ON THE EFFECTS OF INLET SWIRL ON ADIABATIC FILM COOLING EFFECTIVENESS AND NET HEAT FLUX REDUCTION OF A HEAVILY FILM-COOLED VANE

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1 ISABE ON THE EFFECTS OF INLET SWIRL ON ADIABATIC FILM COOLING EFFECTIVENESS AND NET HEAT FLUX REDUCTION OF A HEAVILY FILM-COOLED VANE Duccio Griffini, Massimiliano Insinna, Simone Salvadori, Francesco Martelli Department of Industrial Engineering, University of Florence via di S. Marta, Florence, Italy simone.salvadori@unifi.it Abstract A linear cascade of high-pressure vanes equipped with a realistic film-cooling configuration has been studied. The aim is to provide an accurate analysis of a heavily cooled high-pressure vane subjected to aggressive inlet swirl. The analyzed vane is characterized by the presence of multiple rows of fan-shaped holes along pressure and suction side while the leading edge is protected by a showerhead system. Numerical simulations have been performed on hybrid unstructured grids using a steady approach with the commercial code ANSYS Fluent. The transitional k T-k L-ω model by Walters and Cokljat has been selected as turbulence closure. A realistic computational domain that mimic a combustor/vane count of 1:2 has been used. The classical analysis approach with uniform inlet flow has been compared with an approach that takes into account inlet swirl motion considering two clocking positions of such velocity distortion. This latter have been obtained through a non-reacting swirl generator experimented during the EU-funded TATEF2 Project and representative of modern aeroengines. Results highlight the importance of considering realistic boundary conditions for cooling system analysis and quantify the effects of swirl in affecting external heat transfer. Nomenclature C chord [m] HTC heat transfer [W/m 2 K] coefficient k kinetic energy [m 2 /s 2 ] L length scale [m] NHFR net heat flux [-] reduction p pressure [Pa] q heat flux [W/m 2 ] s curvilinear abscissa [m] T temperature [K] Tu turbulence level [-] ~ average spanwise average pitch-wise average ˆ Subscripts 0 stagnation quantity ax axial aw adiabatic wall c referred to coolant exit referred at cooling holes exit in inlet L laminar m referred to mainstream max maximum min minimum rec recovery T turbulent un referred to uncooled geometry w wall Greek symbols η adiabatic effectiveness [-] ϕ overall film effectiveness [-] ω specific dissipation rate [s -1 ] Abbreviations BR Blowing Ratio DR Density Ratio GCI Grid Convergence Index HPV High-Pressure Vane LE Leading Edge TE Trailing Edge 1

2 Introduction Computational Fluid Dynamics (CFD) analysis needs to reach high levels of accuracy in order to satisfy the continuous demand for increasing turbomachinery performance and reliability. To improve the fidelity of the simulations, especially concerning high-pressure turbine vanes, realistic non-uniform inlet conditions must be included due to their crucial role in affecting the aero-thermal behaviour of such components. A crucial aspect consists in the residual swirl motion coming from the combustion chamber. As demonstrated by Giller and Schiffer 2, swirl strongly affects aero-thermal performance of the high-pressure vanes. Insinna et al. 3,4 recently studied the effects of realistic inflow conditions on film cooled research transonic HPVs showing the crucial importance of considering realistic boundary conditions for the analysis of aerodynamics, thermal loads and cooling system performance. The present activity deals with the study of heavily film cooled geometry of HPV 1,7. The aim is to evaluate critical behavior of the cooling system performance due to the realistic inlet conditions. Description of the test case Two computational domains have been considered for the numerical campaign. The first one, referred as experimental geometry, has been used for the numerical validation (i.e. grid sensitivity analysis and turbulence model assessment) and is characterized by a high aspect ratio equal to The second one, referred as realistic geometry, has been derived from the experimental one in order to be representative of a realistic HPV and has been used with realistic inlet conditions. The test case used for the numerical validation study is a transonic research vane experimentally investigated with uniform inflow conditions in a linear cascade at the Ecole Polythecnique Fédérale de Lausanne during the EU-funded TATEF2 project. The exit Reynolds number based on chord length is 1.46E+06 while the mean exit isentropic Mach number is The cooling system of the vane is shown in Figure 1a. It consists of three rows of fan-shaped holes on both pressure and suction side while four rows of showerhead cylindrical holes inclined by 45 downward protect the LE. The stream-wise injection angle of the fan-shaped holes is different rowby-row and ranges from 31.0 of row 10 to 53.3 of row 3 with respect to the local surface tangential direction. The diffuser shape opens 12 symmetrically in both lateral directions together with a laidback angle of 15. b) Figure 1. Schematic of the cooling system; b) Geometry of the experimental vane model. Experimental geometry The computational domain used for grid sensitivity analysis and turbulence model assessment, reported in Figure 1b, reproduces the experimental configuration 2,11. It includes the fluid region complete of plenum and cooling channels. Inlet and outlet sections are placed respectively 0.65 C ax upstream of the LE and 0.6 C ax downstream of the TE. The coolant inlet is on the top of the plenum. 2

