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arxiv: 2604.23846 · v1 · submitted 2026-04-26 · ⚛️ physics.flu-dyn · physics.comp-ph

An LES model with finite-rate phase change and subgrid spray based on a thermodynamically consistent four-equation multiphase model

Henry Collis , Shahab Mirjalili , Makrand Khanwale , Ali Mani , Gianluca Iaccarino This is my paper

Pith reviewed 2026-05-08 05:26 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn physics.comp-ph
keywords large-eddy simulationmultiphase flowphase changesubgrid sprayEulerian Sigma modelfinite-rate evaporationECN Spray A
0
0 comments X

The pith

A four-equation multiphase model with added subgrid spray and finite-rate phase change predicts evaporating spray behavior accurately.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper develops an LES framework for multiphase multi-component flows built on a four-equation model that enforces strict subgrid equilibrium of pressure, temperature, and velocity. The equilibrium assumption cuts computational cost compared with full non-equilibrium treatments, but the authors add a phase-confined Eulerian Σ model to track subgrid interfacial area without unphysical leakage across interfaces and a finite-rate phase change model whose rates are bounded by Gibbs-free energy equilibration. These two closures are coupled inside the four-equation system to recover predictive capability for complex phase change. The complete framework is shown to reproduce experimental measurements from the ECN Spray A case in both non-evaporating and evaporating regimes.

Core claim

The central claim is that a robust four-equation multiphase model, when augmented with a new phase-confined Eulerian Σ spray equation and an improved finite-rate phase change model thermodynamically bounded by Gibbs-free energy equilibration, satisfies interface equilibrium and phase immiscibility conditions while delivering large computational savings and accurate predictions of subgrid surface area and evaporation rates.

What carries the argument

The phase-confined Eulerian Σ spray model coupled to a Gibbs-free-energy-bounded finite-rate phase change model inside the four-equation multiphase framework.

If this is right

  • The equilibrium assumptions produce substantial computational savings that permit larger domains or finer grids in LES of sprays.
  • The phase-confined Σ model supplies subgrid interfacial area while preventing artificial mass or momentum transfer across resolved interfaces.
  • The bounded phase-change model captures finite-rate evaporation and condensation across a range of spray regimes.
  • Validation on the ECN Spray A case confirms that the combined closures reproduce measured spray penetration and vaporization under both non-evaporating and evaporating conditions.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • If the subgrid equilibrium premise proves robust, analogous closures could be inserted into other four-equation or diffuse-interface models used for boiling or cavitation.
  • The framework suggests that targeted subgrid models for surface area and thermodynamic driving force can compensate for the loss of explicit nonequilibrium variables.
  • Direct comparison against resolved-interface DNS in a regime with strong local temperature or velocity slip would quantify the range of validity of the equilibrium assumption.

Load-bearing premise

The four-equation multiphase model assumes strict subgrid equilibrium of pressure, temperature, and velocity, so the new Σ and phase-change models must restore predictive power under these restrictive conditions.

What would settle it

If the predicted liquid penetration length, vapor mass fraction, or droplet size distribution deviates systematically from experimental data in an evaporating spray test case where subgrid velocity or temperature nonequilibrium is known to be strong, the claim that the equilibrium-based framework remains accurate would be falsified.

Figures

Figures reproduced from arXiv: 2604.23846 by Ali Mani, Gianluca Iaccarino, Henry Collis, Makrand Khanwale, Shahab Mirjalili.

Figure 1
Figure 1. Figure 1: Water-air phase change shock tube. With HEM phase change ( view at source ↗
Figure 2
Figure 2. Figure 2: Air-water phase change shock tube. With HEM phase change ( view at source ↗
Figure 3
Figure 3. Figure 3: Water expansion (cavitation) phase change shock tube. With HEM phase change ( view at source ↗
Figure 4
Figure 4. Figure 4: Grid 1 used for Spray A non-evaporating case. Panel a) shows the view at source ↗
Figure 5
Figure 5. Figure 5: Temporal average of the projected mass density [ view at source ↗
Figure 6
Figure 6. Figure 6: Temporally averaged projected mass density [ view at source ↗
Figure 7
Figure 7. Figure 7: Temporal average of the projected surface area [m view at source ↗
Figure 8
Figure 8. Figure 8: Temporal average of the Sauter mean diameter [m] (SMD) at varying transverse and axial locations compared to view at source ↗
Figure 9
Figure 9. Figure 9: Qualitative comparison between evaporating Spray A experiments [ view at source ↗
Figure 10
Figure 10. Figure 10: Quantitative comparison of liquid penetration into the domain compared to two experimental measurement tech view at source ↗
Figure 11
Figure 11. Figure 11: Comparison of vapor n-dodecane penetration over time between experiments with confidence intervals, and LES view at source ↗
read the original abstract

