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This study aims to develop an experimentally validated three-dimensional numerical model for predicting different flow patterns produced with a gas dynamic virtual nozzle (GDVN).

The physical model is posed in the mixture formulation and copes with the unsteady, incompressible, isothermal, Newtonian, low turbulent two-phase flow. The computational fluid dynamics numerical solution is based on the half-space finite volume discretisation. The geo-reconstruct volume-of-fluid scheme tracks the interphase boundary between the gas and the liquid. To ensure numerical stability in the transition regime and adequately account for turbulent behaviour, the k-ω shear stress transport turbulence model is used. The model is validated by comparison with the experimental measurements on a vertical, downward-positioned GDVN configuration. Three different combinations of air and water volumetric flow rates have been solved numerically in the range of Reynolds numbers for airflow 1,009–2,596 and water 61–133, respectively, at Weber numbers 1.2–6.2.

The half-space symmetry allows the numerical reconstruction of the dripping, jetting and indication of the whipping mode. The kinetic energy transfer from the gas to the liquid is analysed, and locations with locally increased gas kinetic energy are observed. The calculated jet shapes reasonably well match the experimentally obtained high-speed camera videos.

The model is used for the virtual studies of new GDVN nozzle designs and optimisation of their operation.

To the best of the authors’ knowledge, the developed model numerically reconstructs all three GDVN flow regimes for the first time.

This study proposes a novel method utilising a speech-word pair bipartite network to examine the correlation structure between members of parliament (MPs) in the context of the UK- China relationship.

We construct MP-word pair bipartite networks based on the co-occurrence relationship between MPs and words in their speech content. These networks are then mapped into monopartite MPs correlation networks. Additionally, the study calculates correlation network indicators and identifies MP communities and factions to determine the characteristics of MPs and their interrelation in the UK-China relationship. This includes insights into the distribution of key MPs, their correlation structure and the evolution and development trends of MP factions.

Analysis of the parliamentary speeches on China-related affairs in the British Parliament from 2011 to 2020 reveals that the distribution and interrelationship of MPs engaged in UK-China affairs are centralised and discrete, with a few core MPs playing an integral role in the UK-China relationship. Among them, MPs such as Lord Ahmad of Wimbledon, David Cameron, Lord Hunt of Chesterton and Lord Howell of Guildford formed factions with significant differences; however, the continuity of their evolution exhibits unstableness. The core MP factions, such as those led by Lord Ahmad of Wimbledon and David Cameron, have achieved a level of maturity and exert significant influence.

The research has several limitations that warrant acknowledgement. First, we mapped the MP-word pair bipartite network into the MP correlation network for analysis without directly analysing the structure of MPs based on the bipartite network. In future studies, we aim to explore various types of analysis based on the proposed bipartite networks to provide more comprehensive and accurate references for studying UK-China relations. In addition, we seek to incorporate semantic-level analyses, such as sentiment analysis of MPs, into the MP-word -pair bipartite networks for in-depth analysis. Second, the interpretations of MP structures in the UK-China relationship in this study are limited. Consequently, expertise in UK-China relations should be incorporated to enhance the study and provide more practical recommendations.

Firstly, the findings can contribute to an objective understanding of the characteristics and connotations of UK-China relations, thereby informing adjustments of focus accordingly. The identification of the main factions in the UK-China relationship emphasises the imperative for governments to pay greater attention to these MPs’ speeches and social relationships. Secondly, examining the evolution and development of MP factions aids in identifying a country’s diplomatic focus during different periods. This can assist governments in responding promptly to relevant issues and contribute to the formulation of effective foreign policies.

First, this study expands the research methodology of parliamentary debates analysis in previous studies. To the best of our knowledge, we are the first to study the UK-China relationship through the MP-word-pair bipartite network. This outcome inspires future researchers to apply various knowledge networks in the LIS field to elucidate deeper characteristics and connotations of UK-China relations. Second, this study provides a novel perspective for UK-China relationship analysis, which deepens the research object from keywords to MPs. This finding may offer important implications for researchers to further study the role of MPs in the UK-China relationship.

This study proposes a novel scheme for analysing the correlation structure between MPs based on bipartite networks. This approach offers insights into the development and evolving dynamics of MPs.