COBEM99

SR13 Mecânica dos Fluidos

Title:

SPECTRAL ELEMENT INVESTIGATION OF RADIAL FLOW STABILITY

Summary :

DIRECT NUMERICAL SIMULATIONS ARE PERFORMED TO INVESTIGATE THE NONLINEAR STABILITY AND FLOW EVOLUTION OF TWO- AND THREE- DIMENSIONAL RADIAL FLOWS BETWEEN PARALLEL STATIONARY DISKS. THE SPECTRAL ELEMENT METHOD IS EMPLOYED FOR THE SPATIAL DISCRETIZATION OF THE UNSTEADY, INCOMPRESSIBLE NAVIER-STOKES EQUATIONS. FINITE AMPLITUDE PERTURBATIONS ARE INTRODUCED AT THE INLET OF THE DOMAIN TO EMULATE THE EXPERIMENTAL SITUATION WHERE SUCH FINITE-AMPLITUDE DISTURBANCES ARE CONVECTED FROM UPSTREAM SOURCES. IT IS FOUND THAT AXISYMMETRIC MODELS FAIL TO PREDICT THE FLOW PHYSICS FOR RE > 200, DUE TO THE EXISTENCE OF A SECONDARY FLOW WHICH CANNOT BE CAPTURED BY TWO-DIMENSIONAL SIMULATIONS. BY PREDICTING THE FLOW RESPONSES TO INFINITESIMALLY SMALL PERTURBATIONS, A CHARACTERISTIC FREQUENCY IS OBTAINED FOR THE LEAST-STABLE MODE CORRESPONDING TO THE TIME-EVOLUTION OF THE FLOW TOWARDS STEADY STATE. OSCILLATORY PERTURBATIONS ARE THEN IMPOSED AT THE INLET OF THE THREE-DIMENSIONAL DOMAIN WITH A FREQUENCY MATCHING THE LEAST-STABLE FREQUENCY OF THE DECAYING PERTURBATIONS. THIS TUNED OSCILLATORY FORCING OF THE FLOW INDUCES INCREASE IN THE CIRCULATION AND ENHANCEMENT IN MIXING OF THE SECONDARY FLOW. ONCE THIS FORCING IS TURNED OFF, THE FLOW REMAINS UNSTEADY WITH AN INITIAL STAGE OF GROWING OSCILLATIONS, LEADING EITHER TO A SELF-SUSTAINED OSCILLATORY FLOW OR TO A SUB-CRITICAL TRANSITION. KEYWORDS: SPECTRAL ELEMENT, NONLINEAR INSTABILITIES, RADIAL FLOWS, OSCILLATORY PERTURBATIONS.

Author :

Amon, Cristina H.
Oliveira, Jauber C.

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