HEAT PIPE TURBINE VANE INTEGRATION IN GAS TURBINE ENGINES

The results of integrating heat pipes into the vanes of a turbofan engine are presented. These Heat Pipe Turbine Vanes (HPTV) are integrated into the compressor exit, turbine inlet, and exhaust flow for vane cooling and waste heat recovery. Thermodynamic analysis of HPTV turbofan engines is done and comparisons are made between heat pipe turbine vane cooling and conventional film cooling techniques. Heat transfer through the vanes is analyzed using a thermal network model. Limitations on the heat transfer caused by various limiting phenomena within the heat pipe are also determined.


INTRODUCTION
Since the invention of the turbofan engine in the early 20th century, innovations in gas turbine design have significantly improved their power and efficiency at the expense of more extreme operating temperatures. As temperatures within the hot section of modern turbofan engine designs continue to increase, novel airfoil cooling methods are required to improve engine efficiency and reliability.
Most airfoils within the hot gas path of modern turbofan engines maintain safe temperatures through the use of composite materials with ceramic coatings and film cooling, a process by which a film of cooler air from the compressor is layered over the turbine airfoils (Han et al. 2012). This layer of cool air helps to shield the airfoil from the hot gas flow, and can reduce heat transfer from the hot gas flow to the blade by as much as 50% (Louis et al. 1983). Film cooling is often paired with internal cooling methods such as impingement, ribbed channel, and pin fins cooling (Bogard and Thole, 2006). However, these cooling methods require a cool air flow to operate. The cool air must be taken from the compressor, which results in the extraction of a significant portion of the compressor discharge air for cooling (2.5 -4 percent), having an adverse effect on gas turbine efficiency (Han, 2013). Ejection of this air into the hot gas path results in aerodynamic inefficiencies, and can decrease turbine efficiency by up to 0.8% (Day et al. 1998). These cooling methods can lead to high temperature gradients across the turbine vane due to uneven cooling, resulting in increased thermal stresses (Han et al. 2012). Additionally, recent trends in the aviation industry have seen an increased interest in alternative fuel sources for gas turbine engines. Airfoils utilizing film cooling must have passages in the surface to allow for cool air to pass through, which prohibits the use of certain alternative fuels that contain particles after combustion that can block these passages (Sundaram and Thole, 2007).
A cooling method utilizing a completely closed system, with no coolant flow, could resolve these inefficiencies. A novel method for closed system turbine vane cooling is integrating heat pipes into the vanes (Faghri, 2016;Zuo et al. 1998). These Heat Pipe Turbine Vanes (HPTV) do not require a coolant film to shield the vane from the hot gas * Corresponding author. Email: Amir.Faghri@uconn.edu flow, and instead rely on the heat pipe removing sufficient heat from the vane to maintain acceptable component temperatures.
Heat pipes are highly effective heat transfer devices, utilizing the latent heat of an internal working fluid for heat transfer. Heat pipes are completely passive devices, and as such are highly reliable and require little or no maintenance (Faghri and Bergman, 2017;Benn et al. 2016;Faghri, 2016;Shabgard et al. 2015;Faghri, 2012). Conventional heat pipes are composed of a wall, wick, and working fluid in a closed container. The phase change of the working fluid is the primary means of heat transfer, and the wick provides capillary pumping to return the condensed working fluid to the evaporator. Vapor flow is driven by a pressure difference across the heat pipe, while condensate flow is driven by capillary pressure within the wick material. For high temperature applications, such as gas turbine vane cooling, liquid metal working fluids are typically used (Faghri, 2016). At the ranges seen in gas turbine operation, sodium, lithium, and calcium are likely choices for the HPTV working fluid. Langston and Faghri (1995) suggested three possible HPTV configurations. In Configuration A, a wick structure is inserted into the vane along the interior of the vane wall. This HPTV configuration operates like a conventional heat pipe, utilizing the latent heat of a working fluid to transfer heat between the evaporator and condenser sections. In Configuration B, a central channel with a cooling air flow is inserted into the HPTV. The HPTV is divided into two separate heat pipe sections with the coolant channel in between these sections. The heat pipes transfer heat between the evaporator and condenser sections, and