Theoretical and Experimental Study on Coating Uniformity in Automatic Spray-Coating of Pipeline Weld Repairs

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The submitted paper deals with the uniformity of anti-corrosion spray coating used for pipelines. The authors combine numerical simulations by means of Ansys Fluent and experimental work to investigate the influence of the spay distance and gun traverse speed, considered by the authors to be the two most influential parameters regarding the coating thickness and uniformity. Furthermore, response surface methodology is used to model and optimize the parameters of the coating process.

- Theoretical and experimental research related to similar problems have already been conducted and reported in the available literature. Hence, at the end of introduction, the authors should provide a clear statement of the novelty they tend to offer in their manuscript.

- In order to simplify the modelling, the authors have introduced 2 assumptions: “the system operates at moderate working pressure, and the spray cone angle is confined within a small range, ensuring good atomization quality.” How realistic are those assumptions?

- Make sure that all the terms are clearly explained and at latest immediately after the equation in which the terms have been used for the first time.

- Some figures do not have good readability, primarily due to rather small font size. Check for instance Figure 5 and improve accordingly. The same is valid for some further figures.

- Some figure captions are inadequate. For instance, the caption of Fig. 6 has a form of imperative. It could be “mesh convergence analysis”. Furthermore, this figure demands to make it clear how the Y-axis is defined. Where can this axis be seen (in which figure)?

- The authors consider only 2 parameters – the distance and speed. Why not more parameters, such as nozzle angle, spray pressure, droplet size, environmental conditions such as temperature and similar. Is it justify to focus the consideration to only 2 parameters and, if yes, how? This should be addressed in the paper.

- What numerical method is used by the software that the authors apply? The authors should also check if the terms such as “grid, “cell”, etc. are suitable (the authors also use both grid and mesh as terms – the terminology should be consistent). Please, explain what “cell” is, what type of “cell” is used, etc.  

- Figures should not appear before they have been referenced in the text (for instance, check Fig. 12).

- For multi-objective and multi-parameter optimization, metaheuristic optimization methods are usually suitable and quite efficient, but those were not addressed by the authors – why?

- Section 4.3.2 is rather short. The discussion should be extended. In particular, the authors should discuss the scalability of the results to larger structures, i.e. real pipes.

- Conclusions should mention limitations of the authors’ work (some of which are also mentioned in the comments) and give clear statements how future work would address those.

- Among references, there is a relatively high number of Master theses from China. Are those in English and are those available to the readership? If that is not the case, it would be ok to use only 1 maybe 2 of such references. Otherwise, using a relatively large number of references that are not accessible/readable to the readership is not advisable.

Author Response

Comments 1: Theoretical and experimental research related to similar problems have already been conducted and reported in the available literature. Hence, at the end of introduction, the authors should provide a clear statement of the novelty they tend to offer in their manuscript.

Response 1: We thank the reviewer for the suggestion. In the revised manuscript, we have added a statement of the innovation points regarding optimization of spraying in the field-joint region, both at the end of the Introduction and in the latter part of the Conclusions. Spraying in the field-joint domain has a high degree of specificity, including special working environments, process methods, and coating material properties. The region to be sprayed features complex characteristics such as geometric discontinuities, local curvature mutations, and boundary effects. This study focuses on this more challenging local area and develops a simulation model of the spraying region. At the end of the manuscript, we have also added limitations and future research directions, explicitly noting that although the method is currently limited to joint coating, it has potential for extension to other fields. The revised objective now reads: (Page 21, Line 563-567)

This study focuses on the pipeline field-joint region, characterized by geometric discontinuities, abrupt curvature changes, and pronounced boundary effects. A combined numerical–experimental spraying model was established, and optimized strategies for spray distance and traverse speed were proposed, demonstrating strong engineering relevance and innovation.

Comments 2: In order to simplify the modelling, the authors have introduced 2 assumptions: “the system operates at moderate working pressure, and the spray cone angle is confined within a small range, ensuring good atomization quality.” How realistic are those assumptions?

Response 2: We have added clarification in Section 2.1: in pipeline joint spraying operations, medium-pressure operation is common; the spray angle is constrained within a small range partly because of engineering requirements for customized nozzles, and partly because controlling the cone angle can reduce atomization error. The limitations of this assumption have been discussed in the Discussion and Conclusions. The revised objective now reads: (Page 4, Line 137-141)

To simplify the model, the following assumptions are made: the system operates under moderate working pressure, and the spray cone angle is confined within a small range to ensure atomization quality. These assumptions are based on the actual operating parameters of common industrial spraying equipment and are feasible in engineering applications. However, this assumption neglects possible droplet breakup under high-pressure conditions and atomization non-uniformity under large spray-cone angles. Therefore, its applicability is mainly limited to spraying environments with medium pressure and small cone angles. Under these conditions, and when the nozzle operates within a range θ_0, a uniform coating thickness distribution can be achieved. The spray region on the workpiece can be approximately treated as circular [21], as shown in Figure 2 (a). Additionally, the deposition process is modeled using a quadratic Bézier curve, with the growth-rate function depicted in Figure 2 (b).

