**SYNOPSIS**

An alternative configuration for a
regenerative gas turbine engine cycle is presented that yields higher cycle
efficiencies than either simple or conventional regenerative cycles operating
under the same conditions. The essence of the scheme is to preheat compressor
discharge air with high temperature combustion gases before the latter are
fully expanded across the turbine. The efficiency is improved because air
enters the compressor at a higher temperature, and hence heat addition in the
combustor occurs at a higher average temperature. The heat exchanger operating
conditions are more demanding than for a conventional regeneration
configuration, but well with in the capability of modern heat exchangers.
Models of cycle performance exhibit several percentage improvement relative to
either simple cycles or conventional regeneration schemes. The peak
efficiencies of the alternative regeneration configuration occur at optimum
pressure ratios that are significantly lower than those required for simple
cycle. Model calculations for a wide range of parameters are presented, as are
comparisons with simple and conventional regeneration cycles.

#
BACKGROUND

In recent years, ground-based gas turbine engine (GTE)
applications have been appreciably expanded due to significant improvements in
cycle efficiency. Simple cycle
efficiencies of over 40 percent are now possible from some designs, making GTEs
competitive alternatives to Diesel engines and Rankine steam cycles. Most ground-based GTE applications can accommodate
the space and mass requirements associated with adding regeneration to a simple
cycle, with the goal of even higher cycle efficiencies.

For many operating conditions, regenerators (heat
exchangers) can improve found- based GTE performance by recovering heat from
high temperature exhaust gases. Numerous
applications for the recovered heat have been devised, including combined cycle
and cogeneration applications, but on stand alone GTE cycles the recovered heat
is usually used for preheating the air passing between compressor and
combustor. In this way, a well-known
goal of thermodynamic design is satisfied by increasing the average temperature
at which heat is added to the air during combustion resulting in increased
efficiency. Regenerators have traditionally ([1-3]) used product gases leaving
the final turbine stage as the source of heat (referred to herein as
“conventional regeneration”) so that the maximum amount of work is extracted
from the high-enhalpy gas stream before any heat is recovered. How ever, such a regenerator location is
inconsistent with a fundamental lesson from Carnot-cycle thermodynamics,which
is that cycle efficiency is maximized by increasing the average temperature at
which heat is added, and not necessarily by maximizing the work output. Thus, the overall efficiency of conventional
regenerative GTE cycles can be improved through an alternative regenerators
location, and to the author’s knowledge, this paper is the first discussion of
such schemes.

**MODEL DEVELOPMENT**

Computer models of simple, conventional regenerative,
and alternative regenerative cycles were developed to examine the influence of
various parameters on the performance of the cycles. The primary goal in developing the models was
to demonstrate the enhanced performance of the proposed “alternative
regeneration” scheme, and consequently, the models were not comprehensive in
including all details of gas turbine engine performance. An economic analysis was beyond the scope of
this paper, and would be difficult to implement in a general way for the wide
variety of gas turbine engine applications that exist today. However, the case of continuous duty power
generation is noteworthy since fuel costs over the lifetime of the plant are
typically so high that is commonly cost-effective to invest capital to improve
cycle efficiency by even one percent.
The following discussion will show that the alternative regeneration
scheme has the potential to improve cycle efficiency by several percentage
points in some scenarios.

Output by the cycle is proportional to the temperature
drop across the PT. The simple cycle
efficiency can be written as

Net work input

h

_{Cycle}=
External heat input

*mc*h

_{pg}_{T}(T6-T

_{7s}) = h

_{T}(T6-T

_{7s}) h

_{T}(T6-T

_{7s})

= =
(1)

*mc*(T

_{pg }_{4}-T

_{2}) (T

_{4}-T

_{2})

The “S” subscript in Eq.(1) refers to the temperature that is
computed when an isentropic expansion is assumed:

T

_{7s }= (P_{7 })_{ }^{γ}^{g/γg-1 }(2)
T

_{6}(P_{6})
For the simple cycle, the pressure at state 7 is assumed to be
atmosphere and the temperature at state 6 is determined by writing an energy
balance that equates the work input at the compressor to the work output by the
HPT.