between the wall and internal cooling air channel. This configuration provides additional cooling to the leading and trailing edges, reducing temperature variations across the vane surface. Configuration C is an annular design with a cooling air passage. The annular geometry allows for an increased heat transfer rate, however fitting the more complex geometry can be difficult. Heat pipe adopted to these geometries are shown in Fig. 1. Young and Gupta (1980) patented a turbofan engine utilizing HPTV to transfer waste heat from the hot gas stream to the bypass air stream. The design used a ring of vanes in both the hot gas flow and the bypass flow, connected by heat pipes, to transfer heat between the flows. The pressure of the bypass air flow before the HPTV must be greater than that of the hot gas stream before the HPTV for the design to improve performance. Heat pipes within gas turbine engines were discussed by Anderson et al. (1993), including the use of HPTV for turbine inlet vane cooling. The HPTV compressor section was located in the compressor exit guide vanes. A reduction in specific fuel consumption of 1.6% was found when utilizing HPTV alongside heat pipe endwall cooling. Several additional applications of heat pipes in gas turbines were noted, including turbine blade cooling, engine de-icing, and bearing cooling. The effects of heat removal from the system were not fully considered. Heat transfer analysis was not conducted, as the capillary pumping capacity of the HPTV was used to determine the heat transfer rate. As the capillary pumping pressure is typically not the limiting factor in HPTV, the heat transfer rates obtained by this analysis are likely higher than the actual heat transfer rates.
The use of HPTV was also presented in Silverstein et al. (1994). A military turbofan engine was considered, and HPTV were integrated into the low pressure turbine inlet guide vanes for cooling, with the HPTV condenser sections in the bypass air flow. Preliminary results were compared to those for a film cooling method, and a 0.2% improvement in specific fuel consumption was found. However, the method for determining HPTV heat transfer considered only the capillary limit within the heat pipe, with no consideration given to other limiting phenomena. Additionally, no heat transfer analysis was made. Lindemuth and Anderson (1999) patented a concept for heat pipe cooling of turbine vanes. The design features three vapor chambers within the vane, with supporting ribs separating the chambers. An adiabatic section is used to connect the airfoil shaped evaporator to a more conventional box shaped condenser section, outside of the engine and in a cooling air flow. Zuo et al. (1998) developed a numerical method for analyzing the transient performance of HPTV cooling. Results obtained with the method were compared with experimental results, which validated the model and solutions. Results obtained from the numerical analysis showed that HPTV can successfully complete the startup process, with the metal working fluids transitioning from solid to liquid without heat pipe dryout. These authors developed a detailed numerical model for transient HPTV operation, but did not integrate this model into the gas turbine system to determine the performance impacts of HPTV on the system. Norris et al. (2011) patented a HPTV system which placed HPTV into the low pressure turbine of a turbofan engine. The condenser section of these vanes consisted of a heat exchanger within the bypass air flow. A flow guide structure is inserted into the bypass flow to direct a sufficient amount of the flow across the HPTV condenser section.
Previous efforts based on conceptual presentations or preliminary analysis of HPTV systems have shown HPTV to be a promising cooling method to improve gas turbine efficiency. As gas turbine operational temperatures continue to rise, the compressor bleed air required for open cycle cooling methods will lead to increased cooling inefficiencies. HPTV provides a more efficient, closed cycle alternative to film and impingement cooling. HPTV are especially suited to use in turbofan engines, as the bypass airflow can provide a source of cooling for the HPTV that is conveniently located, and the energy transferred from the hot gas path to the bypass flow contributes to the thrust generated by the bypass flow.
Three applications of HPTV in turbofan engines are investigatedtheir use in turbine inlet vane cooling, compressor exit vane cooling, and the use of HPTV after the turbine for waste heat recovery. The analysis of HPTV systems is done in two parts -first, a heat transfer analysis of the HPTV, and secondly a thermodynamic analysis of the entire gas turbine system to determine the effects HPTV have on engine thrust and fuel efficiency.

