International audienceThe effect of small viscosity on the behavior of the incompressible axisymmetric flow with open lateral and outlet boundaries near the critical swirling number has been studied by numerical simulations and asymptotic analysis. This work extends the theoretical studies of Wang and Rusak and numerical results of Beran and Culik to the case of flow with open lateral and outlet boundaries. In the inviscid limit the columnar flow state constitutes a solution that is known to become unstable at a particular swirl parameter. An asymptotic expansion shows that for small perturbations about this inviscid state an exchange of stability gives rise to a double saddle node bifurcation. The solution of the Euler equations breaks into two branches of the Navier-Stokes equations with a gap between the branches in which no near-columnar flow can exist. Around this region, two steady-state solutions exist for the same boundary conditions, one close to the columnar state and the other corresponding to either an accelerated or a decelerated state. This bifurcation structure is verified by numerical simulations, where the Navier-Stokes solutions are computed using branch continuation techniques based on the recursive projection method. For relatively small Reynolds numbers the numerically computed bifurcation curve does not exhibit any characteristic fold, and thus no hysteresis behavior. In this case, only a single equilibrium solution is found to exist, which changes monotonically from the quasicolumnar state to the breakdown solution. For large Reynolds numbers, however, the numerically determined bifurcation diagram confirms the fold structure characterized by the disappearance of the nearly columnar state via a saddle node bifurcation. Using the minimum axial velocity on the axis as a measure of the flow state we show that the agreement between theory and numerics is asymptotically good. © 2009 American Institute of Physics
Flash boiling is the rapid phase change of a pressurised fluid that emerges to ambient conditions below its vapour pressure. Flashing of a flowing liquid through an orifice or a nozzle can occur either inside or outside the nozzle depending on the local pressure and geometry. Vapour generation during flashing leads to interfacial interactions that eventually influence the jet.Empirical models in the literature for simulating the inter-phase heat transfer employ many simplifying assumptions, which limits their applicability. Typical models, usually derived from cavitation, fail to describe the physics of heat and mass transfer, making them unreliable for flashing. The Homogeneous Relaxation Model (HRM) is a reliable model able to capture heat transfer under these conditions accounting for the non-equilibrium vapour generation. This approach uses a relaxation term in the transport equation for the vapour. On the basis of the generic compressible flow solver within the open source computational fluid dynamics (CFD) code OpenFOAM, the HRM has been implemented to create a dedicated new solver HRMSonicELSAFoam. An algorithm that links the standard pressure-velocity coupling algorithm to the HRM is used. In this method, a pressure equation is derived which employs the continuity equation including compressibility effects. A relaxation term has been defined such that the instantaneous quality would relax to the equilibrium value over a given timescale. Although it is possible to consider this timescale constant, it is calculated via an empirical correlation in the present study.Validations have been carried out by simulating two-phase flows through sharp-edged orifices. The relatively good agreement achieved has demonstrated that the solver accurately calculates the pressure and vapour mass fraction. This demonstrates the potential of HRMSonicELSAFoam for flash boiling simulations and predicting the properties of the subsequent flash atomisation.
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