% from their design point area. A brief analysis of mission performance with fixed nozzles will be
presented in section 3.9.
Given the duct and component losses described above, one can easily envision a point in the
power hook where the relative propulsive efficiency improvements and spillage drag reductions are offset
by the increased duct pressure loss and thermodynamic efficiency reductions. If flow holding were
continued below this thrust setting, the fuel efficiency would actually be poorer than if a conventional, non-
0.00
0.20
0.40
0.60
0.80
1.00
1.20
1.40
1.60
1.80
0.0
10.0
20.0
30.0
40.0
50.0
60.0
70.0
80.0
90.0
100.0
60 65 70 75 80 85 90 95 100
Ad
iab
ati
c E
ffic
ien
cy o
r P
ress
ure
Ra
tio
LPC
IGV
Se
ttin
g
% Military Thrust
Unrestricted Flow Holding, LPC Schedule vs. Installed Thrust
LPC IGV Setting
LPC Efficiency
LPC PR
42
Figure 31. Nozzle throat area variations with unrestricted flow holding
flow holding, power hook was performed. Figures 32 and 33 show the performance of this notional
mobility engine at two different cruise points of interests. Notice that the high altitude flow holding power
hook shows an increase in installed TSFC at approximately 87% power (79% power at low altitude); and
Figure 32. High cruise power hook with and without unrestricted flow holding
300
400
500
600
700
800
900
1000
60 65 70 75 80 85 90 95 100
No
zzle
Th
roat
Are
a
% Military Thrust
Unrestricted Flow Holding, Nozzle Throat Area vs. Installed Thrust
Primary Nozzle
Fan Nozzle
43
below this value, a conventional power hook yields superior performance. It should also be noted that the
variable cycle power hooks presented do not show any improved performance at military power; this is
because the variable geometry in these power hooks has only been fully optimized at the cruise points of
interest. Nevertheless, these figures should prove sufficient to reveal the motivation for termination of
flow holding prior to the point of interest. Power hooks with optimized vane and nozzle settings at each
part power point are presented in sections 3.5 thru 3.7.
Figure 33. Low cruise power hook with and without unrestricted flow holding
Unfortunately, formulating a general rule for the location of this minimum in the flow holding
power hook is difficult as it is a strong function of the engine design and the current operating conditions.
For this reason, termination of flow holding is determined real time at either the minimum in the TSFC
curve or the minimum allowable LPC pressure ratio, whichever comes first; a conventional power hook is
then executed to the desired point of interest. It should be mentioned that the mobility mission presented
here has minimal spillage drag and therefore, tends to cease flow holding relatively early. It will later
become apparent that the supersonic strike mission, with a great potential for spillage drag at high speed
cruise, justifies a more prolonged period of flow holding.
44
3.2 Changes in component efficiencies with variable architecture
As noted in the previous section, component efficiency is a strong function of inlet guide vane
setting and component corrected speed, Nc (where ). Therefore, one would expect that
rotating component efficiencies would vary from design point to each cruise point of interest. Figure 34
illustrates this effect for a notional compressor at a given inlet guide vane setting. Notice that as the engine
is throttled from the design point A to the cruise point B, compressor efficiency increases by three percent.
This is a reasonable and expected increase in efficiency.
Figure 34. Expected change in component efficiency from design point to cruise
Early in this study it became evident that the on design optimizer was manipulating design point
location on component maps in an effort to maximize efficiency at the off design point. Figure 35 shows
how this might look on the same notional compressor map in Figure 34. Notice that as the engine is
throttled form design point C to cruise point B, component efficiency now increases by an unrealistic five
percent. This rather simplistic illustration only begins to describe a much larger problem that is further
exacerbated by scale factors and layered component maps.
