pith. sign in

arxiv: 2605.19732 · v1 · pith:Z46X2V63new · submitted 2026-05-19 · ⚛️ physics.flu-dyn

Large-eddy simulation of moderately dense evaporating sprays with particle-informed super-resolution

Ruyue Cheng , Ali Shamooni , Andreas Kronenburg , Jan Wilhelm G\"artner , Thorsten Zirwes This is my paper

Pith reviewed 2026-05-20 02:20 UTC · model grok-4.3

classification ⚛️ physics.flu-dyn
keywords large-eddy simulationevaporating sprayssuper-resolutionevaporation modelingdirect numerical simulationparticle-informedspray combustion
0
0 comments X

The pith

Particle-informed super-resolution reconstructs gas fields to match DNS evaporation rates in large-eddy simulations of moderately dense sprays.

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

The paper develops a particle-informed super-resolution technique for large-eddy simulations of evaporating sprays. When the computational mesh is too coarse to supply realistic conditions to standard droplet evaporation models, evaporation rates become inaccurate especially in dense or clustered sprays. The new approach reconstructs finer-scale gas fields around droplets to correct those rates. A sympathetic reader would care because accurate spray evaporation modeling matters for combustion in engines and other practical devices where full-resolution simulations remain too expensive. Validation shows the corrected large-eddy results closely follow evaporation behavior seen in carrier-phase direct numerical simulations.

Core claim

The paper establishes that integrating particle-informed super-resolution into large-eddy simulation allows the computed evaporation rates to closely replicate those obtained from carrier-phase direct numerical simulation. This correction substantially reduces the difference in the predicted fuel mass fraction field between the two approaches. The trained model further generalizes to spray cases with air temperatures, droplet diameters, and turbulent Reynolds numbers that were not present in the training data.

What carries the argument

Particle-informed super-resolution (PISR), a deep-learning method that takes droplet positions as additional input to reconstruct high-resolution gas velocity and scalar fields between droplets for use in evaporation rate calculations.

If this is right

  • Evaporation rates obtained from large-eddy simulation of moderately dense sprays become comparable to those from carrier-phase direct numerical simulation.
  • The fuel mass fraction field predicted by large-eddy simulation shows markedly smaller deviation from the detailed simulation reference.
  • The correction remains effective when air temperature, droplet diameter, or turbulent Reynolds number change from the values used in training.
  • Practical spray combustion calculations can employ coarser meshes without losing accuracy in the evaporation step.

Where Pith is reading between the lines

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

  • Coarser meshes could be used throughout an entire engine-scale spray simulation, lowering overall computational cost while preserving evaporation accuracy.
  • The same reconstruction idea might be tested on other subgrid phenomena in multiphase flows such as breakup or collision modeling.
  • Coupling the corrected evaporation fields with ignition and flame models could improve predictions of ignition delay in clustered spray regions.

Load-bearing premise

The super-resolution network trained on a limited set of spray configurations can accurately reconstruct inter-droplet gas fields for evaporation modeling across cases that differ in air temperature, droplet diameter, and turbulent Reynolds number.

What would settle it

Running a carrier-phase direct numerical simulation and a PISR large-eddy simulation on a spray configuration whose temperature, droplet size, or Reynolds number lies outside the training distribution and finding large persistent differences in evaporation rate or fuel mass fraction would falsify the central claim.

Figures

Figures reproduced from arXiv: 2605.19732 by Ali Shamooni, Andreas Kronenburg, Jan Wilhelm G\"artner, Ruyue Cheng, Thorsten Zirwes.

Figure 1
Figure 1. Figure 1: Workflow of the (a) PISR and (b) PISR-LES. [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Computational domain [PITH_FULL_IMAGE:figures/full_fig_p003_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: A priori test: fuel mass fraction in a longitudinal section of a model input (LR), output (PISR) and the target (CP￾DNS) [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: A priori test: PDFs of fuel mass fraction in three transverse sections. 4 [PITH_FULL_IMAGE:figures/full_fig_p004_4.png] view at source ↗
Figure 6
Figure 6. Figure 6: One-dimensional velocity spectra in three trans [PITH_FULL_IMAGE:figures/full_fig_p005_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Plane-averaged volumetric evaporation rates. [PITH_FULL_IMAGE:figures/full_fig_p005_7.png] view at source ↗
Figure 5
Figure 5. Figure 5: Decay of turbulent kinetic energy along the stream [PITH_FULL_IMAGE:figures/full_fig_p005_5.png] view at source ↗
Figure 9
Figure 9. Figure 9: One-dimensional velocity spectra in three trans [PITH_FULL_IMAGE:figures/full_fig_p006_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Plane-averaged volumetric evaporation rates of generalization test cases. [PITH_FULL_IMAGE:figures/full_fig_p006_10.png] view at source ↗
Figure 11
Figure 11. Figure 11: PDFs of filtered fuel mass fraction of generalization test cases. [PITH_FULL_IMAGE:figures/full_fig_p006_11.png] view at source ↗
Figure 12
Figure 12. Figure 12: One-dimensional velocity spectra of case Ret84. [PITH_FULL_IMAGE:figures/full_fig_p007_12.png] view at source ↗
read the original abstract

