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Turbulence measurements in a transonic two-passage turbine cascade

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Abstract

This paper presents detailed turbulence measurements in a two-dimensional, transonic, double passage turbine cascade. Particle image velocimetry was used to obtain mean velocity and turbulence measurements all around a single turbine blade within about 2 mm of the blade and wall surfaces. The passage walls were designed using an optimization procedure so that the blade surface pressure distribution matches that of the blade in an infinite cascade. The resulting experimental model captures much of the complexity of a real turbine stage (including high streamline curvature, strong accelerations, and shocks) in a passage with a continuous wall shape, allowing for high measurement resolution and well controlled boundary conditions for comparison to CFD. The measurements show that in the inviscid regions of the passage the absolute level of the turbulent fluctuations does not change significantly as the flow accelerates, while the local turbulence intensity drops rapidly as the flow accelerates. These results provide a benchmark data set that can be used to improve turbulence models.

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Abbreviations

C :

Blade true chord

C xl :

Blade axial chord

C s :

Smagorinsky constant used in dissipation estimate (=0.17)

d p :

Tracer particle diameter

E :

Estimated error for dissipation rate calculation

k :

Turbulent kinetic energy

k inlet :

Turbulent kinetic energy at inlet (=55 m2/s2)

l :

Integral length scale

Re c,exit :

Reynolds number based on blade chord and exit velocity

Re c,inlet :

Reynolds number based on blade chord and inlet velocity

S :

Distance along a streamline

S ij :

Instantaneous velocity gradient tensor

T :

Turbulent time scale (=k/ε)

Tu :

Turbulence intensity [=√(2/3 k)/√(U 2 + V 2)]

u s′, u n′:

RMS velocities in the streamwise and cross-stream directions

u i , u j :

Instantaneous velocity components

U ∞ :

Mean velocity averaged across inlet (=117 m/s)

U, u′:

Local mean and rms velocities in the X-direction

V, v′:

Local mean and rms velocities in the Y-direction

X, Y :

Fixed Cartesian system used for measurements and calculations

Δ:

Filter size (= IR size for PIV measurements)

Δx :

Grid spacing used for derivative calculations

ε :

Dissipation rate

ε 0 :

Average dissipation rate from measurements at inlet (=35,000 m2/s3)

η :

Kolmogorov length scale

λ :

Taylor microscale

μ :

Dynamic viscosity

ρ p :

Density of tracer particles

τ ij :

Sub-grid scale stress tensor

τ p :

Particle relaxation time

υ :

Kinematic viscosity

ξ :

PIV displacement error

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Acknowledgments

This work was funded by the Air Force Office of Scientific Research through contract number F49620-02-1-0284 monitored by Dr. Thomas Beutner. Early funding for the apparatus development was provided by the General Electric Corporation through the University Strategic Alliance Program. Drs Paul Durbin, Chris Elkins, Gorazd Medic, Greg Laskowski, and Paul Kodzwa, and Mr. Lakhbir Johal made substantial contributions to the research.

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  1. Department of Mechanical Engineering, Stanford University, Stanford, CA, 94305-3030, USA

    Amanda Vicharelli & John K. Eaton

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  1. Amanda Vicharelli
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Correspondence to Amanda Vicharelli.

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Vicharelli, A., Eaton, J.K. Turbulence measurements in a transonic two-passage turbine cascade. Exp Fluids 40, 897–917 (2006). https://doi.org/10.1007/s00348-006-0127-8

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  • DOI: https://doi.org/10.1007/s00348-006-0127-8

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