AIAA2000-3714

A COMPARISON OF THERMODYNAMIC LOSS MODELS SUITABLE FOR GAS TURBINE

PROPULSION: THEORY AND TAXONOMY
Bryce A. Roth* and Dimitri N. Mavris✝
Georgia Institute of Technology
Atlanta, GA 30332-0150
Abstract Introduction
The objective of this paper is to describe several A truly good engine design is always a
figures of merit for estimation of loss in work potential compromise between all competing aspects of design
based on the second law of thermodynamics and to performance including thermodynamic performance,
evaluate their relative merits for propulsion system weight, cost, maintainability, etc. A necessary
analysis and design. The loss figures of merit examined prerequisite to achieving this balance is an
are exergy, gas horsepower, stream thrust, and thrust understanding of the fundamental nature of the trades
work potential. Definitions and simplified expressions involved and knowledge of the exact cost (in terms of
for evaluating each are presented, and the relationships performance, weight, and dollars) of every decision
between these four metrics are expressed via contours made during the design process. In particular, one
on a T-S diagram. A general taxonomy classifying the would like to know the magnitude of the work loss
various work potential figures of merit is suggested. incurred in each thermodynamic process inside the
The results indicate that that each method is well suited propulsion system such that the most significant
to a particular type of application, with the most sources of loss can be identified and targeted for
appropriate choice of loss figure of merit depending on improvement. This is especially true for high-speed
the particular application. Finally, thrust work potential propulsion systems where the losses associated with
is shown to be a special case of gas horsepower, which high-speed flow processes can easily become exorbitant
is in turn a special case of exergy. if not properly addressed.
Nomenclature*† The need to accurately calculate loss of flow work
Note: lower case letters denote mass-specific quantities
potential relative to a thermodynamic ideal has led to
A = Cross-Sectional Area (ft2) interest in methods employing the second law of
cp = Constant Pressure Specific Heat (0.24 BTU/lbm-R) thermodynamics as a basis for loss estimation. This
Ex = Exergy (BTU) approach is appealing because it provides an
g = Gravitational Acceleration (ft/sec-sec)
GHP = Gas Horsepower (BTU)
unambiguous definition of an ideal against which the
H = Enthalpy (BTU) actual process can be compared. Thus, whereas
I = Impulse Function (lbf) conventional cycle analysis gives information as to the
J = Work Equivalent of Heat, 778 ft-lb/BTU flow of energy, a second law-based method enables
M = Mach Number
calculation of work potential. This capability will
m& = Mass Flow Rate (lbm/s)
P = Pressure (atm)
enable the creation of loss management models to
R = Gas Constant (0.069 BTU/lbm-R for air) identify and track all sources of thermodynamic loss in
S = Entropy (BTU/R) a propulsion system. Such an approach would make it
Sa = Stream Thrust (lbf/lbm) possible to estimate the absolute loss associated with
T = Temperature (R)
V = Gas Velocity (ft/s)
each loss mechanism in terms of a single figure of merit
WP = Thrust Work Potential (HP or ft-lb/s) (FoM) applicable to all engine components and
W& out = Power Output (HP) processes.
γ = Ratio of Specific Heats (1.4) Several models for evaluation of loss in work
ρ = Gas Density (slug/ft3) potential have appeared in the past several decades,
Subscripts each different from the others in subtle ways. Most of
amb = Ambient Conditions
exp = Isentropically Expanded to Ambient Pressure the published work in this area focuses on a single
model in isolation from the others. As a result, the
relationships amongst these various figures of merit are
* Graduate Research Assistant, Department of Aerospace Engineer- ambiguous and the literature on the subject is somewhat
ing, Georgia Institute of Technology, Atlanta, GA 30332-0150. disjointed. The purpose of this paper is to clarify this
Student Member, AIAA. situation by examining the utility of the various loss
† Assistant Professor, Department of Aerospace Engineering. Senior
Member, AIAA.
estimation methods for gas turbine propulsion
Copyright © 2000 by Bryce Roth. Published by the American applications. This paper defines each method
Institute of Aeronautics and Astronautics, Inc. with permission. separately, discusses the historical context and
compares the relative merits of each method for the

