scholarly journals Inertial dynamics of air bubbles crossing a horizontal fluid–fluid interface

2012 ◽  
Vol 707 ◽  
pp. 405-443 ◽  
Author(s):  
Romain Bonhomme ◽  
Jacques Magnaudet ◽  
Fabien Duval ◽  
Bruno Piar
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Complex Dynamics ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Air Bubbles ◽  
Fluid Interface ◽  
Navier Stokes Equations ◽  
Film Drainage ◽  
Two Fluids

AbstractThe dynamics of isolated air bubbles crossing the horizontal interface separating two Newtonian immiscible liquids initially at rest are studied both experimentally and computationally. High-speed video imaging is used to obtain a detailed evolution of the various interfaces involved in the system. The size of the bubbles and the viscosity contrast between the two liquids are varied by more than one and four orders of magnitude, respectively, making it possible to obtain bubble shapes ranging from spherical to toroidal. A variety of flow regimes is observed, including that of small bubbles remaining trapped at the fluid–fluid interface in a film-drainage configuration. In most cases, the bubble succeeds in crossing the interface without being stopped near its undisturbed position and, during a certain period of time, tows a significant column of lower fluid which sometimes exhibits a complex dynamics as it lengthens in the upper fluid. Direct numerical simulations of several selected experimental situations are performed with a code employing a volume-of-fluid type formulation of the incompressible Navier–Stokes equations. Comparisons between experimental and numerical results confirm the reliability of the computational approach in most situations but also points out the need for improvements to capture some subtle but important physical processes, most notably those related to film drainage. Influence of the physical parameters highlighted by experiments and computations, especially that of the density and viscosity contrasts between the two fluids and of the various interfacial tensions, is discussed and analysed in the light of simple models and available theories.

Mathematical modeling of steady stratified flows

2003 ◽  
Vol 3 ◽  
pp. 195-207
Author(s):  
A.M. Ilyasov ◽  
V.N. Kireev ◽  
S.F. Urmancheev ◽  
I.Sh. Akhatov
Keyword(s):  
Stokes Equations ◽  
Approximate Model ◽  
Immiscible Liquid ◽  
Stratified Flows ◽  
Navier Stokes ◽  
Flat Channel ◽  
Navier Stokes Equations ◽  
Two Fluids ◽  
Flow Parameters ◽  
Direct Numerical Solution

The work is devoted to the analysis of the flow of immiscible liquid in a flat channel and the creation of calculation schemes for determining the flow parameters. A critical analysis of the well-known Two Fluids Model was carried out and a new scheme for the determination of wall and interfacial friction, called the hydraulic approximation in the theory of stratified flows, was proposed. Verification of the proposed approximate model was carried out on the basis of a direct numerical solution of the Navier–Stokes equations for each fluid by a finite-difference method with phase-boundary tracking by the VOF (Volume of Fluid) method. The graphical dependencies illustrating the change in the interfase boundaries of liquids and the averaged over the occupied area of the phase velocities along the flat channel are presented. The results of comparative calculations for two-fluid models are also given, according to the developed model in the hydraulic approximation and direct modeling. It is shown that the calculations in accordance with the hydraulic approximation are more consistent with the simulation results. Thus, the model of hydraulic approximation is the most preferred method for calculating stratified flows, especially in cases of variable volumetric content of liquids.

scholarly journals Numerical Modeling of the Motion and Interaction of a Droplet of an Inkjet Printing Process with a Flat Surface

2021 ◽  
Vol 11 (2) ◽  
pp. 527
Author(s):  
Tim Tofan ◽  
Harald Kruggel-Emden ◽  
Vytautas Turla ◽  
Raimondas Jasevičius
Keyword(s):  
Level Set ◽  
Stokes Equations ◽  
Field Method ◽  
Phase Field Method ◽  
Navier Stokes ◽  
Stable Form ◽  
Fluid Interface ◽  
Velocity Change ◽  
Navier Stokes Equations ◽  
Inkjet Printhead

The numerical simulation and analysis of the ejection of an ink droplet through a nozzle as well its motion through air until its contact with a surface and taking up of a stable form is performed. The fluid flow is modeled by the incompressible Navier–Stokes equations with added surface tension. The presented model can be solved using either a level set or a phase field method to track the fluid interface. Here, the level set method is used to determinate the interface between ink and air. The presented work concentrates on the demonstration how to check the suitability of ink for inkjet printhead nozzles, for instance, for the use in printers. The results such as velocity, change of size, and volume dependence on time of an ink droplet are presented. Recommendations for the use of specific inks are also given.

