Review Reports

Round 1

Reviewer 1 Report

Comments and Suggestions for Authors

The article presents a solid research design and addresses a relevant problem for postharvest grain storage. With the suggested corrections, the manuscript will reach an optimal level of clarity and will make a significant contribution to the field of postharvest engineering and fluid dynamics in porous media. The detailed observations are attached in a Word document to facilitate their review.

Comments for author File: Comments.pdf

Author Response

Reply to reviewer: 1

We are grateful to reviewer#1 for his/her effort in reviewing our manuscript and his/her positive feedback. Here below we address the questions and suggestions raised by reviewer#1.

Comment 1: The abstract adequately presents the objectives and findings of the study; however, it omits key information that would strengthen its clarity and relevance. It is recommended to explicitly state that the numerical results obtained through simulation were compared with experimental data measured in a pilot silo, specifying that this silo consists of a cylindrical body of 3 m in height and 1.5 m in diameter, topped with a conical dome of 0.85 m in height. Including this information in the abstract would highlight the model validation and the strong connection between simulation and experimentation.

Response: Thank you very much for your careful reminder and valuable advice. Following your recommendations, we have made amendments to the manuscript. These include a more specific description of the experimental setup to improve clarity, as well as the addition of critical quantitative results to emphasize the research significance.

Page 1, Lines 17−19:

A study on porosity distribution analysis and ventilation tests was conducted in a pilot silo with a height of 3 m, a diameter of 1.5 m, and a conical dome height of 0.85 m.

Page 1, Lines 26−34:

The results indicate that friction between the maize kernel and the silo wall leads to vertical pressure at the center of the bottom that was 10.7% higher than that near the wall. The average surface porosity of the maize bulk was 2.8% higher than at the bottom. This led to a minimum porosity of 0.409 at the center of the silo bottom, due to the combined effect of impact during the loading process and vertical pressure. The numerical simulation demonstrates excellent consistency with the experimental data. At a supply vent air velocity of 0.126 m/s, an increase in the maize bulk height from 0.725 m to 2.9 m resulted in reductions in airflow rate and average relative humidity of 20.3% and 9.67%.

 

Comment 2: The abstract clearly presents the study objectives and main findings, including the percentage differences in airflow velocity between the central and peripheral regions of the silo. However, it does not specify the magnitude of the airflow velocity to which these percentages refer. This detail is important as it would better contextualize the relative values and allow readers to more accurately assess the practical significance of the reported differences. It is recommended to include the reference velocity in the abstract to provide greater robustness to the results presented.

Response: Thank you very much for your careful reminder and valuable advice. In accordance with your suggestion, we have specified the inlet airflow velocity in the abstract to enhance the completeness and clarity of the presented results.

Page 1, Lines 32−34:

At a supply vent air velocity of 0.126 m/s, an increase in the maize bulk height from 0.725 m to 2.9 m resulted in reductions in airflow rate and average relative humidity of 20.3% and 9.67%.

 

Comment 3: The selected keywords are relevant, but some are too general or redundant with the title. In particular, grain storage and pressure could be removed or replaced, while heat and moisture transfer is too broad. It is recommended to use more specific terms that reflect the study’s contributions, such as pilot silo, anisotropic porosity, experimental validation, or temperature front curve (TFC). This would ensure that the keywords better represent the novelty of the work and increase its visibility in databases.

Response: Thank you very much for your careful reminder and valuable advice. We have updated the keywords to "grain storage; pressure; anisotropic porosity; airflow distribution; temperature front" in accordance with your suggestions to better reflect the novelty of this research.

Page 1, Lines 42−43:

Keywords: grain storage; pressure; anisotropic porosity; airflow distribution; temperature front

 

Comment 4: In line 43, it is stated that the annual maize production in China exceeds 280 million tons. However, it is not entirely clear which type(s) of maize this figure refers to. It is recommended to specify whether this number corresponds to the total production of all maize varieties or to a particular type. If the study focuses on a specific type, it should be explicitly stated to improve the accuracy and reproducibility of the work.

Response: We appreciate your valuable feedback regarding the corn production data cited in Line 45. In response, we have clarified in the manuscript that the "over 280 million tons" annual production refers to the total output of all corn varieties in China, based on the National Bureau of Statistics' 2023 data, rather than a specific type. This macro-scale estimate is appropriate given that our study examines airflow and environmental distribution in grain bulk storage at a systemic level, not at the kernel or varietal level. The revision was made to prevent ambiguity, and we agree with the importance of this clarification for the study's precision. We will certainly specify corn types in any future fine-grained or variety-specific research.

Page 2, Lines 45−46:

The aggregate annual production of all corn varieties in China surpasses 280 million tons.

 

Comment 5: The introduction could be strengthened with a broader discussion of results reported by other authors, which would provide a clearer context of the state of the art. In addition, the novelty and the objective of the article should be stated more explicitly. In line 83, where “the underlying mechanisms” are mentioned, it is necessary to specify which mechanisms are being referred to, as the current wording is ambiguous for the reader.

Response: Thank you very much for your careful reminder and valuable advice. We have thoroughly revised the introduction based on your suggestions. Firstly, we have strengthened it by incorporating a broader discussion of findings from other authors to provide a more comprehensive context. Subsequently, following this expanded literature review, we have explicitly summarized the limitations of existing studies to better highlight the novelty and objectives of our work. Regarding the comment on the "underlying mechanisms," we originally intended to refer to the schematic in Section 4 (Discussion), which visually illustrates both the sieving effect during central-fill maize loading and the impact of grain self-weight on porosity distribution, as well as how this distribution subsequently affects airflow during ventilation. However, to prevent any potential ambiguity for the reader, we have removed the phrase "underlying mechanisms" from the Introduction, as this concept is now explored in sufficient depth in Section 4. Thank you again sincerely for your careful suggestions and professional guidance, which is very important to improve the quality of our manuscript.

Pages 2−3, Lines 45−97:

The aggregate annual production of all corn varieties in China surpasses 280 million tons [1]. A significant portion of this yield requires safe and efficient storage to minimize post-harvest losses. During storage, ventilation is a critical operation for controlling temperature and moisture levels, thereby inhibiting mold growth and insect infestation. However, the inevitable presence of broken kernels and non-uniform kernels distribution during loading, often leads to heterogeneous porosity within the grain bulk [2]. This results in localized areas with low airflow passage where heat and moisture accumulate, creating breeding grounds for pests and mold development that ultimately cause grain quality deterioration [3,4].

As a key parameter governing airflow and convective heat and mass transfer in porous media like grain bulks, porosity has been the focus of several studies [5]. During the loading process of maize kernels into silos, the segregation mechanism causes smaller broken kernels to accumulate directly beneath the feeding point, filling the voids and resulting in lower porosity[6]. The larger intact kernels with lower surface friction tend to flow toward the silo walls, a skeletal framework formed by larger kernels led to higher localized porosity in these regions [7, 8]. Wei et al. [9] simulated the natural accumulation of 12139 maize kernels using the discrete element method, observing lower porosity beneath the filling point compared to the periphery. Gan et al. [10] developed a model relating porosity to the aspect ratio and size of particles through simulations of multi-shape grain packing. However, despite confirming the dependence of porosity on particle size and shape, their small-scale DEM approach does not adequately represent the porosity distribution variations in realistically large grain bulks. The anisotropic porosity distribution, varying in both radial and vertical directions, significantly influences airflow pathways and resistance during ventilation [11,12]. Bartosik and Maier [13] analyzed the differences in airflow resistance between the central and peripheral regions of the silo. Lawrence and Maier [3] assumed a linear radial variation in maize porosity and used finite volume simulations to analyze non-uniform airflow; however, they neglected the effect of vertical porosity variation with depth on airflow and heat and moisture transfer. In contrast, Zheng et al. [14] and Ramaj et al. [15] considered only the vertical porosity gradient caused by self-compaction and its impact on airflow and heat and moisture transfer, treating porosity as uniform at the same grain depth and thereby ignoring radial porosity variations induced by segregation. These studies only qualitatively analyzed the effect of porosity on airflow and temperature-humidity distribution, without incorporating the influence of porosity distribution differences into temperature front models during ventilation. Therefore, two key limitations persist in the current research: first, the lack of an integrated model that couples radial segregation effects with vertical pressure-induced porosity changes; and second, the absence of a quantitative method to describe the ventilation temperature front caused by these porosity variations, which is critical for accurately predicting airflow and heat and moisture transfer in ventilated grain bulk.

Building upon previous analysis of segregation mechanisms during central-fill maize loading [16], this study incorporates a grain stress-strain relationship model into the FLAC^3D finite difference software platform through secondary development to analyze the vertical pressure distribution within the grain bulk. An anisotropic porosity distribution model for maize was subsequently developed, taking into account the combined effects of vertical pressure and segregation mechanisms. Based on this foundation, a comparative analysis was conducted on the differences in airflow and heat and moisture transfer during the ventilation process of maize bulk with isotropic and anisotropic porosity distributions. Furthermore, a nonlinear model was innovatively proposed to predict the temperature front curve (TFC) during ventilation, accounting for the effects of porosity distribution variations to forecast temperature evolution within the ventilated grain bulk.

 

Comment 6: In line 134, the model of the centrifugal fan is mentioned, but the volumetric airflow rate supplied by the fan is not specified. In silo aeration operations, this parameter is typically reported in m³/min × ton, so it would be useful to include this information. Likewise, in line 137, where it is stated that air was delivered at a set velocity, it would be advisable to explicitly show the conversion performed, i.e., the calculation of velocity as the volumetric airflow rate divided by the aeration system area. This would provide greater clarity and enable comparisons with previous studies on silo aeration.

Response: Thank you very much for your careful reminder and valuable advice. During the experiment, the centrifugal fan was connected to a frequency converter, allowing the fan speed to be controlled based on the current intensity. Prior to the experiment, we took into consideration the airflow loss that occurs as the air moves from the centrifugal fan through the duct to the bottom of the grain pile. Therefore, to accurately determine the airflow velocity delivered into the grain bulk, we monitored the wind speed at the Wind-distribution plate. In the simulation, the measured airflow velocity was accordingly used as the boundary condition for the airflow transfer analysis. We believe that this method of direct airflow monitoring provides a more accurate determination of the wind speed entering the grain bulk, and therefore we so we do not recommend modifying it here. Thank you again sincerely for your careful suggestions and professional guidance.

 

Comment 7: In line 136, it is mentioned that the fan air passes through an air-conditioning unit before entering the silo, but the properties of the external air and the conditioned air entering the silo are not specified. It is essential to provide these data, particularly the temperature of the air conditioned and its relative humidity content, since these parameters are critical in ventilation processes and in heat and moisture transfer within the grain bulk. Including this information would allow for better comparison with other silo aeration studies.

Response: Thank you very much for your careful reminder and valuable advice. As noted, we have supplemented the air conditioner's cooling capacity and circulating air flow data per your suggestions. Since PVC ducts are required to connect the pilot silo base, centrifugal fan, and the small refrigeration air conditioner, introducing significant cooling loss. We positioned temperature and humidity sensors at the wind- distribution plate's outlets to monitor the actual conditions entering the grain bulk. The supplied temperature (T_s) and relative humidity (RH_s) are explicitly provided in Figures 7 and 10, respectively.

Page 5, Lines 166−169:

The centrifugal fan was externally coupled to a small refrigeration air conditioner (Cooling capacity: 3650 W; Air flow: 590 m³/h, Dongguan Jinhongsheng Electric Appliance Co., Ltd.) to achieve controlled climate ventilation tests.