Comments 3: Make sure that all the terms are clearly explained and at latest immediately after the equation in which the terms have been used for the first time.

Response 3: All terms and symbols are now explained immediately upon first appearance. We have checked and revised relevant details throughout the manuscript.

Comments 4: Some figures do not have good readability, primarily due to rather small font size. Check for instance Figure 5 and improve accordingly. The same is valid for some further figures.

Response 4: Figures 5 and others with overly small fonts have been redrawn, with font sizes unified to ensure readability.

Comments 5: Some figure captions are inadequate. For instance, the caption of Fig. 6 has a form of imperative. It could be “mesh convergence analysis”. Furthermore, this figure demands to make it clear how the Y-axis is defined. Where can this axis be seen (in which figure)?

Response 5: The caption of Figure 6 has been revised to “Mesh convergence analysis.” In addition, the definition and source of the Y-axis have been clarified in Section 2.4.1. The revised objective now reads: (Page 9-10, Line 298-302)

As illustrated in Figure 5, the spray gun performs coating operations on the pipeline surface. We introduce the following definitions: define the direction of equipment motion (i.e. the axis of the pipeline) as the Y-axis; when the equipment is at rest and placed on the pipeline, its gravitational direction (i.e. the direction opposite to gravity) is defined as the Z-axis. The diameter of the pipeline is D=1219 mm; the spray gun nozzle is positioned at a height S above the surface; and the paint dispersion angle from the nozzle is α. During installation, the nozzle’s extension line passes through the pipe’s center, and the gun sweeps circumferentially around the pipe’s center, facilitating continuous spray application at a linear speed V. All geometric parameters—such as pipe diameter, nozzle diameter, paint viscosity, and spray pressure—remain constant. The study investigates spraying efficiency by varying operational factors like the nozzle-to-pipe distance and the nozzle’s traversal speed. According to Section 8.4 “Joint Coating Quality Inspection” of the national standard GB/T 51241-2017: Technical Code for Field Joint Coatings of Pipeline, this study selected “minimum coating thickness” as one of the quality evaluation criteria. The standard specifies that for liquid coating joints, the minimum thickness must not be less than the design value or the standard requirement (with the exact minimum depending on project specifications), and the thickness distribution must be uniform without severe local thinning. Accordingly, in the experimental stage we employed spark testing to measure the local coating thickness of the joint and compared these values with the simulation results for validation. The spray application model was constructed using ANSYS SpaceClaim.

Comments 6: The authors consider only 2 parameters – the distance and speed. Why not more parameters, such as nozzle angle, spray pressure, droplet size, environmental conditions such as temperature and similar. Is it justify to focus the consideration to only 2 parameters and, if yes, how? This should be addressed in the paper.

Response 6: Since the spraying equipment and coating materials used in this study are mature products recognized in the field-joint repair industry, the nozzle spray angle, spray pressure, and coating properties are already well matched. Compared with traditional manual spraying methods, where non-constant speed and distance affect coating quality, our mechanized spraying device ensures that both speed and distance remain constant. These two parameters—speed and distance—are precisely those previously overlooked, yet they are also the most easily controlled on site. Other parameters, such as temperature, are indeed important and have been discussed as future directions for extension.

Comments 7: What numerical method is used by the software that the authors apply? The authors should also check if the terms such as “grid, “cell”, etc. are suitable (the authors also use both grid and mesh as terms – the terminology should be consistent). Please, explain what “cell” is, what type of “cell” is used, etc.

Response 7: Section 2.2 has been expanded with detailed descriptions of the numerical methods used (e.g., DPM + turbulence model), the type of mesh elements applied (polyhedral cells), and a consistent terminology of “mesh/cell.” The revised objective now reads: (Page 11, Line 344-352)

In the present simulation, paint is treated as discrete particles, and the process is modeled using the Discrete Phase Model (DPM) in ANSYS Fluent, in conjunction with the Wall Film (WF) model to capture deposition and adhesion of particles onto the pipeline surface [25].

During dynamic spraying, the Sliding Mesh technique is employed to simulate the motion of the pipe: the pipe surface is specified as a mesh moving region, while the remaining computational domain remains stationary. The Realizable k-ε turbulence model is selected to resolve turbulent flow and transient calculations are performed. The paint injection is modeled as a conical inlet based on the spray gun’s parameters.

Comments 8: Figures should not appear before they have been referenced in the text (for instance, check Fig. 12).

Response 8: The entire manuscript has been checked to adjust figure order, ensuring that each figure appears only after being referenced in the text.

Comments 9: For multi-objective and multi-parameter optimization, metaheuristic optimization methods are usually suitable and quite efficient, but those were not addressed by the authors – why?

Response 9: This study combines simulations with experimental validation, but the number of experiments was constrained by time and material costs. Response Surface Methodology (RSM) can approximate the response surface with relatively few design points (center points, axial points, factorial combinations), making it well suited for “small-sample + experimental constraints” scenarios. In the future, we will explore metaheuristic approaches such as genetic algorithms and particle swarm optimization for multi-objective optimization.

