Large-eddy simulations (LES) of a laboratory-scale two-phase burner are considered by describing the disperse liquid spray with a mono-disperse Eulerian approach. In this simplified framework, the choice of the size of the injected droplets becomes a critical issue. The impact of this key parameter upon the numerical results is carefully assessed though uncertainty quantification tools. Using Polynomial Chaos Expansion and Clenshaw-Curtis nested quadrature rule, several LES are performed for different injected droplet sizes in order to obtain a response surface of velocity and diameter fields at any point in the computational domain as a function of the injected one. Post-treatment of the response surface gives access to the precise impact of the chosen injected droplet size on the results. It is shown that information obtained from different mono-disperse simulations enables to answer a couple of practical questions in such two-phase flow simulations: How can the mono-disperse simulations be compared to the poly-disperse experimental results and their accuracy evaluated? More importantly, if only one simulation is to be carried out for a larger case, which value of the injected droplet size is the best?