INSTANTANEOUS TRANSIENTS

Generally, a transient event only implies that a system is no longer in steady state. Put another way, parameters like velocity, pressure, and flow direction can change with time during a transient event. These events can take place over a few hours (such as a slow tank filling) or can be analyzed on the scale of milliseconds.

Understanding the time scale of a transient event and its relationship to the system’s communication time is the first step toward understanding the implications of a water hammer event.

Define instantaneous

An instantaneous transient event is determined by a system’s communication time. Hydraulically, communication time is the amount of time for a signal to travel the length of a pipe, reflect, and return to its point of origin. Often this signal is a pressure wave generated from a valve closure traveling up the pipe and back to the closed valve. An analogy for communication time is turning a shower to ice cold, where there is a slight delay before the cold water reaches the signal origin. That slight delay is similar to the communication time of a system.

In a hydraulic piping system, the communication time is the minimum amount of time for the system to adjust to a change, approaching a new intermediate operating condition in the process. For example, if a valve closes in 30 seconds for a system with a 10-second communication time, the valve will see the consequences of its initial closure by the end of its closure. With the shower analogy, there would be a noticeable gradient of temperature change toward cold as an intermediate operating condition is achieved.

A transient event that lasts less than the communication time is considered instantaneous. That means that any change to the system at the start of the transient does not influence the later part of the transient. If a valve is closed in 5 seconds for a system with a 10-second communication time, the signal doesn’t have time to travel and cause an intermediate operating condition before the valve is completely closed. In the shower example, the water would jump from hot to cold essentially instantly.

Instantaneous implications

An instantaneous valve closure implies that the full Joukowsky pressure rise will, at minimum, be seen at the closed valve. As a transient event becomes faster relative to the system’s communication time, more and more of the pipe will see the full Joukowsky predicted pressure rise and the pressure gradient will be more steep as the pressure wave travels through the system.

Figure 1 provides a comparison between 4 instantaneous valve closures for a system with a 10-second communication time. These closures include a 10-second, 5-second, 2.5-second, and 0.5-second valve closure. These examples follow an ideal valve closure in which each degree of closure results in a proportional reduction in flow, for example, half the flow is halted halfway through the closure. Each closure has been synchronized so the valves finish closing at the same time.

Figure 1: A 30-second comparison between instantaneous valve closures to demonstrate differences in pressure wave structure

The first thing to notice is the steepness of the pressure wave front. For a faster closure, fluid is halted in a shorter time, resulting in a rapid pressure increase. As the valve closure time lengthens, fluid is halted more gradually, leading to a gradual increase in pressure that travels through the system according to the water hammer sequence. The influence of closure time on the gradual increase in pressure is best found through animation in Figure 2.

Figure 2: Animation of pressure waves traveling through pipes, with smooth gradients representing smoother changes in pressure.

As the time of the transient increases, more of the initial signal is able to travel down the pipe, reflect, and help mitigate additional high-pressure waves. This helps smooth the later part of the closure by using wave interference to reduce the peak pressure. Since each pressure signal travels up and down the pipe, the amount of pipe which sees the peak pressure rise is informed by how much of the pipe is affected by the returning low-pressure wave.

Figure 3 compares the peak pressure seen along the pipe for the 10, 5, 2.5, and 0.5-second closures found in Figure 1 and Figure 2.

Figure 3: Profile graph comparing the peak pressure experienced along the pipe for different valve closure times

It is evident from the profile graph of max pressure that all instantaneous closures see the full Joukowsky predicted pressure rise at some point in the pipe. For a transient closure equal to the communication time, this occurs only at the valve. This is because the initial wave just reaches the point of origin once the valve is completely closed. For a transient closure which is half of the communication time, only half of the pipe sees the full predicted pressure rise. A closure one-quarter of the communication time shows the full pressure rise for three-quarters of the pipe, and so on. Again, this trend is based on an ideal valve closure in which each degree of closure results in a proportional reduction in flow. Often this ideality is not the case and instead largely depends on a valve’s inherent and installed characteristics. The impact of these non-ideal closures is explored further in the article Effective Closure Time.

Non-instantaneous closures

A common approach to mitigating water hammer pressure surges is by closing a valve more slowly. A non-instantaneous valve closure reduces the peak pressure found anywhere in the system below the Joukowsky predicted pressure rise (in most cases). This peak pressure is avoided by providing adequate time for the initial pressure wave to travel and reflect through the entire system, even back through the valve itself. Figure 4 compares an instantaneous closures to some non-instantaneous closures to demonstrate this reduction in max pressure, represented by the dashed lines.

Figure 4: Comparison between an instantaneous closure and non-instantaneous closures with max pressures represented as dashed lines

Interestingly, making a valve closure non-instantaneous adjusts when the peak pressure is found. A table of the peak pressure and the time it occurs is found in Table 1. As mentioned, this variation is due to the wave interaction between the gradual pressure waves moving through the pipe interfering with the returning low-pressure waves according to the water hammer sequence. This interference is also why the exact water hammer sequence does not appear distinctly in the non-instantaneous closures.

Table 1: Summary of peak pressures and the time at which they occur

For ideal closures as found in these examples, using an overall closure time greater than the system communication time should cause a reduction in surge pressure. However, the valve’s inherent and installed characteristics can drastically impact the effective closure time of the valve, meaning longer overall valve closure times do not guarantee a lower surge pressure. The valve’s effective closure time should be compared to the communication time to determine whether the transient will be instantaneous rather than the overall closure time of the valve. Regardless, understanding the implications of an instantaneous transient is another valuable piece of the water hammer analysis puzzle.