Case Study No: FTLCFD008
Introduction
Liquid jets in crossflow represent a complex multiphase flow phenomenon characterized by a sequence of atomization processes, including the primary breakup of the liquid column, formation of ligaments, and subsequent generation of droplets through secondary breakup. The resulting flow field exhibits a wide range of length scales—from large liquid structures and ligaments of a few centimeters or millimeters down to fine droplets with diameters on the order of a few microns. Capturing this full spectrum of scales poses a significant challenge for numerical simulation.
Within the framework of the Volume of Fluid (VOF) method, resolving all these scales simultaneously demands extremely fine spatial resolution and a correspondingly large computational mesh. As a result, a purely VOF-based approach becomes computationally prohibitive for practical cases involving liquid jet atomization.
To overcome these limitations, the present study adopts a coupled VOF–DPM (Discrete Phase Model) methodology. In this hybrid approach, the VOF model is employed to resolve the larger liquid structures, such as the jet core and ligament formations, that can be captured within the mesh resolution. Once the liquid fragments reach sizes below the mesh’s resolving capability, they are transitioned into Lagrangian particles using the DPM framework, which efficiently tracks tiny droplets and their subsequent evolution.
This coupling strategy provides a balance between accuracy and computational efficiency, enabling the simulation to capture the essential physics of jet breakup and droplet dispersion with enhanced fidelity while maintaining a manageable computational cost.
Computational Domain and Mesh
The computational model represents a liquid jet injected into a crossflowing gaseous medium, a configuration commonly encountered in fuel injection, spray cooling, and mixing applications. The domain is designed to capture the complex interaction between the liquid jet and the surrounding gas flow, encompassing regions where jet penetration, deformation, and breakup occur.
The geometry consists of a jet nozzle region, where the liquid is introduced, and a surrounding crossflow channel that provides a uniform, fully developed gas stream. Adequate domain extents are maintained upstream and downstream to establish fully developed inflow and outflow boundary conditions, minimizing recirculation or artificial reflections at the boundaries.
The computational domain is sufficiently large to include both the primary breakup region, where the liquid column disintegrates into ligaments and large droplets, and the secondary breakup zone, where these droplets further fragment and disperse into the gaseous crossflow. This ensures accurate prediction of droplet trajectories, dispersion patterns, and size evolution within the crossflow field.
Figure 1. The modelled computational domain of the Jet-in-Crossflow Configuration
A poly-hexcore mesh was generated to achieve an optimal balance between numerical accuracy and computational efficiency. The mesh comprises approximately 0.5 million cells, providing fine spatial resolution in critical regions while maintaining a manageable overall cell count.
Local mesh refinement was implemented in the vicinity of the jet injection zone and along the primary breakup region to accurately capture surface deformation, shear-layer instabilities, and ligament formation. Smooth transitions between hexahedral and polyhedral elements were ensured throughout the domain to enhance solver stability and promote robust convergence during the transient simulation.
To further improve local resolution during the atomization process, Adaptive Mesh Refinement (AMR) was activated at runtime. The AMR algorithm dynamically refines the grid in regions exhibiting high velocity gradients, interface curvature, or liquid–gas interfacial deformation. This adaptive approach allows accurate tracking of jet breakup and droplet formation while avoiding the excessive computational cost associated with a uniformly fine mesh.
Figure 2: The computational mesh for the domain, consisting of 22 million poly-hexcore cells.
Numerical Model
The simulation employs a hybrid multiphase modeling approach, combining an interface-resolving Volume of Fluid (VOF) method with a particle-based Discrete Phase Model (DPM). The VOF model captures the liquid–gas interface dynamics, resolving deformation and primary breakup of the liquid jet into ligaments. Once the detached liquid fragments become smaller than the mesh resolution, they are converted into Lagrangian parcels and tracked using the DPM framework. This transition ensures continuous representation of mass and momentum while maintaining computational efficiency.
The coupled VOF–DPM strategy allows detailed resolution of large-scale liquid structures and efficient tracking of dispersed droplets downstream. This hybrid treatment provides a realistic depiction of jet breakup, droplet dispersion, and secondary breakup processes within the crossflow, while avoiding the excessive computational cost associated with a purely interface-resolving method.
Figure 3: VOF <> DPM Coupling illustration
Figure 3 illustrates the VOF–DPM coupling and AMR refinement near the jet interface. The adaptive refinement dynamically enhances grid resolution in regions of high curvature and shear, ensuring accurate capture of interface instabilities. As the liquid fragments detach, they are seamlessly converted into DPM particles for efficient downstream tracking.
The overall flow field is treated as incompressible and multiphase, with turbulence modeled using a hybrid RANS/LES approach to accurately represent both near-wall and unsteady flow features associated with jet–crossflow interaction.
