validity, Reynolds equation, Navier-Stokes equation, spool valve, cavitation


The purpose of this research is to investigate the validity of the Reynolds equation in spool valve analysis under cavitation. This study is carried out for a laminar and isothermal flow between a sleeve and spool with grooves. The pressure and lateral force obtained from the Reynolds equation and the Navier-Stokes equation are compared with variations of aspect ratio, cross sectional area, and number of grooves. The cavitation phenomenon is considered by using a cavitation model in the Navier-Stokes equation and the Reynolds cavitation boundary condition in the Reynolds equation. A large difference of more than 20% is found between the equations for a lateral force of spool valve with many grooves. It was found that the Reynolds equation is not suitable for calculation of a lateral force of the spool valve with multiple-grooves of which the width and depth are even larger than the clearance under cavitation.


Tsinghua University Press