Static Characteristics and Leakage Rates of Smooth Annular Seals Based on a New Solution Method for Gas-Liquid Two-Phase Conditions

Round 1

Reviewer 1 Report

Sealing machinery and equipment in a liquid environment is an important issue and is a significant technical problem. The publication addresses the important topic of leakage of smooth annular seals for gas-liquid two-phase conditions.

The authors propose a new solution method for the leakage of smooth annular seal under a homogeneous flow based on bulk-flow model. Static characteristics of the presented solution method of the seal include: seal leakage, gas volume fraction (GVF) distribution, pressure distribution, mixture density and viscosity.

An important contribution is to compare the results of the calculations with the results of the research.

My comments:

1. The introduction describes the current state of knowledge. You could, however, refer to the advantages and disadvantages of the discussed seals and compare them to other types of seals in liquid environment.
2. Why was a seal selected with the parameters shown in Table 1. It has some technical application?
3. Minor editing errors: Page 7, 221 line „position. νe is”, Page 16, 438 line „ exit decrease.6. Patents”,
4. The conclusions could be better described, for example, by describing the reasons for the results obtained (e.g. why bubble radius has little effects), and not just by describing the trends in charts.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Reviewer 2 Report

This paper presents a theoretical model on the flow induced in the clearance between a rotating circular rod and a static casing subject to a pressure gradient in the axial direction when the flowing fluid is a homogeneous mixture of oil and air, with a given volume fraction at the inlet. The model proposed, which is based on previous studies by other researchers, incorporates the Rayleigh-Plesset equation to characterize the behavior of the bubbles. Predictions are presented for different system parameters, including a comparison with experimental data recently reported in the literature.

The topic of the manuscript is interesting from both technological and scientific points of view. Besides, the paper is well organized and easy to read, and the state of the art and the theoretical formulation of the model are adequate. However there are several significant weak points that advise against publication of the paper unless they are appropriately addressed by the authors after revision. The main weaknesses are:

• It is unclear that the proposed model introduces any novelty with respect to previous models in the literature. What are the specific contributions of this model?
• The experimental contrast of the model is based only on predictions of mass flow rate for different gas volume fractions. But the predictions fit the experimental data poorly and do not even show the same trend (Figure 3): the predicted mass flow rate reduces with gas fraction whereas the experimental data show a slight increase. Why does this happen?
• There is no proper analysis or discussion on the separate effects on the predictions from the different theoretical assumptions of the model (e.g., the usage of the Rayleigh-Pesset equation).
• There is no proper analysis of the results that provides a physical justification for the different predictions reported.

Other specific comments and questions:

• The sentence ‘Mixture density and viscosity both decrease with the increase of inlet GVF and the pressure drop’ is just a repetition of the previous sentence and should be removed.
• Lines 130-137. What’s new in your model with respect to previous studies. In particular, what is new with respect to references [21, 22, 23…], who also used the Rayleigh-Pesset relationship?
• Line 227. Eq. (11) should probably read Eq. (12).
• Line 269. Table 2 should probably read Table 1.
• Lines 267-278. Any explanation for the different trend between predictions and experimental data shown in Figure 3 for the effect of GVF on the mass flow rate for constant inlet pressure?
• There are numerous typos throughout the manuscript. A full revision by a native English speaker is recommended.

Author Response

Please see the attachment.

Author Response File: Author Response.docx

Round 2

Reviewer 2 Report

I advise a further revision of the English grammar and spelling. Besides, please consider the following minor corrections:

• I guess the author 'Luis', who is mentioned and quoted several times throughout the text, is in fact Dr. Luis San Andrés. In consequence he should be mentioned as 'San Andrés', which is his surname, rather than 'Luis', which is his given name. In particular this occurs in Lines 270, 272, 277, 281, 293 and 466. Also in the labelling of Fig. 3.
• For the same reason, references 17, 18, 24, 26, 27 and 34 of the reference list should include 'San Andrés, L.' instead of 'Andrés, L.S.'
• Line 298: 'maxium' should read 'maximum'
• Line 370: 'Then the increasing' should be 'Then increasing'
• Line 373: 'to increase' should be 'increase'
• Line 477: 'little effects' should be 'little effect'

Author Response

Please see the attachment.