Motivation, analysis and control of the variable density Navier-Stokes equations

Due to ever increasing water demand, the preservation of water quality is becoming a very important issue. Eutrophication is amongst the particular problems threatening the quality of water. This paper begins with presenting a mathematical model for aeration process in lake used to combat water eutrophication. Two phases are numerically simulated to study the injected air effect on water by using a corrected one phase model described by Navier–Stokes equations with variable density and viscosity representing the mixture. This model is numerically studied by coupling characteristics scheme for time discretization and mixed finite element method for space approximation. An error estimates in space and time for the velocity are obtained. Numerical results are given firstly in support of the mathematical analysis and secondly to simulate a real application case of the studied problem.

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Mathematical Modeling of Pneumatic Pipes in a Simulation of Heterogeneous Engineering Systems

Journal of Fluids Engineering ◽

10.1115/1.4005261 ◽

2011 ◽

Vol 133 (12) ◽

Cited By ~ 6

Author(s):

Zbigniew Kamiński

Keyword(s):

Stokes Equations ◽

Navier Stokes ◽

Engineering Systems ◽

Test Results ◽

Navier Stokes Equations ◽

Kolmogorov Smirnov ◽

Complex Fluid ◽

Control Circuits ◽

Drive And Control ◽

And Control

Pipes are widely used in hydraulic and pneumatic subsystems for transferring energy or signals. Accurate prediction of pressure transients is very important in the drive and control circuits of complex fluid-line systems. Based on the approximation of Navier-Stokes equations for one-dimensional flow, a mathematical model of the pneumatic pipe with lumped parameters was developed using ordinary differential equations, which can be easily implemented in most computer programs for the simulation of complex heterogeneous engineering systems. Implemented in Matlab-Simulink software, the computer model of the pipe makes it possible to determine the influence of capacitance, inertance, resistance and heat exchange on the dynamic characteristics of the control and power circuits of pneumatic systems. An advantage of the model is that various functions can be selected to describe linear resistances and local resistances are taken into account, particularly at the inlet and outlet. Such resistances largely affect flow resistances in short tubes (up to 10 m) that can be found, e.g., in pneumatic brake systems of road vehicles. Confirmed by Kolmogorov-Smirnov test results, the consistency of the pressure curves obtained in experimental and simulation tests proves the implemented tube model to be useful for the calculations of pneumatic system dynamics.

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Dynamics of a contracting fluid compound filament with a variable density ratio

Science and Technology Development Journal ◽

10.32508/stdj.v24i2.2515 ◽

2021 ◽

Vol 24 (2) ◽

pp. first

Author(s):

Truong V. Vu ◽

Vinh T. Nguyen ◽

Phan H. Nguyen ◽

Nang X. Ho ◽

Binh D. Pham ◽

...

Keyword(s):

Interfacial Tension ◽

Stokes Equations ◽

Weighting Function ◽

Density Ratio ◽

Variable Density ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Front Tracking Method ◽

Fixed Grid ◽

Eulerian Grid

Introduction: Compound fluid filaments appear in many applications, e.g., drug delivery and processing or microfluidic systems. This paper focuses on the numerical simulation of an incompressible, immiscible, and Newtonian fluid for the contraction process of a fluid compound filament by solving the Navier-Stokes equations. The front-tracking method is used to solve this problem, which uses connected segments (Lagrangian grid) that move on a fixed grid (Eulerian grid) to represent the interface between the liquids. Methods: The interface points are advected by the velocity interpolated from those of the fixed grid using the area weighting function. The coordinates of the interface points are used to construct the indicators specifying the different fluids and compute the interfacial tension force. Results: The simulation results show that under the effects of the interfacial tension, the capsuleshaped filament can transform into a spherical compound droplet (i.e., non-breakup) or can break up into smaller spherical compound and simple droplets (i.e., breakup). When the density ratio of the outer to middle fluids increases, the filament changes from non-breakup to breakup upon contraction. Conclusion: Increasing the density ratio enhances the breakup of the compound filament during contraction. The breakup is also promoted by increasing the initial length of the filament.

