Spray and Atomization
Spray and Atomization: Theoretical Foundations
Overview
Professor, what does CFD for spray/atomization actually calculate?
It simulates the process where liquid is injected from a nozzle and breaks up into fine droplets (atomization). It is used in the design of all spray processes such as diesel engine fuel injection, gas turbine fuel injection, spray painting, pesticide spraying, and fire extinguisher sprays.
Is it different from droplet breakup models (secondary breakup)?
The spray process is divided into two stages. The breakup of the liquid column or sheet at the nozzle exit into droplets is primary atomization. The further breakup of the generated droplets into smaller ones is secondary breakup. This article deals with modeling the entire spray from primary atomization.
Basic Spray Parameters
What parameters characterize a spray?
The following are the main parameters.
| Parameter | Definition | Meaning |
|---|---|---|
| Weber number $We$ | $\rho_g U_{rel}^2 d / \sigma$ | Aerodynamic force vs Surface Tension |
| Ohnesorge number $Oh$ | $\mu_l / \sqrt{\rho_l \sigma d}$ | Viscosity vs Surface Tension |
| SMD $d_{32}$ | $\sum d_i^3 / \sum d_i^2$ | Sauter Mean Diameter |
| Injection pressure $\Delta p$ | $p_{inj} - p_{amb}$ | Injection energy |
| Spray angle $\theta$ | Cone angle | Spray spread |
SMD (Sauter Mean Diameter) is the most commonly used representative diameter for sprays. Since evaporation and reaction rates are proportional to surface area, a representative diameter based on the volume/surface area ratio is useful.
Primary Atomization Models
How is primary atomization modeled in CFD?
Directly tracking liquid column breakup from the internal nozzle flow is computationally prohibitive, so engineering models are used.
| Model | Overview | Application |
|---|---|---|
| Blob injection | Injects droplets of nozzle diameter size | Diesel injection |
| LISA (Linearized Instability Sheet Atomization) | Instability of sheet-like liquid film | Pressure spray nozzles |
| ELSA (Eulerian-Lagrangian Spray Atomization) | Eulerian liquid phase → Lagrangian droplet transition | Research use |
The Blob injection method, proposed by Reitz (1987), is the most practical approach. It injects droplets (Blobs) of the same size as the nozzle diameter using DPM and then breaks them down further using secondary breakup models (e.g., KHRT).
Rayleigh Breakup——Why Does a Liquid Column Become Droplets?
The reason water falling from a faucet separates into droplets rather than a continuous stream is due to "Rayleigh instability," explained by Rayleigh (1878). A cylindrical liquid column has an inherent instability where disturbances with wavelengths greater than πD are amplified by surface tension, eventually splitting into a nearly uniform droplet train. This instability growth rate is determined by the Weber number and Ohnesorge number of the liquid column and is directly applied to spray nozzle design. Inkjet printers, which generate monodisperse droplets, are a prime example of intentionally controlling Rayleigh breakup, enabling printing at 600 DPI or higher on A4 paper with droplet diameter control within ±1%.
Computational Methods for Spray and Atomization
Details of Numerical Methods
Please tell me the key numerical points for spray simulation.
The biggest challenge in Lagrangian spray calculation is mesh dependency. A large number of parcels concentrate near the nozzle, so the CFD cell size affects the momentum source from the parcels.
Mesh Dependency Problem
Abraham's (1997) guidelines recommend that the liquid volume fraction occupied by each cell be low (ideally below 1%). In practice, mesh near the nozzle is set to 0.5–2 mm, often combined with AMR.
Why is AMR particularly important for sprays?
The spray tip moves, so the region requiring fine mesh changes over time. Using AMR (Adaptive Mesh Refinement) to automatically refine only the regions where the spray exists can significantly reduce computational cost compared to a fixed mesh. CONVERGE has this AMR natively built-in, giving it an advantage in spray calculations.
Influence of Internal Nozzle Flow
In high-pressure injection nozzles, cavitation occurs inside the nozzle, which promotes spray atomization. A method that calculates the internal nozzle flow beforehand and uses the exit turbulence profile and liquid film distribution as inlet conditions for Lagrangian spray calculation is effective for improving accuracy.
Implementation by Tool
| Tool | Primary Atomization | Secondary Atomization | AMR | Features |
|---|---|---|---|---|
| CONVERGE | Blob, KH-ACT | KHRT, TAB | Native | Benchmark for spray calculation |
| Ansys Fluent | Blob, LISA, Flat Fan | TAB, KHRT, SSD | Gradient-based | VOF-to-DPM conversion |
| STAR-CCM+ | Blob, LISA | TAB, KHRT, Reitz-Diwakar | Table-based | Lagrangian/Eulerian hybrid |
| OpenFOAM (sprayFoam) | BlobInjection, ConeInjection | TAB, ETAB, ReitzKHRT | dynamicRefineFvMesh | Fully OSS |
CONVERGE, with its combination of automatic mesh generation and AMR, can significantly reduce the effort of mesh design, making it a standard tool for spray and combustion calculations among engine manufacturers.
Rosin-Rammler Distribution——The Standard for Droplet Size Setting in Spray CFD
The most common method for setting droplet size distribution in spray CFD is the Rosin-Rammler distribution F(d) = 1-exp(-(d/d_bar)^n). Two parameters, d_bar (characteristic diameter) and n (distribution width coefficient), can represent a wide range of spray characteristics. These parameters are determined from actual measurements using laser diffraction (Malvern, etc.), but they vary greatly depending on measurement conditions (liquid pressure, distance from nozzle), so recording "under which conditions the data was measured" is essential. When using CFD with Rosin-Rammler, calibrating d_bar and n so that D32 (Sauter mean diameter) matches actual measurements is the standard procedure in practice.
Spray and Atomization in Practice
Practical Guide
Please explain the steps for spray simulation.
Let's take diesel injection (ECN Spray A conditions) as an example.
1. Gas phase in constant-volume vessel: Nitrogen atmosphere at 900 K, 60 bar
2. Mesh: 0.25 mm near nozzle (automatically refined by AMR), 2 mm far away
3. Injection conditions: n-dodecane, injection pressure 1500 bar, nozzle diameter 90 μm
4. Primary atomization: Blob injection (Blob diameter = nozzle diameter)
5. Secondary atomization: KHRT model
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