*mc*(T

_{pa }_{2}-T

_{1}) =

*mc*(T

_{pg }_{4}-T

_{6}) (3)

The simple cycle
efficiency computed by Eq.(1) is used here as a comparison case for the
regenerative cycle configurations. It is
important to note that slightly lower values for simple cycle efficiency will
be computed if the cycle is modeled as having only a single turbine that
provides both the compressor work and net shaft work. Single and twin-turbine models give the same
efficiency only when the turbines are modeled as isentropic. This modeling artifact also arises when
modeling non-isentropic Rankine cycle turbines or multistage non isentropic
compression. There are no references
known to the author that discuss this thermodynamic anomaly, both the
calculation is so simple that it presumably has not warranted attention
previously. The alternative regeneration
cycle that is the focus of the present paper is modeled with a non isentropic,

*twin-turbine*configuration; hence it is more appropriate to compare those results to the larger values of
simple cycle efficiency that are computed for the twin-turbine
configuration by using Eq.(1).

Consistent with the
prior comments, a two-turbine model of a conventional regeneration cycle was
developed. In the conventional regeneration
model, heat is added to the cycle between states 2 and 3 as in fig.

**2a, and that heat is extracted from the exhaust gas stream leaving the PT at state 7.**
The resulting expression for cycle efficiency is given by

*mc*h

_{pg}_{T}(T

_{6}-T

_{7s})

hCycle (4)

*mc*(T

_{pg }_{4}-T

_{3})

State 6 is evaluated by an energy balance just as it was for the
simple cycle. Temperature 7S is again
computed with Eq.(2), but the pressure at state 7 will be larger than atmosphere
pressure by an amount equal to the pressure drop through the regenerator. The temperature at state 3 depends on the
effectiveness of the regenerator in transferring heat from the exhaust gases to
the compressed air stream, and can be evaluated from the regenerator
effectiveness, defined as

*Actual heat transferred T*

_{3}-T

_{2}

*n =*= (5)

*Maximum possible heat transferred T*

_{7}-T

_{2 }

In.Eq.(5), the heat exchanger effectiveness is defined
for the fluid with the smaller product of mass flow rate and specified heat,
which corresponds here to the compressor discharge air since it has the smaller
specific heat. The increase in working
fluid mass due to fuel addition at the combustor was ignored in the present
models, but in real engine flows the mass flow rate of the air would be
slightly less than that of the product gases, again supporting the idea that
the minimum fluid for purposes of defining the heat exchanger effectiveness
would be the compressed air stream between states 2 and 3. In Eq(5), the temperature T

_{7 }is the highest possible temperature that could be obtained by the air passing to the cobustor, and this temperature could only be realized at state 3 if the heat exchanger had negligible heat transfer resistance or infinite surface area.
From the states
identified in Fig.1, and expression for the overall cycle efficiency of the
alternative regenerative cycle can be written as

*c*h

_{pg}_{T}(T

_{6}-T

_{7s}) =

*c*h

_{pg}_{T}(T

_{4}-T

_{5s}) -

*c*(T

_{pa}_{2S}-T

_{1})/ h

_{c}

hcycle =
(6)

*c*(T

_{pg }_{4}-T

_{3})

The second and third terms in the numerator of Eq.(6) cancel one
another if the compressor work is supplied entirely by the HPT, but Eq.(6) is
written in its full form because later discussion will consider a second
approach to providing the compressor work.