Comments 10: Section 4.3.2 is rather short. The discussion should be extended. In particular, the authors should discuss the scalability of the results to larger structures, i.e. real pipes.

Response 10: Section 4.3.2 has been expanded with further discussion on scaling-up issues, irregular geometries, temperature effects, and real environmental impacts. The revised objective now reads: (Page 20, Line 522-533)

In addition, to further verify the applicability of the numerical model under actual pipeline conditions, preliminary spraying experiments were conducted on an indoor fixed-pipeline platform. As shown in Figure 20, the spray gun was mounted on an au-tomated trajectory control device to maintain a stable spray distance and uniform motion. After coating deposition in the spraying region was completed, representative areas were sampled and measured with a coating thickness gauge to evaluate consistency between the spraying results and simulation predictions. The results indicate that the obtained coating thickness and uniformity are consistent with those from the aforementioned lo-calized experiments, further supporting the reliability of the model. This small-scale fixed-pipeline experiment lays the groundwork for subsequent field trials on real pipe-lines, where future studies will verify the model’s applicability under larger scales and more complex conditions.

Comments 11: Conclusions should mention limitations of the authors’ work (some of which are also mentioned in the comments) and give clear statements how future work would address those.

Response 11: In the Conclusions, a new paragraph has been added to explicitly list the study’s limitations (e.g., omission of spray pressure, spray angle, and environmental factors) and future research directions.The revised objective now reads: (Page 21, Line 563-581)

This study focuses on the pipeline field-joint region, characterized by geometric discontinuities, abrupt curvature changes, and pronounced boundary effects. A combined numerical–experimental spraying model was established, and optimized strategies for spray distance and traverse speed were proposed, demonstrating strong engineering relevance and innovation. It should be noted that several reasonable simplifications were adopted in the modeling process, such as assuming medium-pressure operation with a small spray cone angle, simplifying the PLC stepwise trajectory to uniform linear motion, and not fully accounting for environmental factors or the temperature dependence of coating properties. The number of experimental validations was also constrained by material and practical limitations. These aspects may introduce localized deviations but do not affect the validity of the main conclusions. Future work will extend in three directions: (i) conducting experiments and simulations across a wider range of spray distances, angles, and pressures to enhance extrapolation capability; (ii) incorporating temperature-dependent viscosity and edge-thinning gradients (dT/dy) into the model to enable full sensitivity analysis and multi-objective optimization; and (iii) integrating PLC-based stepwise trajectory kinematics with online monitoring and feedback control to further improve coating uniformity and adaptive process regulation. Although the present method is mainly applied to field-joint repair, the proposed framework and approach hold promising potential for extension to automated spraying optimization of other complex geometries.

Comments 12: Among references, there is a relatively high number of Master theses from China. Are those in English and are those available to the readership? If that is not the case, it would be ok to use only 1 maybe 2 of such references. Otherwise, using a relatively large number of references that are not accessible/readable to the readership is not advisable.

Response 12: References have been streamlined, retaining only one or two representative and publicly accessible master’s/doctoral theses, while replacing the others with journal or conference articles available to the readership. The revised objective now reads: (Page 21, Line 563-581)

This study focuses on the pipeline field-joint region, characterized by geometric discontinuities, abrupt curvature changes, and pronounced boundary effects. A combined numerical–experimental spraying model was established, and optimized strategies for spray distance and traverse speed were proposed, demonstrating strong engineering relevance and innovation. It should be noted that several reasonable simplifications were adopted in the modeling process, such as assuming medium-pressure operation with a small spray cone angle, simplifying the PLC stepwise trajectory to uniform linear motion, and not fully accounting for environmental factors or the temperature dependence of coating properties. The number of experimental validations was also constrained by material and practical limitations. These aspects may introduce localized deviations but do not affect the validity of the main conclusions. Future work will extend in three directions: (i) conducting experiments and simulations across a wider range of spray distances, angles, and pressures to enhance extrapolation capability; (ii) incorporating temperature-dependent viscosity and edge-thinning gradients (dT/dy) into the model to enable full sensitivity analysis and multi-objective optimization; and (iii) integrating PLC-based stepwise trajectory kinematics with online monitoring and feedback control to further improve coating uniformity and adaptive process regulation. Although the present method is mainly applied to field-joint repair, the proposed framework and approach hold promising potential for extension to automated spraying optimization of other complex geometries.

