Research Papers

Control-Oriented Methods for Turbomachinery Noise Simulation

[+] Author and Article Information
Alex Siu Hong Lau

Department of Mechanical and
Aerospace Engineering,
Hong Kong University of Science
and Technology,
Kowloon, Hong Kong, China
e-mail: alexshlau@ust.hk

Siyang Zhong

Department of Mechanical and
Aerospace Engineering,
Hong Kong University of Science
and Technology,
Kowloon, Hong Kong, China
e-mail: szhongad@connect.ust.hk

Xun Huang

Department of Mechanical and
Aerospace Engineering,
The Hong Kong University
of Science and Technology,
Kowloon, Hong Kong, China;
Department of Aeronautics and Astronautics,
College of Engineering,
Peking University,
Beijing 100871, China
e-mails: huangxun@ust.hk;

1Corresponding author.

Contributed by the International Gas Turbine Institute (IGTI) of ASME for publication in the JOURNAL OF TURBOMACHINERY. Manuscript received May 24, 2017; final manuscript received September 6, 2017; published online October 17, 2017. Assoc. Editor: Rakesh Srivastava.

J. Turbomach 140(1), 011001 (Oct 17, 2017) (15 pages) Paper No: TURBO-17-1067; doi: 10.1115/1.4038022 History: Received May 24, 2017; Revised September 06, 2017

This paper presents an innovative stability analysis and design approach for time-domain impedance boundary conditions to simulate noise propagation and radiation from a lined turbomachinery duct in the presence of a mean flow. A control-oriented model is developed for the stability analysis of the impedance boundary condition by using generalized function at the lining surface. The mean flow effect and sound propagation are considered in the model as well. Then, the numerical stability issue is analyzed by using the Bode plots before stabilized accordingly by employing the phase lead compensator method, which results in a rational transfer function. Finally, the corresponding time-domain implementation is achieved by using the so-called controllable canonical form rather than an inconvenient convolution operation. The performance of the current proposed approach is first validated in an in-duct propagation case by comparing to analytical solutions obtained by employing the Wiener–Hopf method and then demonstrated in a couple of duct acoustic problems with representative turbomachinery setups. The innovative cross-disciplinary nature of the current proposed approach can shed light on impedance problems and is very useful to time-domain acoustic simulations for turbomachinery applications.

