Numerical simulation of undular jumps on graveled bed using volume of fluid method

2012 ◽  
Vol 66 (5) ◽  
pp. 909-917 ◽  
Author(s):  
Fatemeh Rostami ◽  
Saeed Reza Sabbagh Yazdi ◽  
Md Azlin Md Said ◽  
Mahdi Shahrokhi
Keyword(s):  
Free Surface ◽  
Open Channel ◽  
Flow Model ◽  
High Sensitivity ◽  
Navier Stokes ◽  
Stationary Waves ◽  
Hydraulic Jumps ◽  
Volume Of Fluid Method ◽  
Flow Equations ◽  
Proposed Model

Undular hydraulic jumps are characterized by a smooth rise of the free surface, followed by a train of stationary waves. These jumps sometimes occur in natural waterways and rivers. Numerical difficulties are especially distinct when the flow condition is close to the critical value because of the high sensitivity of the near-critical flow field to flow and channel conditions. Furthermore, the free surface has a wavy shape, which may indicate the occurrence of several transitions from supercritical to subcritical states and vice versa (i.e., undular hydraulic jumps). In this study, a flow model is used to predict an undular hydraulic jump in a rectangular open channel. The model is based on the general two-dimensional, Reynolds-averaged, Navier–Stokes flow equations. The resulting set of partial differential equations is solved using the FLOW-3D solver. The results are compared with the experimental data to validate the model. The comparative analysis shows that the proposed model yields good results. Several types of undular hydraulic jumps occurring in different situations are then simulated to prove the potential application of the model.

scholarly journals Using mathematics to avoid blindness in diabetics

2018 ◽  
Vol 2 (1) ◽  
pp. 42-70
Author(s):  
Arieh Helfgott ◽  
Ariella E.R. Helfgott ◽  
Sean Mullany
Keyword(s):  
Laser Surgery ◽  
High Sensitivity ◽  
Navier Stokes ◽  
Pumping Rate ◽  
Simultaneous Application ◽  
Flow Equations ◽  
Retinal Blood Vessels ◽  
Laser Treatments ◽  
Volume Doubling ◽  
Sustained Recovery

Purpose: Avoid diabetic-blindness by applying five simple mathematically-inspired treatments that achieve life-long recovery from advanced diabetic retinopathy (ADR), without laser treatments or Avastin (Hoffmann-La Roche, Basel, Switzerland) injections.Methods: A mathematical model of ADR is derived; it is based on fluid leakage from abnormal ‘holes’ in small retinal blood vessels. First, the volume of a microscopic fluid droplet leaking from a single small vein-hole during a single heartbeat is derived from the Navier-Stokes flow-equations. Then, total fluid volume leaking into the retina from all M vein holes in N heartbeats is determined. Six parameters in the equations of the model with significant influence on leakage rates and leaked volumes are identified. These insights are used to design and then apply five simple, novel, and eff icient therapeutic treatments, T1 to T5, that may achieve recovery from ADR without laser surgery or Avastin injections. Daily rates, as well as total volumes, of macular fluid accumulation, removal (by eye-pumps), and leakage are calculated from optical coherence tomography (OCT)-measured macular thicknesses.Results: Ten years ago, this paper’s primary author, Arieh Helfgott (AH), suffered from ADR that no longer responded to laser surgery. After simultaneous application of treatments T1-T5, AH recovered from ADR in 42 days and has been free of ADR for over ten years, without needing Avastin injections. Leakage-volumes were shown to be very sensitive to small changes in hole diameters. In ADR, modest increases of 2.4%, 5.7%, 10.7%, 15%, and 19% in hole diameters induce impressive 10%, 25%, 50%, 75%, and 100% (volume-doubling) increases in leakage volumes, respectively. In recovery from ADR, modest decreases of −2.6%, −5.4%, −8.5%, −12%, and −15.9% in hole diameters induce equally impressive −10%, −20%, −30%, −40%, and −50% (volume-halving) decreases in leakage volumes, respectively.Conclusion: In AH’s case, mathematics helped in avoiding blindness from ADR. Simultaneous application of mathematics-inspired treatments T1-T5 resulted in reduced leakage from holes, elimination of retinal swelling (RS), and sustained recovery from ADR. With high sensitivity to hole diameters, advancing DR can easily become unmanageable, while recovery from ADR may possibly be achievable in approximately six weeks using efficient blood pressure (BP) control and small ‘repairs’ leading to reduction in hole diameters. The pumping rate of the eye is colossal; eye pumps can remove a macula-volume-equivalent in approximately 44 days. This is very helpful in recovery from ADR, and spectacular for such microscopic pumps 

