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Research Papers: Fundamental Issues and Canonical Flows

On Topology of Flow in a Turbine Cascade

[+] Author and Article Information
Krishna Nandan Kumar

Department of Mechanical &
Aerospace Engineering,
The George Washington University,
Washington, DC 20052
e-mail: krishnagwu@gwu.edu

M. Govardhan

Department of Mechanical Engineering,
Indian Institute of Technology,
Madras, Chennai 600036, India

Contributed by the Fluids Engineering Division of ASME for publication in the JOURNAL OF FLUIDS ENGINEERING. Manuscript received May 19, 2013; final manuscript received November 8, 2013; published online May 15, 2014. Assoc. Editor: Frank C. Visser.

J. Fluids Eng 136(8), 081201 (May 15, 2014) (8 pages) Paper No: FE-13-1325; doi: 10.1115/1.4026056 History: Received May 19, 2013; Revised November 08, 2013

The present study focuses on the study of topological properties of flow in a turbine cascade. Critical-point theory is used to explain the flow phenomenon. Examination and analysis of skin-friction line patterns on three-dimensional bodies such as turbine cascade, compressor cascade, cylinder, etc. enables enhanced understanding of the three-dimensional flow. Topology of flow means types of critical points formed, their interconnection, and relation between numbers of different types of critical points. Present work focuses on rules with regard to the topological consistency of a flow field. It consists of two parts, one is the connectivity of different critical points, and another is deriving the relation between the number of nodal and saddle points of a tangent vector field. Relation between the number of nodal and saddle points is derived for flows such as a turbine cascade with and without tip clearance, turbine cascade with the end wall fence, flow over a three-dimensional obstacle, etc. Relevant mathematical background necessary for derivation is discussed. The results derived for the turbine cascade is independent of the end wall contouring, leading edge modification, trailing edge modification, and blade shape. The derived relations also hold for a compressor cascade. Flow visualization based on CFD calculations is presented for the turbine cascade with and without an end wall fence.

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References

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Figures

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Fig. 1

Critical points with corresponding index [7]

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Fig. 2

Topological transformation of turbine cascade with zero tip clearance

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Fig. 3

Topological transformation of a turbine cascade with tip clearance

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Fig. 4

Topological transformation of a turbine cascade with a streamwise end wall fence

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Fig. 5

Flow over a cylinder kept on a flat floor

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Fig. 6

Cylinder merged in the floor with retention of trajectories

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Fig. 8

Typical mesh and a view of the computational domain with a blade and fence

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Fig. 9

Spanwise variation of tangential velocity (baseline case) at x/a = 1.06, y/s = −0.83

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Fig. 10

Spanwise variation of pitchwise mass averaged exit flow angle (baseline case) at x/a = 1.06

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Fig. 11

Spanwise variation of pitchwise mass averaged nondimensional velocity ratios (baseline case) at x/a = 1.06

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Fig. 12

End wall skin-friction lines (without a fence)

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Fig. 13

End wall skin-friction lines (fence case)

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Fig. 14

Detailed view of critical points near a trailing edge (without a fence)

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Fig. 15

Detailed view of critical points near a trailing edge (with a fence)

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Fig. 16

Skin-friction lines on the suction surface of a blade (without a fence)

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Fig. 17

Skin-friction lines on the suction surface of a blade (with a fence)

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