Flow Theory Research Articles

Mathematical Physics Analysis of Nozzle Shaping at the Gas Outlet from the Aperture to the Differentially Pumped Chamber in Environmental Scanning Electron Microscopy (ESEM)

A combination of experimental measurement preparations using pressure and temperature sensors in conjunction with the theory of one-dimensional isentropic flow and mathematical physics analyses is presented as a tool for analysis in this paper. Furthermore, the subsequent development of a nozzle for use in environmental electron microscopy between the specimen chamber and the differentially pumped chamber is described. Based on experimental measurements, an analysis of the impact of the nozzle shaping located behind the aperture on the character of the supersonic flow and the resulting dispersion of the electron beam passing through the differential pumped chamber is carried out on the determined pressure ratio using a combination of theory and mathematical physics analyses. The results show that nozzle shapes causing under-expanded gas outflow from the aperture to the nozzle have a worse impact on the dispersion of the primary electron beam. This is due to the flow velocity control. The controlled reduction in the static pressure curve on the primary electron beam path thus causes a significantly higher course of electron dispersion values than variants with shapes causing over-expanded gas outflow.

Numerical calibration of the mooring system for a semi-submersible floating wind turbine model

Abstract Numerical modelling of the floating offshore wind turbine (FOWT) dynamics plays a critical role at the design stage of a floating wind project. Still, there exist challenges for verification of efficient engineering models against experimental results. Recently, an experimental campaign was carried out for a 1:96 downscaled model of the OC4-DeepCWind semi-submersible platform with mooring lines made of fibre ropes and chains. Leveraging the results of this campaign, this paper focuses on development and calibration of a numerical model for the semi-submersible platform with a focus on the dynamic responses under bichromatic waves. In the numerical model, the hydrodynamic loads are modelled based on the potential flow theory with Morison drag. The lumped mass method is applied to model the mooring system. Both free decay tests and bichromatic wave conditions are considered in the model calibration process, and key uncertain parameters (e.g., mooring line length) that affect the response have been identified and discussed. Using the proposed calibration procedure, we establish a reasonably good numerical model for prediction of the platform motion and mooring dynamics. The low-frequency responses of the platform under bichromatic waves are well-captured. These outcomes contribute to the development of efficient numerical FOWT models under experimental uncertainty.

Users' continuance intention towards an AI painting application: An extended expectation confirmation model.

With the rapid advancement of technology, Artificial Intelligence (AI) painting has emerged as a leading intelligence service. This study aims to empirically investigate users' continuance intention toward AI painting applications by utilizing and expanding the Expectation Confirmation Model (ECM), Technology Acceptance Model (TAM), Unified Theory of Acceptance and Use of Technology (UTAUT), and the Flow Theory. A comprehensive research model is proposed. A total of 443 questionnaires were distributed to users with AI painting experiences for data collection. The hypotheses were tested through structural equation modeling. The primary conclusions drawn from this research include: 1) Confirmation plays a crucial role, significantly and positively predicting satisfaction and social impact. 2) Personal innovativeness has a significant effect on confirmation. 3) Satisfaction, flow experience, and social influence directly and positively predict intention, with social influence showing the most significant impact, while perceived usefulness, perceived enjoyment, and performance expectancy show no significant impact on intention. 4) Habit plays a negative moderating role in the association between social influence and continued intention to use. These findings offer valuable insights and inspiration for users seeking to understand the appropriate utilization of AI painting and provide actionable directions for the development of AI painting.