In large-eddy simulation (LES) of dense sprays or sprays with pronounced clustering, evaporation rates can be inaccurate when the mesh is too coarse to provide realistic boundary conditions for the widely employed single droplet evaporation model. This is especially relevant to liquid spray combustion in practical applications. Deep learning-based super-resolution (SR) has recently emerged as a promising method for LES subgrid-scale modeling, capable of enhancing flow field resolution. This technique appears well-suited to reconstruct the local gas fields within the inter-droplet space that can be used to correct the evaporation rates. However, it has not yet been applied for this purpose. This paper presents an innovative SR approach $-$ particle-informed super-resolution (PISR) $-$ that approximates high-resolution flow fields for improved evaporation computation. It is validated with a priori, a posteriori and generalization tests on moderately dense sprays. The results show that PISR-LES can closely replicate the evaporation rates computed in a carrier-phase direct numerical simulation (CP-DNS), significantly reducing the discrepancy in the fuel mass fraction field between LES and CP-DNS. Furthermore, the PISR model exhibits robust generalization to cases unseen in training when varying air temperature, droplet diameter, and turbulent Reynolds number.

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

1 major / 2 minor

Summary. The manuscript introduces particle-informed super-resolution (PISR), a deep-learning approach that reconstructs high-resolution gas temperature and vapor fields around droplets from coarse LES data and particle positions. These reconstructed fields are then used to supply improved boundary conditions to the standard single-droplet evaporation model. The method is tested on moderately dense evaporating sprays through a priori tests, a posteriori LES runs, and generalization experiments that vary air temperature, droplet diameter, and turbulent Reynolds number. The central claim is that PISR-LES reproduces evaporation rates obtained from carrier-phase DNS (CP-DNS) and substantially reduces the discrepancy in the fuel mass-fraction field relative to standard LES.

Significance. If the reported accuracy gains hold under realistic LES conditions, the approach could allow coarser meshes to be used for spray combustion simulations without sacrificing evaporation-rate fidelity, which is a practical advantage for engineering-scale computations. The paper is credited for performing the three complementary validation tiers (a priori, a posteriori, generalization) and for explicitly incorporating particle locations into the super-resolution network.

major comments (1)
  1. [Generalization tests] Generalization section: the reported generalization tests vary air temperature, droplet diameter, and turbulent Reynolds number, yet they appear to supply the network with low-resolution fields obtained by filtering high-fidelity DNS rather than with fields that already contain the modeling errors typical of an actual LES (filtered velocity, subgrid scalar transport, etc.). Because the central claim concerns PISR-LES performance, this domain-shift issue is load-bearing; a quantitative assessment of reconstruction error when the input is taken from a standard LES run (rather than filtered DNS) is needed to support the claim that evaporation rates closely replicate CP-DNS.
minor comments (2)
  1. [Abstract] Abstract and results sections: quantitative error metrics (e.g., L2 norms on evaporation rate or fuel mass fraction), mesh resolutions, and training-set size are not stated; these numbers should be added for reproducibility.
  2. [Method] Notation: the distinction between the super-resolved fields used for evaporation and the fields used for the carrier-phase LES evolution is not always explicit; a short clarifying paragraph or diagram would help.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the constructive and detailed review of our manuscript. The single major comment raises an important point about domain shift in the generalization tests, which we address directly below. We agree that this warrants clarification and additional analysis to strengthen the support for our central claims regarding PISR-LES performance.

read point-by-point responses

  1. Referee: [Generalization tests] Generalization section: the reported generalization tests vary air temperature, droplet diameter, and turbulent Reynolds number, yet they appear to supply the network with low-resolution fields obtained by filtering high-fidelity DNS rather than with fields that already contain the modeling errors typical of an actual LES (filtered velocity, subgrid scalar transport, etc.). Because the central claim concerns PISR-LES performance, this domain-shift issue is load-bearing; a quantitative assessment of reconstruction error when the input is taken from a standard LES run (rather than filtered DNS) is needed to support the claim that evaporation rates closely replicate CP-DNS.

