Doctor of Philosophy
Arindam . Banerjee
Rayleigh-Taylor instability (RTI) is observed when a material is accelerated by another material of lower density, and the instability can be mitigated by governing various parameters like yield strength, initial perturbations on the interface, driving acceleration, material thickness, and others. RTI is observed in several natural and engineering applications such as Type Ia supernova formations, salt domes, explosive welding, and inertial confinement fusion. Traditionally, majority of the scientific investigations on RTI have focused primarily on the instability problem in Newtonian fluids by considering hydrodynamic analogs. Comparatively, very few studies have focused on RTI in solids due to the challenges involved in characterizing material properties at extreme temperatures and pressures. Theoretical studies on RTI in solids are based on assumptions that include materials with non-variable properties, infinite material thickness, and a constant driver acceleration. Understanding the effects of finite and realistic parameters is crucial for designing high energy density experiments that are aimed to improve control and efficiency of the inertial confinement fusion.
This dissertation presents a series of laboratory experiments focused on understanding RTI using an elastic-plastic material at room temperature and pressure. A novel rotating wheel experiment that accelerates a two material interface centrifugally was devised. A backlit imaging analysis technique was used in conjunction with a high-speed camera to track the motion of the interface at various phases of the instability. A soft-solid (mayonnaise) was chosen as the EP material for experiments, and the material properties such as shear modulus and yield strength were fully characterized using a vane-spindle type rheometer. Single-mode perturbations (both 2D and 3D) of varying amplitudes and wavelengths were generated on the interface of the solid using sinusoidal cutting guides.
As the material-air interface is accelerated, the perturbation growth shifts from the elastic regime to the plastic regime and becomes unstable where the growth rate is nearly exponential. Firstly, the threshold accelerations at which the transitions between different regimes occur were estimated for different combinations of initial amplitude and wavelength. This exercise allowed for verification of the elastic-plastic (EP) transition process before instability was reached. Results indicated that threshold accelerations increased with a decrease in amplitude and wavelength, and three-dimensional interfaces were more stable than two-dimensional interfaces. Secondly, the temporal effects of driving acceleration/driving pressure on instability and EP transition thresholds were investigated by varying the angular acceleration of the rotating disk to obtain different acceleration rates. The instability- and EP transition threshold accelerations for a perturbation of given amplitude and wavelength are observed to increase with an increase in acceleration rate. Lastly, the effects of finite thickness on instability growth were investigated experimentally by varying the depths of the test section in which soft-solid is infused. A set of experiments is run by employing initial conditions (both finite and negligible amplitude) with different container dimensions and acceleration rates. The instability acceleration was found to be increasing with the increase in slab thickness. Additionally, the combined effects of acceleration rate and finite thickness on the instability threshold were quantified. Experimental results are compared to theoretical models that address the finite thickness effects in the case of interface with negligible amplitude.
Polavarapu, Rinosh, "On Rayleigh-Taylor Instability Experiments in Accelerated Elastic-Plastic Slabs" (2020). Theses and Dissertations. 5696.
Available for download on Saturday, January 29, 2022