A slug length calculation for a contraction with mean flow between two half cylinders

A slug length is widely used to describe additional mass inertia at low frequencies in duct acoustics. It is often used in acoustic energy analysis, e.g. as one of the inputs for semi-analytical or empirical models to obtain the acoustic reflection and transmission coefficients. However, the calculation of slug length is usually empirical and limited to many conditions, such as simple geometric configurations, low frequencies, no mean flow, etc. In this paper, the slug length at a contraction with mean flow between two half cylinders is calculated by different methods: solving the Laplace's equation both analytically and numerically, solving the Helmholtz equation, and using the Cummings - Fant equation based on the numerical results of frequency-domain linearized Navier-Stokes equations. Both the frequency-dependence and the mean flow effect are discussed. The calculated slug lengths are then used in the semi-analytical model to predict the acoustic scattering at tube rows in the presence of a cross mean flow.