    Authors: We appreciate the referee's observation on this domain-shift issue. The generalization experiments were designed to assess robustness to changes in air temperature, droplet diameter, and turbulent Reynolds number while using low-resolution inputs obtained by filtering the high-fidelity DNS data. This choice maintains consistency with the training procedure and isolates the impact of parameter variations on reconstruction quality. The primary validation of PISR-LES performance under realistic conditions is provided by the a posteriori tests, in which the network receives inputs directly from the evolving LES solution (including subgrid-scale modeling effects) and is shown to improve evaporation rates toward CP-DNS levels. Nevertheless, we acknowledge that the generalization section does not yet include a direct quantitative assessment using actual LES-generated fields. In the revised manuscript we will add this assessment: for the same parameter variations, we will extract low-resolution fields from standard (non-PISR) LES runs, apply the trained PISR network, and report the resulting reconstruction errors together with the achieved evaporation-rate accuracy relative to CP-DNS. These results will be presented in an expanded generalization section with an additional figure or table. revision: yes

Circularity Check

0 steps flagged

No circularity: validation against independent CP-DNS provides external grounding

full rationale

The paper trains a particle-informed super-resolution network on selected spray configurations and evaluates it via a priori, a posteriori, and generalization tests that compare reconstructed evaporation rates and fuel mass fraction fields directly to carrier-phase DNS results. These benchmarks are generated from separate high-fidelity simulations whose governing equations and numerical resolution are independent of the trained network weights. No equation or claim reduces a reported prediction to a fitted parameter by construction, nor does any load-bearing step rely on a self-citation chain whose content is itself unverified within the present work. Generalization across air temperature, droplet diameter, and Reynolds number is tested on unseen cases, keeping the derivation self-contained against external data.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Only the abstract is available, so the ledger is necessarily incomplete. The approach likely relies on a trained neural network whose weights constitute fitted parameters, but no explicit free parameters, axioms, or invented physical entities are identifiable from the provided text.

pith-pipeline@v0.9.0 · 5762 in / 1054 out tokens · 27761 ms · 2026-05-20T02:20:42.407104+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

Works this paper leans on

29 extracted references · 29 canonical work pages

  1. [1]

    Current status of droplet and liquid com- bustion,

    G. M. Faeth, “Current status of droplet and liquid com- bustion,”Prog. Energy Combust. Sci., vol. 3, no. 4, pp. 191–224, 1977

    work page 1977

  2. [2]

    Droplet vaporiza- tion model for spray combustion calculations,

    B. Abramzon and W. A. Sirignano, “Droplet vaporiza- tion model for spray combustion calculations,”Int. J. Heat Mass Transf., vol. 32, no. 9, pp. 1605–1618, 1989

    work page 1989

  3. [3]

    Grid dependence of evaporation rates in Euler-Lagrange sim- ulations of dilute sprays,

    M. Sontheimer, A. Kronenburg, and O. T. Stein, “Grid dependence of evaporation rates in Euler-Lagrange sim- ulations of dilute sprays,”Combust. Flame, vol. 232, p. 111515, 2021

    work page 2021

  4. [4]

    Burning characteristics of premixed sprays and gas- liquid coburning mixtures,

    K. Nakabe, Y . Mizutani, T. Hirao, and S. Tanimura, “Burning characteristics of premixed sprays and gas- liquid coburning mixtures,”Combust. Flame, vol. 74, no. 1, pp. 39–51, 1988

    work page 1988

  5. [5]

    Measurement of the local group combustion number of droplet clusters in a premixed spray stream,

    F. Akamatsu, Y . Miutani, M. Katsuki, S. Tsushima, and Y . D. Cho, “Measurement of the local group combustion number of droplet clusters in a premixed spray stream,” Symp. (Int.) Combust., vol. 26, no. 1, pp. 1723–1729, 1996

    work page 1996

  6. [6]

    Observation of combustion characteristics of droplet clusters in a premixed-spray flame by simultaneous monitoring of planar spray images and local chemi- luminescence,