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A Particle-Based Model for Prediction of Cement Diffusion During Osteoporotic Hip Augmentation Surgery: Theory and Validation

Volume 2: Biomedical and Biotechnology Engineering ◽

10.1115/imece2010-38978 ◽

2010 ◽

Cited By ~ 1

Author(s):

E. Basafa ◽

Y. Otake ◽

M. D. Kutzer ◽

R. S. Armiger ◽

M. Armand

Keyword(s):

Bone Cement ◽

Stokes Equations ◽

Navier Stokes ◽

Patient Specific ◽

Osteoporotic Bone ◽

Navier Stokes Equations ◽

Injection Process ◽

Particle Hydrodynamics ◽

Smoothed Particle ◽

And Control

Elderly patients with preexisting osteoporotic hip fracture are at high risk of a subsequent fracture in their contralateral hip. Current preventive approaches commonly have a long delay in restoring bone strength leaving patients at continued risk despite preventive efforts. Femoroplasty — injection of bone cement into the proximal femur — has been proposed as a potential preventive approach. However, it can cause complications because of extravasation of the cement into unwanted regions of the bone and an increased pressure within the bone, if not controlled and planned carefully. Therefore, precise modeling of the diffusion of the bone cement in osteoporotic bone and control over the injection process is of substantial importance. This paper presents a patient-specific fluid dynamics model to simulate the diffusion of the bone cement inside femur. The model is based on the smoothed particle hydrodynamics (SPH) method for particle-based modeling of fluids. The Navier-Stokes equations were built into the SPH formulations and viscosity effects were added to model the flow of cement inside porous media. To validate the model, a new prototype automatic injection device was used to inject acrylic silicone into a porous foam block. Results of simulation of the injection show close matching with experimental data. The model is therefore promising for further development of optimized and fully controlled femoroplasty procedures.

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Iteration penalty method for the incompressible Navier-Stokes equations with variable density based on the artificial compressible method

Advances in Computational Mathematics ◽

10.1007/s10444-020-09757-3 ◽

2020 ◽

Vol 46 (1) ◽

Author(s):

Rong An

Keyword(s):

Penalty Method ◽

Stokes Equations ◽

Variable Density ◽

Navier Stokes ◽

Navier Stokes Equations

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Bilinear Optimal Control Problem for the Stationary Navier–Stokes Equations with Variable Density and Slip Boundary Condition

Bulletin of the Brazilian Mathematical Society New Series ◽

10.1007/s00574-019-00131-6 ◽

2019 ◽

Vol 50 (4) ◽

pp. 871-887

Author(s):

Exequiel Mallea-Zepeda ◽

Eber Lenes ◽

Jonnathan Rodríguez Zambrano

Keyword(s):

Boundary Condition ◽

Optimal Control ◽

Optimal Control Problem ◽

Stokes Equations ◽

Slip Boundary Condition ◽

Variable Density ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Slip Boundary ◽

Stationary Navier Stokes Equations

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A DDFV Scheme for Incompressible Navier-Stokes Equations with Variable Density

Finite Volumes for Complex Applications VII-Elliptic, Parabolic and Hyperbolic Problems - Springer Proceedings in Mathematics & Statistics ◽

10.1007/978-3-319-05591-6_62 ◽

2014 ◽

pp. 627-635 ◽

Cited By ~ 4

Author(s):

Thierry Goudon ◽

Stella Krell

Keyword(s):

Stokes Equations ◽

Variable Density ◽

Navier Stokes ◽

Navier Stokes Equations

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Simulations of Dam-Break Flows Using Free Surface Capturing Method

Journal of Mechanics ◽

10.1017/s1727719100002513 ◽

2008 ◽

Vol 24 (4) ◽

pp. 391-403 ◽

Cited By ~ 5

Author(s):

W.-Y. Chang ◽

L.-C. Lee ◽

H.-C. Lien ◽

J.-S. Lai

Keyword(s):

Free Surface ◽

Stokes Equations ◽

Variable Density ◽

Dam Break ◽

Navier Stokes ◽

Navier Stokes Equations ◽

Flow Equations ◽

Weakly Compressible ◽

Dam Break Flow ◽

Free Surface Capturing

AbstractA model adopting the surface capturing method is developed for the simulation of dam-break flows by solving the Navier-Stokes equations of weakly compressible and variable density flows in open channels. Due to the characteristics of weakly compressible flow equations, a compressibility parameter describing the compressibility of fluid is determined to obtain the time-accurate flow fields in both liquid and gas regions simultaneously. Accordingly, the location of free surface can be captured as a discontinuity of the density field for dam-break flow simulations. The numerical algorithm in the proposed method is based on the framework of the finite volume method for discretization in space. To deal with the discontinuity property of fluid density near the free surface, the TVD-MUSCL scheme is adopted to overcome numerical oscillations and dissipation. For discretization in time, the explicit 4-stage Runge-Kutta scheme is employed in the model. Finally, several typical dam-break flow problems in open channel are simulated to demonstrate the validation and applicability of the proposed model.

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