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Assessment of a Coolant Injection Model on Cooled High-Pressure Vanes with Large-Eddy Simulation

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Abstract

The high-pressure turbine blades are the components of the aero-engines which are the most exposed to extreme thermal conditions. To alleviate this issue, the blades are equipped with cooling systems to ensure long-term operation. However, the accurate prediction of the blade temperature and the design of the cooling system in an industrial context still remains a major challenge. Potential improvement is foreseen with Large-Eddy Simulation (LES) which is well suited to predict turbulent flows in such complex systems. Nonetheless, performing LES of a real cooled high-pressure turbine still remains expensive. To alleviate the issues of CPU cost, a cooling model recently developed in the context of combustion chamber liners is assessed in the context of blade cooling. This model was initially designed to mimic coolant jets injected at the wall surface and does not require to mesh the cooling pipes leading to a significant reduction in the CPU cost. The applicability of the model is here evaluated on the cooled Nozzle Guide Vanes (NGV) of the Full Aerothermal Combustor Turbine interactiOns Research (FACTOR) test rig. To do so, a hole modeled LES using the cooling model is compared to a hole meshed LES. Results show that both simulations yield very similar results confirming the capability of the approach to predict the adiabatic film effectiveness. Advanced post-processing and analyses of the coolant mass fraction profiles show that the turbulent mixing between the coolant and hot flows is however reduced with the model. This finding is confirmed by the turbulent map levels which are lower in the modeled approach. Potential improvements are hence proposed to increase the accuracy of such methods.

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Acknowledgements

The authors wish to gratefully acknowledge FACTOR (Full Aerothermal Combustor-Turbine interactions Research) Consortium for the kind permission of publishing the results herein. FACTOR is a Collaborative Project co-funded by the European Commission within the Seventh Framework Programme (2010- 2017) under the Grant Agreement 265985. This work was granted access to the HPC resources of IDRIS under the allocation 2018 - A0042A06074 made by GENCI.

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  1. CERFACS - 42, Av. Gaspard Coriolis, 31057, Toulouse Cedex 1, France

    M. Harnieh, M. Thomas, R. Bizzari, J. Dombard, F. Duchaine & L. Gicquel

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Appendix: 1: Sensitivity of Resolved Turbulence and Wall Temperature to Mesh Adaptation Process

Appendix: 1: Sensitivity of Resolved Turbulence and Wall Temperature to Mesh Adaptation Process

In the present study, a mesh adaptation process has been performed to accurately refine the regions of mixing between the hot and coolant streams. To do so, an user-defined mesh is first created. Then, an automatic mesh adaptation is performed based on the entropy source terms obtained from the user-defined mesh to identify regions of strong velocity and temperature gradients and refine these regions. The properties of the two meshes are summarized in Table 4. To only refine the freestream and the near wall flow regions of the vanes, the mesh in the cooling system including coolant pipes and plena is frozen during the mesh adaptation process. As a result, the number of cells only increases in the freestream region by 52%. To localize the refined regions, a view of the two meshes at mid-height of the vanes are provided on Fig. 25. The mesh is observed to be mainly refined in the near wall flow region of the vanes. The impact of the mesh adaptation on resolved turbulence is now addressed. To quantify the resolution of turbulence on mesh, the criteria of Pope [45] is studied through the evaluation of ME defined so that,

$$ M_{E} = \frac{k_{\mathit{res}}}{k_{\mathit{res}} + k_{\mathit{sgs}}}, $$
(26)

where ksgs is the sub-grid turbulent kinetic energy, \(k_{\mathit {res}} = 0.5({u}_{\mathit {rms}}^{2} + {v}_{\mathit {rms}}^{2} + {w}_{\mathit {rms}}^{2})\) is the resolved turbulent kinetic energy and urms, vrms, wrms are the RMS of velocity fields. For the above relation, a closure for ksgs is needed. To close ksgs, the following relation is used [46]:

$$ \nu_{t} = C_{m} V^{\frac{1}{3}} \sqrt{k_{\mathit{sgs}}}, $$
(27)
Table 4 Number of cells for the user-defined mesh and adapted mesh
Full size table

where νt is the turbulent viscosity, V the node volume and Cm a constant of the model. To operate suitability of LES, near 80% of the turbulence should be resolved on mesh according to Pope [45]. The map of ME is provided at mid-height of the vanes on Fig. 26 for the two meshes. To evidence the regions where more than 80% of turbulence is resolved on mesh, an iso-line equal to ME = 0.8 is added to Fig. 26. For the user-defined mesh, Fig. 26a, turbulence in the film region of the vanes is clearly under-resolved. Nevertheless in the wakes of the vanes, turbulence is observed to be sufficiently resolved. For the adapted mesh, Fig. 26b, the resolution of turbulence is clearly improved in the film region and locally reaches 80% of the overall turbulence. The resolution of turbulence is also improved in the wakes of the vanes. In the coolant pipes, a good resolution of turbulence is also observed featuring more than 80% of resolution. The impact of the increasing mesh resolution on the prediction of time-averaged adiabatic wall temperature is shown on Fig. 27. For the user-defined mesh, Fig. 27a, a large range of temperature is observed on the vane surfaces and local patterns of hot and cold temperature are observed. For the adapted mesh, Fig. 27b, the wall temperature is more segregated compared to the user-defined mesh. Indeed, finer patterns of hot and cold temperatures are observed on the vane surfaces because a finer turbulence is resolved on the adapted mesh.

Fig. 25
figure 25

View of user-defined mesh (a) and adapted mesh (b) at mid-height of NGV1

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Fig. 26
figure 26

ME map at mid-height of the vanes. White iso-line represents ME = 0.8. User-defined mesh (a) and adapted mesh (b)

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Fig. 27
figure 27

Impact of mesh adaptation on adiabatic wall temperature. User-defined mesh (a) and adapted mesh (b)

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As a consequence of the previous discussion, the mesh adaptation process has improved the resolution of turbulence in the film region of the vanes. Although turbulence resolution remains locally inferior to 80% around the vanes, the adapted mesh allows to capture very fine patterns of hot and cold temperature on the vane surfaces.

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Harnieh, M., Thomas, M., Bizzari, R. et al. Assessment of a Coolant Injection Model on Cooled High-Pressure Vanes with Large-Eddy Simulation. Flow Turbulence Combust 104, 643–672 (2020). https://doi.org/10.1007/s10494-019-00091-3

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