scholarly journals The New Semianalytical Technique for the Solution of Fractional-Order Navier-Stokes Equation

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Nehad Ali Shah ◽  
Mounirah Areshi ◽  
Jae Dong Chung ◽  
Kamsing Nonlaopon
Keyword(s):  
Fractional Order ◽  
Nonlinear Models ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Power Series Method ◽  
Modified Method ◽  
Suggested Technique ◽  
Residual Power Series ◽  
The Impact ◽  
Fractional Order Nonlinear System

In this paper, we introduce a modified method which is constructed by mixing the residual power series method and the Elzaki transformation. Precisely, we provide the details of implementing the suggested technique to investigate the fractional-order nonlinear models. Second, we test the efficiency and the validity of the technique on the fractional-order Navier-Stokes models. Then, we apply this new method to analyze the fractional-order nonlinear system of Navier-Stokes models. Finally, we provide 3-D graphical plots to support the impact of the fractional derivative acting on the behavior of the obtained profile solutions to the suggested models.

scholarly journals The Analysis of Fractional-Order Navier-Stokes Model Arising in the Unsteady Flow of a Viscous Fluid via Shehu Transform

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Pongsakorn Sunthrayuth ◽  
Rasool Shah ◽  
A. M. Zidan ◽  
Shahbaz Khan ◽  
Jeevan Kafle
Keyword(s):  
Fractional Order ◽  
Fractional Derivatives ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Nonlinear Problems ◽  
Navier Stokes ◽  
Power Series Method ◽  
Navier Stokes Equations ◽  
Residual Power Series ◽  
Residual Power

This paper presents a new method that is constructed by combining the Shehu transform and the residual power series method. Precisely, we provide the application of the proposed technique to investigate fractional-order linear and nonlinear problems. Then, we implemented this new technique to obtain the result of fractional-order Navier-Stokes equations. Finally, we provide three-dimensional figures to help the effect of fractional derivatives on the actions of the achieved profile results on the proposed models.

scholarly journals Numerical Simulations of the Impact and Spreading of a Particulate Drop on a Solid Substrate

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Hyun Jun Jeong ◽  
Wook Ryol Hwang ◽  
Chongyoup Kim
Keyword(s):  
Numerical Simulations ◽  
Solid Surface ◽  
Reynolds Numbers ◽  
Suspended Particles ◽  
Solid Substrate ◽  
Oscillatory Behavior ◽  
Navier Stokes ◽  
Droplet Spreading ◽  
Navier Stokes Equation ◽  
The Impact

We present two-dimensional numerical simulations of the impact and spreading of a droplet containing a number of small particles on a flat solid surface, just after hitting the solid surface, to understand particle effects on spreading dynamics of a particle-laden droplet for the application to the industrial inkjet printing process. The Navier-Stokes equation is solved by a finite-element-based computational scheme that employs the level-set method for the accurate interface description between the drop fluid and air and a fictitious domain method for suspended particles to account for full hydrodynamic interaction. Focusing on the particle effect on droplet spreading and recoil behaviors, we report that suspended particles suppress the droplet oscillation and deformation, by investigating the drop deformations for various Reynolds numbers. This suppressed oscillatory behavior of the particulate droplet has been interpreted with the enhanced energy dissipation due to the presence of particles.

Filter-Based Unsteady RANS Computations for Single-Phase and Cavitating Flows

Volume 3 ◽  
2004 ◽  
Author(s):  
Jiongyang Wu ◽  
Wei Shyy ◽  
Stein T. Johansen
Keyword(s):  
Eddy Viscosity ◽  
Single Phase ◽  
Experimental Information ◽  
Time Dependent ◽  
Navier Stokes ◽  
Cavitating Flows ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Filter Size ◽  
The Impact

The widely used Reynolds-Averaged Navier-Stokes (RANS) approach, such as the k-ε two-equation model, has been found to over-predict the eddy viscosity and can dampen out the time dependent fluid dynamics in both single- and two-phase flows. To improve the predictive capability of this type of engineering turbulence closures, a consistent method is offered to bridge the gap between DNS, LES and RANS models. Based on the filter size, conditional averaging is adopted for the Navier-Stokes equation to introduce one more parameter into the definition of the eddy viscosity. Both time-dependent single-phase and cavitating flows are simulated by a pressure-based method and finite volume approach in the framework of the Favre-averaged equations coupled with the new turbulence model. The impact of the filter-based concept, including the filter size and grid dependencies, is investigated using the standard k-ε model and with the available experimental information.