 

Comment 8: In Equation 5, the first term represents the variation for a compressible flow. However, in Table 2, the air properties are considered for an incompressible flow, where density is constant. Therefore, it is necessary to remove the first term from the equation, as it is inconsistent with the incompressibility assumption adopted in the model. This adjustment will provide greater mathematical consistency between the governing equations and the physical properties employed.

Response: Thank you very much for your careful reminder and valuable advice. We agree with your suggestion, under the incompressible flow assumption, the time derivative term in the continuity equation should be omitted. Accordingly, we have revised Equation 5 by removing the first term to ensure consistency with the assumption of constant air density stated in Table 2. Thank you again sincerely for your careful suggestions and professional guidance, which is very important to improve the quality of our manuscript. The modified equation is as follows:

Page 5, Line 198:

(5)

Comment 9: In Equation 6, the absence of the time derivative implies that the formulation corresponds to a steady-state condition. However, in Equations 9 and 10, the system is solved under transient conditions, which creates a conceptual inconsistency. Since the simulation results show the evolution of velocity as a function of time, it would be advisable to clarify the formulation of Equation 6 and include the transient term or explicitly justify the adopted assumption. This is important, as velocity clearly depends on time within the framework of the presented simulations.

Response: Thank you very much for your careful reminder and valuable advice. It should be clarified that Equation 6 aims to describe the constitutive relationship for momentum transport in fluid flow through porous media, and it is directly adopted from established hydrodynamic theory of porous media [Ref.23, Ergun, 1952]. This equation is formulated in a steady-state form because it defines an instantaneous local balance between the flow velocity and the pressure gradient at any given moment and position, where the resistance term (described by the Ergun equation) is a function of the velocity.

In the actual transient simulations, this constitutive relation is embedded within a broader transient solution framework. The transient behavior of the system is primarily governed by the time derivative terms in the continuity equation (Equation 5) and the energy/mass conservation equations (Equations 9 & 10). The evolution of the velocity field over time is achieved indirectly by solving for the pressure field, which couples the transient continuity and momentum equations, at each time step. Therefore, although Equation 6 itself does not contain a time derivative, its integration with the transient solver allows it to fully capture the temporal development of the velocity field, which is consistent with the time-dependent simulation results we have presented. We hope that this clarification addresses the consistency issue highlighted in your comment.

 

Comment 10: In Equations 7 and 8, the constant 150 corresponds to the classical and empirical parameter for the viscous term in the Ergun equation, whereas the value of 3.5, representing the inertial term, does not match the traditional parameter of the Ergun equation. It is necessary to explain the origin of this discrepancy and specify how the value of 3.5 was determined, as well as justify the use of the constant 150. It should be noted that Ergun established these parameters through experiments under specific conditions, using spheres and relatively uniform particles. In the case of maize, it would be necessary to estimate the parameters based on the pressure drop across the bed, and therefore the authors should clarify this aspect.

Response: Thank you very much for your careful reminder and valuable advice. You have correctly noted the discrepancy between the inertial coefficient in the classical Ergun equation and the value of 3.5 used in our study. We would like to clarify that this is not an oversight, but rather a specific adjustment for maize kernels, based on the following considerations:

Formula Origin and Applicability: The form of the equations we employed (Equations 7 and 8) is taken directly from Lawrence and Maier (2011) [3], which is an authoritative study on airflow resistance in maize bulk ventilation. This reference explicitly states that these coefficients are suitable for porous media consisting of non-spherical, rough-surfaced grains such as cereal grains. The parameters of the classical Ergun equation were originally derived from experimental data on uniform spherical particles. In contrast, corn grains differ significantly from ideal spheres in terms of shape, surface texture, and particle size distribution, leading to distinct flow resistance characteristics. Therefore, an adjustment of the inertial resistance coefficient is necessary.

Experimental Validation and Parameter Confirmation: To further verify the suitability of this formula for our experimental material, our research group independently conducted pressure drop experiments in a fixed bed (Liu et al., 2023a; 2023b). By measuring the pressure drop across a bed of corn grains at different flow velocities and fitting the experimental data to various forms of the Ergun equation with different coefficients, we found that the model using a viscous resistance coefficient of 150 and an inertial resistance coefficient of 3.5 provided a relatively accurate prediction of the pressure drop characteristics in the maize bulk bed.

In summary, the use of the coefficient 3.5 is based on a combination of previous research findings and our own experimental validation. It represents an empirical modification tailored to the physical properties of maize kernels, intended to more accurately describe the flow resistance during ventilation.

 

Liu, W.L.; Chen, G.X.; Zheng, D.Q.; Ge, M.M.; Liu, C.S.; An improved anisotropic continuum model for the flow and heat transfer in grain aeration system. J. Food Process Eng. 2023a, 46(11), 14421, https://doi.org/10.1016/10.1111/jfpe. 14421.

Liu, W.L.; Chen, G.X.; Zheng, D.Q.; Ge, M.M.; Liu, C.S.; Effects of the broken kernel on heat and moisture transfer in fixed-bed corn drying using particle-resolved CFD model, Agriculture-Basel, 2023b, 13(8), 1470. https://doi.org/10.3390/agriculture13081470.

 

Comment 11: In lines 184–187, the parameters of the energy equation are defined, including the dry basis moisture content (W) and the hygroscopic heat of sorption/desorption (hs). However, it is not clear how the moisture contents were determined, or which expression was used for calculating hs. It is necessary to explicitly state the procedure used to obtain these values, whether from experimental measurements, empirical correlations, or previous literature. It is also recommended to cite the relevant sources or clarify if the parameters were directly determined in this study. This information is essential to ensure reproducibility and to strengthen the formulation of the model.

Response: Thank you very much for your careful reminder and valuable advice. This helps improve the clarity and reproducibility of our model description. Regarding the parameters in the energy equation, we provide the following clarifications:

Dry-basis moisture content (W): This parameter was calculated directly from the experimentally measured wet-basis moisture content (M) using the formula W=M/(100−M). This definition was clearly provided below Equation (9) on page 7 (line 224). The wet-basis moisture content of the corn used in this study was M=12.7%±0.13% (Table 2), which is an experimentally measured value.

Heat of sorption (h_s): As suggested by the reviewer, the value of this parameter (2476 kJ/kg) was taken from a published authoritative literature source. We have now added an explicit citation for this parameter in the revised Table 2. The cited reference is widely recognized in the field of thermal properties of kernels.  

In summary, the dry-basis moisture content W was calculated based on our experimental measurements, while the heat of sorption h_s was taken from a well-established literature value. We have clearly indicated the sources of these parameters in the revised manuscript to ensure model transparency and reproducibility.

Page 7, Lines 237-238:

Table 2. Parameters related to the ventilation process

Material	Property	Value
Air [27]	Air density (ρa)	1.205 kg/m3
	Air specific heat (ca)	1006 J/(kg∙°C)
	Air tortuosity factor (τ)	1.2
	Air viscosity (μa)	1.79 × 10-5 Pa∙s
	Specific heat capacities of water	1850 J/(kg∙°C)
	Rate coefficient for moisture exchange between air and maize kernels (Dv)	2000exp(-5094 / T)
Maize bulk	Moisture content (M)	12.7% ± 0.13%
	Moisture content (dry basis) (W)	M/(1-M) × 100%
	Average maize kernel diameter (dp)	0.00721 m
	Particle density (ρs)	1256.7 kg/m3
	Density (ρb)	ρs(1−ϕ)
	Thermal conductivity (kb)	0.07257+1.209 × 10-4ρb W/(m∙°C) [26]
	Porosity (ϕ)	Fig. 5
	Specific heat (cb)	1780 J∙kg-1∙ °C -1[5]
	Heat sorption of water on maize (hs)	2476 kJ/kg[25]
	Temperature (T)	Fig. 6

 

Comment 12: In this section, it is necessary to specify why the metabolic heat of stored maize was not considered. Since the silo is insulated, the heat generated by grain respiration as a function of local moisture and temperature plays an important role in simulations and in the reproducibility of the data. The omission of this term should be clearly justified or, alternatively, discussed as a limitation of the model.

Response: Thank you very much for your careful reminder and valuable advice. It is explicitly stated that the heat of respiration was not considered in the model, as its impact on the temperature field was negligible due to the low initial moisture content (12.7%) of the maize and the short ventilation duration. This simplification has been acknowledged as a model limitation in the Discussion section.

Page 20, Lines 596-600:

In addition, the respirable heat was not considered in the model, as its impact on the temperature field was negligible due to the relatively low initial moisture content of the corn and the short duration of ventilation. While maize kernels may absorb a certain amount of moisture from the humid air during ventilation, this process is not expected to cause a sharp increase in local moisture content to a critical level.

 

Comment 13: In line 274, the use of a portable air-conditioning unit is mentioned; however, the conditioning parameters of the air entering the silo, such as temperature and relative humidity, are not specified. These parameters are essential for the interpretation of the results, as they directly influence heat and moisture transfer within the grain bulk. It is recommended to include these values to provide greater clarity and allow reproducibility of the experiments.

Response: Thank you very much for your careful reminder and valuable advice. As noted, we have supplemented the air conditioner's cooling capacity and circulating air flow data per your suggestions. Since PVC ducts are required to connect the pilot silo base, centrifugal fan, and the small refrigeration air conditioner, introducing significant cooling loss. We positioned temperature and humidity sensors at the wind- distribution plate's outlets to monitor the actual conditions entering the grain bulk. The supplied temperature (T_s) and relative humidity (RH_s) are explicitly provided in Figures 7 and 10, respectively. In the simulations, the actual measured temperature and humidity data were directly assigned as the boundary conditions to govern the heat and moisture transfer processes.

Page 5, Lines 166−169:

The centrifugal fan was externally coupled to a small refrigeration air conditioner (Cooling capacity: 3650 W; Air flow: 590 m³/h, Dongguan Jinhongsheng Electric Appliance Co., Ltd.) to achieve controlled climate ventilation tests.

 

Comment 14: In line 276, it is reported that the aeration period lasted 94.25 h to reduce the temperature to 19.12 ºC. This period is excessively long, and even so, the achieved temperatures are not suitable for safe storage, which requires values below 17 ºC. It is suggested to include a table showing different scenarios of inlet airconditioning temperatures to analyze whether fewer hours of aeration would be required. Such an analysis would strengthen the study and highlight the practical advantage of using an air-conditioning system.

Response: We thank you for this valuable suggestion. We fully agree that, from an ideal grain storage perspective, lower temperatures and shorter ventilation durations are more advantageous. As you rightly inferred, the limited capacity of the compact refrigeration air-conditioning unit used in our experiment, combined with the lack of high-grade insulation in the ventilation ducts, made the temperature of the cooled air supplied to the grain bulk susceptible to fluctuations in the ambient conditions (the laboratory temperature was relatively high in summer). This effect can be observed in Figure 9, after about 75 hours of ventilation, temperature rebounds occurred at some measurement points within the grain stack due to changes in the ambient temperature.

We acknowledge that this represents a limitation of the experimental setup under laboratory conditions aimed at mechanistic investigation. Your proposal to "analyze the ventilation efficiency under different air intake temperatures" is highly relevant from a practical standpoint and provides an important direction for our future research. In subsequent work, we will prioritize upgrading the experimental system, for instance, by employing a higher-capacity temperature-control unit and improving duct insulation. On this basis, we will systematically study the ventilation performance under different air supply parameters to develop more instructive and optimized ventilation strategies. Once again, we appreciate your insightful comments.

