Analysis of the Influence of Bubbly Liquids on the Dynamics of Fluid Power Systems

Hydraulic systems and components are subject to increasing demands with respect to power density, versatility and durability. One key aspect is to reduce the risk of resonance, which has an adverse effect on the controllability and durability of the system. In order to assess the system behavior during the design process, simulation has become an indispensable tool. However, accurate modelling and simulation of fluid power systems requires a good knowledge of the fluid’s properties and especially its compliance. If undissolved air is present in the form of bubbles, dynamic effects may need to be considered during the analysis in addition to the well-known (quasi-)static effects. In this work, the compressibility for a fluid containing gas bubbles is derived using the Rayleigh-Plesset equation. The results suggest that dynamic effects can be taken into account by introducing a complex-valued bulk modulus, which implies that a pressure change and an associated change in the mixture’s density do not necessarily have to occur simultaneously. It is shown that each bubble within the two-phase mixture can be modelled as a mass-spring-damper system – implying that every bubble possesses a natural frequency and an individual damping characteristics. Using the transmission line theory, the effect of the mixture dynamics on a pipe is demonstrated. With the help of the subsequently developed solution in the time domain, these effects can be implemented in modern simulation tools. Finally, an experimental setup is presented which allows the demonstration of two different phenomena associated with bubble dynamics: A reduction of the speed of sound and an increase of pressure wave attenuation. Cancellation effects are confirmed, proving the dynamic influence of bubbles in a liquid.