The models for all
the three cycles assume that air is the working fluid between compressor and
combustor inlets (

*c*= 1.005 kJ/kg_{pa }^{o}C, g_{a }= 1.4), but that beyond the combustor inlet the chemical reaction and increased temperature alter the gas properties ([1)] so that they are better represented by c*= 1.147 kJ/kg*_{pg }^{o}C and g_{g }= 1.33. All calculation further assumed the isentropic compressor efficiency was 86 percent, the isentropic turbine efficiencies were 89percent, the combustor pressure drop was 1.3.8 kPa (2 psi), and that the compressor inlet conditions at state I were 21^{o}C(70^{o}F) and 101.4kPa (14.7 psia). In addition, a reference case was established with moderate values estimated for the remaining parameters used in the calculations. The reference case assumed that the regenerator effectiveness was 70 percent, that the turbine inlet temperature was 1100^{o}C (2011^{o}F), and that pressure drops associated with each pass through the heat exchanger were 13.8 kPa (2 psi) each. In the following discussion, the parameters used in the calculations were those associated with the reference case, unless otherwise specified.**DISCUSSION**

Conventional regeneration offers the benefit of improved
cycle efficiency over simple cycles for the ideal case where there is no
pressure drop through the regenerator.
For example, for the reference case conditions, except with co pressure
drops across the regenerator, a conventional regeneration cycle achieves cycles
efficiencies of 43.0 percent at an optimum pressure ratio (PR) of 8, compared
to the simple cycle’s efficiency of 42.7 percent at an optimum, and fairly high
Proof 37 (this small benefit of
conventional regeneration improves as effectiveness increases – eg., for an
effectiveness of 90 percent, the efficiency improves to 50.4 percent at a PR of
4). In addition to the higher cycle
efficiency of the conventional regenerative cycle, the lower optimum pressure
ratio is attractive because the compressor requirements are less
demanding. The alternative regeneration
cycle represented in Fig.1, with no regenerator pressure drops, achieve a peak
efficiency of 45.9 percent at an optimum pressure ratio of 16, which is a
substantial improvement over conventional regeneration.

Even small pressure
drops through the regenerator, like those specified in the reference case, take
a large toll on the performance of the conventional regenerative cycle, as
shown in fig.3.

In fact, for modest regenerator pressure drops of 13.8 kPa (2psi),
the performance of the conventional regenerative cycle is inferior to that of
the simple cycle, illustrating one reason why conventional regeneration is
frequently unsuitable for use on ground based engines. Figure 3 shows that the peak efficiency of
the alternative regeneration cycle (44.6 percent), with the regenerator
pressure losses, is superior to either of the other two cycles, and this peak
again occurs at the modest pressure ration of 16.

It is well known
that the maximum cycle temperature has a large effect on overall efficiency,
and this is demonstrated in fig.5. In
addition to the expected trends, Fig.5 shows two important results. For the reference case pressure drops, the
alternative regeneration cycle is superior to the other two for any turbine
inlet temperature, and the conventional regenerative cycle performance falls
further behind the that of the other two cycles as turbine inlet temperature
increases. However, the simple cycle
results shown in Fig.5 could be misleading because they imply that a simple
cycle could be useful at the higher turbine inlet temperatures, but the optimum
pressure ratios required to achieve the efficiencies at higher turbine inlet
temperature become excessive for a practical design. For example, the simple cycle requires
optimum pressure ratios of about 37.58, and 90 for turbine inlet temperature of
1100