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purposes of jet propulsion. The loss models examined work potential and lost thrust work potential figures of
are exergy, gas horsepower (isentropic expansion work merit and showed that optimization of exergy output
potential), stream thrust, and thrust work potential. does not necessarily lead to the best propulsive cycle
These four were selected based on their promise as a from a thrust production point of view. Finally,
universal loss metric for jet propulsion applications. Riggins suggested a modified definition of exergy,
which he termed “engine-based exergy,” and showed
This paper approaches the comparison of work
that this modified definition yielded results identical to
potential methods from a purely theoretical aspect.
those obtained through stream thrust methods.
However, it is closely related to a second paper that is
focused on demonstrating each of the four methods as A great deal of important work has been published
clearly and concisely as possible on a simplified J-79 over the past several decades in addition to that
turbojet example.1,2 In the second paper, the results of mentioned here, notably in the developing field of
each analysis method are discussed in detail, entropy generation minimization. An excellent
summarized, and compared to draw further inferences discussion of this work and its applications is given in
beyond those given in this paper as to their potential the recent textbook by Bejan.15 For the present
usefulness as a loss figure of merit (FoM) for gas discussion, however, the authors will confine
turbine engines. themselves to the four loss figures of merit previously
mentioned and their direct application to jet propulsion.
Background
Exergy
A substantial body of work has appeared in the past
several decades dealing with second-law approaches to Exergy is a thermodynamic state describing the
measuring loss in gas turbine engines. One such maximum theoretical (Carnot) work that can be
approach is the exergy concept, which has been applied obtained from a substance in taking it from a given
to the gas turbine cycle by several authors, notably chemical composition, temperature, and pressure to a
Clarke and Horlock,3 who applied it to a simple turbojet state of chemical, thermal, and mechanical equilibrium
example and showed where the most significant exergy with the environment. The general definition of exergy
losses were occurring. It is the best-known and most is given by:
formalized method to estimate the magnitude of losses
relative to a thermodynamically ideal process,4,5 and Ex ≡ H − H amb − Tamb (S − S amb ) + (Other Terms ) (1)
first appeared in the United States due largely to the In this case, the “other terms” are used to denote
work of Keenan in the 1940s.6 A considerable body of exergy due to kinetic energy, potential energy, chemical
literature exists describing the theory and application of potential, radiation, heat transfer, etc. Note that while
exergy analysis, and references 7, 8, 9, and 10 are energy is a conserved quantity, exergy is not, and is
standard texts on the subject. More recently, there has always destroyed when entropy is produced. Note also
been a great deal of interest in applying exergy that the definition of exergy depends on the ambient
concepts to combined cycle power generation, of which environment.
El-Masri11 gives an excellent example wherein he is
able to identify in detail all sources of exergy loss The physical significance of the thermodynamic
occurring within a gas turbine topping cycle. In quantity in Eq. 1 is best described in terms of a Mollier
addition, he shows the impact of cycle changes on total diagram as shown in Figure 1. The dashed line with
exergy produced and destroyed. Another approach that slope equal to the ambient temperature is the zero
has been proposed in the past is gas horsepower (of exergy reference line that represents the locus of points
isentropic expansion), which is used by Nichols12 as a from which no work can be extracted through heat
universal figure of merit for combustor loss. It is also transfer. All points above this line have the potential to
used extensively as a figure of merit for gas generator do work via heat transfer from a high temperature
power output, but has received little attention beyond reservoir into the environment. Points below the
this limited application. A third figure of merit was reference line have potential to do work via heat
proposed by Curran and Craig13 based not on energy, transfer from the environment into a low temperature
but force (thrust), known as the stream thrust concept. (perhaps cryogenic) reservoir. Also shown are isobaric
This involves calculation of stream thrust potential contours for the reference ‡ pressure and some
(also known as specific thrust) at each flow station and arbitrarily higher pressure. Exergy is depicted as the
optimizing the cycle to deliver the highest stream thrust difference between the enthalpy delta from the point of
potential. Later, Riggins14 extended this concept by
introducing the lost thrust method which allows ‡
For the purposes of this paper, ambient conditions are taken to be
accurate calculation of stream thrust loss due to the reference conditions.
inefficiencies. In addition, he introduced the thrust

