# Understanding transient Wave Speed Reduction Factor Calculation Option

 Applies To Product(s): HAMMER Version(s): CONNECT Edition, V8i Area: Modeling Original Author: Nancy Mahmoud, Bentley Technical Support Group

# Problem

What does the "Wave Speed Reduction Factor" under Calculation Options do?

# Solution

This Wave Speed Reduction Factor field gives some control over the wave speed in the model at low pressures. It is used in conjunction with the "Decrease Time" and "Increase Time" fields.

In any liquid there is a certain amount of absorbed gas with which it has been in contact through a free surface. When the pressure in a pipeline drops to a sufficiently low level, the dissolved gas comes out of solution. Due to the presence of entrained air or free gas, the celerity of pressure waves is reduced, thereby mitigating the subsequent upsurges when vapor cavities collapse. In contrast to vapor release which typically occurs within milliseconds, the time for gas release and (re)absorption is of the order of seconds. In traditional computer models of hydraulic transients, the occurrence of gas release at low pressure in the liquid is ignored to yield conservative results which may overestimate the peak pressures in the piping system resulting from the collapse of discrete vapor cavities. Bentley HAMMER provides a way to account for the impact of gas release without delving into the complex multi-fluid and multiphase physical phenomena.

The Wave Speed Reduction Factor calculation option allows you to model the reduction in celerity that occurs at low pressure. Entering a value below 1.0 will result in the following behavior:

• At the start of a simulation, the wave speed equals the user entered value.
• If the pressure at any pipe segment drops below the pipe elevation (i.e. negative pressure), then the wave speed will be reduced. The (linear) rate at which it is reduced is equal to: (original wave speed - [Wave Speed Reduction Factor *original wave speed]) / Decrease Time).
• If the pressure becomes positive again before the wave speed has been adjusted down to its fully reduced value (Wave Speed Reduction Factor *original wave speed), then the wave speed will start to increase back up to the original value. The (linear) rate at which it is increased is equal to: (original wave speed - [Wave Speed Reduction Factor *original wave speed]) / Increase Time).
• Alternatively, if the pressure stays negative for long enough, the wave speed will be adjusted all the way down to: (Wave speed reduction factor *original wave speed). It will be held at this value until the pressure in the pipe segment is positive again, at which point it will start to be increased. The rate will be as described in #3 above.

Consider the below graph of wave speed for a pipe segment over time:

[0] indicates that the wave speed is at its original value.

[-1] indicates a reduction in wave speed due to pressure falling below zero.

[1] indicates an increase in wave speed due to pressure becoming positive again

[2] indicates that the wave speed has been fully reduced (to the wave speed reduction factor * the original wave speed)

Therefore, the graph indicates that the pressure first dropped below zero, but became positive shortly after, before the wave speed was fully reduced. It then dropped again and remained negative long enough for the wave speed to fully reduce. Next, the pressure became positive again but fell back below zero shortly after, before the wave speed returned to the original value.

## Example

For example, consider entering the following data in the model: a wavespeed of 1000m/s , a Wave Speed Reduction Factor of 0.5, a Decrease Time of 0.2 seconds, and an Increase Time of 3 seconds. In this case, if the liquid pressure reaches zero pressure, the wave speed in that pipe will start to reduce. Assuming the pressure doesn't increase again in the meantime, the wavespeed will reduce to 500 m/s (1000 m/s x Wave Speed Reduction Factor) linearly over 0.2 seconds (the Decrease Time).

While the pressure stays negative the wavespeed will stay at 500 m/s, but if the pressure becomes positive the wavespeed will also increase linearly back up to 1000 m/s over 3 seconds (the Increase Time).

## How do I decide what to enter for the wave speed reduction factor?

There is no general guidelines for selecting the wave speed reduction factor, since it largely depends on the system.

A good reference text with some information on this is: "Wylie,
E.B. and Streeter, V.L. (1993). Fluid Transients in System," especially chapter 1-3. In this reference, the authors say that the
wavespeed can be reduced by up to 75% in certain cases, but that the user should make their own assessment.

One option to find a good value is to run a series of sensitivity analyses to get an idea of how different reduction factors impact the system.