To fully grasp this dilemma, one must understand that most engine models incorporate existing
component maps and scale them to the required design point mass flow, efficiency and pressure ratio. For
45
Figure 35. Unrealistic change in component efficiency from design point to cruise
example, the efficiency of design point A in figure 34 is 80% on the map; by multiplying this efficiency
with a scale factor of 1.075 a desired design efficiency of 86% is obtained. As this scale factor is also used
at all off design points, the efficiency of point B is scaled to 0.89; again, this 3% increase in efficiency from
design point to off design point of interest is reasonable. Looking at design point C in figure 35, the 78%
map efficiency would need to be scaled by 1.103 to achieve the desired efficiency of 86%. Using this scale
factor the off design point B efficiency jumps to nearly 92%; this 6% increase in efficiency is by no means
a reasonable excursion.
When one also considers that the compressor maps used in this study have multiple layers to
describe performance at different inlet vane settings, the problem becomes immediately obvious. The on
design genetic algorithm quickly determines that optimal off design performance can be achieved by
maximizing the efficiency scale factor at the design point, i.e. minimizing design point map efficiency,
thereby maximizing off design point efficiency as well. Therefore, design point vane angles, corrected
speeds, and operating lines are selected at locations that are completely unreasonable in order to maximize
these scale factors.
46
Two solutions to this problem are readily apparent. The first is to simply fix the design point of
each component at the intersection of the maps operating line, 100% corrected speed line, and on the inlet
guide vane fully open layer (as in Figure 34). While this does yield more reasonable efficiencies, it limits
the variable cycle‟s ability to vary flow while keeping surge margins, corrected speeds, and pressure ratios
within specified limits at each off design point. The second is to have the optimizer itself limit the scale
factors by placing an upper limit on off design efficiency. In this study, the cost function adds a penalty for
deviations in off design efficiency greater than 2.5% from the on design value; this is one of the penalties
for undesirable behavior described in figure 23. This penalty function proved effective in keeping
efficiencies reasonable while allowing internal air flow variations at all off design points of interest.
3.3 Reduction in spillage drag
As mentioned in the introduction, the prospect of matching an engine‟s demand for airflow to the
inlet‟s ability to deliver airflow is one of the classic motivations for creating a variable cycle engine. If one
is able to accomplish this inlet matching across a wide range of power settings and flight conditions,
spillage drag can be essentially eliminated and a corresponding reduction in fuel use realized. The results
presented in this section detail the spillage drag realized using the calculation methodology outlined in
section 2.4 for a variety of flight conditions and across all three candidate missions. Note that this data
does not represent the minimum possible spillage but rather that obtained for an optimized power hook in
which flow holding is ceased consistent with the logic presented in section 3.1 above.
If one assumes level steady state flight, i.e. cruise thrust is equal to aircraft drag, it is possible to
plot the percent increase in aircraft drag due to spillage throughout a power hook, see figures 36-38. These
results confirm that the three stream variable cycle is remarkably adept at reducing spillage drag at all flight
conditions and across the entire power hook. Furthermore, it is evident that there is a location in each
power hook where the benefits of reduced spillage are outweighed by increased duct losses, decreased
component efficiencies, or physical limits on variable features; at this point inlet matching is ceased.
Finally, one notes that spillage drag continually increases as engine thrust is reduced from military power,
and that the rate of increase is a strong function of dynamic pressure. For these reasons the optimizer notes
a greater incentive to hold engine airflow at higher airspeeds or when engine power is greatly reduced; this
47
will become increasingly evident in the subsonic long range strike and supersonic strike missions. These
issues will be addressed here while conclusions as to the overall cycle benefit will be reserved for later
sections.
Figure 36. Variable cycle reduction in spillage drag at tactical mobility mission cruise points
Figure 36 overlays the spillage drag curves for the advanced turbofan with those of the variable
cycle for the tactical mobility mission at the high and low altitude cruise flight conditions. In this particular
mission, the takeoff from a 1500 ft runway at 4000 ft pressure altitude on a 95o F day requires 24,000 lbf of
thrust per engine; this design point sizes these engines. Therefore, the engine is pulled back significantly at
both of the cruise points of interest. The 35,000 ft cruise location requires 63% military thrust and,
therefore, a 1.9% increase in aircraft drag is due to spillage is realized by the advanced turbofan. By
holding airflow to just 84% power, the VCE is able to eliminate the spillage drag at this cruise condition.