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Enthalpy PHigh for mass-specific exergy as a function of ambient
Pamb conditions and gas conditions at a given engine station
by noting that:
=0
Ex > 0 ine
: Ex h − hamb = c p (T − Tamb ) (2)
ceL
Exergy er en
Ref
and using the integrated form of the second TdS
Tamb(S-Samb) H-Hamb relation:
Hamb

Heating

Cooling
s − s amb = c p ln T  − R ln P
  P

 (3)
 amb 
T  amb 
Tamb
Substitution of Eq. 2 and Eq. 3 into Eq. 1 yields:
Samb Entropy
ex = c p (T − Tamb ) − c p Tamb ln T  + RT P 
Figure 1: The Definition of Exergy Plotted on a
 amb ln  P 
Mollier Diagram [From 17].  Tamb   amb 

interest to the zero exergy reference line. Since the (4)

exergy concept relates every state to the Carnot Rote application of this equation to every engine
reference of work, change in exergy is a measure of the station yields the exergy at each station. Clearly, Eq. 4
loss in absolute work potential at every station in an is of limited value for propulsion applications where
engine. It is a comprehensive measure of loss in work vitiation, vibrational excitation, chemical reactions, and
potential that captures the impact of all sources of other effects are important. Fortunately, it is relatively
loss.16 simple to obtain accurate estimates for flow exergy
Contours of constant exergy can be plotted on a T- including these effects using modern thermodynamic
S diagram as shown in Figure 2. Note that the contours properties software packages. The losses associated
of constant exergy are straight lines with the zero with each component can then be calculated based on
exergy contour passing through the dead state. Also, it the idea that the difference between the exergy fluxes
is clear from this figure that the zero exergy contour is into and out of a component must be equal to the sum
tangent to the ambient pressure contour at ambient of the power output and the exergy loss rate:

E& x in − E& x out = W& out + E& x Loss

conditions.
(5)
For the case of calorically perfect air where
chemical potential, kinetic energy, and potential energy Exergy is the most general of the work potential
are negligible it is a simple matter to obtain an equation figures of merit investigated here, and gives an estimate
1600
Exergy 20 atm 15 atm 10 atm 5 atm
(BTU/lbm)
1400
200

1200
Temperature (R).

150

1000
100 1 atm

800
50
Ideal Air
600
γ = 1.4, cp=0.24 BTU/lbm-R
0
Tamb = 518 R, Pamb = 1 atm
400
1.58 1.6 1.62 1.64 1.66 1.68 1.7 1.72 1.74 1.76
Entropy (BTU/lbm-R)
Figure 2: T-S Diagram Showing Contours of Constant Exergy (Solid Lines) and
Isobaric Lines (Dashed Lines) for Ideal Air.
3

