Validation of models for shock-driven hydrodynamic instabilities

The propagation of fluids through space-time is a truly beautiful and mysterious marvel that humankind has spent nearly all our existence trying to comprehend, understand, manipulate, and master. From waves over water to the Sun and the stars in the sky; fluids prove to be as elementary as they are esoteric, as calming as they are chaotic, and as delicate as they are detrimental. The levity in which fluids propagate can be as swift as the milliseconds it takes to observe hydrodynamic instability in say a shock tube facility, to the hundreds if not thousands of years over which a cosmological event's hydrodynamic instability may evolve. Comprehending, studying, manipulating, and mastering the propagation of fluids, specifically within the realm of fluid mechanics, s.c., hydrodynamic instability (HI), is of paramount prominence to the success of humankind. Today, a group of personnel within the scientific and academic community study the evolution and propagation of hydrodynamic instabilities (HIs) through a vast multitude of avenues for a plethora of applications; the two main avenues being experimentally and computationally. However, the ability to experimentally generate, for example, Asymptotic giant branch (AGB) star within a laboratory is as unattainable as the multiple lifetimes for its hydrodynamic instabilities take to develop and evolve, and study. The necessity of generating numerical simulations which match the experimental results of the growth and morphological evolution of hydrodynamic instabilities is a perfectly idealized way to address the capacious and enduring time scales of the hydrodynamic instabilities mentioned. The goal of this dissertation work is to compare the numerical results of the evolution of HIs with experimental results, generate qualitative and quantitative analyses of how the results differ, and improve upon the numerical methods in which the simulation results are generated. To achieve the goal of this dissertation, the evolution and morphology of the two-dimensional hydrodynamic Shock-Driven Multiphase Instability (SDMI) is investigated through experimental measurements obtained within a shock tube facility. The experimental results are then used to validate the results achieved through simulations which utilize identical initialized parameters to model the experiment. The simulations were performed in the open source software FLASH, which is employed to solve the Multi-Phase Particle-in-Cell (MP-PIC) method with the Piecewise Parabolic Method (PPM) for the SDMI's multispecies gas flow. To gather data on the SDMI's morphological evolution experimentally, the planar laser Mie scattering (PLMS) technique was used to illuminate a cylindrical particle-laden flow field (interface), in 2-D, where high-resolution charged-coupled device (CCD) camera captured cross-sectional images of the interface's evolution. The gas flow itself consisted of a mixture of three different species: nitrogen, air, and water vapor; while the dispersed phase consists of water droplets in gas mixture. Utilizing a Mach number, M [subscript alpha] of 1.67, equivalent to a shock wave velocity, v [subscript sh] of 570 (ms [superscript -1]), data was obtained for two different effective Atwood numbers (particles concentrations), A [subscript t] of 0.0479 and 0.0184, at three time intervals for comparison of the experimental data to the computationally acquired data. The results obtained from the computational and experimental data show good quantitative agreement. For example, average dispersed phase speed measured experimentally is 99.5 [percent] of average calculated speed numerically, also, shape wise numerical distance between two developed vortices in dispersed phase is 93.5 [percent] of those measured experimentally. Qualitatively, the morphology of the dispersed phase shows same evolution in both simulated and experimental results. SDMI can also be seen in the circumstellar medium with the infinite number of morphologies due to the complexity of the hydrodynamics evaluations near AGB stars. An attractive solution shows the pulsation of the AGB star producing hot bubble combined with a shock wave and then interacting with dust shell making different types of instabilities.