Turbulence Intensity Characteristics of a Magnetoliquid Seal Interface in a Liquid Environment

Round 1

Reviewer 1 Report

This study presents a set of simulations for the magnetic fluid sealing devices in liquid environments using the common program, FLUENT. The simulation results are then compared with the experimental observations for the verification. It is shown that the maximum turbulence intensity of the liquid interface layer is proportional with the shaft speed. The paper is well-prepared and meaningful to the research community. However, the finite element model plays an important role in this research and its information is very limited. Belows are my comments.

1. Geometry and dimensional parameters of the finite element model should be detailed
2. Meshing information should be provided. The meshed model should be shown. The element types in the model should be explained.
3. The Figure 14 shows obvious differences between the simulation and the experiment, those are quite significant. Is the simulation model reliable to be used for the design of the magnetic liquid sealing device?
4. The simulation studies related to this research should be critically reviewed in the introduction part and emphasize the main contributions of the present simulation.

Author Response

Reply to the letter

Dear reviewer, thank you for your detailed review and correction of my manuscript. According to your suggestion, I have thoroughly considered the content of the manuscript. Overall, I believe that your comments are mainly in line with the lacking content. According to your suggestions, I carefully revised the manuscript. I believe that the quality of the manuscript has significantly improved. Therefore, thank you again for your help and support!

The following are my replies to your revision comments one by one:

1.Geometry and dimensional parameters of the finite element model should be detailed.

In this paper, the finite volume method is applied to study the flow field of the magnetic fluid sealing liquid medium. The central idea of finite volume method is to replace the continuous physical quantities in the time and space domains by the physical quantity set of the finite discrete points. Thus, meshing is highly important, which is the premise of the finite volume method. However, the geometric and grid models are not shown in this paper; thus, this is a major mistake in the manuscript. I have supplemented and revised the manuscript as follows:

Figure 1 shows the fluid computational domain model of the sealed cavity with a shaft diameter (RD) of 200 mm, sealing clearance height of 1 mm, and cavity height (HS) of 40 mm. The OS is slotted on the shaft surface with the starting end of the slot position flushed with the end of the pole piece. The tested slot depths (SDs) are 1, 2, and 3 times the sealing clearance (1SD, 2SD, and 3SD), and the slot lengths (SLs) are 8, 16, and 32 times the sealing clearance (8SL, 16SL, and 32SL). Figure 2 shows the difference between the TS and OS.

Figure 3 presents the computational fluid domain grid model, which adopts the hexahedral structure grid drawn by the ICEM software. The comprehensive quality of the grid is above 0.9, and the grid angle is 87–94°. In the same model, the number of grids in the high-speed flow is generally larger than that in the low-speed flow. Therefore, this study conducted grid independence calculation for each model when the shaft speed is 1000 rpm. When the number of grids in all models is greater than 238531, the physical quantity monitored in the flow field does not vary significantly with the increase of the grid number (less than 3%), indicating that these grid numbers meet the calculation requirements. Thus, the number of grids in the subsequent calculations under all working conditions was set to be greater than 238531.

2.Meshing information should be provided. The meshed model should be shown. The element types in the model should be explained.

Thank you very much for this insight. I added grid information and model in this paper.

Figure 3 presents the computational fluid domain grid model, which adopts the hexahedral structure grid drawn by the ICEM software. The comprehensive quality of the grid is above 0.9, and the grid angle is 87–94°. In the same model, the number of grids in the high-speed flow is generally larger than that in the low-speed flow. Therefore, this study conducted grid independence calculation for each model when the shaft speed is 1000 rpm. When the number of grids in all models is greater than 238531, the physical quantity monitored in the flow field does not vary significantly with the increase of the grid number (less than 3%), indicating that these grid numbers meet the calculation requirements. Thus, the number of grids in the subsequent calculations under all working conditions was set to be greater than 238531.

