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Low-dimensional model of a supersonic rectangular jet.

D Moreno¹, A Krothapalli, M B Alkislar

¹Department of Mechanical Engineering, Florida A&M University and Florida State University, 2525 Pottsdamer Street, Tallahassee, FL 32310, USA.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|March 5, 2004

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Proper orthogonal decomposition (POD) simplifies supersonic jet analysis. The first two modes capture essential dynamics, enabling a reduced-order model that aligns with experimental data.

Area of Science:

Fluid dynamics
Aerospace engineering
Computational physics

Background:

Supersonic jets at underexpanded conditions exhibit complex flow behavior.
Particle Image Velocimetry (PIV) is a key experimental technique for flow visualization.
Dimensionality reduction methods are crucial for analyzing complex fluid phenomena.

Purpose of the Study:

To apply Proper Orthogonal Decomposition (POD) to analyze Particle Image Velocimetry (PIV) data from a supersonic rectangular jet.
To identify dominant flow structures and energy-containing modes.
To develop a low-dimensional dynamical model for the jet's behavior.

Main Methods:

Proper Orthogonal Decomposition (POD) applied to phase-locked PIV velocity field data.
Calculation of eigenfunctions and eigenvalues to determine dominant modes.

Related Experiment Videos

Galerkin projection of isentropic compressible Navier-Stokes equations for model construction.

Main Results:

The first two POD modes contain a significant fraction of the total flow energy.
These dominant modes effectively capture the essential features of the supersonic jet.
A low-dimensional dynamical model was successfully constructed.

Conclusions:

POD effectively reduces the complexity of supersonic jet flow analysis.
A low-dimensional model based on POD and Navier-Stokes equations provides a reasonable approximation of the jet's dynamics.
This approach offers a computationally efficient method for studying underexpanded supersonic jets.