However, the 0.4 Mach low cruise requires just 32% military thrust and the variable cycle would incur too
great a thermodynamic efficiency loss by air flow holding to this point. Nevertheless, by flow holding to
82% the variable cycle is able to reduce the increased drag due to spillage from 5.6% to 3.2%. Thus by
holding airflow to approximately 80% power, the three stream variable cycle is able to reduce aircraft drag
by roughly 2% at each cruise point of interest.
0
2
4
6
8
10
12
14
16
18
20
0 10 20 30 40 50 60 70 80 90 100
% I
ncre
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pil
lag
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% Military Thrust
Tactical Mobility Spillage Drag
Advanced Turbofan, 4000 ft 0.4 Mn
Variable Cycle, 4000 Ft 0.4 Mn
Advanced Turbofan, 35000 ft 0.8 Mn
Variable Cycle, 35000 ft 0.8 Mn
48
Figure 37. Variable cycle reduction in spillage drag at subsonic LRS mission cruise points
Figure 37 shows an overlay of the advanced turbofan and variable cycle power hooks at the two
subsonic long range strike cruise flight conditions. Again these engines are sized for the takeoff condition
from an 8,000 ft runway at sea level 95oF day; this requires 30,000 lbf thrust per engine. For this design
point, both engines are operating at nearly 86% military thrust at high altitude cruise and neither produces
any increase in drag due to spillage. However, low altitude penetration requires only 30% power and the
advanced turbofan realizes a 15.3% increase in aircraft drag due to spillage. As stated earlier, this is in
large part due to the relatively high cruise speed, and hence increased dynamic pressure, of this penetration.
By flow holding to 78% power, the variable cycle is able to reduce the increase in aircraft drag to only
6.0%. This reduction of over 9% in drag suggests that a variable cycle would significantly reduce the fuel
required to accomplish this mission.
The supersonic strike mission spillage drag profile is illustrated in Figure 38 for the two cruise
points of interest. Here the engines are sized to produce 17,200 lbf thrust at Mach 2.5, 55,000 ft on a
standard day. Although this design point results in only a modest reduction in throttle setting at the two
cruise points of interest, the high speed cruise segment notes a very rapid increase in spillage drag as the
thrust is reduced. For this reason, the advanced turbofan suffers from a 16.2% increase in spillage drag at
0
5
10
15
20
25
30
0 10 20 30 40 50 60 70 80 90 100
% I
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ircr
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Dra
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Sp
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% Military Thrust
Subsonic Long Range Strike Spillage Drag
Advanced Turbofan, 500 ft 0.7 Mn
Variable Cycle, 500 Ft 0.7 Mn
Advanced Turbofan, 40000 ft 0.8 Mn
Variable Cycle, 40000 ft 0.8 Mn
49
the 72% military thrust high cruise flight condition. By flow holding to 76% the variable cycle is able to
reduce this to a mere 0.7% increase. Although spillage drag is nearly nonexistent at the 80% power low
altitude loiter condition, the variable cycle is still able to reduce the increase in spillage drag from 0.9% to
zero. As it was the supersonic commercial transport mission that first prompted the exploration of three
stream variable cycles, it should come as no surprise that the supersonic cruise segment of this mission
offers the greatest potential reduction in spillage drag. This substantial decrease in drag is certain to create
a corresponding reduction in mission fuel use.
