Your country is not included? Please visit our global website Language A Train Analogy: Flow and Pressure Waves in Fluid Systems Pressure pulsations in fluid systems containing single-headed liquid diaphragm pumps Whilst diaphragm pumps offer many advantages, such as durability, dry-running safety, suitability to transport abrasive liquids, etc., in some situations, single-headed liquid diaphragm pumps can cause significant pressure pulsations in the fluid system into which they are incorporated. For this reason, some customers are requiring diaphragm pumps with smooth flow and low pressure pulsations. KNF has designed a new FP series of low pulsation pumps which provide a much smoother flow delivery, and eliminate the issues described above, even in more challenging applications. The development process of these FP pumps was greatly accelerated by utilizing a new proprietary simulation tool, which can accurately predict flow and pressure variations in fluid systems. Role of the Pipe in a Fluid System Understanding the behaviour of pipes is crucial in determining how a fluid system reacts to a pulsating flow, as is the case with single-headed diaphragm pumps, for example. This article shows which physical effects play an important role in the behaviour of pipes carrying a pulsating flow. These effects are: Fluid friction (resistance) Capacitance of the pipe wall We will observe the reaction of the pipe to this steady and unsteady flow combination at the upstream end of the pipe at the location which is indicated with a green dash. At this location, the sum of steady \((\overline{p})\) and unsteady pressure \((\tilde{p})\) contributions are measured. The ratio between the measured pressure and injected flow at this location, is the hydraulic impedance \(Z\) of the pipe, which varies with the stroke frequency \(n\) of the piston. Figure 1: Experimental set-up containing a pipe connected to a moving piston and a reservoir. Figure 2: Impedance curve of a fluid system consisting of a PVC-P pipe and a reservoir. The overall impedance response of the pipe, at frequencies up to 5000 strokes per minute, is shown as a solid black curve in figure 2. This impedance response considers all three effects (resistance, inductance, capacitance) listed above, and represents the actual behaviour of the pipe. Each physical effect will now be investigated separately. Fluid Friction To help visualize these fluid resistance effects, a good analogy is a fast-moving train travelling on a straight track. Imagine first, the train travelling at a constant velocity – the air surrounding the train causes friction: this is a steady force that the engine of the train must overcome. Then imagine the train driver accelerates and decelerates the train in a small but harmonic manner: this will cause an additional unsteady friction effect. Fluid Column Inertance Similarly, this is true for the pressure built-up in the experiment as shown in figure 1. If the piston has a low oscillation frequency the pressure built-up in the pipe is small. If the oscillation frequency is increased, however, the pressure increases proportional to the applied frequency. The resulting impedance for such a situation is shown as the solid blue line in figure 2. Surprisingly, the inertance effect causes much higher impedance (or pressure pulsations) than the resistance effect. Furthermore, one can observe that for low piston frequencies, up to 500 strokes per minutes, the actual impedance curve and the curve which represents the inertance effect in the pipe match quite well. For larger piston frequencies, however, the differences become larger and the blue linear impedance curve cannot represent the true non-linear impedance of the PVC-P pipe represented by the black curve. So, there must be an additional effect which causes this special behaviour of polymer pipes. Pipe Wall Capacitance Again, the train analogy can be used to explain this capacitance effect which shows a strong interaction with the inertance effect, described in the previous section. Imagine again, the train consisting of a locomotive and several carriages on a straight track. This time however, instead of using a rigid coupling between the carriages, an elastic connection like a spring or a rubber band is used. Now the locomotive starts moving back and forth in an oscillatory manner. For low frequencies the carriages move synchronously (in phase) with the locomotive and the behaviour of the train is similar to the situation when the coupling between the carriages is rigid. If the oscillation frequency of the locomotive is increased, the carriages and the couplings start to interact with each other, and the movement of the locomotive and the carriages becomes asynchronous. Such a situation is shown in video 1, which represents the same experiment introduced in figure 1, but with a piston frequency of 1200 strokes/min. This content requires your consent To view this content, please accept marketing cookies . This allows us to display videos and maps from external platforms. This content requires your consent To view this content, please accept marketing cookies . This allows us to display videos and maps from external platforms. These two special cases clearly illustrate how pressure and flow waves are created in the pipe and interact with the piston. These wave phenomena are the reason for the special shape of the impedance curve, as shown in figure 2. The shape of the impedance curve depends strongly on the material properties of the pipes, as can be seen in figure 3 for the pipe materials: Polyethylene (PE), Polyurethane (PU) and PVC-P. These material properties can be obtained with a special measurement method which has been developed at KNF (Frey et al., 2020). Figure 3: Impedance curve for different pipe materials all having a length of 1.5m Transfer to a Real Pump Simulation We hope this technical blog helps to understand why in some situations wave phenomena can cause large pressure or flow pulsations in fluid systems. The experts at KNF have a profound knowledge about these situations. If you encounter a problem, do not hesitate to contact the relevant sales center and we will try to find a solution to your case. References Zielke, W. (1968). Frequency-dependent friction in transient pipe flow. Journal of Basic Engineering, 90 (1), 109–115. Related Blog Posts Contact Us Do you want to find out more about our customized pump solutions and service opportunities? Get in touch with our local sales representatives.