Simulation of transient effects in a fuel injector nozzle using real-fluid thermodynamic closure

Abstract

Numerical predictions of the fuel heating and cavitation erosion location indicators occurring during the opening and closing periods of the needle valve inside a five-hole common rail Diesel fuel injector are presented. These have been obtained using an explicit density-based solver of the compressible Navier-Stokes (NS) and energy conservation equations; the flow solver is combined with two thermodynamic closure models for the liquid, vapour and vapour-liquid equilibrium (VLE) property variation as function of pressure and temperature. The first is based on tabulated data for a 4-component Diesel fuel surrogate, derived from the Perturbed-Chain, Statistical Associating Fluid Theory (PC-SAFT) Equation of State (EoS), allowing for the variation of the physical and transport properties of the fuel with the local pressure and temperature to be quantified. The second thermodynamic closure is based on the widely used barotropic Equation of State (EoS) approximation between density and pressure only and neglects viscous heating. The Wall Adapting Local Eddy viscosity (WALE) LES model was used to resolve sub-grid scale turbulence while a cell-based mesh deformation Arbitrary Lagrangian–Eulerian (ALE) formulation is used for modelling the injector's needle valve movement. Model predictions are found in close agreement against 0-D estimates of the temporal variation of the fuel temperature difference between the feed and hole exit during the injection period. Two mechanisms affecting the temperature distribution within the fuel injector have been revealed and quantified. The first is ought to wall friction-induced heating, which may result to local liquid temperature increase up to fuel's boiling point while superheated vapour is formed. At the same time, liquid expansion due to the depressurisation of the injected fuel results to liquid cooling relative to the fuel's feed temperature; this is occurring at the central part of the injection orifice. The spatial and temporal temperature and pressure gradients induce significant variations in the fuel density and viscosity, which in turn, affect the formed coherent vortical flow structures. It is found, in particular, that these affect the locations of cavitation formation and collapse, that may lead to erosion of the surfaces of the needle valve, sac volume and injection holes. Model predictions are compared against corresponding X-ray surface erosion images obtained from injector durability tests, showing good agreement.