Bulk Modulus of Air Content Oil in a Hydraulic Cylinder

Abstract

A model of oil with entrained air content is developed which considers fluid compression and the subsequent dissolving of mixed entrained air. According to the model the mixed entrained air affects the "gross" bulk modulus below some critical pressure, but has no effect above this value due to the complete dissolving of the entrained air into solution. The critical pressure is shown to be proportional to the square root of the amount of the initial mixed entrained air. The temporal pressure gradient has also a substantial effect on the critical pressure value and thus on the bulk modulus. The critical pressure value increases but tends towards an upper value with increasing temporal pressure gradient (a true dynamic condition); the opposite occurs when the pressure gradient decreases as the critical pressure converges to a lower value (essentially a static value). Thus regions of static and dynamic bulk modulus can be established. The model predicts that the upper critical pressure value is some 1.8 times that of the static one. Experiments have been designed to verify the feasibility of the model by measuring the temporal pressure gradient against the variation of compressed oil volume. It is demonstrated that the model is verified not only for the case of positive pressures (above atmospheric pressure) but also for pressures less than atmosphere. Finally a comparison of the proposed model is made with those proposed in the literature. The bulk modulus predicted by the proposed model is a little larger than these given in literature. The reason for such difference is attributed to the result of air being dissolved into oil.