When religion meets mathematics: From mathematical anxiety to mathematical well-being for minority group student

The mission of positive psychology is to mitigate negative emotions while bolstering positive ones, thereby influencing student engagement in classroom learning activities, including mathematics. This study elucidates the Realistic Mathematics Education (RME) approach within the framework of Islamic teachings—specifically, inheritance law and charity—in the context of fractions and number operations. Its objective is to alleviate mathematics anxiety, a prevalent negative emotion, and enhance well-being during mathematical learning. Drawing upon flow theory from positive psychology, the research endeavors to optimize mathematical well-being by crafting appropriately challenging questions. Employing a descriptive qualitative methodology, the study focuses on an Indonesian mother and her ten-year-old son, residing in Uithoorn, Amsterdam, Netherlands, belonging to minority groups in ethnicity and identity, with religion being a significant aspect of their lives. Data collection involves observation, interviews, tests, and documentation, with analysis employing data reduction, presentation, triangulation, and verification techniques. The study utilizes socio-religious problems as a context, one of the characteristics of RME, such as inheritance division, to design mathematical challenges. The findings demonstrate a marked transition from math anxiety to math well-being, manifested through heightened enthusiasm and cheerfulness in learning mathematics, particularly by the mother. Noteworthy transformations include increased engagement, generous gestures towards the teacher, and frequent smiling, contrasting with previous instances of math anxiety during learning sessions. Furthermore, the results indicate that RME facilitates comprehension of mathematical concepts and fosters understanding of the intersection between mathematics and Islamic life among minority groups, as detailed in this article.

A discrete-module-beam hydroelasticity method with finite element theory in analyzing VLFS in different engineering scenarios

A numerical tool is developed in the framework of the Discrete-Module-Beam method to analyze hydroelasticity of very large floating structures (VLFS) such as floating offshore photovoltaic platforms (FOPV). The proposed method utilizes finite element theory to perform structural analysis. The 3D potential flow theory is used to perform a hydrodynamic analysis after macro-submodule division. For the structural analysis part, the platform is divided into macro-submodules and each macro-submodule is represented by a beam, which is then further discretized into micro beam elements with the nodes categorized into three groups, that is, the lumped mass, the boundary nodes and the inner nodes. Derivation of the lumped-mass stiffness matrix and recovery of the displacement distribution are given. Procedures to deal with interconnections, complex boundary conditions and unsteady loads are elaborated. Good agreement is obtained in different loading scenarios to the numerical and experimental results.

Modeling the Unsteady Wake of an Impulsively Started Circular Cylinder Using Refined Potential Flow Theory

Abstract Cylindrical structures find usage in many engineering applications including tethered oil drums and engine canisters slung beneath helicopters in flight. The motion of air around such circular cylindrical structures and the helicopter presents interesting phenomena including flow separation, wakes and turbulence. The physics of these are enshrined in the continuity equation and the Navier-Stokes equations. Therefore, their studies are not only important in mathematics and physics, but they are also required for efficient helicopter operations. In practice, reduced-order models of these operations that take in aerodynamics models of the tethered loads are utilized for stability analysis, flight certification and pilot training because of the prohibitive cost of experimentation and computational analyses of these configurations. However, there is a dearth of realistic analytical models of finite cylinder flows because of the Navier-Stokes problem. Classical potential flow theory provides an avenue to develop such models, but the extant gaps in its predictions significantly preclude its usage for engineering applications. Attempting to bridge these gaps, this article introduces refined potential flow theory in which the governing equations and boundary conditions are satisfied. Viscous effects, fluctuations of the mean flow and three-dimensional effects are also incorporated. For characterization, refined potential flow theory is employed on an incompressible flow over an impulsively started circular cylinder for Reynolds numbers and non-dimensional times in the range 30 < Re < 10^4 and 0.2 ≤ T≤ 77, 047 respectively. There is an excellent prediction of 0.209 for the Strouhal number at Re = 3, 900. At this transitional Reynolds number, the harmonics of the Strouhal frequency are also captured, and the characteristic irregular fluctuations at sub-Strouhal frequencies are discernible in the velocity spectra. As the flow becomes more turbulent, these become more pronounced at Re = 9, 500 when the predicted Strouhal number is within 10% of experimental result. In the fully developed stage, spectra analyses of the wake velocity components at some downstream locations also display Kolmogorov’s Five-Thirds law of homogeneous isotropic turbulence. The present model can thus aid the development of reduced-order models of helicopter operations that feature tethered cylindrical loads.