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Tester, B. , 1973, “ Some Aspects of Sound Attenuation in Lined Ducts Containing Inviscid Mean Flows With Boundary Layers,” J. Sound Vib., 28(2), pp. 217–245. [CrossRef]
Eversman, W. , and Okunbor, D. , 1998, “ AFT Fan Duct Acoustic Radiation,” J. Sound Vib., 213(2), pp. 235–257. [CrossRef]
Zhang, X. , Chen, X. , Morfey, C. , and Nelson, P. , 2004, “ Computation of Spinning Modal Radiation From an Unflanged Duct,” AIAA J., 42(9), pp. 1795–1801. [CrossRef]
Özyörük, Y. , and Ahuja, V. , 2004, “ Numerical Simulation of Fore and Aft Sound Field of a Turbofan,” AIAA J., 42(10), pp. 2028–2034. [CrossRef]
Richards, S. , Chen, X. , Huang, X. , and Zhang, X. , 2007, “ Computation of Fan Noise Radiation Through an Engine Exhaust Geometry With Flow,” Int. J. Aeroacoustics, 6(3), pp. 223–241. [CrossRef]
Huang, X. , Chen, X. , Ma, Z. , and Zhang, X. , 2008, “ Efficient Computation of Spinning Modal Radiation Through an Engine Bypass Duct,” AIAA J., 46(6), pp. 1413–1423. [CrossRef]
Casalino, D. , and Genito, M. , 2008, “ Turbofan Aft Noise Predictions Based on Lilley's Wave Model,” AIAA J., 46(1), pp. 84–93. [CrossRef]
Chen, X. , Huang, X. , and Zhang, X. , 2009, “ Sound Radiation From a Bypass Duct With Bifurcations,” AIAA J., 47(2), pp. 429–436. [CrossRef]
Zhang, X. , and Chen, X. , 2014, “ Broadband Wave Propagation From an Aeroengine Duct,” AIAA J., 52(1), pp. 43–51. [CrossRef]
Bianchi, S. , Corsini, A. , Rispoli, F. , and Sheard, A. G. , 2011, “ Far-Field Radiation of Tip Aerodynamic Sound Sources in Axial Fans Fitted With Passive Noise Control Features,” ASME J. Vib. Acoust., 133(5), p. 051001. [CrossRef]
Jiang, H. , and Huang, X. , 2017, “ Efficient Impedance Eductions for Liner Tests in Grazing Flow Incidence Tube,” ASME J. Vib. Acoust., 139(3), p. 031002. [CrossRef]
Prasad, D. , and Feng, J. , 2005, “ Propagation and Decay of Shock Waves in Turbofan Engine Inlets,” ASME J. Turbomach., 127(1), pp. 118–127. [CrossRef]
Tucker, P. , Eastwood, S. , Klostermeier, C. , Xia, H. , Ray, P. , Tyacke, J. , and Dawes, W. , 2012, “ Hybrid LES Approach for Practical Turbomachinery Flows—Part II: Further Applications,” ASME J. Turbomach., 134(2), p. 021024. [CrossRef]
Ouyang, H. , Yian, J. , Li, Y. , Zheng, Z. , and Du, Z. , 2012, “ Internal Flow and Noise Investigations About the Cross-Flow Fan With Different Blade Angles,” ASME J. Turbomach., 134(5), p. 051023. [CrossRef]
Ingard, U. , 1959, “ Influence of Fluid Motion Past a Plane Boundary on Sound Reflection, Absorption, and Transmission,” J. Acoust. Soc. Am., 31(7), pp. 1035–1036. [CrossRef]
Myers, M. , 1980, “ On the Acoustic Boundary Condition in the Presence of Flow,” J. Sound Vib. 71(3), pp. 429–434. [CrossRef]
Bogey, C. , Bailly, C. , and Juvé, D. , 2002, “ Computation of Flow Noise Using Source Terms in Linearized Euler's Equations,” AIAA J., 40(2), pp. 235–243. [CrossRef]
Brambley, E. , 2011, “ Well-Posed Boundary Condition for Acoustic Liners in Straight Ducts With Flow,” AIAA J., 49(6), pp. 1272–1282. [CrossRef]
Tam, C. , and Webb, J. , 1993, “ Dispersion-Relation-Preserving Finite Difference Schemes for Computational Acoustics,” J. Comput. Phys., 107(2), pp. 262–281. [CrossRef]
Özyörük, Y. , Long, L. , and Jones, M. G. , 1998, “ Time-Domain Numerical Simulation of a Flow-Impedance Tube,” J. Comput. Phys., 146(1), pp. 29–57. [CrossRef]
Rienstra, S. , 2007, “ Acoustic Scattering at a Hard-Soft Lining Transition in a Flow Duct,” J. Eng. Math., 59(4), pp. 451–475. [CrossRef]
Peers, E. , and Huang, X. , 2013, “ High-Order Schemes for Predicting Computational Aeroacoustic Propagation With Adaptive Mesh Refinement,” Acta Mech. Sin., 29(2), pp. 1–11. [CrossRef]
Yu, J. , Ruiz, M. , and Kwan, H. , 2008, “ Validation of Goodrich Perforate Liner Impedance Model Using NASA Langley Test Data,” AIAA Paper No. 2008–2930.
Tam, C. K. W. , and Auriault, L. , 1996, “ Time-Domain Impedance Boundary Conditions for Computational Aeroacoustics,” AIAA J., 34(5), pp. 917–923. [CrossRef]
Eduardo, S. , 1998, Mathematical Control Theory: Deterministic Finite Dimensional Systems, 2nd ed., Springer-Verlag, New York.
Eversman, W. , and Beckemeyer, R. , 1972, “ Transmission of Sound in Ducts With Thin Shear Layers: Convergence to the Uniform Flow Case,” J. Acoust. Soc. Am., 52(1B), pp. 216–220. [CrossRef]