^{o}C, 1300^{ o}C, and 1500^{ o}C, respectively, by contrast, the optimum pressure ratio of 30 for the alternative regeneration cycle operated at 1500^{ o}C is feasible with current compressor designs, and results in a cycle efficiency of 54.2 percent.
For engines that
run continuously, cycle efficiency is likely to be the most important criterion
used in designing the cycle because fuel costs over the lifetime of the engine
will far exceed the initial capital costs, However, for some applications, the
lowest specific cost or smallest engine size may be the more important criteria
[(3)]. The physical size and cost of an
engine are directly related to the specific power output, and Fig.6 shows that
there is a penalty associated with the alternative regeneration scheme in this
regard. To be consistent with this
paper’s theme of improved cycle efficiency, the operating points in Fig.6 were
determined by finding the pressure ratios that gave the highest efficiencies
(alternatively, operating points could have been determined by finding the
pressure ratios that resulted in maximum specific work output if that were the
dominant concern driving engine design).
For effectiveness between 52 percent 75 percent, the alternative
regeneration scheme has efficiency and specific work equal to, or better than
the simple cycle. For effectiveness
greater than 75 percent, the cycle efficiency climbs sharply, but the specific
work decreases below that of the simple cycle.
The conventional regeneration cycle has specific work output superior to
that of the simple cycle for any effectiveness, but the efficiency is inferior
for effectiveness less than 82 percent.
Also, for a particular effectiveness the conventional regeneration cycle
has better specific work output than the alternative regeneration cycle, but
its cycle efficiency is 3.5 to 5.5 percentage points lower, depending on the
particular conditions. Since a heat
exchanger increases the overall size and cost of an engine, the Fig.6 data
would have to be weighted carefully for a particular application to determine
which cycle would be preferable, especially for a space-limited or low cost application
where these characteristics are more important than cycle efficiency. To summarize, for the reference case
effectiveness of 0.7, the cycle incorporating conventional regeneration yields
about 13 percent more specific work output than the alternative regeneration
cycle, suggesting that the engine components could be about 13 percent smaller
than an engine utilizing the alternative regeneration scheme for a given power
requirement, but the cycle with conventional regeneration would have much lower
efficiency (39.7 percent versus 44.6 percent).

**OPTIMIZING PERFORMANCE-SINGLE SHAFT CONFIGURATION**

Figure I depicts the purpose of the HPT as providing
power input to the compressor, consistent with many GTE configurations that
have a gas generator (ie. Compressor, combustor, and HPT) and a power
turbine. There are certain advantages to
this arrangement, including the ability to operate the two turbines at different
speeds. However, there is no thermodynamic
reason why the optimum performance of the alternative regeneration cycle should
correspond to this particular hardware configuration, and in fact, results
discussed below will show that the best overall cycle efficiency usually occurs
when the temperature drop across the HPT, and hence the HPT work output, is
less than that required to drive the compressor. Thus, some work from the PT would also have
to be directed to the compressor in the optimum efficiency, or “single – shaft”
scenario. Figure 7 shows how the
efficiency varies as a function of HPT outlet pressure.

A vertical dashed
line on Fig.7 indicates the HPT outlet pressure when the cycle configuration is
that of a gas generator with separate power turbine. HPT outlet pressures to the left of the
dashed line correspond to cases where the HPT is supplying all of the
compressor work and some net shaft work.
Points to the right of the dashed line indicate that the HPT and PT are
working together to supply the compressor work.
The cycle efficiency peaks at an HPT outlet pressure slightly above that
which would be required if the HPT alone drove the compressor, and this is the
usual case for the range of parameters considered here. In fig.7 the cycle efficiency increases from
the reference case value of 44.6 percent to a maximum value of 45.3 percent
when the PT is utilized to provide 26 percent of the compressor work
requirement. The optimum cycle pressure
ratio increases from 16 in the gas-generator configuration to 20 in the single-shaft
case.

One important
concern with the alternative regeneration scheme is the temperature experienced
by the materials in the heat exchanger itself.
Since the air preheating in the alternative regeneration scheme occurs
at higher pressures and temperatures than in conventional regeneration, the
heat exchanger requirements are more severe. However, for most of the operating
conditions presented herein, the maximum heat exchanger temperatures (i.e., the
peak temperatures at state 5) were in the range 700-900

^{ o}C. Exceptions occurred for cases with higher turbine inlet temperatures and higher effectivenesses, where HPT outlet temperatures as high as 1100^{ o}C were computed for the single-shaft configurations. Modern gas/gas heat exchangers are capable of temperatures as high as 1100^{ o}C and pressures as high as 30 atmospheres ([4]), so the alternative regeneration scheme does not appear to pose any insurmountable problems in this regard. Figure 7 shows that for the optimum HPT outlet pressure and reference case conditions, the peak regenerator temperatures would be about 800^{ o}C. For contrast, if the HPT is used to provide all the compressor work in a gas-generator configuration, then the peak temperature in the regenerator is only about 690^{ o}C for the reference case conditions.
For consistency with other calculations presented
herein, Fig.7 was generated for the reference case conditions. However, fig.7
is somewhat misleading because the improvement in cycle efficiency when using
the single-shaft configuration is much more significant when considering
lower-technology regenerators having low values of effectiveness and/or large
pressure drops. Figure 8 demonstrates
how the single-shaft configuration is superior to the gas-generator
configuration, as a function of regenerator performance parameters.

