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We present a numerical study of the structure and stability of laminar isothermal flows formed by two counterflowing jets of an incompressible Newtonian fluid. We demonstrate that symmetric counterflowing jets with identical mass flow rates exhibit multiple steady states and, in certain cases, time-dependent (periodic) steady states. Two geometric configurations were studied based on the inlet jet shapes: planar and axisymmetric. Stagnation flows formed by planar counterflowing jets exhibit both steady-state multiplicity and time-dependent behaviour, while axisymmetric jets exhibit only a steady-state multiplicity. A linearized bifurcation and stability analysis based on the continuity and Navier–Stokes equations revealed transitions between a single (symmetric) steady state and multiple steady states or periodic steady states. The dimensionless quantities forming the parameter space of this system are the inlet Reynolds number (R$e$) and a geometric aspect ratio ($\alpha$), equal to the jet inlet characteristic length (used for calculating R$e$) divided by the jet separation. The boundaries separating different flow regimes have been identified in the (R$e$, $\alpha$) parameter space. The resulting flow maps are useful for the design and operation of counterflow jet reactors.
Experiments have been performed on the stability of buoyancy-driven flows of a high-Prandtl-number fluid in an inclined rectangular enclosure. Visualization of the stable planform of convection for various Rayleigh numbers and inclination angles is provided by a temperature-sensitive liquid crystal and gold-coated film heater assembly which serves as the lower surface of the enclosure. This assembly produces a nearly constant heat flux surface with a thermal conductivity of the same order as that of the test fluid. The results indicate that for large angles of inclination from the horizontal a steady transverse roll(s) structure is stable. As the angle of inclination is decreased steady longitudinal rolls replace the transverse roll(s) and for low angles a steady square-cell convection planform is observed. A region of unsteady wavy longitudinal rolls is also observed at sufficiently high Rayleigh numbers for low to moderate angles of inclination. In general the wavenumber of the longitudinal rolls increases with angle of inclination from the horizontal. Two distinct types of instability mechanisms are observed which modify the wavenumber of the longitudinal rolls: a cross-roll instability, which is a disturbance perpendicular to the original roll axis; and a pinching mechanism which combines two neighbouring longitudinal roll pairs into a longer wavelength roll pair.
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