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Jet Noise Prediction Using Turbulent Scales from LES and RANS

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Fluid Mechanics and Fluid Power, Volume 2 (FMFP 2022)

Part of the book series: Lecture Notes in Mechanical Engineering ((LNME))

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Abstract

This paper studies the modelling of turbulent scales used in an existing steady Reynolds averaged Navier–Stokes solution-based acoustic analogy. The turbulence in the flow has been described as a statistical model of the two-point cross-correlation of the velocity fluctuations, characterized by the turbulent length and time scales. The modelling of the turbulent length and time scales from the \(\overline{K} {-} \overline{\varepsilon }\) data used in the steady RANS-based acoustic analogy has been validated with those computed from the cross-correlation of the velocity fluctuations. This was pursued with an LES database comprising an isothermal and a heated ideally-expanded Mach 1.5 round jets. The far-field noise has been computed using the turbulent scales from both the cross-correlation data and the \(\overline{K} {-} \overline{\varepsilon }\) data. The two results agree very well, and also display reasonable match with direct predictions from the time-resolved LES data using the Ffowcs Williams-Hawkings method.

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Abbreviations

p:

Pressure

u:

Velocity

a:

Local speed of sound

t:

Time

γ:

Specific heat ratio

f0:

Unsteady dilatation

f:

Unsteady force vector

x:

Position vector

ω:

Radial frequency

δ:

Dirac delta function

δij:

Kronecker delta function

LL:

Lilley’s operator

\(\hat{g}\):

Green’s function of LL

Sp:

Spectral density

Ï„:

Time lag

η:

Spatial lag vector

R:

Polar radius of the observer

Θ:

Polar angle of the observer

Bn:

Amplitude constants for various n

St:

Strouhal number

Dj:

Jet diameter

Uj:

Jet exit velocity

Ï„s:

Turbulent time scale

â„“s:

Turbulent length scale

us:

Turbulent velocity scale

K:

Turbulent kinetic energy

ε:

Dissipation

\(\overline{\left( \cdot \right)}\):

Time-averaged quantity

\(\left( \cdot \right){\prime}\):

Perturbation quantity

\(\widehat{\left( \cdot \right)}\):

Temporal Fourier-transformed

\(\left( \cdot \right)^{*}\):

Complex conjugate

\(\left( \cdot \right)_{\infty }\):

Freestream quantity

\(\left( \cdot \right)_{s}\):

Source quantity

\(\left( \cdot \right)\):

Ensemble average

\(\left( \cdot \right)_{g}^{n}\):

nth component of vector Green’s function

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Acknowledgements

The authors are grateful to Guillaume Brès for sharing the LES solutions for the two supersonic jets, without which this work would not have been possible. Funding from a research grant from Indian Space Research Organization is also gratefully acknowledged.

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Authors and Affiliations

  1. Department of Aerospace Engineering, IIT Bombay, Mumbai, 400076, India

    N. P. Shabeeb & Aniruddha Sinha

Authors
  1. N. P. Shabeeb
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  2. Aniruddha Sinha
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Correspondence to N. P. Shabeeb .

Editor information

Editors and Affiliations

  1. Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Krishna Mohan Singh

  2. Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Sushanta Dutta

  3. Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Sudhakar Subudhi

  4. Department of Mechanical and Industrial Engineering, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Nikhil Kumar Singh

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Shabeeb, N.P., Sinha, A. (2024). Jet Noise Prediction Using Turbulent Scales from LES and RANS. In: Singh, K.M., Dutta, S., Subudhi, S., Singh, N.K. (eds) Fluid Mechanics and Fluid Power, Volume 2. FMFP 2022. Lecture Notes in Mechanical Engineering. Springer, Singapore. https://doi.org/10.1007/978-981-99-5752-1_17

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  • DOI: https://doi.org/10.1007/978-981-99-5752-1_17

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-99-5751-4

  • Online ISBN: 978-981-99-5752-1

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