HEAT PIPE TURBINE VANE HEAT TRANSFER
The HPTV acts as a heat exchanger between the vanes in the hot gas path, and the HPTV condensers placed within the bypass air flow. Heat transfer through the HPTV system was analyzed using a thermal network approach. Shabgard et al. (2015) developed a thermal network model for heat pipe heat exchangers utilizing cylindrical heat pipes. This model was extended to HPTV, including the effects of the airfoil geometry.

3
The HPTV geometry used was proposed in Faghri and Langston (1995) as Option #1, and is shown as Configuration A in Fig. 1.

Vane Geometry
The 11-parameter airfoil geometry developed by Pritchard (1985) was used to model the HPTV. The airfoil is described using five critical points, that are joined in series by either a third order polynomial or an arc. The model developed by Pritchard (1985) describes the outer geometry of the vane and was adapted to include two additional parameters -wall and wick thickness -required for the HPTV cross section. This HPTV design utilizes a uniform wall and wick thickness, however adjusting these values at different points along the vane could improve cooling and lead to a more uniform vane temperature.
This method of developing the vane geometry splits the vane into 5 sections, described by arcs or polynomials -the pressure surface polynomial, suction surface polynomial, suction surface arc, leading edge arc, and trailing edge arc. These sections are further described in Appendix B.

Heat Transfer Methodology
The thermal network model was used to analyze the heat transfer rate through the HPTV, based on the model developed for heat pipe heat exchanger in Shabgard et al. (2015). The full thermal network model of a HPTV system including nomenclature is shown in Fig. 2.
As the airfoil geometry is divided into five distinct sections the thermal resistance across the wall and wick must be calculated for each of these sections independently. These five thermal resistances can then be added in parallel to obtain the thermal resistance of the wall or wick, shown as Rw and Rwk in Fig. 2.
The heat output into the coolant stream is equal to the heat input into the evaporator section of the HPTV, assuming ideal operation. The heat transfer load required to cool the HPTV can be determined by the convection between the vane and the hot gas flow.
Where is the heat transfer rate through the HPTV, ℎ is the average convective heat transfer coefficient, is the HPTV evaporator surface area, is the hot gas flow temperature, and is the acceptable vane wall temperature.
The convective heat transfer coefficient, ℎ, will vary across the HPTV. To get the total heat transfer rate, the average heat transfer rate, ℎ , should be considered.
Vanes operating in the hot gas flow typically employ a ceramic coating to protect the metal from the high temperature gas flow. The thermal resistance through the ceramic can be added to the external resistance.
Where is the thermal conductivity of the ceramic coating, and is the ceramic coating thickness.

Heat Transfer Limitations
The heat transfer rate determined using thermal network analysis neglects several different forms of limiting phenomena, which may result in significantly reduced heat flux than what would be expected from the thermal network results. Limiting phenomena which must be considered include the capillary, sonic, entrainment, condenser, and boiling limitations (Faghri, 2016). The solutions to these limiting phenomena are well known for the cylindrical geometry, and are adopted for a vane geometry.

