A Thermodynamic Model to Quantify the Impact of Cooling Improvements on Gas Turbine Efficiency

The ultimate goal in engine design is to produce the highest available power or thrust at the maximum efficiency with minimal fuel consumption and emissions. Turbine blade cooling increases the performance of both aero-engines and industrial gas turbines through higher allowable combustor exit temperatures and providing longer engine life. Numerous cooling techniques have been and continue to be developed by researchers and engine producers for internal and external disk and blade cooling.

There are a wide variety of cooling techniques that have been applied to certain engine designs. This required the need of assessing the relative benefits of a certain cooling technique compared to other techniques from an overall engine performance perspective. To accomplish this, a thorough thermodynamic model of the gas turbine including the turbine cooling effects needs to be used.

Several researchers have developed thermodynamic models for cooled turbine analysis. One of the most detailed models is by Consonni [1]; with other prominent ones such as GASCAN by El-Marsi [2], CPF by NASA [3], TURBOMATCH by Lallini et al. [4], and IGCC by Li et al. [5]. The latter two models have a typical aero-engine or industrial gas turbine cycle calculation coupled with a cooled turbine model (CTM). TURBOMATCH [4] differs by also including a turbomachinery algorithm. In general, cooled turbine analysis models contain a coolant fraction calculation subroutine followed by a first law analysis. This first law analysis involves a continuity and energy balance for each stage component. The analysis is then completed with estimations of cooling-related losses (e.g., exergy loss from blade heat transfer, cooling air friction losses, and fluid mixing) through a pressure loss correlation term [6], or in advanced models with a detailed second law analysis, which involves the calculation of entropy generation through a relevant heat transfer and momentum analysis.

A detailed analysis of a cooled turbine involving the second law losses was proposed by Young and Wilcock [7], which also includes rotational effects and stage loading information in rotor equations. In the current study, the methodology and approach by Young and Wilcock [7] are used to develop a cooled turbine model, and this model is later integrated into an engine performance estimation model by Uysal [8], to quantify the effects of improvements in various cooling techniques on overall engine performance. The models presented in this paper are used in a more detailed study by Uysal [9], in which the cooling technology impact on overall engine performance parameters are analyzed by using these models with experimental and/or computational fluid dynamics input data obtained for various internal and external cooling features.

The cooled turbine stage considered in this analysis is assumed to be formed by the following components: a purge before stator, a stator stage, another purge between the stator and rotor, and the rotor stage. Figure 1 shows this sequence with mainstream and coolant flow notations.

In Eq. (1), Bi_total is the total Biot number calculated for the metal and TBC materials, $ε0$ is the overall cooling effectiveness for the blade, $ηfc$ is the film cooling effectiveness, and $ηc$ is an internal cooling effectiveness. K_cool is a parameter given by Young and Wilcock [7] as well but modified here to include internal and external Stanton numbers, as well as the flow-turning angle across the stage, and the solidity of the cooled blade [12] which provides more information on the blade passage geometry to the calculations. If one of the considered cooling techniques is not present in the stage, then Eq. (1) can still be used by eliminating the relevant efficiency or Biot number.

In Eq. (3), $s0(T)$ indicates the entropy rise from absolute zero to the temperature T, which can be calculated using reduced pressures that is usually tabulated for most of the working fluids used in gas turbines [13].

The purge cooling term in Eq. (4) can be obtained from a mixing analysis of two flows. However, for the stators and rotors cooling losses should be calculated with an advanced model that includes all possible cooling losses introduced in these components. Such a model was introduced by Young and Wilcock [7], which is schematized in Fig. 2, and can be used in the cooled turbine calculations conveniently.

The assumed one-dimensional heat transfer model used for the cooled blade and the associated entropy terms from Ref. [7] are shown in Fig. 3.

Equations and derivations with assumptions to compute each of the entropy terms shown in Fig. 2 are given in detail by Young and Wilcock [7].

Based on the presented theory, a CTM is developed. The model consists of three main subsystems: a coolant calculator for coolant fraction calculations based on the semi-empirical approach in Eq. (1), an enthalpy calculation subsystem (first law analysis) that calculates the component enthalpies from Eq. (2) by using the coolant fractions calculated by the coolant calculator, and an entropy calculation subsystem (second law analysis) that employs the method by Young and Wilcock [7] to calculate the associated cooling losses. The developed algorithm, that makes use of the discussed cooled turbine theory to calculate the engine performance variables, is shown in Fig. 4.

