The dynamic characteristics of a pulsating turbulent flow of compressible gas in a pipe under the effect of time-average flow

The effect of time-average flow with the values of Mach number $\mathrm{M}=0.03–0.3$ on the transfer functions of a gas pipeline is investigated. A set of cross section-averaged equations of motion, continuity, and energy, written in a narrow-channel approximation, are solved by the finite difference method. The variability of the gas density and sound velocity is taken into account. The heat flux to the wall is assumed to be constant. The wall friction is calculated using the data previously obtained by solving a nonstationary equation of motion simultaneously with relaxation equations for turbulent stress and turbulent viscosity. The calculations are performed in three characteristic frequency regions, namely, regions of quasi-stationary and frozen turbulence and an intermediate region. It is demonstrated that the effect of time-average flow leads to a decrease in the amplitudes of oscillation of velocity and pressure in the resonance mode.