Fig. 2 Thermal Network Model of a HPTV System
The pumping ability of a capillary (wick) structure is limited. This limitation is referred to as the capillary limit in heat pipes. As this limit is approached, the wick will be unable to return sufficient condensate to the evaporator, limiting heat transport capability. This limit is most dependent on the working fluid used by the heat pipe, and the wick design. Proper wick design can improve capillary pumping ability, avoiding the capillary limit in HPTV.
If the radial heat flux through the heat pipe wall becomes excessively high, nucleation begins to occur in the wick. The boiling of the working fluid can interfere with its circulation, limiting the heat transfer rate. This is referred to as the boiling limit in heat pipes. Boiling is undesirable in wick heat pipes because bubbles will form and block the flow of liquid through the wick. The boiling limit can also be negated through proper wick design in HPTV.
Heat pipes may encounter heat transfer limitations if the vapor velocity reaches the speed of sound inside the heat pipe. This choked working condition is called the sonic limit in heat pipes. Unlike the capillary and boiling limits, the sonic limit is primarily dependent on the geometry of the system, not the wick design. As the geometry of a HPTV system is primarily dependent on the requirements of the external flow, it can be difficult to design the system to improve the sonic limit.
The heat transferred to the HPTV system must be fully removed in the condenser, under steady-state operation. In cases where the condenser heat transfer rate is insufficient, the condenser limit is reached. Silverstein et al. (1995) encountered the condenser limit in their analysis of a HPTV system, and resolved the issue by adding fins external to the HPTV condenser section. The HPTV design patented by Norris et al. (2011) uses a duct in the bypass air flow to ensure sufficient cooling air flows past the condenser. Additional condenser section and coolant flow alterations can ensure sufficient condenser heat transfer rate.
When the velocity of the vapor becomes sufficiently high, the shear force existing at the liquid-vapor interface may tear the liquid from the wick and entrain it into the vapor stream. This is referred to as the entrainment limit in heat pipes. This phenomenon reduces condensate return to the evaporator, limiting the heat transport capability. While the vapor velocity is primarily tied to the HPTV geometry, the wick can be designed to reduce the impact of entrainment. A composite wick, with a less permeable layer between the liquid and vapor flows, can reduce the impact of entrainment on the system. Compared to cylindrical heat pipes of a similar size, HPTV encounter the entrainment and sonic limitations at a lower heat transfer rate. This is due to the geometry of the system, as the ratio between the perimeter and the area of a HPTV cross section is much greater than that of a similarly sized cylinder. As such, the sonic and entrainment limitations must be given greater attention than in conventional heat pipe designs.

HPTV THERMOSYNAMIC ANALYSIS
The effects of HPTV integration can be determined by analyzing the thermodynamics of a turbofan engine with HPTV components. Three applications of HPTV were considered -HPTV turbine inlet guide vanes, HPTV compressor exit vanes, and HPTV for waste heat recovery. An idealized approach was used for the thermodynamic analysis, as the objective is to compare the HPTV and film cooling systems. The flow through the gas turbine was treated as an ideal gas, and the gas turbine components, not including the vanes studied, were considered adiabatic.

Turbine Inlet Guide Vanes
The turbine Inlet Guide Vanes (IGV) experience the highest temperatures in the turbofan engine, as they are the first set of airfoils in the hot gas flow after the combustor. IGV cooling is required to maintain safe airfoil temperatures and prevent large temperature differences across the vane, which can lead to thermal fractures. The cross-section of a turbofan engine with HPTV IGV is shown in Fig. 3.

Fig. 3 HPTV Turbine Inlet Guide Vane Cooling in a Turbofan Engine
The turbofan engine was analyzed following the gas path, and the different stages 0 -6 are shown in red circles in Fig. 3.
Flow properties after the fan can be determined using the fan pressure ratio (FPR) and bypass ratio (BPR).
Where 0 is the atmospheric pressure, 1 is the flow pressure after the fan, is the fan pressure ratio, is the engine bypass ratio, ̇ is the inlet mass flow rate, ̇ is the main gas flow mass flow rate, ̇ is the bypass flow mass flow rate, is the fan work, 0 is the inlet enthalpy and 1 is the flow enthalpy after the fan. The enthalpy before and after the fan, 0 and 1 , can be determined from the pressure (Bergman and Incropera, 2011).
The compressor exit conditions can be obtained similarly to those of the fan.
Where is the compressor pressure ratio, is the compressor work, 2 is the main flow pressure after the compressor, and 2 is the main flow enthalpy after the compressor.
Properties after the combustor can be solved using the known heat input. The system is idealized, as the addition of fuel to the air flow is neglected, and the flow exiting the combustor is assumed to be pure air.

