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.

The Effects of Hydrodynamics Characteristics on Mass Transfer During Droplet Formation Using Computational Approach

2006 ◽  
Author(s):  
A. Javadi ◽  
M. Taeibi-Rahni ◽  
D. Bastani ◽  
K. Javadi
Keyword(s):  
Mass Transfer ◽  
Stokes Equations ◽  
Computational Simulation ◽  
Mass Transfer Rate ◽  
Droplet Formation ◽  
Continuous Phase ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Two Phases ◽  
Expansion Model

For the reason that flow expansion model (developed in our previous work) for evaluating mass transfer during droplet formation involves with manifest hydrodynamic aspects, in this research computational simulation of this phenomenon was done for characterization of hydrodynamics effects on the mass transfer during droplet formation. For this purpose, an Eulerian volume tracking computational code based on volume of fluid (VOF) method was developed to solve the transient Navier-Stokes equations for the axisymmetric free-boundary problem of a Newtonian liquid that is dripping vertically and breaking as drops into another immiscible Newtonian fluid. The effects of hydrodynamics effects on the mass transfer during droplet formation have been discussed in the three features, including: 1- The intensity of the interaction between two phases 2-The strength and positions of the main vorticities on the nozzle tip 3-The effects of local interfacial vorticities (LIV). These features are considered to explain the complexities of drop formation mass transfer between Ethyl Acetoacetate (presaturated with water) as an organic dispersed phase and water as continuous phase for two big and small nozzle sizes (0.023 and 0.047 cm, ID) which have different level of mass transfer rate particularly in first stages of formation time.

scholarly journals NUMERICAL SIMULATIONS OF LOW REYNOLDS NUMBER FLOWS PAST ELASTICALLY MOUNTED CYLINDER

2012 ◽  
Vol 11 (1-2) ◽  
pp. 61
Author(s):  
R. A. Gonçalves ◽  
P. R. F. Teixeira ◽  
E. Didier
Keyword(s):  
Vortex Shedding ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Body Motion ◽  
Petroleum Exploration ◽  
Navier Stokes ◽  
Generation Process ◽  
Navier Stokes Equations ◽  
Eulerian Formulation ◽  
Low Reynolds

The vortex-induced vibration (VIV) phenomenon has drawn the attention of researchers in Engineering for several decades. An example is the riser used for petroleum exploration, in which it is subjected to marine flows that may cause oscillations due to vortex shedding. In this paper, numerical analyses of the phenomena that occur in the interaction among flows at low Reynolds numbers and elastically mounted cylinders are presented. The simulation is carried out by using the numerical model Ifeinco that uses a semi-implicit two-step Taylor-Galerkin method to discretize the Navier-Stokes equations and the arbitrary Lagrangean-Eulerian formulation to follow the cylinder motion. The rigid body motion description is calculated by using the Newmark method. Firstly, the characteristics of the vortex generation process for the fixed cylinder are analyzed. In this case, the Strouhal number, the mean drag and the RMS lift coefficients for Reynolds numbers ranging from 90 to 140 are shown. Afterwards, an analysis of a flexible supported cylinder (with a spring and a damper) in transverse direction subject to flows with Reynolds numbers ranging from 90 to 140 is carried out. The cylinder displacement and the vibration frequencies are studied; the synchronization between the vortex shedding and the vibration frequency (lock-in) is analyzed. Similar results to the experimental ones developed by Anagnostopoulos and Bearman (1992) were obtained in this study.

scholarly journals Self-attenuation of extreme events in Navier–Stokes turbulence

2020 ◽  
Vol 11 (1) ◽  
Author(s):  
Dhawal Buaria ◽  
Alain Pumir ◽  
Eberhard Bodenschatz
Keyword(s):  
Rotation Rate ◽  
Stokes Equations ◽  
Fluid Flows ◽  
Local Strain ◽  
Turbulence Theory ◽  
Navier Stokes ◽  
Spontaneous Generation ◽  
Navier Stokes Equations ◽  
Attenuation Mechanism ◽  
Non Local

AbstractTurbulent fluid flows are ubiquitous in nature and technology, and are mathematically described by the incompressible Navier-Stokes equations. A hallmark of turbulence is spontaneous generation of intense whirls, resulting from amplification of the fluid rotation-rate (vorticity) by its deformation-rate (strain). This interaction, encoded in the non-linearity of Navier-Stokes equations, is non-local, i.e., depends on the entire state of the flow, constituting a serious hindrance in turbulence theory and even establishing regularity of the equations. Here, we unveil a novel aspect of this interaction, by separating strain into local and non-local contributions utilizing the Biot-Savart integral of vorticity in a sphere of radius R. Analyzing highly-resolved numerical turbulent solutions to Navier-Stokes equations, we find that when vorticity becomes very large, the local strain over small R surprisingly counteracts further amplification. This uncovered self-attenuation mechanism is further shown to be connected to local Beltramization of the flow, and could provide a direction in establishing the regularity of Navier-Stokes equations.