Reviewer 2 Report

Comments and Suggestions for Authors

This paper examines coating uniformity during automated spraying of pipeline weld repair sections, a key factor in the durability and reliability of corrosion protection. Uneven coatings result in weakened areas, blisters, and cracks, which accelerate corrosion and reduce the service life of the pipeline. The paper proposes a combined methodology, including numerical modeling in ANSYS Fluent and experimental testing, to identify the influence of spray distance and gun travel speed on coating thickness and uniformity. Parameter optimization reduced thickness deviation from ±25% to ±10%, as confirmed by field tests. The results have practical value for the design of automated spraying systems, improving the quality of corrosion protection and reducing economic losses from premature corrosion, which amount to hundreds of billions of dollars annually. The study provides a scientific basis and practical recommendations for improving the efficiency and reliability of pipeline transportation. However, the article requires revision:
1. The formulation of the research gap in the introduction (a drawback of the "gun trajectory-curved surface" dynamic modeling) is sound, but the transition to your proposed model could more clearly indicate which of the "dynamic" components you are actually considering: instantaneous nozzle kinematics, the evolution of the jet imprint on the cylinder scan, or both.
2. In Section 2.1, you introduce a piecewise defined deposition distribution function over a radius, approximated by a quadratic Bézier curve. However, the procedure for calibrating the parameters of this approximation using actual nozzle spray characteristics (spray angle, flow rate diagram, droplet spectrum) is not shown. Specify how R and R0 were selected: from the nozzle datasheet, from the CFD field, or from experimental spot tests. Otherwise, the model's relationship to physical spraying remains empirical.
3. The transition to the cylindrical case (Section 2.2) neatly introduces a double coordinate transformation and cosine corrections to the flows. However, it remains unclear how gravity is accounted for in the up-down orientations of the pipeline (droplet flow along an arc), especially for thicknesses > 1 mm. You mention a thin-film model, but the relationship between macro-deposition (T_s) and film evolution (h, u_l) could be shown for 1–2 characteristic regimes.
4. The description of the scene and grid (S, α, D, polyhedral grid, prism layers) is thorough, including the grid-independence criterion (≈ 52,910 cells). It would be useful to provide the dimensionless parameters (Re, We, Oh) of the droplet flow so that readers can relate the spray regime to known regime maps (adhesion, spreading, splashing). This will help understand the applicability of the parameters beyond the epoxy system considered. 5. The representation of the material parameters (ρ = 3000 kg/m³, μ = 40 kg/(m s), σ = 0.03 N/m) is unusually high for an "epoxy primer" (a viscosity of 40 Pa s seems plausible, but a density of 3000 kg/m³ is atypical). Please clarify on what basis these values ​​are specified: data sheet, rheometry, or assumptions? Also, indicate the temperature dependence of μ(T) and the sensitivity of the solution for ±20% property variation.
6. The description of the PLC algorithm and rotation/shear kinematics is useful for reproducibility, but lacks connection to the modeling: was this discrete stepping logic (15° steps, 180° reversal) taken into account in the CFD/track stacking model? If not, discuss how the transition from "ideal uniform motion" to a ladder-like trajectory affects ridge and uniformity.
7. The experiment-simulation comparison yields a maximum relative error of 13.5% and a deviation from the standard of 12.25% at V = 0.3 m/s. This is a good result, but its representativeness is limited to a single speed and a single L. Please add at least two points (low and high L) to demonstrate agreement across the entire operating range that you claim is optimal in your conclusions.
8. The "Conclusions" mention "powder flow rate" in the context of RSM, whereas the methods and experiments discussed a two-component liquid epoxy primer (airless/air-assisted). The terminological inconsistency needs to be resolved: either clarify that the flow rate of the liquid composition Q is meant, or justify why "powder" is used correctly.
9. When discussing the influence of speed, "maximum thickness" is used as the primary quality indicator, but in real-world practice, profile waviness and edge thinning are also monitored. You mention this phenomenon in the abstract, but the main text lacks a quantitative assessment (e.g., dT/dy gradient at the edges). Add this KPI to confirm edge thinning and the effectiveness of optimization.

10. You cite the national standard GB/T 51241-2017 for quality assessment. It would be helpful to clearly list the criteria used from the standard (minimum primer thickness, non-uniformity tolerance, adhesion requirements after curing) and show the corresponding tests (spark testing, peel test).
11. The abstract promises a reduction in variation to ±10%, but the main text uses "deviation from standard thickness 12.25%" and "max. relative error 13.5%" for the CFD experiment. A clear distinction should be made between (a) model error vs. experiment and (b) process deviation from the target/standard.

Comments on the Quality of English Language

The text is generally clear but requires polishing: there are tracings, unnecessary repetitions, inconsistencies, and typos ("p<0.05p < 0.05," spaces in numbers and units, "Figure 1. Diagram of Different Spray Distances" is renumbered). Recommendations:

Unify tenses (Abstract — Present Simple; Methods — Past Simple/Present Simple for equations).

Convert units to SI with non-breaking spaces and correct punctuation (e.g., "0.3 m/s," "400 µm").

Remove duplicates ("In spray operations…" is repeated verbatim).

Correct terminology: "powder flow rate" → "coating flow rate"/"material feed rate" for epoxy primer.

Author Response

Comments 1: The formulation of the research gap in the introduction (a drawback of the "gun trajectory-curved surface" dynamic modeling) is sound, but the transition to your proposed model could more clearly indicate which of the "dynamic" components you are actually considering: instantaneous nozzle kinematics, the evolution of the jet imprint on the cylinder scan, or both.

