Quench propagation velocity and hot spot temperature models in Nb$_{3}$Sn racetrack coils

Since 2010 to present, several subsize magnet assemblies, designed as test beds for the validation of impregnated Nb$_{3}$Sn-based coil technology, have been tested at the Superconducting Magnet Test Facility (SM18) at CERN. These short model coils and racetrack model coils have been used to study two types of Rutherford cables foreseen for the coils of the Nb$_{3}$Sn magnets in the framework of the HL-LHC upgrade and High Field Magnet program of CERN. During several test campaigns, the Rod Restack Process and the Powder-In-Tube conductors have been characterized in terms of performance and quench propagation velocity (QPV). Moreover, hot spot temperature (HST) increase during quenches has been estimated from the analysis of the registered voltage and current signals. In this paper, the multiphysics problem of quench propagation in Nb$_{3}$Sn cables is addressed under adiabatic conditions by means of a set of analytical formulae and several finite element models with different level of complexity in ANSYS APDL, COMSOL Multiphysics, and MATLAB. These models are aimed at describing the conductor behavior in terms of HST and QPV observed during the training of racetrack coils at SM18.