Injectors and Sprays

CFD is well suited to analyzing and optimizing injectors and sprays by accounting for fluid flows, droplet formation, fluid-structure interactions, and more. It allows engineers to visualize and improve injector designs efficiently, reducing the need for costly and time-consuming experimental testing. 

Effectively modeling injectors and sprays can benefit a number of industries, including electromobility, automotive, chemical processing, and more. For example, spray cooling systems for electronics or other machinery enhance heat dissipation and prevent wear. The agricultural industry may use sprays to evenly distribute pesticides or fertilizers, and the biomedical industry may use injectors and sprays to deliver certain medications. CONVERGE, our state-of-the-art CFD solver, offers a full spectrum of modeling options for injectors and sprays, from traditional Lagrangian modeling to an Eulerian volume of fluid (VOF) methodology to innovative techniques like one-way coupling.

Lagrangian Modeling and Efficient Meshing

Lagrangian approaches track individual particles as they move through a flow field, measuring their trajectories separately and accounting for forces such as gravity, drag, and buoyancy. Because this framework treats the liquid as compact parcels of mass, it is highly suitable for most spray simulations, where the spray initiates, propagates, and dissipates quickly on a small spatial scale. To dynamically capture the important physics of the injection process, you need a high-density grid around the spray. CONVERGE’s Adaptive Mesh Refinement (AMR) technology provides the resolution you need exactly when and where you need it—in these cases, near the injector and along the path of the spray. The combination of AMR and powerful spray models makes CONVERGE uniquely suited to help you achieve grid convergent results in a timely manner.

Submodels for Spray Processes

CONVERGE introduces parcels into the domain at the injector exit, where each parcel represents a collection of liquid drops. Parcels undergo several different physical processes, all of which are critical to capture in a simulation. Since these phenomena occur on length scales that are too small to be resolved economically, CONVERGE includes sub-grid models for simulating liquid atomization, drop breakup, collision and coalescence, turbulent dispersion, and drop evaporation. 

Spray atomization, also known as liquid parcel breakup, can be predicted in CONVERGE through several models. The Kelvin-Helmholtz (KH) breakup model is based on the KH instability, which occurs when there is a velocity difference between the interface of two fluids, leading to the growth of wave-like disturbances at the surface. In the KH breakup model, the atomization process is modeled using the stability analysis of liquid jets, and the breakup of the parcels is calculated based on the fastest growing unstable surface wave. The Rayleigh-Taylor (RT) breakup model accounts for the unstable RT waves that result from the rapid deceleration of drops due to the drag force. Additionally, the Linearized Instability Sheet Atomization (LISA) model [1] is another option for modeling liquid sheet breakup. This model includes a general liquid sheet breakup mechanism and a liquid injection methodology specifically designed for pressure-swirl atomizers. 

When an under-resolved mesh is used in combination with a dense spray, the parcel collision outcomes can become highly grid-sensitive. Higher grid resolutions may be employed to resolve this issue, but they can greatly increase the runtime. To mitigate this problem, CONVERGE offers an adaptive collision mesh option for more accurate collision outcomes on coarse grids, which allows the grid to be tailored to accurately solve the necessary equations without needing to resolve the grid-related artifacts in the dense spray.

Turbulent dispersion submodels may be employed in CONVERGE to account for the effect of turbulent flow on spray parcels. CONVERGE’s RANS and LES turbulence models include source terms that can account for the turbulent eddies that disperse the liquid spray droplets. 

CONVERGE also includes drop vaporization models to simulate the process of a liquid parcel absorbing heat and transitioning into vapor. You can calculate how the radius of a drop changes over time with the Frossling or Chiang correlations in CONVERGE.

Eulerian Modeling

In addition to traditional Lagrangian modeling, CONVERGE offers powerful Eulerian modeling techniques to capture multi-phase flows through a volume of fluid (VOF) approach, which tracks the volume of fluid in each cell, as represented by the void fraction. While the Lagrangian approach views the liquid phase in a simulation as parcels, the Eulerian approach treats all phases as a continuum. CONVERGE offers two solution methods for VOF simulations, including the void fraction solution (VFS) method and the individual species solution (ISS) method. The VFS method solves the transport equation for the void fraction, but is limited to simulations of two-phase flows. On the other hand, the ISS method solves the transport equation for each individual species, which enables the generation of accurate flow solutions with sharp phase interfaces while conserving mass and energy. Another option for modeling multi-phase flow is the MFMF model, which separately solves the momentum equation for each species/phase. This method is able to predict more realistic flow fields for simulations like bubbly, slurry, droplet- or particle-laden flows, pneumatic transport, and mixture separation in a gravitational or rotational field. 

CONVERGE offers a suite of models to capture additional phenomena that may occur in multi-phase flows, such as surface tension, wall adhesion, cavitation with rapid heat transfer, large-scale cavitation, cavitation with high-speed flows, boiling, cavitation with turbulent flows, and dissolved gas.

