CFD analysis of a ringless piston's secondary motion and the validity of Reynolds equation

In the present study the validity of Reynolds equation for the lubrication flow within a ringless piston-cylinder system, with dynamic effects, is considered. The secondary motion, due to perturbations, of a stepped profiled piston is investigated to assess its dynamic response and stability. A variety of problems with different geometries and operating conditions are solved, for different initial conditions, using both Reynolds equation and Navier–Stokes based model. To examine the validity of Reynolds equation, normalized parameters were established. Two dimensionless parameters were considered—the reduced Reynolds number, \({\text{Re}}^{*}\) and the unsteady Reynolds number, \({\text{S}} \cdot {\text{Re}}^{*}\). The discussion is separated to the steady state solution and the initial transient response. Generally, it is found that the stability of the steady solution acquired by Reynolds equation is valid even for higher values of the reduced Reynolds number, \({\text{Re}}^{*}\) (up to 2) which includes most of hydrodynamic lubrication applications and it is not affected by the unsteady Reynolds number, \({\text{S}} \cdot {\text{Re}}^{*}\). For unstable steady solution, the unsteady Reynolds number, \({\text{S}} \cdot {\text{Re}}^{*}\), may affect the validity of Reynolds equation. For the transient response, it was found that the Reynolds equation is not valid for \({\text{S}} \cdot {\text{Re}}^{*} > 0.05\), since its solution is over damped, compared to the Navier–Stokes based model. Therefore, using Reynolds equation might lead to a failure in detection of a collision between the vibrating piston and the cylinder.