Moving Solid Fluid Simulation Using Fixed Mesh Volume Fractions
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Solution Overview
Problem
Existing methods for simulating fluid flow in contact with moving solids, such as the lubrication system in aircraft turboshaft engines, are either too costly in terms of calculation time, not robust enough, or lack accuracy and conservation of mass and momentum.
Innovation Solution
A method involving a fixed meshing approach with auxiliary lattices to model the solid, using a finite volume method to solve the Navier-Stokes equations, ensuring accurate, robust, and conservative simulation of fluid flow with reasonable calculation time.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If interface capture and conformal remeshing finite volume approach is used, then accuracy of local magnitudes is improved, but calculation time increases significantly and numerical stability deteriorates
Solution Approach 1:
The domain is segmented into fixed Eulerian mesh cells, with the moving solid represented by Lagrangian particles. This segmentation allows the fluid domain to remain fixed while the solid moves through discrete particle positions, eliminating the need for continuous remeshing and reducing calculation time while maintaining accuracy.
Solution Approach 2:
An auxiliary mesh is introduced as an intermediary structure to map particle positions to Eulerian mesh cells. This auxiliary mesh serves as a mediator that tracks solid position without requiring regeneration of the main computational mesh, thus improving numerical stability and reducing calculation time.
2Loss of time
If immersed boundary interface capture finite volume approach is used, then calculation time is reduced, but numerical stability deteriorates due to distorted lattices
Solution Approach 1:
The solid is segmented into multiple particles distributed over an auxiliary mesh, with each particle carrying a portion of the solid's volume. This segmentation allows the solid to be represented in a fixed Eulerian mesh without generating distorted lattices, maintaining numerical stability while reducing calculation time.
Solution Approach 2:
The approach changes the representation parameter from continuous boundary surfaces to discrete particles with volume fractions. By using particles that carry volume information and distributing them over a fixed mesh, the method avoids lattice distortion while maintaining computational efficiency.
3Loss of time
If Lattice-Boltzmann interface capture and immersed boundary approach is used, then calculation time is reduced, but precision and conservation of mass and momentum deteriorate
Solution Approach 1:
The method substitutes the Lattice-Boltzmann kinetic theory approach with a finite volume method based on continuum mechanics and Navier-Stokes equations. This substitution maintains computational efficiency through the fixed Eulerian mesh while improving precision and ensuring conservation of mass and momentum through the rigorous finite volume formulation.
Solution Approach 2:
The approach changes from the Lattice-Boltzmann distribution function parameter to direct volume fraction parameters in the Navier-Stokes equations. This parameter change enables better conservation properties and precision while maintaining reasonable calculation time through the fixed mesh approach.
Applied Scientific Principles
This section explains which scientific principles are used to turn an abstract innovation direction into a practical engineering solution.
Function Achieved in This Case
The method provides accurate, robust, and conservative simulation of fluid flow around moving solids, particularly in turboshaft engines, optimizing lubrication systems and reducing micro-scaling and viscous losses.
Implementation Method 1
solving the Navier-Stokes equations of the mechanic of the fluids discretised by local flow balance in each lattice
Implementation Method 2
the lattices NAA1 located on the boundary YAA2 are reconstructed, this operation being referred to as 'cut-cell'
Data Source
AI summary
The invention relates to a method for simulating a fluid in contact with a moving solid modelled by a series of fixed positions (XA), the method comprising the steps of: —generating (E1) a fixed lattice (M1); —generating (E2) an auxiliary lattice (M2) of the solid (S) in a first position (XA) wherein each auxiliary lattice (N2) comprises a particle (P) comprising information on the volume (V2) of the auxiliary lattice (N2); —determining (E3) the position (XPA) of the particles (P) in the fixed lattice (M1); —calculating (E4, E5) the volume of the solid (V1s) and the volume fraction of the fluid (εF) in each fixed lattice (N1) based on the particles (P); —solving (E6) discretised Navier-Stokes equations using the finite volume approach applied to the volume fraction of the fluid (εF); —and, for each subsequent position (XB, XC) of the solid (S), a step (E7) of moving the particles (P) followed by the determining (E3), calculating (E4, E5) and solving (E6) steps.