How Celebrity Endorsement Affects Travel Intention: Evidence From Tourism Live Streaming

Celebrity endorsements via live streaming continue to draw attention in the tourism industry. This research examines the effects of such endorsements on tourism live streaming. We specifically compared celebrity streamers to key opinion leader streamers and brand streamers across two types of live streaming (travel live streaming vs. tourism e-commerce live streaming). Drawing on the flow theory, we developed a theoretical framework to explain why and how celebrity streamers can inspire travel intention more effectively than key opinion leader streamers and brand streamers. Results indicate that celebrity streamers’ endorsements enhance travel intention via informativity, entertainment, and interactivity, compared with endorsements from key opinion leaders and brand streamers. This effect is further amplified during travel live streaming.

How game-based learning supports the creativity of university students? The context of China

ABSTRACT Nowadays, gamification has gained widespread acceptance in education. However, limited studies have focused on whether and how game-based learning impacts university students’ creativity. This study aims to explore the relationship between university students’ engagement in game-based learning and their creativity. By drawing upon flow theory principles, we conducted interviews with nine actively participating university students in game-based learning. The findings highlight that game-based learning stimulates the generation of novel ideas and fosters the adoption of innovative behaviours among students. Subsequently, an empirical study involving 142 undergraduate students was conducted, utilising game-based learning as an intervention. The results demonstrate a significant positive effect of game-based learning on university students’ creativity. Furthermore, the effect varied among individuals with different personality traits: game-based learning exhibited stronger effects for individuals characterised by high conscientiousness, low openness, or a combination of low neuroticism and high openness.

Nonsimilar analysis of forced convection radially magnetized ternary hybrid nanofluid flow over a curved stretching surface

This study focuses on analyzing the rheological properties of the Carreau–Yasuda ternary hybrid nanofluid model on a curved stretched sheet considering the molybdenum disulfide ( Mo S 2 ) , graphene oxide ( GO ) , and Nichrome ( NiCr ) immersed in the base fluid ethylene glycol ( EG ) . This study employs a radial magnetic force that is directed perpendicular to the direction of flow to manipulate the motion characteristics of a nonNewtonian fluid. Augmenting the value of the magnetic number leads to a decrease in the velocity of the flow as resistance is introduced against its principal direction. Thermal radiation and viscous dissipation effects are considered in the energy equation. Assumptions that are fundamental to fluid flow theories are incorporated into the mathematical formulation of this problem. Following this, the governing equations are transformed into dimensionless nonsimilar partial differential equation (PDE) by applying nonsimilarity transformation to a nonsimilarity transformation, and subsequently analyzed as ordinary differential equations utilizing the local nonsimilarity method up to second level of truncation. By using the MATLAB-integrated bvp4c solver, numerical solutions are obtained. The results of these various solutions are examined using visual and tabular representations to thoroughly evaluate the variances across different parameter settings. Furthermore, the flow velocity is reduced by the Lorentz force caused by a more curved surface, and we gain insight into the impact of different physical quantities under different parametric considerations related to the stretching curved surface, which adds to our knowledge of this complex fluid dynamic phenomenon.

The analysis of the factors influencing the operation of the piston wind in the cage of the hybrid hoisting shaft and the simulation study of the operation effect

The mixed shaft in the mine is used as the main inlet and return air shaft and also as the lifting shaft. The piston wind effect caused by the frequent operation of large and efficient lifting equipment in the shaft will disturb the normal air flow in the shaft and cause the air flow disorder. So It is important to study influencing factors and the series of piston effects of inner cage operation in the hoisting shaft. This paper firstly derives a theoretical model of piston wind for double cage operation in a wellbore based on the non-constant flow theory of Bernoulli’s equation, and derives the influencing factors of piston wind. Then, according to the actual situation of the mine, a 3D fluid simulation model of cage hoisting is established. Based on the verified simulation method, the transient division of labor of piston wind effect and its influencing factors is simulated and the influence of various factors on the development law of piston wind is analyzed in detail. The study results show that the main factors influencing the piston wind are the cage operating conditions, the cage operating speed, the shaft blockage ratio and the initial ventilation speed in the shaft. The operation of the cage produces an eddy current zone, which causes air flow disorder in the wellbore and affects the ventilation effect of the shaft. The piston wind speed is the highest when the cage running against the wind, while the speed is lower running with the wind. The most complex wind flow disturbance occurs when the two cages meet, which is almost block the flow of wind in the shaft. The change of cage operating speed and wellbore blockage ratio is related to the piston wind speed and pressure changes linearly in different conditions. There is the best blockage ratio between the hoisting cage and the shaft, which can cause the highest average ventilation speed in the shaft, and the best blockage ratio of the study model is 0.32.

