Plug Regime Flow Velocity Measurement Problem Based on Correlability Notion and Twin Plane Electrical Capacitance Tomography: Use Case

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Remark 

Answer 

1 

It is clear, that for the proposed algorithm (detection of plugs via threshold before setting a time window for x-corr) some inappropriate threshold values may create errors. The extent of this problem depends on the appearance (shape) of the plugs in the data. This holds for any detection technique and is not specific for ECT. 

Yes, we agree. As mentioned in your remark we cite "the extent of this problem depends on the appearance (shape) of the plugs in the data". Therefore, the study of the cited above problem i.e., the influence of inappropriate threshold values, is a goal of the article.   

2 

The authors use a single set of data from ECT to show this problem. Neither a deep analysis nor an improved aproach is presented. This is too little! 

The authors have a huge file recording the half of hour experiment. The investigated flow had the same phenomena therefore, in our opinion, the chosen set of data represent the pneumatic conveying flow enough. 

3 

In many places writing is ambiguous or unclear, not only lingual. Examples are: 

What means "the signal value x()/y()" on page 4 and 5? Is it a division? I would rather interpret it as x() or y(). 

The ambiguity has been deleted and an explanation was inserted (see p. 5) 

4 

A laminar flow has a parabolic profile, not a plug one! 

Because the velocity is measured in each image pixel, therefore, the flow profile was not considered in the article. The applying introduced notion of "correlability" allows excluding the calculation of velocity in cases when signals are not suitable. 

5 

Why is it a pixel-wise correlation, why not correlating cross-sectional averages? 

The flow velocity values are not the same in the pipe cross-section. Moreover, tomography tools allow a velocity profile calculation in the volume of interest instead of average values. 

6 

What means that s_0 and m_0 are arbitrarily chosen? Why not basing them on some assumptions at least? 

Yes, agreed, sometimes some assumptions are default. We also assume that normalized threshold values should be higher than the noise level. An additional explanation was added.  

7 

Why does N_bT+m_0T determine the beginning of signal pattern (p5, top). What means signal pattern? 

It is not correct. In text we cite  “...moment NbT-m0T determines beginning of signal pattern” i.e., not “+”  but “-”. This assumption means that the considered signal will have a pulse-shape form. 

Many publications assume that input data can automatically be used for further calculations. In our opinion, it is not true.  

Therefore, it was introduced the notion of "correlibility" of input signals. In terms of the article, the signal pattern means that it is suitable for cross-correlation function calculation.  

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Answer 

1 

At present, it seems to be popular to calculate the separated phase velocity of multiphase flow based on cross correlation principle is no matter what flow pattern. The author only studies the plug flow and assumes the laminar character of the investigated flow, In fact, the above conditions may not be satisfied, as long as the multiphase flow is assumed to be stable, i.e. the so-called 'fixed flow', for example, it is widely used in the monitoring of vulcanization process in fluidized bed, and Its flow pattern is not necessarily plug flow pattern 

The article pays attention to plug flow only. It is underlined in the title. 

To our knowledge, the cross-correlation function can be applied to all input data; however,  practical use of cross-correlation of input data has sense when such function has an extremum (minimum/maximum). 

Otherwise, such a cross-correlation function is not useful. Therefore, not all input data can be analyzed by the cross-correlation technique. Without previous analysis of the suitability of considered input data, as shown in the article, the cross-correlation technique will not be applicable. It is worth to underline that cross-correlation can be calculated for a chosen time window. But such a time window may not cover suitable input signals. Hence the choice of a time window that covers suitable input signals called in the article as patterns, plays a crucial role. We suppose that the choice of the appropriate time window is also considered the monitoring of the vulcanization process in a fluidized bed. Unfortunately, we do not know more details. 

2 

The key problem of this research is the efficiency of flow pattern identification, so the accuracy of the data obtained by the sensor and the resolution of reconstruction algorithm is very important, a simple LBP algorithm may not be appropriate. 

Agreed. We assume the noised signals may have an influence on measurement accuracy, but the article concerns a flow velocity measurement, and we are not sure that image quality plays a crucial role in the accuracy of velocity measurement. 

3 

The meaning of formula (7) is not clear,  

Added description to formula (p(n)- time shift for n-th plug between planes) 

4 

Is this study applicable to actual gas-solid flow measurements, such as vulcanization processes, how to correct measurement results? 

The approach is applicable to use in practice when measured signals (data) are quasi-stationary or nonstationary processes. If a studied process has a stationary character, there will not be necessary to apply the proposed approach, and enough to consider a choice of the suitable time window. 

5 

different color marks in the figure 9 should be explained. 

Added to text: The colour of circles indicates the value of m0 parameter (scale shown on right hand) 

6 

There are still some errors in the paper which should be corrected, 

This is expectant that the manuscript would be further improved. 

The found errors are corrected 

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Remark 

Answer 

1 

In the caption of the figures (for example Fig. 2), the itemization (a,b) should come before their description, not after. 

The text was corrected according to the reviewer’s remark. 

2 

You should indicate that the expression for the voltage vector provided just before eq. (5) is simply and example, "...for example..." 

The text was corrected according to the reviewer’s remark.  

3 

The sensitivity matrix is rectangular (non-square) and strictly speaking not invertible because of that. So, please clarify the meaning of the inverse operation indicated in eq. (6). Is this a pseudo-inverse? 

There are many numerical problems associated with the sensitivity matrix. This matrix is not a square matrix. Its dimensions depend on the number of independent measurements and from a significantly greater number of image points. Hence 

it is impossible to calculate the  

the inverse of matrices and in various known methods the pseudo-reverse of the image reconstruction is used 

The problem is considered as ill-conditioned and sub-defined. In the LBP algorithm, pseudo-inverse sensitivity matrix is computed 

through its transpositions. 

4 

The numbering in the list of references and in the body of the text is offset by one for many references. For example, Fusch et al. is indicated as [18] in the text but it is listed as [19] in the list of references. 

All list of reference was corrected 

5 

At the top of Fig. 8, what is "depens"? Please spell it out. 

The article was corrected according to the reviewer’s remark. 

6 

On top of Fig. 9(a), please spell it out. 

The article was corrected according to the reviewer’s remark. 

7 

Fig. 10: "error ratio" => "relative error". 

The article was corrected according to the reviewer’s remark. 

8 

The English language usage should be improved. 

The English have been improved 

Remark 

Answer 

For example, in Fig. 8(b), it is not clear what is p=9. 

Right, the description could be ambiguous. Corrections made in the form of a new drawing description.