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Research Papers

Large Eddy Simulation of Boundary Layer Transition Mechanisms in a Gas-Turbine Compressor Cascade

[+] Author and Article Information
Ashley D. Scillitoe

CFD Laboratory,
Department of Engineering,
University of Cambridge,
Cambridge CB2 1PZ, UK
e-mail: as2341@cam.ac.uk

Paul G. Tucker

CFD Laboratory,
Department of Engineering,
University of Cambridge,
Cambridge CB2 1PZ, UK

Paolo Adami

CFD Methods,
Rolls-Royce Deutschland,
Eschenweg 11,
Blankenfelde-Mahlow 15827, Germany

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received September 18, 2018; final manuscript received November 14, 2018; published online January 22, 2019. Editor: Kenneth Hall.

J. Turbomach 141(6), 061008 (Jan 22, 2019) (10 pages) Paper No: TURBO-18-1249; doi: 10.1115/1.4042023 History: Received September 18, 2018; Revised November 14, 2018

Large eddy simulation (LES) is used to explore the boundary layer transition mechanisms in two rectilinear compressor cascades. To reduce numerical dissipation, a novel locally adaptive smoothing (LAS) scheme is added to an unstructured finite volume solver. The performance of a number of subgrid scale (SGS) models is explored. With the first cascade, numerical results at two different freestream turbulence intensities (Ti's), 3.25% and 10%, are compared. At both Ti's, time-averaged skin-friction and pressure coefficient distributions agree well with previous direct numerical simulations (DNS). At Ti = 3.25%, separation-induced transition occurs on the suction surface, while it is bypassed on the pressure surface. The pressure surface transition is dominated by modes originating from the convection of Tollmien–Schlichting waves by Klebanoff streaks. However, they do not resemble a classical bypass transition. Instead, they display characteristics of the “overlap” and “inner” transition modes observed in the previous DNS. At Ti = 10%, classical bypass transition occurs, with Klebanoff streaks incepting turbulent spots. With the second cascade, the influence of unsteady wakes on transition is examined. Wake-amplified Klebanoff streaks were found to instigate turbulent spots, which periodically shorten the suction surface separation bubble. The celerity line corresponding to 70% of the free-stream velocity, which is associated with the convection speed of the amplified Klebanoff streaks, was found to be important.