3. The Figure 14 shows obvious differences between the simulation and the experiment, those are quite significant. Is the simulation model reliable to be used for the design of the magnetic liquid sealing device?

At the beginning of the test and measurement, vibration was noted in the test device, which led to significant error in the results. We conducted a test again in September, and reduced the vibration of the device by adding rubber gaskets in the contact part. The test results were significantly corrected, and I modified the new test data into the original text.

4. The simulation studies related to this research should be critically reviewed in the introduction part and emphasize the main contributions of the present simulation.

The Introduction should provide key concepts that highlight the significance of the research, which is currently lacking in the manuscript. To this end, I conducted an extensive literature review, including all the papers cited in this paper. This section is subsequently modified as follows:

When the interface of two liquids with different densities is subjected to an external force, the interface is disturbed and instability occurs. Interface instability can be categorized as Rayleigh–Taylor, Richmyer–Meshkov, or KH instability, which are caused by gravity fields [11], shock waves [12–13], and speed differences [14], respectively. When the magnetic liquid rotates and seals, the rotation of the main shaft drives the rotation of the liquid in the sealed cavity; the speed difference between the magnetic liquid and liquid in the sealed cavity causes KH instability. In static sealing, there is no speed difference between the magnetic and sealing liquids, thereby inhibiting KH instability and resulting in a superior sealing effect. As the rotation speed increases, the nature of the flow between the magnetic liquid and sealing medium changes from laminar to turbulent, and the interfacial layer of the fluid medium becomes unstable, immersed, and permeated, thereby damaging the O-shaped sealing ring formed by the magnetic fluid under the action of the magnetic field, resulting in seal failure. The sealing ring is first damaged near the main shaft, where the maximum turbulence intensity of the fluid medium interface layer occurs. Therefore, reducing the maximum turbulence intensity of the interface layer can effectively improve the sealing effect of the magnetic liquid. At present, research on magnetic fluid seal is mostly based on the design and improvement of the magnetic circuit device. Further, there are few studies on the flow field of liquid in sealed media through a single research method, which is mainly through theoretical derivation. The influence of the sealing flow field on the stability of the magnetic fluid seal should be considered and discussed from different angles through expanded research methods.

Author Response File: Author Response.pdf

Reviewer 2 Report

Please see the attachment.

Comments for author File: Comments.pdf

Author Response

Reply to the letter

Dear reviewer, thank you for your detailed review and correction of my manuscript. According to your suggestion, I have thoroughly considered the content of the manuscript. Overall, I believe that your comments are mainly in line with the lacking content. According to your suggestions, I carefully revised the manuscript. I believe that the quality of the manuscript has significantly improved. Therefore, thank you again for your help and support!

The following are my replies to your revision comments one by one:

1. Equations (1), (2) and (3): The authors defined the nomenclatures at the end of the paper, which is a bit confusing. They should at least mention that please see the end of the paper, etc. The quantities u and u’ in (3) are not even defined.

We apologize for not completely writing the formula and defining the variables. We agree that the theoretical formula should be explained in detail in the text and that the formula table at the end of the paper is not conducive to readers' reading. Therefore, we made the following modifications to the paper.

The internal flow of the sealed liquid is approximated as a three-dimensional incompressible flow, in which the flow field should satisfy the mass and momentum conservation equation [15]. Mass conservation can be described as the equality of the mass of the fluid flowing out of the control body to that reduced by the density change in the control body in the same time interval. The mass conservation equation, or continuity equation, is as follows:

Where is the fluid density;,, and  are the velocity of the fluid along the x, y, and z directions, respectively; and t is the unit time.

Momentum conservation is defined as the equality of the rate of change of the momentum of the control body with respect to time to the sum of various external forces acting on the control body, as follows:

where u is the fluid velocity, P is the fluid pressure,  is the viscous shear stress of the fluid, and F is the volumetric force acting on the fluid.

