Showing papers by "David A. Kessler published in 2023"

Non-normalizable quasi-equilibrium states under fractional dynamics

Abstract: We study non-normalizable quasi-equilibrium states (NNQE) arising from anomalous diffusion. Initially, particles in contact with a thermal bath are released from an asymptotically flat potential well, with dynamics that is described by fractional calculus. For temperatures that are sufficiently low compared to the potential depth, the properties of the system remain almost constant in time. We use the fractional-time Fokker-Planck equation (FTFPE) and continuous-time random walk approaches to calculate the ensemble averages of observables. We obtain analytical estimates of the duration of NNQE, depending on the fractional order, from approximate theoretical solutions of the FTFPE. We study and compare two types of observables, the mean square displacement typically used to characterize diffusion, and the thermodynamic energy. We show that the typical time scales for stagnation depend exponentially on the activation energy in units of temperature multiplied by a function of the fractional exponent.

Numerical Investigation of Liquid Droplet Interactions with Cylindrical Bow Shocks

Abstract: Precipitation and suspended droplets in the atmosphere present a significant erosion risk to vehicles traveling at high-supersonic and hypersonic speeds. We will present the results of simulations considering the interactions of droplets with blunt projectiles in a high-supersonic (Mach 2-4) flow environment. We use a volume of fluid method implemented in the compressibleInterFoam solver of OpenFOAM to simulate the interaction of a water droplet with the bow shock generated by a cylindrical blunt body. The droplet size and freestream Mach number are varied to determine the regimes where direct impact, partial impact, or no impact occur as governed by the degree of droplet breakup driven by aerodynamic forces in the shock layer.

The Influence of Chemical Reaction Models on Combustion Dynamics in an Opposed-Flow Solid Fuel Burner

Abstract: We describe the differences in the combustion behavior within a model opposed-flow solid fuel burner produced by three different chemical reaction models: a two-step global mechanism, a six-step global mechanism, and a pressure-comprehensive skeletal model, all of which assume butadiene as the primary fuel source. Details of the implementation of these models in conjunction with an equilibrium interfacial pyrolysis model for the solid gas phase change process are provided. Of particular interest are the differences in flame structure and dynamics predicted by each reaction model in comparison to the performance benefits gained by model simplifications. We provide some observations regarding the use of these global reaction models in a purely non-premixed combustion setting. A preliminary flamelet generated manifold is presented to be explored in future work.

Radiative Heat Transfer in a Counterflow Diffusion Flame Containing Reacting Metal Particles

Abstract: The radiation effects are significant in amplifying the regression rate of a solid-fuel ramjet, especially when reacting metal particles or soot are present, or when the oxidizer mass flux is small. We study a simplified flame structure within the solid-fuel ramjet using a counterflow diffusion flame. The radiation transport equation is numerically solved using the spherical harmonics method. The radiation transport equation is coupled with a 1D axisymmetric counterflow solver within an open-source code, Cantera, using a source term in the energy equation. Validation cases are performed using different fuel types and good agreement with the experimental measurements are obtained. We analyse the effect of radiation from reacting metal particles on the flame profile and perform a parametric study by varying the particle diameters. The rate at which aluminum particles are injected from the fuel inlet depends on the fuel regression and the particle loading density within the fuel. The location and temperature of the particles are tracked using the Lagrangian equations of motion. A simplified model of combustion of aluminum particles is implemented using the D^2 law.