    S. Tsushima, H. Saitoh, F. Akamatsu, and M. Katsuki, “Observation of combustion characteristics of droplet clusters in a premixed-spray flame by simultaneous monitoring of planar spray images and local chemi- luminescence,”Symp. (Int.) Combust., vol. 27, no. 2, pp. 1967–1974, 1998

    work page 1967

  7. [7]

    Combustion of partially premixed spray jets,

    M. Mikami, K. Yamamoto, O. Moriue, and N. Kojima, “Combustion of partially premixed spray jets,”Proc. Combust. Inst., vol. 30, no. 2, pp. 2021–2028, 2005

    work page 2021

  8. [8]

    Optical characterization of droplet clusters and group combustion in spray diffusion flames,

    M Manish and S. Sahu, “Optical characterization of droplet clusters and group combustion in spray diffusion flames,”Proc. Combust. Inst., vol. 38, no. 2, pp. 3409– 3416, 2021

    work page 2021

  9. [9]

    Group combustion of liq- uid droplets,

    H. H. Chiu and T. M. Liu, “Group combustion of liq- uid droplets,”Combust. Sci. Technol., vol. 17, no. 3-4, pp. 127–142, 1977

    work page 1977

  10. [10]

    Group evaporation of small- and large-scale droplet clusters in a fuel spray- laden homogeneous and isotropic turbulent airflow,

    N. Pandurangan and S. Sahu, “Group evaporation of small- and large-scale droplet clusters in a fuel spray- laden homogeneous and isotropic turbulent airflow,” Proc. Combust. Inst., vol. 40, no. 1, p. 105434, 2024

    work page 2024

  11. [11]

    Fuel droplet vaporization and spray combustion theory,

    W. A. Sirignano, “Fuel droplet vaporization and spray combustion theory,”Prog. Energy Combust. Sci., vol. 9, no. 4, pp. 291–322, 1983

    work page 1983

  12. [12]

    Advances in droplet array combus- tion theory and modeling,

    W. A. Sirignano, “Advances in droplet array combus- tion theory and modeling,”Prog. Energy Combust. Sci., vol. 42, pp. 54–86, 2014

    work page 2014

  13. [13]

    Using physics-informed enhanced super-resolution generative adversarial networks for subfilter modeling in turbulent reactive flows,

    M. Bode, M. Gauding, Z. Lian, D. Denker, M. Davi- dovic, K. Kleinheinz, J. Jitsev, and H. Pitsch, “Using physics-informed enhanced super-resolution generative adversarial networks for subfilter modeling in turbulent reactive flows,”Proc. Combust. Inst., vol. 38, no. 2, pp. 2617–2625, 2021

    work page 2021

  14. [14]

    Applying physics-informed enhanced super- resolution generative adversarial networks to large-eddy simulations of ECN spray C,

    M. Bode, “Applying physics-informed enhanced super- resolution generative adversarial networks to large-eddy simulations of ECN spray C,”SAE Int. J. Adv. Curr . Prac. Mobil., vol. 4, no. 2022-01-0503, pp. 2211–2219, 2022

    work page 2022

  15. [15]

    M. Bode, M. Gauding, D. Goeb, T. Falkenstein, and H. Pitsch, “Applying physics-informed enhanced super- resolution generative adversarial networks to turbulent premixed combustion and engine-like flame kernel di- rect numerical simulation data,”Proc. Combust. Inst., vol. 39, no. 4, pp. 5289–5298, 2023

    work page 2023

  16. [16]

    Unsupervised and super- vised machine learning pipeline for super-resolution- based subgrid scale modelling in coarse-grid large-eddy simulations,

    S. Maejima and S. Kawai, “Unsupervised and super- vised machine learning pipeline for super-resolution- based subgrid scale modelling in coarse-grid large-eddy simulations,”J. Fluid Mech., vol. 1013, p. A28, 2025

    work page 2025

  17. [17]

    Super-resolution of turbu- lent velocity fields in two-way coupled particle-laden flows,

    A. Shamooni, R. Cheng, T. Zirwes, H. Tofighian, O. T. Stein, and A. Kronenburg, “Super-resolution of turbu- lent velocity fields in two-way coupled particle-laden flows,”Phys. Fluids, vol. 37, no. 9, p. 093383, 2025

    work page 2025

  18. [18]

    Three-dimensional super-resolution reconstruction of turbulent spray flow fields,

