Abstract
The paper reports on 3D numerical simulations of unsteady compressible airflow in a blade cascade consisting of flat profiles using a hybrid LES/RANS approach including a transition model. As a first step towards simulation of blade flutter in turbomachinery, various incidence angle offsets of the middle blade were modeled. All simulations were run for the flow regime characterized by outlet isentropic Mach number Mis=0.5 and zero incidence. The results of the LES/RANS simulations (pressure and Mach number distributions) were compared to a baseline RANS model, and to experimental data measured in a high-speed wind tunnel. The numerical results show that both methods overpredict flow separation taking place at the leading edge. In this regard, the hybrid LES/RANS method does not provide superior results compared to the traditional RANS simulations. Nevertheless, the LES/RANS results also capture vortex shedding from the blunt trailing edge. The frequency of the trailing edge vortex shedding in CFD simulations matches perfectly the spectral peak recorded during wind tunnel measurements.
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Abbreviations
- \(a_{ij}^{\left( {{\rm{ex}}} \right)}\) :
-
extra-anisotropy tensor
- C f :
-
skin friction coefficient
- C k, C DES :
-
model constants
- C μ;, C τ :
-
model constants
- c :
-
blade chord length
- f :
-
frequency
- f w :
-
wall function
- h :
-
channel height
- k :
-
turbulent kinetic energy
- L :
-
pressure gradient parameter
- l :
-
coordinate measured along pressure taps
- M :
-
Mach number
- \(\hat n\) :
-
spot propagation rate
- P k :
-
production term
- p :
-
static pressure
- P d :
-
dynamic pressure
- Re :
-
Reynolds number
- S ij :
-
strain rate tensor
- St :
-
Strouhal number
- s :
-
cascade pitch
- Tu :
-
turbulence level
- \(\bar U\) :
-
filtered/averaged velocity
- U e :
-
external velocity
- w :
-
channel width
- α :
-
blade incidence offset angle
- β, β* :
-
model constants
- γ :
-
cascade stagger angle
- γ :
-
intermittency coefficient
- γ :
-
specific heat ratio
- Δ:
-
length scale (local grid size)
- δ ij :
-
Kronecker delta
- η :
-
non-dimensional wall distance
- σ k, σ ω :
-
model constants
- μ :
-
dynamic viscosity
- ν :
-
kinematic viscosity
- ρ :
-
fluid density
- τ t :
-
turbulent time scale
- τ ij :
-
turbulent shear stress tensor
- τ w :
-
skin shear stress
- Ω ij :
-
vorticity tensor
- ω :
-
specific dissipation rate
- 1:
-
blade cascade inlet
- 2:
-
blade cascade outlet
- 3:
-
outlet of the computational domain
- eff:
-
effective (viscosity)
- is:
-
isentropic
- o:
-
total (pressure, temperature)
- sgs:
-
subgrid scale
- t:
-
turbulent
References
Kielb R., Chiang H.W., Recent advancements in turbomachinery forced response analyses. 30th Aerospace Sciences Meeting and Exhibit, American Institute of Aeronautics and Astronautics, 1992. DOI: https://doi.org/10.2514/6.1992-12
Dowell E.H., ed., A modern course in aeroelasticity. Springer Dordrecht, 2004.
Stapelfeldt S., Brandstetter C., Non-synchronous vibration in axial compressors: lock-in mechanism and semi-analytical model. Journal of Sound and Vibration, 2020, 488: 115649. DOI: https://doi.org/10.1016/j.jsv.2020.115649
Day I.J., Stall, surge, and 75 years of research. Journal of Turbomachinery, 2016, 138(1): 011001. DOI: https://doi.org/10.1115/1.4031473
Ziada S., Oengören A., Vogel A., Acoustic resonance in the inlet scroll of a turbo-compressor. Journal of Fluids and Structures, 2002, 16(3): 361–373. DOI: https://doi.org/10.1006/jfls.2001.0421
Masserey P.A., McBean I., Lorini H., Analysis and improvement of vibrational behaviour on the ND37 a last stage blade. VGB PowerTech Journal, 2012, 92(8): 42–48.
