Theoretical Model of Dynamic Bulk Modulus for Aerated Hydraulic Fluid

Abstract

Existing models of bulk modulus for aerated hydraulic fluids primarily focus on the effects of pressure and air fraction, whereas the effect of temperature on bulk modulus is disregarded. Based on the lumped parameter method and the full cavitation model, combined with the improved Henry’s law and the air polytropic course equation, a theoretical model of dynamic bulk modulus for an aerated hydraulic fluid is derived. The effects of system pressure, air fraction, and temperature on bulk modulus are investigated using the controlled variable method. The results show that the dynamic bulk modulus of the aerated hydraulic fluid is inconsistent during the compression process. At the same pressure point, the dynamic bulk modulus during expansion is higher than that during compression. Under the same initial air faction and pressure changing period, a higher temperature results in a lower dynamic bulk modulus. When the pressure is lower, the dynamic bulk modulus of each temperature point is more similar to each other. By comparing the theoretical results with the actual dynamic bulk modulus of the Shell Tellus S ISO32 standard air-containing oil, the goodness-of-fit between the theoretical model and experimental value at three temperatures is 0.9726, 0.9732, and 0.9675, which validates the theoretical model. In this study, a calculation model of dynamic bulk modulus that considers temperature factors is proposed. It predicts the dynamic bulk modulus of aerated hydraulic fluids at different temperatures and provides a theoretical basis for improving the analytical model of bulk modulus.