SPH Simulation of Multiple Droplets Impact and Solidification on a Cold Surface

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

1. The novelty of the manuscript does not rely on physics or modeling advances; it relies on parametric observations.
2. The abstract and the conclusions should include quantitative results.
3. The elasticity and the shrinkage stress of the sold phase were neglected.
4. The thermal properties of the sloid and liquid were identical, which was physically inaccurate for most metals.
5. The transition to a neatly solid state via large viscosity requires physical justification.
6. A discussion is required for the 2D against 3D limitations, and how the dimensional reduction affects the heat transfer or sulfidation time.
7. The influence of wettability on spreading and solidification needs analysis in the results.
8. The Grid/particle convergence for droplet impact simulation needs to be presented clearly.
9. The comparison between this study with VOF, LBM, or experimental studies should be discussed.
10. Minor language revision is required, void using we in the manuscript.
11. There was no direct experimental validity for the multi-droplet solidification, a quantitative comparison with published experimental images is required for the multi-droplet thermal spraying images.
12. A table summarizing validation convergence for the surface tension, wetting, impact and phase change is required.
13. Add dimensionless plots (normalized time, normalized energy release).
14. Discussion for the implications for the coating uniformity, and porosity formation is required.
15. Table for a numerical parameter for the kernel type, smoothing length coefficient, time-step limits, and the material properties should be added.
16. In industrial applications, the simplifications used (No consideration of Temperature-dependent properties, Substrate deformation, and Oxidation, splashing) may limit the use of the manuscript results
17. No uncertainty or sensitivity analysis to Kernel choice, time step, and surface attraction coefficient. This should be stated clearly as a limit in the presented work and can be investigated in the future.
18. In the manuscript, the simulation appears limited to one fluid, one substrate condition, and one fixed Stefan number, this should be stated clearly in the manuscript.

 

 

Comments on the Quality of English Language

A revision is required. Avoid using we in the text.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

This manuscript presents a novel and sound numerical study on multi-droplet impact and solidification on a cold surface using a GPU-accelerated Smoothed Particle Hydrodynamics method. The authors combine fluid-solid interaction, wetting phenomena, heat transfer, and phase change processes in their study on complex droplet behaviors. The detection of both convex and concave solidification morphologies offers interesting information for applications in the thermal spraying or additive manufacturing techniques. This manuscript has a proper structure with a fully articulated methodology, and the numerous figures are generally informative. All these issues are representative of a complete work.

While the research uses a number of classical verification tests such as the Stefan problem, Young-Laplace pressure law, and dynamics of collision between a droplet and the wall, the validation process could be assisted by quantitative verification. While the visual validation provided is useful and convincing, the accuracy of the SPH model could be more robustly demonstrated by including numerical measures, such as error metrics or fit quality indicators, as is usually done in computational fluid dynamics. The comparison involving the Stefan problem, for example, would be assisted by the use of an RMSE value indicating the deviation from the theoretical solution, among others. Similarly, for the surface tension validation, the research could include an R² value for comparison between the model solutions for pressure and the theoretical Young-Laplace formula. Finally, for the collision problem, quantitative validation involving comparison with the reference simulation, such as matching the timing for the maximum spread diameter, would be useful.

These requested amendments are merely clarifying and do not mandate the conduct of any new simulations or alterations to the computational model. I suppose such implementations would enhance transparency and reproducibility by informing the reader more clearly on the accuracy level of the computational solutions compared with existing knowledge.

Therefore, it seems to me that the manuscript can be accepted and published after making minor revisions to support the accuracy of the calculations.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript presents a GPU-accelerated SPH framework for simulating the impact, interaction, and solidification of multiple molten droplets on a cold substrate, with particular relevance to thermal spraying. The topic is timely, and the extension from single-droplet to interacting multi-droplet solidification is a clear contribution. The numerical framework is carefully constructed and validated against several classical benchmarks, including surface tension, wettability, droplet impact, and the Stefan problem, which strengthens confidence in the implementation.

However, several methodological clarifications, quantitative analyses, and presentation improvements are required before the work can be considered for publication.

 

Major comments

1. Physical modeling assumptions

• The solidification model relies on a simplified enthalpy-based criterion that incorporates velocity freezing and artificially increased viscosity. While this approach is common, its limitations should be discussed more explicitly, particularly the neglect of shrinkage, density changes, and differences in solid–liquid properties.
• Heat transfer is limited to conduction; convective effects within the liquid and any interfacial thermal resistance are ignored. The authors should justify this assumption for the chosen Reynolds and Stefan numbers.

2. Validation scope

• Validation is comprehensive for single-droplet cases, but no experimental or high-fidelity numerical comparison is provided for multiple-droplet interactions. Even a qualitative comparison with available experimental splat morphologies from the thermal spraying literature would significantly strengthen the paper.

3. Dimensionality and parameter space

• All simulations appear to be two-dimensional. This limitation should be clearly stated, and its impact on splat morphology, spreading ratios, and solidification time should be discussed, given that real splats are inherently three-dimensional.
• Key dimensionless numbers (Re, Ste) are fixed or varied over a narrow range. The generality of the conclusions (e.g., convex vs. concave patterns) should therefore be stated more cautiously.

