10 Inertial and wave effects

Page 1

Inertial effects, produced by the gas unsteady flow. Fluid system included in the intake manifold and engine cylinder during the induction stroke (schematic): This system can be modelled like a single mass ma connected to the piston by a single spring (elasticity ke). All the air mass in the system is supposed to be in the pipe. This air is accelerated and decelerated with relative high velocities (30-60 m/s), hence only its inertia will be considered. Air, already inside the cylinder, is expanded and compressed with small velocities. For this reason, only its elasticity will be considered. The resulting system has the following intrinsic resonance frequency (Helmholtz): A: cross section of the pipe L: duct length from the valve seat to the nearest large volume Vm: mean cylinder volume during induction, Vm= V/2 (r+1)/(r-1) a: air characteristic sound velocity (340-350 m/s). We would expect that the filling capacity of the engine depend on the relation between this system frequency f0 and the piston frequency fp equal ton. A resonant peak occurs when the system frequency f0is about twice the frequency fp of the piston motion. When piston is no more able to suck air (at about half stroke), the air mass inertia helps filling the cylinder since the spring is compressing during the second half of the intake phase. In fact if the fluid system frequency f0 is twice the piston motion fp, the air mass ma, that is compressing the spring becomes fully extended at the half of the inlet stroke. At the end of the inlet stroke (after only half crankshaft revolution), because its oscillation is already complete, ma is again compressed, thus forcing the new charge to enter the cylinder and completely fill it. From the expression above, it becomes possible to compute the engine speed…