Numerical Simulation on the Opening Delay of a Discharge Reed Valve in Compressors

The opening delay of a discharge reed valve for compressors caused by the stiction force of the oil film between the reed and the valve seat is investigated. The coupling simulation algorithm including models of cavitation in the oil film is developed. In order to check the validity, the numerical simulation is performed under several conditions of a model experiment. The coupling model consists of the reed deformation, the gas flow, and the oil film flow with cavitation. The two-dimensional reed deformation is expressed by expanding natural modes that are obtained by the finite element method using shell elements. The gas flow is expressed by the thermodynamic model under the assumption of the internal reversible process. The two-dimensional oil film pressure distribution is obtained by solving numerically the Reynolds’ equation through the finite volume method. On the model of cavitation in the oil film, in addition to the case in which cavitation is not taken into account, two cavitation models are tested; the static cavitation model (Reynolds’ condition) in which the minimum oil pressure is set to absolute zero, and the dynamic cavitation model in which the oil film pressure can fall to the absolute negative (tensile in the liquid) due to the direct simulation of the bubble expansion. Comparisons on the opening delay time between simulation results and the experimental result show that the static cavitation model gives the earlier delay time than that in the experiment, and the dynamic cavitation model which simulates the absolute negative pressure in the oil film reproduces accurately the experimental delay time. The simulation through the dynamic cavitation model also reproduces well behaviors of cavitation and blow-by flow (oil film rupture) in the oil film captured by the high-speed camera in the experiment. The relation among the pressure, the thickness, and the cavitation area of the oil film that are obtained in the simulation shows the mechanism of the oil film rupture (valve opening), i.e., the cavitation bubbles promote the increase of the oil film thickness during the stiction and the increased oil film thickness causes the recovery of the oil film pressure, and the subsequent blow-by flow (oil film rupture)

Temperature Error Reduction of DPD Fluid by Using Partitioned Runge-Kutta Time Integration Scheme

This study puts emphasis on reducing the temperature error of dissipative particle dynamics (DPD) fluid by directly applying a minimal-stage third-order partitioned Runge-Kutta (PRK3) method to the time integration, which does not include any of additional governing equations and change in the DPD thermostat formulation. The error is estimated based on the average values of both kinetic and configurational temperatures. The result shows that the errors in both temperatures errors are greatly reduced by using the PRK3 scheme as comparing them to those of previous studies. Additionally, the comparison among three different PRK3 schemes demonstrates our recent findings that the symplecticity conservation of the system is important to reduce the temperature error of DPD fluid especially for large time increments. The computational efficiencies are also estimated for the PRK3 scheme as well as the existing ones. It was found from the estimation that the simulation using the PRK3 scheme is more than twice as efficient as those using the existing ones. Finally, the roles of both kinetic and configurational temperatures as error indicators are discussed by comparing them to the velocity autocorrelation function and the radial distribution function. It was found that the errors of these temperatures involve different characteristics, and thus both temperatures should be taken into account to comprehensively evaluate the numerical error of DPD