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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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. 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. 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. 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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