The defined algorithm was modeled in MATLAB/Simulink in order to use it within the engine design model (EDM) developed by Uysal [8]. The EDM is an aerothermal engine performance calculation model that includes on-design, off-design, and a turbomachinery design sections for high by-pass turbofan engines. The model is based on the theory given by Mattingly [13], which is based on the conservation of continuity and energy of the flow across the gas turbine components. The model assumes a steady-state quasi-one-dimensional flow with variable-specific heat and uses mean-line calculations with free vortex design in the turbomachinery section. Polytropic efficiencies include the effects of pressure and aerodynamic losses in compressor and turbine sections. Further details on the development and the theory behind the EDM can be found in the study by Uysal [8,9] and will not be reproduced here. The EDM was validated both with aedsys software [13] and published engine data for CFM-56 and GE90 engines.

The CTM was verified with the example case results from Young and Wilcock [7] for a single-staged turbine using pure air in both hot gas and coolant sides. Mass flowrates and component exit total temperatures were the main parameters shown in the comparison in Table 1.

Small discrepancies in the comparison are likely due to the use of different thermodynamic property tables.

For the same example case, the results of the second law analysis were also given by Young and Wilcock [7] for individual entropy terms. By using this information, a comparison of the results of second law analysis was also made and is shown for a stator stage in Fig. 5.

The differences in results were within the range of error associated from plot digitizing of the data from Ref. [7] and variations in thermodynamic property tables.

Cooled engine models are developed in MATLAB Simulink to perform the cycle calculations that will calculate engine performance parameters. These models are developed for a turbofan (aero-engine) case and for an industrial gas turbine case and named as cooled engine design model (CEDM) and cooled gas turbine model (CGTM), respectively. Both models are based on the EDM developed and validated by Uysal [8] for a high by-pass turbofan engine.

Engine design model, the basis engine model for development, is an engine design and performance calculation model, which also has an aerothermal turbomachinery design section and is based on the theory given by Mattingly [13]. In this model, turbine cooling was included in calculations through the usage of two “coolant mixer” stations; the first one is before the high-pressure turbine and the second one is after the high-pressure turbine and before the first stator vane of the low-pressure turbine. In the cooled engine models, these stations are removed, and cooled turbine stage exit properties are calculated in a separate subsystem, which has the CTM algorithm. Extending the capabilities of EDM through the addition of the cooling model also allows calculation of the cooling related heat transfer and pressure losses, instead of using a lumped polytropic efficiency to reflect the influence of these effects on the component performance.

Cooled turbine calculations require parameters from the uncooled engine cycle calculations and turbomachinery design. To obtain this information, the on-design and turbomachinery design sections of EDM are retained in the cooled engine models. A schematic of the cooled engine models with their major subsystems is shown in Fig. 6.

In the cooled engine models, the cooled engine performance is treated as an off-design point, that is, a performance cycle modeling approach is used. The flowchart of the cooled off-design section of CEDM is given in Fig. 7. The same flowchart is also valid for CGTM, except the low-pressure spool components, fan, and secondary exhaust sections. For CGTM case, turbine represents a power turbine and the exhaust nozzle is replaced by a diffuser that applies the defined back-pressure ratio.

The cooled off-design section starts calculations with a cooling analysis submodel, which uses uncooled engine compressor supply pressures and temperatures to calculate the coolant fractions in the cooled engine. These fractions are then later used in the high-pressure compressor subsystem to include the effect of coolant extraction on compressor performance. This effect is calculated by dividing the compressor of the cooled engine into multiple small compressors operating with different air flowrates calculated by subtracting the turbine coolant flows (includes purge flows). Determination of coolant extraction stages from the compressor is achieved within the cooling analysis section automatically, by using the turbomachinery section results for stage pressures of each rotating component [9]. The high-pressure turbine subsystem uses coolant fractions together with entropy rise calculated at the cooling analysis section to calculate the cooled turbine performance parameters (pressure ratio, temperature ratio, isentropic efficiencies, etc.).

In Eq. (5), R_avg is the average real gas constant between the cooled turbine inlet and exit states.