Response 1: At the end of the Introduction and in Section 2.1, we have explicitly distinguished two dynamic layers: the instantaneous kinematics of the nozzle—i.e., the effect of gun velocity and gun height on coating impingement and accumulation—and the temporal evolution of the coating footprint, especially in the field-joint area. We have clarified that this study mainly simulates the coupling process of nozzle trajectory and jet imprint, while transient effects of high acceleration or deceleration are neglected under the assumption of steady motion. The revised objective now reads: (Page 3, Line 115-121)

Although previous studies using CFD have revealed the effects of spray-gun height, angle, and geometry on coating thickness, most of these works are restricted to static conditions and lack dynamic modeling of the “spray-gun trajectory–geometric surface coupling” scenario. They do not simultaneously capture the instantaneous kinematic characteristics of the nozzle along its path and the temporal evolution of the spray imprint on the curved surface (under the assumption of steady motion).

Comments 2: In Section 2.1, you introduce a piecewise defined deposition distribution function over a radius, approximated by a quadratic Bézier curve. However, the procedure for calibrating the parameters of this approximation using actual nozzle spray characteristics (spray angle, flow rate diagram, droplet spectrum) is not shown. Specify how R and R0 were selected: from the nozzle datasheet, from the CFD field, or from experimental spot tests. Otherwise, the model's relationship to physical spraying remains empirical.

Response 2: In the revised Section 2.1, we added a description of how parameters R and R_0 were calibrated: some values were taken from the spray-gun manufacturer’s datasheet (spray angle, atomization cone angle, etc.), some were obtained from initial CFD boundary simulations, and others were fitted using thickness measurements from small-scale spot-spray experiments.The revised objective now reads: (Page 3,  Line 156-174)

To ensure that the piecewise deposition distribution function  is consistent with the actual spray pattern, this study calibrates the coverage radius R and the central uniform radius  based on spray-gun parameters. First, according to the atomization cone angle  and spray distance  provided in the nozzle datasheet, the initial value of the coverage radius is obtained geometrically as

Without altering the spray pressure or nozzle structure (in this study: spray pressure 0.7 MPa, nozzle diameter 1 mm), this  is taken as the initial value of the spray footprint boundary. Second, the radial profile of near-wall coating deposition flux obtained from ANSYS Fluent is used to perform a fitting of the central “plateau region” width, which is defined as

where  is determined from the ratio of the plateau width to the outer radius, obtained either from the nozzle flow-rate distribution curve or from CFD profiles. Third, a calibration experiment was conducted by spraying onto a steel plate for 1s (under the same material and environmental conditions as in Section 3.3). Thickness–radius curves were measured with a film-thickness gauge, and  and  were adjusted via least-squares fitting so that the quadratic Bézier approximation  simultaneously matched the measured plateau width and edge decay region. The final  values were confirmed once both the mean-square error and plateau-region deviation were below the prescribed thresholds.

Comments 3: The transition to the cylindrical case (Section 2.2) neatly introduces a double coordinate transformation and cosine corrections to the flows. However, it remains unclear how gravity is accounted for in the up-down orientations of the pipeline (droplet flow along an arc), especially for thicknesses > 1 mm. You mention a thin-film model, but the relationship between macro-deposition (T_s) and film evolution (h, u_l) could be shown for 1–2 characteristic regimes.

Response 3: We appreciate the comment. In Section 2.2, after Eq. (11), we added an explanation of a correction factor for coating thickness. When thickness exceeds 1 mm, gravity induces liquid-film flow along the pipe wall, and we present the coupling formula (11) relating macroscopic deposition T_s to film thickness h and velocity u_l. We also distinguish viscosity-dominated and gravity-dominated regimes, thereby explaining thickness differences between the upper and lower pipe walls. The revised objective now reads: (Page 7, Line 220-240)

In the actual spraying process, when the deposited thickness grows beyond approximately 1 mm, gravitational forces along the circumferential direction of the cylindrical wall drive the wet film to flow, leading to a redistribution of thickness between the upper and lower surfaces of the pipeline. To capture this effect, we treat the macroscopic deposition rate term  (see Equation (11)) as the source term input for the thin-film model. The film thickness  and the average velocity  in the wall-surface coordinates satisfy the following equations:

By coupling the geometric deposition distribution Equation (11) with the thin-film dynamics model (10), the corrected film-thickness evolution equation can be obtained as follows:

Here,  and  denote the density and dynamic viscosity of the coating material;  is the gravitational acceleration; and  is the circumferential angle of the pipeline (with the top at  and the bottom at ). When the film is thin (e.g., ), viscous resistance dominates and gravity-driven flow is negligible; in this case,  can be approximated as the final deposited thickness. When the film is thicker (e.g., ), gravity drives the liquid film to flow from the upper to the lower surface, leading to increased thickness at the bottom and thinning at the top, thereby introducing thickness asymmetry. This model thus couples the macroscopic deposition distribution  with the temporal evolution of the liquid film, providing an explanation for the occurrence of “thicker bottom and thinner top” or other asymmetric distributions during spraying on curved surfaces.

