Flow Simulation of Lid-Driven Rectangular Cavity by Using Lattice Boltzmann Method

TL;DR

This paper uses the Lattice Boltzmann Method to simulate and analyze flow characteristics and state transitions in lid-driven rectangular cavities across various Reynolds numbers and aspect ratios, revealing complex flow behaviors.

Contribution

It applies LBM to rectangular cavity flow, exploring flow states and vortex dynamics across a range of parameters, which was less studied compared to square cavities.

Findings

Flow transitions from stable to unstable with increasing Re.

Flow state varies non-monotonically with aspect ratio.

Cycle length of periodic flow depends on Re and Ar.

Abstract

Wall-driven flow in square cavity has been studied extensively, yet it is more frequently for the rectangular cavity flow occurring in practical problems, and some flow characteristics about rectangular cavity have not been fully investigated. As a promising numerical simulation tool, the Lattice Boltzmann Method (LBM) is employed to simulate the lid-driven flow in a two-dimensional rectangular cavity in this paper. First, the code is validated for the standard square cavity, the velocity profiles, stream function values and center positions of the primary and second vortexes at different Re are presented and compared with previous researches. Then, the eddy dynamics of rectangular cavities is simulated and discussed with Reynolds number (Re) in the range of 4000-8000 and vertical to horizontal axis ratio (Ar) varied from 0.4 to 2.0, and the streamline and center migration of the primary vortex are drawn realistically for rectangular cavity. In the end, the steady, periodic, aperiodic and unstable phenomenon in the rectangular cavity is produced by LBM, Re and Ar which play the significant role in the state transition of lid-driven rectangular cavity flow are analyzed and summarized in detail. By the LBM numerical simulation with 500x(500*Ar) grid, we have discovered that the flow state in the rectangular cavity with a fixed Ar changes monotonically from stable state, periodic state to aperiodic and unstable state with the increase of Re, while the flow state in the rectangular cavity with a fixed Re varies non-monotonically with the increase of Ar. Additionally, the cycle length of periodic states varies with the change of Ar and Re.