 

Comment 15: The current manuscript structure could be improved to enhance the flow of the presentation. The Physical Model and Mesh Generation section should be placed before 3.7. Numerical Model Validation, so that the model description naturally precedes its validation. In addition, sections 3.4 and 3.5 should be moved to the Results section, as they correspond to findings and analyses that are better understood in that context. This reorganization would allow for more coherent reading and make the study’s logic easier to follow.

Response: Thank you very much for your careful reminder and valuable advice. We completely agree that a well-organized article structure is essential for logical coherence and reader comprehension. In response to your comments, we have optimized the organization of the paper. The original Section 3.6, "Physical Model and Mesh Generation," has been relocated in its entirety to Section 2, "Materials and Methods," where it now naturally extends the description of the model development. This adjustment ensures that the physical model and mesh information—essential for the simulations—are presented immediately after the introduction of the numerical methods and experimental setup. As a result, the logical flow is improved and the structure better aligns with conventional academic writing practice.

Pages 7−8, Lines 238−264:

2.6 Physical Model and Mesh Generation

To ensure comparability with experimental results, a full-scale numerical model replicating the actual geometry of the pilot silo was created within the COMSOL Multiphysics 6.3 finite element analysis environment. As shown in Fig. 3, with appropriate simplifications, the simulation objects include the silo structure, the maize bulk, the wind-distribution plate, the air layer between the distribution plate and the silo floor, and the air layer above the grain bulk. A tetrahedral mesh scheme was applied to the optimized geometric model of the simulated silo, resulting in a total of 380,000 elements for the numerical simulation.

During the simulation of the ventilation process, the air was assumed to be an incompressible fluid. The air-inlet was set to normal inflow, with the inlet temperature corresponding to the monitored air supply temperature from the experiment. The air enters the bottom of the silo and rapidly flows through the plenum formed between the wind-distribution plate and the silo floor. It then passes through the vents of the distribution plate into the computational domain of the maize bulk. The air-outlet boundary was defined as a pressure outlet condition. Since it is open to the atmospheric environment, the outlet pressure was set to 0. All boundary conditions and computational parameters were consistent with the experimental setup. An anisotropic porosity model of the maize bulk was incorporated into the porous media computational model. To compare the impact of porosity distribution on heat transfer within the maize bulk, the porosity was also assumed to be uniformly distributed isotropically. The overall average porosity value was used for this homogeneous distribution scenario, enabling a comparative study on the effects of different porosity models on the coupled heat and moisture transfer during ventilation. The overall average porosity of the grain bulk is 0.442, with an average density of 702.5 kg/m³.

 

Figure 3. Physical model of the silo, (a) the silo, (b) mash the model.

 

Comment 16: In this section, the use of COMSOL is mentioned, but the reference should be corrected to include the full name COMSOL Multiphysics®. It is also important to specify the version used (e.g., 6.1, 6.2, or 6.3), as different versions may vary in numerical capabilities and available modules. In addition, the numerical method used by COMSOL to solve the equations should be explicitly stated (e.g., finite element method, timestepping scheme, tolerances).

Response: Thank you very much for your careful reminder and valuable advice. Thank you very much for your careful reminder and valuable advice. As suggested, we have specified the COMSOL Multiphysics version used in our simulations. The time step during the calculation process is 0.05 hours, and the relative tolerance is the system default value.

Page 7, Lines 239−241:

To ensure comparability with experimental results, a full-scale numerical model replicating the actual geometry of the pilot silo was created within the COMSOL Multiphysics 6.3 finite element analysis environment.

 

Comment 17: Furthermore, a mesh independence analysis should be carried out and reported, comparing results obtained with different mesh sizes against the experimental measurements. This would justify the use of 380,000 elements in the model, providing robustness to the procedure and ensuring that the results are not solely dependent on the chosen refinement. Finally, it is recommended to include the specifications of the computing equipment (processor, RAM, GPU if applicable) and the computational times, since this information is essential to assess reproducibility and computational efficiency.

Response: Thank you very much for your careful reminder and valuable advice. During the simulation, we systematically compared the temperature predictions obtained from coarse (approximately 150,000 cells), medium (approximately 250,000 cells), and fine (approximately 380,000 cells) grid resolutions. Analysis revealed only minor differences in the results across the three grid levels, indicating that the numerical solution had achieved convergence. As expected, the fine grid (380,000 cells) demonstrated the best agreement with the experimental data among all configurations. Therefore, we selected the results from this configuration for presentation in the manuscript to provide the most accurate comparison. The final choice of the 380,000-cell grid was based on an optimal balance between computational accuracy and efficiency. Regarding the computational setup, we do not deem such hardware-specific details essential for reproducing the core physical models and numerical methodologies presented in this study. To maintain the focus and conciseness of the manuscript, we have chosen to omit these hardware configurations and computation times from the main text. Thank you again sincerely for your careful suggestions and professional guidance, which is very important to improve the quality of our manuscript.

 

Comment 18: In line 361, it is stated that the air enters from the bottom of the silo, but the temperature and humidity conditions of the inlet air are not specified. These parameters are critical, as they determine the heat and moisture transfer gradients within the bulk and directly affect the simulation results. It is recommended to explicitly include the temperature and relative humidity of the inlet air to ensure reproducibility and allow comparison with the experiments.

Response: Thank you very much for your careful reminder and valuable advice. We fully agree that the air intake parameters are critical to the accuracy of the model. In our study, these key parameters were monitored and are clearly presented in the manuscript. Inlet air temperature is explicitly indicated as the “T_s” curve in each subplot of Figure 7. Inlet air relative humidity is clearly shown as the “RH_s” curve in Figure 10(a). In the numerical simulations, the actual measured, time-varying data for inlet temperature and humidity, obtained from the experimental monitoring system, were directly prescribed as the inlet boundary conditions of the model to accurately govern the heat and moisture transfer processes within the grain bulk. We believe that by referring to the figures already provided, the transparency of the model boundary conditions and the reproducibility of the study are adequately ensured. Thank you again sincerely for your careful suggestions and professional guidance

 

Comment 19: Although the Numerical Model Validation section presents model validation, it is recommended to perform a mesh independence analysis to determine whether the differences between predictions and experimental data arise from the mesh or the mathematical model. For greater clarity, it would be useful to indicate whether the mesh corresponds to the categories defined in COMSOL (fine, extra fine, or extremely fine), and to specify whether the same mesh was applied throughout the entire domain or if different refinements were used at the boundaries. This information would strengthen the robustness of the numerical model.

Response: Thank you very much for your careful reminder and valuable advice. During the simulation, we systematically compared the temperature predictions obtained from coarse (approximately 150,000 cells), medium (approximately 250,000 cells), and fine (approximately 380,000 cells) grid resolutions. Analysis revealed only minor differences in the results across the three grid levels, indicating that the numerical solution had achieved convergence. As expected, the fine grid (380,000 cells) demonstrated the best agreement with the experimental data among all configurations. Therefore, we selected the results from this configuration for presentation in the manuscript to provide the most accurate comparison. The final choice of the 380,000-cell grid was based on an optimal balance between computational accuracy and efficiency. Regarding mesh generation, the model utilized a hybrid mesh comprising triangular and quadrilateral elements, which was automatically created within the COMSOL finite element platform. Local refinement was applied in boundary regions where steep physical field gradients were anticipated.

 

Comment 20: The conclusions are well aligned with experimental evidence and numerical simulations, particularly regarding the influence of anisotropic porosity on airflow, pressure distribution, and the shape of the temperature front. This consistency adds robustness to the study. However, the conclusions could be strengthened by explicitly acknowledging some limitations and suggesting directions for future research.

Response: Thank you very much for your careful reminder and valuable advice. We sincerely thank the reviewer for their high recognition of the consistency between the research conclusions and the experimental/simulation evidence, as well as for their highly constructive and valuable suggestions. In response, we have integrated and strengthened the detailed discussion regarding the model's preconditions, scope of application, and future prospects into the corresponding parts of Section 4 "Discussion" (e.g., at the end of Section 4.1, and in newly added content in Sections 4.2 and 4.3). Considering that the Conclusions section should remain highly concise to summarize the core findings, we have only added a brief final remark on the applicability of this study and its guiding significance for grain storage.

Page 21, Lines 631−633:

The findings are positioned to provide theoretical insight and technical guidance for optimizing grain storage ventilation strategies and predicting cooling front dynamics.

 

Other suggestions:

First, the study was carried out in a pilot silo under controlled conditions, where the influence of external climatic variability was minimized. In real storage scenarios, silos cannot be completely isolated from environmental fluctuations such as diurnal and seasonal changes in temperature and relative humidity. These variations significantly affect airflow distribution, heat transfer, and moisture migration. Future work should therefore extend the anisotropic porosity model to incorporate boundary conditions that reflect environmental variability. This would improve the practical applicability of the model for grain management in large-scale storage systems.Second, the conclusions could better emphasize the scalability of the model. Although the pilot silo provides valuable insights, the compaction and segregation effects may intensify in industrial silos of greater depth and volume. Incorporating validation with large-scale experimental data or field trials would enhance confidence in applying the anisotropic porosity model to commercial storage operations. Finally, it is recommended that the conclusions briefly outline potential future research directions, such as:Evaluating the combined impact of anisotropic porosity and environmental variations on long-term storage stability.Extending the model to other grains with different shapes and densities.Assessing the effect of anisotropic airflow on biological factors, such as mold growth and insect development.Highlighting these aspects in the conclusions would broaden the scope and underline the real-world relevance of the proposed model.

Response: Thank you very much for your careful reminder and valuable advice. We sincerely thank the reviewer for their high appreciation of the value of this study and for their valuable suggestions to enhance the depth and breadth of the paper. The comments regarding environmental fluctuations, model scalability, and future research directions are particularly insightful. In response, we have integrated and strengthened the discussion of certain limitations in the relevant parts of Section 4 "Discussion". Additionally, a new concluding paragraph has been added to summarize the applicability and practical implications of our findings. Looking forward, we plan to incorporate field monitoring data to evaluate the model's predictive performance in commercial grain storage facilities, with the aim of advancing intelligent ventilation control for grain piles. We greatly appreciate your insightful input and look forward to potential future exchanges.

 

If you and reviewers have any other questions, please do not hesitate to contact us as soon as possible. We thank you and reviewers again for your patience, help and constant attention to our manuscript.

Sincerely yours,

Jun Wang

wangj@haut.edu.cn

Author Response File: Author Response.pdf

Reviewer 2 Report

Comments and Suggestions for Authors

Authors tried to model a maize silo but this paper lacks scientific rigor and presentation.

Line 53: Porosity increases towards the side wall. Please revise this statement.

Line 72 to 75: This statement is not correct. There are many studies that have conducted this study. Pilot scale studies have been numerous but not the farm-scale levels. The model developed using pilot scale set ups cannot be extrapolated to far-scale silos.

Line 79: Anisotropic porosity distribution are already developed. What new are the authors proposing?

Introduction does not show much of the information on the knowledge gap.

Line 96: There are known equations that are used to calculate porosity with varying vertical heights in the standards. Why did author use this equation?

Eq 7 and 8 are for default systems. When grain medium is introduced a separate constant is needed to make sure the equation handles the non-uniformity of the medium.

Nevertheless, the equations used in this study are not described or introduced properly that will be relevant for grain storage systems. Reviewer strongly suggests to review relevant papers to frame a proper knowledge gap. There is no description Finite element model and how it was used.

