María Dolores Roselló

Validation of a code for modeling cavitation phenomena in Diesel injector nozzles

In this paper, the validity of a code implemented for OpenFOAM^(R) for modeling cavitation phenomena has been checked by comparing data acquired by numerical simulations against data obtained for a simple contraction nozzle and for a real diesel injector nozzle. The comparison of numerical and experimental data has been performed, for the simple nozzle, in terms of mass flow rate, velocity at the exit and pressure and cavitation distributions. The numerical results for the real diesel nozzle geometry have been validated with experimental measurements of mass flow rate, momentum flux and effective injection velocity. The results obtained in both cases and their comparison with available experimental data showed that the model is able to predict with a high level of confidence the behavior of the fluid in such conditions.

Computational study of the cavitation phenomenon and its interaction with the turbulence developed in diesel injector nozzles by Large Eddy Simulation (LES)

Abstract In the present paper, a homogeneous equilibrium model with a barotropic equation of state has been used for modeling cavitation in a real multi-hole microsac nozzle. The turbulence effects have been taking into account by Large Eddy Simulation (LES), using the Smagorinsky model as the sub-grid scale turbulent model and the Van Driest model for the wall damping. Firstly, the code has been validated at real operating diesel engine conditions with experimental data in terms of mass flow, momentum flux and effective velocity, showing that the model is able to predict with a high level of confidence the behavior of the internal flow at cavitating conditions. Once validated, the code has allowed to study in depth the turbulence developed in the discharge orifices and its interaction with cavitation phenomenon.

A semi-implicit space-time CE-SE method to improve mass conservation through tapered ducts in internal combustion engines

In this work, we present a semi-implicit method based on the CE-SE numerical scheme (space time conservation-element and solution-element). In particular, we apply this method to a hyperbolic system that models the dynamics of an unsteady flow along a tapered duct with friction and heat transfer. Conditions on the scheme in order to get real numerical solutions are given. The improvement that offers the semi-implicit method versus the scheme CE-SE is compared by means of numerical simulations based on the property of the mass conservation.

Influence of biofuels on the internal flow in diesel injector nozzles

In this paper, the behavior of the internal nozzle flow of a standard diesel fuel has been compared against a biodiesel fuel (soybean oil) at cavitating and non-cavitating conditions, using a homogeneous equilibrium model. The model takes into account the compressibility of both phases (liquid and vapour) and use a barotropic equation of state which relates pressure and density to calculate the growth of cavitation. Furthermore, turbulence effects have been introduced using a RNG k-@e model. The comparison of both fuels in a real diesel injector nozzle has been performed in terms of mass flow, momentum flux, effective velocity at the outlet and cavitation appearance. The decrease of injection velocity and cavitation intensity for the biodiesel noticed by numerical simulation at different injection conditions, predict a worse air-fuel mixing process.

Numerical simulation of primary atomization in diesel spray at low injection pressure

Atomization involves complex physical processes and gas-liquid interaction. Primary atomization on diesel spray is not well understood due to the difficulties to perform experimental measurements in the near nozzle field. Hence computational fluid dynamics (CFD) has been used as a key element to understand and improve diesel spray.A recent new code for incompressible multiphase flow with adaptive octree mesh refinement has been used to perform simulations of atomization at low injection pressure conditions. The multiphase flow strategy to manage different flows is the volume of fluid (VOF) method. The adaptive mesh allows to locally refine the mesh at each time step where a better resolution is needed to capture important gradients instead of using a static mesh with a fixed and high number of cells which, in turn, would lead to an unaffordable computational cost. Even with this approach, the cell number is very high to achieve a Direct Numerical Simulation (DNS) at reasonable computational cost. To reduce the computational cost, an idea has been explored, the possibility of setting a maximum number of cells of the domain. Following this idea, the code has been tested with different configurations to understand their effects on numerical stability, the change in different spray parameters and the benefits achieved in terms of execution time. The outcomes have been validated against a theoretical model.

