An All-Mach Number HLLC-Based Scheme for Multi-Phase Flow with Surface Tension

Round 1

Reviewer 1 Report

The authors developed a numerical method for compressible multiphase flow with surface tension by combining the HLLC solver and the VoF (CICSAM) method. Plenty of numerical tests were provided to demonstrate the accuracy and effectiveness of the proposed method. Overall, this manuscript is of good quality. The following questions should be addressed in the revision.

1. In Fig. 3, I can see numerical oscillations at the shockwave. But such oscillations are not present in Ref. [1]. What is causing the oscillation? Grid points should be added to the plots (as symbols) so that the readers can easily see how sharp the interface and the shockwave are. Besides, references should be added if this test case is adopted from the literature.
2. In sections 4.2.2 and 4.2.3, the authors should present density contours instead of internal energy. It is difficult to compare the latter with Schlieren-type images in the literature.
3. In Fig. 15, the deviation of numerical curves from the analytical solution is not because of boundary shape. It is actually because of the domain size --- the Rayleigh-Plesset equation is obtained in an infinite domain.

Author Response

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Author Response File: Author Response.pdf

Reviewer 2 Report

In this investigation, an all-Mach method for two-phase inviscid flow in the presence of surface tension is presented. A modified version of the Hartens-Lax-van Leer Contact (HLLC) solver as per Garrick et al. [1] is developed. In contrast with [1], in this work, HLLC is combined with a widely used Volume-of-Fluid (VoF) method: the Compressive Interface Capturing Scheme for Arbitrary Meshes (CICSAM).

The paper’s subject is very practical and interesting. The research procedure has been logically carried out. Therefore, I highly recommend this paper for publication in this journal but before that, I have some few comments on the text:

 

Comments:

1)In abstract section, line 11 (The results show flow features that are in sensible agreement with experimental and numerical work), the authors declared that their numerical approach results are in good agreement with experimental results, but I don’t see experimental validation in this paper. Please explain it more in details in the text what you mean exactly by this sentence.

 

2) Since the subject of this paper is relevant to multiphase flows, I highly recommend the authors to add some references in the manuscript about different techniques used for measuring mutiphase flow characteristics. I recommend the others to add all the following references, which are the newest references in this field. In fact, the references refer to the most typical techniques (electrical capacitance [1], photon (gamma and X-ray) attenuation [2,3] and ultrasound [4]) for determining void fraction and flow regime in two-phase flows.

[1] Xu, Z., Wu, F., Yang, X. and Li, Y., 2020. Measurement of gas-oil two-phase flow patterns by using CNN algorithm based on dual ECT sensors with venturi tube. Sensors, 20(4), p.1200.

[2] Roshani, M.,, et al., 2021. Combination of X-ray tube and GMDH neural network as a nondestructive and potential technique for measuring characteristics of gas-oil–water three phase flows. Measurement, 168, p.108427.

[3] Roshani, M.,, et al., 2021. Evaluation of flow pattern recognition and void fraction measurement in two phase flow independent of oil pipeline’s scale layer thickness. Alexandria Engineering Journal.

[4] Fang, L., Zeng, Q., Wang, F., Faraj, Y., Zhao, Y., Lang, Y. and Wei, Z., 2020. Identification of two-phase flow regime using ultrasonic phased array. Flow Measurement and Instrumentation, 72, p.101726.

 

3)As I understood, the proposed method in this paper is only applicable for homogenous regime of two phase flow. Does this method the capability to be applied to other two-phase flow regimes, such as annular, stratified, etc.?

 

4)From caption of figure 7, it is not possible to understand the plots in this figure. What are plots in rows 1, 2 and 3?

Author Response

Please see the attachment.

Author Response File: Author Response.pdf

Round 2

Reviewer 2 Report

All the comments were addressed correctly.