1 ISABE-2015-20186 Analysis of Temperature Distribution Using Conjugate Heat Transfer in a HPT Stage via CFD Lucilene Moraes da Silva Jesuino Takachi Tomita Cleverson Bringhenti Turbomachines Department Aeronautics Institute of Technology São José dos Campos Brazil Abstract The turbine blade surface is exposed to the hot gas temperatures from combustion chamber, so the heat transfer parameters affect the turbine performance characteristics and blade life. A common practice, in turbomachinery simulations, to get a good prediction of the metal temperature distribution on the blade surface is to determine the flowfield and heat transfer based on the use of Conjugate Heat Transfer (CHT) technique. Hence, it is possible to investigate some performance parameters when the blade is treated with different heat transfer conditions. The CHT in a HPT stage performance was performed using commercial CFD software to evaluate the turbine performance and flowfield variations. Three cases were performed: blade with zero wall Thickness condition, blade with CHT without convection (but, with different temperatures at adjacent walls) and blade with heat flux. The results obtained shows the importance of CHT analysis to predict the turbine blade metal temperature, because considerable temperature variations on blade suction and pressure sides can be observed for different blade heat transfer treatments. Nomenclature Tw T0 hc qw qrad qcond temperature on the wall Wall Adjacent Temperature Wall Heat Transfer Coefficient Wall Heat Flux Radiation Heat Flux Conduction Heat Flux Introduction Gas turbines engines are used in aircraft propulsion and power generation applications. The gas turbine advantage is that it produces a great amount of energy in reduced size and weight and can be drived using different type of fuel. For a power generation application increasing the turbine inlet temperature (TIT), at a given pressure ratio, increases specific power, as well as increasing pressure ratio increases the overall efficiency at a given temperature. The heat transfer increases with the TIT. However, there are constraints as thermal stresses, metal temperature and blade lifes. In typical gas turbine engines the nozzle guide vanes (NGV) support the highest operating temperatures. The present gas turbine engines requires higher turbine inlet temperatures as engines are operating at higher thrust and thermal efficiency at the same time operating a turbine at higher temperature reduces the life of blades or vanes due to thermal stresses. Due to the temperatures far above the permissible metal temperature melting point) in HP stage turbine blades, high temperature material development and sophisticated cooling techniques have been studied with the aim to operate without failure and with high performance also resulting in greater fuel economy. In the past decades, numerous studies have been accomplished to simulate the Conjugate Heat Transfer (CHT) in HPT.
Commonly, the CHT can be solved in two ways: fluid and solid domains separately or coupled. In the separately method, the fluid domain is solved and then the boundaries of the fluid are used as boundary conditions for the solid domain. In the coupled method, solid usually is treated as a different block in the overall grid space as solid and fluid domains interacting through interfaces. In this research, was used the coupled method. This paper investigates a non-cooled HPT, although researches about heat transfer, CHT and metal temperature are necessary to evaluate the blade and vane life. According Gardner (1979), both the vane and blade materials are nickel base single crystal alloys which offer superior creep strength properties, along with good resistance to thermal fatigue. In this work, CHT analysis will be carried out to determine the efficiency, pressure ratio and temperature distribution variations in a HPT for different conditions using the commercial software, ANSYS CFX v.16. The CFD analysis will be carried out using Reynolds Averaged Navier-Stokes(RANS) equations at steady-state regime. Brief Background about Heat transfer predictions The heat transfer predictions is a subject vastly studied on gas turbine area, in which in the last two decades, this theme has been studied, as described in Azad et al. (2000) and Bunker (2014). Salazar (2005) describe that, standard practices to solve heat transfer problems on gas turbine components usually may not be adequate to predict metal temperatures. The enormous amount of time spent to generate an appropriate mesh and to solve the fluid mechanics equations coupled with heat conduction, for the solid parts, is the causes that CHT is not commonly used. However, an appropriate metal temperature prediction is important to study techniques that increases 2 the blade life and overall turbine efficiency. In thermal machines, it is essential to determine the local fluid temperature at walls (Tw), adjacent wall temperature (T0), wall heat transfer coefficient (hc) and wall heat flux (qw). An example of different domains (fluid and solid) is represented in Fig. 1: Figure 1 General representation of CHT (ANSYS CFX Tutorial) There are different assumptions to study the blade metal temperature, as follows: 1. The blade temperature is determined by total energy equation: Considering that there is no blade wall thickness (zero wall thickness). 2. The solid blade wall thickness is considered: There is heat conduction across the blade wall, but the convective heat flux is zero, internally. 3. The solid blade wall thickness is considered with Conjugate Heat Transfer imposition (T w T 0 and q w 0): It is used to evaluate the interaction between solid and fluid considering that there is a local heat transfer coefficient (hc). In this work, hc was adopted as 500 W/m 2 K and 2,000 W/m 2 K. In studies involving cooled blades, hc should be carefully calculated based on the design of cooling system and cold air characteristics, that was bleed from compressor. To adopted a more accurate hc value, it is necessary to determine the flow conditions inside of the blade. Cases Studied The aim of this work, was to evaluate the heat transfer in a HPT, NGV and rotor blade surfaces. The