scholarly journals Flow Pressure Behavior Downstream of Ski Jumps

Fluids ◽  
2020 ◽  
Vol 5 (4) ◽  
pp. 168 ◽  
Author(s):  
Agostino Lauria ◽  
Giancarlo Alfonsi ◽  
Ali Tafarojnoruz
Keyword(s):  
High Speed ◽  
Stokes Equations ◽  
Dynamic Pressure ◽  
Pressure Head ◽  
Navier Stokes ◽  
Maximum Pressure ◽  
Navier Stokes Equations ◽  
Free Jet ◽  
Jet Characteristics ◽  
The Impact

Ski jump spillways are frequently implemented to dissipate energy from high-speed flows. The general feature of this structure is to transform the spillway flow into a free jet up to a location where the impact of the jet creates a plunge pool, representing an area for potential erosion phenomena. In the present investigation, several tests with different ski jump bucket angles are executed numerically by means of the OpenFOAM® digital library, taking advantage of the Reynolds-averaged Navier–Stokes equations (RANS) approach. The results are compared to those obtained experimentally by other authors as related to the jet length and shape, obtaining physical insights into the jet characteristics. Particular attention is given to the maximum pressure head at the tailwater. Simple equations are proposed to predict the maximum dynamic pressure head acting on the tailwater, as dependent upon the Froude number, and the maximum pressure head on the bucket. Results of this study provide useful suggestions for the design of ski jump spillways in dam construction.

Complex dynamics in a stratified lid-driven square cavity flow

2018 ◽  
Vol 855 ◽  
pp. 43-66 ◽  
Author(s):  
Ke Wu ◽  
Bruno D. Welfert ◽  
Juan M. Lopez
Keyword(s):  
Stokes Equations ◽  
Complex Dynamics ◽  
Boussinesq Approximation ◽  
Navier Stokes ◽  
Square Cavity ◽  
Navier Stokes Equations ◽  
Stable Temperature ◽  
Wide Range ◽  
Side Walls ◽  
Steady State Solutions

The dynamic response to shear of a fluid-filled square cavity with stable temperature stratification is investigated numerically. The shear is imposed by the constant translation of the top lid, and is quantified by the associated Reynolds number. The stratification, quantified by a Richardson number, is imposed by maintaining the temperature of the top lid at a higher constant temperature than that of the bottom, and the side walls are insulating. The Navier–Stokes equations under the Boussinesq approximation are solved, using a pseudospectral approximation, over a wide range of Reynolds and Richardson numbers. Particular attention is paid to the dynamical mechanisms associated with the onset of instability of steady state solutions, and to the complex and rich dynamics occurring beyond.

Numerical simulation of the stalled flow within a vaned centrifugal pump

2004 ◽  
Vol 218 (4) ◽  
pp. 425-435 ◽  
Author(s):  
K M Guleren ◽  
A Pinarbasi
Keyword(s):  
Numerical Simulation ◽  
Centrifugal Pump ◽  
High Speed ◽  
Stokes Equations ◽  
Reverse Flow ◽  
Flow Characteristics ◽  
Navier Stokes ◽  
Leakage Flow ◽  
Navier Stokes Equations ◽  
Low Pass

The main goal of the present work is to analyse the numerical simulation of a centrifugal pump by solving Navier-Stokes equations, coupled with the ‘standard k-∊’ turbulence model. The pump consists of an impeller having five curved blades with nine diffuser vanes. The shaft rotates at 890r/min. Flow characteristics are assumed to be stalled in the appropriate region of flowrate levels of 1.31-2.861/s. Numerical analysis techniques are performed on a commercial FLUENT package program assuming steady, incompressible flow conditions with decreasing flowrate. Under stall conditions the flow in the diffuser passage alternates between outward jetting when the low-pass-filtered pressure is high to a reverse flow when the filtered pressure is low. Being below design conditions, there is a consistent high-speed leakage flow in the gap between the impeller and the diffuser from the exit side of the diffuser to the beginning of the volute. Separation of this leakage flow from the diffuser vane causes the onset of stall. As the flowrate decreases both the magnitude of the leakage within the vaneless part of the pump and reverse flow within a stalled diffuser passage increase. As this occurs, the stall-cell size extends from one to two diffuser passages. Comparisons are made with experimental data and show good agreement.