In this work, an LES model with finite-rate phase change and subgrid spray based on a high-resolution numerical scheme for multiphase multi-component simulations which satisfies interface equilibrium and phase immiscibility conditions is proposed. The multiphase model is based on a robust implementation of the four-equation multiphase model which assumes a strict subgrid equilibrium of pressure, temperature, and velocity. Critically, the equilibrium assumptions of the four-equation model provide large computational savings compared to modeling the full non-equilibrium multiphase system. To obtain predictive capabilities with these restrictive equilibrium assumptions, a new phase-confined form of the Eulerian $\Sigma$ spray model is proposed to predict subgrid interfacial surface area while avoiding unphysical leakage across interfaces. Additionally, an improved finite rate phase change model which is thermodynamically bounded by the equilibration of the Gibbs-free energy is coupled with the $\Sigma$ equation to model complex phase change regimes. The full modeling framework is validated using the Engine Combustion Network (ECN) Spray A case in non-evaporating and evaporating conditions and shows excellent agreement with experimental measurements.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript proposes an LES framework for multiphase multi-component flows with phase change, built on a four-equation equilibrium model that assumes strict subgrid equilibrium of pressure, temperature, and velocity for computational efficiency. To restore predictive capability under these restrictive assumptions, the authors introduce a phase-confined Eulerian Σ spray model that avoids unphysical interfacial leakage and a finite-rate phase-change model thermodynamically bounded by Gibbs-free energy equilibration. The full framework is validated on the ECN Spray A case under both non-evaporating and evaporating conditions, with the abstract claiming excellent quantitative agreement with experimental measurements.

Significance. If the reported agreement with the ECN Spray A benchmark is robust, the work demonstrates a practical route to accurate LES of sprays and phase change at reduced cost relative to fully non-equilibrium multiphase solvers. The targeted closures for subgrid surface area and bounded phase change directly address the limitations of the equilibrium assumptions while preserving thermodynamic consistency, which is a notable strength for applications in combustion and fluid dynamics.

minor comments (2)
  1. The abstract states 'excellent agreement' but does not specify the quantitative metrics (e.g., integrated error norms, pointwise comparisons, or visual metrics) used to support this claim; adding this detail would improve clarity.
  2. The manuscript would benefit from explicit discussion of mesh convergence and sensitivity to the equilibrium assumptions in the validation section, given that these assumptions are described as restrictive.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for the positive assessment of the manuscript and the recommendation for minor revision. We are encouraged that the significance of combining the four-equation equilibrium model with the phase-confined Eulerian Σ spray closure and Gibbs-free-energy-bounded phase change is recognized as a practical route to accurate yet efficient LES of sprays.

Circularity Check

0 steps flagged

No significant circularity detected

full rationale

The paper develops a new modeling framework by extending the four-equation multiphase model with a phase-confined Eulerian Σ spray closure and a thermodynamically bounded finite-rate phase-change model. These additions are introduced to compensate for the restrictive subgrid equilibrium assumptions, and the framework is then validated directly against independent external experimental measurements from the public ECN Spray A dataset under both non-evaporating and evaporating conditions. No load-bearing derivation step, equation, or prediction is shown to reduce by construction to a parameter fit, self-definition, or self-citation chain within the paper itself; the reported agreement therefore constitutes external evidence rather than tautological reproduction of inputs.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the equilibrium assumptions of the four-equation model plus the new subgrid closures; no explicit free parameters or invented physical entities are named in the abstract.

axioms (1)
  • domain assumption Strict subgrid equilibrium of pressure, temperature, and velocity
    Invoked to obtain computational savings while still requiring additional models for predictive accuracy.

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