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Research Papers

# Direct Numerical Simulations of Transitional Separation-Bubble Development in Swept-Blade Flow Conditions

[+] Author and Article Information
Joshua R. Brinkerhoff

Ph.D. Candidate

Metin I. Yaras

Professor
e-mail: metin yaras@carleton.ca
Department of Mechanical
and Aerospace Engineering,
Carleton University,

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the Journal of Turbomachinery. Manuscript received June 29, 2012; final manuscript received August 8, 2012; published online June 3, 2013. Assoc. Editor: David Wisler.

J. Turbomach 135(4), 041006 (Jun 03, 2013) (10 pages) Paper No: TURBO-12-1102; doi: 10.1115/1.4007528 History: Received June 29, 2012; Revised August 08, 2012

## Abstract

This paper describes numerical simulations of the instability mechanisms in a separation bubble subjected to a three-dimensional freestream pressure distribution. Two direct numerical simulations are performed of a separation bubble with laminar separation and turbulent reattachment under low freestream turbulence at flow Reynolds numbers and streamwise pressure distributions that approximate the conditions encountered on the suction side of typical low-pressure gas-turbine blades with blade sweep angles of $0 deg$ and $45 deg$. The three-dimensional (3D) pressure field in the swept configuration produces a crossflow-velocity component in the laminar boundary layer upstream of the separation point that is unstable to a crossflow instability mode. The simulation results show that crossflow instability does not play a role in the development of the boundary layer upstream of separation. An increase in the amplification rate and the most amplified disturbance frequency is observed in the separated-flow region of the swept configuration and is attributed to boundary-layer conditions at the point of separation that are modified by the spanwise pressure gradient. This results in a slight upstream movement of the location where the shear layer breaks down to small-scale turbulence and modifies the turbulent mixing of the separated shear layer to yield a downstream shift in the time-averaged reattachment location. The results demonstrate that although crossflow instability does not appear to have a noticeable effect on the development of the transitional separation bubble, the 3D pressure field does indirectly alter the separation-bubble development by modifying the flow conditions at separation.

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## Figures

Fig. 1

Schematic of the computational domain

Fig. 2

Wall-normal node distribution

Fig. 3

Companion DNS study of a zero-pressure-gradient turbulent boundary layer at Reθ = 900. Results from Grid 1 are compared with the (a) turbulence kinetic energy budgets, (b) streamwise velocity fluctuation profiles of Spalart [44], and (c) mean velocity profile of Wu and Moin [45]. Adapted from Azih et al. [36].

Fig. 4

Companion DNS studies in a zero-pressure-gradient turbulent boundary layer at Reθ = 500. Results from Grid 2 and Grid 3 are compared with the (a) turbulence kinetic energy budgets of Spalart [44], and (b) mean velocity profile of Djenidi and Antonia [46]. Adapted from Brinkerhoff and Yaras [47].

Fig. 5

Streamwise distribution of the time-averaged freestream velocity magnitude for the Λ = 0 deg and Λ = 45 deg cases

Fig. 6

Axial distribution of the time-averaged freestream acceleration parameter for the Λ = 0 deg and Λ = 45 deg cases

Fig. 7

Axial distribution of the time-averaged spanwise pressure gradient and freestream flow angle for the Λ = 45 deg case

Fig. 8

Axial variation of the crossflow velocity profile near the separation point for the Λ = 45 deg case

Fig. 9

Axial distribution of the time-averaged displacement thickness for the Λ = 0 deg and Λ = 45 deg cases

Fig. 10

Axial distribution of the time-averaged momentum thickness for the Λ = 0 deg and Λ = 45 deg cases

Fig. 11

Axial distribution of the root-mean-square of the streamwise fluctuation velocity for the Λ = 0 deg and Λ = 45 deg cases

Fig. 12

Time-averaged contours of the (a) tangential velocity at zc/L = 0.00, (b) crossflow velocity at zc/L = 0.00, and (c) crossflow velocity at (xt-xts)/L = 0.19 in the separated region of the Λ = 45 deg case. Contour lines are plotted in dimensionless increments of 0.2.

Fig. 13

Periodic roll-up of the separated shear layer observed through contours of the spanwise vorticity at zc/L = 0.00 for the (a) Λ = 0 deg, and (b) Λ = 45 deg cases. The development of a shed spanwise vortex is traced by a white line.

Fig. 14

Frequency spectra of the wall-normal fluctuation velocity at zc/L = 0.00 and at several streamwise locations in the separated-flow region for the (a) Λ = 0 deg, and (b) Λ = 45 deg cases

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