3 CO 2 is used as coolant in order to match coolant-to-main-flow DR of 1.6 of an engine-like condition. The nominal BR for showerhead is about 2.8, while varies from 1.0 to 1.5 moving from row 1 to row 3 and from 3.4 to 1.5 moving from row 8 to row 10. Realistic geometry In order to study the effects of realistic inlet conditions the computational domain has been modified with respect of the experimental vane model to be representative of a real machine configuration. The novel geometry, shown in Figure 2, has identical cooling system but is composed of two vanes with a reduced aspect ratio of E+06, 6.4E+06, 14.2E+06, and 25.9E+06 elements. Grid effects have been quantified for the mass flows and total pressure losses using the GCI suggested by Roache 9. The value of the GCI for coolant mass flow on the finest meshes is 1.18% while for the total pressure loss coefficient is 0.45%. It can be concluded that increasing the computational cost from the 14.2E+06 elements to the 25.9E+06 does not imply substantial variations in terms of the aforementioned quantities. The 14.2E+06 elements grid, shown in Figure 3, is then selected for the numerical campaign. Once the distribution of the characteristic grid dimensions has been assessed it has also been applied to the realistic configuration obtaining about 30.0E+06 elements. Figure 2. Geometry of the realistic vane model. Numerical approach and grids Numerical simulations on hybrid unstructured grids have been performed using a steady approach with the commercial code ANSYS Fluent. A second-order accurate upwind discretization has been applied in space, while gradients are reconstructed with the Green- Gauss node based approach. The SIMPLE scheme has been used for the pressure-velocity coupling. A grid dependence analysis has been carried out on the experimental domain 6 using hybrid unstructured grids generated with the commercial software Centaur. Four different grids have been generated, consisting of about Figure 3. Detail of the computational grid. The transition k T-k L-ω model has been selected as turbulence closure for the numerical studies but, instead of using its original formulation proposed by Walters and Cokljat 11, a recalibrated set of parameters has been used. The model was previously re-calibrated 3,5 by fitting the experimental data of another HPV. Model validation Model validation has been carried out on the experimental geometry using uniform inlet flow. Boundary conditions are coherent with the experimental campaign 1 and are reported in Table 1. 3