Turbulence intensity is important for determining the microscopic pulsation characteristics of the flow field, as described by [16]:

where  is the fluid pulsation velocity and  is the average fluid velocity.

2. At first glance these three equations do not seem to have any variable related to the magnetic fluid. If we check reference 18 (section: Critical pressure of the seal), we can notice how the authors of that paper implemented the effect of the magnetic liquid in their equations.

We sincerely apologize for the confusion. These three equations are not the equations of motion of the magnetic fluid; instead, they are the equations of motion of the sealed medium fluid. In this paper, FLUENT software was used to calculate the flow of the sealed liquid (water) based on the three basic equations. As this paper discussed magnetic fluid, we agreed that the equation for magnetic fluid should also be presented. Thus, we added the formula of magnetic fluid sealing ability as follows:

In the process of magnetoliquid sealing, the sealing capacity generated by the magnetic field gradient is significantly greater than the sum of the sealing pressure generated by the magnetoliquid magnetization and centrifugal force. In addition, as magnetic fluid gravity and velocity have minimal influence on the sealing ability, the magnetic fluid dynamic sealing formula can be simplified as [17]:

因磁液密封过程中，磁场梯度产生的密封能力远远大于磁液磁化产生与离心力产生的密封压力之和，且磁液重力与速度对密封能力得影响较小，故可将磁液动密封公式简化为：

where  is the sealing pressure,  is the vacuum permeability, M is the magnetization of the magnetic liquid, and H is the magnetic field intensity at the sealing gap.

3. The authors mention reference 16 to regarding equation (3). Could they specify the number of that equation in Reference 16 because I could not find it?

Reference 16 studies turbulence amplification caused by the interaction between shock waves and turbulent boundary layer; however, it did not provide the basic definition of turbulence intensity. Thus, we changed the reference to one with a clear definition of the formula:

16. Deng WQ, Pan SY, Li ZG, Huang M (2020) Experimental study on flow characteristics of natural gas pipelines based on PIV. J Eng Thermal Energy Power 35(01):171–177.

4. The authors did not give the properties of the magnetic fluid even later in third paragraph. While if we check the third paragraph in Reference 18 (Test Method), the authors of that paper illustrate the values of the magnetic field. Later, in line 220 the authors mention that “the saturation magnetization of the magnetic liquid is essentially equal to that of air,” which is strange because the magnetization of the air is almost zero and the magnetic liquid has a higher density and it is magnetic after all.

We apologize for the clerical error here. We were referring to the relative permeability, not the saturation magnetization. Under an external magnetic field, the magnetization of the magnetic liquid gradually increases until saturation, whereas the change in relative permeability is extremely small. Thus, the relative permeability of the magnetic fluid is approximately equal to that of air (approximately 1.050), which is available in relevant literature quoted in this paper:

Yang XL, Li DC, He XZ, Zhang HT (2014) Numerical and experimental studies of alternative combined magnetic fluid and labyrinth seal with large gap. J Mech Eng 50(20):175–179.

The calculation of the magnetic field is performed using Maxwell software. The pole piece and shaft are made of AISI 1008 steel. The B–H curve of this material is shown in Figure 11. The permanent magnet is NdFe30. Its residual magnetic flux density Br is 1.2 T and the coercivity Hc is 8.38 × 10⁵ A/m. Because the magnetic liquid sealing structure is rotating, a two-dimensional (2D) axisymmetric model can be employed. The remaining structural parameters are presented in Table 1. In addition, because the relative permeability of the magnetic liquid is essentially equal to that of air, the magnetic liquid can be treated as air[21].

5. Due to the friction between the liquids (water and magnetic fluid), an amount of heat will appear causing some changes in the properties of the fluids (and it might cause other changes). How did the authors manage these changes in the simulations? In other words which set up has been used to capture all these changes? Maybe the k-e turbulence model considers that?