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of the absolute work potential that could be obtained by where the temperature after isentropic expansion to
any heat engine operating under specified conditions. reference (ambient) pressure is:
The work potential estimates obtained using exergy
γ −1
assume that the working substance is taken to thermal
T (P = Pamb, S = const ) = T  amb  γ
P
and mechanical equilibrium with the environment, the (8)
first of which cannot be enforced using the simple  P
Brayton cycle. As a result, even the perfect (no combining Eq. 7 and Eq. 8 yields:
component loss) Brayton cycle will have exergy losses
due to non-equilibrium combustion and exhaust heat  γ −1 
loss. Moreover, when the objective is to produce jet  
ghp = c p T 1 − 
Pamb  γ 
P 
(9)
thrust, a portion of the work done on the working fluid   
must appear as exhaust residual kinetic energy as  
viewed in the earth-fixed reference frame. Thus, there Rote application of Eq. 9 to the results of a
is a portion of the exergy content of the fuel that is standard first law cycle analysis yields the gas
inherently unavailable to the Brayton cycle and appears horsepower at each station in the engine. These results
as a loss. In general, these inherent losses are far larger can then be used to calculate the loss in gas horsepower
than exergy losses due to component inefficiencies for in each component of the engine based on a
gas turbine engines. Consequently, optimization of a “conservation of gas horsepower” principle similar to
thrust-producing device to produce maximum exergy that used for calculation of exergy losses:
output may yield a less-than-optimal result if the
objective is to produce thrust for propulsion, as GH& Pin − GH& Pout = W& out + GH& Ploss (10)
observed by Riggins.14
One can obtain a physical feel for the meaning of
However, for some applications such as combined Eq. 6 by comparison to the definition of exergy, as
cycle power generation, it appears that there is expressed in terms of a Mollier diagram, as shown in
justification for optimizing exergy output in order to Figure 3. Note that whereas the contour of zero exergy
obtain maximum power output. The reason for this is is a line passing through the reference (dead) state, the
that the steam bottoming cycle is able to extract the contour of zero gas horsepower is the isobaric line
exhaust exergy of the gas turbine topping cycle, and corresponding to the reference pressure. The space
therefore, all of the exhaust exergy becomes inherently between the zero exergy line and the zero gas
available. One would thus expect that optimization of horsepower contour is labeled as “thermal exergy” and
the topping cycle for maximum exergy output (in the constitutes the difference between gas horsepower and
form of shaft power and exhaust exergy) will naturally exergy. Clearly, gas horsepower and exergy are
lead to more efficient combined-cycle plants. identical at the reference entropy, but diverge as
Gas horsepower (Work Potential) entropy increases. This idea is further explained by
plotting lines of constant gas horsepower on a T-S
Gas horsepower is defined as the work that would diagram, as shown in Figure 4. Note that as
be obtained by isentropically expanding a gas at a temperature and pressure increase above the ambient
specified temperature and pressure to a prescribed value, the contours of constant gas horsepower diverge
reference pressure (usually taken to be local
atmospheric). Thus, the temperature at the imaginary Phigh
Enthalpy

expanded condition is a fall-out of the isentropic Pamb

expansion process. Expressed mathematically:
(
Gas Horsepower = GHP ≡ H (Ti , Pi ) − H P = Pref , S = S i ) =0
e : Ex
(6) Gas Horsepower L in
nce
e re
Thermal Exergy: Tamb(S(P=1atm)-Samb) Ref
where i is used to denote the thermodynamic state of
the gas at point i. Note that gas horsepower is a Tamb(S-Samb)
H-Hamb
Hamb

function of ambient pressure only, and is independent

of ambient temperature, unlike exergy. Gas
horsepower is commonly used to measure the
theoretical power output of core engines and gas Tamb
generators. A simple expression for gas horsepower of
Samb Entropy
a calorically perfect gas is easily derived by noting that:
Figure 3: Gas Horsepower Plotted on a Mollier Diagram.
ghp = c p (Ti − T (P = Pamb , S = S i )) (7) Gas Horsepower is the Quantity Lying between the
Isobaric Contours [From 17].
4

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 1600
Gas Horsepower 20 atm 15 atm 10 atm 5 atm
(BTU/lbm)
1400
200

1200
Temperature (R).

150

1000
100 1 atm

800
50
Ideal Air
600
γ = 1.4, cp=0.24 BTU/lbm-R
0
Tamb = 518 R, P amb = 1 atm
400
1.58 1.6 1.62 1.64 1.66 1.68 1.7 1.72 1.74 1.76
Entropy (BTU/lbm-R)
Figure 4: T-S Diagram Showing Contours of Constant Gas Horsepower (Dashed Lines) and
Isobaric Lines (Solid Lines) for Ideal Air.
from the isobaric contours. Also, it is clear from Eq. 9 entropy. This is also reflected in the T-S diagram
that the gas horsepower is directly proportional to the shown in Figure 5, which depicts lines of constant
gas temperature for a given pressure ratio (for the exergy and gas horsepower superimposed on the same
calorically perfect gas model only). plot for ideal air. The fundamental difference between
these two quantities is that gas horsepower requires
It was pointed out previously that gas horsepower
only mechanical (pressure) equilibrium with the
and exergy are thermodynamically identical quantities
environment, while exergy requires both mechanical
at the reference entropy, and diverge with increasing
and thermal equilibrium. Thus, gas horsepower is a
1600
Exergy 200 150
(BTU/lbm)
1400
200 100

1200
Temperature (R).

150 50

1000
0
100

800
Gas HP
50
(BTU/lbm)
600 Ideal Air
0 γ = 1.4, cp=0.24 BTU/lbm-R
Tamb = 518 R, Pamb = 1 atm
400
1.58 1.6 1.62 1.64 1.66 1.68 1.7 1.72 1.74 1.76
Entropy (BTU/lbm-R)
Figure 5: T-S Diagram Showing Contours of Constant Exergy (Solid Lines) and Constant Gas
Horsepower (Dashed Lines) for Ideal Air.