Prediction of Particle Impact on an Archimedes Screw Runner Blade for Micro Hydro Turbine

2013 ◽  
Vol 465-466 ◽  
pp. 552-556
Author(s):  
Muhammad Ammar Nik Mutasim ◽  
Nurul Suraya Azahari ◽  
Ahmad Alif Ahmad Adam
Keyword(s):  
Three Dimensional ◽  
Leading Edge ◽  
Navier Stokes ◽  
Particle Impact ◽  
Three Dimensional Flow ◽  
Navier Stokes Equation ◽  
Runner Blade ◽  
Computational Fluid Dynamics Cfd ◽  
The Subject ◽  
The Impact

Energy is one of the most important sources in the world especially for developing countries. The subject study is conducted to predict the behaviour of particle due to errosion from the river through the achimedes screw runner and predict the impact of particle toward blade surface. For this reason, computational fluid dynamics (CFD) methods are used. The three-dimensional flow of fluid is numerically analyzed using the Navier-Stokes equation with standard k-ε turbulence model. The reinverse design of archimedes screw blade was refered with the previous researcher. Flow prediction with numerical results such as velocity streamlines, flow pattern and pressure contour for flow of water entering the blade are discussed. This study shows that the prediction of particle impact occurs mostly on the entering surface blade and along the leading edge of the screw runner. Any modification on the design of the screw runner blade can be analyze for further study.

scholarly journals ISWFoam: A numerical model for internal solitary wave simulation in continuously stratified fluids

2021 ◽  
Author(s):  
Jingyuan Li ◽  
Qinghe Zhang ◽  
Tongqing Chen
Keyword(s):  
Numerical Model ◽  
Stokes Equation ◽  
Nonlinear Models ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Discrete Equation ◽  
Stratified Fluids ◽  
Flat Bottom ◽  
Navier Stokes Equation ◽  
Laboratory Test Results

Abstract. A numerical model, ISWFoam, for simulating internal solitary waves (ISWs) in continuously stratified, incompressible, viscous fluids is developed based on a fully three-dimensional (3D) Navier-Stokes equation using the open source code OpenFOAM. This model combines the density transport equation with the Reynolds-averaged Navier-Stokes equation with the Coriolis force, and the model discrete equation adopts the finite volume method. The k-ω SST turbulence model has also been modified accordingly to the variable density field. ISWFoam provides two initial wave generation methods to generate an ISW in continuously stratified fluids, including solving the weakly nonlinear models of the extended Korteweg–de Vries (eKdV) equation and the fully nonlinear models of the Dubreil-Jacotin-Long (DJL) equation. Grid independence tests for ISWFoam are performed, considering the accuracy and computing efficiency, the appropriate grid size of the ISW simulation is recommended to be one-one hundred and fiftieth of the characteristic length and one-twenty fifth of the ISW amplitude. Model verifications are conducted through comparisons between the simulated and experimental data for ISW propagation examples over a flat bottom section, including laboratory scale and actual ocean scale, a submerged triangular ridge, a Gaussian ridge and slope. The laboratory test results, including the ISW profile, wave breaking location, ISW arrival time, and the spatial and temporal changes in the mixture region, are well reproduced by ISWFoam. The ISWFoam model with unstructured grids and local mesh refinement can accurately simulate the generation and evolution of ISWs, the ISW breaking phenomenon and the interaction between ISWs and complex structures and topography.

scholarly journals ISWFoam: a numerical model for internal solitary wave simulation in continuously stratified fluids

2022 ◽  
Vol 15 (1) ◽  
pp. 105-127
Author(s):  
Jingyuan Li ◽  
Qinghe Zhang ◽  
Tongqing Chen
Keyword(s):  
Numerical Model ◽  
Stokes Equation ◽  
Nonlinear Models ◽  
Waveform Inversion ◽  
Navier Stokes ◽  
Discrete Equation ◽  
Stratified Fluids ◽  
Flat Bottom ◽  
Navier Stokes Equation ◽  
Laboratory Test Results

Abstract. A numerical model, ISWFoam, for simulating internal solitary waves (ISWs) in continuously stratified, incompressible, viscous fluids is developed based on a fully three-dimensional (3D) Navier–Stokes equation using the open-source code OpenFOAM®. This model combines the density transport equation with the Reynolds-averaged Navier–Stokes equation with the Coriolis force, and the model discrete equation adopts the finite-volume method. The k–ω SST turbulence model has also been modified according to the variable density field. ISWFoam provides two initial wave generation methods to generate an ISW in continuously stratified fluids, including solving the weakly nonlinear models of the extended Korteweg–de Vries (eKdV) equation and the fully nonlinear models of the Dubreil–Jacotin–Long (DJL) equation. Grid independence tests for ISWFoam are performed, and considering the accuracy and computing efficiency, the appropriate grid size of the ISW simulation is recommended to be 1/150th of the characteristic length and 1/25th of the ISW amplitude. Model verifications are conducted through comparisons between the simulated and experimental data for ISW propagation examples over a flat bottom section, including laboratory scale and actual ocean scale, a submerged triangular ridge, a Gaussian ridge, and slope. The laboratory test results, including the ISW profile, wave breaking location, ISW arrival time, and the spatial and temporal changes in the mixture region, are well reproduced by ISWFoam. The ISWFoam model with unstructured grids and local mesh refinement can effectively simulate the evolution of ISWs, the ISW breaking phenomenon, waveform inversion of ISWs, and the interaction between ISWs and complex topography.

