Their errors are detailed shown in Table 2. It shows that maximum error between the real and ideal values is about 8.69%. Generally, the error is less than 10%, when the gas Mach number is 1.15–1.87. Therefore, we suggest that we can adopt the Eq. (14) to estimate the PRC in the supersonic separation process to improve the design efficiency. Moreover, the numerical results agree well with the theoretical data, which validates that our developed numerical model can accurately predict the supersonic flow a supersonic separator.
5. Conclusions
The characteristic and capability of a supersonic separator to recovery the pressure of natural gas flows were investigated both in theory and numerical simulation. The theoretical equation of PRC was derived with shock wave dynamics. It indicated that the PRC depended on the adiabatic exponent and the gas Mach number in the upstream of the shock wave. A higher adiabatic exponent induced a larger PRC when the gas Mach number is more than 1.3. The gas Mach number was obtained by adapting the expansion ratio of a nozzle. A mathematical model was developed with SST turbulence model to evaluate the gas dynamic parameters with various Mach numbers and their effects on the PRC. The numerical results showed that the increases of the expansion ratio generated a larger gas Mach number and leaded to the lower pressure and temperature accordingly. The theoretical and numerical results both presented that the PRC declined with the increase of the Mach number at the upstream of the shock wave. The numerical results are smaller than the ideal data with the maximum error of about 8.69% in the whole computed gas Mach number from 1.15 to 1.87. It validated that our developed numerical model can accurately predict the supersonic flow a supersonic separator. The suggestion is that the derived theoretical equation can be employed to estimate the PRC in the supersonic separation process to improve the design efficiency.