Transition modelling represents a key ingredient for improving the performance predictions of many industrial applications. Among transition models, local formulations seem to guarantee better robustness, accuracy and easiness of implementation in modern CFD solvers. These models have been proposed in the finite volume context to predict the laminar-turbulent transition, but only few attempts have been made in the high-order framework. In this paper a new phenomenological transition model based on the concept of laminar kinetic energy has been proposed and implemented in a high-order accurate Discontinuous Galerkin code, named MIGALE. The transition model is validated and assessed by computing the transitional flow around flat plates with zero/adverse pressure gradients and through different turbine nozzles (T106A and LS89) for different values of Reynolds number and turbulence intensity. The computed results have been compared with experimental data and reference numerical solutions.