Numerical Evaluation of Aerosol Propagation in Wind Instruments Using Computational Fluid Dynamics
, Julien Néchab 1,†, Romain Viala 2,3,*, Milena Creton 4 and Michael Jousserand 4Round 1
Reviewer 1 Report
Comments and Suggestions for Authors
The research article titled "Numerical evaluation of the aerosol propagation in wind instruments using computed fluid dynamics" by Soubrié et al., is an article interested in a topic of growing interest, that is, aerosol-mediated disease spread in closed spaces. The article is well structured, and provides a good overview of the state of the art.
However, I am concerned about the material and methods section, which provides detailed information on the computational setup used in this article, but in my opinion a statement on the validation and verification of the methods used would be necessary, then this is a point to reinforce in the paper and the main reason why my suggestion is that the paper needs improvements prior publication.
A explicit mention of the validation and verification into the material and methods section would be necessary to add, and of course, if available, a description on how the computational results were compared to experimental data or benchmark cases, explaining any discrepancies observed as well. The article would also benefit from a sensitivity analysis.
Comments for author File: 
Comments.pdf
Comments on the Quality of English Language
The article would benefit from grammatical corrections. Please see the attached pdf in which some suggestions have been made in the first few paragraphs, although the entire manuscript needs to be carefully reviewed.
Author Response
We appreciate the time and effort dedicated to reviewing our manuscript, and we thank you for recognizing its potential contribution. Regarding your concerns about the methodology and the use of doctoral thesis citations, we have carefully considered your comments and have made several revisions to our manuscript. Please find below our responses to your specific points.
The research article titled "Numerical evaluation of the aerosol propagation in wind instruments using computed fluid dynamics" by Soubrié et al., is an article interested in a topic of growing interest, that is, aerosol-mediated disease spread in closed spaces. The article is well structured, and provides a good overview of the state of the art. However, I am concerned about the material and methods section, which provides detailed information on the computational setup used in this article, but in my opinion a statement on the validation and verification of the methods used would be necessary, then this is a point to reinforce in the paper and the main reason why my suggestion is that the paper needs improvements prior publication.
A explicit mention of the validation and verification into the material and methods section would be necessary to add, and of course, if available, a description on how the computational results were compared to experimental data or benchmark cases, explaining any discrepancies observed as well. The article would also benefit from a sensitivity analysis.
Response :
In the current version, the Appendix C details the different elements that have been raised, further numerical analysis is proposed here to demonstrate the attention paid to numerical quality. It is applied on the case of the clarinet. Regarding the mesh, it is
automatically computed, although manually tuned to achieve targeted cell sizes. It uses a cartesian meshing technology, meaning that cells are cubic. Local refinement is achieved by progressively cutting cells by two in all directions up to the targeted cell sizes (octree technique). The nominal mesh contains 0.6 million cells. The basic cell size is 15 mm. It is increased by a factor of 3 in the farfield. On the opposite, it is refined so that the mesh contains at least 10 cells in all cross-sections (tube, tone-holes). It is also refined up to 5 times close to walls, reaching 0.5 mm at the wall. For the considered flow rate, the y+ ranges from 4 close to the injection plane to 0.5 at the bell inlet. It is therefore below 5, allowing for the resolution of the viscous sub-layer instead of its modelling through the use of wall laws.
Two other meshes have been investigated for mesh convergence analysis: a coarser mesh and a finer one. They are basically obtained by multiplying or dividing, respectively, the basic cell size by a factor of 2. For the coarse mesh however, cell size is maintained at walls to the same level as in the basic mesh, in order to ensure satisfactory y+. Figure A5 shows how the ratio of air coming out through the bell varies with respect to the mesh. Since the discrepancy between the nominal mesh and the fine mesh is low, the set-up corresponding to the nominal mesh is applied for all instruments. Regarding the convergence toward a steady state, about 250 iterations are necessary to reach the stabilisation of physical quantities defined as goals in the simulation. These quantities are chosen by the user. In the present study, we monitored the convergence for the following quantities:
• average and maximum velocity for each component in the computational domain,
• min, max and average pressure in the computational domain,
• flow rate and average total pressure through bell exit.
