Transient Sonic Choking

During the transient solution sonic choking may begin at any of the geometries described in the Sonic Choking Detailed Description topic, including all junctions except for the dead end junctions. In addition to the geometries previously discussed, sonic choking may occur at a junction at the inlet of a pipe in response to rapid system changes. Choking at the inlet of a pipe is not sustainable, and may result in shock waves moving through the system, as is discussed further below.

AFT xStream evaluates every boundary calculation (i.e. junction inlet/outlets) at every time step to determine if sonic choking would occur. If sonic choking is detected at a junction, xStream will adjust the solution method at that junction accordingly.

Under sonic conditions, the defined boundary condition at the choke point is no longer meaningful, as it cannot be reached. However, because the flow is sonic the velocity must be equal to the sonic velocity, a. Sonic velocity depends on the local state, which is unknown. Therefore, iteration is required to determine the velocity.

Iterations will be performed on the velocity using the appropriate wave compatibility equation to calculate pressure. To calculate the density for an inflow the pressure and the specified temperature/enthalpy will be used. For an outflow boundary the density is calculated using the particle path compatibility equation.

Shock Waves

A shock wave is a compression wave across which velocity transitions from supersonic to subsonic, and also causes discontinuities in other properties such as pressure, temperature, and density. (Saad, 1993Saad, M.A., Compressible Fluid Flow, 2nd Edition, Prentice-Hall, Englewood Cliffs, NJ, 1993) It is simplest to discuss shock waves by discussing how compression waves are formed. Compression waves may or may not become shock waves, depending on the conditions.

A compression wave is generated in a pipe or duct due to a series of incremental, instantaneous velocity changes in the flow. Each velocity change generates a sound wave that begins traveling through the gas. As the gas compresses each subsequent wave will have a higher sonic velocity caused by the increasing temperature. Eventually the faster waves will catch up to the initial wave, causing the compression wave to steepen and the pressure drop across the wave to increase. If an abrupt enough velocity change occurs, then the compression wave will become a shock wave.

AFT xStream does not employ any shock wave solution methods in the solver. However, the method of characteristics, which is frequently used to model wave movement, can approximate the movement of shock waves through gas systems.