The current design of low-pressure turbines (LPTs) with steady-blowing vortex generating jets (VGJs) uses steady computational fluid dynamics (CFD). The present work aims to support this design approach by proposing a new semiempirical transition model for injection-induced laminar-turbulent boundary layer transition. It is based on the detection of cross-flow vortices in the boundary layer which cause inflectional cross-flow velocity profiles. The model is implemented in the CFD code TRACE within the framework of the - transition model and is a reformulated, recalibrated, and extended version of a previously presented model. It is extensively validated by means of VGJ as well as non-VGJ test cases capturing the local transition process in a physically reasonable way. Quantitative aerodynamic design parameters of several VGJ configurations including steady and periodic-unsteady inflow conditions are predicted in good accordance with experimental values. Furthermore, the quantitative prediction of end-wall flows of LPTs is improved by detecting typical secondary flow structures. For the first time, the newly derived model allows the quantitative design and optimization of LPTs with VGJs.