Simulation of the subsonic flow in a high-speed centrifugal compressor impeller by the pressure-based method

1998 ◽  
Vol 212 (4) ◽  
pp. 269-287 ◽  
Author(s):  
Y Wang ◽  
S Komori
Keyword(s):  
High Speed ◽  
Compressible Flows ◽  
Incompressible Flows ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Centrifugal Impeller ◽  
Navier Stokes Equations ◽  
Compressor Impeller ◽  
Collocated Grid

A pressure-based finite volume procedure developed previously for incompressible flows is extended to predict the three-dimensional compressible flow within a centrifugal impeller. In this procedure, the general curvilinear coordinate system is used and the collocated grid arrangement is adopted. Mass-averaging is used to close the instantaneous Navier-Stokes equations. The covariant velocity components are used as the main variables for the momentum equations, making the pressure-velocity coupling easier. The procedure is successfully applied to predict various compressible flows from subsonic to supersonic. With the aid of the k-ɛ turbulence model, the flow details within a centrifugal impeller are obtained using the present procedure. Predicted distributions of the meridional velocity and the static pressure are reasonable. Calculated radial velocities and flow angles are favourably compared with the measurements at the exit of the impeller.

Two-Fluid Flow Between Rotating Annular Disks

1976 ◽  
Vol 98 (2) ◽  
pp. 214-222 ◽  
Author(s):  
J. E. Zweig ◽  
H. J. Sneck
Keyword(s):  
Annular Flow ◽  
Stokes Equations ◽  
Fluid Flows ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Two Fluids ◽  
Small Clearance ◽  
Annular Disks ◽  
Two Fluid

The general hydrodynamic behavior at small clearance Reynolds numbers of two fluids of different density and viscosity occupying the finite annular space between a rotating and stationary disk is explored using a simplified version of the Navier-Stokes equations which retains only the centrifugal force portion of the inertia terms. A criterion for selecting the annular flow fields that are compatible with physical reservoirs is established and then used to determine the conditions under which two-fluid flows in the annulus might be expected for specific fluid combinations.

Computations of the Compressible Multiphase Flow Over the Cavitating High-Speed Torpedo

2003 ◽  
Vol 125 (3) ◽  
pp. 459-468 ◽  
Author(s):  
F. M. Owis ◽  
Ali H. Nayfeh
Keyword(s):  
High Speed ◽  
Multiphase Flows ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Multiphase System ◽  
System Of Equations ◽  
Cavitating Flows ◽  
Navier Stokes Equations ◽  
Compressible Multiphase Flow ◽  
Speed Flow

For high-speed cavitating flows, compressibility becomes significant in the liquid phase as well as in the vapor phase. In addition, the compressible energy equation is required for studying the effects of the propulsive jet on the cavity. Therefore, a numerical method is developed to compute cavitating flows over high-speed torpedoes using the full unsteady compressible Navier-Stokes equations. The multiphase system of equations is preconditioned for low-speed flow computations. Using the mass fraction form, we derive an eigensystem for both the conditioned and the nonconditioned system of equations. This eigensystem provides stability for the numerical discretization of the convective flux and increases the convergence rate. This method can be used to compute single as well as multiphase flows. The governing equations are discretized on a structured grid using an upwind flux difference scheme with flux limits. Single as well as multiphase flows are computed over a cavitating torpedo. The results indicate that the preconditioned system of equations converges rapidly to the required solution at very low speeds. The theoretical results are in good agreement with the measurements.

Calculation of Debris Trajectories During High-Speed Snowplowing

2002 ◽  
Author(s):  
H. K. Nakhla ◽  
B. E. Thompson
Keyword(s):  
Particle Tracking ◽  
High Speed ◽  
Turbulence Modeling ◽  
Stokes Equations ◽  
Cutting Edge ◽  
Navier Stokes ◽  
Engineering Model ◽  
Navier Stokes Equations ◽  
Snow Plowing ◽  
Reynolds Averaged Navier Stokes

An engineering model is presented to calculate the trajectory of airborne debris that adversely affects visibility during high-speed snow plowing. Reynolds-averaged Navier-Stokes equations are solved numerically with turbulence-modeling, particle-tracking, and cutting-edge approximations. Results suggest snow can be divided into splash and snow-cloud when designing treatments to improve visibility for snowplow drivers and following traffic. Calculated results confirm the findings of windtunnel and road tests, specifically that the trap angle of overplow deflectors should be less than 50 degrees to eliminate snow debris blowing over top of the plow onto the windscreen.

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