Research on Theoretical Model of Dynamic Bulk Modulus of Elasticity of Gas-liquid Mixed Fluid

Abstract

The bulk modulus is one of the basic properties of gas-liquid mixed fluid. But the matching between the existing model and the real dynamic bulk modulus of the fluid during compression and decompression still needs to be further improved. Based on the lumped parameter method and the full cavitation model, combined with the improved Henry's law and the gas polytropic process equation,a theoretical model of dynamic bulk modulus of gas-liquid mixed fluid (Model1) is derived. The calculation results show that due to the different content of free gas in the mixed fluid during compression and expansion, the dynamic bulk modulus exhibits a more obvious "hysteresis" phenomenon. Under the same pressure, the calculation results of the compression process are smaller than that of the decompression process. From the parameter influence analysis, it can be seen that when the pressure change cycle is the same,the initial gas content rate is higher, and the dynamic bulk modulus at the same pressure is smaller whether in compression or decompression process. When the initial gas content is the same and the fluid pressure is higher than the air separation pressure, the pressure change cycle is longer, the dynamic bulk modulus at the same pressure is larger. When the pressure exceeds the air separation pressure for a long enough time, the air contained in the oil will be completely dissolved, and the bulk modulus will remain substantially unchanged. By comparing the experimental results and the calculation results of Model 1, three steady-state models and another dynamic model(Sakama model), it can be seen that, in the process of compression and decompression, the goodness of fit between the calculated results of Mode1 and the experimental results is 0.976 3 and 0.985 9 respectively and the goodness of fit between the Sakama model and experimental data is 0.969 7 and 0.952 1, which show that the calculation results of Model 1 are closer to the experimental results and improve the accuracy of dynamic bulk modulus. This study can provide theoretical basis for accurate calculation of dynamic bulk modulus of gas-liquid mixed fluid.