4. Quantitative interpretation of results

• The identification of convex and concave solidification patterns is visually clear, but a more objective criterion (e.g., height-to-width ratio, curvature metric, or volume distribution) would enhance rigor.
• The discussion of energy exchange and solidification time would benefit from clearer scaling arguments that link spreading, contact area, and heat flux.

 

Minor comments

• Several typographical errors and inconsistencies are present (e.g., “Renolds” instead of “Reynolds”, inconsistent spacing and punctuation).
• Some figures lack clear axis labels, units, or legends (e.g., spreading ratios and energy-rate plots).
• The manuscript would benefit from a brief comparison table summarizing key differences between CVP and CCP regimes.

Comments on the Quality of English Language

Recommendations for improvement (Priority order)

1. Professional English copy-editing
   Strongly recommended before resubmission.
2. Targeted revision of Abstract and Conclusion
   These sections should be rewritten, not just corrected.
3. Systematic correction of recurring errors
• Articles (a/the)
• Pluralization
• Reynolds spelling
• Spacing and punctuation
4. Reduce redundancy in the Results section
   Especially in figure-related explanations.
5. Final proofreading by a fluent academic English speaker
   Ideally, with experience in fluid mechanics or heat transfer.

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 3 Report

Comments and Suggestions for Authors

This manuscript presents a numerical investigation of multiple molten droplets impacting and solidifying on a cold substrate using a GPU-accelerated SPH framework. The topic is relevant to thermal spraying and related applications, and the extension from single droplet to multi-droplet solidification is of practical interest.

The numerical model is clearly formulated and validated against several benchmark problems, including surface tension, wettability, droplet impact, and the Stefan problem. The identification of two distinct solidification patterns (convex and concave) and the parametric study of droplet spacing provide valuable physical insights into droplet–droplet interactions during solidification.

However, the manuscript still requires major revision before publication. In particular, the quality of the English language needs significant improvement, as grammatical and typographical errors appear throughout the text. Several modeling assumptions (e.g., solidification criteria, identical thermal properties of the solid and liquid phases, and the neglect of interfacial thermal resistance) should be more clearly justified, and their influence on the results should be discussed in greater depth. The conclusions regarding regime classification would also benefit from a broader parametric perspective or more cautious wording.

Overall, the study is technically sound and potentially publishable after major revision, provided it addresses the issues above.

Suggestions for Improvement:

1. Improve English language and clarity
   The manuscript contains numerous grammatical, typographical, and stylistic errors. A thorough language revision by a proficient English speaker or professional editing service is strongly recommended.
2. Clarify and justify solidification criteria
   The criterion requiring a particle to have two solidified neighbors before being treated as solid should be better justified, as it may influence solidification morphology and timing.
3. Discuss modeling assumptions more explicitly
   The assumptions of identical thermal properties for solid and liquid phases and the neglect of interfacial thermal resistance should be discussed earlier in the manuscript, with more explicit statements on how they may affect quantitative accuracy.
4. Justify key numerical parameters
   Critical parameters such as the numerical speed of sound, surface attraction coefficient, and time-step constraints should be briefly justified, and their potential influence on results discussed.
5. Moderate claims on solidification regime classification
   The identification of convex and concave solidification patterns is interesting; however, conclusions about “distinct regimes” should be phrased more cautiously or supported by a broader parametric study (e.g., additional Reynolds or Stefan numbers).
6. Improve consistency of notation and definitions
   Some variables (e.g., characteristic velocity and time scales) are introduced late or inconsistently. All symbols should be clearly defined at first appearance.
7. Strengthen discussion of 2D vs. 3D limitations
   While the use of 2D simulations is justified on computational grounds, the implications for quantitative accuracy and applicability to real thermal spraying processes should be discussed more explicitly.
8. Enhance physical interpretation of energy analysis
   The internal-energy change rate analysis is informative; however, clearer links between mixing, contact area evolution, and heat-transfer mechanisms would strengthen the physical interpretation.
9. Minor technical corrections
   Correct typographical errors in figures and captions (e.g., misspellings, inconsistent axis labels) and ensure consistent formatting throughout the manuscript.

Comments on the Quality of English Language

The text contains frequent grammatical errors, awkward sentence constructions, incorrect article usage, inconsistent verb tenses, and numerous typographical mistakes. In several places, sentences are difficult to follow or ambiguous, which negatively affects the clarity of the scientific arguments. While the overall meaning is usually understandable, the current language quality significantly reduces readability and professionalism.

Common issues include:

• Incorrect or missing articles (“a”, “the”)
• Run-on sentences and sentence fragments
• Repetition of words and phrases
• Inconsistent terminology and phrasing
• Misspellings (e.g., “igored”, “horizentally”, “varises”)
• Non-idiomatic expressions typical of direct translation

Although the scientific content appears technically sound, the manuscript cannot be accepted in its current linguistic form. A comprehensive English revision by a fluent English speaker or a professional language editing service is strongly recommended before resubmission.

Failure to adequately improve the language may prevent reviewers from fully assessing the scientific merit of the work.

Author Response

Please see the attachment

Author Response File: Author Response.pdf