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POD-Galerkin advection model for convective flow: application to a flapping rectangular supersonic jet

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Abstract

This article describes a model obtained by applying proper orthogonal decomposition to the advection equation. The resulting set of equations links the POD modes, their temporal and spatial derivatives and the flow convection velocity. It provides a technique to calculate the convection velocity of coherent structures. It follows, from the model, that a priori knowledge of the convection velocity suffices to construct a dynamical model of the flow. This is demonstrated using experimental data.

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Abbreviations

, x :

Space derivative

, t :

Time derivative

e :

External flow

j :

Jet flow

\(\varPhi ^{(n)}(\mathbf x )\) :

Spatial POD mode of order n

\(a^{(n)}(t)\) :

Temporal POD coefficient of order n

\(f_\mathrm{s}\) :

Screech frequency

\(g(\mathbf x ,t)\) :

Spatiotemporal field

\(h_j\) :

Size of the nozzle

\(L_j\) :

Height of the nozzle

M :

Mach number

\(M_e\) :

External flow Mach number

\(U_\mathrm{c}\) :

Convection velocity

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Acknowledgments

The authors wish to thank the Region Poitou-Charentes and DGA-Spae for supporting part of this study.

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Authors and Affiliations

  1. Institut Pprime, CNRS, ISAE-ENSMA, Université de Poitiers, 86962, Futuroscope Chasseneuil, France

    V. Jaunet, E. Collin & J. Delville

Authors
  1. V. Jaunet
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  2. E. Collin
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  3. J. Delville
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Correspondence to V. Jaunet.

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Jaunet, V., Collin, E. & Delville, J. POD-Galerkin advection model for convective flow: application to a flapping rectangular supersonic jet. Exp Fluids 57, 84 (2016). https://doi.org/10.1007/s00348-016-2156-2

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  • DOI: https://doi.org/10.1007/s00348-016-2156-2

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