Effective design of liquid fuel injection systems is a function of good understanding of liquid breakup mechanisms. A transient liquid breakup model is developed on the classical interfacial breakup theory by modifying the classical linear perturbation process to include time-dependent base and perturbed flow parameters. The non-isothermal condition on liquid jet instability and breakup is theoretically modelled; with the particular consideration of a spatially variation of surface tension along the liquid-gas interface. The model combines the classical interface hydrodynamic instability and breakup theory and heat-transfer through semi-infinite medium. Analytical liquid breakup model, which combines transient and non-isothermal effects on liquid jet breakup, is suggested. The suggested model could be simplified to the transient breakup model and the non-isothermal breakup model equivalents. A novel mechanistic model, which is based on a simple momentum balance between the injected jet and the aerodynamic drag force, is suggested for breakup length. A new model, which combines energy criterion and dual-timescale for turbulent shear in droplet dispersion, is suggested for droplet breakup criteria on the basis of critical Webber number. All developed models showed good predictions of available experimental data, and established empirical correlation, within the operational conditions of contemporary ICEs, specifically diesel engines. Continued research in these areas could benefit the development of the next generation of liquid fuel injectors and combustors – by accounting for transient effects and non-isothermal conditions in liquid jet breakup, and turbulent shear in droplet breakup.

Effective design of liquid fuel injection systems is a function of good understanding of liquid breakup mechanisms. A transient liquid breakup model is developed on the classical interfacial breakup theory by modifying the classical linear perturbation process to include time-dependent base and perturbed flow parameters. The non-isothermal condition on liquid jet instability and breakup is theoretically modelled; with the particular consideration of a spatially variation of surface tension along the liquid-gas interface. The model combines the classical interface hydrodynamic instability and breakup theory and heat-transfer through semi-infinite medium. Analytical liquid breakup model, which combines transient and non-isothermal effects on liquid jet breakup, is suggested. The suggested model could be simplified to the transient breakup model and the non-isothermal breakup model equivalents. A novel mechanistic model, which is based on a simple momentum balance between the injected jet and the aerodynamic drag force, is suggested for breakup length. A new model, which combines energy criterion and dual-timescale for turbulent shear in droplet dispersion, is suggested for droplet breakup criteria on the basis of critical Webber number. All developed models showed good predictions of available experimental data, and established empirical correlation, within the operational conditions of contemporary ICEs, specifically diesel engines. Continued research in these areas could benefit the development of the next generation of liquid fuel injectors and combustors – by accounting for transient effects and non-isothermal conditions in liquid jet breakup, and turbulent shear in droplet breakup.

This master thesis deals with the optimal initial perturbation problem for a 1D unsteady self-similar ablation flow in an inertial confinement fusion context. The physical modelling consists of the compressible Euler equations with nonlinear heat conduction. The base flow and linear 3D perturbations are computed using a multidomain Chebyshev collocation method. Longitudinal optimal initial perturbations are computed by means of a non-modal analysis method for stationary perturbation evolution operators (Schmid, 2001 & 2007) after transformation of the time-dependent perturbation problem. Results of optimal gain and initial perturbation differ significantly from those produced by a non-stationary direct-adjoint method (Varillon, 2019). This discrepancy is analyzed to be a consequence of a diagonalization failure of the discrete perturbation evolution operator.

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