give a detailed map of the pressure in each point of the domain, fundamental when designing containment surfaces. A large number of authors in the literature use a 2D approach to model DDT, mostly because a 3D approach is computationally very expensive.
LNG
LNG Spill Spreading and Dispersion Pool Fire
Flashing Jet
Cascade and Flammable Cloud Formation
De agration to Detonation Rollover
Figure 1.4: All the scenario addressed in the SafeLNG project
This study focuses on liquid cascades (pictured in Figure 1.4) of flammable liquid such as gasoline or LNG. The main risk of a liquid cascade of a hydrocarbon is that there is a high evaporation rate due to the presence of a large number of droplets which will eventually form a flammable cloud that if ignited can lead to catastrophic consequences.
1.5 Physics of the process
The physics of liquid sprays is highly complicated and their modelling is chal-lenging from both an experimental and computational point of view.
Figure 1.5 shows a generic spray. The initial liquid discharged through an orifice starts deforming due to external pressure and hydrodynamic instabilities, and ligaments will detach from the bulk of the liquid. These ligaments are unsta-ble and will later form droplets of quite a large diameter. This initial process is called primary breakup, or also atomization, and it is difficult to model because the timescales related to the process are small and the mechanism depends widely
1.5. PHYSICS OF THE PROCESS
Figure 1.5: Schematic picture of a jet spray
on the orifice size, pressure at which the liquid is discharged and material used.
Once the droplets have become spherical, the forces acting around them due aerodynamics cause the droplets to deform, and if the shape they assume dur-ing the deformation is unstable, breakup will take place, shatterdur-ing the bigger droplets in smaller ones [15]. This process is defined as secondary breakup and several models exist in the literature to account for it [16]. Depending on the We-ber numWe-ber (W e = ρu2d/σ, where d is the droplet diameter, ρ is the fluid density, u is the droplet velocity and σ its surface tension) of the droplet, a different kind of breakup will take place.
Another force acting on liquids in contact with gases is the capillary pressure.
This is defined as the pressure difference across the interface between two im-miscible fluids. This is a result of forces such as surface tension and interfacial tension acting on the fluids. In a wide range of applications the capillary pressure is of high importance, but in the current work it will be neglected mainly because the liquid phase, made primarily by droplets, is at a pressure equal or similar to the one of the surrounding air, therefore the capillary pressure can be neglected.
The importance of gravity acting on the droplets is best represented by the Morton and Eotvos numbers. These numbers are usually very important in the simulation of rising bubbles in liquids and their shape, but in the current appli-cation they will not be considered, mainly because the problems examined are driven by inertia and surface tension.
In order to model a spray completely, two main approaches are ideally used,
1.5. PHYSICS OF THE PROCESS
depending on the region modelled. In the area close to the nozzle, where the bulk of the liquid is present, a Eulerian formulation is advantageous, in order to model properly all the hydrodynamic instabilities due to surface tension and inertia. In the region far from the nozzle, where the droplets have ideally broken up to a stable condition and spherical shape, a Lagrangian approach is more suitable and computationally achievable. Due to growing computational resources, in the past years some researchers [17, 18] have developed hybrid solvers capable to handle both Eulerian and Lagrangian formulations in the same application, where the Eulerian model is used in the close region to the nozzle, while when the droplets have reached a diameter small enough for the cell size the solver switches to a Lagrangian formulation.
In industrial applications, spray can occur widely and their structure and droplet diameter distribution varies case-by-case. For example, in the beauty industry, the nozzle is built in such a way to have the finest droplet distribution possible, so to maximise the vapourisation. This is achieved by controlling the primary atomization using a specific pressure and nozzle diameter. In the current work, atomization and droplet breakup is not attained by the willing of the user, but the liquid release through some kind of orifice in a storage tank is such that the atomization process takes place and the bulk of liquid forms a large number of droplets in the very early stage of the cascade. This is also eased by the fact that hydrocarbons have a low surface tension if compared to water and other liquids, therefore it is easier for the ligaments to break up. Due to the large size of the domain to be analysed, it would be too costly in terms of computational resources to use a Eulerian approach to model the cascade, even only in the spill region in order to model the primary atomization. For this reason, and also using the results available in the literature, a known profile for the droplets diameter is used and a fully Lagrangian approach will be used in the following chapters.
It is worth mentioning that although the two phenomena have few things in common, sprays from pressure nozzles and fuel cascades have some fundamental differences. Although for both cases droplets are formed from the breakup of liquid due to hydrodynamic instabilities, in the case of a fuel cascade droplets accelerate constantly until reaching an asymptotic velocity or hitting the ground.
The size of the droplets and the spill size is also such that liquid formed onto the ground or any solid surface evaporates slowly therefore creating a large pool where droplets interact with a relatively thick liquid region if compared to more conventional sprays where the liquid region is very limited and evaporates much
1.5. PHYSICS OF THE PROCESS
faster. This means that the interaction between liquid particles and walls can lead to different outcomes in the two applications, and that models cannot be exported from one to another easily.