Numerical Simulations of Swirling Water Jet Atomization: A Mesh Convergence Study

Round 1

Reviewer 1 Report

This is an interesting paper, but I think the authors need to do more to relate the mesh they use to that from previous studies ( without swirl) and discuss their and justify their use of VOF compared to the LES and DNS used in the literature review.

In the literature review, a number of papers using LES or DNS are described with respect to their ability to resolve the flow. For example, in [8] the results are found to be mesh dependant and [16] has the drops smaller than the mesh size. It would be beneficial if the authors also included some detail about the mesh size (e.g. in term of the Kolmogorov length scale) so that the reader can get a feel for how they all compare and also how they compare with the simulations presented in this paper.

 

 

In the literature review various simulations using LES and DNS are described and in many cases the mash resolution is not sufficient. In third paper the authors use VOF. It would be beneficial if the authors discussed these in terms of the resolution. Although they ay find mesh convergence, would superior results be found using LES or DNS on a more refined mesh?

 

Equation (3) describes the characterisation function. More description is needed here. E.g. how is the density etc. calculated when c is not at its asymptotical values?

 

Figure 2 is missing a ‘c’.

 

In the figures, level 8 and level 9 results are fairly similar, but can the authors quantitate this similarity?

 

The results in figure 9 suggest there is not convergence. If this parameter has not converged, is it reasonable to assume that the others have? The 6.6% change discussed by the authors is smaller than the differences observed between other levels because the difference in cell size is smaller. The graph remains linear.

 

No Issues

Author Response

We thank the referee for valuable comments. The article has been revised to reflect your comments.

 

Reviewer’s comment: This is an interesting paper, but I think the authors need to do more to relate the mesh they use to that from previous studies ( without swirl) and discuss their and justify their use of VOF compared to the LES and DNS used in the literature review.

Authors’ comment: We have added a table with flow parameters in comparison with the results of other authors.

	Nozzle Diameter, µm	Rel	Wel	Min Linear Cell Size, µm	Colmogorov Scale, µm	Hinze scale (σWecr/ρl U2), µm	Sauter Mean Diameter, µm
Present paper	800	6100	650	6	1.2	12	300
Pairetti et al. [7]	100	5800	11600	0.37	0.13	0.08	<8
Constante-Amores et al. [31]	4000	1000 - 10000	10 - 1000	26	5.7 - 26	40 - 4000	300 - 4000
Jiao et al. [16]	100	4300 - 5800	6000 - 8000	5	0.81	0.1 - 0.2	15
Torregrosa et al. [17]	90	5037	27000	2.34	0.5	0.03	<5

 

 

RC: In the literature review, a number of papers using LES or DNS are described with respect to their ability to resolve the flow. For example, in [8] the results are found to be mesh dependent and [16] has the drops smaller than the mesh size. It would be beneficial if the authors also included some detail about the mesh size (e.g. in term of the Kolmogorov length scale) so that the reader can get a feel for how they all compare and also how they compare with the simulations presented in this paper.

AC: The table was added.

 

RC: In the literature review various simulations using LES and DNS are described and in many cases the mash resolution is not sufficient. In third paper the authors use VOF. It would be beneficial if the authors discussed these in terms of the resolution. Although they ay find mesh convergence, would superior results be found using LES or DNS on a more refined mesh?

AC: Analyzing the existing data in the literature, we come to the conclusion that when modeling the atomization of a jet, it is necessary to focus not only on the Kolmogorov scale, since in most such cases it does not significantly affect the atomization and structure of the flow of the jet and drops. The other important parameter is the Hinze scale (HS). In the majority of studies the grid does not resolve the HS. The lack of complete grid convergence shows that physical processes are underresolved. In our work, we show that at sufficiently fine grid for HS resolution, grid dependence of the results is still observed, however, this dependence is likely not related to physical processes. In our opinion, this occurs as a result of numerical errors arising when, with a change in the topology of the interfacial surface, the liquid layer width decreases to zero and the liquid layer breaks.