study was conducted, as Fig. 2. In case 1, the shown in fluid was considered as zero wall Thickness at boundary. In case 2, the fluid and solid were considered and the wall was set as CHT without convection. In case 3, the fluid and solid were considered, and a heat transfer coefficient was imposed at wall boundary. I. Geometry and CFD domain model The axial turbine geometry used in this study is a HPT stage from GE E³ program described by Thulin (1982). This HPT was also studied by Tomita and Silva (2014), in which the authors improve the HPT performance changing the rotor tip geometry. The comparison between the experimental data and numerical results considering the rotor with flat-tip are reported in the work of Tomita et al.(2012), Silva (2012) and Tomita and Silva (2014). 3 Figure 2 Different set-up used in the simulations. In case 1, the mesh consists only in fluid domain. In cases 2, 3 and 4, the mesh consists of fluid and solid domains. The solid domain was considered CHT without convection in case 2 and in case 3 and 4 a heat transfer coefficient of 500 W/m 2 K and other of 2,000 W/m²K were set. Methodology The model of computational domain and boundary conditions were considered according to Thulin (1982). The modelling of solid part was developed using SpaceClaim software and the mesh generation was carried out using ANSYS ICEM CFD v.16. Appropriate tetrahedral mesh was generated in the geometry considering the quality of control volumes as edge angles and its smoothing along the domain. The procedure adopted is shown in Fig. 3. Figure 3 Methodology adopted for the simulation. Figure 4 3D view of HPT stage and CFD domain model. II. CFD Mesh The full mesh consist of fluid and solid domain. In solid regions, the mesh requirements are quite different of fluid mesh, in which high gradients can be found in discontinuous regions, as shock waves and due to the fact that there is convective terms associated with the flow transport. Table 1 shows the number of nodes and the number of elements used in each mesh domain. Commonly, CHT simulation requires a good boundary layer resolution, usually mesh at wall surfaces needs to be rather refined to obtain realistic heat flux results at the fluid/solid interface. Numerically speaking, the simulation process of flow and heat transfer calculations requires different time steps to maintain a good numerical stability
and to reach a converged solution for a realistic steady-state condition. Figure 5 shows the HPT computational domain with the mesh at boundaries. Table 1 Number of nodes and elements for each computational domain Domain Nodes Elements NGV Solid 263,228 1312,141 NGV Fluid 282,110 1090,751 Rotor Solid 193,591 1379,301 Rotor Fluid 162,179 1291,768 4 IV. Numerical Issues a) Boundary Conditions: At inlet: total conditions (pressure and temperature), velocity vector angles and turbulence intensity; At Outlet: static pressure fixed at hub and varying from hub-totip, using radial equilibrium equation; At inter-blade surfaces: periodicity; At inter-blade rows: mixingplane approach; At Walls: non-slip condition; Fluid-Solid interfaces: GGI connections. b) Turbulence Model Two-equation Shear Stress Turbulence model developed by Menter(1993). In this work, the SST turbulence model was set based on the previous experiences of the authors as described by Tomita et al. (2012). Figure 5 ICEM CFD fluid mesh. III. HPT data, Boundary Conditions and Numerical Issues The main data of the HPT studied in this work are presented bellow: a) Design Data Tangential velocity at blade tip = 390 m/s External gas total temperature = 697 K Inlet total pressure = 607.8 KPa Outlet static pressure = 135 KPa b) Geometrical Data NGV: Number of blades = 24 Blade span = 50.3 mm Blade chord = 94.8 mm Blade aspect ratio = 0.53 ROTOR: Number of blades = 54 Blade span = 42.6 mm Blade chord = 43 mm Blade aspect ratio = 0.95 c) Discretization Schemes for Convective Terms from Momentum Equations First Order (only to start the numerical iterations) High Resolution (after 200 iterations from first-order scheme) Due to the fact that the flow is complex within the HPT, a more dissipative scheme (first-order) was set to start the first 200 iterations. After this, the secondorder scheme is turn-on (high resolution) to ensure good numerical stability. d) Heat Transfer Model Total Energy CHT without convection CHT with heat transfer coefficient The numerical procedure was monitored based on the residual decayment of continuity and momentum equations as shown in Fig. 6. The overshoot at iteration 200 is due to the change in numerical discretization order as aforementioned. The mass-flow and efficiency variation were also monitored until its stabilization.