Calibration of the CEDM was carried out for a CFM56-5A high by-pass turbofan engine with available published engine data [14]. The comparison of published engine data with CEDM results is documented in Table 2.

In the comparison case of Table 2, internal cooling, film cooling, and TBC layer are all assumed to be used in the high-pressures stages of the turbine. Variations in results are a result of different purge flow fractions, cooling technology parameters, and fan and exhaust losses.

Further validation was carried out for individual component performance parameters such as isentropic efficiencies, temperature ratios, and pressure ratios. Validation was accomplished by comparing the results of CEDM with GasTurb12 [15] for an aero-engine with the input set provided in Ref. [9]. In order to make both models comparable, calculated coolant fractions from CEDM (9.46% of the core flow, including purge flows) were also used as an input to GasTurb12. The comparison is shown in Table 3.

Use of additional pressure loss correlations [15] in the fan and exhaust sections by GasTurb12 is a possible explanation for slightly lower temperature and pressure ratios. Using different cooled turbine models also results in differences in turbine exit temperatures and lower temperature ratios in CEDM calculations. However, for all compared parameters the differences are within reasonable limits (less than 3%).

The effect of cooling the turbine on overall engine performance parameters can be demonstrated by comparing the uncooled and cooled version of the same engine. This comparison is shown for the input case used in the comparison in Table 4.

When turbine cooling is present, the effect of coolant extraction from the compressor reduces the air flowrate to the burner, which reduces the fuel to air ratio by a small fraction (0.4%). Due to increased entropy at the turbine due to cooling, the primary effect on high-pressure turbine physical parameters is a reduction in turbine pressure ratio (6.4%). However, reducing the turbine exit temperature to a lower temperature than the uncooled turbine results in an increase in isentropic turbine efficiency (0.04%) and a reduction in turbine temperature ratio (2.3%). Low-pressure turbine performance is also affected by the cooling of the high-pressure turbine due to a reduced inlet temperature and lower inlet pressure. With constant polytropic efficiency, in order to supply the constant amount of work to the fan and low-pressure compressor, the low-pressure turbine has a reduced exit pressure, and this results in a reduction in low-pressure turbine pressure (5%) and temperature ratio (1%). The overall effect was a 4% reduction in primary exhaust temperature. However, for fixed exhaust nozzle angle, reducing the exit pressure results in a reduction in thrust (3%), whereas increased turbine efficiencies result in an increase in propulsive efficiency (0.7%). Reduction in the fuel consumption was also noted for the engine case considered, but this effect might be case dependent as also noted by Esgar and Ziemer [16].

In order to observe the differences in the cooled engine performance prediction by CEDM and GasTurb12 over a range of input parameters, flight Mach Number, engine by-pass ratio and turbine inlet temperature inputs were changed within a predetermined range, and the predictions of turbofan engine performance parameters were compared.

In a turbofan engine design given a fixed fan pressure ratio, increasing the engine by-pass ratio reduces the fuel consumption due to reduction in the core air flowrate [15]. This well-known effect is used as the first comparison case, and the results obtained from CEDM and GasTurb12 is compared in Fig. 8 while varying the by-pass ratio from 4 to 8. The differences between the results are within 3% throughout the input range.

Figure 9 shows the comparison made for an increase in turbine inlet temperature from 2469 °R to 3669 °R. The maximum difference between the predictions by CEDM and GasTurb12 in Fig. 9 is within 3%. As the turbine inlet temperature is increased, due to the increase in required turbine cooling flows, the thrust curve slope is less positive after ∼2750 °R because of increased turbine losses and compressor work. Reduction rate in propulsive efficiency also increased after this temperature value. In turbofan engine design, this point corresponds to an optimum design point.

Modification of EDM to CEDM required only the addition of the cooled off-design section. CGTM development, however, required several additional considerations. Aside from removing turbofan related engine components, this development process included the following: an adjustment of the cycle calculations of turbine and exhaust sections for a land based engine, changing performance parameter definitions, usage of natural gas fuel combustion tables instead of kerosene, adding a transition cooling model, and modification of the turbomachinery design section per industrial gas turbine design principles.

