Internal Flow Temperature and Vorticity Dynamics Due to Transient Mass Addition

A model is developed for coexisting acoustic and rotational disturbances in internal flows arising from spatial distributed, transient mass addition of a constant temperature gas. The heat transfer and temperature dynamics within a channel flow are explored, in addition to the spatial distribution of the transient velocity and vorticity fields. The compressible Navier-Stokes equations are solved computationally subject to boundary conditions on the sidewalls and the exit plane, written in Navier-Stokes characteristics form to facilitate proper wave reflections. Transient solutions consist of coexisting, equal magnitude acoustics (irrotational) and vorticity as well as surprisingly large, nonacoustic transverse temperature gradients across the chamber. Results for low-Mach- and large-Reynolds-number channel flow describe spatial patterns for velocity, vorticity, temperature, and temperature gradient. The temperature gradient transient at the sidewall implies a larger amount of surface heat transfer than expected for constant temperature mass addition. The time-dependent numerical data are used to calculate the mean axial velocity distribution across the chamber and rms values for the velocity and vorticity fields to characterize flow with coexisting acoustics and vorticity. The computational solutions for a channel flow bear a strong qualitative resemblance to results obtained from an asymptotics-based modeling effort for flow in a cylinder.