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Hopf Bifurcations of Moore-Greitzer PDE Model with Additive Noise.
Yiming Meng1, N Sri Namachchivaya1, Nicolas Perkowski2
1Department of Applied Mathematics, Waterloo University, Waterloo, ON Canada.
Journal of Nonlinear Science
|June 20, 2023
Summary
This study analyzes instabilities in jet engine compressors using stochastic partial differential equations (PDEs). It develops reduced-order models to approximate instability margins under noise, aiding in designing more efficient engines.
Area of Science:
- Fluid dynamics
- Aerospace engineering
- Nonlinear dynamics
Background:
- The Moore-Greitzer partial differential equation (PDE) models flow and pressure in jet engines.
- Hopf bifurcations (surge, stall) in deterministic PDEs limit engine operating range.
- Hopf bifurcations in stochastic PDEs are not well understood.
Purpose of the Study:
- Develop low-dimensional approximations for stochastic PDEs near stall bifurcations.
- Analyze the impact of additive noise on instability.
- Enable approximation of instability margins under uncertainty.
Main Methods:
- Multiscale analysis approach.
- Focus on additive noise acting on fast modes.
- Derivation of reduced-dimensional stochastic differential equations (SDEs).
Main Results:
- Successfully developed low-dimensional approximations (SDEs) for stochastic PDEs.
- Demonstrated that reduced approximations contain multiplicative noise.
- Provided a method to approximate instability margins in the presence of uncertainties.
Conclusions:
- The developed SDEs offer insights into Hopf bifurcations in stochastic systems.
- Approximating instability margins can lead to improved jet engine design.
- This work contributes to understanding and mitigating instabilities in aerospace applications.
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