Method for simulating the flow of a fluid in contact with a moving solid

A method for dimensioning a lubrication system of a reducer of an aircraft turboshaft engine, said reducer being configured to reduce the speed of rotation transmitted to a fan of the aircraft turboshaft engine and comprising a plurality of meshed toothed wheels, said lubrification system being configured to project a spray of lubricant on the toothed wheels of the reducer, said method being implemented by computer and modelling the movement of the toothed wheels of the reducer by a series of fixed positions, the fluid being in the form of a mixture of lubricant and surrounding air forming a two-phase flow, the method comprising:

• A step of generating a fixed meshing of an area of the reducer, the fixed meshing comprising a plurality of fixed lattices,
• A step of generating an auxiliary meshing of at least one toothed wheel of the reducer in a first fixed position, the auxiliary meshing comprising a plurality of auxiliary lattices whose sum of volumes is equal to the volume of the toothed wheel, each auxiliary lattice comprising a particle comprising an information on the volume of said auxiliary lattice,
• A step of determining the position of the particles in the fixed meshing corresponding to the first fixed position of the toothed wheel,
• A step of calculating the toothed wheel volume in each fixed lattice from the position and the information on the volume of the particles, so as to locate the toothed wheel in said first fixed position in the area of the reducer,
• A step of calculating the volume fraction of fluid in each fixed lattice from the calculated toothed wheel volume, so as to locate the fluid in the area of the reducer, said volume fraction of fluid comprising a volume sub-fraction of lubricant and a volume sub-fraction of surrounding air separated by an interface,
• A step of solving the discretised Navier-Stokes equations according to the finite volume approach with interface capture and applied to the fluid volume fraction in each fixed lattice, so as to determine the output local characteristics of the fluid in contact with the toothed wheel in said first fixed position,
• And, for each subsequent fixed position of the toothed wheel, a step of moving the particles into said subsequent fixed position of the toothed wheel and then implementing the determination step, the calculating step and the solving step so as to determine the output local characteristics of the fluid in contact with the toothed wheel at each said fixed position, so as to dimension the lubrification system of the reducer, the local characteristics of the fluid comprising at least one the following data:
• local velocity of the lubricant, local pressure of the lubricant and local temperature of the lubricant.