Eulerian-Lagrangian Spray Atomization (ELSA)

In some cases, applying Eulerian modeling to capture the initial spray behavior is not enough to capture how downstream environmental conditions affect the internal nozzle flow and the ensuing spray. In such situations, a fully Eulerian simulation may become prohibitively expensive due to the requirement of an increasingly fine mesh to accommodate a fluid spray with tiny droplets. In CONVERGE, the ELSA method is a fully coupled approach that provides an accurate solution with a reduced computational expense. The ELSA model tracks the surface area density of the fluid and transitions from Eulerian VOF modeling to Lagrangian parcels once the fluid is sufficiently dispersed. This enables a variety of atomization applications, such as fuel injectors, shower heads, water splashes, and more.

VOF-Spray One-Way Coupling

For an even more computationally efficient approach, CONVERGE offers VOF-spray one-way coupling. In this approach, an Eulerian VOF simulation of internal nozzle flow provides detailed boundary conditions at the nozzle exit. These conditions are then used to initialize parcels for a separate Lagrangian spray simulation. In this manner, the Lagrangian simulation does not need to include the injector geometry, which reduces overall runtime. CONVERGE can use VOF-spray one-way coupling to reproduce hole-to-hole variation in multi-hole injectors.

Example Applications

Fuel Injection

The combustion process can be strongly affected by the exact nature of the fuel spray: droplet velocity, size, and distribution, among other physical attributes. CONVERGE allows you to tailor the degree of accuracy of the fuel injection simulation to the needs of your particular study. You can analyze the injection of liquid fuel via physical models for blob injection, injection distribution, discharge coefficient, and hollow cone and solid cone sprays. With the appropriate use of these models, you can generate an accurate prediction of fuel mass flow through the nozzle. CONVERGE can also simulate the mixing and evaporation of multi-component fuel sprays.

Oil Jets

CFD can be used to study heat transfer of impinging jets, which are used to cool windings and rotors through oil jets in drip, spray, dip, or rotational forms.

In CONVERGE, oil jets designed for cooling applications can be modeled in a VOF simulation. These studies can help you determine what size and shape the inlet and outlet should be to effectively capture the oil stream, how much oil will enter the gallery compared to how much was sprayed (i.e., the capture ratio), the best design of the gallery so that the oil optimally absorbs heat from the piston, and more.

CONVERGE’s conjugate heat transfer (CHT) modeling can improve the accuracy of the simulation by solving the heat distribution within the metal components. Performing CHT modeling in these types of simulations is often computationally expensive because of the disparity in time scales between the heat transfer in the fluid and solid domains. To accelerate these simulations without sacrificing accuracy, CONVERGE offers super-cycling, which freezes the fluid solver periodically to allow the solid solver to progress to steady state. The fixed flow method is another available acceleration method that works particularly well for multi-stream simulations.

Urea Deposition in Aftertreatment Systems

CONVERGE’s state-of-the-art physical models allow you to effectively capture the complex physics of aftertreatment systems, including sprays, catalysts, heat transfer, chemistry, and solid deposit formation. 

Urea deposits are hard crystalline structures that may form on the walls of engine aftertreatment systems. They can affect the system’s efficiency by hindering exhaust gas flow and increasing the pressure drop, which leads to increased backflow. CONVERGE’s fixed flow feature can speed up urea deposit simulations by taking advantage of the time scale disparity between the gas flow and spray pulses, solving the spray and Navier-Stokes equations only during the spray pulse. In this case, the transient spray pulse stream, which progresses more rapidly than the steady-state gas flow, is frozen periodically, allowing the gas to progress before resuming. This scheduled progression efficiently simulates cases that would otherwise be overly computationally expensive.

Fire Management

Lightweight, nimble, and easy to operate, drones are positioned to become a major player in the future of firefighting. CFD can be used to design and optimize drone systems for effective fire suppression. 

If you don’t already have an injector incorporated in your drone geometry, you can easily add one in CONVERGE. The solver can then refine the mesh for the computational domain using AMR and fixed embedding. CONVERGE includes several rotor models to efficiently capture rotor motion, including the actuator-line model and the rotational actuator-disk model. Different kinds of fires, such as pool fires, can be captured by CONVERGE’s detailed chemistry solver and wide variety of combustion models, and the spray of water can be simulated as Lagrangian spray parcels. CONVERGE allows you to observe whether or not the modeled spray will extinguish the fire and tweak parameters accordingly to optimize the drone’s firefighting potential.  

References

[1] Senecal, P.K., Schmidt, D.P., Nouar, I., Rutland, C.J., Reitz, R.D., and Corradini, M.L., “Modeling High-Speed Viscous Liquid Sheet Atomization,” International Journal of Multiphase Flow, 25(6-7), 1073-1097, 1999. DOI: 10.1016/S0301-9322(99)00057-9