scholarly journals Dynamics of dusty vortices – I. Extensions and limitations of the terminal velocity approximation

2019 ◽  
Vol 488 (4) ◽  
pp. 5290-5299 ◽  
Author(s):  
Francesco Lovascio ◽  
Sijme-Jan Paardekooper
Keyword(s):  
Fluid Model ◽  
Velocity Model ◽  
Terminal Velocity ◽  
Viscous Stress Tensor ◽  
Spatial Convergence ◽  
Two Fluid Model ◽  
Numerical Solver ◽  
The Stability ◽  
Velocity Approximation ◽  
Protoplanetary Discs

ABSTRACT Motivated by the stability of dust laden vortices, in this paper we study the terminal velocity approximation equations for a gas coupled to a pressureless dust fluid and present a numerical solver for the equations embedded in the FARGO3D hydrodynamics code. We show that for protoplanetary discs it is possible to use the barycentre velocity in the viscous stress tensor, making it trivial to simulate viscous dusty protoplanetary discs with this model. We also show that the terminal velocity model breaks down around shocks, becoming incompatible with the two-fluid model it is derived from. Finally we produce a set of test cases for numerical schemes and demonstrate the performance of our code on these tests. Our implementation embedded in FARGO3D using an unconditionally stable explicit integrator is fast, and exhibits the desired second-order spatial convergence for smooth problems.

The stability of the Couette flow of helium II

1988 ◽  
Vol 197 ◽  
pp. 551-569 ◽  
Author(s):  
C. F. Barenghi ◽  
C. A. Jones
Keyword(s):  
Couette Flow ◽  
Fluid Model ◽  
Taylor Instability ◽  
Mutual Friction ◽  
Helium Ii ◽  
Two Fluid Model ◽  
The Stability ◽  
Superfluid Vortices ◽  
Two Fluid

The stability of Couette flow in HeII is considered by an analysis of the HVBK equations. These equations are based on the Landau two-fluid model of HeII and include mutual friction between the normal and superfluid components, and the vortex tension due to the presence of superfluid vortices. We find that the vortex tension strongly affects the nature of the Taylor instability at temperatures below ≈ 2.05 K. The effect of the vortex tension is to make non-axisymmetric modes the most unstable, and to make the critical axial wavelength very long.We compare our results with experiments.

scholarly journals Coronal fluid-dynamics in laser fusion

1989 ◽  
Vol 7 (2) ◽  
pp. 219-228 ◽  
Author(s):  
Juan R. Sanmartín
Keyword(s):  
Fluid Dynamics ◽  
Fluid Model ◽  
Laser Fusion ◽  
Additional Parameter ◽  
Direct Drive ◽  
Magnetic Field Generation ◽  
One Dimensional ◽  
Two Fluid Model ◽  
Inverse Bremsstrahlung Absorption ◽  
The Stability

The fluid-dynamics of the corona ejected by laser-fusion targets in the direct-drive approach (thermal radiation and atomic physics unimportant) is discussed. A two-fluid model involves inverse bremsstrahlung absorption, refraction, different ion and electron temperatures with energy exchange, different ion and electron velocities and magnetic field generation, and their effect on ion-electron friction and heat flux. Four dimensionless parameters determine coronal regimes for one-dimensional flows under uniform irradiation. One additional parameter is involved in two-dimensional problems, including the stability of one-dimensional flows, and the smoothing of non-uniform driving.

scholarly journals Flow stability and correctness of the Cauchy problem for a two-speed medium model with different phase pressures

2021 ◽  
Vol 52 ◽  
pp. 66-77
Author(s):  
Alexander Evgenievich Kroshilin ◽  
Mikhail Evgenievich Kroshilin
Keyword(s):  
Cauchy Problem ◽  
Fluid Model ◽  
Stationary Solutions ◽  
System Of Equations ◽  
Two Phase ◽  
System A ◽  
The Cauchy Problem ◽  
The Difference ◽  
Two Fluid Model ◽  
The Stability

At present, to describe the two-velocity flow of a dispersed mixture, as a rule, a two-fluid model is used with equal pressure of the phases of the medium and different velocities of the phases. The corresponding system of equations without special, postulated, stabilizing terms is non-hyperbolic. This can lead to difficulties in finding a solution. Recently, it has been proposed to use similar models more widely, but with different pressures of the phases of the medium. Such models allow one to take into account new physical effects associated with different phase pressures and often provide hyperbolicity of the corresponding system of equations. This article analyzes the influence of the difference in the pressure of the phases of the medium on the properties of the system: the importance of the corresponding new effects, the hyperbolicity of the system of equations, the stability of its stationary solutions, and the correctness of the corresponding Cauchy problem are investigated. Three systems are considered. The first, simplest model system is based on the well-known non-hyperbolic system, which has been modernized. It is shown that the Cauchy problem for the modified system is formally correct, but the practical possibility of using the calculation results obtained from the solution of this system should be investigated in each specific case, and depends on the calculated step and duration of the process under study. The techniques worked out to solve the first simplest system were used for other systems. As the second system, a model of the flow of a two-phase medium with different phase pressures and two momentum equations is considered. We will assume the phases are barotropic. Let us postulate an equation relating the pressure in the phases. It is proved that this system is always hyperbolic. The stability of its stationary solutions is investigated. Relationships are derived that make it possible to determine under what conditions, due to instability, the obtained solutions are unreliable. The properties of this system are compared with the system of two-speed flow of a dispersed mixture with equal pressure of the phases of the medium. As a third system, a two-pressure model describing bubble pulsations is considered. We will assume the phases are barotropic. Conditions are determined when the system is non-hyperbolic and the Cauchy problem is incorrect. It is investigated for what conditions the ill-posedness of the Cauchy problem leads to the unreliability of the solution, and under what conditions the ill-posedness of the Cauchy problem does not lead to the unreliability of the solution.

