In any dynamic fluid system, modelling the medium is a crucial step for achieving accurate and realistic simulations. For hydraulic system modelling, the fluid’s bulk modulus which represents the resistance of the fluid to compression, significantly affects the system’s behaviour and stiffness. Since fluid in a hydraulic system is most times under extreme pressure for system operation, it is essential to determine the correct bulk modulus and understand the factors influencing its behaviour. Temperature, pressure, and the presence of air are the main factors affecting the bulk modulus. However, in this blog post, I will focus on the presence of air in oils, which significantly reduces the fluid’s bulk modulus, and discuss the modelling approach used in the Claytex FluidPower library.
In a hydraulic system, air exists in three forms: free air, entrained air, and dissolved air. Free air consists of air pockets trapped in the hydraulic circuit due to improper system installation and component issues, and it can be removed by venting the system. In the Claytex FluidPower model, we assume there is no free air. Entrained air consists of tiny air bubbles distributed throughout the hydraulic fluid, significantly reducing the fluid’s resistance to compression. Conversely, dissolved air refers to air molecules dispersed among the oil molecules. Dissolved air does not affect the fluid’s bulk modulus.
There are different modelling approaches for the effective bulk modulus of an air-oil mixture in the literature. These approaches are grouped into two categories: compression-only models and compression-and-dissolve models. Compression-only models consider only the volumetric compression of entrained air. In contrast, compression-and-dissolve models account for both the compression of entrained air and the reduction of entrained air due to its dissolution under changing system conditions over time. Claytex models employ the “Compression and Dissolve” approach to achieve more accurate simulations.
Pressure Conditions Considered in Claytex FluidPower Library
As previously discussed, the Claytex FluidPower library utilises the “Compression and Dissolve” approach to effectively model the bulk modules behaviour in the hydraulic systems, and three specific pressure conditions are considered within the library:
- P > Pa: When the system pressure is higher than the air release pressure (saturation pressure), there is no entrained air in the system. All the air is dissolved, and the oil behaves like pure oil.
- Pv < P < Pa: When the system pressure is between the oil vapor pressure and the air release pressure, some of the air is dissolved while some remains entrained in the system.
- P < Pv: When the system pressure is below the oil vapor pressure, there is vapor and air in the system, but no oil.
Figure 1: Variation of Fluid Bulk Modulus with Increasing System Pressure at Different Air-Oil Mixture Ratios (0, 2, 4, 6, 8 % respectively)
Figure 1 illustrates that the fluid bulk modulus in the system changes significantly with increasing system pressure. For a 0 percent air content in the oil, the fluid behaves like pure oil from ambient pressure up to 90 bar. However, for air-oil mixtures with 2, 4, 6, and 8 percent air, the bulk modulus increases rapidly until the system pressure reaches 20 bar, which is the air release pressure (saturation pressure) defined as a fluid property. At this pressure, all the air dissolves in each of these air-oil mixtures. Beyond 20 bar, the oil behaves like pure oil as the air content is fully dissolved.
Additionally, the graphs indicate that in fluid power system simulations, the air-oil ratio must be set carefully. Even a 2 percent air content significantly decreases the fluid bulk modulus, especially at lower pressures. For example, at a system pressure of around 10 bar, the fluid bulk modulus for pure oil is approximately 15,000 bar. In contrast, for a 2 percent air-oil mixture, the bulk modulus drops to around 6,000 bar, for a 4 percent mixture it drops to around 4,000 bar, and for a 6 percent mixture it drops to around 2,000 bar. Therefore, the presence of air in the oil profoundly alters the system characteristics, particularly when the system pressure is below the saturation pressure.
In the following section, I will illustrate how different air-oil mixtures influence the stiffness and dynamic behaviour of a hydraulic system. Employing the Claytex FluidPower library within the Dymola simulation environment, I will develop a master-slave cylinder model. This model will facilitate the examination of how varying air-oil mixtures alter the system’s characteristics.
Figure 2: Master-Slave Cylinder Model Using FluidPower Library Components in Dymola.
Figure 2 illustrates a model comprising a master and slave cylinder. The master cylinder is actuated by a force model, which drives the slave cylinder, generating pressure and force. Simulations were run with different air-oil mixtures: pure oil (0%), 2%, 4%, 6%, and 8% air content.
Figure 3: Figure 3: Pressure and Force Output Characteristics of the Master-Slave Cylinder Model
Figure 3 demonstrates that at low pressures, the system behaves more stiffly and responds immediately to pressure increases when using pure oil. However, with 2%, 4%, 6%, and 8% air-oil mixtures, the system responds more slowly due to the low bulk modulus with entrained air. The system recovers and reaches the bulk modulus of pure oil after all the air is dissolved at around 20 bar.
In conclusion, the Claytex FluidPower library provides a robust framework for accurately modelling the behaviour of bulk modulus in hydraulic systems. By considering the effects of varying air-oil mixtures, this library demonstrates how air content significantly influences system stiffness and performance. The implementation of the “Compression and Dissolve” approach improves the realism of simulations, allowing for a more comprehensive understanding of system dynamics under different conditions. Overall, this highlights the importance of managing air-oil ratios carefully in hydraulic system design and analysis.
Written by: Kadir Sahin – Project Engineer
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