Abstract

Turbulent noise prediction is integral to fluid equipment design, and multiple simulations or experiments are often required for noise distribution under varying operating conditions during the design optimization process, which could be expensive. Recently, the physics informed neural networks (PINNs) method has emerged as an efficient machine learning method for solving parameterized partial differential equations with geometric shapes, boundary conditions, and equation parameters as variable parameters through a single training session without data. In this study, a parameterized prediction method is developed to predict turbulent jet noise based on PINNs without any training datasets. Both 2D and 3D jet flow problems are solved. The 2D problem is solved with the Reynolds number as a variable parameter, and the 3D problem is solved with the Reynolds number and nozzle eccentricity as variable parameters. The predicted results are in good agreement with those from conventional computational fluid dynamics (CFD), with average errors of 3% and 6% for the 2D and 3D flow and acoustic power fields, respectively. In terms of computational efficiency, the time required by the method for the three-dimensional problem with two variable parameters is only one-seventh of that of the traditional CFD method. This study demonstrates that for engineering noise scenarios with varying parameters, the method based on PINNs offers a more efficient parameterized predicting approach and is promising for future applications.

References

1.
Basner
,
M.
,
Babisch
,
W.
, and
Davis
,
A.
,
2014
, “
Auditory and Non-Auditory Effects of Noise on Health
,”
Lancet.
,
383
(
9925
), pp.
1325
1332
.
2.
Yankaskas
,
K. D.
, and
Komrower
,
J. M.
,
2019
, “
Military and Industrial Performance: The Critical Role of Noise Controls
,”
Int. J. Audiol.
,
58
(
Supp.1
), pp.
S74
S80
.
3.
Tam
,
C. K.
, and
Auriault
,
L.
,
1999
, “
Jet Mixing Noise From Fine-Scale Turbulence
,”
AIAA J.
,
37
(
2
), pp.
145
153
.
4.
Lighthill
,
M. J.
,
1952
, “
On Sound Generated Aerodynamically I. General Theory
,”
Proc. R. Soc. Lond., A. Math. Phys. Sci.
,
211
(
1107
), pp.
564
587
.
5.
Khavaran
,
A.
,
Krejsa
,
E. A.
, and
Kim
,
C. M.
,
1994
, “
Computation of Supersonic Jet Mixing Noise for an Axisymmetric Convergent-Divergent Nozzle
,”
J. Aircraft
,
31
(
3
), pp.
603
609
.
6.
Khavaran
,
A.
,
1999
, “
Role of Anisotropy in Turbulent Mixing Noise
,”
AIAA J.
,
37
(
7
), pp.
832
841
.
7.
Bachute
,
M. R.
, and
Subhedar
,
J. M.
,
2021
, “
Autonomous Driving Architectures: Insights of Machine Learning and Deep Learning Algorithms
,”
Mach. Learn. Appl.
,
6
, p.
100164
.
8.
Bochenek
,
B.
, and
Ustrnul
,
Z.
,
2022
, “
Machine Learning in Weather Prediction and Climate Analyses-Applications and Perspectives
,”
Atmosphere
,
13
(
2
), p.
180
.
9.
Duraisamy
,
K.
,
2021
, “
Perspectives on Machine Learning-Augmented Reynolds-Averaged and Large Eddy Simulation Models of Turbulence
,”
Phys. Rev. Fluids
,
6
(
5
), p.
050504
.
10.
Chi
,
C.
,
Xu
,
X.
, and
Thévenin
,
D.
,
2022
, “
Efficient Premixed Turbulent Combustion Simulations Using Flamelet Manifold Neural Networks: A Priori and a Posteriori Assessment
,”
Combust. Flame
,
245
, p.
112325
.
11.
Li
,
S.
, and
Ukeiley
,
L.
,
2022
, “
Pressure-Informed Velocity Estimation in a Subsonic Jet
,”
Phys. Rev. Fluids
,
7
(
1
), p.
014601
.
12.
Tenney
,
A. S.
,
Glauser
,
M. N.
,
Ruscher
,
C. J.
, and
Berger
,
Z. P.
,
2020
, “
Application of Artificial Neural Networks to Stochastic Estimation and Jet Noise Modeling
