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Brehm, Christop ; Pandya, Shishir (Ed.)Paraffin wax is a prominent solid fuel for hybrid rockets. The atomization process of the paraffin wax fuel into he hybrid rocket combustion involves the droplets pinching off from the fuel surface. Therefore, droplet formation and pinchoff dynam ics is analyzed using a onedimensional axisymmetric approximation to understand droplet size distribution and pinchoff time. A mixed finite element formulation is used to solve the numerical problem. The computational algorithm uses adaptive mesh refinement to capture singularity and runs selfconsistently to calculate droplet elongation. The code is verified using the Method of Manufactured Solution (MMS) and validated against laboratory experiments. Moreover, paraffin wax simulations are explored for varying inlet radius and it is found that the droplet size increases very slightly with the increasing inlet radius. Also, the pinchoff time increases up to a point where it starts to decrease as we increase the inlet radius. This behavior leads to a conjecture for the theoretical maximum radius that the droplet approaches as the inlet radius increases, which is a motivation for the future work.more » « less

Nathawani, Darsh K. ; Knepley, Matthew G. ( , Physics of Fluids)Droplet formation happens in finite time due to the surface tension force. The linear stability analysis is useful to estimate the size of a droplet but fails to approximate the shape of the droplet. This is due to a highly nonlinear flow description near the point where the first pinchoff happens. A onedimensional axisymmetric mathematical model was first developed by Eggers and Dupont [“Drop formation in a onedimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] using asymptotic analysis. This asymptotic approach to the Navier–Stokes equations leads to a universal scaling explaining the selfsimilar nature of the solution. Numerical models for the onedimensional model were developed using the finite difference [Eggers and Dupont, “Drop formation in a onedimensional approximation of the Navier–Stokes equation,” J. Fluid Mech. 262, 205–221 (1994)] and finite element method [Ambravaneswaran et al., “Drop formation from a capillary tube: Comparison of onedimensional and twodimensional analyses and occurrence of satellite drops,” Phys. Fluids 14, 2606–2621 (2002)]. The focus of this study is to provide a robust computational model for onedimensional axisymmetric droplet formation using the Portable, Extensible Toolkit for Scientific Computation. The code is verified using the Method of Manufactured Solutions and validated using previous experimental studies done by Zhang and Basaran [“An experimental study of dynamics of drop formation,” Phys. Fluids 7, 1184–1203 (1995)]. The present model is used for simulating pendant drops of water, glycerol, and paraffin wax, with an aspiration of extending the application to simulate more complex pinchoff phenomena.more » « less