Wavespeed and Communication Time

Wavespeed

The wavespeed (sometimes referred to as characteristic speed) for gas transients is the velocity at which the pressure waves will propagate through the gas, as is calculated by the Method of Characteristics. For gas flow the wavespeed is equivalent to the sonic velocity of the gas (c) plus/minus the velocity of the gas (V) which is direction dependent. The sonic velocity and velocity will vary with pressure and density.

Communication Time

An important consideration in fluid transient studies is how long it takes a wave to propagate through the system.

The time it takes for a wave to travel from one end of a system to the other is the distance (L) divided by the wavespeed (a).

However, in compressible gas systems the wavespeed is not constant since both the sonic velocity (c) and velocity (V) will vary across the system. The sonic velocity will vary based on temperature, and the velocity will vary based on typical compressible flow theory with pressure, density, area changes, etc. However, a minimum communication time can be estimated using the maximum sonic velocity (i.e. sonic velocity at the maximum temperature) and maximum velocity (i.e. sonic velocity), as is discussed in Pipe Sectioning - Introduction to Method of Characteristics. In this case, a = c + c = 2c.

When a transient event occurs at one end of a pipe, the wave travels at the wavespeed to the other end of the pipe. However, this is not sufficient time to analyze the problem. While the disturbance has propagated through the entire system, the point of transient initiation has not yet seen the result of the reflected wave. For the wave to both travel to the end of the pipe and back requires double the above time. This time is known as the Pipe Period or Communication Time. For liquid systems the Communication Time can be a good estimate for how much simulation time is needed, however, for compressible gas systems since the wavespeed can vary throughout the system, it is only an approximation for initial runs. Results should be checked to ensure that enough simulation time was run for a proper analysis of transient wave interactions.