Parametric Effect of Steady and Unsteady Friction on the Origin and Initial Propagation of the Shock Pulse

The phenomenon of unsteady flow is widespread in engineering. It is known to generate a shock pulse (water hammer). The nature of this phenomenon is nonlinear and depends on several factors: steady friction, unsteady friction, convection of velocity and pressure fields, bulk viscosity, and the conditions under which the shock pulse occurs. Using models in modern software requires an accurate understanding of the physics of the generation and primary propagation of a shock pulse—a nonlinear process that, under certain conditions, allows for the existence of more than one fluid flow mode. Therefore, a parametric study of previously obtained analytical solutions is of practical interest. The results presented in this paper highlight the importance of parameters corresponding to steady and unsteady friction. While steady friction affects the size of the shock pulse region (the size decreases with increasing friction), unsteady friction has a completely different effect. As the parameter responsible for unsteady friction increases, the possibility of the existence of two shock pulses—one weaker and one stronger—emerges. In this case, hydraulic concepts based on the Bernoulli equation prove inapplicable: higher pressure values correspond to higher shock pulse propagation velocities. This is entirely logical: the greater the non-stationarity (and the shock pulse propagation velocity), the greater the pressure surges.