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Hybrid rocket motors with paraffinbased fuels are of interest due to higher regression rates compared to other polymers. During paraffin combustion, a liquid layer forms on the fuel surface that, together with shearing forces from the oxidizer flow, results in the formation of instabilities at the fueloxidizer interface. These instabilities lead to the formation and entrainment of heterogeneous sized liquid droplets into the main flow and the combusting droplets result in higher motor output. The atomization process begins with droplet formation and ends with droplet pinchoff. The goal of this paper is to conduct an uncertainty quantification (UQ) analysis of the pinchoff process characterized by a pinchoff volume ($V_{po}$) and time ($t_{po}$). We study these quantities of interest (QoIs) in the context of a slab burner setup. We have developed a computationally expensive mathematical model that describes droplet formation under external forcing and trained an inexpensive Gaussian Process surrogate of the model to facilitate UQ. We use the pinchoff surrogate to forward propagate uncertainty of the model inputs to the QoIs and conduct two studies: one with gravity present and one without gravity effects. After forwardpropagating the uncertainty of the inputs using the surrogate, we concluded that both QoIs have rightskewed distributions, corresponding to larger probability densities towards smaller pinchoff volumes and times. Specifically, for the pinchoff times, the resulting distributions reflect the effect of gravity acting against droplet formation, resulting in longer pinchoff times compared to the case where there is no gravity.more » « lessFree, publiclyaccessible full text available January 4, 2025

We present a study of the standard plasma physics test, Landau damping, using the ParticleInCell (PIC) algorithm. The Landau damping phenomenon consists of the damping of small oscillations in plasmas without collisions. In the PIC method, a hybrid discretization is constructed with a grid of finitely supported basis functions to represent the electric, magnetic and/or gravitational fields, and a distribution of delta functions to represent the particle field. Approximations to the dispersion relation are found to be inadequate in accurately calculating values for the electric field frequency and damping rate when parameters of the physical system, such as the plasma frequency or thermal velocity, are varied. We present a full derivation and numerical solution for the dispersion relation, and verify the PETSCPIC numerical solutions to the VlasovPoisson for a large range of wave numbers and charge densities.more » « less

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

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