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special case of exergy for which work extraction Sa ≡ I & (13)
through mechanical equilibrium is assumed while m
thermal equilibrium is not enforced. It is generally inconvenient to work in terms of
Note that gas horsepower losses in a given velocity, Mach number, and area when analyzing the
component will always be larger than their thermodynamic cycle of an engine. Instead, it is
corresponding exergy losses. This is because the loss preferable to evaluate the stream thrust in terms of
in work will appear as an increase in heat (by the first temperatures and pressures at each flow station in the
law) and temperature of the exhaust gas. A portion of engine. This is done by calculating the velocity that
this exhaust heat is recoverable and can be used to would be obtained by an imaginary isentropic
produce work in a bottoming cycle, and is thus not seen expansion from the conditions of interest to
as an irretrievable loss using exergy, but is an atmospheric pressure, where the expanded fluid
unrecoverable loss in gas horsepower. velocity is related to the stream thrust via:
The primary difference between gas horsepower Vexpanded
Sa = (14)
and exergy for analysis of gas turbine (Brayton) cycles g
is that exhaust heat does not appear as a gas horsepower
loss, but is instead transparent. Thus, a perfect Brayton This expanded velocity can be evaluated based on the
cycle will appear to have no losses in gas horsepower.§ gas horsepower at each flow station by noting that:

2(ae )J
Therefore, the distribution of losses is considerably
different between the exergy and gas horsepower V2 = J (ae )g ⇒ V = 2(ae )Jg ⇒ Sa = (15)
2 g
methods. In particular, the role of component losses
and useful work production is considerably magnified,
as non-equilibrium combustion and exhaust heat losses or, simplifying slightly:
no longer appear in the loss stack-up. However,
Sa = 6.955 ae (16)
exhaust residual kinetic energy still appears as a large
loss when the gas turbine is used to produce jet thrust. where stream thrust is in lbf/lbm and gas horsepower is
Stream Thrust in BTU/lbm. An appealing attribute of stream thrust as
a figure of merit is that it is a force-based quantity, and
Whereas exergy and gas horsepower concepts are therefore independent of the observer’s frame of
based on work potential, the stream thrust concept is reference (though Eq. 16 implicitly assumes that gas
based on thrust potential at each flow station in the horsepower is measured with respect to the vehicle-
engine. Thrust potential is defined as the thrust that fixed reference frame). This is in contrast to exergy
would be obtained in expanding a flow from a given and gas horsepower, wherein the measured value of
temperature and pressure to atmospheric pressure. these quantities depends on the reference frame. In
Stream thrust is based on the impulse function, which is addition, it is directly linked to what is arguably the
defined in compressible fluid mechanics as:18 ultimate figure of merit for jet propulsion applications:

(
I ≡ PA + ρAV 2 = PA 1 + γM 2 ) (11)
jet thrust.
A disadvantage of stream thrust is that it has no
The impulse function is nothing more than a form of the “conservation property” analogous to Eqs. 5 and 10 that
momentum equation and can be used to find the net allows direct estimation of stream thrust loss due to
force (drag or thrust) exerted on a fluid stream between irreversibilities. That is to say:
arbitrarily specified inlet and exit planes via evaluation
of the impulse function at the inlet and exit planes: Sa lost ≠ Sa out − Sa in (17)