Numerical Simulation of 2D Hydraulic Jump Flow in a Vertical Plane

2012 ◽  
Vol 482-484 ◽  
pp. 16-20
Author(s):  
Wen Li Wei ◽  
X.J Zhao ◽  
Y. L Liu
Keyword(s):  
Free Surface ◽  
Hydraulic Jump ◽  
Flow Model ◽  
Vertical Plane ◽  
Surface Profile ◽  
Governing Equations ◽  
Proposed Model ◽  
2D Flow ◽  
Time Changes ◽  
Volume Method

This paper was concerned with a vertical two-dimensional (2D) flow model with free surface. The water governing equations were discretized with finite difference method. The function of volume method was employed to track the moving free surface. The model was used to predict the characteristics of hydraulic jump flow in a 2D vertical plane. The surface profile and time averaged velocity were calculated, which shows the proposed model can be capable of capturing sharp water and gas interface configuration as time changes.

Simulations of Dam-Break Flows Using Free Surface Capturing Method

2008 ◽  
Vol 24 (4) ◽  
pp. 391-403 ◽  
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.

Numerical Simulation of 2D Dam-Break Flow in a Vertical Plane

2011 ◽  
Vol 130-134 ◽  
pp. 3620-3623
Author(s):  
Ming Qin Liu ◽  
Y.L. Liu
Keyword(s):  
Free Surface ◽  
Flow Model ◽  
Vertical Plane ◽  
Surface Profile ◽  
Dam Break ◽  
Governing Equations ◽  
Proposed Model ◽  
2D Flow ◽  
Dam Break Flow ◽  
Volume Method

This paper was concerned with a vertical two-dimensional (2D) flow model with free surface. The water governing equations were discretized with finite difference method. The function of volume method was employed to track the moving free surface. The model was used to predict the characteristics of dam-break flow in a 2D vertical plane. The surface profile and time averaged velocity were calculated, which shows the proposed model can be capable of capturing sharp water and gas interface configuration as time elapses.

URANS Simulations of a Cruise Ship in Crabbing Motion

2021 ◽  
Author(s):  
Lu Zou ◽  
Zao-jian Zou
Keyword(s):  
Free Surface ◽  
Degrees Of Freedom ◽  
Navier Stokes ◽  
Volume Of Fluid Method ◽  
Cruise Ship ◽  
Free Surface Elevation ◽  
Time Step ◽  
Quay Wall ◽  
Mesh Technique ◽  
Ship Speed

Abstract In ship manoeuvrability, the crabbing test is critical to evaluate the hydrodynamic quantities for the guidance of an efficient and safe berthing or unberthing manoeuvres. In the present study, the crabbing performance of a cruise ship is investigated by an unsteady Reynolds-averaged Navier-Stokes (URANS) method considering the instantaneous relative motion between the ship and the quay. In the numerical simulations, the cruise ship is approaching the quay wall at a constant lateral speed. The crabbing motion with five degrees of freedom is modeled by the dynamic overset mesh technique, while the free surface elevation is simulated by the Volume of Fluid method. For reliable predictions of the crabbing performances, the timestep dependency study is conducted and a suitable time step is determined. From the computations, the hydrodynamic performances of the cruise ship, including forces and moments, as well as the surge, sinkage, roll, trim and yaw motions are predicted. The numerical results indicate variations of the hydrodynamic quantities under the impacts of ship speed and blockage effects by the quay wall. The present results can be used to evaluate the crabbing ability of the cruise ship and to provide guidance for estimating and designing the crabbing model test in further investigations.