Friction between water and magnetic fluid causes magnetic fluid emulsification, dilution, and eventually, seal failure, which is the key reason for the failure of the magnetic fluid sealing liquid. However, this part is extremely difficult to obtain using CFD calculation. To our knowledge, the general method for magnetic flux coupling is the addition of volume force. However, in CFD, when a magnetic fluid is given a magnetic field force, it inevitably flows and is not absorbed on the polar teeth. Therefore, we simplified this part of the calculation by treating the interface of the two fluids as a wall. The problems you mentioned are indeed key difficult problems for our research team to solve urgently. We are still currently doing working our best to address them. I believe you must have unique insights on this issue and I really hope to get your contact information to consult you regarding this.

6. The number of mesh elements (229,312 and 238,531) is tested at 1000 rpm. What about other speeds? Can the authors justify that it is enough to verify the independent mesh by testing the model at the highest speed (1000 rpm)?

I did a lot of numerical calculation work before sending this manuscript to Coatings and obtained the following conclusion: For the same calculation model, the number of grids suitable for high flow rate calculation could sufficiently meet the requirements of low flow rate calculations. Therefore, mesh-independent verification was performed for the maximum speed of all models. However, this expression is prone to ambiguity; thus, we changed it to:

Figure 3 presents the computational fluid domain grid model, which adopts the hexahedral structure grid drawn by the ICEM software. The comprehensive quality of the grid is above 0.9, and the grid angle is 87–94°. In the same model, the number of grids in the high-speed flow is generally larger than that in the low-speed flow. Therefore, this study conducted grid independence calculation for each model when the shaft speed is 1000 rpm. When the number of grids in all models is greater than 238531, the physical quantity monitored in the flow field does not vary significantly with the increase of the grid number (less than 3%), indicating that these grid numbers meet the calculation requirements. Thus, the number of grids in the subsequent calculations under all working conditions was set to be greater than 238531.

7. In line 86 the authors used the word “gap value”. What is the gap value? I do not think it is the

sealing clearance. And if it is not the sealing clearance, how could you get it before you start your

simulation?

We apologize for the confusion. The “gap value” is indeed synonymous to the “sealing clearance”.” The discussion regarding the sealing clearance can then follow this statement.

The sealing clearance in this study was 1 mm, which was larger for the general clearance (less than 0.3 mm). This sealing clearance was chosen because of the large vibration spindle vibration under some specific working conditions, which require a larger shaft clearance. For example, in a shield machine project we recently received, the vibration of its shaft is approximately 3 mm.

The overall idea of the paper is as follows: As there is no buffer flow channel, water and magnetic liquid are in direct contact in the sealed cavity. The initial idea of this model comes from literature: Wang HJ (2018) Theoretical and experimental study on magnetic fluid rotary seal for sealing liquid, PhD thesis, Beijing, Jiaotong University:

https://kns.cnki.net/kcms/detail/detail.aspx?dbcode=CDFD&dbname=CDFDLAST2018&filename=1018144572.nh&uniplatform=NZKPT&v=QTHynoP02e65%25mmd2FzJW5DRzXkIMNp%25mmd2FOHr3euWvZdinKZtDjdP%25mmd2BRaMeEr6sMSipHMlfG

Your question must be the reason why I did not express the geometric model clearly. For this reason, I added a detailed model explanation in the paper and attached the grid model.

Figure 1 shows the fluid computational domain model of the sealed cavity with a shaft diameter (RD) of 200 mm, sealing clearance height of 1 mm, and cavity height (HS) of 40 mm. The OS is slotted on the shaft surface with the starting end of the slot position flushed with the end of the pole piece. The tested slot depths (SDs) are 1, 2, and 3 times the sealing clearance (1SD, 2SD, and 3SD), and the slot lengths (SLs) are 8, 16, and 32 times the sealing clearance (8SL, 16SL, and 32SL). Figure 2 shows the difference between the TS and OS.

