scholarly journals A second-order multi-fluid model for evaporating sprays

2005 ◽  
Vol 39 (5) ◽  
pp. 931-963 ◽  
Author(s):  
Guillaume Dufour ◽  
Philippe Villedieu
Keyword(s):  
Fluid Model ◽  
Second Order

Modeling Interfacial Interactions and Turbulence in the Near-Wall Region of a Vertical Bubbly Boundary Layer

2020 ◽  
Vol 142 (6) ◽  
Author(s):  
Jamel Chahed ◽  
Lucien Masbernat
Keyword(s):  
Boundary Layer ◽  
Void Fraction ◽  
Fluid Model ◽  
Second Order ◽  
Turbulence Closure ◽  
Wall Region ◽  
Turbulence Structure ◽  
Two Fluid Model ◽  
Two Fluid ◽  
Near Wall

Abstract A two-fluid model with second-order turbulence closure is used for the simulation of a turbulent bubbly boundary layer. The turbulence model is based on the decomposition of the Reynolds stress tensor in the liquid phase into two parts: a turbulent part and a pseudo-turbulent part. The reduction in second-order turbulence closure in the near-wall region is interpreted according to a modified wall logarithmic law. Numerical simulations of bubbly boundary layer developing on a vertical flat plate were performed in order to analyze the bubbles effect on the liquid turbulence structure and to evaluate the respective roles of turbulence and of interfacial forces in the near-wall distribution of the void fraction. The two-fluid model with the second-order turbulence closure succeeds in reproducing the diminution of the turbulent intensity observed in the near-wall region of bubbly boundary layer and the increase in turbulence outside the boundary layer. The analysis of the interfacial force in the near-wall zone has led to the development of relatively simple formulation of the lift-wall force in the logarithmic zone that depends on dimensionless distances to the wall. After appropriate adjustment, this formulation makes it possible to reproduce the shape of the near-wall void fraction peaking observed in bubbly boundary layer experiments.

Transient behavior of drift and ionization in atmospheric pressure nitrogen discharge

2021 ◽  
Author(s):  
S K Dhali
Keyword(s):  
Electric Field ◽  
Electron Energy ◽  
Fluid Model ◽  
High Energy ◽  
Second Order ◽  
Rate Coefficients ◽  
Transient Phase ◽  
Transport Parameters ◽  
Streamer Discharge ◽  
Local Mean

Abstract The fluid models are frequently used to describe a non-thermal plasma such as a streamer discharge. The required electron transport data and rate coefficients for the fluid model are parametrized using the local field approximation (LFA) in first order models and the local-mean-energy approximation (LMEA) in second order models. We performed Monte Carlo simulations in Nitrogen gas with step changes in the E/N (reduced electric field) to study the behavior of the transport properties in the transient phase. During the transient phase of the simulation, we extract the instantaneous electron mean energy, which is different from the steady state mean electron energy, and the corresponding transport parameters and rate coefficients. Our results indicate that the mean electron energy is not a suitable parameter for mobility/drift of electrons due to big difference in momentum relaxation and energy relaxation. However, the high energy threshold rates such as ionization show a strong correlation to mean electron energy. In second order models where the energy-balance equation is solved, we suggest that it would rather be appropriate to use the local electric field to find electron drift velocity in gases such as Nitrogen and the local mean electron energy to determine the ionization and excitation rates.

Large Eddy Simulation of Gas - Second Order Moment of Particle Approach for Riser

2013 ◽  
Vol 274 ◽  
pp. 596-599 ◽  
Author(s):  
Ju Hui Chen ◽  
Ting Hu ◽  
Jiu Ru Li
Keyword(s):  
Large Eddy Simulation ◽  
Fluid Model ◽  
Flow Behavior ◽  
Second Order ◽  
Order Moment ◽  
Eddy Simulation ◽  
Large Eddy ◽  
Two Fluid Model ◽  
Two Fluid ◽  
Particle Approach

Flow behavior of gas and particles is performed by means of gas–solid two-fluid model with the large eddy simulation for gas and the second order moment for particles in the riser. This study shows that the computed solids volume fractions of two cases are compared with the experimental data using a two-dimensional model. The gas and solid velocity is computed.

