This paper describes the large eddy simulation modelling of unconfined large-scale explosions. The simulations are compared with the largest hydrogen-air deflagration experiment in a 20m diameter hemispherical polyethylene shell in the open. Two combustion sub-models, one developed on the basis of the renormalization group (RNG) theory and another derived from the fractal theory, were applied. Both sub-models include a sub-grid scale model of the turbulence generated by flame front itself based on Karlovitz's theory and the observation by Gostintsev et al on a critical distance for transition from laminar to self-similar flame propagation regime. The RNG sub- model employs Yakhot's formula for turbulent premixed flame propagation velocity. The best fit flame propagation dynamics is obtained for the fractal sub- model with a fractal dimension D = 2.22. The fractal sub- model reproduces the experimentally observed flame acceleration during the whole duration of explosion, accurately simulating the negative phase of the pressure wave but overestimating by 50% the positive phase amplitude. The RNG sub- model is closer to the experiment in predicting the positive phase but under-predicts by 30% the negative phase amplitude. Both sub- models simulate experimental flame propagation up to 20m and pressure dynamics up to 80m with reasonable accuracy.