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References

Steinert, W. , and Starken, H. , 1996, “Off-Design Transition and Separation Behavior of a CDA Cascade,” ASME J. Turbomach., 118(2), pp. 204–210. [CrossRef]
Lardeau, S. , Leschziner, M. , and Zaki, T. , 2011, “Large Eddy Simulation of Transitional Separated Flow Over a Flat Plate and a Compressor Blade,” Flow Turbul. Combust, 88(1–2), pp. 19–44.
Scillitoe, A. D. , Tucker, P. G. , and Adami, P. , 2016, “Numerical Investigation of Three-Dimensional Separation in An Axial Flow Compressor: The Influence of Freestream Turbulence Intensity and Endwall Boundary Layer State,” ASME J. Turbomach., 139(2), p. 021011. [CrossRef]
Adamczyk, J. J. , Hansen, J. L. , and Prahst, P. S. , 2007, “A Post Test Analysis of a High-Speed Two-Stage Axial Flow Compressor,” ASME Paper No. GT2007-28057.
Zaki, T. A. , Wissink, J. G. , Rodi, W. , and Durbin, P. A. , 2010, “Direct Numerical Simulations of Transition in a Compressor Cascade: The Influence of Free-Stream Turbulence,” J. Fluid Mech., 665, pp. 57–98. [CrossRef]
Menter, F. R. , Langtry, R. , and Völker, S. , 2006, “Transition Modelling for General Purpose CFD Codes,” Flow Turbul. Combust, 77(1–4), pp. 277–303. [CrossRef]
Leggett, J. , Priebe, S. , Shabbir, A. , Sandberg, R. , Richardson, E. , and Michelassi, V. , 2017, “Loss Prediction in An Axial Compressor Cascade at Off-Design Incidences With Free Stream Disturbances,” ASME Paper No. GT2017-64292.
Coull, J. D. , and Hodson, H. P. , 2011, “Unsteady Boundary-Layer Transition in Low-pressure Turbines,” J. Fluid Mech., 681, pp. 370–410. [CrossRef]
Medic, G. , Zhang, V. , Wang, G. , Joo, J. , and Sharma, O. P. , 2016, “Prediction of Transition and Losses in Compressor Cascades Using Large-Eddy Simulation,” ASME J. Turbomach., 138(12), p. 121001. [CrossRef]
Gao, F. , Zambonini, G. , Boudet, J. , Ottavy, X. , Lu, L. , and Shao, L. , 2015, “Unsteady Behavior of Corner Separation in a Compressor Cascade: Large Eddy Simulation and Experimental Study,” Proc. Inst. Mech. Eng. Part A: J. Power Energy, 229(5), pp. 508–519. [CrossRef]
Gbadebo, S. A. , 2003, “Three-Dimensional Separations in Compressors,” Ph.D. thesis, University of Cambridge, Cambridge, UK.
Hilgenfeld, L. , and Pfitzner, M. , 2004, “Unsteady Boundary Layer Development Due to Wake Passing Effects on a Highly Loaded Linear Compressor Cascade,” ASME J. Turbomach., 126(4), pp. 493–500. [CrossRef]
Piomelli, U. , and Chasnov, R. , 1996, “Large-Eddy Simulations: Theory and Applications,” Turbul. Transition Modell., 2, pp. 2269–336.
Crumpton, P. , Moinier, P. , and Giles, M. , 1997, “An Unstructured Algorithm for High Reynolds Number Flows on Highly Stretched Grids,” Numerical Methods Laminar Turbulent Flow, Swansea, Wales, pp. 1–13.
Cui, J. , Nagabhushana Rao, V. , and Tucker, P. , 2015, “Numerical Investigation of Contrasting Flow Physics in Different Zones of a High-Lift Low-Pressure Turbine Blade,” ASME J. Turbomach., 138(1), p. 011003. [CrossRef]
Rogers, S. E. , Kwak, D. , and Kiris, C. , 1991, “Steady and Unsteady Solutions of the Incompressible Navier-Stokes Equations,” AIAA J., 29(4), pp. 603–610. [CrossRef]
Roe, P. , 1986, “Characteristic-Based Schemes for the Euler Equations,” Annu. Rev. Fluid Mech., 18(1), pp. 337–365. [CrossRef]
Tajallipour, N. , Babaee Owlam, B. , and Paraschivoiu, M. , 2009, “Self-Adaptive Upwinding for Large Eddy Simulation of Turbulent Flows on Unstructured Elements,” J. Aircr., 46(3), pp. 915–926. [CrossRef]
Bassenne, M. , Urzay, J. , Park, G. I. , and Moin, P. , 2016, “Constant-Energetics Physical-Space Forcing Methods for Improved Convergence to Homogeneous-Isotropic Turbulence With Application to Particle-Laden Flows,” Phys. Fluids, 28(3), p. 035114. [CrossRef]
Smagorinsky, J. , 1963, “General Circulation Experiments With the Primitive Equations,” Mon. Weather Rev., 91(3), pp. 99–164. [CrossRef]
Schumann, U. , 1975, “Subgrid Scale Model for Finite Difference Simulations of Turbulent Flows in Plane Channels and Annuli,” J. Comput. Phys., 18(4), pp. 376–404. [CrossRef]
Nicoud, F. , and Ducros, F. , 1999, “Subgrid-Scale Stress Modelling Based on the Square of the Velocity Gradient Tensor,” Flow Turbul. Combust, 62(3), pp. 183–200. [CrossRef]
Nicoud, F. , Toda, H. B. , Cabrit, O. , Bose, S. , and Lee, J. , 2011, “Using Singular Values to Build a Subgrid-Scale Model for Large Eddy Simulations,” Phys. Fluids, 23(8), p. 085106. [CrossRef]
Saad, T. , Cline, D. , Stoll, R. , and Sutherland, J. C. , 2016, “Scalable Tools for Generating Synthetic Isotropic Turbulence With Arbitrary Spectra,” AIAA J., 55(1), pp. 1–14.
Bailly, C. , and Juve, D. , 1999, “A Stochastic Approach to Compute Subsonic Noise Using Linearized Euler's Equations,” AIAA Paper No. 99-1872.
Wu, X. , Jacobs, R. G. , Hunt, J. C. R. , and Durbin, P. A. , 1999, “Simulation of Boundary Layer Transition Induced by Periodically Passing Wakes,” J. Fluid Mech., 398, pp. 109–153. [CrossRef]
Saric, W. S. , 1994, “Gortler Vortices,” Annu. Rev. Fluid Mech., 26(1), pp. 379–409. [CrossRef]
Jacobs, R. G. , and Durbin, P. A. , 2001, “Simulations of Bypass Transition,” J. Fluid Mech., 428, pp. 185–212. [CrossRef]
Zaki, T. A. , and Durbin, P. A. , 2006, “Continuous Mode Transition and the Effects of Pressure Gradient,” J. Fluid Mech., 563, pp. 357–388. [CrossRef]
Cumpsty, N. A. , Dong, Y. , and Li, Y. S. , 1995, “Compressor Blade Boundary Layers in the Presence of Wakes,” ASME Paper No. 95-GT-443.
Sayadi, T. , and Moin, P. , 2012, “Large Eddy Simulation of Controlled Transition to Turbulence,” Phys. Fluids, 24(11), p. 114103. [CrossRef]