Viscous correction to the potential flow analysis of Rayleigh–Taylor instability in a Rivlin–Ericksen viscoelastic fluid layer with heat and mass transfer

AbstractThe current investigation focuses on examining viscous corrections for viscous potential flow (VCVPF) analysis concerning the Rayleigh–Taylor instability occurring at the interface of a Rivlin–Ericksen (R–E) viscoelastic fluid and a viscous fluid during the transfer of heat and mass between phases. The R–E model is a fundamental framework in the study of viscoelastic fluids, providing insights into their complex rheological behavior. It characterizes the material's response to both deformation and flow, offering valuable predictions for various industrial and biological applications. Within the framework of viscous potential flow (VPF) theory, viscosity is exclusively accounted for in the normal stress balance equation, disregarding the influence of shearing stress entirely. This study introduces a viscous pressure term into the normal stress balance equation alongside the irrotational pressure, presuming that this addition will improve the discontinuity of tangential stresses at the fluid interface. Through derivation of a dispersion relationship and subsequent theoretical and numerical stability analyses, the stability of the interface is investigated across various physical parameters. Multiple plots are generated using the dispersion relation, and a comparative analysis between VPF and VCVPF is conducted to establish improved stability criteria. The investigation highlights that the combined impact of heat/mass transport and shearing stress serves to delay the instability of the interface.

A Constitutive Law Modeling the Mixed Hardening Behavior of Particle-Reinforced Composites

Abstract A homogenized elasto-plastic constitutive law (including both constitutive equations and inversed constitutive equations) is proposed in an incremental form for the particle-reinforced composites based on the flow theory of plasticity and the asymptotic homogenization method. The constitutive law can be used to predict the mixed hardening behavior of particle-reinforced composites under arbitrary loading conditions if the uniaxial tension test curve of matrix materials is known. It is found that the constitutive law of particle-reinforced composites is similar in form to the law of matrix materials. There is a simple proportional relationship between the yield stress, the plastic modulus, and the deviatoric back stress of particle-reinforced composites and the corresponding parameters of matrix materials, which is equal to the ratio of the shear modulus of composites to the shear modulus of matrix materials. The tangent modulus of particle-reinforced composites can be calculated using a simple arithmetic formula according to the tangent modulus of matrix materials. A numerical algorithm is suggested.

Study of Activation Energy for Viscous Flow of Mixtures as a Measure of Dilution Efficiency for Heavy Oil-Diluent Systems

As the demand for crude oil continues to increase in response to the continued global needs for it, the development of unconventional crude oil reserves is the only way to sustain global supply. However, the excessively higher viscosity of heavy crude oil makes it less attractive for conventional pipeline transportation. Therefore, reducing the viscosity of heavy crude oil to meet crude oil transporting pipeline regulations is a necessity. This paper has assessed the dilution efficiency of well-known diluents in the petroleum industry, using different dilution ratios based on a thermodynamic approach involving activation energy and heat of vaporization determination. Based on selected dilution ratios, kinematic viscosities of binary and ternary systems of toluene and natural gas condensate as diluents, and Saudi Heavy crude oil as the base oil were measured, using anticipated field based temperatures reported in the literature, which facilitated the experimental approach. The study shows that although the ternary systems have the lowest activation energy for viscous flow and heat of vaporization in accordance with the thermal activation theory of viscous flow, natural gas condensate binary systems have the lowest cost of transportation per barrel of total fluid in the transporting pipeline. The study further shows that the binary systems for toluene and Saudi Heavy crude oil have higher activation energy for viscous flowed compared to the toluene systems.