,”
AIAA J.
,
58
(
2
), pp.
647
658
.
13.
Lu
,
L.
,
Jin
,
P.
, and
Karniadakis
,
G. E.
,
2019
, “DeepoNet: Learning Nonlinear Operators for Identifying Differential Equations Based on The Universal Approximation Theorem of Operators,” arXiv:1910.03193.
14.
Li
,
Z.
,
Kovachki
,
N.
,
Azizzadenesheli
,
K.
,
Liu
,
B.
,
Bhattacharya
,
K.
,
Stuart
,
A.
, and
Anandkumar
,
A.
,
2020
, “Fourier Neural Operator for Parametric Partial Differential Equations,” arXiv:2010.08895.
15.
Raissi
,
M.
,
Perdikaris
,
P.
, and
Karniadakis
,
G. E.
,
2019
, “
Physics-Informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations
,”
J. Comput. Phys.
,
378
, pp.
686
707
.
16.
Baydin
,
A. G.
,
Pearlmutter
,
B. A.
,
Radul
,
A. A.
, and
Siskind
,
J. M.
,
2018
, “
Automatic Differentiation in Machine Learning: A Survey
,”
J. Machine Learn. Res.
,
18
(
1
), pp.
1
43
.
17.
Daw
,
A.
,
Bu
,
J.
,
Wang
,
S.
,
Perdikaris
,
P.
, and
Karpatne
,
A.
,
2022
, “Rethinking the Importance of Sampling in Physics-Informed Neural Networks,” arXiv:2207.02338.
18.
Sliwinski
,
L.
, and
Rigas
,
G.
,
2023
, “
Mean Flow Reconstruction of Unsteady Flows Using Physics-Informed Neural Networks
,”
Data-Centric Eng.
,
4
, p.
e4
.
19.
Eivazi
,
H.
,
Tahani
,
M.
,
Schlatter
,
P.
, and
Vinuesa
,
R.
,
2022
, “
Physics-Informed Neural Networks for Solving Reynolds-Averaged Navier-Stokes Equations
,”
Phys. Fluids
,
34
(
7
), p.
075117
.
20.
Jin
,
X.
,
Cai
,
S.
,
Li
,
H.
, and
Karniadakis
,
G. E.
,
2021
, “
NSFNets (Navier–Stokes Flow Nets): Physics-Informed Neural Networks for the Incompressible Navier-Stokes Equations
,”
J. Comput. Phys.
,
426
, p.
109951
.
21.
Sun
,
Y.
,
Sengupta
,
U.
, and
Juniper
,
M.
,
2023
, “
Physics-Informed Deep Learning for Simultaneous Surrogate Modeling and PDE-Constrained Optimization of an Airfoil Geometry
,”
Comput. Methods Appl. Mech. Eng.
,
411
, p.
116042
.
22.
Liu
,
K.
,
Luo
,
K.
,
Cheng
,
Y.
,
Liu
,
A.
,
Li
,
H.
,
Fan
,
J.
, and
Balachandar
,
S.
,
2023
, “
Surrogate Modeling of Parameterized Multi-Dimensional Premixed Combustion With Physics-Informed Neural Networks for Rapid Exploration of Design Space
,”
Combust. Flame
,
258
, p.
113094
.
23.
Cao
,
Z.
,
Liu
,
K.
,
Luo
,
K.
,
Cheng
,
Y.
, and
Fan
,
J.
,
2023
, “
Efficient Optimization Design of Flue Deflectors Through Parametric Surrogate Modeling With Physics-Informed Neural Networks
,”
Phys. Fluids
,
35
(
12
), p.
125149
.
24.
Proudman
,
I.
,
1952
, “
The Generation of Noise by Isotropic Turbulence
,”
Proc. R. Soc. Lond., A. Math. Phys. Sci.
,
214
(
1116
), pp.
119
132
.
25.
Morris
,
P. J.
, and
Farassat
,
F.
,
2002
, “
Acoustic Analogy and Alternative Theories for Jet Noise Prediction
,”
AIAA J.
,
40
(
4
), pp.
671
680
.
27.
Rodi
,
W.
,
2017
,
Turbulence Models and Their Application in Hydraulics
,
Routledge
,
London
.
28.
Modulus
,
2023
, “Turbulent Physics: Zero Equation Turbulence Model,” https://docs.nvidia.com/deeplearning/modulus/modulus-v2209/user_guide/foundational/zero_eq_turbulence.html.
29.
Van der Hegge Zijnen
,
B.
,
1958
, “
Measurements of the Velocity Distribution in a Plane Turbulent Jet of Air
,”
Appl. Sci. Res., Sec. A
,
7
, pp.
256
276
.
31.
Pope
,
S.
,
1978
, “
An Explanation of the Turbulent Round-Jet/Plane-Jet Anomaly
,”
AIAA J.
,
16
(
3
), pp.
279
281
.
32.
Kingma
,
D. P.
, and
Ba
,
J.
,
2014
, “Adam: A Method for Stochastic Optimization,” arXiv:1412.6980.
33.
ANSYS
,
2024
, “Ansys-Fluent,” https://www.ansys.com/products/fluids/ansys-fluent.
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