FNet = I Exit − I Inlet (12) for the general case where there are work interactions
with other components, as in the compressor or turbine.
Stream thrust is defined as the impulse per unit Therefore, one must resort to the “lost thrust” method
mass of flow, more commonly known as specific described by Riggins14 and demonstrated in the second
thrust.19 It is therefore related to impulse function by: paper of this series.1
Thrust Work Potential
Thrust work potential is defined as the thrust work
§
The authors are unaware of any treatment by which the maximum that would be obtained in expanding a flow at a given
gas horsepower of a fuel has been calculated, and this appears to be a temperature and pressure to ambient pressure such that
topic worthy of further investigation.
the thrust work obtained is equal to the thrust produced
multiplied by the flight velocity of the aircraft.20 This
6

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 1600
Net Thrust Work 20 atm 15 atm 10 atm 5 atm
Pot. (BTU/lbm)
1400
80

1200
Temperature (R).

60
1000
1 atm
40
800
20
600 0 Ideal Air
γ = 1.4, cp=0.24 BTU/lbm-R

400
1.58 1.6 1.62 1.64 1.66 1.68 1.7 1.72 1.74 1.76
Entropy (BTU/lbm-R)
Figure 6: T-S Diagram with Lines of Constant Thrust Work Potential at M0.9, 20,000 ft
(Solid Lines) and Isobaric Lines (Dashed Lines).

can be normalized by airflow rate to give specific thrust its relationship to stream thrust, which also varies as the
work potential at each station: square of temperature. The displacement of the zero
point physically corresponds to the thrust work required
Wp ≡ Sa(u ) (18) to offset the ram work of inlet compression. Thus, the
J
zero thrust work potential line will move further
For the purposes of air-breathing propulsion, thrust upwards as flight velocity increases.** Finally, note that
work potential is inherently anchored in the Earth-fixed there is far less thrust work potential available than gas
observer’s frame of reference because it is based on the horsepower for a given flow temperature and pressure,
velocity of the vehicle relative to the Earth. Note that especially at high temperature and pressure. This is due
the thrust work potential is always less than the gas to increasing exhaust residual kinetic energy (lower
horsepower of the gas stream due to the fact that some propulsive efficiency), which is characteristic of the
of the gas horsepower must necessarily emerge as high specific thrust produced by high enthalpy flows.
residual kinetic energy of the exhaust gasses (as viewed
Since thrust work potential is proportional to the
by the stationary observer). Thrust work potential is
stream thrust at each station, it does not yield any
therefore linked to the gas horsepower through
information beyond that which is obtained from the
propulsive efficiency, which is in turn a function of
stream thrust analysis, and has the disadvantage that it
exhaust velocity and flight velocity. In this regard,
is not a meaningful FoM for comparison of engines at
thrust work potential can be viewed as a special case of
static operation. However, because losses are
gas horsepower that measures only work produced with
expressed in terms of power rather than force, it can be
respect to a particular reference frame. By extension
directly compared against exergy and gas horsepower
then, thrust work potential is a special case of exergy.
methods. In addition, thrust work potential does not
Lines of constant thrust work potential can be count exhaust residual kinetic energy as being available
plotted on a T-S diagram as shown in Figure 6. Note for propulsive purposes. Therefore, it is not accounted
that the contours are shaped the same as gas as a loss, unlike exergy and gas horsepower.
horsepower contours, but with two differences: their
spacing is not constant, and the zero thrust work
potential line does not coincide with the zero gas **
Note that thrust work potential for a rocket is the same as shown in
horsepower (atmospheric pressure) line. In fact, the the figure, except that the zero thrust potential line is equal to the zero
spacing of thrust work potential contours is gas horsepower line for all flight velocities.
proportional to the square of the temperature because of

