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Research Papers

# Modeling Vortex Generating Jet-Induced Transition in Low-Pressure Turbines

[+] Author and Article Information
Florian Herbst

Research Assistant
Member of ASME
Institute of Turbomachinery and Fluid Dynamics,
Leibniz Universitaet Hannover,
Hanover 30167, Germany
e-mail: Herbst@tfd.uni-hannover.de

Andreas Fiala

Turbine Aerodynamics MTU Aero Engines GmbH,
Munich 80995, Germany
e-mail: Andreas.Fiala@mtu.de

Joerg R. Seume

Professor
Member ASME
Institute of Turbomachinery and Fluid Dynamics,
Leibniz Universitaet Hannover,
Hanover 30167, Germany
e-mail: Seume@tfd.uni-hannover.de

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received August 13, 2013; final manuscript received September 13, 2013; published online January 2, 2014. Editor: Ronald Bunker.

J. Turbomach 136(7), 071005 (Jan 02, 2014) (16 pages) Paper No: TURBO-13-1188; doi: 10.1115/1.4025735 History: Received August 13, 2013; Revised September 13, 2013

## Abstract

The current design of low-pressure turbines (LPTs) with steady-blowing vortex generating jets (VGJs) uses steady computational fluid dynamics (CFD). The present work aims to support this design approach by proposing a new semiempirical transition model for injection-induced laminar-turbulent boundary layer transition. It is based on the detection of cross-flow vortices in the boundary layer which cause inflectional cross-flow velocity profiles. The model is implemented in the CFD code TRACE within the framework of the $γ$-$Reθ$ transition model and is a reformulated, recalibrated, and extended version of a previously presented model. It is extensively validated by means of VGJ as well as non-VGJ test cases capturing the local transition process in a physically reasonable way. Quantitative aerodynamic design parameters of several VGJ configurations including steady and periodic-unsteady inflow conditions are predicted in good accordance with experimental values. Furthermore, the quantitative prediction of end-wall flows of LPTs is improved by detecting typical secondary flow structures. For the first time, the newly derived model allows the quantitative design and optimization of LPTs with VGJs.

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## Figures

Fig. 1

Characteristic vortices of a single round jet in cross-flow according to [21]

Fig. 2

Isosurfaces of the logical conjunction of the model parameters for an injection in the cross-flow boundary layer of a flat plate without pressure gradient

Fig. 3

Isosurfaces of the logical conjunction of the model parameters for a swept cylinder according to [42] (diameter d = 150 mm, sweep angle Λ = 47 deg, freestream velocity U∞ = 20 m/s)

Fig. 4

Model functions for vortex generating jet-induced transition

Fig. 5

Characteristics of the relative vorticity Ωrel of the transitional regions fVGJ>0.0 as a function of blowing and operating point parameters of a flat plate without pressure gradient ((a) test case according to Fig. 2) and of the T161 LPT cascade with VGJ ((b) test case according to corresponding section)

Fig. 6

Mesh and boundary conditions of the T161 type 1 VGJ configuration for steady inflow conditions (every second grid line shown; geometry distorted)

Fig. 7

Integral total pressure losses (a) and integral outlet flow angles (b) of T161 type 1 B = 0.5 with steady inflow

Fig. 8

Integral total pressure losses of T161 type 1 B = 1.0 (a) and T161 type 2 B = 1.0 (b) with steady inflow

Fig. 9

Surface pressure distribution of Re2,is = 70×103 T161 type I B = 0.5 with steady inflow and associated magnification of the trailing edge region

Fig. 10

Isosurfaces of the transitional regions fVGJ>0.0 and boundary layer state (derived from τw) of Re2,is = 70×103 T161 type I B = 0.5 with steady inflow

Fig. 11

Shape factor (a) and maximum eddy viscosity of the boundary layer (b) of the suction side of the T161 type I configuration at Re2,is = 70×103 and B = 0.5 with steady inflow

Fig. 12

Computational domain, mesh, and boundary conditions of the T165 type A configuration (every second grid line shown; geometry distorted)

Fig. 13

Integral total pressure losses (a) and surface pressure distribution at Re2,is = 120×103 (b) of the T165 type A configuration

Fig. 14

Computational mesh with wake generator at midspan (a) and the eddy viscosity at Re2,is = 200×103 and B = 0.5 (b) of the T161 type 1 configuration (every second grid line shown; geometry distorted)

Fig. 15

Integral total pressure losses of the T161 without VGJs (a) and with type 1 B = 0.5 (b) with periodic-unsteady inflow

Fig. 16

Integral total pressure losses (a) and surface pressure distribution at Re2,is = 70×103 (b) of the T161 without VGJs and with steady inflow

Fig. 17

Isosurfaces of the transitional regions fVGJ > 0.0 with relative streamwise vorticity color contour of the T161 without VGJs and with no-slip end-walls (Re2,is = 90×103; steady inflow)

Fig. 18

Radial distributions of the integral total pressure loss (a), the integral outflow angle (b), and the integral eddy viscosity (c) at the outlet measurement plane of the T161 without VGJs and with no-slip end-walls at z/H = 0.0 and z/H = 1.0 (Re2,is = 90×103; steady inflow)

Fig. 19

Radial-pitchwise distribution of the total pressure losses at the outlet measurement plane in the experiment (a), with standard-transition model (b), and with VGJ-transition mode (c) of the T161 without VGJs and with no-slip end-walls z/H = 0.0 and z/H = 1.0 (Re2,is = 90×103; steady inflow)

Fig. 20

Computational domain of the 1.5-stage turbine (geometry distorted and mirrored at the x,z plane)

Fig. 21

Characteristic curves of the isentropic turbine efficiency of the 1.5-stage turbine and at reference rotational speed n = 7000 min−1

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