Figure 38. Variable cycle reduction in spillage drag at supersonic strike mission cruise points
3.4 Reduction in aft body drag
It was suggested early in this study that an engine with a higher mass flow rate would necessarily
have a larger nozzle exit area for a given operating condition. Therefore, it follows that a variable cycle
engine which is flow holding would be able to fill the aft body area with exhaust better than its
conventional engine counterpart. Although aft body drag is typically much smaller in magnitude than
spillage drag, the potential drag reduction was deemed sufficient enough to warrant investigation. The
results presented in this section detail the aft body drag realized using the calculation methodology outlined
0
5
10
15
20
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30
35
40
45
50
0 10 20 30 40 50 60 70 80 90 100
% I
ncr
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ircr
aft
Dra
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to
Sp
illa
ge
% Military Thrust
Supersonic Strike Spillage Drag
Advanced Turbofan, 30000 ft 0.5 Mn
Variable Cycle, 30000 Ft 0.5 Mn
Advanced Turbofan, 50000 ft 2.2 Mn
Variable Cycle, 50000 ft 2.2 Mn
50
in section 2.5 for a variety of flight conditions and across all three candidate missions. Again, this data
does not necessarily represent the minimum possible aft body drag but rather that obtained for an optimized
power hook in which flow holding is ceased consistent with the logic presented in section 3.1 above.
Percent increase in aircraft drag due to aft body effects is plotted as a function of throttle setting in
figure 39 for the tactical mobility mission cruise points. Two conclusions are immediately evident from
this plot. First, the very small coefficient of aft body drag at subsonic speeds (reference figure 22) results
in a very modest increase in drag as thrust, and hence exhaust area, is reduced in a conventional engine.
Second, the variable cycle is more effective in filling the aft body area than its conventional counterpart.
While the reduction in drag is quite small, roughly a half percent reduction in drag is possible at each of the
cruise points of interest.
Figure 39. Variable cycle reduction in aft body drag at tactical mobility mission cruise points
The long range strike mission‟s aft body drag curves, given in Figure 40, follow the same trends
noted in the tactical mobility mission. Again, the variable cycle engine has a relatively constant aft body
drag across the entire power hook. While the high altitude cruise curves are essentially unchanged, the
higher dynamic pressure of the low altitude penetration increases the magnitude of the aft body drag and
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
0 10 20 30 40 50 60 70 80 90 100
% I
ncre
ase
in
Air
cra
ft D
rag
du
e t
o A
ft B
od
y
% Military Thrust
Tactical Mobility Aft Body Drag
Advanced Turbofan, 4000 ft 0.4 Mn
Advanced Turbofan, 35000 ft 0.8 Mn
Variable Cycle, 4000 ft 0.4 Mn
Variable Cycle, 35000 ft 0.8 Mn
51
hence the potential savings. The variable cycle was effective in reducing the aft body drag by roughly one
quarter percent at high cruse and one percent during the low altitude penetration.
Figure 40. Variable cycle reduction in aft body drag at subsonic lrs mission cruise points
The supersonic strike aft body drag profiles are different from the preceding two in both
magnitude and in nature, see figure 41. While the Mach 0.5 low altitude loiter aft body drag is essentially
constant across the entire power hook, the Mach 2.2 high altitude aft body drag rises abruptly for both the
advanced turbofan and the variable cycle. This is a direct result of the steep slope in the Cd curve at this
higher Mach number (see figure 22); therefore, even a modest reduction in exhaust gas area yields a
significant rise in aft body drag. Nonetheless, the variable cycle is able to achieve a modest 1.5% reduction
in aft body drag at high speed cruise while no significant change in aft body drag is realized at the slow
speed loiter condition.