 

RC: Equation (3) describes the characterisation function. More description is needed here. E.g. how is the density etc. calculated when c is not at its asymptotical values?

AC: We have added the dependence of density and viscosity depending on the value of the "c" function.

 

RC: Figure 2 is missing a ‘c’.

AC: Corrected.

 

RC: In the figures, level 8 and level 9 results are fairly similar, but can the authors quantitate this similarity?

AC: We have added longitudinal velocity profiles

 

RC: The results in figure 9 suggest there is not convergence. If this parameter has not converged, is it reasonable to assume that the others have? The 6.6% change discussed by the authors is smaller than the differences observed between other levels because the difference in cell size is smaller. The graph remains linear.

AC: In the current paper, we do not claim to achieve a complete grid convergence of the results. We show how the grid resolution affect different flow characteristics, in particular we assume that an important parameter is the area of the interfacial surface. This parameter is the main one for practical applications where the rate of evaporation is crucial. As our results show, the area of the interfacial surface increases with decreasing cell size. However, extrapolating the obtained linear trend, we assume that when the grid cell size tends to zero, the area of the interfacial surface will remain finite and increase only slightly from our obtained result. It is not clear whether full grid convergence is possible, since with increasing resolution the spatial scale of the numerical instability decreases, which leads to the formation of smaller and smaller droplets. It is possible to avoid this by changing the numerical schemes for sampling the interfacial surface.

According to the conventional model, the Laplace pressure at the microscale becomes so large that capillary forces will, whenever possible, form droplets of the smallest possible size. This might be achieved in a very thin conical sheet of the rotating liquid. If such a thin layer of liquid is formed in a numerical simulation, then these smallest droplets scale will correlate with the grid cell size. However, the total volume of these small droplets should not be large. In reality, on micron scales other physical mechanisms come into play limiting the number of small droplets. One of them is the presence of impurities in the liquid, which, concentrating on the droplet surface, strongly change the physical properties of the interfacial surface on small scales. It leads, in particular, to the fact that the drops begin to behave like elastic balls. Another limiting mechanism is  the evaporation of small droplets. On the other hand, the physics of the interfacial surface on the micro and nanoscales is currently a rapidly developing area, and so far, even a qualitative understanding of the processes has not been achieved. In this regard, further refinement of the grid is impractical.

 

Author Response File: Author Response.docx

Reviewer 2 Report

Dear authors of the paper "Numerical simulations of a swirling water jet atomization: mesh convergence study".

Please find below my recommendations in order to increase the paper quality:

- the first chapter of the paper is well-documented and with many good references in this domain.

- for chapter two, please explain why it was chosen this configuration of the swirling jet. The computational domain and the conditions are related to an application from engineering.

- for the results chapter. Do the authors have the possibility to validate the numerical results with experimental results? Usually when a numerical study is analyzed, the results are compared with the experiments for validation.

Author Response

We thank the referee for the comments. Below you can find our answer.

Dear authors of the paper "Numerical simulations of a swirling water jet atomization: mesh convergence study".

Please find below my recommendations in order to increase the paper quality:

- the first chapter of the paper is well-documented and with many good references in this domain.

- for chapter two, please explain why it was chosen this configuration of the swirling jet. The computational domain and the conditions are related to an application from engineering.

 

AC: This article considers a model problem for an aircraft engine injector. The jet configuration was chosen based on the characteristic parameters of the injectors in the engines.

 

- for the results chapter. Do the authors have the possibility to validate the numerical results with experimental results? Usually when a numerical study is analyzed, the results are compared with the experiments for validation.

 

AC: This is planned for the next phase of the study. For this, it is necessary to use specific geometric parameters.

Basilisk has proven itself well in modeling two-phase flows. There are several works in the literature with validation of this package. Here are some of them:

Fudge, B. D., Cimpeanu, R., Antkowiak, A., Castrejón-Pita, J. R., & Castrejón-Pita, A. A. (2023). Drop splashing after impact onto immiscible pools of different viscosities. Journal of Colloid and Interface Science, 641, 585-594.

