Erratum to: Numerical method to compute acoustic scattering effect of a moving source
Song et al. SpringerPlus (2016) 5:2117
DOI 10.1186/s40064-017-3790-8
Open Access
ERRATUM
Erratum to: Numerical method
to compute acoustic scattering effect of a
moving source
Hao Song, Mingxu Yi*, Jun Huang, Yalin Pan and Dawei Liu
*Correspondence:
School of Aeronautic Science
and Engineering, Beihang
University, Beijing 100191,
People’s Republic of China
Erratum to: SpringerPlus (2016) 5:1404
DOI 10.1186/s40064‑016‑3080‑x
The description of “innovation” and “references” in our article (Song et al. 2016) needs
additional clarification.
Firstly, in the paper “Acoustic velocity formulation for sources in arbitrary motion”
(Ghorbaniasl et al. 2013) the theory and the method are particularly good and valuable,
and its general method is not only applied to their proposed fields, but is also good at
handling the scattering effects appearing in the aviation field.
Secondly, we (Song et al. 2016) studied the theory and method described by Ghorbaniasl et al. (2013) and found they are very suitable for reducing the scattering effect of
noise. In the aviation field, the prediction problem of acoustic noise of the ducted tail
rotor is very important and difficult to solve; therefore, we tried to use their method
to solve the problem. According to our simulation, the perfect results of the acoustic
noise of the ducted tail rotor are acquired. To the best of our knowledge, this is the first
attempt to predict the acoustic noise of the ducted tail rotor using the theory and the
method proposed by Ghorbaniasl et al. (2013).
Thirdly, we omitted to cite three articles (Ghorbaniasl et al. 2013; Mao et al. 2008; Hu
et al. 2013). We apologize to readers and to the authors of these articles. We therefore
present the following corrections:
1. The procedure of the velocity formulation for the thickness and loading sources was
proposed by Farassat (2007). Following the same procedure gives the thickness and
loading acoustic velocity as follows (Ghorbaniasl et al. 2013):
Q
∂
dS
S ∂xi r(1 − Mr ) ret
(8)
t
∂
∂
Lr
Lr
dS −
dS
dt ∗
2
0
S ∂xi r (1 − Mr ) ret ∗
S ∂xi r(1 − Mr ) ret
(9)
4πρ0 a′Ti (x, t) = −
1
c0
4πρ0 a′Li (x, t) = −
© The Author(s) 2017. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License
(http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium,
provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and
indicate if changes were made.
Song et al. SpringerPlus (2016) 5:2117
Page 2 of 2
2. Next, simplifying Eq. (12) further, one can rewrite it as follows (Ghorbaniasl et al.
2013):
4πρ0 a′Li (x, t) =
Lr
Lr
∂
1
∂ r̂i
dS + 2
dS
r̂i
c0 S r(1 − Mr ) ∂t ret
S ∂t r(1 − Mr ) ret
t
Li − 3r̂i Lr
Li − 3r̂i Lr
1
dS−
dS
dt ∗
−
3
c0 S r 2 (1 − Mr ) ret
0
S r (1 − Mr ) ret ∗
1
c0
(21)
3. The sound pressure on the outside of the surface S + s is denoted by P ′− and that on
the inside is denoted by P ′+. The integral equation can be used to each subdomain
(Wu and Wan 1992; Mao et al. 2008; Hu et al. 2013)
C + (x)P ′+ (x, ω) = PI′ (x, ω) +
−
′−
C (x)P (x, ω) =
S+s
S+s
∂P ′+ (y, ω)
∂G(x, y, ω)
dS(y)
G(x, y, ω) − P ′+ (y, ω)
∂n1 (y)
∂n1 (y)
∂G(x, y, ω)
∂P ′− (y, ω)
′−
G(x, y, ω) − P (y, ω)
dS(y)
∂n2 (y)
∂n2 (y)
(27)
(28)
The online version of the original article can be found under doi:10.1186/s40064-016-3080-x.
Received: 9 February 2017 Accepted: 16 February 2017
References
Farassat F (2007) Derivation of formulations 1 and 1A of Farassat. NASA, TM: 214853
Ghorbaniasl G, Carley M, Lacor C (2013) Acoustic velocity formulation for sources in arbitrary motion. AIAA J 51(3):632–
642. doi:10.2514/1.J051958
Hu B, OuYang H, Wu Y et al (2013) Numerical prediction of the interaction noise radiated from an axial fan. Appl Acoust
74(4):544–552. doi:10.1016/j.apacoust.2012.09.009
Mao Y, Qi D, Liu X et al (2008) Numerical prediction of aerodynamic tonal noise radiated from a centrifugal fan. Proc Inst
Mech Eng A J Power Energy 222(8):831–842. doi:10.1243/09576509JPE655
Song H, Yi M, Huang J, Pan Y, Liu D (2016) Numerical method to compute acoustic scattering effect of a moving source.
SpringerPlus 5:1404. doi:10.1186/s40064-016-3080-xThe online version of the original article can be found under
doi:10.1186/s40064-016-3080-x.
(...truncated)
