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Impact of an Adjacent Surface on a Rectangular Overexpanded Supersonic Jet

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Abstract

Flow and acoustic fields of a rectangular over-expanded supersonic jet interacting with an adjacent parallel plate are investigated using compressible Large Eddy Simulations (LES). The jet exits from a converging diverging rectangular nozzle of aspect ratio 2 with a design Mach number 1.5. Four distances (0 to 3 equivalent diameters) between the plate and the adjacent lip of the rectangular jet in the minor axis plane are studied. The geometry of the nozzle, the positions of the plate, and the exit conditions are identical to the ones of an experimental study. Snapshots and mean velocity fields are presented. Good agreement with the PIV experimental measurements is obtained. Previously, the corresponding free jet has been found to undergo a strong flapping motion in the minor axis plane due to screech. Here, it is shown that the intensity of the screech increases for certain distances from the plate and decreases for others, as compared to the corresponding free jet. Two points space-time cross correlations of the pressure along the jet’s shear-layers show, in two cases, an amplification of the aeroacoustic feedback mechanism leading to screech noise in the jet shear-layer closer to the plate. This amplification is due to acoustic waves impinging on the plate, and generating propagating waves back towards the jet, thus exciting the shear-layer at the screech frequency, around the tenth shock cell. Moreover, when the jet develops as a wall jet on the plate, the screech frequency and its associated flapping motion is canceled but a symmetrical oscillation of the jet at a lower frequency becomes dominant and radiates in the near acoustic field. This oscillation mode, as the ones associated with the screech tones for the other cases studied, can be explained by the use of a vortex sheet model of the ideally expanded equivalent planar jet.

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Abbreviations

\(\delta _{0.5}\) :

Half velocity width of the jet (m)

\(\theta\) :

Angle of observation (degrees)

\(\mu _j\) :

Viscosity in the ideally expanded jet, computed using Sutherland’s Law (\(kg\,(m\,s)^{-1}\))

\(\nu _j = \mu _j/\rho _j\) :

Kinematic viscosity in the ideally expanded jet (\(m^2\,s^{-1}\))

\(\omega\) :

Frequency (\(rad\,s^{-1}\))

\(\rho _j\) :

Density in the ideally expanded equivalent jet (\(kg\,m^{-3}\))

\(a_0\) :

Speed of sound in the ambient (\(m\,s^{-1}\))

\(a_j\) :

Speed of sound in the ideally expanded equivalent jet (\(m\,s^{-1}\))

\(A_d=2h \times h\) :

Exit area of the nozzle (\(m^2\))

\(A_j\) :

Exit area of the ideally expanded equivalent nozzle (\(m^2\))

b :

Depth of the nozzle (m)

\(b_j\) :

Depth of the ideally expanded equivalent nozzle (m)

\(D_{eq} = \sqrt{8/\pi } \times h\) :

Equivalent diameter of the jet (m)

f :

Frequency (Hz)

h :

Height of the nozzle (m)

\(h_j\) :

Height of the ideally expanded equivalent nozzle (m)

k :

Wavenumber (\(rad\,m^{-1}\))

\(L_n\) :

Length of the n-th shock cell (m)

\(L_s\) :

Length of the first shock cell (m)

\(L_{sh}\) :

Length scale related to the shock cell size (m)

\({\mathcal {M}}_c\) :

Convective Mach number

\({\mathcal {M}}_d\) :

Design Mach number of the jet

\({\mathcal {M}}_j\) :

Mach number of the ideally expanded equivalent jet

n :

Mode number of the oscillation mode of the planar jet

\(u_c\) :

Convection velocity (m/s)

\(u_j\) :

Velocity of the ideally expanded equivalent jet (m/s)

\(St = fD_{eq}/u_j\) :

Strouhal number based on \(D_{eq}\)

\(St_{hj} = fh_j/u_j\) :

Strouhal number based on \(h_j\)

x :

Coordinate along the major axis of the nozzle (m)

y :

Coordinate along the minor axis of the nozzle (m)

z :

Coordinate along the jet axis (m)

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Funding

The computations were performed using HPC resources provided by the Swedish National Infrastructure for Computing (SNIC) at the PDC center, by GENCI [CCRT-CINES-IDRIS] (Grant 2021-[A0102A07178]), and by CALMIP (Project 1425-21A). Professor Ephraim Gutmark and Dr. Florian Baier at University of Cincinnati are acknowledged for providing the experimental data used in this paper.

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Authors and Affiliations

  1. ISAE-SUPAERO, Université de Toulouse, 10 av. Edouard Belin, 31400, Toulouse, France

    Romain Gojon

  2. FLOW Centre, KTH Royal Institute of Technology, Brinellvägen 8, 11428, Stockholm, Sweden

    Mihai Mihaescu

Authors
  1. Romain Gojon
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  2. Mihai Mihaescu
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Contributions

RG: Writing, Methodology, Software; MM: Conceptualization, Writing (review and editing).

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Correspondence to Romain Gojon.

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Gojon, R., Mihaescu, M. Impact of an Adjacent Surface on a Rectangular Overexpanded Supersonic Jet. Flow Turbulence Combust (2023). https://doi.org/10.1007/s10494-023-00505-3

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  • DOI: https://doi.org/10.1007/s10494-023-00505-3

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