Comments 4: The description of the scene and grid (S, α, D, polyhedral grid, prism layers) is thorough, including the grid-independence criterion (≈ 52,910 cells). It would be useful to provide the dimensionless parameters (Re, We, Oh) of the droplet flow so that readers can relate the spray regime to known regime maps (adhesion, spreading, splashing). This will help understand the applicability of the parameters beyond the epoxy system considered. 5. The representation of the material parameters (ρ = 3000 kg/m³, μ = 40 kg/(m s), σ = 0.03 N/m) is unusually high for an "epoxy primer" (a viscosity of 40 Pa s seems plausible, but a density of 3000 kg/m³ is atypical). Please clarify on what basis these values are specified: data sheet, rheometry, or assumptions? Also, indicate the temperature dependence of μ(T) and the sensitivity of the solution for ±20% property variation.

Response 4: Following the suggestion, we supplemented the Methods section with dimensionless spray parameters (Re, We, Oh). Parameter definitions and calculation formulas have been added; d values are based on nozzle data, U from near-wall CFD velocity, and material properties from technical datasheets. This allows readers to map the spray regime to standard adhesion/spreading/splashing domains. The revised objective now reads: (Page 12-13, Line 362-377)

To further characterize the physical mechanisms of the spraying conditions, we define the following dimensionless parameters together with their typical value ranges. These enable the spray-droplet conditions in this study to be compared with adhesion, spreading, and splashing regimes reported in the existing spray-coating literature.

Where,  is density of the coating material;  is dynamic viscosity of the coating (in droplet state);  surface tension of the liquid;  is characteristic droplet diameter;  is droplet impact velocity (or velocity near the substrate surface).

Under the spraying conditions of this study (, , 3N/m, , ), the typical dimensionless parameters are obtained as: ,  and . The results indicate that due to the high viscosity, the Reynolds number is extremely low, and the flow is in a strongly viscosity-dominated regime; meanwhile, the Weber number is very large, suggesting that inertia is sufficient to overcome surface tension, but droplet splashing is suppressed by the high Ohnesorge number. This combination positions the spraying condition in the “high-We, high-Oh, low-Re” regime, where inertial effects are pronounced, yet droplets on the wall tend to adhere and spread rather than undergo secondary splashing.

Comments 5: The representation of the material parameters (ρ = 3000 kg/m³, μ = 40 kg/(m s), σ = 0.03 N/m) is unusually high for an "epoxy primer" (a viscosity of 40 Pa s seems plausible, but a density of 3000 kg/m³ is atypical). Please clarify on what basis these values are specified: data sheet, rheometry, or assumptions? Also, indicate the temperature dependence of μ(T) and the sensitivity of the solution for ±20% property variation.

Response 5: We thank the reviewer for pointing out the abnormal density value. Indeed, the original 3000 kg/m³ was a textual error. After verification, the parameter used in the simulations was 1350 kg/m³, which has been corrected throughout the revised manuscript. This value is based on the coating product datasheet. Regarding temperature-dependent viscosity \mu(T) and sensitivity analysis of material property perturbations: we acknowledge this is an important direction to improve the model. However, in the current stage there are practical constraints. Our experiments were conducted under controlled temperature, with fluctuations kept minimal, so assuming a constant viscosity is a reasonable simplification with limited effect on main thickness-distribution trends. Moreover, while a ±20 % perturbation analysis is theoretically valuable, without a reliable \mu(T) model such perturbation could yield misleading conclusions. Given these factors, we prioritized improving model structure, geometric coupling, experimental validation, and RSM optimization. We plan to extend to temperature-dependent viscosity models and full sensitivity analyses in future work to further validate generality and robustness. We hope the reviewers understand the choices and trade-offs made during this stage of the manuscript.

Comments 6: The description of the PLC algorithm and rotation/shear kinematics is useful for reproducibility, but lacks connection to the modeling: was this discrete stepping logic (15° steps, 180° reversal) taken into account in the CFD/track stacking model? If not, discuss how the transition from "ideal uniform motion" to a ladder-like trajectory affects ridge and uniformity.

Response 6: We thank the reviewer for the attention to the PLC control logic and stepwise trajectory characteristics. In the actual equipment, a discrete step control mode is indeed used (e.g., 15° increments and 180° reversals). However, in the current simulation model, to reduce complexity and computational load, only uniform linear motion along straight segments were modeled and analyzed, and the full stepwise trajectory was not incorporated into the CFD stacking calculation. In the Discussion section, we have added an analysis of the impact of this simplification: thickness ridges or local overlaps may occur in trajectory transition zones, but within the overall coating area, this error remains relatively small and does not significantly alter the overall distribution trend. Future work will seek to integrate stepwise trajectory kinematics into the simulation model to more precisely assess their minor perturbation effects on thickness non-uniformity.

