A strategy to perform unsteady numerical simulations of selective non-catalytic reduction (SNCR) of nitrogen oxides by ammonia is discussed. The conversion process of NO by ammonia is known to be highly sensitive to the temperature level. The intricate coupling between spray evaporation, turbulent mixing and ammonia-NO chemistry is numerically studied. First, canonical flow problems are addressed with both quasi-direct and large eddy simulations, to seek out the key ingredients that must be included in the simulations of industrial SNCR systems, in view of their optimization. Second, from this preliminary analysis, a downsizing procedure preserving characteristic numbers of SNCR is proposed to build a numerical lab-model. In this downsized version, all lengths have been reduced by a given factor to allow for conducting highly resolved unsteady simulations of NO reduction units featuring complex geometries, with turbulent flow convection over lengths of more than 10 m. Using high performance computing, unsteady simulations of a representative SNCR system are finally reported, both in its full size and downsized versions. (C) 2015 Elsevier Ltd. All rights reserved.