An Alternative For Regenerative Gas Turbine Engine - Engineering Report

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_pgh_T(T6-T_7s) = h_T(T6-T_7s)                            h_T(T6-T_7s)

                    =                                                              =                                             (1)

                                 mc_pg (T₄-T₂)                                               (T₄-T₂)         

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

                        T_7s   =    (P₇ ) ^γg/γg-1                                                                                                          (2)

                       T₆           (P₆)                                                                            

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_pa (T₂-T₁) =  mc_pg (T₄-T₆)                                                                    (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_pgh_T(T₆-T_7s)

            hCycle                                                                        (4)                   

 mc_pg (T₄-T₃)

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                           T₃-T₂

   n =                                                               =                                  (5)

            Maximum possible heat transferred           T₇-T₂

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 T₇ 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_pgh_T(T₆-T_7s) =  c_pgh_T(T₄-T_5s) - c_pa(T_2S-T₁)/  h_c

            hcycle     =                                                                                               (6)

                                                            c_pg (T₄-T₃)                                                       

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_pa = 1.005 kJ/kg^oC, 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_pg = 1.147 kJ/kg^oC 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^oC(70^oF) 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^oC (2011^oF), 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^oC, 1300 ^oC, and 1500 ^oC, respectively, by contrast, the optimum pressure ratio of 30 for the alternative regeneration cycle operated at 1500 ^oC 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 ^oC.  Exceptions occurred for cases with higher turbine inlet temperatures and higher effectivenesses, where HPT outlet temperatures as high as 1100 ^oC were computed for the single-shaft configurations.  Modern gas/gas heat exchangers are capable of temperatures as high as 1100 ^oC 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 ^oC.  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 ^oC 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 ^oC and 850 ^oC, 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^oC, 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^oC, 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^oC.  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.