4 Table 1. Boundary conditions used for validation. Objective η q Boundary condition Main Coolant Inlet p [bar] Inlet T [K] Inlet Tu 10 5 [%] Inlet LT [m] Outlet p [bar] Inlet p [bar] Mass flow [g/s] Inlet T [K] Inlet Tu 10 5 [%] Inlet LT [m] Outlet p [bar] Results, in terms of spanwise averaged adiabatic effectiveness and heat flux are compared with the available experimental data. The first quantity is defined in equation 1, where ~ T rec, m is the local recovery temperature calculated from the simulation of the uncooled vane in experimental configuration. ~ rec, m aw (1) T ~ T 0, m, in ~ T T 0, c, exit Adiabatic boundary conditions have been used at the walls in order to extract T aw necessary to calculate η while, for heat flux calculation, the wall is fixed to 323K. The averaging windows are positioned consistently with experiments between 29% and 61% of the total vane height. Results are shown in Figure 4. Despite some local discrepancies and considered the complexity of the test case, a general good agreement is achieved between prediction and experiments. Other turbulence models have been tested 3,5, including the fully turbulent SST k-ω and the original formulation of the k T-k L-ω, but the selected turbulence model showed the best performance in reproducing experimental distributions of both η and q. b) Figure 4. spanwise averaged quantities: η; b) q (> 0 if fluid is heated). Suction side for s/c > 0. Non-uniform inlet conditions Swirl derives from the experimental campaign of the EUfunded TATEF2 project 8,10. Measurements have been performed on an annular swirl generator 8 aimed to reproduce the flow field originated by a modern aero engine burner. The swirl core is moved by half a pitch to simulate two different clocking positions. The two configurations obtained are shown in Figure 5 and are respectively referred as Passage ( and Leading Edge (b). In the first one, the swirl core is with the vane passage while, in the second one with the vane leading edge. b) Figure 5. Swirl profiles: Passage b) Leading edge. 4

5 Effect of inlet swirl on adiabatic effectiveness and Net Heat Flux Reduction The inlet swirl presented above is used in this section for the study of the cooling system performance by comparing a uniform inlet case with the two previously defined clocking configurations. Performance of the external cooling system are estimated by means of adiabatic effectiveness (equation 2) and heat transfer coefficient (equation 3). These parameters can be combined to calculate the Net Heat Flux Reduction (NHFR), defined in equation 4, to quantify the efficacy of the film cooling. NHFR definition makes use of HTC un and ϕ. The first one is the heat transfer coefficient obtained on the uncooled model (equation 5) while the second parameter is the overall film effectiveness, estimated to be 0.45 through conjugate heat transfer simulations 3. 0, m, in aw (2) T T 0, m, in T T 0, c, exit q HTC T aw T w (3) HTC NHFR 1 1 HTC un (4) qun HTCun T T (5) 0, m, in Simulations are carried out on the realistic configuration using air instead of CO 2 as coolant, with the coolant temperature rescaled in order to maintain the same density ratio of the experimental case. Except for the coolant temperature, the other average conditions have been maintained the same indicated in Table 1 relatively to η. For the HTC estimation an isothermal boundary condition of 400K has been imposed along the external vane surfaces, while internal channels and plenums are adiabatic. w Results in terms of η are reported in Figure 6 and Figure 7 respectively on pressure side and suction side for the various cases. The uniform case shows a good overall covering effect of the film even if low effectiveness is present at the leading edge in the shroud region due to the downward angle of the showerhead holes. Area-weighted average values of 0.38 and 0.39 are respectively found for pressure and suction side. Swirling cases show a general reduction of the averaged values of adiabatic effectiveness (see Table 2) that are particularly related to two main effects. The first one is the effect of the main-flow incidence variation along the leading edge. This affects mainly showerhead behaviour since the external pressure field is modified, leading to performance deterioration with respect to the uniform case. Figure 8 shows the shape of stagnation lines along the vanes for the two swirl clocking configurations compared with the uniform inlet case. Strong incidence effects are observable, especially along the vane (the most penalized by swirl). Passage and LE configurations lead to qualitatively the same behavior of stagnation lines with local differences near the end-walls. Table 2 Variations of the cooling system parameters with respect to the uniform case Passage LE vane side NHFR [%] S1 S1 η [%] HTC/HTCun [%] PS SS PS SS PS SS PS SS

6 S1 Uniform Passage b) c) LE d) e) Figure 6. Adiabatic film cooling effectiveness: pressure side. S1 Uniform Passage b) c) LE d) e) Figure 7. Adiabatic film cooling effectiveness: suction side. Figure 8. Stagnation lines (obtained on uncooled vanes) reported on the cooled geometry. The similitude between the two cases is due the shape of the swirl profile. In fact, a shift of this latter by half pitch does not lead to inversion of incidence but only to a variation of its magnitude (see Figure 5). The second effect of swirl on adiabatic effectiveness is due to its migration and interaction with cooling jets and secondary flows (enforcing lower passage vortex and suppressing higher). For the passage case (Figure 6b, Figure 6c, Figure 6