Stability Analysis of Chaotic Wavy Stratified Fluid-Fluid Flow With the 1D Fixed-Flux Two-Fluid Model

2016 ◽  
Author(s):  
Avinash Vaidheeswaran ◽  
William D. Fullmer ◽  
Krishna Chetty ◽  
Raul G. Marino ◽  
Martin Lopez de Bertodano
Keyword(s):  
Stability Analysis ◽  
Linear Stability ◽  
Two Phase Flow ◽  
Chaotic Behavior ◽  
Fluid Model ◽  
Phase Flow ◽  
Two Phase ◽  
Two Fluid Model ◽  
The Stability ◽  
Two Fluid

The one-dimensional fixed-flux two-fluid model (TFM) is used to analyze the stability of the wavy interface in a slightly inclined pipe geometry. The model is reduced from the complete 1-D TFM, assuming a constant total volumetric flux, which resembles the equations of shallow water theory (SWT). From the point of view of two-phase flow physics, the Kelvin-Helmholtz instability, resulting from the relative motion between the phases, is still preserved after the simplification. Hence, the numerical fixed-flux TFM proves to be an effective tool to analyze local features of two-phase flow, in particular the chaotic behavior of the interface. Experiments on smooth- and wavy-stratified flows with water and gasoline were performed to understand the interface dynamics. The mathematical behavior concerning the well-posedness and stability of the fixed-flux TFM is first addressed using linear stability theory. The findings from the linear stability analysis are also important in developing the eigenvalue based donoring flux-limiter scheme used in the numerical simulations. The stability analysis is extended past the linear theory using nonlinear simulations to estimate the Largest Lyapunov Exponent which confirms the non-linear boundedness of the fixed-flux TFM. Furthermore, the numerical model is shown to be convergent using the power spectra in Fourier space. The nonlinear results are validated with the experimental data. The chaotic behavior of the interface from the numerical predictions is similar to the results from the experiments.

On the stability of a one-dimensional two-fluid model

2001 ◽  
Vol 204 (1-3) ◽  
pp. 101-115 ◽  
Author(s):  
Jin Ho Song ◽  
Mamoru Ishii
Keyword(s):  
Fluid Model ◽  
One Dimensional ◽  
Two Fluid Model ◽  
The Stability ◽  
Two Fluid

scholarly journals The Effect of Slightly Upward and Downward Inclined Pipes on the Stability of Gas-Oil Two-Phase Flow

2014 ◽  
Vol 14 (1) ◽  
pp. 13
Author(s):  
Peyman Sabzi ◽  
Saheb Noroozi
Keyword(s):  
Two Phase Flow ◽  
Flow Instability ◽  
Fluid Model ◽  
Phase Flow ◽  
Momentum Exchange ◽  
Two Phase ◽  
Two Fluid Model ◽  
The Stability ◽  
Inclined Pipes ◽  
Two Fluid

Pipeline inclination has an important effect on the stability of two-phase flow and flow assurance in the pipeline. This inclination may be intentional; it may be inevitable in pipeline installation; or it may be due to an error in pipeline installation. In this situation, even the slight inclination of the pipe plays an important role in the growth or elimination of the instability of the two-phase flow. In this study using a code designed for the analysis of pipelines’ two-phase flow, the stability of the two-phase flow for Kerosene oil flow along with methane gas has been compared in downward inclined pipes, upward inclined pipes, and horizontal pipes. Using the mentioned computer code, it has been proved that the pipe’s upward inclination results in the increase of two-phase flow instability, while the pipe’s downward inclination is helpful in two-phase flow stability. In order to model two-phase flow in the pipe, two-fluid model has been used. This model considers each phase separately and the equations of mass conservation and momentum are written for each phase. The momentum exchange between the two phases and between each phase and the pipe wall has been considered. Conservation equations have been solved using SIMPLE algorithm in a numerical form with finite volume method.Keywords: Pipes, Two-Phase Flow, Inclined Stability, Two-Fluid Model

scholarly journals Natural modes of the two-fluid model of two-phase flow

2021 ◽  
Vol 33 (3) ◽  
pp. 033324
Author(s):  
Alejandro Clausse ◽  
Martín López de Bertodano
Keyword(s):  
Two Phase Flow ◽  
Fluid Model ◽  
Phase Flow ◽  
Two Phase ◽  
Natural Modes ◽  
Two Fluid Model ◽  
Two Fluid
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