Numerical quenchback in thermofluid simulations of superconducting magnets

One of the most important thermoßuid processes encountered in internally cooled superconducting magnets is that of quenching. Numerical simulation of the quench propagation involves accurately modelling a moving boundary layer at the quench front. Due to the highly non-linear nature of the quench process, slightest numerical errors can rapidly grow to unacceptable limits. The quench propagation in such a non-converged solution exhibits a very rapid propagation velocity which resembles a ÔquenchbackÕ e¤ect. Hence, the term ÔNumerical QuenchbackÕ is used to characterize a numerically unstable solution of the governing quench model. This paper presents the underlying physical phenomena that causes a numerical discretization scheme to have error terms that increase exponentially with time, causing the numerical quenchback e¤ect. SpeciÞcally, by analytically solving the equivalent di¤erential equation of the numerical scheme, we are able to obtain closed-form relations for the error terms associated with the propagation velocity. This allows us to deÞne error criteria on the space and time steps used in the simulation. The reliability of the error criteria is proven by detailed convergence studies of the quench process