7 7b and Figure 7c), swirl is convected inside the central passage thus affecting mainly pressure side of the S1 vane and suction side of the vane with detrimental effects respectively over the mid-span and under the mid-span. In particular, considering the averaged adiabatic effectiveness, a variation of -16% is highlighted for the pressure side of the S1 vane and -21% for the suction side of the vane (Table 2). For the LE case (Figure 6d, Figure 6e, Figure 7d and Figure 7e) the vortex core is convected in the other passage thus affecting vane pressure side and S1 vane suction side, with a reduction of the averaged adiabatic effectiveness respectively of about -28% and -10%. Moreover the incidence variation on the vane entails a -12% decrease in averaged adiabatic effectiveness (Table 2). Figure 9. Heat transfer coefficient: uniform case. Figure 9 shows the behavior of HTC for the uniform inlet case. The heat transfer enhancement promoted by cooling jets is well visible downstream of each channel and is particularly strong where the surface curvature is high. Due to such local heat transfer increase the average HTC/HTC un results to be 1.20 for the pressure side and 1.05 for the suction side (where the HTC ratio benefits of the transition of the uncooled case). For sake of brevity, HTC maps are not reported for the swirling cases but the same qualitative considerations done for adiabatic effectiveness are still valid for the characteristic patterns of HTC. Moreover, variations of averaged HTC ratio, shown on Table 2, results to be limited between -1.7% and -9.1% showing a slight benefit on the swirling cases with respect to the uniform one. In particular leading edge case results to be the more positively affected with a - 8.5% on the suction side and -9.1% on the pressure side. Results about the NHFR are shown in Figure 10 and Figure 11 respectively for pressure and suction side of the various cases. The uniform case shows a good overall cooling efficacy with a NHFR that overtakes 1.0 downstream of the cooling channels. In fact, despite the increase of local HTC shown in Figure 9, with peak values over +100% with respect to the uncooled case, the NHFR is balanced by a strong coverage effect downstream of the holes as shown when describing the effectiveness. Critical zones are highlighted along the mid-span of the LE, particularly downstream of row 6 moving to the pressure side and on the shroud region. This is due to a local increase in HTC within a less covered region. In particular the increase in HTC close to the shroud, that is about +10% with respect to the uncooled case, is mainly due to the blockage effect of the upper cooling holes accelerating the flow in the pressure side direction and promoting the heat exchange. However, it is reasonable to state that this increase of HTC is not critical as it would be at mid-span due to the fact that usually inlet temperature profiles of modern high-pressure vanes is characterized by the lower temperature near the end-walls, due to cooling of combustor liner. In any case a globally good overall efficacy is found for the uniform case with an average value of 0.8 for the pressure side and an average value of 0.9 for the suction side. 7

8 S1 Uniform Passage b) c) LE d) e) Figure 10. Net Heat Flux Reduction: pressure side. S1 Uniform Passage b) c) LE d) Figure 11. Net Heat Flux Reduction: suction side. e) About the effects of swirl on the NHFR it is possible to observe a blockage effect similar to the one previously highlighted for the uniform case. Moreover the NHFR decreases on the regions more affected by the swirl motion (see Table 2), particularly on the pressure side of the S1 vane with a -15% and on the suction side of the vane with a -21% for the passage case and on the pressure side of the vane with a -26% and on the suction side of the S1 vane with a -11% (even though the lower region of the SS of the vane is also affected by incidence variation showing an average decrease of -12%). In any case the cooling system efficacy remains effective everywhere except for the leading edge region where critical zones are evidenced (the lower value of averaged NHFR is highlighted for the pressure side of the vane on 8

