Shuxin Huang

The effect of studying the Navier-Stokes (NS) equation of undergraduate student is examined again in this work based on the exams in the recent four years from 2019 to 2022. Proportion test method is adopted in the research. A result shows that the students can remember the equation much better via one semester study than that via semi-semester study, which seems normal but conflicts the teaching plan of the fluid mechanics course including a midterm.

]]>Shuxin Huang

By comparing and analyzing the exam scores of exercising the Navier-Stokes (NS) equation in 2019, 2020 and 2021, the effect of studying the NS equation for undergraduate student is studied in the present work. The results show that at least more than 80% students can remember and use the NS equation properly. Moreover, the high correctness in 2020 is also analyzed, in which the ‘web-home’ mode for study is a feature and could have some merit.

]]>S. Maddah Kolur, F. Kolahdouzan, M. Khabari, H. Afzalimehr, V. P. Singh

Submarine pipelines are an important infrastructure and constitute vital vessels for transporting water, natural gas, oil, and petroleum products. In this study, scouring in one, two, and three tube models were experimentally investigated. The aim of this study was to investigate scour profiles for cases where pipes of different diameters were placed next to each other without any gap. In this regard, 15 experiments were performed in a flume 13 meters long, 0.46 meters wide, and 0.6 meters deep. For bed material, sand with a median particle size of 0.24 mm was used. The validity of experimental results was evaluated by performing 4 experiments under one-tube conditions and comparing the results with similar studies. When two pipes of the same diameter were placed next to each other without distance, they acted as an interconnected object and the maximum scouring depth formed between the two pipes. In the case where two pipes had different diameters, the greatest scouring depth formed near the larger diameter pipe. The scour depth formed under two pipes of different diameters was less when the larger diameter pipe was placed upstream, showing the pipes were placed in descending order (in terms of diameter). The results obtained for two pipes with different diameters also applied in the case of three pipes.

]]>Jay P. Narain

Lattice Boltzmann method (LBE) has attracted enormous interest to analyze this two-dimensional incompressible Navier-Stokes flow in a Lid Driven square cavity. A few papers have applied it to deep aspect ratio cavities. For the most part, the Reynolds number (Re) have been limited to 5,000. The aspect ratio (Ar) has also been limited to four. In most of the analyses, single relaxation time model (SRT) known as, Bhatnagar, Gross and Krook [8] model (LGBK) is used. The present work extends the Re capability beyond 10,000 for cavities with Ar up to six. It also uses two relaxation time (TRT) approach and half way bounce back boundary conditions. For square cavities, results were obtained for Re up to 60,000.

]]>Hassan Abdulmouti

Multi-phase flows appear in numerous forms in Nature. They can be found in sediment-laden flows in rivers, in underflows associated with volcanic eruptions, in turbidity currents, in the bubbly wake of ships, in many engineering fields as materials, mechanical, and in liquid-vapor mixtures in nuclear reactors, waste treatment, gas mixing and resolution, heat and mass transfer among many others. Multiphase flows, the simultaneous flow of more than one phase, encompasses a vast field, a host of different technological contexts, a wide spectrum of different scales, a broad range of engineering disciplines, and a multitude of different analytical approaches. Basic aspects of the flow in a bubble plume were addressed by many researchers. Furthermore, multiphase flow occurs in many facets of chemical engineering, e.g., distillation, absorption, evaporation, condensation, solvent extraction. It is particularly prevalent and important in hydrocarbon production and refining, minerals transport, power generation as well as in many environmental applications. Bubble plume, which is a typical form of bubble flow, has received considerable attention in the last four decades and has recently become a very important topic of research due to its large and wide range of application value and its effect on many processes the efficiency of many devices. The motivation for studying bubble plumes is evident, from the fact that these plumes are encountered in a variety of engineering problems. In the past 40 years, the range of its application prompted scholars to do experiments and numerical research about this phenomenon. The bubble plume is known as one of the transport phenomena able to drive large-scale convection due to the buoyancy of the bubbles. The flow in the vicinity of a free surface induced by a bubble plume is utilized as an effective way to control surface floating substances on lakes, oceans, as well as in various kinds of reactors and industrial processes handling a free surface. The surface flows generated by bubble plumes are considered key phenomena in many kinds of processes in modern industries. In our two earlier papers (Bubbly Two-Phase Flow: Part I- Characteristics, Structures, Behaviors and Flow Patterns and Bubbly Two-Phase Flow: Part II- Characteristics and Parameters) the major finding of the previous research of bubbly two-phase flow characteristics, structures, behaviors and flow patterns were demonstrated, reviewed and summarized. Moreover, some important models and techniques to measure the two-phase bubbly flow parameters such as bubble motion, flow regime, bubble shape which play a considerable role in many engineering applications were elucidated. Furthermore, our earlier papers also demonstrated, reviewed, and summarized the major finding of the previous research of the techniques and the important models for the measurement of the dominated two-phase bubbly flow/ bubble plume parameters such as gas flow rate bubble size, bubble velocity, and void fraction which are considered important and play an important role in operational safety, process control and reliability of continuum processes of many engineering applications. Beyond that, the turbulent bubbly flow structure was explained in detail. The motivation of the present work (part 3) which is extended to parts 1 and 2 is the dement to demonstrate, review, and summarize the major finding of previous research of the following points: 1) The differences of surface flow generation mechanisms among single-phase liquid jet, single-phase buoyant plume, and bubble plume. 2) The study of bubble plumes, their properties, characteristics, features, and their effects on the applications. 3) The important applications of bubbly flow and gas-liquid two-phase flow especially on bubble plumes and their associated surface flow since they can contribute to improvements in various directions including the conventional oil fence (function, problems, oil accidents on seas and oceans). The techniques of gas injection have been widely utilized in many engineering fields. The surface flows generated by bubble plumes are considered key phenomena in many kinds of processes in modern industries. It is utilized as an effective way to control surface floating substances on lakes, oceans, as well as in various kinds of reactors and industrial processes handling a free surface. 4) Summary of the above applications as a table of industrial processes that employ bubbly flow, a table of the environmental and naval engineering applications of bubbly flow, and a table of the applications: aerospace, biomedical, electrical, and mechanical.