Author Response

Reply to reviewer 2:

We are grateful to reviewer#2 for his/her effort in reviewing our manuscript and his/her positive feedback. Here below we address the questions and suggestions raised by reviewer#2

Comment 1: Line 53: Porosity increases towards the side wall. Please revise this statement.

Response: Thank you very much for your careful reminder and valuable advice. The clarity regarding the porosity distribution in the grain bulk has been improved by refining the relevant text, in accordance with your suggestions.

Page 2, Lines 55−60:

During the loading process of maize kernels into silos, the segregation mechanism causes smaller broken kernels to accumulate directly beneath the feeding point, filling the voids and resulting in lower porosity[6]. The larger intact kernels with lower surface friction tend to flow toward the silo walls, a skeletal framework formed by larger kernels led to higher localized porosity in these regions [7, 8]. 

 

Comment 2: Line 72 to 75: This statement is not correct. There are many studies that have conducted this study. Pilot scale studies have been numerous but not the farm-scale levels. The model developed using pilot scale set ups cannot be extrapolated to far-scale silos.

Response: Thank you very much for your careful reminder and valuable advice. We have thoroughly revised the Introduction in accordance with your suggestions. Specifically, we have strengthened this section by incorporating a broader discussion of findings reported by other researchers, thereby providing a more comprehensive background on the subject. As a key parameter influencing ventilation control in stored grain, the porosity of the grain bulk has indeed attracted widespread attention. However, through a critical analysis of the existing literature, we have identified two main limitations in current research: (1) There is a lack of an experimentally validated anisotropic porosity distribution model that simultaneously accounts for both radial segregation and vertical compression effects in grain bulks. (2) A quantitative description of the ventilation temperature front under such anisotropic porosity conditions is missing, which is essential for accurately predicting temperature evolution during grain ventilation. Although this study does not involve porosity and ventilation analysis in full scale silos, the model developed in this work has been well validated in the pilot silo. In our subsequent research, we plan to combine real scale silo experiments with numerical simulations to further extend the findings of this study and optimize the proposed model. We sincerely thank you for your valuable comments and patient guidance. We also look forward to the opportunity for further exchange and discussion in future research.

Page 2, Lines 77−85:

These studies only qualitatively analyzed the effect of porosity on airflow and temperature-humidity distribution, without incorporating the influence of porosity distribution differences into temperature front models during ventilation. Therefore, two key limitations persist in the current research: first, the lack of an integrated model that couples radial segregation effects with vertical pressure-induced porosity changes; and second, the absence of a quantitative method to describe the ventilation temperature front caused by these porosity variations, which is critical for accurately predicting airflow and heat and moisture transfer in ventilated grain bulk.

 

Comment 3: Line 79: Anisotropic porosity distribution are already developed. What new are the authors proposing?

Response: Thank you very much for your careful reminder and valuable advice. Current research on the porosity distribution in grain bulk can be categorized into several limited approaches: some studies employ discrete element simulations to analyze porosity in small scale particle assemblies; others focus solely on porosity variations induced by vertical grain loading; while another group considers only radial segregation effects. Moreover, most existing studies provide only qualitative descriptions of porosity, often merely demonstrating through simulation that boundary porosity exceeds that at the center. Crucially, none have accounted for the actual porosity distribution resulting from natural loading processes incorporating genuine kernel breakage, segregation, and the influence of grain self weight. This study innovatively integrates spatial grain pressure analysis with central-fill loading experiments to develop a porosity distribution model that comprehensively incorporates both radial segregation and vertical compression effects. Furthermore, we conducted ventilation experiments and numerical simulations to establish a temperature front curve (TFC) model that quantitatively characterizes how anisotropic porosity distribution influences temperature evolution during grain ventilation, thereby enabling more accurate prediction of thermal dynamics in ventilated grain bulk.

Page 2, Lines 80−97:

Therefore, two key limitations persist in the current research: first, the lack of an integrated model that couples radial segregation effects with vertical pressure-induced porosity changes; and second, the absence of a quantitative method to describe the ventilation temperature front caused by these porosity variations, which is critical for accurately predicting airflow and heat and moisture transfer in ventilated grain bulk.

Building upon previous analysis of segregation mechanisms during central-fill maize loading [16], this study incorporates a grain stress-strain relationship model into the FLAC^3D finite difference software platform through secondary development to analyze the vertical pressure distribution within the grain bulk. An anisotropic porosity distribution model for maize was subsequently developed, taking into account the combined effects of vertical pressure and segregation mechanisms. Based on this foundation, a comparative analysis was conducted on the differences in airflow and heat and moisture transfer during the ventilation process of maize bulk with isotropic and anisotropic porosity distributions. Furthermore, a nonlinear model was innovatively proposed to predict the temperature front curve (TFC) during ventilation, accounting for the effects of porosity distribution variations to forecast temperature evolution within the ventilated grain bulk.

 

 

Comment 4: Introduction does not show much of the information on the knowledge gap.

Response: Thank you very much for your careful reminder and valuable advice. We have thoroughly revised the introduction based on your suggestions. Firstly, we have strengthened it by incorporating a broader discussion of findings from other authors to provide a more comprehensive context. Subsequently, following this expanded literature review, we have explicitly summarized the limitations of existing studies to better highlight the novelty and objectives of our work.

Page 2, Lines 64−85:

However, despite confirming the dependence of porosity on particle size and shape, their small-scale DEM approach does not adequately represent the porosity distribution variations in realistically large grain bulks. The anisotropic porosity distribution, varying in both radial and vertical directions, significantly influences airflow pathways and resistance during ventilation [11,12]. Bartosik and Maier [13] analyzed the differences in airflow resistance between the central and peripheral regions of the silo. Lawrence and Maier [3] assumed a linear radial variation in maize porosity and used finite volume simulations to analyze non-uniform airflow; however, they neglected the effect of vertical porosity variation with depth on airflow and heat and moisture transfer. In contrast, Zheng et al. [14] and Ramaj et al. [15] considered only the vertical porosity gradient caused by self-compaction and its impact on airflow and heat and moisture transfer, treating porosity as uniform at the same grain depth and thereby ignoring radial porosity variations induced by segregation. These studies only qualitatively analyzed the effect of porosity on airflow and temperature-humidity distribution, without incorporating the influence of porosity distribution differences into temperature front models during ventilation. Therefore, two key limitations persist in the current research: first, the lack of an integrated model that couples radial segregation effects with vertical pressure-induced porosity changes; and second, the absence of a quantitative method to describe the ventilation temperature front caused by these porosity variations, which is critical for accurately predicting airflow and heat and moisture transfer in ventilated grain bulk.

Comment 5: Line 96: There are known equations that are used to calculate porosity with varying vertical heights in the standards. Why did author use this equation?

Response: Thank you very much for your careful reminder and valuable advice. The porosity of the grain bulk is comprehensively influenced by factors such as the moisture content, particle size, and composition of the kernels. Most existing models are applicable only to specific experimental conditions studied by their respective authors. In this study, the maize used for the uniaxial compression tests was sampled from the loading process of the pilot silo. The physical properties of the maize may differ from the materials on which published equations are based. Therefore, directly applying existing models may not accurately capture the true mechanical behavior or porosity variation of the maize bulk under uniaxial compression in our experiments. 

As cited in our literature review (e.g., Bartosik & Maier [13]; Lawrence & Maier [3]), the internal porosity distribution within the maiez bulk is highly heterogeneous both radially and vertically. This heterogeneity is primarily caused by the combined effects of self-compaction and kernel segregation. Existing models, however, often focus on only one of these aspects. Our objective is to develop a model that more accurately describes the distribution of porosity under complex stress states in actual grain silos. The research methodology is as follows: First, the relationship between vertical pressure and porosity is determined by measuring the deformation of the maize bulk under stepwise loading. Next, a previously validated finite difference model for analyzing spatial pressure fields in grain bulk, developed by our research group, is used to calculate the pressure at various spatial locations within the pilot silo. Finally, building upon our previously established porosity distribution model, which considered only radial segregation, we introduce modifications to account for porosity changes induced by vertical pressure. This integration allows us to develop an anisotropic porosity distribution model that comprehensively reflects the combined effects of grain bulk pressure, kernel breakage, and segregation. Thank you again sincerely for your careful suggestions and professional guidance, which is very important to improve the quality of our manuscript.

 

Page 3, Lines 111−115:

The compressive deformation of the maize bulk during testing was recorded by measuring the vertical displacement with a dial indicator. Finally, a mapping relationship between the porosity of the grain bulk and the vertical pressure was established at each load level based on the grain mass, the dimensions of the test box, the measured sample height and the kernel density:

(1)

Where is the porosity of the grain bulk at each load level; m_b is the mass of maize used in the uniaxial compression test, kg; h_i is the height of the grain bulk at each load level, m.

 

Comment 6: Eq 7 and 8 are for default systems. When grain medium is introduced a separate constant is needed to make sure the equation handles the non-uniformity of the medium.

Response: Thank you very much for your careful reminder and valuable advice. In Equations 7 and 8, both the viscous and inertial loss coefficients are functions of the corn kernel diameter and the porosity of the grain pile. During the experiment, the equivalent mean diameter of the corn kernels was determined as 0.00721 m through multiple random sampling measurements and calculated using . The porosity value was obtained from the results presented in Figure 5. Both parameters have been provided in Table 2. Thank you again sincerely for your careful suggestions and professional guidance.

 

Comment 7: Nevertheless, the equations used in this study are not described or introduced properly that will be relevant for grain storage systems. Reviewer strongly suggests to review relevant papers to frame a proper knowledge gap. There is no description Finite element model and how it was used.

Response: Thank you very much for your careful reminder and valuable advice. In accordance with your suggestions, we have provided a detailed explanation of how Equation 1 calculates porosity under corresponding pressure. Additionally, all equations have been supplemented with appropriate citations, and the literature sources for the parameters used are now documented in Table 2.

Page 4, Lines 104−119:

450 g maize sample was placed in the test box for uniaxial compression testing. The specific procedure was as follows: A conventional geotechnical lever-loading device was employed[19], where counterweights drove a loading frame connected to the lever, as shown in Fig.1. This action applied force through a loading screw to the top plate of the maize bulk, following a sequence of predetermined load levels of 3, 13, 34, 76, 117, 159, and 200 kPa. The compressive deformation of the maize bulk during testing was recorded by measuring the vertical displacement with a dial indicator. Finally, a mapping relationship between the porosity of the grain bulk and the vertical pressure was established at each load level based on the grain mass, the dimensions of the test box, the measured sample height and the kernel density:

(1)

Where is the porosity of the grain bulk at each load level; m_b is the mass of maize used in the uniaxial compression test, kg; h_i is the height of the grain bulk at each load level, m.

 

Figure 1. Uniaxial compression test.

Page 4, Lines 124−126:

The E-B constitutive model well captures the stress-strain behavior of granular materials. The tangent deformation modulus E_t and bulk deformation modulus B are calculated as follows[22].

 

Page 6, Lines 196−197:

the grain volume fraction term was incorporated into the fluid continuity equation[3].

Page 6, Lines 201−202:

Thus, a resistance term attributable to the grain bulk is incorporated into the momentum equation of fluid flow[3, 23].

Page 6, Lines 212−213:

ϕ is the porosity of maize bulk[3, 23].

Page 6, Lines 217−218:

The convective heat transfer process during grain bulk ventilation can be described by the following equation[24, 25].

