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Research Papers

An Implicit Harmonic Balance Method in Graphics Processing Units for Oscillating Blades

[+] Author and Article Information
Javier Crespo

Technology and Methods Department,
Industria de TurboPropulsores S.A.,
Alcobendas 28108, Madrid, Spain
e-mail: Javier.Crespo@itp.es

Roque Corral

Advanced Engineering Direction,
Industria de TurboPropulsores S.A.,
Alcobendas 28108, Madrid, Spain
e-mail: Roque.Corral@itp.es

Jesus Pueblas

Technology and Methods Department,
Industria de TurboPropulsores S.A.,
Alcobendas 28108, Madrid, Spain
e-mail: Jesus.Pueblas@itp.es

1Also at the Department of Fluid Dynamics and Aerospace Propulsion of the School of Aeronautics, UPM, Madrid 28040, Spain.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received July 20, 2015; final manuscript received October 20, 2015; published online November 17, 2015. Editor: Kenneth C. Hall.

J. Turbomach 138(3), 031001 (Nov 17, 2015) (10 pages) Paper No: TURBO-15-1163; doi: 10.1115/1.4031918 History: Received July 20, 2015; Revised October 20, 2015

An implicit harmonic balance (HB) method for modeling the unsteady nonlinear periodic flow about vibrating airfoils in turbomachinery is presented. An implicit edge-based three-dimensional Reynolds-averaged Navier–Stokes equations (RANS) solver for unstructured grids, which runs both on central processing units (CPUs) and graphics processing units (GPUs), is used. The HB method performs a spectral discretization of the time derivatives and marches in pseudotime, a new system of equations where the unknowns are the variables at different time samples. The application of the method to vibrating airfoils is discussed. It is shown that a time-spectral scheme may achieve the same temporal accuracy at a much lower computational cost than a backward finite-difference method at the expense of using more memory. The performance of the implicit solver has been assessed with several application examples. A speed-up factor of 10 is obtained between the spectral and finite-difference version of the code, whereas an additional speed-up factor of 10 is obtained when the code is ported to GPUs, totalizing a speed factor of 100. The performance of the solver in GPUs has been assessed using the tenth standard aeroelastic configuration and a transonic compressor.

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References

Figures

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Fig. 1

Amplitude (a) and phase (b) of the distribution along chord of the first harmonic of the pressure coefficient for the tenth standard configuration: M = 0.7, k = 0.5, σ = 0 deg, and α = 2 deg

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Fig. 2

Convergence histories of explicit and implicit methods for the inviscid airfoil case

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Fig. 3

First (a) and second (b) harmonics of the unsteady pressure coefficient distribution for different inlet Mach numbers for the tenth standard configuration: k = 0.5, σ = 0 deg, and α = 2 deg

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Fig. 4

First (a) and second (b) harmonics of the unsteady pressure coefficient distribution for different torsion amplitudes: k = 0.5, σ = 0 deg, and M = 0.8

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Fig. 5

Aerodynamic work per cycle as a function of IBPA (a) and distribution along airfoil chord (b), for different torsion amplitudes: k = 0.5, σ = −180 deg, and M = 0.8

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Fig. 6

Time average ((a) and (b)), first harmonic ((c) and (d)), and second harmonic ((e) and (b)) of the pressure distribution for the HB ((a), (c), and (e)) and the BDF ((b), (c), and (f))

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Fig. 7

Mean value ((a)–(c)), modulus ((d)–(f)), and phase ((g)–(i))) of the first harmonic of the unsteady pressure at h/c = 50% ((a), (d), and (g)), h/c = 75% ((b), (e), and (h)), and h/c = 90% ((c), (f), and (i)) sections

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Fig. 8

Second harmonic of the unsteady pressure distribution along the chord at 90% span

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Fig. 9

Time average of the relative total pressure along the chord over the tip patch (area averaged)

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Fig. 10

Critical aerodynamic damping ratio versus nodal diameter

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