]]>Jay P. Narain

The lid driven cavity flow has been of considerable interest for decades [1]. A number of numerical methods have been developed to analyze this two-dimensional incompressible Navier-Stokes flow problem [2]. Presently, a finite volume solver will be used to solve this problem for cavities of various aspect ratios. The cases for various slip configurations and various Reynolds numbers will be investigated. Next, a number of physics informed neural network solvers will be evaluated. The status of physics informed neural network will be presented.

]]>Ighoroje W. A. Okuyade, Tamunoimi M. Abbey, Aloysius T. Gima-Laabel

A magneto-hydrodynamic model of the merging flow of two rivers is presented. The governing non-linear partial differential equations are reduced to single independent variable problems using the similarity transformation. The resulting equations are linearized using the regular perturbation series expansion solutions, and solved for the velocity characteristic. Expressions for the velocity are quantified and presented graphically. The analyses of results show that increase in the magnetic field strength and merging angle reduce the flow velocity, whereas the increase in the Grashof number increases it. The concurrencies of the parameter effects make some to cushion the others. The results have some significant implications on transport of the bed-loads/sediments in the rivers courses toward standing water bodies.

]]>Jay P. Narain

The solution of Blasius Equation with various numerical methods is reviewed. The Falkner-Skan equation is also solved with these methods. The application methods range from classical Euler, Runge-Kutta, to Artificial Intelligence Machine Learning methods. The code for each method is available for verification in python scripting language.

]]>Harizo Lahatra Razafindramisa, Nirilanto Miaritiana Rasolozaka, Adolphe A. Ratiarison

The aim of this work is to study the ocean velocity around the Anony lake in order to test the existence of upwelling in that zone, and to model the phenomenon. The model is created using Regional Ocean Modelling System or ROMS software. We lead a 30 days’ simulation along the geographical coordinates: 25°S-27°S of latitude and 45°E-47°E of longitude, containing 44×59 horizontal grids and 32 vertical grids. The horizontal view of the results shows that both vertical and horizontal components of the velocity represent the existence of the upwelling around the site since vertical velocity is strong and positive and horizontal velocity veers to the coastline. Moreover, in vertical view, according to a section and a grid point, vertical component of velocity shows positive and high value. All these results justify the existence of the upwelling phenomenon in the seawater around the Anony lake.

]]>Ighoroje W. A. Okuyade, Tega Okor

The problem of transient MHD free convective chemically reacting fluid flow past a hot vertical porous plate with the attendant effects of thermal radiation, heat source and varying wall temperature, concentration and suction is investigated. The governing non-linear and coupled partial differential equations are non-dimensionalized, and linearized using the oscillating perturbation series expansion solutions. The resulting equations are solved and the expressions for the temperature, concentration, velocity, Nusselt number, Sherwood number and force on the plate wall are obtained. The flow characteristics are quantified and presented graphically. The results, amidst others, show that increase in the Hartmann number increases the velocity and skin friction; increase in the convection force increases the velocity and skin friction. Furthermore, it is seen that increase in the Raleigh number increases the temperature, velocity and skin friction but decreases the rate of heat transfer; increase in the heat source parameter increases the temperature, velocity and skin friction but decreases the rate of heat transfer; increase in the chemical reaction rate increases the concentration, Sherwood number, and velocity and skin friction. These results are bench-marked with the results in some existing literatures and they are in agreement.

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