Δt —Time increment。 

(2)  Oil  flow  over  the  top  side  face  of  the  first compression  ring。  The  oil  flow  from  the  area  behind  the ring to the area above the ring is caused by squeezing effect, when  the ring moves  towards  to  the  piston  (axial  pumping of  the  ring)  and  due  to  the  pressure  gradient  (Fig。  2)。  The rate is given in Eq。 (3)

of the first compression ring, 

  bf—Overlapping of ring and groove flank, 

  pg—Pressure behind the ring, 

  pc--Pressure of combustion chamber, 

 hf—Gap  height  between  the  ring  and  the  groove flank, 

 fa —Proportional constant。 

(3)  Oil  flow  through  the  gap  into  the  first  inter  ring。  If the pressure in the combustion chamber is greater than that in the first inter ring volume, the gas flow through the ring end of the first piston ring will cause oil transport。 The flow 

rate is given in Eq。 (4)

where  wm—Mass  flow  of  oil  flow  through  the  gap  into the first inter ring, 

       a—Actual area at ring end, 

       η —Dynamic viscosity of the oil, 

       b —Width of ring running surface, 

       fw--Proportional constant。 

The total oil mass is given in Eq。 (5): 

where   ma—Total mass of the throw-off。 

For  the  simulation  of  the  throw-off  mass  of  the  accumulated  oil  between  the  piston  top  land  and  the  liner  wall,  the  entire  film  is  pided  into  several  layers。  Within these  layers  a  constant  acceleration  is  assumed。  The  shear stress  of  the  adjacent  layers  is  defined  by  Newton’s  Law 

(Fig。 3)。 By means of the equilibrium of forces at each layer, the velocity distribution u 

iat the layers can be determined。 The throw-off oil volume can be estimated by Eq。 (6)

where  tm—Mass flow of the throw-off, 

       u—Difference velocity of the oil film, 

       ρ —Density of oil, 

       D —Cylinder bore diameter, 

       Δt —Time increment, 

       ft—Proportional constant, 

       hf—Height of the oil film between top land  and liner。 

2。3   Oil blow through the top ring end gap 

The  pressure  gradient  over  the  top  ring  allows  to compute  the  oil  blow  through  the  end  gap  into  the combustion  chamber,  as  shown  in  Fig。  4。  With  the existence  of  negative  pressure  gradient  over  the  top  ring (combustion  pressure  is  lower  than  that  at  the  first  ring area),  oil  is  blown  through  the  end  gap。  The  oil  quantity due  to  this  effect  is  assumed  as  an  instantaneous  oil  loss and  is  not  exposed  to  the  inertial  forces。  The  blow-back mass rate is given in Eq。 (7)