A reduced order model of a weakly-confined twin jet flow and its stability analysis

The bifurcation and stability analyses of a twin jet flow, which is weakly-confined by its side-walls, have been performed by a reduced order model consisting few ordinary differential equations (ODEs) representing the full flow partial differential equations. Reduced order models are constructed by applying the proper orthogonal decomposition (POD) to the flow data obtained by direct numerical simulations for the laminar twin-jet flow. The numerical simulations of the governing equations with the related boundary conditions are performed using a finite volume technique (based on FLUENT software). The ability of the reduced order models to mimic the full model (Navier-Stokes eqs.) solution for both design and off design conditions is investigated numerically by solving the reduced order models with a Runge-Kutta solver. Frequencies and corresponding amplitudes of the expansion coefficients are well predicted by the reduced order models at design condition. The performance of the 4-equation model, a reduced order model consisting of 4 non-linear coupled ODEs is investigated by the stability analysis. The norm of the equilibrium (fixed) points reveals that steady solution exists for Re≤29. At a critical value of Reynolds number, Re_c=30, stable branch undergoes a Hopf bifurcation where solution becomes unsteady (time-periodic). In addition, the frequency of the full model is accurately predicted by the frequency of the oscillations obtained by stability theory.