According to Soares [17], industrial gas turbines are similar to turbojet aero-engines, in which zero thrust is produced. Therefore, the turbojet relations given by Mattingly [13] are used by equating the thrust equation to zero. Resulting cycle analysis required the back-pressure ratio (P_t9/P_t0) to be a user input, which is the case in all industrial gas turbine simulations. The transition cooling between the combustor and the turbine is modeled as a constant pressure mixer that mixes the hot gas from the combustor with the coolant extracted from the last stage of the compressor and calculates the regarding enthalpy change.

The CGTM uses a variable-specific heat model for the air and combustion products. Therefore, thermodynamic property tables of fuel combustion products are used throughout the model to extract required thermodynamic properties (reduced pressure, temperature, enthalpy, and entropy) once the fuel to air ratio and a secondary thermodynamic parameter (temperature, enthalpy, reduced pressure or entropy) at that location is known. Values are tabulated for pure air and several predetermined fuel to air ratios. For turbofan engines, these tables were for kerosene–air combustion [11,12], which may cause additional errors up to 8% for each engine component if they are used in an engine using natural gas as the fuel [18].

In order to eliminate this potential error source, thermodynamic property tables for natural gas combustion (assumed 100% methane) was generated with a complete methane combustion reaction for four different fuel-to-air ratio conditions. gaseq software [19] was used to obtain molar fractions of the combustion products, and refprop software [20] was used to generate thermodynamic tables. Obtained results were compared with the validation data by Guha [21] given for the calculated enthalpy differences between two specified temperatures for different fuel-to-air ratios for low and high temperature ranges. The comparison showed agreement with the compared data, and details of the validations are given in Ref. [9].

The parameters in the turbomachinery design section of the CEDM model (based on a turbofan engine) for application to the CGTM model (based on an industrial engine), as described by Giampaolo [22], include slower shaft speeds (i.e., lower rpm), lower internal flow speeds, lower compressor pressure ratios, lower aspect ratio in turbine blades, constant disk diameter, and longer blades. Calculations based on Mattingly [13] in the CEDM were modified with the design equations from Wilson and Korakianitis [23] to obtain the design in the CGTM. The methodology used in aircraft engines was also modified here to make a constant rotational shaft speed design. Aside from usage of different materials, it was also found that the disk shape factors, compressor loss factors, and turbine stage loadings can be lower in industrial gas turbines than typical values used for aero-engines.

A validation [9] was carried out for the CGTM with available H-Class industrial gas turbine data by using blade heights, number of stages, and disk dimensions as the comparison parameters.

Results on overall engine performance parameters such as shaft power delivered, heat rate and thermal efficiency, obtained for the calibration of CGTM with selected published H-Class industrial gas turbine data is given in Table 5. Input information on cycle inputs such as compressor pressure ratio, turbine inlet temperature, engine mass flowrate, and ambient conditions were taken from the published values in Ref. [24].

A case-specific comparison was carried out for the CGTM by using the same approach used for CEDM. The results obtained by CGTM and GasTurb12 for the same input set (given in Ref. [9]) generated for an average H-Class industrial gas turbine case are shown in Table 6.

In the industrial gas turbine case, the differences between the results obtained by the CGTM and GasTurb12 for the component performance parameters are lower, mainly due to fewer engine components that have specific pressure or temperature loss models used in GasTurb12.

Similar to the continuity tests carried out for the CEDM, selected cycle input parameters such as turbine inlet temperature, ambient temperature, and back pressure ratio were changed within a predetermined interval, and the trends obtained by the CGTM were compared with GasTurb12.

Increasing the turbine inlet temperature has a well-known enhancing effect on the shaft power delivered and thermal efficiency. Due to increased combustor exit temperature, this increase will also reduce the overall fuel consumption. However, due to the increased coolant requirements to cool the turbine blades to a fixed lower temperature (fixed by the blade material used), the performance curves will have an optimum point as also observed in the turbofan engine case. Figure 10 shows the comparison made for thermal efficiency and power-specific fuel consumption when the turbine inlet temperature is increased from 2660 °R to 3460 °R.

Similar to turbofan engine case, there exists an optimum point around a certain turbine inlet temperature (∼3050 °R), which was predicted the same by both the CGTM and GasTurb12. Above this optimum point, the advantages obtained from increasing the turbine inlet temperature are offset by the increased turbine losses and result in a reduction in engine performance.

