A NEW MODEL FOR CAVITATION INDUCED PRIMARY BREAK-UP OF DIESEL SPRAYS

In the case of high pressure diesel injection the flow conditions inside the injection holes have an important influence on the development of the spray. The existence of cavitation structures is known to contribute to the instantaneous break-up of the liquid when it leaves the nozzle. Today the majority of CFD-codes use an Eulerian /Lagrangeian way of description in order to calculate the temporal and spatial distribution of the continuous gas phase and the dispersed liquid. Because of the Lagrangeian way to track the liquid the spray calculation starts with big spherical fuel droplets that are subject to secondary aerodynamic induced break-up. The origin of these drops (primary break-up) is usually not modelled but replaced by assumptions. Today it is well known that this method of treating the primary break-up is not sufficient at all and that the primary break-up in the near nozzle region is mainly dependent on the flow conditions inside the injection holes. In this paper a new model for cavitation and turbulence induced primary break-up is presented, which is able to map the influence of the cavitating nozzle flow on spray break-up. Different locations and sizes of both vapour and liquid zones inside the injection holes lead to different spray structures and cone angles near the nozzle. The model includes cavitation bubble dynamics. It describes the transition from the cavitating flow inside the injection hole to the dense spray near the nozzle and provides all necessary starting conditions for the spray simulation like spray cone angle, drop sizes, velocities etc. The Kelvin-Helmholtz model is used to calculate the secondary break-up. The model has been implemented in the 3-d-CFD code KIVA-3V and a first validation has been done. Introduction In direct injection diesel engines the fuel atomization process strongly affects combustion and exhaust emissions [1]. Fig.1 shows details of the disintegration process which is divided into the primary and the secondary break-up. The primary break-up is the first disintegration of the coherent liquid into big droplets and ligaments near the nozzle. It strongly depends on the flow conditions inside the injection holes that give the starting conditions for the spray break-up. In the case of high pressure injection the presence of cavitation makes the disintegration already begin inside the holes: because of the strong acceleration of the fuel at the inlet of the holes the static pressure decreases considerably. The curvature of the streamlines superimposes an additional radial pressure gradient because of centrifugal forces [2]. At the inlet edge the pressure falls to the vapour pressure resulting in the formation of cavitation structures along the walls. These cavitation structures extend to the exit, leave the nozzle and collapse outside (Fig.1). This results in instantaneous break-up and spray divergence. The turbulent and cavitating nozzle flow has been recognized as the most important influence parameter on the primary break-up in the case of high pressure diesel injection [2,3,4]. The secondary break-up is the further break-up of droplets into smaller ones. Because of the relative velocity between droplet and gas aerodynamic forces make surface waves grow which are then split off and generate small droplets. Today quite sophisticated models for the description of the secondary break-up like Taylor Analogy, KelvinHelmholtz and Rayleigh-Taylor Break-up are implemented in modern CFD-codes. The Lagrangeian way to describe the liquid implies the existence of drops. In order to describe the transition from the coherent liquid inside the nozzle to the primary droplets, sub-models have to be used. Usually uniform droplets whose diameter is equal to the nozzle diameter are assumed to leave the nozzle (Fig.1, blob-method). The starting conditions of these blobs have to be adjusted for each calculation in order to get reasonable results. The influence of the cavitating nozzle flow on the drop size distribution, the spray angle etc. cannot be mapped satisfying. Arcoumanis et al. [5] have developed a cavitation induced atomization model which uses the total area at the exit of the injection hole occupied by cavitation bubbles to calculate the radius of an equivalent bubble having the same area as all bubbles together. The collapse time of this artificial bubble is used as time scale for the atomization process. The collapse energy which contributes to the production of droplets in the primary break-up zone is not included. Huh and Gosman [6] have published a phenomenological model based on the assumption that cavitation and turbulence inside the nozzle holes can be attributed to turbulent fluctuations in the exit flow being the dominant source of perturbations to the free surface. The analysis reproduces measured spray angles tolerably well. However the effects of cavitation are represented in a very crude fashion. Nishimura and Assanis [7] have presented a model for primary atomization based on cavitation bubble collapse energy. It tracks bubble dynamics inside the injector and transfers collapse energy to turbulent kinetic energy. The latter induces an additional break-up force that is balanced with aerodynamic and surface tension forces to determine primary break-up time and total mass of child droplets. The model gives good results but is not able to map the influence of flow asymmetries inside the holes on the 3-d primary spray. Figure 1: Cavitation induced primary break-up (high pressure diesel injection) and blob-method In order to develop an improved primary break-up model for high pressure diesel injection detailed experimental and numerical investigations of the nozzle hole flow have been performed [8]. These investigations have shown that during the quasi-stationary injection phase (full needle lift) there is a stationary distribution of cavitation and liquid regions. Thus the flow can be divided into two zones (Fig. 2): zone 1 (liquid, high momentum) and zone 2 (mixture of cavitation bubbles and liquid ligaments, low momentum). The shape, extension and position of the zones is strongly dependent on the nozzle geometry. Fig. 2 shows the two-zone distribution for an axis-symmetric (geometry A) and a non-axis-symmetric single hole nozzle (geometry B). Details about the exact geometries are published in [8]. In case of geometry A the exit flow consists of an inner liquid flow surrounded by the cavitation zone. This leads to a symmetric primary spray. In case of geometry B the cavitation zone is concentrated at the upper wall resulting in a larger divergence of the upper part of the primary spray. Both geometries are used in this paper to study the behaviour of the new primary break-up model. Figure 2: Two-zone structure of nozzle hole flow Primary break-up model The purpose of the new primary break-up model is to describe the transition from the flow inside the nozzle to the first primary droplets and to provide all starting conditions for the calculation of secondary break-up and spray formation. The input data for the new model like average flow velocity u of the liquid zone, extension, shape and position of liquid (zone 1) and cavitation (zone 2), mass flow of both zones and the average void fraction α = (ρ ρl)/(ρv ρl) of zone 2 are extracted from a CFD calculation of the nozzle hole flow. The indices “v” and “l” indicate vapour and liquid, ρ is the average density. Fig. 3 shows the structure of the primary break-up model. The model assumes that the primary break-up begins already inside the nozzle and that large cylindrical primary ligaments of length L and Diameter D leave the nozzle hole. D is equal to the nozzle diameter and L is equal to the effective diameter of the liquid zone (deff = (4 areazone1/π) ). Smaller areas of zone 1 result in shorter primary ligaments and represent an increased part of the primary break-up that has already taken place inside the nozzle. According to the two-zone nozzle hole flow the primary ligaments also consist of two zones whose distribution is equal to the one at the nozzle exit. The flow velocity u in axial direction is the average velocity of the liquid zone at the nozzle exit. Because the stochastic parcel method is used to simulate the spray break-up process, all cavitation bubbles inside a primary ligament have the same size, but from ligament to ligament the sizes differ. No detailed experimental data about bubble sizes is available in the literature, and a size distribution has to be assumed. For the investigations described in this paper bubble sizes are sampled from a Gaussian distribution ( = r 10 μm, std.dev.:10 μm), but only the part of the curve between a minimum radius of 2 μm and a maximum one of Lcav, max/2 is used ( Lcav, max: see Fig. 4). From the known average void fraction and size of zone 2 the volume of pure vapour and the number of bubbles inside a primary ligament can be calculated. The calculation of bubble dynamics gives the total collapse energy Ecav and the bubble collapse time tcoll . Figure 3: Structure of the new two-zone primary break-up model The break-up of the primary ligament into secondary droplets is assumed to occur at the time tcoll after leaving the nozzle. Furthermore it is assumed that the bubble collapse is homogeneously distributed in zone 2 and that it results in pressure waves which propagate to the interfaces. At the interface between gas and zone 2 the collapse energy Ecav2 reinforces the break-up of zone 2. At the interface between zone 2 and zone 1 the energy Ecav1 is absorbed from zone 1 and contributes to the break-up of the liquid. The ratio Ecav2/Ecav1 is therefore calculated as area of the interface between gas and zone 2 divided by the one between zone 1 and zone 2. The larger the cavitation zone, the bigger the part of energy that is available for the break-up of zone 2. A concentration of a fixed volume of zone 2 e.g. at the upper wall (Fig. 2, geometry B) also make