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 Taxonomy of Work Potential Figures of Merit propulsion system’s ability to project thrust work into
another arbitrary (usually Earth-fixed) reference frame.
Based on the discussion up to this point, it appears
It is a special case of gas horsepower to which it is
profitable to construct a rough taxonomy of the various
related through propulsive efficiency. Gas Horsepower
loss figures of merit and classify them relative to one
is merely a special case of exergy wherein only
another, as shown in Table I. An “x” is placed in the
mechanical equilibrium with the environment is
appropriate matrix cells to indicate which sources of
enforced. Exergy is a special case of what Evans16
work potential are accounted for by each method. This
refers to as essergy, which can presumably be
table is by no means exhaustive, and is only intended to
generalized to include atomic and subatomic work
cover those concepts that appear to have the most use as
potential, both of which are quite beyond the realm of
propulsive work FoMs. Since this is a relatively new
the authors’ practical experience.
and maturing field, the definitions given in this table are
the authors’ interpretation of each FoM, and other Comparison of Methods
authors have offered alternative definitions to those
Table II summarizes the relative strengths and
given here. Note that none of the work potential FoMs
weaknesses of each loss figure of merit. Both exergy
discussed here have been extended to account for the
and gas horsepower are physically intuitive and possess
potential available in nuclear and subnuclear bonds.
a “conservation” property that allows direct estimation
The authors are unaware of any figures of merit that
of losses via Eqs. 5 and 10. However, neither produces
capture this aspect of work potential, and this is
results that are reflective of the true “costs” due to
apparently an area for future theoretical exploration in
component losses in jet propulsion applications because
the physics, thermodynamics, and power generation
they book-keep work potential sources that are
communities.
inherently unavailable to jet propulsive machines. This
Based on the discussion thus far, the relationship point is discussed in the context of a simple
between exergy, gas horsepower, and thrust work optimization problem in Ref. 14 and is further
potential becomes relatively clear. Thrust work elaborated upon in Ref. 1.
potential is nothing more than a measure of the

Table I: A Taxonomy of Prominent Work Potential Figures of Merit.

Thermal Mechanical Mixture Chemical Nuclear
Equilib. Equilib. Equilib. Equilib. Equilib.
Essergy16 X X X X
Exergy X X X
Gas Horsepower X
Thrust Work Potential X
Gibbs Free Energy X
Energy Source Internal Energy Contained in Molecular Chemical Nuclear
Ensembles of Particles Diffusion Bonds Bonds
General Scale of Effect Macroscopic Ensembles of Particles Molecular Atomic
Scale Scale

Table II: Advantages and Disadvantages of Various Loss Figures of Merit for Jet Propulsion Applications.
Advantages Disadvantages
Exergy +Very General (Comprehensive) -Counts Exhaust Heat, Irrev. Comb., Residual
A Combined Cycle Figure of Merit +Requires only Temp. & Press. to Calculate KE as Chargeable
+“Conservation Law” Simplifies Loss Calcs. -Dependent on Reference Frame
+Physically Intuitive Quantity (Power Loss)
Gas Horsepower +Realistic Loss Estimate for Turbomachines -Counts Residual KE as Chargeable
A Turboshaft Figure of Merit +Requires only T & P to Calculate -Dependent on Reference Frame
+“Conservation Law” Simplifies Loss Calcs.
+Physically Intuitive Quantity (Power Loss)
Stream Thrust +Force-Based; Independent of Ref. Frame -No “Conservation Law” Applies
A Jet Thrust Figure of Merit +Physically Intuitive Quantity (Thrust Loss) -Not Directly Comparable to Available
+Doesn’t Count Residual KE as Chargeable Energy or Exergy
Thrust Work Potential +Physically Intuitive Quantity (Power Loss) -No “Conservation Law” Applies
A Jet Work Figure of Merit +Doesn’t Count Residual KE as Chargeable -Dependent on Earth-Fixed Reference Frame
+Directly Comparable to Exergy, Avail. Ener. -Work Potential = f(Flight Condition)
-Not Meaningful for Static Operation

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 Stream thrust and thrust work potential account for would like to thank Mr. Ron Giffin of General Electric
jet propulsive losses in a physically realistic way, but Aircraft Engines (retired) for his invaluable insights and
do not possess a conservation property analogous to advice during the course of this project.
Eqs. 5 and 10 for direct estimation of loss. Thus, losses
References
due to non-equilibrium combustion, exhaust heat, and
exhaust residual kinetic energy are transparent (non- 1
Roth, B.A., Mavris, D.N., “A Comparison of Thermodynamic Loss
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Acknowledgements Hypersonic Engines Part 1: Methodology,” Journal of Propulsion
and Power, Vol. 13, No. 2, Mar-Apr 1997.
The authors would like to thank the National
Science Foundation for supporting portions of this
research under grant DMI 9734234. In addition, we
9

American Institute of Aeronautics and Astronautics