scholarly journals Two-phase flow equations for a dilute dispersion of gas bubbles in liquid

1984 ◽  
Vol 148 ◽  
pp. 301-318 ◽  
Author(s):  
A. Biesheuvel ◽  
L. Van Wijngaarden
Keyword(s):  
Acoustic Waves ◽  
Equations Of Motion ◽  
Gas Bubbles ◽  
Local Stress ◽  
Mass Conservation ◽  
Ensemble Averaging ◽  
Two Phase ◽  
Average Force ◽  
Gas Concentration ◽  
Flow Equations

Equations of motion correct to the first order of the gas concentration by volume are derived for a dispersion of gas bubbles in liquid through systematic averaging of the equations on the microlevel. First, by ensemble averaging, an expression for the average stress tensor is obtained, which is non-isotropic although the local stress tensors in the constituent phases are isotropic (viscosity is neglected). Next, by applying the same technique, the momentum-flux tensor of the entire mixture is obtained. An equation expressing the fact that the average force on a massless bubble is zero leads to a third relation. Complemented with mass-conservation equations for liquid and gas, these equations appear to constitute a completely hyperbolic system, unlike the systems with complex characteristics found previously. The characteristic speeds are calculated and shown to be related to the propagation speeds of acoustic waves and concentration waves.

Virtual mass and drag in two-phase flow

1991 ◽  
Vol 225 ◽  
pp. 177-196 ◽  
Author(s):  
B. U. Felderhof
Keyword(s):  
Equilibrium Distribution ◽  
Hard Spheres ◽  
Equations Of Motion ◽  
Fluid Phase ◽  
Spherical Particles ◽  
Inviscid Fluid ◽  
Virtual Mass ◽  
Ensemble Averaging ◽  
Two Phase ◽  
Numerical Predictions

We study virtual mass and drag effects in a fluid suspension consisting of spherical particles immersed in an incompressible, nearly inviscid fluid. We derive average equations of motion for the fluid phase and the particle phase by the method of ensemble averaging. We show that the virtual mass and drag coefficients may be expressed exactly in terms of the dielectric constant of a corresponding dielectric suspension with the same distribution of particles. We make numerical predictions for the case of an equilibrium distribution of hard spheres.

From disturbance to measurement: Application of Coriolis meter for two-phase flow with gas bubbles

2021 ◽  
Vol 79 ◽  
pp. 101892
Author(s):  
Hao Zhu ◽  
Alfred Rieder ◽  
Wolfgang Drahm ◽  
Yaoying Lin ◽  
Andreas Guettler ◽  
...  
Keyword(s):  
Two Phase Flow ◽  
Gas Bubbles ◽  
Phase Flow ◽  
Two Phase

Acoustic Waves in Two-Phase Media

1991 ◽  
pp. 457-460
Author(s):  
Jozef Lewandowski
Keyword(s):  
Acoustic Waves ◽  
Two Phase

A physically motivated approach for filtering acoustic waves from the equations governing compressible stratified flow

2008 ◽  
Vol 601 ◽  
pp. 365-379 ◽  
Author(s):  
DALE R. DURRAN
Keyword(s):  
Acoustic Waves ◽  
Large Scale ◽  
Mass Conservation ◽  
Simple Expression ◽  
Reference State ◽  
Small Scale ◽  
Sound Waves ◽  
State Equations ◽  
Planetary Scale ◽  
Atmospheric Motions

An incompressibility approximation is formulated for isentropic motions in a compressible stratified fluid by defining a pseudo-density ρ* and enforcing mass conservation with respect to ρ* instead of the true density. Using this approach, sound waves will be eliminated from the governing equations provided ρ* is an explicit function of the space and time coordinates and of entropy. By construction, isentropic pressure perturbations have no influence on the pseudo-density.A simple expression for ρ* is available for perfect gases that allows the approximate mass conservation relation to be combined with the unapproximated momentum and thermodynamic equations to yield a closed system with attractive energy conservation properties. The influence of pressure on the pseudo-density, along with the explicit (x,t) dependence of ρ* is determined entirely by the hydrostatically balanced reference state.Scale analysis shows that the pseudo-incompressible approximation is applicable to motions for which ${\cal M})$2 ≪ min(1,${\cal R})$2, where ${\cal M})$ is the Mach number and ${\cal R}$ the Rossby number. This assumption is easy to satisfy for small-scale atmospheric motions in which the Earth's rotation may be neglected and is also satisfied for quasi-geostrophic synoptic-scale motions, but not planetary-scale waves. This scaling assumption can, however, be relaxed to allow the accurate representation of planetary-scale motions if the pressure in the time-evolving reference state is computed with sufficient accuracy that the large-scale components of the pseudo-incompressible pressure represent small corrections to the total pressure, in which case the full solution to both the pseudo-incompressible and reference-state equations has the potential to accurately model all non-acoustic atmospheric motions.

NUMERICAL SOLUTION FOR HYPERBOLIC CONSERVATIVE TWO-PHASE FLOW EQUATIONS

2007 ◽  
Vol 04 (02) ◽  
pp. 299-333 ◽  
Author(s):  
D. ZEIDAN ◽  
A. SLAOUTI ◽  
E. ROMENSKI ◽  
E. F. TORO
Keyword(s):  
Numerical Solution ◽  
Riemann Problem ◽  
Two Phase Flow ◽  
Numerical Dissipation ◽  
Phase Flow ◽  
Two Phase ◽  
Flow Equations ◽  
Flow Problems ◽  
Slope Limiter ◽  
Two Phases

We outline an approximate solution for the numerical simulation of two-phase fluid flows with a relative velocity between the two phases. A unified two-phase flow model is proposed for the description of the gas–liquid processes which leads to a system of hyperbolic differential equations in a conservative form. A numerical algorithm based on a splitting approach for the numerical solution of the model is proposed. The associated Riemann problem is solved numerically using Godunov methods of centered-type. Results show the importance of the Riemann problem and of centered schemes in the solution of the two-phase flow problems. In particular, it is demonstrated that the Slope Limiter Centered (SLIC) scheme gives a low numerical dissipation at the contact discontinuities, which makes it suitable for simulations of practical two-phase flow processes.

scholarly journals The Finite Element Numerical Investigation of Free Surface Newtonian and Non-Newtonian Fluid Flows in the Rectangular Tanks

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
Puyang Gao
Keyword(s):  
Finite Element ◽  
Free Surface ◽  
Level Set ◽  
Newtonian Fluid ◽  
Mass Conservation ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Two Phase ◽  
Navier Stokes Equation ◽  
Correction Technique

In this paper, we develop a new computational framework to investigate the sloshing free surface flow of Newtonian and non-Newtonian fluids in the rectangular tanks. We simulate the flow via a two-phase model and employ the fixed unstructured mesh in the computation to avoid the mesh distortion and reconstruction. As for the solution of Navier–Stokes equation, we utilize the SUPG finite element method based on the splitting scheme. The same order interpolation functions are then used for velocity and pressure. Moreover, the moving interface is captured via the concise level set method. We take advantage of the implicit discontinuous Galerkin method to handle the solution of level set and its reinitialization equations. A mass correction technique is also added to ensure the mass conservation property. The dam break-free surface flow is simulated firstly to demonstrate the validity of our mathematical model. In addition, the sloshing Newtonian fluid in the tank with flat and rough bottoms is considered to illustrate the feasibility and robustness of our computational scheme. Finally, the development of free surface for non-Newtonian fluid is also studied in the two tanks, and the influence of power-law index on the sloshing fluid flow is analyzed.

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