Page 6, Lines 225−226:

During the ventilation process, the moisture variation within the grain bulk is governed by the following equation[24, 25].

References

24. de Mattos, R.; Garreiro, J.M.; Meghirditchian, G.; Ferrari, A.; Zecchi, B.; Effect of modeling simplifications on behavior and computational cost for simulation of fixed bed wheat drying process. Dry. Technol. 2022, 40(7), 1338-1355. https://doi.org/10.1080/07373937.2020.1867564.
25. Ge, M.M.; Chen, G.X.; Liu, W.L.; Liu, C.S.; Study of heat and mass transfer during drying process of maize grain pile based on computed tomography. Biosyst. Eng. 2024, 248, 82-96. https://doi.org/10.1016/j.biosystemseng.2024.10.003.

 

Response: A key innovation of this work lies in the experimental development of an anisotropic porosity distribution model that incorporates radial segregation and vertical compression. This model was integrated into a coupled heat and moisture transfer model to analyze ventilation processes, specifically airflow resistance and associated heat and mass transfer. Furthermore, the introduction has been strengthened with an expanded literature review that more clearly summarizes prior research and identifies the existing knowledge gap.

Page 2, Lines 54−85:

As a key parameter governing airflow and convective heat and mass transfer in porous media like grain bulks, porosity has been the focus of several studies [5]. During the loading process of maize kernels into silos, the segregation mechanism causes smaller broken kernels to accumulate directly beneath the feeding point, filling the voids and resulting in lower porosity[6]. The larger intact kernels with lower surface friction tend to flow toward the silo walls, a skeletal framework formed by larger kernels led to higher localized porosity in these regions [7, 8]. Wei et al. [9] simulated the natural accumulation of 12139 maize kernels using the discrete element method, observing lower porosity beneath the filling point compared to the periphery. Gan et al. [10] developed a model relating porosity to the aspect ratio and size of particles through simulations of multi-shape grain packing. However, despite confirming the dependence of porosity on particle size and shape, their small-scale DEM approach does not adequately represent the porosity distribution variations in realistically large grain bulks. The anisotropic porosity distribution, varying in both radial and vertical directions, significantly influences airflow pathways and resistance during ventilation [11,12]. Bartosik and Maier [13] analyzed the differences in airflow resistance between the central and peripheral regions of the silo. Lawrence and Maier [3] assumed a linear radial variation in maize porosity and used finite volume simulations to analyze non-uniform airflow; however, they neglected the effect of vertical porosity variation with depth on airflow and heat and moisture transfer. In contrast, Zheng et al. [14] and Ramaj et al. [15] considered only the vertical porosity gradient caused by self-compaction and its impact on airflow and heat and moisture transfer, treating porosity as uniform at the same grain depth and thereby ignoring radial porosity variations induced by segregation. These studies only qualitatively analyzed the effect of porosity on airflow and temperature-humidity distribution, without incorporating the influence of porosity distribution differences into temperature front models during ventilation. Therefore, two key limitations persist in the current research: first, the lack of an integrated model that couples radial segregation effects with vertical pressure-induced porosity changes; and second, the absence of a quantitative method to describe the ventilation temperature front caused by these porosity variations, which is critical for accurately predicting airflow and heat and moisture transfer in ventilated grain bulk.

 

Response: We have provided a detailed explanation of the finite difference method and the implementation of the E-B constitutive model in FLAC^3D.

Page 4, Lines 147−156:

FLAC^3D employs an explicit lagrangian algorithm and a mixed-discretization zoning technique to discretize the continuum into a mesh. Based on the velocities of all nodes at the current time step, the strain rate tensor of each element is calculated via spatial differencing. Multiplying the strain rate by the time step yields the strain increment. The stress increment is then computed according to the E-B constitutive model for maize bulk. This stress increment is added to the stress from the previous time step to obtain the updated stress at the current time step. Using the updated stresses of all elements, the contribution force of each element to its nodes is recalculated through spatial differencing. The gravitational force from the overlying grain is applied to the nodes, and vector summation is performed to determine the resultant forces.

 

 

If you and reviewers have any other questions, please do not hesitate to contact us as soon as possible. We thank you and reviewers again for your patience, help and constant attention to our manuscript.

Sincerely yours,

Jun Wang

wangj@haut.edu.cn

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The results presented in this manuscript are solid and demonstrate significant potential and value. The findings are well analyzed and contribute meaningfully to the field. However, the Methods section requires substantial improvement to ensure clarity, reproducibility, and scientific rigor. In particular, more detailed descriptions of experimental procedures, numerical setup, and equipment specifications are necessary. Therefore, I recommend this manuscript for publication after major revision. The detailed comments are following.

1. The abstract lacks important numerical results and is overly descriptive. Please include key quantitative findings to highlight the significance of the study.
2. The research gap is not clearly stated in the Introduction. This section should be revised to articulate the gap in knowledge or practice that this study addresses.
3. While the modeling results are thoroughly presented, the literature review in the Introduction is insufficient. A more comprehensive review is needed to establish the context and justify the research gap.
4. In lines 89–90, the maize properties are cited—please clarify whether these were taken from the literature or measured in this study. If they were not measured, provide justification.
5. In Section 2.1, please add details and specifications of the uniaxial compression test equipment used.
6. Porosity was calculated using Equation (1), but it is unclear how porosity values at each loading level were obtained. Please describe the measurement method.
7. References should be added for all equations presented in the manuscript.
8. Please include the reference source for Table 1.
9. Provide additional details for GB 50077-2017 and the finite difference method mentioned in line 117.
10. There are no details describing the finite difference method used. Please elaborate on the methodology.
11. Specifications for all equipment used in the experiments should be included for clarity and reproducibility.
12. In lines 136–140, please provide more details on the refrigeration air conditioner (e.g., BTU rating), air velocity, and controlled air temperature and relative humidity.
13. Units for all dimensions should be added to Figure 1.
14. Specify the types and models of sensors used for measuring temperature and humidity.
15. Please add the reference for Table 2.
16. The numerical setup should be clearly described in the Methods section, not only by presenting the governing equations. This is essential for reproducibility and for other researchers to build on this work.
17. In line 211, clarify why samples were taken from the silo—was this for porosity analysis or another purpose?
18. Please explain how porosity values in Figure 2 were measured, including whether measurements were replicated.
19. The compression test figure (currently Figure 2) should be moved to the Methods section for better organization.
20. Explain how the correlation in Equation (12) was obtained, as this is not described in the Methods section.
21. The numerical setup should be thoroughly explained in the Methods section, rather than being scattered in Sections 3.6 and 3.7.
22. Specify which version of COMSOL was used for the simulations.
23. In the Conclusions, discuss the applicability and practical implications of the model results.

 

Author Response

Reply to reviewer 3:

We are grateful to reviewer#3 for his/her effort in reviewing our manuscript and his/her positive feedback. The summary of our work as written by this reviewer is precise. Here below we address the questions and suggestions raised by reviewer#3

Comment 1: The abstract lacks important numerical results and is overly descriptive. Please include key quantitative findings to highlight the significance of the study.

Response: Thank you very much for your careful reminder and valuable advice. Following your feedback, we have incorporated key quantitative findings and streamlined some of the text to better highlight the significance of this research. Thank you again sincerely for your careful suggestions and professional guidance, which is very important to improve the quality of our manuscript.

Page 1, Lines 26−34:

The results indicate that friction between the maize kernel and the silo wall leads to vertical pressure at the center of the bottom that was 10.7% higher than that near the wall. The average surface porosity of the maize bulk was 2.8% higher than at the bottom. This led to a minimum porosity of 0.409 at the center of the silo bottom, due to the combined effect of impact during the loading process and vertical pressure. The numerical simulation demonstrates excellent consistency with the experimental data. At a supply vent air velocity of 0.126 m/s, an increase in the maize bulk height from 0.725 m to 2.9 m resulted in reductions in airflow rate and average relative humidity of 20.3% and 9.67%.

 

Comment 2: The research gap is not clearly stated in the Introduction. This section should be revised to articulate the gap in knowledge or practice that this study addresses.

Response: Thank you very much for your careful reminder and valuable advice. Current research on the porosity distribution in grain bulk can be categorized into several limited approaches: some studies employ discrete element simulations to analyze porosity in small scale particle assemblies; others focus solely on porosity variations induced by vertical grain loading; while another group considers only radial segregation effects. Moreover, most existing studies provide only qualitative descriptions of porosity, often merely demonstrating through simulation that boundary porosity exceeds that at the center. Crucially, none have accounted for the actual porosity distribution resulting from natural loading processes incorporating genuine kernel breakage, segregation, and the influence of grain self weight. This study innovatively integrates spatial grain pressure analysis with central-fill loading experiments to develop a porosity distribution model that comprehensively incorporates both radial segregation and vertical compression effects. Furthermore, we conducted ventilation experiments and numerical simulations to establish a temperature front curve (TFC) model that quantitatively characterizes how anisotropic porosity distribution influences temperature evolution during grain ventilation, thereby enabling more accurate prediction of thermal dynamics in ventilated grain bulk.

Page 2, Lines 80−97:

Therefore, two key limitations persist in the current research: first, the lack of an integrated model that couples radial segregation effects with vertical pressure-induced porosity changes; and second, the absence of a quantitative method to describe the ventilation temperature front caused by these porosity variations, which is critical for accurately predicting airflow and heat and moisture transfer in ventilated grain bulk.

Building upon previous analysis of segregation mechanisms during central-fill maize loading [16], this study incorporates a grain stress-strain relationship model into the FLAC^3D finite difference software platform through secondary development to analyze the vertical pressure distribution within the grain bulk. An anisotropic porosity distribution model for maize was subsequently developed, taking into account the combined effects of vertical pressure and segregation mechanisms. Based on this foundation, a comparative analysis was conducted on the differences in airflow and heat and moisture transfer during the ventilation process of maize bulk with isotropic and anisotropic porosity distributions. Furthermore, a nonlinear model was innovatively proposed to predict the temperature front curve (TFC) during ventilation, accounting for the effects of porosity distribution variations to forecast temperature evolution within the ventilated grain bulk.

 

Comment 3: While the modeling results are thoroughly presented, the literature review in the Introduction is insufficient. A more comprehensive review is needed to establish the context and justify the research gap.

Response: Thank you very much for your careful reminder and valuable advice. We have thoroughly revised the introduction based on your suggestions. Firstly, we have strengthened it by incorporating a broader discussion of findings from other authors to provide a more comprehensive context. Subsequently, following this expanded literature review, we have explicitly summarized the limitations of existing studies to better highlight the novelty and objectives of our work.

Pages 2−3, Lines 45−97:

The aggregate annual production of all corn varieties in China surpasses 280 million tons [1]. A significant portion of this yield requires safe and efficient storage to minimize post-harvest losses. During storage, ventilation is a critical operation for controlling temperature and moisture levels, thereby inhibiting mold growth and insect infestation. However, the inevitable presence of broken kernels and non-uniform kernels distribution during loading, often leads to heterogeneous porosity within the grain bulk [2]. This results in localized areas with low airflow passage where heat and moisture accumulate, creating breeding grounds for pests and mold development that ultimately cause grain quality deterioration [3,4].