Figure 3 presents the computational fluid domain grid model, which adopts the hexahedral structure grid drawn by the ICEM software. The comprehensive quality of the grid is above 0.9, and the grid angle is 87–94°. In the same model, the number of grids in the high-speed flow is generally larger than that in the low-speed flow. Therefore, this study conducted grid independence calculation for each model when the shaft speed is 1000 rpm. When the number of grids in all models is greater than 238531, the physical quantity monitored in the flow field does not vary significantly with the increase of the grid number (less than 3%), indicating that these grid numbers meet the calculation requirements. Thus, the number of grids in the subsequent calculations under all working conditions was set to be greater than 238531.

8. Could the authors show the spindle interface and the radial distance by taking a picture for the contours of their simulations and illustrating them clearly and how he calculated them?

The geometric model used in the experiment and numerical model size has a scale of 1. Before the experiment, we tried to capture a close shot of the test device; however, in terms of aesthetically, it was not ideal to place the image in the paper due to its simplicity. Thus, we made a schematic of the test device instead as follows:

This schematic can explain the test process and principle. The test applies the PIV technology, which is widely used in the measurement flow field; thus, it was not introduced in detail in the paper. Since the thickness of the light source is approximately 1 mm, the flow field at the interface of the spindle cannot be measured. We can only measure the flow field around the sealed cavity to verify the reliability of the numerical calculation. During the image capturing, the radial distance was determined by the ruler and compared with the velocity field at the same position in the numerical calculation

9. In Figure 3 and 4, I can see the speed domain {100, 200, …,1000}, while in line 97 the authors

mentioned different speed domain which is {100,300,500,1000}.

We apologize for this typographical error. We correct the text to 100, 300, 500, and 1000 rpm as follows:

The results show that when the spindle speed is 100、300、500、1000 rpm, the 2 SD and 3SD  values were above 22 %. Although the turbulence intensity at the axial interface is reduced, the eddy current of the sealed liquid causes fluid-induced vibration, which is not conducive to the stability of the magneto-liquid interface. Moreover, the larger the slotting scale, the stronger the eddy effect. Compared with 1 SD, the φ value of 2 SD is larger, and the vortex effect of 2 SD is smaller than that of 3 SD. so after comprehensive consideration, a slot depth of 2 SD was determined to be optimal.

10. In formula (5) they define ，and the next line the symbols are missing: “Where, ??? is the

turbulence intensity at the interface of the axis of the OS, ??? is the…”. In the next sentence they use  which they think is the same as

We sincerely apologize for this mistake. I have modified this errors and changed it into a unified variable (), which is the turbulence intensity at the interface between the magnetic and sealing liquid. The maximum turbulence intensity occurs at the spindle interface. Therefore, the shear stress is the greatest near the spindle interface. The following corrections are as follows:

Where,  is the turbulence intensity at the interface of the axis of the OS,  is the turbulence intensity at the interface of the axis of the TS, and  is the effect value. At rotational speeds of 300 rpm, 500 rpm and 1000 rpm,  were 25.8%, 22.1% and 22%, respectively, and the slotting depth had no obvious effect on the turbulence intensity at the axis interface.

The results show that when the spindle speed is 100、300、500、1000 rpm, the 2 SD and 3SD  values were above 22 %. Although the turbulence intensity at the axial interface is reduced, the eddy current of the sealed liquid causes fluid-induced vibration, which is not conducive to the stability of the magneto-liquid interface. Moreover, the larger the slotting scale, the stronger the eddy effect. Compared with 1 SD, the  value of 2 SD is larger, and the vortex effect of 2 SD is smaller than that of 3 SD. so after comprehensive consideration, a slot depth of 2 SD was determined to be optimal.

In the optimal slotted structure (SL = 16 mm, SD = 2 mm), the relationship between  and rotational speed is shown in FIG. 10:

At all calculated rotational speeds, are all above 20%, indicating that the reduction in the turbulence intensity of the sealing liquid interface layer at the seal clearance owing to the optimized structure is not affected by the rotational speed. The optimal slotted structure can significantly reduce the maximum turbulence intensity of the liquid interface layer at the seal clearance and reduce the washout effect of the sealing liquid on the o-ring formed by the magnetic field in the magnetic liquid, thereby improving the stability of the magnetic fluid rotary seal.