=̇∆
(9) Where is the heat input to the system from combustion, ̇ is the mass flow rate of the fuel, ∆ is the lower heating value of the fuel, and 3 is the main flow enthalpy after the combustor.
The required cooling, , can be determined using Eqs. (1) and (2), substituting 3 for . The change in enthalpy of the main flow and the bypass flow due to heat transfer through the HPTV can be determined with the heat transfer rate and the mass flow rates.
Where 4 is the enthalpy of the main flow after the HPTV, is the number of HPTV, and 4 is the enthalpy of the bypass flow after the HPTV. When the pressure change across the HPTV is determined for the main and bypass flows, a pressure loss factor is included to account for the interruption of the flow by the insertion of the vanes.
The turbine work in a turbofan engine is equal to the sum of the fan and compressor work. This can be used to determine the enthalpy of the flow after the turbine.
Where is the turbine work and 5 is the enthalpy of the main flow after the turbine.
The velocity of the main and bypass flow after the nozzle is required to calculate the thrust of the engine. The enthalpy of the main and bypass flows after the nozzle can be calculated using the pressure difference across the nozzle. A conversion factor of 1000 is included to convert the enthalpy, in kilojoules, to velocity in meters per second.
Where is the final velocity of the main flow, is the final velocity of the bypass flow, 6 is the enthalpy of the main flow after the nozzle, 6 is the velocity of the bypass flow after the nozzle, and ℎ is the thrust of the engine.

Compressor Exit Guide Vanes
While the compressor operates at significantly lower temperatures than the turbine, increasing pressure ratios can create temperatures high enough at the compressor exit to require cooling. HPTV can be integrated into the compressor exit vanes to provide cooling in a similar fashion to the turbine inlet guide vanes. A HPTV compressor exit vane cooling system is shown in Fig. 4.
The allowable compressor exit temperature can be determined using the heat transfer rate of the HPTV, found using Eqs. (1) and (2).
Where ℎ is the average convective heat transfer coefficient across the compressor exit vane and , is the allowable compressor exit temperature. Young and Gupta (1980) found that transferring heat from the main stream to the bypass air stream of a turbofan engine can improve performance under certain conditions and patented an engine design using a heat exchanger to do this. A HPTV system based on this concept is investigated, as shown in Fig. 5.

Fig. 5 HPTV for Waste Heat Recovery in a Turbofan Engine
The HPTV design and limitations in the waste heat recovery role differ significantly from those of the IGV and CEV HPTV designs, as the primary goal in waste heat recovery is heat transfer, not cooling. This concept will only improve turbofan engine performance in certain cases, depending on the pressure of the bypass air flow and whether the bypass and main flows are mixed.

Initial Submission
In the HPTV turbofan engine, the HPTV uses the bypass air flow to cool the HPTV condenser section. This process removes heat from the main gas flow and transfers it into the bypass flow, increasing the thrust provided by the bypass air, while decreasing the energy available in the main gas flow.
The HPTV airfoil must be constructed of a material capable of withstanding the forces within the engine, with a high melting point to decrease the required cooling, and a high thermal conductivity to improve HPTV heat transfer. The HPTV design investigated used a nickel-based alloy, IN-100, as the vane wall material. The properties and aerospace applications of IN-100 and other nickel-based alloys were investigated by Pollock and Tin (2006). A homogeneous screen mesh wick was used, with mesh diameter of 0.2 mm. The working fluid chosen was sodium, due to its ideal properties for heat pipe operation at the desired temperatures. Heat pipe working fluids across a variety of temperature ranges are presented and discussed in Faghri (2016).
The parameters of the turbofan turbine IGV system are presented in Table 1. Convective heat transfer coefficients used include the exterior surface area of the HPTV, as such the units are kW/K. The method for determining the vane convective heat transfer coefficient is presented in Gauntner and Sucec (1978). The engine was also analyzed with the use of film cooling for the IGV, based on the film cooling performance values studied in Kumar and Singh (2008). The engine was studied in flight at an altitude of 10 km. Results of both the HPTV and film-cooled engines are presented in Table  2. HPTV resulted in a 1.3% increase in thrust compared to a film cooling system. This led to a 1.24% decrease in thrust specific fuel consumption (TSFC), a significant improvement in gas turbine fuel efficiency. The reduction in required bleed air from the compressor offered the greatest improvement in efficiency, while the improved turbine efficiency due to the removal of the cool air film was offset by the loss of energy through the HPTV to the bypass air flow.
Heat transfer limitations in the HPTV were calculated to ensure no limiting phenomena occurred that could lead to reduced heat transfer or HPTV dryout. Results of the heat transfer analysis are presented in Table  3.