As a key parameter governing airflow and convective heat and mass transfer in porous media like grain bulks, porosity has been the focus of several studies [5]. During the loading process of maize kernels into silos, the segregation mechanism causes smaller broken kernels to accumulate directly beneath the feeding point, filling the voids and resulting in lower porosity[6]. The larger intact kernels with lower surface friction tend to flow toward the silo walls, a skeletal framework formed by larger kernels led to higher localized porosity in these regions [7, 8]. Wei et al. [9] simulated the natural accumulation of 12139 maize kernels using the discrete element method, observing lower porosity beneath the filling point compared to the periphery. Gan et al. [10] developed a model relating porosity to the aspect ratio and size of particles through simulations of multi-shape grain packing. However, despite confirming the dependence of porosity on particle size and shape, their small-scale DEM approach does not adequately represent the porosity distribution variations in realistically large grain bulks. The anisotropic porosity distribution, varying in both radial and vertical directions, significantly influences airflow pathways and resistance during ventilation [11,12]. Bartosik and Maier [13] analyzed the differences in airflow resistance between the central and peripheral regions of the silo. Lawrence and Maier [3] assumed a linear radial variation in maize porosity and used finite volume simulations to analyze non-uniform airflow; however, they neglected the effect of vertical porosity variation with depth on airflow and heat and moisture transfer. In contrast, Zheng et al. [14] and Ramaj et al. [15] considered only the vertical porosity gradient caused by self-compaction and its impact on airflow and heat and moisture transfer, treating porosity as uniform at the same grain depth and thereby ignoring radial porosity variations induced by segregation. These studies only qualitatively analyzed the effect of porosity on airflow and temperature-humidity distribution, without incorporating the influence of porosity distribution differences into temperature front models during ventilation. Therefore, two key limitations persist in the current research: first, the lack of an integrated model that couples radial segregation effects with vertical pressure-induced porosity changes; and second, the absence of a quantitative method to describe the ventilation temperature front caused by these porosity variations, which is critical for accurately predicting airflow and heat and moisture transfer in ventilated grain bulk.

Building upon previous analysis of segregation mechanisms during central-fill maize loading [16], this study incorporates a grain stress-strain relationship model into the FLAC^3D finite difference software platform through secondary development to analyze the vertical pressure distribution within the grain bulk. An anisotropic porosity distribution model for maize was subsequently developed, taking into account the combined effects of vertical pressure and segregation mechanisms. Based on this foundation, a comparative analysis was conducted on the differences in airflow and heat and moisture transfer during the ventilation process of maize bulk with isotropic and anisotropic porosity distributions. Furthermore, a nonlinear model was innovatively proposed to predict the temperature front curve (TFC) during ventilation, accounting for the effects of porosity distribution variations to forecast temperature evolution within the ventilated grain bulk.

 

Comment 4: In lines 89–90, the maize properties are cited—please clarify whether these were taken from the literature or measured in this study. If they were not measured, provide justification.

Response: Thank you very much for your careful reminder and valuable advice. The moisture content and kernel density of the maize used in the experiments were determined through laboratory measurements following established standards. The moisture content was measured by drying randomly selected samples at 103 °C for 72 hours in accordance with the ASAE 2017. The kernel density was obtained following the experimental procedure outlined in the GB/T 5518-2008.

Page 3, Lines 100−102:

The moisture content M of the maize used in the experiment was 12.7 ± 0.13% w.b. after drying at 103 °C for 72 h[17]. The kernel density ρ_s was 1256.7 kg/m³ according to GB/T 5518-2008[18].

17. ASAE S352.2 APR1988 (R2017); Moisture Measurement–Unground Grain and Seeds. ASAE: St. Joseph, MI, USA, 2017.
18. GB/T 5518-2008; Inspection of grain and oil–determination of relatively density of grain and oilseeds. National Standardization Administration. 2008.

 

Comment 5: In Section 2.1, please add details and specifications of the uniaxial compression test equipment used.

Response: Thank you very much for your careful reminder and valuable advice. In accordance with the testing procedure specified in GB/T 4935.1-2008, a standard geotechnical consolidation lever-loading device was used to apply load sequentially to the maize sample, as shown in the Fig.1 . The compressive deformation of the grain bulk was recorded by a dial indicator fixed at the top of the loading plate.

Page 3, Lines 102−109:

A standard geotechnical consolidation ring (inner diameter: 61.8 mm) was modified into a rectangular test box with a side length of 120 mm and a height of 55 mm. 450 g maize sample was placed in the test box for uniaxial compression testing. The specific procedure was as follows: A conventional geotechnical lever-loading device was employed[19], where counterweights drove a loading frame connected to the lever, as shown in Fig.1. This action applied force through a loading screw to the top plate of the maize bulk, following a sequence of predetermined load levels of 3, 13, 34, 76, 117, 159, and 200 kPa.  

 

Figure 1. Uniaxial compression test

 

Comment 6: Porosity was calculated using Equation (1), but it is unclear how porosity values at each loading level were obtained. Please describe the measurement method.

Response: Thank you very much for your careful reminder and valuable advice. We have revised Equation 1 in accordance with your suggestions. The deformation of the grain bulk under each load level was recorded by a dial indicator fixed on the top plate. Under the condition of constant mass of the maize sample, the porosity at each loading level was calculated based on the volume of the maize bulk after compression at each stage and the kernel density of the maize.

Page 3, Lines 109−117:

The compressive deformation of the maize bulk during testing was recorded by measuring the vertical displacement with a dial indicator. Finally, a mapping relationship between the porosity of the grain bulk and the vertical pressure was established at each load level based on the grain mass, the dimensions of the test box, the measured sample height and the kernel density:

(1)

Where is the porosity of the grain bulk at each load level; m_b is the mass of maize used in the uniaxial compression test, kg; h_i is the height of the grain bulk at each load level, m.

 

Comment 7: References should be added for all equations presented in the manuscript.

Response: Thank you very much for your careful reminder and valuable advice. In accordance with your suggestion, we have added appropriate citations to the proposed equation.

Page 4, Lines 134−136:

The E-B constitutive model well captures the stress-strain behavior of granular materials. The tangent deformation modulus E_t and bulk deformation modulus B are calculated as follows[22].

Page 6, Lines 196−197:

the grain volume fraction term was incorporated into the fluid continuity equation[3].

Page 6, Lines 201−202:

Thus, a resistance term attributable to the grain bulk is incorporated into the momentum equation of fluid flow[3, 23].

Page 6, Lines 212−213:

ϕ is the porosity of maize bulk[3, 23].

Page 6, Lines 217−218:

The convective heat transfer process during grain bulk ventilation can be described by the following equation[24, 25].

Page 6, Lines 225−226:

During the ventilation process, the moisture variation within the grain bulk is governed by the following equation[24, 25].

References

24. de Mattos, R.; Garreiro, J.M.; Meghirditchian, G.; Ferrari, A.; Zecchi, B.; Effect of modeling simplifications on behavior and computational cost for simulation of fixed bed wheat drying process. Dry. Technol. 2022, 40(7), 1338-1355. https://doi.org/10.1080/07373937.2020.1867564.
25. Ge, M.M.; Chen, G.X.; Liu, W.L.; Liu, C.S.; Study of heat and mass transfer during drying process of maize grain pile based on computed tomography. Biosyst. Eng. 2024, 248, 82-96. https://doi.org/10.1016/j.biosystemseng.2024.10.003.

 

Comment 8: Please include the reference source for Table 1.

Response: Thank you very much for your careful reminder and valuable advice. The methodology of introducing the E-B model into the FLAC^3D finite difference platform to analyze grain bulk pressure was previously validated by our group through triaxial tests, with the findings published in the J. Henan Univ. Technol. (Nat. Sci. Ed.). As such, the relevant parameters used in this study were sourced from that publication, and the reference has been duly cited in Table 1. Thank you again sincerely for your careful suggestions and professional guidance, which is very important to improve the quality of our manuscript.

Table 1. Parameters of maize[22]

Average density, ρab kg/m3	μ	Rf	c/kPa	φ/ °	K	n	m	Kb
702.5	0.32	0.88	6.03	28	36.06	0.92	0.83	19.4

 

21. Zhang, D. Zheng, D.Q.; Chen, G.X.; Jiang, M.M.; Chen, J.H.; Numerical simulation on pressure field of bulk grain pile in large warehouse by Flac^3D. J. Henan Univ. Technol. (Nat. Sci. Ed.), 2017, 38(6), 98-103. https://doi.org/10.16433/j.cnki.issn1673-2383.2017.06.017.

 

Comment 9: Provide additional details for GB 50077-2017 and the finite difference method mentioned in line 117.

Response: Thank you very much for your careful reminder and valuable advice. Regarding the calculation method for vertical pressure in silo grain piles, the GB 50077-2017 provides relatively detailed specifications. To ensure clarity and precision in our manuscript, we have directly referenced these provisions. As for the finite difference method, we have refined its description following your suggestions.

Page 4, Lines 124−127:

The vertical pressure in the pilot silo is calculated using a combined approach of the standard and numerical simulation. According to the GB 50077-2017 [21]，The vertical pressure p_h at depth s within the grain bulk is given by:

(4)

Page 4, Lines 147−156:

FLAC^3D employs an explicit lagrangian algorithm and a mixed-discretization zoning technique to discretize the continuum into a mesh. Based on the velocities of all nodes at the current time step, the strain rate tensor of each element is calculated via spatial differencing. Multiplying the strain rate by the time step yields the strain increment. The stress increment is then computed according to the E-B constitutive model for maize bulk. This stress increment is added to the stress from the previous time step to obtain the updated stress at the current time step. Using the updated stresses of all elements, the contribution force of each element to its nodes is recalculated through spatial differencing. The gravitational force from the overlying grain is applied to the nodes, and vector summation is performed to determine the resultant forces.

 

Comment 10: There are no details describing the finite difference method used. Please elaborate on the methodology.

Response: Thank you very much for your careful reminder and valuable advice. In accordance with your suggestions, we have provided a detailed explanation of the finite difference method and the implementation of the E-B constitutive model in FLAC^3D.

Page 4, Lines 147−156:

FLAC^3D employs an explicit lagrangian algorithm and a mixed-discretization zoning technique to discretize the continuum into a mesh. Based on the velocities of all nodes at the current time step, the strain rate tensor of each element is calculated via spatial differencing. Multiplying the strain rate by the time step yields the strain increment. The stress increment is then computed according to the E-B constitutive model for maize bulk. This stress increment is added to the stress from the previous time step to obtain the updated stress at the current time step. Using the updated stresses of all elements, the contribution force of each element to its nodes is recalculated through spatial differencing. The gravitational force from the overlying grain is applied to the nodes, and vector summation is performed to determine the resultant forces.

 

Comment 11: Specifications for all equipment used in the experiments should be included for clarity and reproducibility.

Response: Thank you very much for your careful reminder and valuable advice. As requested, we have provided the detailed technical specifications for the experimental equipment that were previously not elaborated.

Page 5, Lines 164−169:

An opening at the center of the floor plate served as the air inlet during ventilation, connected to a centrifugal fan (Model 4-72-2.8A, Foshan Xing Chen Zhao Ye Environmental Technology Co., Ltd.) of the ventilation system. The centrifugal fan was externally coupled to a small refrigeration air conditioner (Cooling capacity: 3650 W; Air flow: 590 m³/h, Dongguan Jinhongsheng Electric Appliance Co., Ltd.) to achieve controlled climate ventilation tests.

Pages 5−6, Lines 184−186:

These sensors were connected to a paperless recorder (Model KSF60A0R, Ningbo Keshun Instrument Co., Ltd.) 