Figures

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Fig. 1

Contours of converged ε2 smoothing field with LASW scheme, for case C1

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Fig. 2

Turbulence intensity, Ti, at midpitch of cascade 1

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Fig. 3

Time-averaged pressure and skin friction coefficients on the pressure surface of cascade 1: (a) pressure coefficient, Cp and (b) skin friction coefficient, Cf

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Fig. 4

Case C1. Contours of the tangential velocity perturbations on a plane inside the pressure surface boundary layer, d+ ≈ 15 from the wall. An iso-surface of Q = 200U0/Cx is superimposed. Also shown is an xnxt slice bisecting the Λ-structure, at a time instance 0.15T* prior to the main image.

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Fig. 5

Görtler number, G, (upstream of transition/separation) on the pressure surface

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Fig. 6

Case C1. Two of the vortical structures present on the pressure surface, visualized using iso-surfaces of Q = 200U0/Cx. Case C1. Contours of −0.1<ut′<0.1 are also shown: (a) inner mode Λ-structure and (b) overlap mode structures.

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Fig. 7

Case C1. Contours of the normal velocity perturbations, un′, on the d+ ≈ 15 pressure surface plane. An iso-surface of Q = 200U0/Cx is superimposed.

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Fig. 8

Case C1. Contours of the tangential velocity perturbations, ut′, on an xtxn plane bisecting the overlap mode structure highlighted in Fig. 7. The time is 0.1T * prior to that in Fig. 7.

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Fig. 9

Pressure and skin friction coefficients on the suction surface of cascade 1: (a) pressure coefficient, Cp and (b) skin friction coefficient, Cf

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Fig. 10

Case C1. Contours of the tangential velocity perturbations, ut′, on a plane inside the suction surface boundary layer d+ ≈ 15 from the wall. Iso-surfaces of Q = 300U0/Cx (gray) and ut < 0 (black) are superimposed.

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Fig. 11

Case C5. Contours of the normal velocity perturbations, un′, on a plane inside the suction surface boundary layer d+ ≈ 15.

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Fig. 12

Skin friction coefficient distributions for cascade 1 with inflow Ti = 3.25%, with various SGS models used: (a) suction surface and (b) pressure surface

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Fig. 13

Profiles of un′∂u¯t/∂xn and u¯t on the suction surface: (a) u¯t at x/Cx=0.4 and (b) un′∂u¯t/∂xn at x/Cx=0.1

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Fig. 15

Phase-averaged and time-averaged skin friction coefficient distributions for cascade 2. The filled area shows the range of ⟨Cf⟩(ϕ) variation throughout the wake passing period: (a) suction surface and (b) pressure surface.

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Fig. 16

Phase-averaged space-time plots of the suction surface boundary layer skin friction coefficient Cf. The dotted lines annotated with WLE and WTE represent the leading and trailing edges of the wake. For clarity the range 0 ≤ ϕ ≤ 1 is repeated to 1 ≤ ϕ ≤ 2.

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Fig. 14

Profiles of the tangential (ut′ut′¯) and shear (ut′un′¯) components of the Reynolds stresses on the suction surface at x/Cx = 0.025. Solid lines show the total (ui′uj′¯=ui′uj′¯SGS+ui′uj′¯r) stresses, filled areas show only the resolved stresses (ui′uj′¯r): (a) σ SGS model and (b) SM SGS model.

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Fig. 17

Contours of the tangential and normal velocity perturbations (f′(ϕ)=f−⟨f⟩(ϕ)) on the suction surface d+ ≈ 15 plane. To show the passing wake, contours of instantaneous vorticity magnitude are shown at z = 0 (in the background): (a) tangential velocity perturbations, ϕ = 0.6 and (b) normal velocity perturbations ϕ = 0.8.

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