The levels of convergence are below 0.001 Pa for pressures, below 0.004 m/s (0.7%) for velocities and 0.01 l/min (0.1%) for flow rate. The solver does not provide the monitoring of residuals. Besides, the time step is automatically chosen, in order to fulfill internal stability criteria such as Courant number while enabling the fastest convergence.
Currently, the state of the art lacks benchmark cases, which is an important perspective for the musical instruments domain, that would enable V&V studies.
Reviewer 2 Report
Comments and Suggestions for Authors
- In the title it should be "computational" not "computed."
- Page 1, lines 43 - 44. The references to the literature are not properly edited.
- Page 4, line 135 - should be "Brownian motion," not "Brown motion."
The paper should be improved by:
- Providing the formula for the drag coefficient and explanation why Henderson's formula was chosen.
- Discussion of the range of Reynolds number for the airflow and droplet motion and Weber number range.
- Discussion if the assumption of no internal oscillations and/or deformation of 50 microns froplets was accurate.
- The neglection of Brownian motion for 500 nm droplets needs more explanation, as Brownian force is of the same order as inertial one.
Author Response
We appreciate the time and effort dedicated to reviewing our manuscript, and we thank you for recognizing its potential contribution. Regarding your concerns about the methodology and the use of doctoral thesis citations, we have carefully considered your comments and have made several revisions to our manuscript. Please find below our responses to your specific points.
- In the title it should be "computational" not "computed."
This has been modified.
- Page 1, lines 43 - 44. The references to the literature are not properly edited.
This has been corrected.
- Page 4, line 135 - should be "Brownian motion," not "Brown motion."
this has been corrected.
- Providing the formula for the drag coefficient and explanation why Henderson's formula was chosen.
Henderson's formula was chosen because it provides a reliable estimation for the drag force acting on spherical particles across a range of Reynolds numbers typical of conditions within wind instruments. This is particularly relevant for our simulations where particles of various sizes (0.5, 5, and 50 µm) are transported within airflow fields that vary in velocity and turbulence due to the instrument's geometry and the musician's playing technique.
The drag coefficient (CD​) by Henderson simplifies to Stokes-Oseen equation in subsonic continuum flow: CD=24/Re+4.5
where Re is the particle Reynolds number, defined as:
Re=(ρ.u.d)/µ
ρ representing the air density, u the relative velocity between particle and gas, d the particle diameter, and μ the dynamic viscosity of air.
We acknowledge that other formulas for drag coefficient exist, but Henderson’s formula offers a good compromise between computational feasibility and accuracy for the range of conditions analyzed in wind instruments.
- Discussion of the range of Reynolds number for the airflow and droplet motion and Weber number range.
Thank you for your request to further discuss the range of Reynolds and Weber numbers utilized in our study.
Reynolds Number: In our simulations, the Reynolds number (Re) for the airflow within wind instruments was calculated using the relationship: Re=ρudμRe=μρud​ where ρρ is the air density, uu is the characteristic velocity of the airflow, dd is a characteristic length (diameter of the instrument bore or particle diameter), and μμ is the dynamic viscosity of air. The range of Reynolds numbers varied significantly depending on the specific conditions within each instrument type, typically spanning from laminar to transitional flows. For airflow, the characteristic diameters considered were those of the instrument bores, leading to higher Reynolds numbers due to larger characteristic lengths. Conversely, for particle motion, the smaller diameters of the aerosol particles resulted in lower Reynolds numbers, reflecting the differing fluid dynamic environments experienced by the air and droplets.
Weber Number: The Weber number (We) was considered primarily to understand the behavior of droplets within the airflow, particularly their stability against breakup. It is defined as: We=ρu2dσWe=σρu2d​ where σσ is the surface tension of the fluid. For the droplets in our study, the Weber numbers were generally low, indicating that droplet breakup was not prevalent under the simulated conditions. This aligns with the observed behavior in wind instruments, where droplet coalescence and deposition are more critical than breakup.
Our analysis across these dimensionless numbers helped to frame the fluid dynamics within wind instruments, providing insights into both air and particle behaviors. This approach also facilitates the understanding of aerosol transmission risks associated with playing wind instruments, particularly relevant in the context of airborne disease transmission.