 

Comment 12: In lines 136–140, please provide more details on the refrigeration air conditioner (e.g., BTU rating), air velocity, and controlled air temperature and relative humidity.

Response: Thank you very much for your careful reminder and valuable advice. As noted, we have supplemented the air conditioner's cooling capacity and circulating air flow data per your suggestions. Since PVC ducts are required to connect the pilot silo base, centrifugal fan, and the small refrigeration air conditioner, introducing significant cooling loss. We positioned temperature and humidity sensors at the wind- distribution plate's outlets to monitor the actual conditions entering the grain bulk. The supplied temperature (T_s) and relative humidity (RH_s) are explicitly provided in Figures 7 and 10, respectively.

Page 5, Lines 166−169:

The centrifugal fan was externally coupled to a small refrigeration air conditioner (Cooling capacity: 3650 W; Air flow: 590 m³/h, Dongguan Jinhongsheng Electric Appliance Co., Ltd.) to achieve controlled climate ventilation tests.

 

Comment 13: Units for all dimensions should be added to Figure 1.

Response: Thank you very much for your careful reminder and valuable advice.We apologize for the unclear labeling of units in the figure. The units for the dimensions have now been added to the figure as suggested.，Thank you again sincerely for your careful suggestions and professional guidance, which is very important to improve the quality of our manuscript.

Page 5, Line 174:

 

Figure 2. Pilot silo experimental setup (a) and sensor layout inside the silo (b).

 

Comment 14: Specify the types and models of sensors used for measuring temperature and humidity.

Response: Thank you very much for your careful reminder and valuable advice. We apologize for the lack of clarity in describing the types and models of the sensors used for measuring temperature and humidity. These details have now been supplemented as recommended. Thank you again sincerely for your careful suggestions and professional guidance, which is very important to improve the quality of our manuscript.

Page 5, Lines 177-179:

Temperature (Model PT100,Ningbo Keshun Instrument Co., Ltd.) and humidity sensing (Model KS-SHTE15T, Ningbo Keshun Instrument Co., Ltd.) cables were installed inside the grain bulk.

 

Comment 15: Please add the reference for Table 2.

Response: Thank you very much for your careful reminder and valuable advice. As suggested, we have added the relevant citations to Table 2.

Page 7, Lines 237-238:

Table 2. Parameters related to the ventilation process

Material	Property	Value
Air [27]	Air density (ρa)	1.205 kg/m3
	Air specific heat (ca)	1006 J/(kg∙°C)
	Air tortuosity factor (τ)	1.2
	Air viscosity (μa)	1.79 × 10-5 Pa∙s
	Specific heat capacities of water	1850 J/(kg∙°C)
	Rate coefficient for moisture exchange between air and maize kernels (Dv)	2000exp(-5094 / T)
Maize bulk	Moisture content (M)	12.7% ± 0.13%
	Moisture content (dry basis) (W)	M/(1-M) × 100%
	Average maize kernel diameter (dp)	0.00721 m
	Particle density (ρs)	1256.7 kg/m3
	Density (ρb)	ρs(1−ϕ)
	Thermal conductivity (kb)	0.07257+1.209 × 10-4ρb W/(m∙°C) [26]
	Porosity (ϕ)	Fig. 5
	Specific heat (cb)	1780 J∙kg-1∙ °C -1[5]
	Heat sorption of water on maize (hs)	2476 kJ/kg[25]
	Temperature (T)	Fig. 6

Comment 16: The numerical setup should be clearly described in the Methods section, not only by presenting the governing equations. This is essential for reproducibility and for other researchers to build on this work.

Response: Thank you very much for your careful reminder and valuable advice. As recommended, we have relocated the numerical details originally presented in Section 3 (Results) to Section 2 (Methods). Furthermore, appropriate citations have been added to the governing equations. The parameters used in the numerical simulation are now summarized in Table 2, where we have explicitly distinguished between values obtained from our direct measurements and those sourced from the literature, with corresponding references provided for the latter.

Page 4, Lines 134−136:

The E-B constitutive model well captures the stress-strain behavior of granular materials. The tangent deformation modulus E_t and bulk deformation modulus B are calculated as follows[22].

Page 6, Lines 196−197:

the grain volume fraction term was incorporated into the fluid continuity equation[3].

Page 6, Lines 201−202:

Thus, a resistance term attributable to the grain bulk is incorporated into the momentum equation of fluid flow[3, 23].

Page 6, Lines 212−213:

ϕ is the porosity of maize bulk[3, 23].

Page 6, Lines 217−218:

The convective heat transfer process during grain bulk ventilation can be described by the following equation[24, 25].

Page 6, Lines 225−226:

During the ventilation process, the moisture variation within the grain bulk is governed by the following equation[24, 25].

Page 7, Lines 237-238:

Table 2. Parameters related to the ventilation process

Material	Property	Value
Air [27]	Air density (ρa)	1.205 kg/m3
	Air specific heat (ca)	1006 J/(kg∙°C)
	Air tortuosity factor (τ)	1.2
	Air viscosity (μa)	1.79 × 10-5 Pa∙s
	Specific heat capacities of water	1850 J/(kg∙°C)
	Rate coefficient for moisture exchange between air and maize kernels (Dv)	2000exp(-5094 / T)
Maize bulk	Moisture content (M)	12.7% ± 0.13%
	Moisture content (dry basis) (W)	M/(1-M) × 100%
	Average maize kernel diameter (dp)	0.00721 m
	Particle density (ρs)	1256.7 kg/m3
	Density (ρb)	ρs(1−ϕ)
	Thermal conductivity (kb)	0.07257+1.209 × 10-4ρb W/(m∙°C) [26]
	Porosity (ϕ)	Fig. 5
	Specific heat (cb)	1780 J∙kg-1∙ °C -1[5]
	Heat sorption of water on maize (hs)	2476 kJ/kg[25]
	Temperature (T)	Fig. 6

 

Pages 7−8, Lines 238−264:

2.6 Physical Model and Mesh Generation

To ensure comparability with experimental results, a full-scale numerical model replicating the actual geometry of the pilot silo was created within the COMSOL Multiphysics 6.3 finite element analysis environment. As shown in Fig. 3, with appropriate simplifications, the simulation objects include the silo structure, the maize bulk, the wind-distribution plate, the air layer between the distribution plate and the silo floor, and the air layer above the grain bulk. A tetrahedral mesh scheme was applied to the optimized geometric model of the simulated silo, resulting in a total of 380,000 elements for the numerical simulation.

During the simulation of the ventilation process, the air was assumed to be an incompressible fluid. The air-inlet was set to normal inflow, with the inlet temperature corresponding to the monitored air supply temperature from the experiment. The air enters the bottom of the silo and rapidly flows through the plenum formed between the wind-distribution plate and the silo floor. It then passes through the vents of the distribution plate into the computational domain of the maize bulk. The air-outlet boundary was defined as a pressure outlet condition. Since it is open to the atmospheric environment, the outlet pressure was set to 0. All boundary conditions and computational parameters were consistent with the experimental setup. An anisotropic porosity model of the maize bulk was incorporated into the porous media computational model. To compare the impact of porosity distribution on heat transfer within the maize bulk, the porosity was also assumed to be uniformly distributed isotropically. The overall average porosity value was used for this homogeneous distribution scenario, enabling a comparative study on the effects of different porosity models on the coupled heat and moisture transfer during ventilation. The overall average porosity of the grain bulk is 0.442, with an average density of 702.5 kg/m³.

 

Comment 17: In line 211, clarify why samples were taken from the silo—was this for porosity analysis or another purpose?

Response: Thank you very much for your careful reminder and valuable advice. As suggested, we have clarified the rationale for sampling from the silo.

Pages 7−8, Lines 273−277:

Due to the potential for kernel breakage from the spiral grain suction machine and possible moisture changes during the extended loading process [16], samples were randomly taken from the pilot silo. Uniaxial compression tests were then conducted on these samples to establish the correspondence between vertical pressure and porosity, as shown in Fig. 4. 

 

Comment 18: Please explain how porosity values in Figure 2 were measured, including whether measurements were replicated.

Response: Thank you very much for your careful reminder and valuable advice. We have revised Equation 1 in accordance with your suggestions. The deformation of the grain bulk under each load level was recorded by a dial indicator fixed on the top plate. Under the condition of constant mass of the maize sample, the porosity at each loading level was calculated based on the volume of the maize bulk after compression at each stage and the kernel density of the maize.Our research group has previously conducted extensive uniaxial compression tests to analyze the effect of vertical pressure on porosity[Liu et al, 2022; Liu et al, 2023], which have demonstrated the repeatability of this experimental and computational methodology.

References

Liu, C.S.;Chen, G.X.; Zhou, Y.; Zheng, D.Q.; Zhang Z.J.; Element tests and simulation of effects of vertical pressure on compression and mildew of wheat. Comput. Electron. Agr. 2022, 203, 107447.

Liu, C.S.;Chen, G.X.; Zhou, Y.; Yue, L.F.; Liu, W.L.; Investigation on compression and mildew of mixed and separated maize. Food Sci. Nutr. 2023, 11(5),2118-2129.

 

Page 3, Lines 104−119:

450 g maize sample was placed in the test box for uniaxial compression testing. The specific procedure was as follows: A conventional geotechnical lever-loading device was employed[19], where counterweights drove a loading frame connected to the lever, as shown in Fig.1. This action applied force through a loading screw to the top plate of the maize bulk, following a sequence of predetermined load levels of 3, 13, 34, 76, 117, 159, and 200 kPa. The compressive deformation of the maize bulk during testing was recorded by measuring the vertical displacement with a dial indicator. Finally, a mapping relationship between the porosity of the grain bulk and the vertical pressure was established at each load level based on the grain mass, the dimensions of the test box, the measured sample height and the kernel density:

(1)

Where is the porosity of the grain bulk at each load level; m_b is the mass of maize used in the uniaxial compression test, kg; h_i is the height of the grain bulk at each load level, m.

 

Figure 1. Uniaxial compression test.

 

Comment 19: The compression test figure (currently Figure 2) should be moved to the Methods section for better organization.

Response: Thank you very much for your careful reminder and valuable advice. In accordance with your suggestion, we have relocated the figure illustrating the uniaxial compression test to the "Methods" section and provided a more detailed description of the testing procedure.

Page 3, Lines 104−119:

450 g maize sample was placed in the test box for uniaxial compression testing. The specific procedure was as follows: A conventional geotechnical lever-loading device was employed[19], where counterweights drove a loading frame connected to the lever, as shown in Fig.1. This action applied force through a loading screw to the top plate of the maize bulk, following a sequence of predetermined load levels of 3, 13, 34, 76, 117, 159, and 200 kPa. The compressive deformation of the maize bulk during testing was recorded by measuring the vertical displacement with a dial indicator. Finally, a mapping relationship between the porosity of the grain bulk and the vertical pressure was established at each load level based on the grain mass, the dimensions of the test box, the measured sample height and the kernel density:

(1)

Where is the porosity of the grain bulk at each load level; m_b is the mass of maize used in the uniaxial compression test, kg; h_i is the height of the grain bulk at each load level, m.

 

Figure 1. Uniaxial compression test.

 

 

Comment 20: Explain how the correlation in Equation (12) was obtained, as this is not described in the Methods section.