11. In figure (5), I can see 4 slot depths while it is mentioned in line 86 that they would test 3 slot

Depth

Only three slots deep were indeed used in the study; the other data is that of a general structure, which has no slot (slot depth of 0 mm). The results for this structure is shown in the figure for convenient comparison to show the sharp contrast between TS and OS.

12. In line 169, the authors claimed that they fixed the depth of the slot while the length was changing. That seems to be inconsistence with what is mentioned before. I will give two examples: First in lines 86-87, the slot depths are (1 SD, 2 SD, and 3 SD), the slot length are (8 SL,

SL, and 32 SL). For me it seems that you have three cases which are {(1 SD, 8 SL), (2 SD,16 SL), (3 SD, 32 SL)}. If you really have three cases and you fixed the slot depth, then the length of the slot cannot change as you mentioned in line 169. Please clarify this point in lines 86-87. Second: let me say that what I assumed (in first) is not correct, and you have 9 possible cases. It means that there are different possible lengths for each depth of the slot, and vice versa. But in lines 141-144, the authors kept many variable constants without mentioning if the length is constant or changing

We agree with your insight. In the initial stage of the manuscript, we applied the second scheme you mentioned, as we conducted in the early stage of our work. However, upon writing the manuscript, the depth of 2SD was found to be optimal when calculating the groove depth. Therefore, we fixed the depth at 2SD. According to the law of viscosity, velocity gradient is an important factor that affects shear stress in fluid. Therefore, the groove depth plays a key role in changing the shear stress at the interface of the magnetic fluid seal. However, after slotting, vortices inevitably occur in the center of the groove, which generate pulse force for the sealing interface and the position of the vortex changes with the groove length; thus, we added a vorticity cloud diagram in this paper.

At a fixed slotting depth of 2 SD, the slotting length has no obvious effect on the turbulence intensity at the axial interface (Fig. 8). This is because the shear force caused by the circumferential movement of the sealing fluid increases the turbulence intensity at the sealing interface. The shear force of the sealing liquid therefore exhibits a strong response to the groove depth at the front of the sealing interface, but no obvious response to the groove length was observed. However, the length of the slot has a significant effect on the location of the sealed liquid vortex caused by the slot structure. FIG. 9 shows the vorticity distribution cloud diagram with different structures at the speed of 1000 rpm. As shown in Figure 9, when the slot length is 8 SL, the sealing fluid vortex occurs near the sealing interface. The magnetoliquid seal interface is subjected to the pulsating force caused by the eddy motion of the sealing liquid, and the magnetoliquid seal depends on the magnetic field gradient at the bottom of the pole tooth. Both the magnetic field gradient of the position of the magnetic fluid and its sealing ability are different, so the magnetoliquid seal interface fluctuates with the fluctuations in the external sealing pressure. Under the influence of the pulsating force, the sealing interface moves at the same frequency as the pulsating force, which significantly affects the sealing stability. With the increase of groove length, the position of eddy current movement is far away from the sealing interface along the axial direction, so the pulsating force of eddy current movement on the sealing interface gradually weakens. When the grooving length is 16 SL and 32 SL, the vorticity distribution at the sealing clearance is similar, and the grooving length is too long, which will affect the spindle rigidity. So the optimal slotting length was determined to be 16 SL.

13. In page 12 from Author Contributions etc. the original explanations and instructions should be removed.

Thank you very much for reminding us. I have deleted it accordingly.

Thank you again for the help and support of the reviewer. I am willing to accept all your suggestions. In the process of revising the paper, I have learned a lot, such as the specific aspects of writing the paper and correct language expression.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

I think the paper is considerably improved and can be published now.