We hope this response addresses the concerns raised regarding the range of Reynolds and Weber numbers in our simulations. Please let us know if further details are required.
- Discussion if the assumption of no internal oscillations and/or deformation of 50 microns droplets was accurate.
In our computational fluid dynamics (CFD) model, we assumed that droplets, including those with a diameter of 50 microns, maintain spherical shapes without internal oscillations or deformations during their trajectory. This assumption was primarily based on the low Weber number observed in our simulations. The Weber number (We) quantifies the ratio of inertial forces to surface tension forces acting on a droplet, given by the formula:
We=(ρ.u².d)/σ
where ρ is the density of the fluid, u the relative velocity of the droplet, d the droplet diameter, and σ the surface tension of the liquid.
For the 50-micron droplets in our study, the calculated Weber numbers were low, generally well below the threshold (We < 1) where droplet breakup or significant deformation might occur. This suggests that the forces due to airflow are insufficient to overcome the surface tension that maintains the droplet's spherical shape. Additionally, the droplets are unlikely to experience internal oscillations significant enough to affect their trajectory or interaction with the airflow, given the relatively stable conditions within the instrument bores and the absence of turbulent airflow velocities that could induce such behaviors.
The assumptions of no significant deformation or internal oscillations are commonly employed in similar aerosol studies, where the focus is often on the transport and deposition of droplets rather than their dynamic behavior in the air. However, it is important to acknowledge that in more turbulent flows or different environmental conditions, these assumptions might need to be revisited to ensure accuracy in modeling droplet behavior.
- The neglection of Brownian motion for 500 nm droplets needs more explanation, as Brownian force is of the same order as inertial one.
In our computational fluid dynamics (CFD) simulations, we primarily focused on the aerodynamic behavior of droplets, considering forces such as drag and gravitational forces. The decision to neglect Brownian motion for 500 nm droplets was based on the assumption that these droplets, due to their relatively larger size compared to truly nanoscale particles (e.g., those smaller than 100 nm), would be more influenced by inertial and aerodynamic forces than by Brownian motion.
However, it is a valid point that for particles around 500 nm, Brownian motion can still play a significant role, especially in conditions where airflow velocities are low and the surrounding medium is quiescent. The Brownian force, driven by the random thermal motion of air molecules, can indeed be comparable in magnitude to the inertial forces acting on such small particles. The formula for Brownian force might be approximated as:
FBrownian ≈kB.T.((3.π.µ.d)/(kB.T.τ))
where kB​ is the Boltzmann constant, T the absolute temperature, μ the dynamic viscosity of air, d the particle diameter, and τ the relaxation time.
Recognizing this, the simplification in our model may omit a critical aspect of particle dynamics in specific settings. This simplification was made to maintain computational tractability and focus on the primary transmission vectors in musical instrument environments, where airflow are often dominant.
Round 2
Reviewer 1 Report
Comments and Suggestions for Authors
Grammatically corrections are still required for the manuscript, the authors have ignored most of my recommendations regarding this matter, including correction of detected erratum. For example, "airbone" at the end of the first paragraph, which should be "airborne". Another example is line 43, where the citation style is different from the rest of the manuscript.
There are also some question not answered. About the introduction section I kindly asked to add some details into the second paragraph of the third page (line 50), and it was completely ignored. Specifically, this comment lies in the non-replicability that underline your statement. Therefore, the lack of explanations may lead to a non-relevant (apparently) study.
For these reasons I am moving toward to recommend rejection of the manuscript and kindly recommend the authors thoroughly review the grammar of the article before re-submitting it.
Comments on the Quality of English Language
The revised manuscript has not improved grammar enough; consider sending it to a native speaker.
Author Response
Dear Reviewer,
We sincerely apologize for missing some corrections in our initial response. The revision process, involving different authors, caused us to overlook elements in the annotated pdf document. We have now taken this into account and responded to each question and comment. Additionally, we have continued the proofreading and grammatical review of the entire document to meet your requirements.
Best regards.
Reviewer 2 Report
Comments and Suggestions for Authors
All of my remarks and questions were properely adressed and appropriate changes to the manuscript were applied. I recommend publication of the manuscript in current form.
Author Response
Thank you for your feedback and the recommendation for the publication of the paper.
