Sloshing and Thermal Mixing

Modern aircraft increasingly use fuel as a heat sink to help manage the ever-growing thermal loads generated during flight operations. As warm fuel is recirculated into cooler tanks, fuel streams of varying temperature are mixed together. This, coupled with dynamic sloshing of the free surface in response to aircraft accelerations gives rise to a highly complex system that is not well understood. In this thesis, a computational methodology is established for studying such flows. The ability of the Volume of Fluid (VOF) OpenFOAM solver \texttt{interFoam} to accurately predict sloshing under resonant conditions is tested over a range of excitation frequencies, including the first 3 natural modes. Its performance in doing so is validated against experiments. Issues regarding two-equation RANS models and their overproduction of turbulence beneath the free surface are reviewed extensively. A variety of turbulence modelling strategies to help overcome this are identified and tested against benchmark experimental data. These model formulations are then applied to the simulation of sloshing at resonance across a range of forcing amplitudes. A profound sensitivity to turbulence model is demonstrated --- subsurface eddy viscosity is found to vary by up to 4 orders of magnitude when modelling sloshing at the first natural frequency. This is found to have only a subtle damping effect on free surface response. However, erroneous levels of turbulent diffusivity in the subsurface have much more serious implications when attempting to model the transport of heat by unresolved eddies. A stabilised $ k-\omega $ SST model, featuring an additional buoyancy source term in the $ k $-equation is identified as the most robust in accurately predicting subsurface turbulence. Having established a numerical model that can properly account for free surface motions and subsurface turbulence, a parametric study of sloshing and thermal mixing is undertaken. In order to establish a base-line case, buoyancy-driven mixing in partially filled static tanks is analysed. The ability of 2D models to model convective mixing is validated against high fidelity 3D LES simulations. Despite some differences in the developed flow patterns, good agreement is found when comparing macroscopic mixing rates over a range of initial temperature conditions. Sloshing is then introduced with tank motions across a range of forcing amplitudes, modal frequencies and fill heights. A metric is established for measuring the mixing enhancement from slosh-induced motions relative to the static tank cases. At low amplitude excitations, sloshing does not significantly enhance mixing, which remains buoyancy-dominated. At medium to high forcing amplitude excitations, the effects of sloshing are highly variable depending on the characteristic behaviour of each mode shape. Shallow and intermediate flow regimes are found to produce superior environments for mixing. A transition from standing to travelling waves results in a subsurface flow field more broadly influenced by the dynamic free surface. An interesting case is identified in which high amplitude sloshing is observed to suppress mixing. The interaction of convective currents with the dynamic surface region is found to restrict the circulation of warmer liquid into low-energy regions away from the surface. The role of sloshing in thermal mixing is demonstrated to be highly complex, with a particularly high degree of sensitivity to the parameters. However, this thesis makes a first step in identifying some of the key physics. Furthermore, by taking a rigorous approach in assessing the relevant physical models, a numerical framework is established for simulating such flows. This tool can be used in the design and analysis of aircraft fuel systems, and easily extends to other applications.