Multiple Node Breakup of a Liquid Jet Into Drops in Another Immiscible Liquid

2002 ◽  
Author(s):  
Shunji Homma ◽  
Jiro Koga ◽  
Shiro Matsumoto ◽  
Gre´tar Tryggvason
Keyword(s):  
Stokes Equations ◽  
Immiscible Liquid ◽  
Capillary Waves ◽  
Navier Stokes ◽  
Unstable Wave ◽  
Liquid Jet ◽  
Navier Stokes Equations ◽  
Axisymmetric Jet ◽  
Multiple Node ◽  
Liquid Systems

We investigate numerically the breakup of an axisymmetric jet into drops in liquid-liquid systems, specifically focus on multiple node breakup, where more than one node of the most unstable wave becomes one drop. The unsteady Navier-Stokes equations for incompressible Newtonian fluids are solved with a Front-Tracking / Finite Difference method. Various combinations of the non-dimensional numbers (Re = 80, 160, 320; We = 5, 8; Fr = 4, 8, 32, ∞) are examined for constant ratios of density (ρc, ρj = 1.25) and viscosity (µc, µj = 1). Capillary waves grow on the jet surface and the multiple node breakup is observed in all cases examined. A “shoulder” is observed on the jet right behind the bulb when the double-node breakup occurs. Unlike the breakup of a jet in air, vortical motions in the external fluid affect the breakup process.

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.

Impingement Heat Transfer of Free-Surface Liquid Jets

2002 ◽  
Author(s):  
Albert Y. Tong
Keyword(s):  
Heat Transfer ◽  
Free Surface ◽  
Stokes Equations ◽  
Numerical Study ◽  
Navier Stokes ◽  
Liquid Jets ◽  
Liquid Jet ◽  
Stagnation Region ◽  
Navier Stokes Equations ◽  
Impingement Heat Transfer

The problem of convective heat transfer of a circular liquid jet impinging onto a substrate is studied numerically. The objective of the study is to understand the hydrodynamics and heat transfer of the impingement process. The Navier-Stokes equations are solved using a finite-volume formulation. The free surface of the jet is tracked by the volume-of-fluid method. The energy equation is modeled by using an enthalpy-based formulation. Detailed flow fields as well as free surface contours and pressure distributions on the substrate have been obtained. Local Nusselt number variations along the solid surface have also been calculated. The effects of several key parameters on the hydrodynamics and heat transfer of an impinging liquid jet have been examined. It has been found that the jet-inlet velocity profile and jet elevation have a significant effect on the hydrodynamics and heat transfer, particularly in the stagnation region, of an impinging jet. The numerical results have been compared with experimental data obtained from the literature. The close agreement supports the validity of the numerical study.

scholarly journals Numerical investigations on bubble-induced jetting and shock wave focusing: application on a needle-free injection

2019 ◽  
Vol 475 (2222) ◽  
pp. 20180548 ◽  
Author(s):  
Nikolaos Kyriazis ◽  
Phoevos Koukouvinis ◽  
Manolis Gavaises
Keyword(s):  
Change Process ◽  
Thermal Equilibrium ◽  
Mass Fraction ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Liquid Jet ◽  
Navier Stokes Equations ◽  
Numerical Investigations ◽  
Barotropic Equation ◽  
Shock Wave Focusing

The formation of a liquid jet into air induced by the growth of a laser-generated bubble inside a needle-free device is numerically investigated by employing the compressible Navier–Stokes equations. The three co-existing phases (liquid, vapour and air) are assumed to be in thermal equilibrium. A transport equation for the gas mass fraction is solved in order to simulate the non-condensable gas. The homogeneous equilibrium model is used in order to account for the phase change process between liquid and vapour. Thermodynamic closure for all three phases is achieved by a barotropic Equation of State. Two-dimensional axisymmetric simulations are performed for a needle-free device for which experimental data are available and used for the validation of the developed model. The influence of the initial bubble pressure and the meniscus geometry on the jet velocity is examined by two different sets of studies. Based on the latter, a new meniscus design similar to shaped-charge jets is proposed, which offers a more focused and higher velocity jet compared to the conventional shape of the hemispherical gas–liquid interface. Preliminary calculations show that the developed jet can penetrate the skin and thus, such configurations can contribute towards a new needle-free design.