Hashemi, M., Shalbaf, S., Jadidi, M., & Dolatabadi, A. (2023). Effects of gas viscosity and liquid-to-gas density ratio on liquid jet atomization in crossflow. AIP Advances, 13(3).

Li, S., Saade, Y., van der Meer, D., & Lohse, D. (2021). Comparison of boundary integral and volume-of-fluid methods for compressible bubble dynamics. International journal of multiphase flow, 145, 103834.

 

Author Response File: Author Response.docx

Reviewer 3 Report

The article titled "Numerical Simulation of Swirling Water Jet Atomization: Effect of Grid Resolution on Results" presents a study on the primary breakup and atomization of a swirling water jet as it flows out of a nozzle into a still air atmosphere. The main focus of the research is to investigate the impact of grid resolution on the obtained results. The authors conducted numerical simulations using various grid resolutions, with the smallest cell size being 6 µm.

 

In the experimental setup, the jet inlet diameter (D) was fixed at 0.8 mm, while the bulk velocity was set at 7.6 m/s. Additionally, a swirl rate of 0.3 was applied to the jet. The authors employed an adaptive mesh refinement procedure for interface tracking in order to achieve convergent results in terms of droplet volume and surface area distributions.

 

The findings of the study indicate that the use of adaptive mesh refinement enables the attainment of convergent results in terms of droplet volume and surface area distributions. The article provides valuable insights into the effect of grid resolution on the atomization process of a swirling water jet. By employing numerical simulations and analyzing the near region of the jet, the authors shed light on the influence of grid resolution on droplet characteristics. The use of an adaptive mesh refinement procedure for interface tracking is an important contribution, as it allows for obtaining convergent results in terms of droplet volume and surface area distributions. This work contributes to the understanding of the atomization process and sets the stage for further explorations in the field.

It is worth noting that the research is limited to the near region of the jet, up to x/D = 16. Further investigations encompassing a broader region of the jet and exploring the influence of other parameters such as nozzle geometry and flow conditions could provide additional valuable insights.

Author Response

The article titled "Numerical Simulation of Swirling Water Jet Atomization: Effect of Grid Resolution on Results" presents a study on the primary breakup and atomization of a swirling water jet as it flows out of a nozzle into a still air atmosphere. The main focus of the research is to investigate the impact of grid resolution on the obtained results. The authors conducted numerical simulations using various grid resolutions, with the smallest cell size being 6 µm.

In the experimental setup, the jet inlet diameter (D) was fixed at 0.8 mm, while the bulk velocity was set at 7.6 m/s. Additionally, a swirl rate of 0.3 was applied to the jet. The authors employed an adaptive mesh refinement procedure for interface tracking in order to achieve convergent results in terms of droplet volume and surface area distributions.

The findings of the study indicate that the use of adaptive mesh refinement enables the attainment of convergent results in terms of droplet volume and surface area distributions. The article provides valuable insights into the effect of grid resolution on the atomization process of a swirling water jet. By employing numerical simulations and analyzing the near region of the jet, the authors shed light on the influence of grid resolution on droplet characteristics. The use of an adaptive mesh refinement procedure for interface tracking is an important contribution, as it allows for obtaining convergent results in terms of droplet volume and surface area distributions. This work contributes to the understanding of the atomization process and sets the stage for further explorations in the field.

It is worth noting that the research is limited to the near region of the jet, up to x/D = 16. Further investigations encompassing a broader region of the jet and exploring the influence of other parameters such as nozzle geometry and flow conditions could provide additional valuable insights.

 

Authors’ comment: We thank the referee for reading our work and its high appreciation. In the future we plan to study the influence of the internal structure of the flow inside the nozzle on the jet breakup and to increase the liquid flow rates to the realistic values achieved in aircraft engine combustion chambers.

 

Author Response File: Author Response.docx