The accuracy and performance of entropic multi-relaxation time lattice Boltzmann models are assessed for transitional flows of engineering interest. A simulation of the flow over a low-Reynolds-number$SD7003$airfoil at$Re=6\times 10^{4}$, at an angle of attack$\unicode[STIX]{x1D6FC}=4^{\circ }$, is performed and thoroughly compared to available numerical and experimental data. In order to include blockage and curvature effects, simulations of the flow in a low-pressure turbine passage composed of$T106$blade profiles, at a chord Reynolds number of$Re=6\times 10^{4}$or$Re=1.48\times 10^{5}$, for different free-stream turbulence intensities are presented. Using a multi-domain grid refinement strategy in combination with Grad’s boundary conditions yields good agreement for all simulations. The results demonstrate that the entropic lattice Boltzmann model is a viable, parameter-free alternative to modelling approaches such as large-eddy simulations with similar resolution requirements.