scholarly journals A Study of the Impact of Methanol, Ethanol and the Miller Cycle on a Gasoline Engine

Energies ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 4847
Author(s):  
Luke Oxenham ◽  
Yaodong Wang
Keyword(s):  
High Performance ◽  
Gasoline Engine ◽  
Navier Stokes ◽  
Miller Cycle ◽  
Navier Stokes Equation ◽  
Efficiency Increase ◽  
And Performance ◽  
The Impact ◽  
Emission Output ◽  
Turbo Engine

This paper focuses on the investigation and optimisation of the Miller cycle, methanol, ethanol and turbocharging when applied to a high-performance gasoline engine. These technologies have been applied both individually and concurrently to test for potential compounding effects. Improvements have been targeted with regards to both emission output and performance. Also assessed is the capability of the engine to operate when exclusively powered by biofuels. This has been carried out numerically using the 1D gas dynamics tool ‘WAVE’, a 1D Navier–Stokes equation solver. These technologies have been implemented within the McLaren M838T 3.8L twin-turbo engine. The Miller cycle early intake valve close (EIVC) improved peak efficiency by 0.17% and increased power output at low and medium loads by 11%. Reductions of 6% for both NOx and CO were also found at rated speed. The biofuels achieved NOx and CO reductions of 60% and 96% respectively, alongside an efficiency increase of 2.5%. Exclusive biofuel use was found to be feasible with a minimum 35% power penalty. Applied cooperatively, the Miller cycle and biofuels were not detrimental to each other, compounding effects of a further 0.05% efficiency and 2% NOx improvements were achieved.

Analysis of Capillary Flow in Rounded Corners

Volume 1 ◽  
2004 ◽  
Author(s):  
Yongkang Chen ◽  
Mark M. Weislogel
Keyword(s):  
Numerical Solutions ◽  
Flow Problem ◽  
Capillary Flow ◽  
Outer Region ◽  
Cross Flow ◽  
Numerical Data ◽  
Navier Stokes ◽  
Navier Stokes Equation ◽  
Inner Region ◽  
The Impact

The problem of capillary flow in interior corners that are rounded is re-visited analytically in this work. By the appropriate geometric scaling, and through the introduction of a new parameter that features the roundedness of the corner, the Navier-Stokes equation is reduced to a convenient form for both numerical and analytical solution. The scaling and analysis of the problem is expected to significantly reduce the reliance on numerical data for such problems, and the design process can be both shortened and improved as a result. For capillary flows of perfect wetting fluids in the rounded corner with an advancing tip, a finite interfacial curvature related to the corner roundedness results at the tip. Accordingly, an outer and inner region of the flow is suggested based on the impact of the corner roundedness on the flow. In this study, asymptotic solutions of the geometrical ‘cross-flow’ problem for the outer region are sought under several constraints and are expected to narrowly bracket parallel numerical solutions. A complete understanding of the flow will be obtained only after the cross-flow problem for the inner region is solved. However, for the flow in the outer region a similarity solution is obtained and presented that reveals how roundedness retards the flow.

scholarly journals Approximate and generalized solutions of conformable type Coudrey–Dodd–Gibbon–Sawada–Kotera equation

2020 ◽  
pp. 2150021
Author(s):  
Mehmet Senol ◽  
Lanre Akinyemi ◽  
Ayşe Ata ◽  
Olaniyi S. Iyiola
Keyword(s):  
Fractional Order ◽  
Approximate Solutions ◽  
Generalized Solutions ◽  
Analysis Method ◽  
Approximate Methods ◽  
Power Series Method ◽  
Closed Form Solutions ◽  
Homotopy Analysis ◽  
Residual Power Series ◽  
Residual Power

In this study, we consider conformable type Coudrey–Dodd–Gibbon–Sawada–Kotera (CDGSK) equation. Three powerful analytical methods are employed to obtain generalized solutions of the nonlinear equation of interest. First, the sub-equation method is used as baseline where generalized closed form solutions are obtained and are exact for any fractional order [Formula: see text]. Furthermore, residual power series method (RPSM) and [Formula: see text]-homotopy analysis method ([Formula: see text]-HAM) are then applied to obtain approximate solutions. These are possible using some properties of conformable derivative. These approximate methods are very powerful and efficient due to the absence of the need for linearization, discretization and perturbation. Numerical simulations are carried out showing error values, [Formula: see text]-curve for [Formula: see text]-HAM and the effects of fractional order on the solution profiles.

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