Large Eddy Simulations (LES) are carried out targeting an unconfined premixed bluff body burner operated with ethanol, n-heptane, Jet A, and a Sustainable Aviation Fuel (SAF) labeled C1. The purpose is to validate the chosen simulation methodology for these fuels, which have not been simulated in the targeted case before, and to provide new information about how they burn and stabilize. The combustion of each fuel is modeled using Finite Rate Chemistry (FRC) and a pathway-centric chemical reaction mechanism. Subgrid-scale turbulence-chemistry interactions are modeled using a Partially Stirred Reactor (PaSR) approach. In accordance with previous experiments, snapshots of the OH and CH2O distributions, as well as velocity, are extracted from the simulations and subjected to statistical analysis to obtain mean flame progress variable distributions, flame surface density, and CH2O layer thickness. A mesh sensitivity analysis is carried out for all fuels, revealing that a crucial filter width threshold between 0.375 and 0.25 mm must be reached to achieve a stable flame and low mesh sensitivity. Statistically, the simulations show good agreement with previous experimental measurements. The flame sheet diameter is found to be approximately linearly correlated with extinction strain rate and Damköhler number, suggesting that resistance to turbulence is the determining factor for the flame size. The C1 flame is found to experience the weakest fluctuations, and a mechanism based on the relative time scales of flame propagation and the ignition of fuel decomposition products is proposed to explain this effect. Novelty and significance statement Sustainable aviation fuels are of major importance in reducing the climate impact of aviation, but their combustion is not nearly as well-understood as that of fossil jet fuels. Both experimental and numerical research is needed to map out the relationship between fuel composition and combustion performance, so that blending limits can be increased while guaranteeing safety, operability, and performance in aircraft engines. This work explores the turbulent flame dynamics of one commercial sustainable aviation fuel, C1. It is also the first numerical study to consider ethanol, n-heptane, Jet A, or C1 in the Cambridge bluff body burner, a case which has primarily been studied with methane. The results reveal several trends among the fuels which may be investigated further in future studies. C1 is found to be particularly resistant to outward fluctuations into the reactants, which connects fuel decomposition to flame stability.