Dimensional analysis of hydrogen Knudsen compressor

The genetic algorithm for enhancing the elite preservation strategy is extended to data-driven dimensional analysis and validated in the laminar boundary layer and the temperature difference characteristics of the Knudsen compressor. Microchannel positions, stages, and media are analyzed to verify the unification. The research shows that the pressure rise, Poiseuille flow, and thermal transpiration flow of the Knudsen compressor have a first-order linear relationship with dimensionless numbers. The statistic R2, which measures the accuracy of the prediction, is close to 1, and the error in predicting the maximum pressure rise is within 0.5%. The dimensionless number of pressure rise lies in the relative size of the square of high-pressure and low-pressure Knudsen numbers. The velocity dimensionless number lies in the product of the temperature rise rate and the flow direction Knudsen number. Introducing dimensionless numbers of pressure rise and velocity benefits hydrogen transport, compression, and control. The dimensional analysis method proposed in this study is also helpful for revealing and quantifying the flow mechanism of rarefied gases in microchannels.