Relationship between Artistic Expression and Mental Well-being

Purpose: This study sought to investigate the relationship between artistic expression and mental well-being. Methodology: The study adopted a desktop research methodology. Desk research refers to secondary data or that which can be collected without fieldwork. Desk research is basically involved in collecting data from existing resources hence it is often considered a low cost technique as compared to field research, as the main cost is involved in executive’s time, telephone charges and directories. Thus, the study relied on already published studies, reports and statistics. This secondary data was easily accessed through the online journals and library. Findings: The findings reveal that there exists a contextual and methodological gap relating to artistic expression and mental well-being. Preliminary empirical review revealed that engaging in creative activities offers therapeutic benefits such as emotional expression, self-discovery, and social connection. Through various forms of art, individuals were able to reduce stress, improve mood, and foster a sense of belonging within their communities. Moreover, artistic expression served as a catalyst for personal transformation and empowerment, enabling individuals to overcome challenges and find meaning in their experiences. These findings highlight the importance of incorporating arts-based interventions into mental health care to promote holistic well-being. Unique Contribution to Theory, Practice and Policy: Art as Therapy theory, Flow theory and Socio-Emotional Selectivity theory may be used to anchor future studies. The studies exploring the relationship between artistic expression and mental well-being offered valuable recommendations that contributed to theoretical advancements, informed practical applications, and guided policy development. By elucidating the therapeutic mechanisms of artistic expression, practitioners integrated arts-based interventions into clinical practice, educators incorporated arts into school curricula, and policymakers advocated for increased funding and support for arts initiatives in healthcare and community settings. These efforts aimed to foster creativity, resilience, and social connection, ultimately enhancing mental well-being across diverse populations.

Nonassociative cosmological solitonic R-flux deformations in gauge gravity and G. Perelman geometric flow thermodynamics

We elaborate on a model of nonassociative and noncommutative gauge gravity for the de Sitter gauge group SO(4,1) embedding extensions of the affine structure group Af(4,1) and the Poincaré group ISO(3,1). Such nonassociative gauge gravity theories are determined by star product R-flux deformations in string theory and can be considered as new avenues to quantum gravity and geometric and quantum information theories. We analyze physically important and geometric thermodynamic properties of new classes of generic off-diagonal cosmological solitonic solutions encoding nonassociative effective sources. Particularly, we focus on modelling by such solutions of locally anisotropic and inhomogeneous dark matter and dark energy structures generated as nonassociative solitonic hierarchies. Such accelerating cosmological evolution scenarios can’t be described in the framework of the Bekenstein-Hawking thermodynamic formalism. This motivates a change in the gravitational thermodynamic paradigm by considering nonassociative and relativistic generalizations of the concept of W-entropy in the theory of Ricci flows. Finally, we compute the corresponding modified G. Perelman’s thermodynamic variables and analyze the temperature-like evolution of cosmological constants determined by nonassociative cosmological flows.

Numerical Simulation of Ship-added Resistance Based on a Numerical Wave Tank

The wave resistance increase of a ship during its actual voyage can affect its speed and safety. To design ships with excellent sailing performance, it is necessary to accurately predict the wave resistance increase of a ship in waves, as well as the motion response and wave resistance prediction of ships in waves, which involves complex hydrodynamic problems. This paper first establishes a physical model of the KCS vessel, then utilizes the numerical wave tank platform independently developed by our university. Based on viscous flow theory, it calculates the resistance of the KCS under calm water conditions. Using three-dimensional potential flow methods and spectral analysis, it computes the wave-induced resistance values for the KCS under six-degree sea states, analyzes the wave-induced resistance performance of the KCS, and ultimately, based on the calculation results of calm water resistance and wave-induced resistance combined with propeller efficiency parameters, calculates the effective power of the engine.