scholarly journals WAVE MOTION NEAR A BREAKWATER ROUNDHEAD

2012 ◽  
Vol 1 (33) ◽  
pp. 71
Author(s):  
Takahide Honda ◽  
Peter Wellens ◽  
Marcel Van Gent
Keyword(s):  
Free Surface ◽  
Wave Motion ◽  
Flow Model ◽  
Stokes Equations ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Flow Solver ◽  
Physical Model Tests

COMFLOW is a general 3D free-surface flow solver. The numerical method is based on the Navier-Stokes equations in a porous medium, with additional force terms to represent the (turbulent) interaction of the flow with the medium. The free surface is displaced by means of the Volume-Of-Fluid method. The main objective in this paper is to validate the permeable flow model in 3D. Tailor-made physical model tests were performed for this purpose. In the experiment surface elevations are measured inside and around a permeable structure with 18 wave gauges in total. The measurements are represented well by the simulation results.

scholarly journals 3D SIMULATION OF WAVE INTERACTION WITH PERMEABLE STRUCTURES

2011 ◽  
Vol 1 (32) ◽  
pp. 28 ◽  
Author(s):  
Peter Wellens ◽  
M.J.A. Borsboom ◽  
M.R.A. Van Gent
Keyword(s):  
Free Surface ◽  
Reflection Coefficient ◽  
Flow Model ◽  
Wave Interaction ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Navier Stokes ◽  
Flow Solver ◽  
Simulation Results ◽  
Rubble Mound Breakwaters

COMFLOW is a general 3D free-surface flow solver. The main objective in this paper is to extend the solver with a permeable flow model to simulate wave interaction with rubble-mound breakwaters. The extended Navier-Stokes equations for permeable flow are presented and we show the discretization of these equations as they are implemented in COMFLOW. An analytical solution for the reflection coefficient of a permeable structure is derived and the numerical model is compared to the solution. In addition, a validation study has been performed, in which we compare the numerical results with an experiment. In the experiment, pressures and surface elevations are measured inside a permeable structure. The measurements are represented well by the simulation results. At the end, a 3D application of the model is shown.

scholarly journals Micropolar Blood Flow in a Magnetic Field

Fluids ◽  
2021 ◽  
Vol 6 (3) ◽  
pp. 133
Author(s):  
George C. Bourantas
Keyword(s):  
Magnetic Field ◽  
Blood Flow ◽  
Flow Model ◽  
Navier Stokes ◽  
Point Collocation ◽  
Electrical And Magnetic Properties ◽  
Proposed Model ◽  
Particle Strength ◽  
Derivatives Of

In this paper we numerically solve a flow model for the micropolar biomagnetic flow (blood flow) in a magnetic field. In the proposed model we account for both electrical and magnetic properties of the biofluid and we investigate the role of microrotation on the flow regime. The flow domain is in a channel with an unsymmetrical single stenosis, and in a channel with irregular multi-stenoses. The mathematical flow model consists of the Navier–Stokes (N–S) equations expressed in their velocity–vorticity (u–ω) variables including the energy and microrotation transport equation. The governing equations are solved by using the strong form meshless point collocation method. We compute the spatial derivatives of the unknown field functions using the discretization correction particle strength exchange (DC PSE) method. We demonstrate the accuracy of the proposed scheme by comparing the numerical results obtained with those computed using the finite element method.

Numerical Simulation of Wind Effects on Breaking Solitary Waves by Navier-Stokes Equations

2009 ◽  
Author(s):  
Zhihua Xie ◽  
Xianyun Wen ◽  
Andrew N. Ross
Keyword(s):  
Solitary Waves ◽  
Wave Breaking ◽  
Flow Model ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Wind Effects ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Proposed Model ◽  
The Waves

A two-phase flow model is addressed in this study to investigate effects of wind on breaking solitary waves, by solving the Reynolds-averaged Navier-Stokes (RANS) equations simultaneously for the flows both in the air and water, in which the free surface is calculated by the Volume-of-Fluid (VOF) method. First, the proposed model is validated with the experiment by Synolakis [1] of a breaking solitary wave without wind on a 1 : 19.85 impermeable beach. Then the wind effects are taken into account for modelling breaking solitary waves and it is found that the wind alters the air flow structure above the water wave; affects the wave breaking and runup process; increases the velocity in the water and causes the waves to break earlier, which agrees with previous laboratory experiment by Douglass [2].

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