The revised objective now reads: (Page 21, Line 577-581)

This study focuses on the pipeline field-joint region, characterized by geometric discontinuities, abrupt curvature changes, and pronounced boundary effects. A combined numerical–experimental spraying model was established, and optimized strategies for spray distance and traverse speed were proposed, demonstrating strong engineering relevance and innovation. It should be noted that several reasonable simplifications were adopted in the modeling process, such as assuming medium-pressure operation with a small spray cone angle, simplifying the PLC stepwise trajectory to uniform linear motion, and not fully accounting for environmental factors or the temperature dependence of coating properties. The number of experimental validations was also constrained by material and practical limitations. These aspects may introduce localized deviations but do not affect the validity of the main conclusions. Future work will extend in three directions: (i) conducting experiments and simulations across a wider range of spray distances, angles, and pressures to enhance extrapolation capability; (ii) incorporating temperature-dependent viscosity and edge-thinning gradients ( into the model to enable full sensitivity analysis and multi-objective optimization; and (iii) integrating PLC-based stepwise trajectory kinematics with online monitoring and feedback control to further improve coating uniformity and adaptive process regulation. Although the present method is mainly applied to field-joint repair, the proposed framework and approach hold promising potential for extension to automated spraying optimization of other complex geometries.

Comments 7: The experiment-simulation comparison yields a maximum relative error of 13.5% and a deviation from the standard of 12.25% at V = 0.3 m/s. This is a good result, but its representativeness is limited to a single speed and a single L. Please add at least two points (low and high L) to demonstrate agreement across the entire operating range that you claim is optimal in your conclusions.

Response 7: We thank the reviewer for suggesting multiple spray distances to strengthen validation. We fully recognize that including more points would enhance representativeness and persuasiveness. At this stage, however, since the main contribution lies in coupling of nozzle trajectory and curved-surface deposition plus RSM optimization, we consider the verification under V=0.3 m/s sufficient to support model reliability within the parameter range studied. To balance feasibility with reviewer concerns, we explicitly list the lack of multi-distance validation as a limitation and add in the Conclusions our plan to conduct further experiments and simulations over wider spray-distance ranges in future work.

Comments 8: The "Conclusions" mention "powder flow rate" in the context of RSM, whereas the methods and experiments discussed a two-component liquid epoxy primer (airless/air-assisted). The terminological inconsistency needs to be resolved: either clarify that the flow rate of the liquid composition Q is meant, or justify why "powder" is used correctly.

Response 8: We have unified terminology throughout the manuscript, replacing “coating flow rate” with “coating flow rate” or “material feed rate Q,” and specifying that the subject of study is the spraying of a two-component liquid epoxy primer.

Comments 9: When discussing the influence of speed, "maximum thickness" is used as the primary quality indicator, but in real-world practice, profile waviness and edge thinning are also monitored. You mention this phenomenon in the abstract, but the main text lacks a quantitative assessment (e.g., dT/dy gradient at the edges). Add this KPI to confirm edge thinning and the effectiveness of optimization.

Response 9: We appreciate the suggestion to add edge-thinning (dT/dy) as a KPI. We agree this metric is important in practice. Unfortunately, in the current stage our model and experiments did not explicitly output edge-gradient data, so we cannot provide quantitative analysis for all conditions. To address this, we have added in the Discussion/Limitations a statement that while edge-thinning was mentioned in the Abstract, quantitative gradient extraction was not included in this work. We acknowledge this limitation and outline plans for future research in two directions: (i) extracting edge-gradient curves from CFD and trajectory-stacking models; and (ii) incorporating gradient or waviness as an additional response variable in optimization to better control local thinning and edge consistency. We hope the reviewers understand the choices and trade-offs made during this stage of the manuscript.

Comments 10: You cite the national standard GB/T 51241-2017 for quality assessment. It would be helpful to clearly list the criteria used from the standard (minimum primer thickness, non-uniformity tolerance, adhesion requirements after curing) and show the corresponding tests (spark testing, peel test).

Response 10: We have added a new passage in the manuscript explicitly stating the quality criteria adopted from GB/T 51241-2017 (such as minimum primer thickness, non-uniformity tolerance, and adhesion requirements) together with the corresponding testing methods (e.g., spark testing, peel test, microscopic cross-section thickness measurement). This information is taken directly from the full text of the standard. The revised objective now reads: (Page 10, Line 309-314)

According to Section 8.4 “Joint Coating Quality Inspection” of the national standard GB/T 51241-2017: Technical Code for Field Joint Coatings of Pipeline, this study selected “minimum coating thickness” as one of the quality evaluation criteria. The standard specifies that for liquid coating joints, the minimum thickness must not be less than the design value or the standard requirement (with the exact minimum depending on project specifications), and the thickness distribution must be uniform without severe local thinning.

Comments 11: The abstract promises a reduction in variation to ±10%, but the main text uses "deviation from standard thickness 12.25%" and "max. relative error 13.5%" for the CFD experiment. A clear distinction should be made between (a) model error vs. experiment and (b) process deviation from the target/standard.

Response 11: In the Abstract, we have rephrased the statement to clarify that “thickness variation ±10%” refers to process deviation relative to the target standard thickness. In the main text, we retain the model–experiment errors (maximum relative error 13.5% and deviation 12.25%) but add notes clarifying the distinction between the two. We have also made this distinction explicit in both the Introduction and the Conclusions.