Marti F., Liu F., Flutter study of NACA 64A010 airfoil using URANS and eN transition models coupled with an integral boundary layer code. AIAA Paper 2017-1648, 2017. DOI: https://doi.org/10.2514/6.2017-1648
Im H., Chen X., Zha G., Detached eddy simulation of transonic rotor stall flutter using a fully coupled fluid-structure interaction. ASME Paper No GT2011-45437, 2011. DOI: https://doi.org/10.1115/GT2011-45437
Barnes C.J., Visbal M.R., On the role of flow transition in laminar separation flutter. Journal of Fluids and Structures, 2018, 77: 213–230. DOI: https://doi.org/10.1016/j.jfluidstructs.2017.12.009
Naung S.W., Nakhchi M.E., Rahmati M., Prediction of flutter effects on transient flow structure and aeroelasticity of low-pressure turbine cascade using direct numerical simulations. Aerospace Science and Technology, 2021, 119: 107151. DOI: https://doi.org/10.1016/j.ast.2021.107151
Casoni M., Benini E., A review of computational methods and reduced order models for flutter prediction in turbomachinery. Aerospace, 2021, 8(9): 242. DOI: https://doi.org/10.3390/aerospace8090242
Michelassi V., Wissink J., Rodi W., Direct numerical simulation, large eddy simulation and unsteady Reynolds-averaged Navier-Stokes simulations of periodic unsteady flow in a low-pressure turbine cascade: A comparison. Proceedings of the Institution of Mechanical Engineers, Part A: Journal of Power and Energy, 2003, 217(4): 403–411. DOI: https://doi.org/10.1243/095765003322315469
Tucker P.G., Computation of unsteady turbomachinery flows: Part 1 - Progress and challenges, Part 2 - LES and hybrids. Progress in Aerospace Sciences, 2011, 47(7): 522–545, 546–569. DOI: https://doi.org/10.1016/j.paerosci.2011.06.004
Hodara J., Smith M.J., Hybrid Reynolds-averaged Navier-Stokes/Large-Eddy simulation closure for separated transitional flows. AIAA Journal, 2017, 55(6): 1948–1958. DOI: https://doi.org/10.2514/1.J055475
Tester B.W., Coder J.G., Combs C.S., Schmisseur J.D., Hybrid RANS/LES simulation of transitional shockwave/boundary-layer interaction. 2018 Fluid Dynamics Conference, Atlanta, Georgia, 2018, AIAA Paper 2018–3224. DOI: https://doi.org/10.2514/6.2018-3224
Langtry R.B., Menter F.R. Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes. AIAA Journal, 2009, 47(12): 2894–2906. DOI: https://doi.org/10.2514/1.42362
Coder J.G., Maughmer M.D., Computational fluid dynamics compatible transition modeling using an amplification factor transport equation. AIAA Journal, 2014, 52(11): 2506–2512. DOI: https://doi.org/10.2514/1.J052905
Wang X., **ao Z., Transition-based constrained large-eddy simulation method with application to an ultrahigh-lift low-pressure turbine cascade flow. Journal of Fluid Mechanics, 2022, 941: A22. DOI: https://doi.org/10.1017/jfm.2022.286
Davidson L., Peng S.H., Hybrid LES-RANS modelling: A one-equation SGS model combined with a k-ω model for predicting recirculating flows. International Journal for Numerical Methods in Fluids, 2003, 43: 1003–1018. DOI: https://doi.org/10.1002/fld.512
Hellsten A., New two-equation turbulence model for aerodynamics applications. Helsinki University of Technology, Helsinki, Finland, 2004.
Straka, P., Příhoda, J., Application of the algebraic bypass-transition model for internal and external flows. Experimental Fluid Mechanics, 2010, Liberec, Czech Republic, 2010, 636–641.
Fürst J., Lasota M., Lepicovsky J., Musil J., Pech J., Šidlof P., Šimurda D., Effects of a single blade incidence angle offset on adjacent blades in a linear cascade. Processes, 2021, 9(11): 1974. DOI: https://doi.org/10.3390/pr9111974
Fürst J., Musil J., Šimurda D., Investigation of transonic flow through linear cascade with single blade incidence angle offset. Topical Problems of Fluid Mechanics 2022, Prague, Czech Republic, 2022, 51–58. DOI: https://doi.org/10.14311/TPFM.2022.008
Lepicovsky J., Šidlof P., Šimurda D., Štěpán M., Luxa M., New test facility for forced blade flutter research. AIP Conference Proceedings, 2021, 2323: 030001. DOI: https://doi.org/10.1063/5.0041990
Kubacki S., Rokicki J., Dick E., Hybrid RANS/LES computations of plane im**ing jets with DES and PANS models. International Journal of Heat and Fluid Flow, 2013, 44: 596–609. DOI: https://doi.org/10.1016/j.ijheatfluidflow.2013.08.014
Launder B.E., On the computation of convective heat transfer in complex turbulent flows. ASME Journal of Heat Transfer, 1988, 110: 1112–1128. DOI: https://doi.org/10.1115/1.3250614
Menter F.R., Two-equation eddy-viscosity turbulence models for engineering applications. AIAA Journal, 1994, 32(8): 1598–1605. DOI: https://doi.org/10.2514/3.12149
Straka P., Příhoda J., Numerical simulation of compressible flow through high-loaded turbine blade cascade. Topical Problems of Fluid Mechanics, Prague, Czech Republic, 2014, pp. 131–134.
Narasimha R., The laminar-turbulent transition zone in the boundary layer. Progress in Aerospace Science, 1985, 22(1): 29–80. DOI: https://doi.org/10.1016/0376-0421(85)90004-1
Mayle R.E., The role of laminar-turbulent transition in gas turbine engines. Journal of Turbomachinery, 1991, 113(4): 509–537. DOI: 10.1115/1.2929110
Walker G.J., Transitional flow on axial turbomachine blading. 25th AIAA Aerospace Sciences Meeting, Reno, NV, U.S.A. 1987, 27: 595–607. DOI: https://doi.org/10.2514/6.1987-10
Langtry R.B, Menter F.R., Correlation-based transition modeling for unstructured parallelized computational fluid dynamics codes. AIAA Journal, 2009, 47(12): 2894–2906. DOI: https://doi.org/10.2514/1.42362
Luxa M., Příhoda J., Šimurda D., Straka P., Synáč J., Investigation of the compressible flow through the tip-section turbine blade cascade with supersonic inlet. Journal of Thermal Science, 2016, 25(2): 138–144. DOI: https://doi.org/10.1007/s11630-016-0844-0
Straka P., Modelling of unsteady secondary vortices generated behind the radial gap of the axial turbine blade wheel. ECCOMAS Congress 2016, Crete, Greece, 2016. DOI: https://doi.org/10.7712/100016.2350.9777
Acknowledgements
The research has been supported by the Czech Science Foundation (GAČR) (Grant No. 20-11537S). Institutional support RVO: 61388998 is also gratefully acknowledged.
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Příhoda, J., Straka, P., Šimurda, D. et al. Hybrid LES/RANS Simulations of Compressible Flow in a Linear Cascade of Flat Blade Profiles. J. Therm. Sci. (2024). https://doi.org/10.1007/s11630-024-1995-z
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DOI: https://doi.org/10.1007/s11630-024-1995-z