scholarly journals Machine-aided turbulence theory

2018 ◽  
Vol 854 ◽  
Author(s):  
Javier Jiménez
Keyword(s):  
Turbulent Flow ◽  
Turbulent Flows ◽  
Stokes Equations ◽  
A Priori ◽  
Turbulence Theory ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Future Evolution ◽  
Decaying Turbulence

The question of whether significant subvolumes of a turbulent flow can be identified by automatic means, independently of a priori assumptions, is addressed using the example of two-dimensional decaying turbulence. Significance is defined as influence on the future evolution of the flow, and the problem is cast as an unsupervised machine ‘game’ in which the rules are the Navier–Stokes equations. It is shown that significance is an intermittent quantity in this particular flow, and that, in accordance with previous intuition, its most significant features are vortices, while the least significant ones are dominated by strain. Subject to cost considerations, the method should be applicable to more general turbulent flows.

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.

Modeling and computation of the cavitating flow in injection nozzle holes

2015 ◽  
Vol 06 (01) ◽  
pp. 1550003 ◽  
Author(s):  
Hatem Kanfoudi ◽  
Ridha Zgolli
Keyword(s):  
Transport Equation ◽  
Source Term ◽  
Stokes Equations ◽  
Volume Fraction ◽  
Variable Density ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Cavitating Flows ◽  
Navier Stokes Equations ◽  
Injection Nozzle

Cavitating flows inside a diesel injection nozzle hole were simulated using a mixture model. A two-dimensional (2D) numerical model is proposed in this paper to simulate steady cavitating flows. The Reynolds-averaged Navier–Stokes equations are solved for the liquid and vapor mixture, which is considered as a single fluid with variable density and expressed as a function of the vapor volume fraction. The closure of this variable is provided by the transport equation with a source term Transport-equation based methods (TEM). The processes of evaporation and condensation are governed by changes in pressure within the flow. The source term is implanted in the CFD code ANSYS CFX. The influence of numerical and physical parameters is presented in detail. The numerical simulations are in good agreement with the experimental data for steady flow.

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.

The Effect of Film Thickness on EHD-Driven Instability of Interface Separating Two Liquids

2009 ◽  
Author(s):  
Payam Sharifi ◽  
Asghar Esmaeeli
Keyword(s):  
Stokes Equations ◽  
Thin Liquid Film ◽  
Front Tracking ◽  
Thin Layers ◽  
Navier Stokes ◽  
Physical Parameters ◽  
Interface Instability ◽  
Navier Stokes Equations ◽  
Dielectric Model ◽  
Leaky Dielectric Model

Most of the studies conducted so far on EHD-driven instability of superimposed fluids have been concerned with liquid layers of modest depths. In many applications, however, the liquid layers can be very thin. Since the dynamics in thin films is generally governed by lubrication equations rather than full Navier-Stokes equations, it is expected that the interface dynamics will be quite different from that of the liquids with modest depths. The objective of this study is to explore the effect of initial liquid thickness on the dynamics of the phase boundary. To do this end, we perform Direct Numerical Simulations (DNS) using a front tracking/finite difference scheme, in conjunction with Taylor’s leaky dielectric model. For the physical parameters used here, it is shown that for sufficiently thick liquid layers, the interface instability leads to formation of liquid columns that merge together to form a big column. However, for thin layers, the interactions between the columns are weaker and lead to a short and a longer column that are connected by a thin liquid film.

scholarly journals Numerical Simulation of Thermoacoustic Wave Induced by Thermal Effects by Using Discontinuous Galerkin Method

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Pranowo Pranowo ◽  
Adhika Widyaparaga
Keyword(s):  
Galerkin Method ◽  
Discontinuous Galerkin ◽  
Discontinuous Galerkin Method ◽  
Thermal Effects ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Temporal Domain ◽  
Flux Corrected Transport ◽  
Wave Induced

This paper describes a numerical model based on discontinuous Galerkin method for thermoacoustic investigation. Numerical investigation was conducted to study the behaviour of thermoacoustic wave propagations induced by thermal effects in 2-dimensional enclosure. The compressible Navier-Stokes equations are used as the governing equations. The spatial domain was discretized by using unstructured discontinuous Galerkin method and the explicit fourth-order Runge-Kutta was used to integrate the temporal domain. The accuracy of the numerical results was assessed against other numerical methods and linear solutions. The comparisons with linear solutions show excellent agreement and comparisons with flux corrected transport (FCT) method show fair agreement.

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