Numerical and Experimental Studies of Air Bubbles Coalescence in a Quiescent Water Column

2005 ◽  
Vol 3 (1) ◽  
Author(s):  
Jean-Michel Martinez ◽  
Xavier Chesneau ◽  
Belkacem Zeghmati
Keyword(s):  
Surface Tension ◽  
Water Column ◽  
Stokes Equations ◽  
Experimental Studies ◽  
Numerical Results ◽  
Navier Stokes ◽  
Liquid Jet ◽  
Air Bubbles ◽  
Navier Stokes Equations ◽  
Effect Of Surface

Numerical and experimental studies of the dynamics of bubbles coalescence is reported. The numerical method based on the PLIC-VOF method and our advection and surface tension algorithms has been applied to analyse the effect of surface tension and convective terms of the Navier-Stokes equations on air bubbles' coalescence in a quiescent water column. Experimental and numerical results show a mechanical attraction between both bubbles' interface before the coalescence. We analyse the effect of the type of discretization of the convective terms of the Navier-Stokes equations on the shape of bubble after the coalescence phenomenon. Numerical results are in agreement with the images of bubbles' coalescence of our experimental device recorded by a camera. Somes images show obviousness bubbles' coalescence caracterized by an intense liquid jet within the following bubble.

Numerical Simulation of Drop Formation From a Nozzle in Liquid-Liquid Systems

2003 ◽  
Author(s):  
Shunji Homma ◽  
Haruhisa Honda ◽  
Jiro Koga ◽  
Shiro Matsumoto ◽  
Museok Song ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Staggered Grid ◽  
Navier Stokes ◽  
Simulation Code ◽  
Navier Stokes Equations ◽  
Liquid Drops ◽  
Front Tracking Method ◽  
Satellite Drops ◽  
Liquid Systems

Numerical simulation code is developed to study the formation of liquid drops from a nozzle into another quiescent liquid. The Navier-Stokes equations for two immiscible, incompressible, Newtonian fluids are solved on a fixed, staggered grid of cylindrical axisymmetric coordinates. Interfacial motion is captured using a Front-Tracking Method. The time variation of interfacial shape simulated by the code is in excellent agreement with experiments. Simulation results show that the viscosity ratio affects the size of the satellite drops.

scholarly journals Growth and spectra of gravity–capillary waves in countercurrent air/water turbulent flow

2015 ◽  
Vol 777 ◽  
pp. 245-259 ◽  
Author(s):  
Francesco Zonta ◽  
Alfredo Soldati ◽  
Miguel Onorato
Keyword(s):  
Stokes Equations ◽  
Capillary Waves ◽  
Turbulence Theory ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Generation Process ◽  
Navier Stokes Equations ◽  
Interface Waves ◽  
Two Phases ◽  
Wave Induced

Using direct numerical simulation of the Navier–Stokes equations, we analyse the dynamics of the interface between air and water when the two phases are driven by opposite pressure gradients (countercurrent configuration). The Reynolds number ($\mathit{Re}_{{\it\tau}}$), the Weber number ($\mathit{We}$) and the Froude number ($\mathit{Fr}$) fully describe the physical problem. We examine the problem of the transient growth of interface waves for different combinations of physical parameters. Keeping$\mathit{Re}_{{\it\tau}}$constant and varying$\mathit{We}$and$\mathit{Fr}$, we show that, in the initial stages of the wave generation process, the amplitude of the interface elevation${\it\eta}$grows in time as${\it\eta}\propto t^{2/5}$. The wavenumber spectra,$E(k_{x})$, of the surface elevation in the capillary range are in good agreement with the predictions of wave turbulence theory. Finally, the wave-induced modification of the average wind and current velocity profiles is addressed.

Effects of stator splitter blades on aerodynamic performance of a single-stage transonic axial compressor

2020 ◽  
Vol 14 (4) ◽  
pp. 7369-7378
Author(s):  
Ky-Quang Pham ◽  
Xuan-Truong Le ◽  
Cong-Truong Dinh
Keyword(s):  
Stokes Equations ◽  
Three Dimensional ◽  
Axial Compressor ◽  
Aerodynamic Performance ◽  
Numerical Results ◽  
Single Stage ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Operating Stability ◽  
Length Coverage

Splitter blades located between stator blades in a single-stage axial compressor were proposed and investigated in this work to find their effects on aerodynamic performance and operating stability. Aerodynamic performance of the compressor was evaluated using three-dimensional Reynolds-averaged Navier-Stokes equations using the k-e turbulence model with a scalable wall function. The numerical results for the typical performance parameters without stator splitter blades were validated in comparison with experimental data. The numerical results of a parametric study using four geometric parameters (chord length, coverage angle, height and position) of the stator splitter blades showed that the operational stability of the single-stage axial compressor enhances remarkably using the stator splitter blades. The splitters were effective in suppressing flow separation in the stator domain of the compressor at near-stall condition which affects considerably the aerodynamic performance of the compressor.

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