Brambley, E. J. , 2009, “ Fundamental Problems With the Model of Uniform Flow Over Acoustic Linings,” J. Sound Vib., 322(4–5), pp. 1026–1037. [CrossRef]
Renou, Y. , and Auregan, Y. , 2011, “ Failure of the Ingard–Myers Boundary Condition for a Lined Duct: An Experimental Investigation,” J. Acoust. Soc. Am., 130(1), pp. 52–60. [CrossRef] [PubMed]
Rienstra, S. , and Darau, M. , 2011, “ Boundary-Layer Thickness Effects of the Hydrodynamic Instability Along an Impedance Wall,” J. Fluid Mech., 671, pp. 559–573. [CrossRef]
Fung, K. , Ju, H. , and Tallapragada, B. , 2000, “ Impedance and Its Time-Domain Extensions,” AIAA J., 38(1), pp. 30–38. [CrossRef]
Fung, K. , and Ju, H. , 2001, “ Broadband Time-Domain Impedance Models,” AIAA J., 39(8), pp. 1449–1454. [CrossRef]
Ju, H. , and Fung, K. , 2001, “ Time-Domain Impedance Boundary Conditions With Mean Flow Effects,” AIAA J., 39(9), pp. 1683–1690. [CrossRef]
Gabard, G. , 2013, “ A Comparison of Impedance Boundary Conditions for Flow Acoustics,” J. Sound Vib., 332(4), pp. 714–724. [CrossRef]
Richter, C. , Hay, J. , Panek, L. , and Schönwald, N. , 2011, “ A Review of Time-Domain Impedance Modelling and Applications,” J. Sound Vib., 330(1), pp. 3859–3873. [CrossRef]
Liu, X. , Huang, X. , and Zhang, X. , 2014, “ Stability Analysis and Design of Time-Domain Acoustic Impedance Boundary Conditions for Lined Duct With Mean Flow,” J. Acoust. Soc. Am., 136(5), pp. 2441–2452. [CrossRef] [PubMed]
Liu, X. , and Huang, X. , 2015, “ Stabilized Time-Domain Impedance Model and the Application in Bypass Duct Noise Simulations,” AIAA Paper No. 2015-2676.
Zhong, S. , Zhang, X. , and Huang, X. , 2016, “ A Controllable Canonical Form of Time Domain Impedance Boundary Condition for Broadband Aeroacoustics Computation,” J. Comput. Phys., 313(5), pp. 713–725. [CrossRef]
Zhang, X. , Chen, X. , and Morfey, C. , 2005, “ Acoustic Radiation From a Semi-Infinite Duct With a Subsonic Jet,” Int. J. Aeroacoustics, 4(1–2), pp. 169–184. [CrossRef]
Huang, X. , Zhang, X. , and Richards, S. , 2008, “ Adaptive Mesh Refinement Computation of Acoustic Radiation From an Engine Intake,” Aerosp. Sci. Technol., 12(5), pp. 418–426. [CrossRef]
Reymen, Y. , Baelmans, M. , and Desmet, W. , 2008, “ Efficient Implementation of Tam and Auriault's Time-Domain Impedance Boundary Condition,” AIAA J., 46(9), pp. 2368–2376. [CrossRef]
Li, X. , Li, X. , and Tam, C. , 2012, “ Improved Multipole Broadband Time-Domain Impedance Boundary Condition,” AIAA J., 50(4), pp. 980–984. [CrossRef]
Richter, C. , Thiele, F. , Li, X. , and Zhuang, M. , 2007, “ Comparison of Time-Domain Impedance Boundary Conditions for Lined Duct Flows,” AIAA J., 45(6), pp. 1333–1345. [CrossRef]
Munt, R. , 1977, “ The Interaction of Sound With a Subsonic Jet Issuing From a Semi-Infinite Cylindrical Pipe,” J. Fluids Mech., 83(4), pp. 609–640. [CrossRef]
Rienstra, S. , 1984, “ Acoustic Radiation From a Semi-Infinite Annular Duct in a Uniform Subsonic Mean Flow,” J. Sound Vib., 94(2), pp. 267–288. [CrossRef]
Gabard, G. , and Astley, R. , 2006, “ Theoretical Model for Sound Radiation From Annular Jet Pipes: Far- and Near-Field Solutions,” J. Fluid Mech., 549, pp. 315–341. [CrossRef]
Ffowcs-Williams, J. , and Hawkings, D. , 1969, “ Sound Generation by Turbulence and Surfaces in Arbitrary Motion,” Philos. Trans. R. Soc. London, A, 264(1151), pp. 321–342. [CrossRef]
Hu, F. , Hussaini, M. , and Manthey, J. , 1996, “ Low-Dissipation and Low-Dispersion Runge-Kutta Schemes for Computational Acoustics,” J. Comput. Phys., 124(1), pp. 177–191. [CrossRef]
Ashcroft, G. , and Zhang, X. , 2003, “ Optimized Prefactored Compact Schemes,” J. Comput. Phys., 190(2), pp. 459–477. [CrossRef]
Ray, J. , Kennedy, C. , Lefantzi, S. , and Najm, H. , 2007, “ Using High-Order Methods on Adaptively Refined Block-Structured Meshes—Discretizations, Interpolations, and Filters,” SIAM J. Sci. Comput., 29(1), pp. 139–181. [CrossRef]
Richards, S. , Zhang, X. , and Nelson, P. A. , 2004, “ The Evaluation of Non-Reflecting Boundary Conditions for Duct Acoustic Computation,” J. Sound Vib., 270(3), pp. 539–557. [CrossRef]
Agarwal, A. , Morris, P. , and Mani, R. , 2004, “ Calculation of Sound Propagation in Nonuniform Flows: Suppression of Instability Waves,” AIAA J., 42(1), pp. 80–88. [CrossRef]
Liu, X. , Jiang, H. , Huang, X. , and Chen, S. , 2016, “ Theoretical Model of Scattering From Flow Ducts With Semi-Infinite Axial Liner Splices,” J. Fluid Mech., 786, pp. 62–83. [CrossRef]