Determining the First Probability Density Function of Linear Random Initial Value Problems by the Random Variable Transformation (RVT) Technique: A Comprehensive Study

Deterministic differential equations are useful tools for mathematical modelling. The consideration of uncertainty into their formulation leads to random differential equations. Solving a random differential equation means computing not only its solution stochastic process but also its main statistical functions such as the expectation and standard deviation. The determination of its first probability density function provides a more complete probabilistic description of the solution stochastic process in each time instant. In this paper, one presents a comprehensive study to determinate the first probability density function to the solution of linear random initial value problems taking advantage of the so-called random variable transformation method. For the sake of clarity, the study has been split into thirteen cases depending on the way that randomness enters into the linear model. In most cases, the analysis includes the specification of the domain of the first probability density function of the solution stochastic process whose determination is a delicate issue. A strong point of the study is the presentation of a wide range of examples, at least one of each of the thirteen casuistries, where both standard and nonstandard probabilistic distributions are considered.

Study of the influence of the needle eccentricity on the internal flow in diesel injector nozzles by computational fluid dynamics calculations

In the present paper, a computational study has been performed in order to clarify the effects of the needle eccentricity in a real multihole microsac nozzle. This nozzle has been simulated at typical operating conditions of a diesel engine, paying special attention to the internal flow development and cavitation appearance within the discharge orifices. For that purpose, a multiphase flow solver based on a homogeneous equilibrium model with a barotropic equation of state has been used, introducing the turbulence effects by Reynolds-averaged Navier–Stokes methods with a re-normalization group k–ϵ model. The results obtained from this investigation have demonstrated the huge influence of the needle position on the flow characteristics, showing important hole to hole differences.

Using a homogeneous equilibrium model for the study of the inner nozzle flow and cavitation pattern in convergent-divergent nozzles of diesel injectors

In this paper, the behaviour of the internal nozzle flow and cavitation phenomenon are numerically studied for non-conventional Diesel convergent-divergent nozzles in order to assess their potential in terms of flow characteristics. The used nozzles differ each other in the convergence-divergence level of the orifices but all of them keep the same diameter at the middle of the nozzle orifice. The calculations have been performed using a code previously validated and able to simulate cavitation phenomenon using a homogeneous equilibrium model for the biphasic fluid and using a RANS method (RNG k - e ) as a turbulence modelling approach. For the simulations, one injection pressure and different discharge pressures were used in order to assess the characteristics of nozzles for different Reynolds conditions involving cavitating and non-cavitating conditions.The comparison of the nozzles has been carried out in terms of flow characteristics such as mass flow, momentum flux, effective velocity and other important dimensionless parameters which help to describe the behaviour of the inner flow: discharge coefficient ( C d ), area coefficient ( C a ) and velocity coefficient ( C v ). Additionally, the nozzles have been compared in terms of cavitation inception conditions and cavitation development.The study has shown a high influence on the results of the level of convergence-divergence used in the nozzles. In these nozzles, the vapour originated from cavitation phenomenon came from the throttle of the orifice at the midpoint, and it extended along the whole wall of the divergent nozzle part towards the outlet of the orifice. The main results of the investigation have shown how the different geometries modify the cavitation conditions as well as the discharge coefficient and effective velocity. In particular, the nozzle with highest convergence-divergence level showed cavitation for all the tested conditions while for the nozzle with lowest convergence-divergence level, the cavitation phenomenon could be avoided for high discharge pressures. Additionally, the nozzle with highest convergence-divergence level showed the lowest discharge coefficient values but similar effective injection velocity than the nozzle with lowest level of convergence-divergence level despite of its higher orifice outlet area. Three non-conventional convergent-divergent diesel nozzles are compared.The nozzle with higher convergence-divergence level shows the higher mass flow and momentum flux.The nozzle with higher convergence-divergence level exhibits similar effective velocity than the nozzle with lower level.The nozzle with higher convergence-divergence level is more prone to cavitate.Better mixing process is expected for the nozzle with highest convergence-divergence level.

Probabilistic solution of random homogeneous linear second-order difference equations

Abstract This paper deals with the computation of the first probability density function of the solution of random homogeneous linear second-order difference equations by the Random Variable Transformation method. This approach allows us to generalize the classical solution obtained in the deterministic scenario. Several illustrative examples are provided.

Solving initial and two-point boundary value linear random differential equations: A mean square approach

Abstract This paper deals with the construction of mean square real-valued solutions to both initial and boundary value problems of linear differential equations whose coefficients are assumed to be stochastic processes and, initial and boundary conditions are random variables. A key result to conduct our study is the extension of the Leibniz integral rule to the random framework taking advantage of the so-called random Fourth Calculus. Exact expressions for the main statistical functions (average and variance) associated to the solutions to both problems are also provided. Illustrative examples computing the average and standard deviation are included.