0
Research Papers

Simulating Periodic Unsteady Flows Using a Cubic-Spline-Based Time Collocation Method

[+] Author and Article Information
Pengcheng Du

e-mail: dupengcheng22@163.com

Fangfei Ning

e-mail: fangfei.ning@buaa.edu.cn
School of Energy and Power Engineering,
Beihang University,
National Key Laboratory of
Science and Technology on Aero-Engines,
37 Xueyuan Road,
Beijing 100191, China

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received June 30, 2013; final manuscript received July 4, 2013; published online October 23, 2013. Editor: Ronald Bunker.

J. Turbomach 136(4), 041014 (Oct 23, 2013) (12 pages) Paper No: TURBO-13-1120; doi: 10.1115/1.4025203 History: Received June 30, 2013; Revised July 04, 2013

Time-periodical unsteady flows are typical in turbomachinery. Simulating such flows using a conventional time marching approach is the most accurate but is extremely time consuming. In order to achieve a better balance between accuracy and computational expenses, a cubic-spline-based time collocation method is proposed. In this method, the time derivatives in the Navier–Stokes equations are obtained by using the differential quadrature method, in which the periodical flow variables are approximated by cubic splines. Thus, the computation of a time-periodical flow is substituted by several coupled quasi-steady flow computations at sampled instants. The proposed method is then validated against several typical turbomachinery periodical unsteady flows, i.e., transonic compressor rotor flows under circumferential inlet distortions, single stage rotor–stator interactions, and IGV–rotor interactions. The results show that the proposed cubic-spline-based time collocation method with appropriate time sampling can well resolve the dominant unsteady effects, while the computational expenses are kept much less than the traditional time-marching simulation. More importantly, this paper provides a framework on the basis of a time collocation method in which one may choose more compatible test functions for the concerned specific unsteady flows so that better modeling of the flows can be expected.

Copyright © 2014 by ASME
Your Session has timed out. Please sign back in to continue.

References

Figures

Grahic Jump Location
Fig. 1

Illustration of the time collocation method

Grahic Jump Location
Fig. 2

Spectral radius of the weighting coefficient matrix

Grahic Jump Location
Fig. 3

Computational mesh

Grahic Jump Location
Fig. 4

Convergence histories of the TCM computations

Grahic Jump Location
Fig. 5

Unsteady rotor efficiency

Grahic Jump Location
Fig. 6

Snapshots of normalized total pressure: (a) DTS, (b) TCM-NT7, and (c) TSM-NT7

Grahic Jump Location
Fig. 7

Square-wave form inlet distortion

Grahic Jump Location
Fig. 8

Unsteady blade forces variation

Grahic Jump Location
Fig. 9

Comparison of instantaneous total pressure: (a) 50% axial chord upstream the rotor and (b) 50% axial chord downstream the rotor

Grahic Jump Location
Fig. 10

Close-spacing computational mesh

Grahic Jump Location
Fig. 11

Blade row interface interpolation process

Grahic Jump Location
Fig. 12

Time-averaged efficiency with respect to different time sampling at close spacing

Grahic Jump Location
Fig. 13

Unsteady efficiency at close spacing

Grahic Jump Location
Fig. 14

Time-averaged performances: (a) efficiency and (b) total pressure ratio

Grahic Jump Location
Fig. 15

Snapshots of entropy (J/K) at close spacing: (a) DTS, (b) TCM-NT15, and (c) TSM-NT11

Grahic Jump Location
Fig. 16

Amplitude of the unsteady static pressure on blade surface: (a) rotor and (b) stator

Grahic Jump Location
Fig. 17

Residual convergence histories

Grahic Jump Location
Fig. 18

Computation speed-up factor

Grahic Jump Location
Fig. 19

Whole annulus computational mesh

Grahic Jump Location
Fig. 20

Residual convergence histories

Grahic Jump Location
Fig. 21

Time-averaged efficiency with respect to different time sampling at near stall

Grahic Jump Location
Fig. 22

Time-averaged performances: (a) efficiency and (b) total pressure ratio

Grahic Jump Location
Fig. 23

Snapshots of normalized static pressure (normalized by inlet total pressure): (a) DTS, (b) TCM-NT13, and (c) TSM-NT11

Grahic Jump Location
Fig. 24

Normalized unsteady pressure on IGV blade: (a) real part, (b) imaginary part, and (c) amplitude

Tables

Errata

Discussions

Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In