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Theoretical modelling of perturbation dynamics for compressible swirling flows in arbitrary varying ducts

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State-of-the-art research has solved the problem of perturbation dynamics for compressible swirling flows in slowly varying ducts based on multiple scales approximation which models the problem as one-dimensional partial differential equations. The present research mathematically models perturbation dynamics in arbitrary varying ducts where the multiple scales approximation may be limited. From the conservations of mass, momentum and energy for compressible inviscid flow, we derive a mathematical model of steady compressible inviscid flow in terms of flow stream functions and density in radial and axial directions. Secondly, we introduce a local orthogonal coordinate transformation to establish the linearized perturbation dynamics in a natural coordinate system under the assumption that flow separations are absent and the pipeline wall is non-invasive to steady flow. The benefits are excellent as the steady flow in the new coordinates is only in the axial direction and azimuthal direction if the swirls are present. Furthermore, the radial and axial directions are independent. In the natural coordinate system, perturbation dynamics are modelled in terms of linearized pressure, velocity and entropy as first-order partial differential equations. To handle the complicated boundary condition, a two-dimensional Chebyshev collocation method will be introduced to numerically solve the problem.

This talk is part of the Waves Group (DAMTP) series.

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