Another test was made by increasing the ambient temperature (while keeping turbine inlet temperature, and component efficiencies constant), which has an expected effect of reducing engine performance. This is due to the nature of the Brayton cycle; increasing the engine inlet temperature will result in an increase in required compressor work, while the turbine is operating between the same pressure difference. In addition, increased coolant supply temperatures from the compressor will also reduce cooling performance in the turbine and results in a decrease in turbine performance as well. Figure 11 shows the comparison made for this test case, and the differences between the results obtained from CGTM and GasTurb12 are within 2%.

The sensitivity of selected cooling performance parameters was sought by comparing a percent change from the reference generic H-Class engine performance (Table 7). The reference values of Table 7 were determined from the values given by Wilcock et al. [25] for “advanced cooling technology” levels, which is a viable assumption for recent H-Class engine technology. Sensitivity on a chosen parameter was then obtained by fixing other parameters at their reference values and changing the selected parameter within the limits given in Table 7. The upper limits were determined by considering the values given as “super-advanced technology” by Wilcock et al. [25]. The results of reducing those parameters were also investigated, in order to observe the effect on engine performance when cooling techniques are negatively impacted during operations by conditions such as erosion, corrosion, and sand/dust particles.

Sensitivity charts were then obtained for shaft power delivered, coolant flowrates (chargeable), and thermal efficiency by plotting the percent change in these parameters against the percent change in each selected cooling parameter of Table 7. In this type of analysis, the slope shows the comparative impact strength of various cooling parameters on the engine performance variables.

The thermal efficiency sensitivity is plotted in Fig. 12. The sensitivity curves are not linear, due to changes in associated loss parameters when a cooling parameter is varied.

In Fig. 12, the slopes of sensitivity plots indicate that advancements in blade materials (through an increase in maximum allowable blade metal temperature, T_b,max) have the highest impact on the thermal efficiency, which is expected since it is the primary parameter that affects the overall blade cooling effectiveness. Advancements in film cooling techniques have the second highest impact followed by the advancements in internal cooling techniques and advancements in TBC materials. According to the heat transfer model used from Young and Wilcock [7], if the blade material has a higher conductivity (thus a lower Bi_m), it can be cooled easier from the inside, resulting in a lower coolant flow requirement by external cooling techniques. Using less external coolant flow would eventually result in a decrease in turbine losses (mixing associated losses will be reduced) and the engine performance would be affected positively. It should be noted that this is valid only when advanced TBC materials and high film cooling effectiveness exist on the blade; with less advanced TBC technology and lower film cooling efficiency, cooling the blade metal internally might be compensated by the higher heat flux coming from the hot gas side.

Shaft power delivered is directly affected by increases in thermal efficiency of the gas turbine, and thus similar trends result, as shown in Fig. 13.

As discussed, the sensitivities are directly dependent on how much a certain cooling technology is able to reduce the required coolant flowrates to cool the blade to the same maximum allowable temperature. Thus, the sensitivities of the coolant flowrates on considered cooling parameters are shown in Fig. 14. Following the results on the other performance parameters, an increase in the maximum allowable blade temperature reduces the coolant requirement most, and this is followed by the advancements in film cooling techniques, internal cooling techniques, and TBC materials, respectively. Due to the definition used for Bi_m, the slope has an opposite sign and the effect of using advanced blade materials should read in the opposite direction. Similar trends were obtained by Young and Wilcock [7]; however, the numerical values of the slopes are different due to different values for cycle inputs.

The sensitivities obtained in this section also provide information about negative changes in cooling parameters as well. For instance, erosion of TBC material during operation might reduce the TBC thickness and reduce Bi_TBC. Sand or dust particles in the incoming airflow might fill the internal and external cooling channels, resulting in lower effectiveness values. Corrosion of the blade materials might change the maximum allowable blade metal temperature negatively. In such cases, the effects on the engine performance would be strongly influenced by changes in blade metal properties and then followed by negative effects on internal and external cooling channels and TBC erosion.

A cooled turbine model was developed using the model given by Young and Wilcock [7] and was integrated into engine performance calculation models developed for high by-pass turbofan engines (CEDM) and industrial gas turbines (CGTM). Development of the CEDM was made from an earlier model developed for the same engine type [8] with changes in the usage of coolant flows in cycle calculations. This process also included defining the cooled engine case as an off-design point and modifying the related section accordingly. The CEDM, including the cooled turbine model, was then validated with GasTurb12 [15], and the effects of cooling the turbine on several engine parameters were analyzed. The effects of increasing turbine inlet temperature, by-pass ratio, and flight Mach number show the expected trends for such engines.

