Reduction of the mathematical model of liquid flow within an instability

29th IAHR Symposium on Hydraulic Machinery and Systems

Pochylý, F.^1 ; Urban, O.^1 ; Fialová, S.^1

Brno University of Technology, Energy Institute, Viktor Kaplan Department of Fluid Engineering, Technická 2896/2, Brno

616 69, Czech Republic^1

关键词: Characteristic shapes;    Constitutive modes;    Dynamic mode decompositions;    Finite dimensional space;    Fundamental frequencies;    Inhomogeneous boundary conditions;    Unstable oscillation;    Vortex structures;   

Others  :  https://iopscience.iop.org/article/10.1088/1755-1315/240/7/072026/pdf
DOI  :  10.1088/1755-1315/240/7/072026

来源: IOP

【 摘 要 】

The instability of stationary vortex structures is manifested by an oscillation at several fundamental frequencies which are associated with characteristic shapes. It is caused by the non-linear convective terms in the Navier-Stokes equations. The frequency of unstable oscillation can be detected by the Fourier transform of the velocity and the pressure field themselves or their constitutive modes. It is this knowledge of the constitutive modes that is the basis for using the inverse method to define a reduced mathematical model in a finite-dimensional space. This model allows to analyze the vortex structures in the region of instability and their dependence on inhomogeneous boundary conditions. Present paper describes the essential steps of deriving an inverse method. The inverse method is applied to fluid flow in the draft tube of a swirl generator. The dynamic mode decomposition and the discrete Fourier transform of the flow field are assessed as possible methods that can provide the modal and spectral matrix for the model.