3.5 Lift augmentation
An often touted benefit of variable cycles is that it can provide a readily available source of
constant pressure ratio air for lift augmentation. A skeptic might immediately respond that a conventional
0.0
0.5
1.0
1.5
2.0
2.5
3.0
3.5
4.0
0 10 20 30 40 50 60 70 80 90 100
% I
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Air
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o A
ft B
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% Military Thrust
Subsonic Long Range Strike Aft Body Drag
Advanced Turbofan, 500 ft 0.7 Mn
Advanced Turbofan,40000 ft 0.8 Mn
Variable Cycle, 500 ft 0.7 Mn
Variable Cycle, 40000 ft 0.8 Mn
52
Figure 41. Variable cycle reduction in aft body drag at supersonic strike mission cruise points
engine could also provide a readily available source of pressurized air; however, this air would be much
more costly from an overall cycle efficiency standpoint. For example, a three stream variable cycle like
the one in this study could be configured so that the third stream air is pressurized by a single stage of
compression. By properly scheduling the variable features this source of pressurized air could be
maintained at a pressure ratio of 1.89, to permit choked flow through the discharge orifice, throughout the
period of lift augmentation. In contrast, a conventional engine would note a significant decrease in fan
pressure ratio as the throttle is reduced. This would require a conventional engine to use at least two stages
of compression when pressurizing air for lift augmentation. As such pressurization requires significant
energy extraction by the turbine and no appreciable thrust is produced by the lift augmentation system, the
fuel efficiency of the conventional engine would be appreciably worse than that of the variable cycle.
Each of these concepts is clearly visible in the following graphs. In figure 42 the pressure ratio of
the advanced turbofan second stream and the variable cycle third steam air is plotted as a function of
percent military thrust. As expected, fan pressure drops rapidly as the throttle is reduced in both the
conventional two stream engine and in the variable cycle optimized for fuel efficiency. Nonetheless, the
advanced turbofan with its two stages of fan compression is able to maintain the desired 1.9 pressure ratio
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
0 10 20 30 40 50 60 70 80 90 100
% I
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Air
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o A
ft B
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y
% Military Thrust
Supersonic Strike Aft Body Drag
Advanced Turbofan, 30000 ft 0.5 Mn
Advanced Turbofan,50000 ft 2.2 Mn
Variable Cycle, 30000 ft 0.5 Mn
Variable Cycle, 50000 ft 2.2 Mn
53
thru 40% military thrust. What is more impressive is that the variable cycle is able to deliver the same
desired pressure ratio through 60% military thrust, as requested in the vision mission, with a single stage of
compression. This is accomplished primarily by decreasing the fan nozzle throat area as power is reduced
below 80% thereby back pressuring the fan. Unfortunately, this reduction in fan nozzle throat area
discourages flow to the third stream and is counterproductive from a propulsive efficiency standpoint
(optimal variable feature settings will be presented in sections 3.6 thru 3.8).
Figure 42. Fan pressure ratio during approach and landing
The question remains as to whether the performance of the less than fuel optimal operation of the
variable cycle exceeds that of the advanced turbofan. The throttle hooks in Figure 43 provide a clear
answer to this query. This figure reveals many of the variable cycle attributes outlined in this and previous
sections. First, reductions in spillage and aft body drag as well as improvements in propulsive efficiency
make the variable cycle more fuel efficient across the entire power hook. Second, use of single stage
compression air for lift augmentation further improves the efficiency of the variable cycle over the
advanced turbofan. Finally when the additional constraint of maintaining 1.89 pressure ratio air in the third
stream is added to this cycle, the two benefits above are reduced and the variable cycle efficiency begins to
approach that of the conventional two stream cycle.
54
Figure 43. Tactical mobility power hook during approach and landing
As stated earlier, the means of maintaining third stream pressure ratio was primarily to restrict the
fan nozzle throat area below 80% military thrust. As this does discourage mass flow into the third stream,
it is necessary to confirm that sufficient airflow remains to provide for both the lift augmentation and aft
deck cooling through 60% thrust. Figure 44 overlays the third stream airflow during the short field landing,
in which the 1.89 or greater fan pressure ratio is maintained, with the airflow demand. As expected, the
third stream flow decreases below 80% as the fan nozzle closes; however, the third stream airflow exceeds
demand throughout the approach and landing by 20% or more. The claim that a variable cycle can provide
a readily available source of near constant pressure ratio air for lift augmentation is easily justified.