A unified fractional flow framework for predicting the liquid holdup in two-phase pipe flows

Two-phase pipe flow occurs frequently in oil & gas industry, nuclear power plants, and CCUS. Reliable calculations of gas void fraction (or liquid holdup) play a central role in two-phase pipe flow models. In this paper we apply the fractional flow theory to multiphase flow in pipes and present a unified modeling framework for predicting the fluid phase volume fractions over a broad range of pipe flow conditions. Compared to existing methods and correlations, this new framework provides a simple, approximate, and efficient way to estimate the phase volume fraction in two-phase pipe flow without invoking flow patterns. Notably, existing correlations for estimating phase volume fraction can be transformed and expressed under this modeling framework. Different fractional flow models are applicable to different flow conditions, and they demonstrate good agreement against experimental data within 5% errors when compared with an experimental database comprising of 2754 data groups from 14 literature sources, covering various pipe geometries, flow patterns, fluid properties and flow inclinations. The gas void fraction predicted by the framework developed in this work can be used as inputs to reliably model the hydraulic and thermal behaviors of two-phase pipe flows.

Numerical simulation of the slamming effect of regular waves and freak waves on ultra heavy-lift amphibious connector

The Ultra Heavy-lift Amphibious Connector can be used for sea and land operations. When the amphibious connector opens the bow door, it will inevitably suffer from the combined action of wind, waves, currents, and other factors, resulting in the slamming of the wave on the hatch and various landing ship hull movements in the process. Due to the complexity of the actual UHAC model, in order to save computing resources, this paper selects the external load on the UAHC hatch when it is operated in water when the door is closed. The effects of crest height, draught, and focus position on UHAC slamming under the action of regular waves and freak waves were analyzed. Based on the viscous flow theory, the CFD commercial software FLUENT is used to simulate the interaction between the reduction of regular waves and floating structures. The simulation results are compared with the experimental results to verify the feasibility of the proposed method. Since the published UHAC data cannot be found in the network environment, this paper draws the UHAC based on the only data on the Internet and studies the slamming load of the wave on the UHAC on this basis.

Enhancing engagement and learning in advanced biochemistry through the application of flow theory.

This study identified a lackluster classroom atmosphere in advanced biochemistry, characterized by low levels of active student participation in interactive communication and subpar quality of after-class learning tasks. The issues stemmed not only from students' learning attitudes, such as insufficient attention to the curriculum, but also from the course's inherent lack of challenge. Employing flow theory, we optimized teaching content, enhanced course difficulty, reformed assessment methods, and incorporated information-based teaching tools to redesign the instructional process. Through a questionnaire survey, students evaluated teaching effectiveness after implementation of the changes: a majority expressed satisfaction with the moderate difficulty of the course and enjoyment of the classroom instruction, and reported experiencing positive emotional flow. Peer experts commended the course, noting its lively atmosphere and the students' acquisition of both basic research methods and foundational knowledge. The findings will be used to continually enhance graduate students' innovation abilities and sense of achievement through ongoing reforms.

A mathematical introduction to complex dynamical systems

This work proposes an investigation of the theory of dynamic systems, focusing on the analysis of entropy in its classical and topological manifestations. Initially, the fundamental concepts of dynamical systems theory are presented, with an emphasis on topological dynamical systems (TDS). Next, definitions of discrete topological entropy and its relationship to dynamical systems are discussed, followed by the introduction of topological entropy pressure as a weighted form of topological entropy. Subsequently, some applications of topological entropy in dynamic systems are examined, highlighting its role in the analysis of chaotic systems and in ergodic theory. Furthermore, we present a new theory, called Topological Ergodic Entropy Theory (TEET), which offers an innovative approach to the analysis of ergodic dynamical systems. Finally, the Ergodic Theory of Turbulent Flow (ETTF) is introduced, exploring the relationship between topological entropy and the ergodic properties of dynamic systems governed by the Navier-Stokes equations. The results presented contribute to a deeper understanding of the complexity of dynamical systems and their applications in various areas of mathematics and physics. The investigation of topological entropy and its applications in dynamical systems offers new insights into the chaotic and stochastic behavior of these systems, while the introduction of new theories, such as ETTF, provides a new perspective for the analysis and modeling of turbulent phenomena.