An industrial gas turbine version of the model, CGTM, was then developed from CEDM by including a methane combustion model, removal of components, and modification to cycle calculations as well as the mean-line turbomachinery design section. The CGTM was then validated with published available H-Class gas turbine data and GasTurb12. Validations made with turbine inlet temperature and ambient temperature show good agreement with referenced software and provided expected trends.

A sensitivity analysis using the CGTM was done with selected cooling technology parameters. The results of this analysis show that using a blade material that allows a higher maximum allowable blade temperature has the highest impact on increasing the gas turbine performance, followed by advancements in film cooling techniques (through increased adiabatic efficiency), advancements in internal cooling technologies, and advancements in TBC materials.

When the blade material is fixed by structural design, following conclusions can be drawn from the sensitivity analysis:

• •

  Although advancements in film cooling techniques provide the highest impact on increasing thermal efficiency, following this path only to increase engine thermal efficiency might require major changes in hole geometry, plenum and supply channel design

• •

  Advancements in internal cooling techniques might also require major and costly design changes to internal cooling channel geometry and their configurations but internal cooling efficiency can also be increased by cooling of the coolant flow; which might be less expensive in development costs

• •

  Although advancements in TBC materials show the lowest impact on increasing thermal efficiency, this path is also the easiest to achieve since only the coating needs to be changed and not the engine design.

It should be noted that the focus in this research was only to analyze the effects on the gas turbine performance; in the case of the sensitivity of a combined cycle performance on these parameters, the effect in the changes of exhaust temperature and pressure on other plant components would also need to be considered. The two models, CEDM and CGTM, have been validated and provide a valuable tool for turbine cooling, materials, and durability researchers to take results from experimental and numerical design studies to determine the impact on overall engine performance of their designs, including cooling effectiveness, pressure drop, and aerodynamic losses. The codes have been developed in-house at the Department of Energy, National Energy Technology Laboratory, and flowcharts of the algorithms are be made available to the turbine research and development community [9].

This research was supported by an appointment to the National Energy Technology Laboratory Research Participation Program, sponsored by the U.S. Department of Energy and administered by the Oak Ridge Institute for Science and Education.

• Oak Ridge Institute for Science and Education (ORISE Post-Doctoral and Post-Doctoral Research Fellowships).

Bi =

Biot number (hot gas side)

f =

fuel-to-air ratio (at burner)

HR =

heat rate

i =

cooled turbine stage number

PSFC =

power-specific fuel consumption

TBC =

thermal barrier coating

TSFC =

thrust-specific fuel consumption

ε =

cooling effectiveness

η =

isentropic efficiency

π =

exit to inlet total pressure ratio of the component

τ =

exit to inlet total temperature ratio of the component

Subscripts

c =

compressor (single spool)

cH =

high-pressure compressor

cL =

low-pressure compressor

g =

hot-gas

m =

metal

p =

propulsive efficiency

rc =

coolant (rotor)

sc =

coolant (stator)

t =

turbine (single spool)

th =

thermal efficiency

tH =

high-pressure turbine

tL =

low-pressure turbine

tot =

total properties

Indexing of Engine Stations

0 =

inlet

1 =

diffuser inlet

2 =

low-pressure compressor inlet

3 =

high-pressure compressor inlet (compressor inlet in single spool)

4 =

combustor exit/turbine inlet

4.1i =

cooled turbine purge station before stator

4.2i =

cooled turbine stator exit

4.3i =

cooled turbine intermediate purge station/rotor inlet

4.4 =

high-pressure turbine exit (turbine exit in single spool)

4.5 =

low-pressure turbine inlet

5 =

low-pressure turbine exit

9 =

primary exhaust exit (exhaust exit in single spool)

13 =

secondary exhaust exit

Indexing of Turbine Stations

p1 =

station after first purge injection

p2 =

station after second purge injection

r =

rotor exit

s =

stator exit

station,in =

inlet of the cooled turbine

station,ext =

exit of the cooled turbine