3.6 Heat sink capacity of third stream
Modern aircraft systems generate profuse amounts of heat as a byproduct of their increasingly
complex onboard systems. Sources include advanced avionics, electric actuators, sensor suites, directed
energy weapons and electronic countermeasures just to name a few. Traditional thermal management
approaches shed this heat to the environment or use it to preheat the fuel. This approach is often frustrated
by supersonic flight in which ram air loses much of its cooling capability (Edwards, 2003). Furthermore,
55
the quest for increased fuel efficiency reduces not only fuel flow but also the heat sink capacity of the entire
fuel system. For these reasons additional heat sink capacity must be sought.
Figure 44. Variable cycle third stream air flow during assault landing
The variable cycle‟s third stream would seem to be an obvious location to exhaust this aircraft
thermal load. There are however a number of concerns with placing a heat exchanger in this bypass stream
including increased engine weight, pressure loss through the heat exchanger, duct sizing to accommodate
the heat exchanger, and additional hardware to carry the heat load from each source to the exchanger. As
each of these is beyond the scope of this research, the analysis here will simply concentrate on the capacity
of this stream to accept this heat load. Heat flux can be readily calculated with the equation,
Where: is the specific heat at constant pressure
is the mass flow rate of the working fluid
is the temperature increase of the working fluid
is the heat flux
56
Therefore, finding the theoretically available heat capacity of the third stream requires that one know the
mass flow rate of air, a single gas property and the maximum permissible temperature rise of the air.
As the mass flow and specific heat at constant pressure in the third stream can be readily found at
any given throttle setting and flight condition, the only remaining question is how much increase in air
temperature is allowable. To find the maximum heat capacity of this stream one should increase the air
temperature until a predetermined material limit is reached. The first such limit noted is the maximum air
temperature for effective nozzle cooling. Remember that bypass air is used to cool the nozzle aft deck in
both baselines and in the variable cycle (see figures 14 and 17). It is assumed that 15% of the total engine
airflow is sufficient to cool the aft deck at any flight condition, and hence at any given fan exit temperature.
Therefore, the upper limit for the third stream cooling air would be the air temperature of the advanced
turbofan second stream air at maximum fan pressure ratio and maximum airspeed. For the subsonic long
range strike mission this occurs at military power, Mach 0.7 low altitude penetration where the fan exit
temperature reaches 375 oF. Using this maximum temperature, the third stream heat sink capacity per
engine is plotted in figure 45 for the subsonic LRS mission at the 40,000 ft Mach 0.8 cruise condition.
Figure 45. Theoretical heat sink capacity of third stream, subsonic LRS high altitude cruise
57
In figure 45 it is clear that reducing power increases third stream heat sink capacity; this is a direct
result of increased third stream airflow and reduced fan pressure ratio. Note also that at this cruise
condition the compressor exit temperature is sufficiently low and cooling of the cooling air for the
compressor disk and turbines is not required; therefore, all of this heat sink capacity is available to dissipate
aircraft heat loads. Therefore, if only 13% of the heat flux capacity were utilized, a two engine aircraft
could effectively dissipate one megawatt of aircraft heat load at the 86% cruise power setting. This is
particularly appealing for thermal management as this variable cycle is most capable of accepting heat
loads at part power conditions where fuel flow is reduced and it is impractical to transfer significant heat to
the fuel system. This inherent capability to dissipate aircraft thermal loads makes a three stream variable
cycle very attractive for military applications.
The following sections will address how the effects of reduced drag and increased propulsive
efficiency combine to create an overall reduction in required mission fuel. During these discussions, it is
important to note which components vary, in what manner they vary, and to what extent flow is affected.
Such observations will provide the basis for subsequent results that attempt to maximize mission
performance with the minimum number of variable features.