scholarly journals On nonlinear self-interaction of geodesic acoustic mode driven by energetic particles

2010 ◽  
Vol 77 (4) ◽  
pp. 457-467 ◽  
Author(s):  
G. Y. FU
Keyword(s):  
Electric Field ◽  
Plasma Density ◽  
Second Harmonic ◽  
Fluid Model ◽  
Density Perturbation ◽  
Radial Electric Field ◽  
Energetic Particles ◽  
Acoustic Mode ◽  
Second Order ◽  
Geodesic Acoustic Mode

AbstractIt is shown that nonlinear self-interaction of energetic particle-driven geodesic acoustic mode does not generate a second harmonic in radial electric field using the fluid model. However, kinetic effects of energetic particles can induce a second harmonic in the radial electric field. A formula for the second-order plasma density perturbation is derived. It is shown that a second harmonic of plasma density perturbation is generated by the convective nonlinearity of both thermal plasma and energetic particles. Near the midplane of a tokamak, the second-order plasma density perturbation (the sum of second harmonic and zero frequency sideband) is negative on the low field side with its size comparable to the main harmonic at low fluctuation level. These analytic predictions are consistent with the recent experimental observation in DIII-D.

Constitutive equations in suspension mechanics. Part 2. Approximate forms for a suspension of rigid particles affected by Brownian rotations

1976 ◽  
Vol 76 (1) ◽  
pp. 187-208 ◽  
Author(s):  
E. J. Hinch ◽  
L. G. Leal
Keyword(s):  
Constitutive Equations ◽  
Fluid Model ◽  
Second Order ◽  
Order Tensor ◽  
Rigid Particles ◽  
Dilute Suspension ◽  
Suspension Mechanics ◽  
Made In

Approximate constitutive equations are derived for a dilute suspension of rigid spheroidal particles with Brownian rotations, and the behaviour of the approximations is explored in various flows. Following the suggestion made in the general formulation in part 1, the approximations take the form of Hand's (1962) fluid model, in which the anisotropic microstructure is described by a single second-order tensor. Limiting forms of the exact constitutive equations are derived for weak flows and for a class of strong flows. In both limits the microstructure is shown to be entirely described by a second-order tensor. The proposed approximations are simple interpolations between the limiting forms of the exact equations. Predictions from the exact and approximate constitutive equations are compared for a variety of flows, including some which are not in the class of strong flows analysed.

Use of Thomas Algorithm for Shock Wave Analysis in Bubbly Flow

2012 ◽  
Author(s):  
Mark A. Chaiko
Keyword(s):  
Shock Wave ◽  
Diffusion Equation ◽  
Fluid Model ◽  
Bubbly Flow ◽  
Bubble Radius ◽  
Gas Bubbles ◽  
Uniform Continuity ◽  
Second Order ◽  
Two Phase ◽  
Thomas Algorithm

A numerical approach is developed for simulation of pressure wave propagation in a tube containing a dilute concentration of small gas bubbles. The two-phase fluid is considered homogeneous and spatial distribution of bubbles is assumed to be uniform. Bubble oscillations are modeled using the Keller equation which accounts for liquid compressibility. Heat transfer between liquid and gas is included in the analysis through solution of the radial conduction equation for a spherical gas bubble with moving interface. An energy balance over the bubble surface determines bubble internal pressure, which is assumed to be uniform. Continuity and momentum relations for the homogenous mixture along with the Keller equation are used to derive an alternate set of equations, which are more amenable to application of elementary numerical methods. These alternate equations include a diffusion equation, which is linear in the homogeneous mixture pressure. Two additional equations define the bubble radius and gas-liquid interface speed in terms of the local spatial variation in the homogeneous pressure field. The diffusion equation is solved easily using the second-order accurate Crank-Nicolson method in conjunction with the Thomas algorithm for the discretized tridiagonal algebraic system. The remaining equations comprising the fluid model are solved with an explicit, second-order accurate predictor-corrector scheme. The present approach avoids the need for staggered grids and iterative pressure correction methods used in previous work. Numerical calculations are carried out for a shock wave in a liquid column containing gas bubbles. Results show good agreement with experimental data available in the literature.

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