Research Papers

Filtering Mixing Planes for Low Reduced Frequency Analysis of Turbomachines

[+] Author and Article Information
G. Pullan

Whittle Laboratory,
University of Cambridge,
1 JJ Thomson Avenue,
Cambridge CB3 0DY, UK
e-mail: gp10006@cam.ac.uk

J. J. Adamczyk

Visiting Researcher
Whittle Laboratory,
University of Cambridge,
1 JJ Thomson Avenue,
Cambridge CB3 0DY, UK

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received February 7, 2017; final manuscript received March 1, 2017; published online April 19, 2017. Editor: Kenneth Hall.

J. Turbomach 139(9), 091009 (Apr 19, 2017) (8 pages) Paper No: TURBO-17-1024; doi: 10.1115/1.4036296 History: Received February 07, 2017; Revised March 01, 2017

A class of problems in turbomachinery is characterized by unsteady interactions at low reduced frequencies. These interactions are often the result of perturbations with length-scale on the order of the machine circumference and examples include axial compressors operating with inlet distortion, fans with downstream pylons, and turbine rotors downstream of midframe struts. Typically, this unsteadiness is accompanied by higher frequency fluctuations caused by perturbations with a length-scale on the order of a blade pitch. Conventional numerical analysis of this class of problem requires computations with a time step governed by the high-frequency content but a greatly reduced run time could be achieved if the time step was dictated solely by the low reduced frequency, long length-scale, interaction of interest. In this paper, a filtering mixing plane technique is proposed that removes unwanted short length-scale perturbations at the interfaces between blade rows. This approach gives the user control over the amount of mixing that occurs at these interfaces with the limits being fully mixed-out to pitchwise uniformity (conventional mixing plane) or no mixing (conventional sliding plane). By choosing to retain only enough harmonics to resolve the low reduced frequency interaction of interest, an order of magnitude reduction in run time can be achieved.

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Fig. 1

Schematic of three-block single advection equation test case domain

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Fig. 2

Transport of a sinusoidal inlet profile through the three-block advection equation domain

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Fig. 3

Transport of a Gaussian wake inlet profile through the three-block advection equation domain

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Fig. 4

Profile of scalar f at the domain outlet (Gaussian wake at domain inlet)

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Fig. 5

Scalar transport of a long-wavelength distortion and 50 short wavelength wakes: (a) NΔt=50, no filter; (b) NΔt=55, no filter; (c) NΔt=60, no filter; and (d) NΔt=50, nharm=1

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Fig. 6

Postfiltering velocity profiles of a Gaussian wake

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Fig. 7

Reduction of mixing loss coefficient Yp,mix, as nharm is increased, of an analytic mixing calculation of a Gaussian wake. The fully mixed-out loss remains constant.

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Fig. 8

Flow chart of implementation of filtering mixing planes

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Fig. 9

Stagnation pressure loss coefficient, Yp, for a filtering mixing plane with a 2D wake: (a) nharm = 0, (b) nharm = 1, (c) nharm = 2, and (d) nharm = 3

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Fig. 10

Reduction of mixing loss coefficient, Yp,mix, as number of retained harmonics is increased for 2D wake case

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Fig. 11

A 1.5-stage axial compressor with inlet distortion (full domain not shown), contours of entropy function e−Δs/R: (a) NΔt=30, no filter; (b) NΔt=30, nharm=1; and (c) NΔt=100, nharm=1

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Fig. 12

Detail of NΔt=30, no filter, computation of Fig. 11(a)—contours of entropy function e−Δs/R. Aliasing means the computation is effectively “frozen rotor.”

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Fig. 13

Three-dimensional turbine stage with low aspect ratio vane, midspan entropy e−Δs/R: (a) NΔt=100, no filter; (b) NΔt=100, nharm=4; and (c) NΔt=100, nharm=5

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Fig. 14

Three-dimensional turbine stage rotor exit absolute swirl angle (degrees): (a) NΔt=100, no filter; (b) NΔt=100, no filter, time-averaged; and (c) NΔt=100, nharm=4, time-averaged




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