Grahic Jump Location
Fig. 1

The block diagram of a feedback system that describes the LEE model P(s) (from Eq. (7)) at r = 1 (the feedforward loop) with a lined wall satisfying the Ingard boundary condition (the feedback loop). For clarity δ(r) is not explicitly shown in this figure.

Grahic Jump Location
Fig. 2

The Bode plots of P(s) at various working conditions. Details of each setup are given in the title of the associated panel. The distinctive setups that might eventually lead to computational instability are highlighted by arrows. It can be seen that certain working conditions, such as m (a), ω (d), and the real part of the impedance (e) impose little influence, while n (b), mean flow speed u0 (c) and the imaginary part of the impedance (f) affect the computational stability. The following part of this work will try to improve the computational stability by reducing the sensitivity to those working conditions.

Grahic Jump Location
Fig. 3

The Bode plots of the transfer functions: Ig(s)=(s−iu0κmn+)/s; 1/Z(s)=ω0/(ℜω0+Xs) for X>0; and L(s)=P(s)Ig(s)/Z(s), where m=4,n=1,u0=0.1,ω0=10,Z=ℜ+Xi=1+i

Grahic Jump Location
Fig. 4

The entire system with the inclusion of a control block, C(s)

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Fig. 5

The Bode plots of the control blocks, Ca(s) and Cb(s), to resolve unstable issues at low and high frequency ranges, respectively

Grahic Jump Location
Fig. 8

The phase plot of Ca(s), where ωmax = 100 and ω0=10, (×)Ka=1, (◻)Ka=2, (°)Ka=3, (+)Ka=4, (⋄)Ka=5

Grahic Jump Location
Fig. 9

Setups of computational aeroacoustic simulations for duct (not to scale): (a) the validation case and (b) the generic bypass duct case (mean flow velocity u0 is shown here). A spinning modal sound wave propagates from left to right. Buffer zones are used around the computational domain. Axial-symmetrical boundary condition is used along r = 0. The circumferential angle θ is not shown in this two-dimensional presentation.

Grahic Jump Location
Fig. 10

Numerical results from the LEE model are compared to analytical solutions using the Wiener–Hopf method. The case setup is as follows: m = 9, n = 1, ω = 20, u0 = 0.3, Z = 1 + i, where (a) shows instantaneous sound pressure with ten contour levels between ±10−4, where lined walls are represented by white dashed lines and (b) shows acoustic power across the x axis, where (–) is computational solution, and (⋯) is analytical solution.

Grahic Jump Location
Fig. 11

The difference between the numerical and the analytical results, where Imag(Z)=X is varied, while Real(Z)=ℜ=1, (◻) m=4,n=1,ω=20,u0=0.2, (Δ) m=9,n=1,ω=20,u0=0, (⋄) m=9,n=1,ω=20,u0=0.1, (°) m=9,n=1,ω=20,u0=0.2, and (+) m = 13, n = 1, ω = 20, u0 = 0.2

Grahic Jump Location
Fig. 12

Instantaneous sound pressure field, where u0 = 0, ω = 15, ((a) and (b)) (m, n) = (4, 1), ((c) and (d)) (m, n) = (4, 2), ((a) and (c)) hard-wall, ((b) and (d)) Z = 0.5 − 1.5i

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Fig. 13

As Fig. 12 but for an annular geometry with an infinite central hub

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Fig. 14

Far-field directivity with respect to the elevation angle ϕ (with respect to the downstream direction) for the hollow duct radiation case with two different setups. “APE” and “WH” denote far-field predictions obtained by using the APE model with the Ffowcs-Williams and Hawkings method (for u0 ≠ 0), and the analytical solution generated by the Wiener–Hopf method, respectively.

Grahic Jump Location
Fig. 15

Instantaneous sound pressure field is shown with ten contour levels between ±10−5, where m = 13, n = 1, ω = 28, (a) the hard-walled case; ((b) and (c)) the lined walls at two different positions are highlighted with thick lines and indicated by arrows

Grahic Jump Location
Fig. 16

Far-field directivities of the cases in Fig. 15




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