The boundary conditions for the air and liquid domains are summarized below:
| Boundary | Condition Type | Description |
|---|---|---|
| Inlet | Velocity Inlet | Specifies the uniform air crossflow velocity at domain entry |
| Jet Nozzle | Mass Flow Inlet | Defines the liquid jet injection rate and direction |
| Outlet | Pressure Outlet | Allows smooth outflow of air and entrained droplets |
| Walls | No-Slip Walls | Represents the solid domain boundaries and wall region |
Table 1: Boundary conditions
Results
The coupled VOF–DPM framework effectively reproduces the multistage breakup sequence of a liquid jet in crossflow. The hybrid approach captures the transition from the continuous liquid phase to dispersed droplets with high physical fidelity while maintaining computational efficiency.
Figure 4 illustrates the transition region between the interface-resolved (VOF) and particle-based (DPM) domains. The VOF model accurately resolves jet deformation, surface instabilities, and primary breakup, capturing the formation of ligaments and large droplets. Once the liquid fragments detach and fall below the mesh resolution, they are seamlessly transferred into the DPM phase, where the secondary breakup and droplet dispersion are tracked in a Lagrangian framework.
The adaptive mesh refinement (AMR) dynamically enhances resolution in regions of high curvature and shear, allowing precise representation of interface dynamics and downstream droplet transport without excessive computational cost.
Figures 4 confirm that the simulation successfully captures the multiscale breakup physics, including interface deformation, ligament detachment, and aerodynamically driven droplet dispersion. The results demonstrate that the hybrid VOF–DPM methodology provides a physically consistent and computationally efficient framework for simulating atomizing liquid jets in crossflow.
Figure 5:Cross-flow jet with AMR
| Injection Type | Total Number of Particles | Total Mass (kg) | Minimum Particle Diameter (m) | Overall Sauter Diameter, D (m) |
|---|---|---|---|---|
| Resolved | 19,274 | 6.6065 × 10⁻⁵ | 1.0003 × 10⁻⁴ | 2.0744 × 10⁻⁴ |
| Tiny | 667 | 2.9948 × 10⁻⁷ | 7.4661 × 10⁻⁵ | 9.5256 × 10⁻⁵ |
Table 2. Summary of particle and droplet characteristics for different injection types.
The droplet statistics obtained from the coupled VOF–DPM simulation are summarized in Table 2. The resolved injection (captured by the VOF model) contributes the majority of the particles and total liquid mass, representing the larger droplets and ligaments resulting from the primary breakup process. These droplets exhibit a comparatively larger Sauter mean diameter (D₃₂), indicating dominance of coarse structures near the jet core region.
In contrast, the tiny injection (handled by the DPM model) corresponds to the secondary breakup regime, where finer droplets are produced under the influence of aerodynamic shear and turbulence in the crossflow. These droplets are fewer in number and carry a smaller fraction of the overall mass, but they play a significant role in enhancing spray dispersion and increasing surface area for mixing and evaporation processes.
The absence of droplet formation in the diffuse injection region confirms that the breakup and atomization processes are predominantly governed by the primary and secondary injection zones. Overall, the results in Table 2 demonstrate that the main jet injection controls the bulk of the droplet distribution, while secondary mechanisms enrich the spray field with finer, more uniformly distributed droplets, improving the overall fidelity of the atomization model.
Conclusion
A computational fluid dynamics (CFD) simulation of a liquid jet breakup in a gaseous crossflow was performed using a hybrid VOF–DPM multiphase modeling approach. The interface-resolving VOF model effectively captured the primary breakup of the liquid column, while the DPM framework efficiently tracked the secondary breakup and droplet dispersion processes in the downstream region.
A poly-hexcore mesh with an initial cell count of approximately 0.5 million cells, combined with adaptive mesh refinement (AMR), ensured fine resolution in regions of strong interface deformation while maintaining computational efficiency. The adaptive approach dynamically refined the grid near regions of high curvature and shear, allowing detailed representation of atomization physics without excessive computational cost.
The simulation successfully demonstrated the following key aspects:
- Accurate prediction of primary breakup using interface-resolving VOF techniques.
- Efficient droplet tracking through DPM for secondary breakup and dispersion.
- Adaptive mesh refinement (AMR) in critical flow regions to enhance resolution dynamically.
- Realistic representation of multiphase interactions between liquid and gas phases.
Overall, the hybrid VOF–DPM–AMR framework provides a robust and computationally economical methodology for simulating multiscale liquid jet breakup phenomena in crossflows, achieving a balance between fidelity and performance suitable for both research and engineering applications.
References
- Multiscale modeling of liquid jet breakup in crossflow using VOF with adaptive mesh refinement and particle conversion. Physics of Fluids, 35(12), 125146.
- Bhatia, B., Johny, A., & De, S. (2023). A compressible VOF–LPT coupled solver in OpenFOAM with adaptive mesh refinement for liquid jet breakup simulations. arXiv preprint.
- Hybrid CLSVOF method for primary and secondary breakup of liquid jets in supersonic crossflow. Computers & Fluids, 218, 104840.
- Liu, N., et al. (2019). Numerical simulation of liquid jet primary breakup in Mach 1.5 crossflow using a five-equation compressible two-phase model with adaptive mesh refinement. University of Southampton ePrints.
- High-fidelity compressible multiphase LES with AMR for angled liquid jet breakup in supersonic crossflow. Aerospace Science and Technology, 154, 109453.
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