    R. Cheng, A. Shamooni, T. Zirwes, and A. Kronenburg, “Three-dimensional super-resolution reconstruction of turbulent spray flow fields,” inILASS Europe 2025

    work page 2025

  19. [19]

    Super-resolution reconstruction of scalar fields from the pyrolysis of pulverised biomass using deep learning,

    A. Shamooni, R. Cheng, T. Zirwes, O. T. Stein, and A. Kronenburg, “Super-resolution reconstruction of scalar fields from the pyrolysis of pulverised biomass using deep learning,”Proc. Combust. Inst., vol. 41, p. 105982, 2025

    work page 2025

  20. [20]

    ESRGAN: Enhanced super-resolution generative adversarial networks,

    X. Wang, K. Yu, S. Wu, J. Gu, Y . Liu, C. Dong, Y . Qiao, and C. C. Loy, “ESRGAN: Enhanced super-resolution generative adversarial networks,” inECCV 2018 Work- shops, pp. 63–79, 2019

    work page 2018

  21. [21]

    Investigation of the generalization capabil- ity of a generative adversarial network for large eddy simulation of turbulent premixed reacting flows,

    L. Nista, C. D. K. Schumann, T. Grenga, A. Attili, and H. Pitsch, “Investigation of the generalization capabil- ity of a generative adversarial network for large eddy simulation of turbulent premixed reacting flows,”Proc. Combust. Inst., vol. 39, no. 4, pp. 5279–5288, 2023

    work page 2023

  22. [22]

    Influence of ad- versarial training on super-resolution turbulence recon- struction,

    L. Nista, H. Pitsch, C. D. K. Schumann, M. Bode, T. Grenga, J. F. MacArt, and A. Attili, “Influence of ad- versarial training on super-resolution turbulence recon- struction,”Phys. Rev. Fluids, vol. 9, no. 6, p. 064601, 2024

    work page 2024

  23. [23]

    Improved super-resolution reconstruction of turbulent flows with spectral loss function,

    R. Cheng, A. Shamooni, T. Zirwes, and A. Kronenburg, “Improved super-resolution reconstruction of turbulent flows with spectral loss function,”Phys. Fluids, vol. 37, no. 3, p. 035208, 2025

    work page 2025

  24. [24]

    On the physical mech- anisms of two-way coupling in particle-laden isotropic turbulence,

    A. Ferrante and S. Elghobashi, “On the physical mech- anisms of two-way coupling in particle-laden isotropic turbulence,”Phys. Fluids, vol. 15, no. 2, pp. 315–329, 2003

    work page 2003

  25. [25]

    Decaying versus sta- tionary turbulence in particle-laden isotropic turbu- lence: Turbulence modulation mechanism,

    A. H. Abdelsamie and C. Lee, “Decaying versus sta- tionary turbulence in particle-laden isotropic turbu- lence: Turbulence modulation mechanism,”Phys. Flu- ids, vol. 24, no. 1, p. 015106, 2012

    work page 2012

  26. [26]

    Modelling sub-grid passive scalar statistics in moderately dense 8 Preprint submitted to Proceedings of the Combustion Institute evaporating sprays,

    B. Wang, A. Kronenburg, and O. T. Stein, “Modelling sub-grid passive scalar statistics in moderately dense 8 Preprint submitted to Proceedings of the Combustion Institute evaporating sprays,”Flow Turbul. Combust., vol. 103, no. 2, pp. 519–535, 2019

    work page 2019

  27. [27]

    BasicSR: Open source image and video restoration toolbox

    X. Wang, L. Xie, K. Yu, K. C. Chan, C. C. Loy, and C. Dong, “BasicSR: Open source image and video restoration toolbox.” https://github.com/XPixelGroup/BasicSR

    work page

  28. [28]

    A condi- tional deep learning model for super-resolution recon- struction of small-scale turbulent structures in particle- laden flows,

    H. Tofighian, J. A. Denev, and N. Kornev, “A condi- tional deep learning model for super-resolution recon- struction of small-scale turbulent structures in particle- laden flows,”Phys. Fluids, vol. 36, no. 11, p. 115173, 2024

    work page 2024

  29. [29]

    Unsupervised deep learning for super-resolution reconstruction of tur- bulence,

    H. Kim, J. Kim, S. Won, and C. Lee, “Unsupervised deep learning for super-resolution reconstruction of tur- bulence,”J. Fluid Mech., vol. 910, p. A29, 2021. 9

    work page 2021