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Research Papers

A Novel Mixing Plane Method Using Nonreflecting Boundary Conditions for Multirow Analysis in Turbomachines

[+] Author and Article Information
Fernando Gisbert

Technology and Methods Department,
Industria de Turbopropulsores S.A.,
Madrid 28830, Spain
e-mail: Fernando.Gisbert@itp.es

Roque Corral

Technology and Methods Department,
Industria de Turbopropulsores S.A.,
Madrid 28830, Spain;
Associate Professor
Department of Engine Propulsion and
Fluid Dynamics of the School of Aeronautics,
UPM,
Madrid 28040, Spain
e-mail: Roque.Corral@itp.es

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received December 11, 2015; final manuscript received December 30, 2015; published online February 17, 2016. Editor: Kenneth C. Hall.

J. Turbomach 138(7), 071009 (Feb 17, 2016) (9 pages) Paper No: TURBO-15-1299; doi: 10.1115/1.4032539 History: Received December 11, 2015; Revised December 30, 2015

A new formulation of the mixing plane boundary condition to analyze the steady-state interaction between adjacent rows of a turbomachine, used in conjunction with steady two-dimensional nonreflecting boundary conditions, is presented. Existing mixing plane formulations rely on the differences between some variables at the interface of adjacent rows to determine the boundary condition. These differences are driven to zero as the case is converged to the steady state. By contrast, the proposed approach determines the differences that result in the conservation of mass, momentum, and energy after the boundary condition is enforced, ensuring conservation at any instant during the iterative process. The reverse flow within the mixing plane boundary is naturally treated, but both inlet and outlet boundary conditions fail when the mixing plane normal velocity tends to zero, giving rise to sharp variations of the fluid variables that must be properly limited to prevent convergence problems. Some examples will be given to demonstrate the ability of the new method to resolve these cases while preserving the boundary condition robustness.

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References

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Figures

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Fig. 1

Meridional view of the MAGPI LPT stage with cavities. The mixing plane is marked with a thick line that separates the rotor and stator main flow path domains.

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Fig. 2

Left: Nondimensional mass flow at both sides of the mixing plane of the MAGPI LPT. Right: absolute error between them.

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Fig. 3

Left: Nondimensional x-momentum at both sides of the mixing plane of the MAGPI LPT. Right: absolute error between them.

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Fig. 4

Left: Nondimensional θ-momentum at both sides of the mixing plane of the MAGPI LPT. Right: absolute error between them.

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Fig. 5

Left: Nondimensional r-momentum at both sides of the mixing plane of the MAGPI LPT. Right: absolute error between them.

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Fig. 6

Left: Nondimensional energy at both sides of the mixing plane of the MAGPI LPT. Right: absolute error between them.

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Fig. 7

Meridional view of the FUTURE compressor stage. The mixing plane is marked with a thick line that separates the stator and rotor domains.

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Fig. 8

History of convergence for the FUTURE compressor stage

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Fig. 9

Isolines of pressure for the FUTURE rotor compressor. Black: New formulation, Gray: Mixed-out variables formulation. The mixing plane location is marked with a thick black line.

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Fig. 10

Convergence of the mass flow relative differences at both sides of the mixing plane for the FUTURE compressor stage

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Fig. 11

Convergence of the x-momentum relative differences at both sides of the mixing plane for the FUTURE compressor stage

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Fig. 12

Convergence of the energy relative differences at both sides of the mixing plane for the FUTURE compressor stage

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Fig. 13

Meridional view of an LPT stage with cavities. The mixing plane is marked with a thick line that separates the stator and rotor domains.

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Fig. 14

History of convergence for the LPT stage with reverse flow at the mixing plane

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Fig. 15

Left: Nondimensional mass flow at both sides of the mixing plane of the LPT stage with reverse flow at mixing plane. Right: absolute error between them.

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Fig. 16

Zoom of Fig. 15 between 0 and 5% of the span. Left: Nondimensional normal velocity. Right: relative error of the normal velocity in the mixing plane.

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