Response: Thank you very much for your careful reminder and valuable advice. Building on our previous work [16], which established a porosity distribution model accounting for kernel breakage and segregation via pilot silo loading experiments and included model validation, this study determines the vertical pressure within the grain bulk and correlates it with porosity. By integrating porosity variations induced by this vertical pressure with those resulting from kernel breakage and segregation, we develop an enhanced porosity distribution model that incorporates both radial segregation and vertical compression.

Figure Comparison between prediction of the developed model and experimental data for BKDFn. [16]	Figure Relationship between porosity and normalized BKDF. [16]

 

Comment 21: The numerical setup should be thoroughly explained in the Methods section, rather than being scattered in Sections 3.6 and 3.7.

Response: Thank you very much for your careful reminder and valuable advice. As recommended, we have relocated the methodological and numerical descriptions to Section 2 (Materials and Methods). Thank you again sincerely for your careful suggestions and professional guidance, which is very important to improve the quality of our manuscript.

Pages 7−8, Lines 238−264:

2.6 Physical Model and Mesh Generation

To ensure comparability with experimental results, a full-scale numerical model replicating the actual geometry of the pilot silo was created within the COMSOL Multiphysics 6.3 finite element analysis environment. As shown in Fig. 3, with appropriate simplifications, the simulation objects include the silo structure, the maize bulk, the wind-distribution plate, the air layer between the distribution plate and the silo floor, and the air layer above the grain bulk. A tetrahedral mesh scheme was applied to the optimized geometric model of the simulated silo, resulting in a total of 380,000 elements for the numerical simulation.

During the simulation of the ventilation process, the air was assumed to be an incompressible fluid. The air-inlet was set to normal inflow, with the inlet temperature corresponding to the monitored air supply temperature from the experiment. The air enters the bottom of the silo and rapidly flows through the plenum formed between the wind-distribution plate and the silo floor. It then passes through the vents of the distribution plate into the computational domain of the maize bulk. The air-outlet boundary was defined as a pressure outlet condition. Since it is open to the atmospheric environment, the outlet pressure was set to 0. All boundary conditions and computational parameters were consistent with the experimental setup. An anisotropic porosity model of the maize bulk was incorporated into the porous media computational model. To compare the impact of porosity distribution on heat transfer within the maize bulk, the porosity was also assumed to be uniformly distributed isotropically. The overall average porosity value was used for this homogeneous distribution scenario, enabling a comparative study on the effects of different porosity models on the coupled heat and moisture transfer during ventilation. The overall average porosity of the grain bulk is 0.442, with an average density of 702.5 kg/m³.

 

Figure 3. Physical model of the silo, (a) the silo, (b) mash the model.

 

 

Comment 22: Specify which version of COMSOL was used for the simulations.

Response: Thank you very much for your careful reminder and valuable advice. As suggested, we have specified the COMSOL Multiphysics version used in our simulations.

Page 7, Lines 239−241:

To ensure comparability with experimental results, a full-scale numerical model replicating the actual geometry of the pilot silo was created within the COMSOL Multiphysics 6.3 finite element analysis environment.

 

Comment 23: In the Conclusions, discuss the applicability and practical implications of the model results.

Response: Thank you very much for your careful reminder and valuable advice. As suggested, we have elaborated on the applicability and practical implications of our model's findings in the Conclusion section.

Page 21, Lines 631−633:

The findings are positioned to provide theoretical insight and technical guidance for optimizing grain storage ventilation strategies and predicting cooling front dynamics.

 

If you and reviewers have any other questions, please do not hesitate to contact us as soon as possible. We thank you and reviewers again for your patience, help and constant attention to our manuscript.

Sincerely yours,

Jun Wang

wangj@haut.edu.cn

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

Comments and Suggestions for Authors

Reviewer is still not convienced with the novelty of the study. 

Some relevant studies as mentioned below should be read properly. Authors are encouraged to review these paper and then work or redesign the methodology to show the novelty:
- CFD modelling of physical velocity and anisotropic resistance components in a peaked stored grain with aeration ducting systems
- Modeling the Compressibility Behavior of Hard Red Wheat Varieties
- Stored Grain Pack Factor Measurements for Soybeans, Grain Sorghum, Oats, Barley, and Wheat
- Pack Factor Measurements for Corn in Grain Storage Bins
and related articles. 

Author Response

Reply to reviewer 2:

We are grateful to reviewer#2 for his/her effort in reviewing our manuscript and his/her positive feedback. Here below we address the questions and suggestions raised by reviewer#2

Comment 1: Reviewer is still not convienced with the novelty of the study. Some relevant studies as mentioned below should be read properly. Authors are encouraged to review these paper and then work or redesign the methodology to show the novelty:

• CFD modelling of physical velocity and anisotropic resistance components in a peaked stored grain with aeration ducting systems
• Modeling the Compressibility Behavior of Hard Red Wheat Varieties
• Stored Grain Pack Factor Measurements for Soybeans, Grain Sorghum, Oats, Barley, and Wheat
• Pack Factor Measurements for Corn in Grain Storage Bins
• and related articles.

 

Response: Thank you very much for your careful reminder and valuable advice. We apologize for not having more clearly articulated the novelty of this study. We have carefully reviewed the literature you suggested and reorganized the research background. Existing standard formulas typically describe porosity as a function of geometric depth, implicitly assuming that the vertical pressure in the grain bulk is uniform at the same depth. However, as shown in Fig. 5 of this study, due to the presence of silo wall friction, the vertical pressure distribution inside the grain bulk is highly non-uniform, with the pressure in the central region being significantly higher than that in the peripheral areas. Since the contact between grain kernels and pressure sensors is point-to-surface, measurement errors often occur during actual grain bulk pressure measurements. Moreover, the actual pressure in the grain bulk often differs from the results calculated by the standard formula. In our preliminary work, we first validated the effectiveness of the FLAC^3D model and then used this model to analyze the spatial pressure field of the grain bulk, obtaining the pressure at every point within the grain bulk space.

The advancement of our method lies in the fact that we do not establish a general porosity formula related to depth. Instead, we aim to obtain the compressive constitutive relationship of the maize bulk under different stress levels, i.e., the functional relationship between porosity and vertical pressure. By substituting the non-uniform stress field calculated by FLAC^3D into this relationship, we can more realistically predict the anisotropic porosity distribution inside the grain bulk caused by pressure non-uniformity. If we directly used the depth-based standard formula, we would not be able to account for the radial pressure variation due to silo wall friction, nor could we seamlessly couple the results of mechanical analysis (FLAC^3D) with fluid/heat transfer analysis (COMSOL). Therefore, the uniaxial compression test serves as an indispensable bridge connecting the two key modules of "grain bulk pressure analysis" and "ventilation process simulation." It provides the physical basis for converting the stress field calculated by FLAC^3D into the porosity field required for COMSOL simulations. This study establishes a porosity model that simultaneously considers the combined effects of radial segregation and vertical pressure, and innovatively proposes a nonlinear equation to accurately quantify the evolution of the ventilation temperature front dominated by non-uniform porosity.

We sincerely apologize if our previous explanations regarding the novelty of our work did not fully meet your expectations. We have endeavored to the best of our ability to clarify our contributions. If our current response and proposed revisions still fall short, we humbly hope for your understanding. We genuinely value your expertise and would be deeply grateful for any further specific suggestions you might have. We are fully committed to doing everything we can to further modify and improve the manuscript accordingly. Thank you again sincerely for your careful suggestions and professional guidance, which is very important to improve the quality of our manuscript.

 

 

Pages 2−3, Lines 60−101:

 Existing standard formulas typically express porosity or density as a function of geometric depth, assuming that the vertical pressure is uniform at the same depth within the grain bulk, with greater emphasis placed on the overall average compression effect induced by self-weight [8-11]. However, due to the presence of silo wall friction, the vertical pressure distribution inside the grain bulk becomes highly non-uniform. The pressure calculated using standard formulas deviates from the actual pressure within the bulk. Therefore, it is necessary to clarify the stress state inside the grain bulk and the constitutive relationships governing compressibility under different pressure levels. The anisotropic porosity distribution, varying in both radial and vertical directions, significantly influences airflow pathways and resistance during ventilation [12]. Understanding the non-uniform three-dimensional distribution of porosity is essential for revealing the heat and mass transfer mechanisms within the grain bulk during ventilation. Bartosik and Maier [13] analyzed the differences in airflow resistance between the central and peripheral regions of the silo. Lawrence and Maier [3, 14] assumed that the porosity of the maize bulk varied linearly in the radial direction and remained uniform along the vertical direction, employing the finite volume method to simulate airflow and temperature changes during ventilation. Building on this, Panigrahi et al. [15] measured porosity at only two points on the bulk surface, at the center and at a location 4.5 m from the center, obtaining values of 0.3907 and 0.4088, respectively. They then assumed that porosity increased linearly from 0.3907 at the center to a higher value in the peripheral region, while maintaining the same uniform vertical distribution with depth as assumed by Lawrence and Maier [3, 14]. Although both studies accounted for variations in porosity along the radial and vertical directions, their analyses of the ventilation process were based on assumed porosity distributions and failed to accurately represent the actual porosity distribution within the grain bulk using models. In summary, existing models exhibit significant limitations in predicting heat and mass transfer during grain bulk ventilation. Most overlook the radial pressure variations caused by silo wall friction and do not integrate the radial segregation effects occurring during grain loading. As a result, they fall short of precisely characterizing the anisotropic distribution of porosity.

To address these limitations, building upon previous analysis of segregation mechanisms during central-fill maize loading [16], this study incorporates a grain stress-strain relationship model into the FLAC^3D finite difference software platform through secondary development to analyze the vertical pressure distribution within the grain bulk. An anisotropic porosity distribution model for maize was subsequently developed, taking into account the combined effects of vertical pressure and segregation mechanisms. Based on this foundation, a comparative analysis was conducted on the differences in airflow and heat and moisture transfer during the ventilation process of maize bulk with isotropic and anisotropic porosity distributions. Furthermore, a nonlinear model was innovatively proposed to predict the temperature front curve (TFC) during ventilation, accounting for the effects of porosity distribution variations to forecast temperature evolution within the ventilated grain bulk.

Page 3, Lines 106−109:

To establish the connection between the grain bulk pressure and the subsequent heat and moisture transfer analysis based on COMSOL Multiphysics, a standard geotechnical consolidation ring (inner diameter: 61.8 mm) was modified into a rectangular test box with a side length of 120 mm and a height of 55 mm.

 

If you and reviewers have any other questions, please do not hesitate to contact us as soon as possible. We thank you and reviewers again for your patience, help and constant attention to our manuscript.

Sincerely yours,

Jun Wang

wangj@haut.edu.cn

Author Response File: Author Response.pdf

Reviewer 3 Report

Comments and Suggestions for Authors

The manuscript has been improved with respect to all comments. Therefore, I recommend it for publication.

Author Response

Reply to reviewer 3:

We are grateful to reviewer#2 for his/her effort in reviewing our manuscript and his/her positive feedback. Here below we address the questions and suggestions raised by reviewer#3

Comment 1: The manuscript has been improved with respect to all comments. Therefore, I recommend it for publication.

Response: Thank you very much for your careful reminder and valuable advice. We are delighted to hear that the reviewer finds our manuscript significantly improved and recommends it for publication. We sincerely thank the reviewer for their time, insightful comments, and valuable suggestions throughout the review process, which have been instrumental in enhancing the quality of our work.

 

Sincerely yours,

Jun Wang

wangj@haut.edu.cn

Author Response File: Author Response.pdf

Round 3

Reviewer 2 Report

Comments and Suggestions for Authors

Authors have addressed the comments effectively.