Ral Bielawski’s research while affiliated with University of Michigan and other places

Detonation-based propulsion devices, such as rotating detonation engines (RDEs), must be able to leverage the higher energy densities of liquid fuels in order for them to be utilized in practical contexts. This necessitates a comprehensive understanding of the physical processes and timescales that dictate the shock-induced breakup of liquid droplets. These processes are difficult to probe and quantify experimentally, often limiting measurements to macroscopic properties. Here, fundamental mechanisms in such interactions are elucidated through detailed numerical simulation of Mach 2 and 3 shock waves interacting with 100 $\mu$m water droplets. Using a thermodynamically consistent two-phase formulation with adaptive mesh refinement, the simulations capture droplet surface instabilities and atomization into secondary droplets in great detail. The results show that droplet breakup occurs through a coupled multi-stage process, including droplet flattening, formation of surface instabilities and piercing, and the shedding of secondary droplets from the ligaments of the deformed primary droplet. When considering the dimensionless timescale of Ranger and Nicholls ($\tau$), these processes occur at similar rates for the different shock strengths. The PDFs for the Sauter mean diameters of secondary droplets are bimodal log-normal distributions at $\tau=2$. Modest differences in the degree and rate of liquid mass transfer into droplets less than 5 $\mu$m in diameter are hypothesized to partially derive from differences in droplet surface piercing modes. These results are illustrative of the complex multi-scale processes driving droplet breakup and have implications for the ability of shocks to effectively process liquid fuels.

Conical oblique detonation waves (ODWs) are studied with high-fidelity numerical simulations, including complex chemical kinetics for an ethylene-air mixture at standard temperature and pressure at a stoichiometric equivalence ratio and 14.6 μm spatial resolution resulting in 42 cells per induction length at a minimum. Control volume analysis is proposed through an equilibrium-based detonation polar algorithm to identify ODW regimes and perform thermodynamic analysis. This analysis enables the correct conditions for the three-dimensional simulation of conical ODWs that further informs their practical use in engine design. Detonation instabilities are shown to behave differently in three dimensions as multiple detonation instabilities collide, forming Mach stems with increased strength compared to two-dimensional detonations. The weak overdriven conical ODW allows cellular detonation structure that is highly irregular with instabilities moving axially along the detonation front. Large subsonic regions also provide opportunities for pressure waves to impact the detonation surface, potentially influencing the formation of detonation instability. The detonation structure observed in conical systems resembles that of two-dimensional oblique detonations formed by wedges and of planar cellular detonations.

This study investigates the structure of conical detonations in premixed ethylene–air mixtures through two complementary approaches. First, a control volume-based model identifies the weakly overdriven region for stable wave formation, showing dependence on the inflow Mach number and highlighting the impact of incomplete heat release. Second, high-fidelity simulations with multistep chemical kinetics capture the formation of surface instabilities and the nature of the detonation waves. The thermodynamic analysis tool, validated against experimental data, computes detonation polars using a multi-species gas description and provides crucial insights into post-detonation properties and deflection angles for various cone half-angles. The results indicate that the regime of weakly overdriven detonations is confined by flow conditions and turning angles, with net heat release diminishing as these parameters increase. For the highest Mach number and turning angle considered, the heat release is observed to be less than 25% of the reaction enthalpy for the mixture. High-fidelity simulations corroborate the thermodynamic analysis and further demonstrate the formation of cellular instabilities on the detonation surface. For a conical system characterized by significant isentropic expansion and weaker initial shock compared to two-dimensional wedges, transverse waves reflecting off the cone surface lead to the formation of triple points, which catalyze instabilities. The overall detonation structure in conical systems is similar to that of two-dimensional wedge-based oblique detonations and planar cellular detonations.

This work presents a comprehensive framework for the efficient implementation of finite-volume-based reacting flow solvers, specifically tailored for high speed propulsion applications. Using the exascale computing project (ECP) based AMReX framework, a compressible flow solver for handling high-speed reacting flows is developed. This work is complementary to the existing PeleC solver, emphasizing specific applications that include confined shock-containing flows, stationary and moving shocks and detonations. The framework begins with a detailed exposition of the numerical methods employed, emphasizing their application to complex geometries and their effectiveness in ensuring accurate and stable numerical simulations. Subsequently, an in-depth analysis evaluates the solver's performance across canonical and practical geometries, with particular focus on computational cost and efficiency. The solver's scalability and robustness are demonstrated through practical test cases, including flow path simulations of scramjet engines and detailed analysis of various detonation phenomena.

Numerical simulations of detonation-containing flows have emerged as crucial tools for designing next-generation power and propulsion devices. As these tools mature, it is important for the combustion community to properly understand and isolate grid resolution effects when simulating detonations. To this end, this work provides a comprehensive analysis of the numerical convergence of unsteady detonation simulations, with focus on isolating the impacts of chemical timescale modifications on convergence characteristics in the context of operator splitting. With the aid of an adaptive mesh refinement based flow solver, the convergence analysis is conducted using two kinetics configurations: (1) a simplified three-step model mechanism, in which chemical timescales in the detonation are modified by adjusting activation energies, and (2) a detailed hydrogen mechanism, in which chemical timescales are adjusted through ambient pressure modifications. The convergence of unsteady self-sustained detonations in one-dimensional channels is then analyzed with reference to steady-state theoretical baseline solutions using these mechanisms. The goal of the analysis is to provide a detailed comparison of the effects of grid resolution on both macroscopic (peak pressures and detonation wave speeds) and microscopic (detonation wave structure) quantities of interest, drawing connections between the deviations from steady-state baselines and minimum chemical timescales. This work uncovers resolution-dependent unsteady detonation regimes, and highlights the important role played by not only the chemical timescales, but also the ratio between chemical and induction timescales in the detonation wave structure on simulation convergence properties.