RESEARCH FOR THE TURBULENT TWO-PHASE FLOW GOVERNING EQUATIONS IN DIRECT-INJECTION ENGINE

Abstract

To calculate the governing equations for the turbulent two-phase flow an Extended TAB-model (TP) model is presented to fit for the gas phase and the liquid phase. In the gas phase, Favre-averaging is used for continuity equation, momentum equation. As a result of the averaging, unclosed terms appear which require modeling. In order to close the turbulent Reynolds stress tensor in the momentum equation, the so-called Boussinesque-approximation, which is based on an analogy between molecular diffusion and diffusion turbulent eddies, has been employed. Turbulent kinetic energy k equation and turbulent dissipation ε equation are added to close the Navier-Stokes equations. The temporal differencing scheme in CFD(computational fluid dynamics) code (KIVA-3V) is largely implicit. In the Lagragian phase, implicit differencing is used for all diffusion terms and terms associated with pressure wave propagation. A method similar to the Semi-Implicit Method for Pressure Linked Equations (SIMPLE)-algorithm is used to solve the couple implicit set of equations. In the liquid phase, probability density function (PDF) method is used for solving droplet spray equation. Taylor Analogy Breakup (TAB) model used in the standard KIVA-code is extended with a deformation velocity such that their lifetime is extended to match experimentally observed jet breakup lengths. Furthermore, other models such as Rayleigh-Taylor (R-T) model, Discrete Droplet Models (DDM) etc are discussed. Finally, cylinder pressure and corresponding heat release rates in a directed-injection diesel engine are calculated and compared with the experiments. It gives the theory and method about calculating turbulence exactly in directed-injection diesel engine.

DOI: http://dx.doi.org/10.5755/j01.mech.18.1.1283