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Projecte llegit

Títol: Limit cycles in square cavity flow driven by the simultaneous motion of its four lids

Estudiants que han llegit aquest projecte:

Director/a: MELLIBOVSKY ELSTEIN, FERNANDO PABLO

Departament: FIS

Títol: Limit cycles in square cavity flow driven by the simultaneous motion of its four lids

Data inici oferta: 05-02-2024     Data finalització oferta: 05-10-2024


Estudis d'assignació del projecte:
    MU AEROSPACE S&T 21
Tipus: Individual
 
Lloc de realització: EETAC
 
Segon director/a (UPC): MESEGUER SERRANO, ALVARO
 
Paraules clau:
Cavity Flow
 
Descripció del contingut i pla d'activitats:
 
Overview (resum en anglès):
The cavity flow problem is of high interest for two main reasons: it is a benchmark in computational fluid mechanics for validating different numerical solvers of the Navier-Stokes equation, and it acts as a test benchmark for studying a variety of fluid flow phenomena.
In this study, we will focus on the square cavity four-lid-driven by the tangential motion of its four sides at the same speed, with opposite walls moving in opposite directions.
The fluid motion is determined by solving the Navier-Stokes equation. This study focuses on the periodic solutions that arise for this configuration.
The problem is regularized by setting the wall speed to follow a double-exponential distribution to avoid corner singularities caused by the discontinuities of the velocity at the boundary. This allows for exponential convergence in spectral discretization schemes.
The time integration of the discretized Navier-Stokes equation is carried out by the Implicit Euler Method. Limit cycles are found by the Newton-Krylov numerical solver, in which the method intends to search for the roots of the equation that compares a given initial state of the flow with a state after time integration has been applied.
In particular, we study the upper and lower limits of the Long Periodic Orbit (LPO), mentioned in some recent studies, as well as, the behavior past these critical values. The lower bound the orbit disappears in a Heteroclinic bifurcation caused by the collision with an unstable steady state. On the other hand, at the upper bound the flow becomes chaotic.
Finally, a Hopf bifurcation has been identified recently but no periodic orbit arising from it has been reported. This Hopf bifurcation is found to be subcritical.

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