Limitation
Heat Transfer Limit (kW)

Capillary 7123
Boiling 76415 Sonic 150 Entrainment 8.5 The capillary, boiling, and sonic limitations far exceeded the actual heat transfer rate of 7.7 kW. The entrainment limit is the closest limitation, occurring with a 10% increase in the heat transfer rate. A composite wick design, with a finer mesh between the vapor flow and liquid flow, could be implemented in the HPTV design if a greater margin is desired between the heat transfer rate and limiting phenomena.

Compressor Exit Vanes
With high gas turbine pressure ratios, the temperature at the compressor exit can approach or exceed material limits. Compressor exit vane (CEV) cooling allows for higher pressure ratios to be achieved, as higher temperatures can be withstood at the compressor exit. The use of heat pipes for compressor exit vane cooling was patented by McGarry (1978). A turbofan engine was analyzed, both with and without HPTV CEV. The system was run at the highest pressure ratio possible without exceeding temperature limits at the compressor exit. Input parameters are shown in Table 4. The results of increasing compressor pressure rations allowed by higher exit temperatures are presented in Table 5.
HPTV cooling allows for higher compression rations, greatly increasing system thrust and fuel efficiency. The analysis only considers the increase in pressure ratio -the impact this increase has on later cooling system loads, and the additional changes to the compressor required by this higher pressure flow are not considered. Integrating HPTV into the turbine vanes is significantly easier than into compressor vanes, due to the required airfoil geometry. Turbine airfoils have sufficient thickness to contain a wick and vapor chamber, while compressor airfoils have difficulty fitting these while maintaining structural integrity.

Waste Heat Recovery
Waste heat recovery is a common practice in land-based gas turbine systems. Combined cycle and cogeneration plants increase their overall efficiency by utilizing the waste heat from the gas turbine system to provide heating, or power secondary steam cycles. Young and Gupta (1980) proposed a similar system for turbofan engines, where heat is transferred from the main gas flow to the bypass air flow after the turbine. It was found that in certain cases this redistribution of energy increased the overall thrust provided by the engine. An analysis of a turbofan engine using HPTV to transfer heat from the main gas flow to the bypass flow was conducted. Input parameters for the turbofan system are presented in Table 6. A 2% pressure loss was assumed in the main and bypass flows due to the insertion of additional vanes into the fluid path. As there is fewer restraints on HPTV design in the waste heat recovery system, the thermal resistance values can be fine-tuned to achieve peak performance at specific operating conditions. Results of the analysis are presented in Table 7.
HPTV waste heat recovery vanes led to a 1.2% decrease in specific fuel consumption by redistributing energy from the main flow to the bypass flow.

CONCLUSIONS
HPTV offer significant performance increases in a variety of applications within turbofan engines, compared to conventional film cooling methods. HPTV offer improved cooling, with a more uniform temperature distribution across the airfoil. HPTV eliminate the need for bleed air from the compressor for cooling and allow for greater control over hot gas flow by removing the interference caused by a cool air film. In design, the removal of the cooling film makes computational analysis of flow across turbine vanes easier, allowing for faster analysis and development of turbofan engines. Removal of the film cooling passages in the turbine vane allows for a greater variety of fuels to be employed, as there is no threat of cool air passage blockage due to particulates from some alternative fuels.
Due to the proximity of the bypass air flow, turbofan engines are uniquely positioned to take advantage of HPTV compared to other gas turbine systems. HPTV improve many aspects of turbofan engine operation, including vane part life and fuel efficiency that are important to the aerospace industry. HPTV are a promising new method for vane cooling as engine temperatures continue to increase and alternative fuels see more development