Modern industrial computational fluid dynamics tools employing either implicit time steppers or linear harmonic methods have a strong requirement for the efficient iterative solution of large and sparse linear systems of equations, often relying on Krylov subspace methods, necessitating the best possible preconditioning approach to minimise the computational burden. In this work, a range of preconditioners are implemented and assessed in the flow solver TAU, developed by the German Aerospace Center, including Jacobi-type iterations that iteratively apply an ILU factorisation as the generalised diagonal. The main test case is the NASA Common Research Model with up to 500 million complex degrees of freedom. On previous best practices, we demonstrate an approximate 5x speed-up across a range of grids for linear systems arising from frequency domain analysis. Up to 3x speed-up is also demonstrated for a large-scale global stability eigenvalue problem for which unstable modes represent the shock-buffet instability. This work highlights that improved preconditioners have the potential to vastly accelerate large-scale industrial computational fluid dynamics tasks.