Modélisation de l'écoulement diphasique dans les injecteurs Diesel

CAV2001:sessionB6.005 410 910 710 5Pressure (Pa)10 310 110 −110 −310 −50.0 200.0 400.0 600.0 800.0 1000.0Mixture density (kg/m 3 )Fig. 2 – HEMlaw of state : P = H(ρ).Kutta advancement, ρ k and U k at pseudo time-step k can be written as, with k = 1, 2, 3 :( ) k ( ) k−1 ∂ρ∂ρρ k = γ k ∆t + ψ k ∆t + ρ k−1∂t∂t( ) k ( ) k−1γ k ∂ρUU k ∂t ∆t + ψk ∂ρU∂t ∆t + ρk−1∗ U k−1(9)=ρ k−1∗P k = H ( ρ k)ρ k ∗ is the density calculated at vertices for the pseudo-time step k, γ k and ψ k the Runge-Kuttascheme constants.As we use an explicit scheme the time step has to obey the following stability criterions :2.4 Boundary conditions(|U| + a) ∆t∆x < 1,µ∆tρ∆x 2 < 1. (10)Due to the strongly transient behaviour of the flow and pressure waves propagation, one hasto compute boundary conditions which allow control of the different waves that cross the boundaries.Indeed, most of the simulation codes which are used nowadays model the injector exit asan imposed pressure, i.e. chamber pressure (P ch ). But as cavitation is closely related to pressurefield, numericals results show that no cavitation structures can reach the injector exit. In fact, they“collapse” numerically as soon as they reach the exit boundary.To prevent from this problem, one has to model more appropriate boundary conditions thatcan take in account pressure waves propagation. For the inlet, the Bernoulli equation is written