As with previous figures, the overall cycle pressure
ratio has been optimized to achieve the highest cycle efficiency for each point
on the curve. The fig.8 data correspond
to optimum PRs of between 8 and 33, with the larger values required for the
lower effectivenesses. Figure 8 shows
that the single-shaft configuration effectively decreases the slope of the
efficiency curves, resulting in improved performance, especially for larger
regenerator pressure drops.
Consequently, there are more combinations of regenerator pressure drop
and effectiveness that result in performance superior to the simple cycle. The maximum regenerator temperatures required
for the single-shaft operating points shown in Fig.8 lie between 760

^{ o}C and 850^{ o}C, with the higher temperatures required for the higher effectiveness.
For the
single-shaft configuration, the peak in cycle efficiency is fairly flat and
incentive to overall cycle pressure ratio, as shown in Fig.9. For each value of overall PR in fig.9, the
cycle efficiency has been determined at the optimum HPT outlet pressure. Because the efficiency curve is fairly flat
near its peak. It is conceivable that
certain compromises might be attractive when designing a cycle’s operating
point. For example, fig.9 shows that if
a designer were willing to use a larger compressor to increase the pressure
ratio from the optimum value of 20 to a value of 30, then the cycle efficiency
would drop from 45.3 percent to 44.9 percent, and the regenerator heat ratio
would decrease by 30 percent. A 30
percent decrease in the regenerator heat ratio implies a corresponding
reduction in size of the heat exchanger that is often the bulkiest component of
a regenerative GTE. Hence the larger
compressor and small reduction in efficiency might represent tolerable design
compromise for a compact engine where overall size is a critical issue. Increasing the turbine inlet temperature
obviously results in improved cycle efficiency, but the regenerator
requirements become more severe at the same time.

Earlier
discussion pointed out that the over all pressure ratio for the gas-generator
configuration was feasible even for turbine inlet temperatures of 1500

^{o}C, whereas the simple cycle at the same temperatures requires PRs much higher than modern compressors can supply. The maximum regenerator pressure is the same as the compressor outlet pressure, so the PRs required for the gas-generator configuration (£30) are feasible in the heat exchanger as well. However, the principle drawback of the single-shaft configuration is that optimum PR increases relative to the values required for the gas-generator configuration, with negative consequences on both compressor and heat exchanger requirements.The chief attraction to the single shaft configuration appears to be in improving cycle efficiency at lower turbine inlet temperatures where optimum cycle pressure ratios are more modest.##
Conclusion

An alternative configuration for a regenerative GTE
cycle with numerous favourable operating characteristics is discussed. For practical ranges of operating parameters,
the alternative configuration always results in a cycle efficiency superior to
either a conventional regenerative cycle or a simple cycle. This performance improvement is robust and
not limited to a narrow range of operating conditions or component
efficiencies. Although the demands on
the heat exchanger are severe, the regenerator temperatures and pressures are
well below the limits of existing heat exchanger designs. The alternative regeneration scheme is
particularly attractive at high turbine inlet temperatures. For turbine inlet temperatures as high as
1500

^{o}C, optimum PRs are only 30, whereas for the same conditions the optimum pressure ratio of a simple cycle is excessive (>40) for temperatures larger than 1115^{o}C. When a power turbine and gas generator can be configured on the same shaft, operating at the same speed, then the alternative regeneration cycle efficiency can be improved even further and this situation is particularly useful if the heat exchanger is limited by low effectiveness or large pressure drops.
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