5 Figure 6 Decayment residual. Results The results for the case 1(zero wall thickness), case 2 (CHT without convection condition) and cases 3 and 4 (CHT with heat transfer coefficient condition) are presented in Tab. 2. Table 2 Pressure ratio, efficiency and mass flow at design point. Cases Studied Pressure Ratio Efficiency [%] Mass Flow [Kg/s] Zero wall Thickness 3.75 88.7 14.9 CHT w/o conv. 3.77 87.3 14.8 CHT-HTC 500 3.77 88.3 14.9 CHT-HTC 2000 3.76 88.8 14.9 Experimental Data 4.0 88.0 15.0 Note that, the efficiencies are different for each blade heat transfer condition. Different blade wall temperature cause changes in main flow along the turbine streamwise. Hence, internal loss sources will vary, changing also the velocity triangles and turbine performance characteristics. This is more remarkable for changes in the velocity field close to the blade trailing edge. It is possible to observe differences in the Mach number, pressure and temperature fields for each heat transfer condition as shown in Figs. 7, 8 and 9, in which all cut plane are done at midspan. Certainly, the velocity field are affected by blade wall temperature.
6 Figure 7 Mach Number contours in HPT stage. In Fig. 8, it is possible to observe the influence of solid walls in the turbine heat transfer. Figure 8 Static pressure contours in HPT stage.
7 agreement with the work of Andreini et al. (2012). Table 3 Total temperature at inlet and outlet of HPT. Cases Studied Total Temperature at Inlet [K] Total Temperature at Outlet [K] Zero wall 697.0 532.3 Thickness CHT w/o conv. 697.0 523.2 HTC 500 697.0 515.3 HTC 2000 697.0 512.7 The average local heat transfer coefficient at NGV and rotor blade walls are shown in Tab. 4. Table 4 Average Local Heat Transfer Coefficient at blades surfaces. Cases Studied NGV Wall Heat Transfer Coefficient [W/m² K] Rotor Wall Heat Transfer Coefficient [W/m² K] Zero wall Thickness 1.92 10 3 1.26 10 3 CHT w/o conv. 2.24 10 3 1.32 10 3 HTC 500 2.32 10 3 1.40 10³ HTC 2000 3.74 10 3 1.62 10 3 The Tab. 5 show average values of wall heat flux on blade surfaces. Table 5 Wall Heat Flux at NGV and rotor blades surfaces. Cases Studied NGV Wall Heat Flux [W/m²] Rotor Wall Heat Flux [W/m²] HTC 500 2.85 10 4 3.95 10 4 HTC 2000 1.14 10 5 1.58 10 5 Figure 9 Temperature contours in HPT stage. The Tab. 3 show the total temperature at HPT inlet and outlet for all heat transfer condition. Note that, different solid wall treatment supply different values of temperature at outlet affecting the turbine power. These results, are in Figures 10 and 11 shows the temperature distribution at NGV and rotor midspan walls for all heat transfer condition. The cases 3 and 4, is a common case to use during the cooled blade design, in which the metal temperature is lower than other cases (1 and 2), aiming temperature distribution improvements to protect the blade wall against high gas temperatures.
8 of CHT in predicting the blade metal temperatures, in which there are differences when we consider CHT. Future work can be performed using different values of hc obtained from a specific cooling system design. Figure 10 Comparison of blade metal temperature for all cases - NGV blade. The methodology presented in this work can be applied to simulate the turbine performance characteristics considering a simple passage convection cooling system in turbine blades. A more detailed study can be done evaluating the thermal boundarylayer changes for different heat transfer conditions and its relation with the changes in velocity triangles. Acknowledgements This research was supported by the Turbomachines Department at Aeronautics Institute of Technology (ITA). References Figure 11 Comparison of blade metal temperature for all cases - rotor blade. Conclusion A simple methodology to solve CHT problems was demonstrated and discussed for a HPT. The results of this work, are relevant to highlight the importance of CHT in predicting the blade metal temperatures mainly for cooled blades. The goal of this work, was analyze the efficiency, pressure ratio and blade wall temperatures heat transfer impositions are set at solid walls. Hence: The results show that HPT performance (pressure ratio and efficiency) are very slightly affected when we consider the CHT compared with the zero wall thickness case. The results of this work, are relevant to highlight the importance Gardner, W. B.,1979, Energy Efficient Engine High-Pressure Turbine Uncooled Rig Technology Report. NASA. Cleveland, Ohio. (NASA-CR-165149) Azad, Gm S.; Hart, Je-Chin; Teng, Shuye and Boyle, Robert J.. Heat transfer and pressure distributions on a gas turbine blade tip. ASME Turbo Expo 2000, Munich. GT2000-0194, May. 2000, 8p. Bunker, R. S. Turbine Heat Transfer and Cooling: An Overview. ASME Turbo Expo 2014, San Antonio, Texas. GT2013-94174.Jun. 2014, 50p. Salazar, Santiago, 2005, Conjugate Heat Transfer on a Gas Turbine Blade. Thesis of Master of Science, University of Central Florida. Orlando, Florida. 46 p. Ansys CFX Tutorials. ANSYS, INC. Release 16.0 Thulin, R. D.; Howe, D. C.; Singer, I. D., 1982, Energy Efficient Engine - High-Pressure Turbine Detailed Design Report. NASA. Cleveland, Ohio. (NASA CR-165608).
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