9 the LE case and is about 0.59). As previously stated both cases show a decrease in NHFR in the leading edge zone, particularly in the shroud region except for the vane in the passage case that shows such a detrimental effect for the whole vane span. Such critical zones are related to a strong increase in the HTC not balanced by an increase in the coolant coverage. Finally, the uncovered zones in the lower LE region for vanes in both clocking configurations (see Figure 7) results in a decrease in the NHFR reaching a value between 0 and 0.1 but not yet showing a critical zone. In fact the reduced coverage effect is balanced by a decrease in the HTC with respect to the uncooled configuration. Conclusions Cooling system performance of a HPV have been analyzed by means of steady RANS simulations. After grid sensitivity study and turbulence model assessment the effects of inlet swirl have been investigated considering two clocking positions. Results, compared with a uniform inlet case, have shown that inlet swirl is detrimental in terms of NHFR and cooling coverage. The convection of the vortex cores inside the passages and their interaction with secondary flows determines remarkable modifications of the coolant behavior with variations peaks of about -26% for the averaged NHFR and -21% for the averaged adiabatic effectiveness, evidencing remarkable differences also between the two clocking positions. Acknowledgments The European Commission and the TATEF2 project consortium are acknowledged. The authors would also like to acknowledge Prof. Peter Ott and Dr. Magnus Jonsson from EPFL for the information provided on the test case studied. References 1. Charbonnier D, Ott P, Jonnson M, Köbke T, Cottier F, Comparison of numerical investigations with measured heat transfer performance of a film cooled turbine vane, Proc. of the ASME Turbo Expo 2008: Power for Land, Sea and Air, Volume 4: Heat Transfer, Parts A and B, Berlin Germany, June 9-13, pp , doi: /GT Giller L, Schiffer H. Interactions Between the Combustor Swirl and the High Pressure Stator of a Turbine. Proc. of IGTI, ASME Turbo Expo 2012, June 11-15, Copenhagen, Denmark, Volume 8: Turbo Expo 2012, Paper No. GT , pp , doi: /GT Insinna M, Griffini D, Salvadori S, Martelli F. Conjugate heat transfer analysis of a film cooled high-pressure turbine vane under realistic combustor exit flow conditions, Proc. of the ASME Turbo Expo 2014: Turbine Technical Conference and Exposition, Volume 5A: Heat Transfer, Dusseldorf, Germany, June 16-20, 2014, doi: /gt Insinna M, Griffini D, Salvadori S, Martelli F, Effects of Realistic Inflow Conditions on the Aero- Thermal Performance of a Film-Cooled Vane, Proc. of the 11 th European Turbomachinery Conference. 2015, Madrid, Spain, March

10 5. Insinna M, Griffini D, Salvadori S, Martelli F. Film cooling performance in a transonic high-pressure vane: decoupled simulation and conjugate heat transfer analysis. Energy Procedia, 45, 2014, pp , doi: /j.egypro Insinna M, Griffini D, Salvadori S, Martelli F, On the Effect of an Aggressive Inlet Swirl Profile on the Aero-Thermal Performance of a Cooled Vane, Proc. of the 69 th Conference of the Italian Thermal Machines Engineering Association. 2014, Milan, Italy, September Published by Energy Procedia (in press). 7. Jonsson M, Ott P, Heat transfer experiments on a heavily film cooled nozzle guide vane, Proc. of the Seventh European Conference on Turbomachinery Fluid Dynamics and Thermodynamics, 2007, pp , March 5-9, Athens, Greece. 8. Qureshi I, Beretta A, Chana K, Povey T, Effect of aggressive inlet swirl on heat transfer and aerodynamics in an unshrouded transonic HP turbine. Journal of Turbomachinery, 134(6) (Sep 04, 2012) (11 pages) doi: / Roache PJ, Kirti NG, White FM, Editorial policy statement on the control of numerical accuracy, Journal of Fluids Engineering 108, 1986, pag. 2, doi: / Salvadori S, Montomoli F, Martelli F, Chana KS, Qureshi I, Povey T. Analysis on the effect of a nonuniform inlet profile on heat transfer and fluid flow in turbine stages. Journal of Turbomachinery, 2012, 134(1), Paper No , 14 pages, doi: / Walters DK, Cokljat D. A three-equation eddyviscosity model for Reynoldsaveraged Navier-Stokes simulations of transitional flow. Journal of Fluids Engineering, (12), Paper No , 14 pages, doi: /