Comments 12: The text is generally clear but requires polishing: there are tracings, unnecessary repetitions, inconsistencies, and typos ("p<0.05p < 0.05," spaces in numbers and units, "Figure 1. Diagram of Different Spray Distances" is renumbered).

Response 12: Thank you for your correction. We have made corrections to the text errors, tenses, and other related issue.

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

Reviewer Report

The manuscript entitled “Theoretical and Experimental Study on Coating Uniformity in Automatic Spray-Coating of Pipeline Weld Repairs” investigates the effect of spray distance and traverse speed on coating uniformity using ANSYS Fluent simulations combined with experimental validation. The topic is relevant for pipeline anti-corrosion applications and the results provide useful insights for process optimization.

However, before acceptance, the paper requires revisions to improve clarity and presentation. My main remarks are:

1. Abstract

• Some sentences are too long:

“Pipeline anti-corrosion patch spray-coating is a critical process in pipeline construction and maintenance, directly affecting the adhesion between the pipe exterior and the heat-shrink sleeve and indirectly determining the coating’s adhesion quality.”  Split into two shorter sentences for readability.

2. Introduction

• Redundancy: the phrase “spray-coating is a critical step in pipeline construction and maintenance” appears multiple times in slightly different forms , merge or simplify.
• Vague statement: “According to statistics, the direct global economic loss…” , provide a precise reference or remove.

3. Equations and Figures

• Equation formatting inconsistent (e.g., misaligned integrals, missing spaces).
• Figures mentioned without sufficient description in the text (e.g., Figure 1).

4. Language and Keywords

• Keywords: use lowercase for consistency, e.g., “parameter optimization” instead of “Parameter optimization”.
• Overgeneralization: “significantly improving efficiency” , should be supported by data or rephrased.

The study is relevant and interesting, but these corrections are necessary to improve clarity, coherence, and scientific presentation before acceptance.

Comments for author File: Comments.pdf

Comments on the Quality of English Language

Comments on the quality of the English language (to be communicated to the authors):

The language used in the manuscript is generally understandable; however, several sentences are long and complex, which reduces clarity. Rewriting some sentences is recommended to improve readability. Some expressions are repetitive or slightly awkward. Overall, spelling and grammar are correct, but it is advisable to check punctuation and consistency of technical terms. A thorough language revision would make the text more fluent and professional.

Author Response

Comments 1: Some sentences are too long:" Pipeline anti-corrosion patch spray-coating is a critical process in pipeline construction and maintenance, directly affecting the adhesion between the pipe exterior and the heat-shrink sleeve and indirectly determining the coating's adhesion quality." Split into two shorter sentences for readability.

Response 1: We thank the reviewer for the suggestion. We have split the relevant sentence in the Abstract into two shorter sentences to improve readability and logical flow.

Comments 2:Redundancy: the phrase “spray-coating is a critical step in pipeline construction and maintenance” appears multiple times in slightly different forms , merge or simplify. Vague statement: “According to statistics, the direct global economic loss…” , provide a precise reference or remove.

Response 2: We have removed the vague expression “According to statistics…” and replaced it with specific references (e.g., NACE reports).The revised objective now reads: (Page 2, Line 43-45)

According to reports from NACE and related studies [1–4], the global direct economic loss caused annually by pipeline corrosion—including failures associated with inadequate field-joint coating—amounts to more than one hundred billion USD.

Comments 3: Equation formatting inconsistent (e.g., misaligned integrals, missing spaces). Figures mentioned without sufficient description in the text (e.g., Figure 1).

Response 3: We have added descriptions of Figure 1 and other figures in the main text to ensure that each figure is clearly explained before its first citation.

Comments 4: Keywords: use lowercase for consistency, e.g., “parameter optimization” instead of “Parameter optimization”. Overgeneralization: “significantly improving efficiency” , should be supported by data or rephrased.

Response 4: We have revised “significantly improving efficiency” to “improves efficiency and stability” to avoid unnecessary exaggeration.

Comments 5: The language used in the manuscript is generally understandable; however, several sentences are long and complex, which reduces clarity. Rewriting some sentences is recommended to improve readability. Some expressions are repetitive or slightly awkward. Overall, spelling and grammar are correct, but it is advisable to check punctuation and consistency of technical terms. A thorough language revision would make the text more fluent and professional.

Response 5: Thank you for your correction. We have made corrections to the text errors, tenses, and other related issues.

Round 2

Reviewer 1 Report

Comments and Suggestions for Authors

The authors have suitably revised the manuscript. It is acceptable for publishing as it is. 

Reviewer 2 Report

Comments and Suggestions for Authors

Overall, the authors have indeed made significant and relevant revisions: they clarified the research gap and the "dynamics" of the problem; described the calibration of the deposition distribution function; expanded the cylindrical case by adding a thin film-gravity coupling; introduced dimensionless numbers (Re, We, Oh) and corrected the anomalous density parameter; and partially clarified the terminology and quality control standards. All of this is confirmed in the text of the updated article.