scholarly journals On the Evolution of Compressible and Incompressible Viscous Fluids with a Sharp Interface

Mathematics ◽  
2021 ◽  
Vol 9 (6) ◽  
pp. 621
Author(s):  
Takayuki Kubo ◽  
Yoshihiro Shibata
Keyword(s):  
Analytic Semigroup ◽  
Viscous Fluids ◽  
Two Phase ◽  
Contraction Mapping Theorem ◽  
Unique Existence ◽  
Time Dependent Domain ◽  
Linearized Problem ◽  
Incompressible Viscous Fluids ◽  
Initial Domain ◽  
Dependent Domain

In this paper, we consider some two phase problems of compressible and incompressible viscous fluids’ flow without surface tension under the assumption that the initial domain is a uniform Wq2−1/q domain in RN (N≥2). We prove the local in the time unique existence theorem for our problem in the Lp in time and Lq in space framework with 2<p<∞ and N<q<∞ under our assumption. In our proof, we first transform an unknown time-dependent domain into the initial domain by using the Lagrangian transformation. Secondly, we solve the problem by the contraction mapping theorem with the maximal Lp-Lq regularity of the generalized Stokes operator for the compressible and incompressible viscous fluids’ flow with the free boundary condition. The key step of our proof is to prove the existence of an R-bounded solution operator to resolve the corresponding linearized problem. The Weis operator-valued Fourier multiplier theorem with R-boundedness implies the generation of a continuous analytic semigroup and the maximal Lp-Lq regularity theorem.

A Two-Phase Flow Solver for Incompressible Viscous Fluids, Using a Pure Streamfunction Formulation and the Volume of Fluid Technique

2014 ◽  
Vol 348 ◽  
pp. 9-19 ◽  
Author(s):  
Raphaël Comminal ◽  
Jon Spangenberg ◽  
Jesper Henri Hattel
Keyword(s):  
Two Phase Flow ◽  
Volume Of Fluid ◽  
Viscous Fluids ◽  
Phase Flow ◽  
Two Phase ◽  
Flow Solver ◽  
Incompressible Viscous Fluids ◽  
Multi Phase Flow ◽  
Low Reynolds ◽  
Multi Phase

Accurate multi-phase flow solvers at low Reynolds number are of particular interest for the simulation of interface instabilities in the co-processing of multilayered material. We present a two-phase flow solver for incompressible viscous fluids which uses the streamfunction as the primary variable of the flow. Contrary to fractional step methods, the streamfunction formulation eliminates the pressure unknowns, and automatically fulfills the incompressibility constraint by construction. As a result, the method circumvents the loss of temporal accuracy at low Reynolds numbers. The interface is tracked by the Volume-of-Fluid technique and the interaction with the streamfunction formulation is investigated by examining the Rayleigh-Taylor instability and broken dam problem. The results of the solver are in good agreement with previously published theoretical and experimental results of the first and latter mentioned problem, respectively.

scholarly journals A new upper bound for the largest growth rate of linear Rayleigh–Taylor instability

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Changsheng Dou ◽  
Jialiang Wang ◽  
Weiwei Wang
Keyword(s):  
Surface Tension ◽  
Growth Rate ◽  
Upper Bound ◽  
Viscous Fluids ◽  
Instability Condition ◽  
Interface Surface ◽  
Incompressible Viscous Fluids ◽  
Rayleigh Taylor Instability ◽  
Surface Tensor ◽  
Rt Instability

AbstractWe investigate the effect of (interface) surface tensor on the linear Rayleigh–Taylor (RT) instability in stratified incompressible viscous fluids. The existence of linear RT instability solutions with largest growth rate Λ is proved under the instability condition (i.e., the surface tension coefficient ϑ is less than a threshold $\vartheta _{\mathrm{c}}$ ϑ c ) by the modified variational method of PDEs. Moreover, we find a new upper bound for Λ. In particular, we directly observe from the upper bound that Λ decreasingly converges to zero as ϑ goes from zero to the threshold $\vartheta _{\mathrm{c}}$ ϑ c .

scholarly journals A stable method for 4D CT-based CFD simulation in the right ventricle of a TGA patient

2020 ◽  
Vol 35 (5) ◽  
pp. 315-324
Author(s):  
Yuri Vassilevski ◽  
Alexander Danilov ◽  
Alexander Lozovskiy ◽  
Maxim Olshanskii ◽  
Victoria Salamatova ◽  
...  
Keyword(s):  
Right Ventricle ◽  
Cfd Simulation ◽  
Fluid Motion ◽  
4D Ct ◽  
Post Surgery ◽  
Surgery Patient ◽  
Time Dependent Domain ◽  
Flow Domain ◽  
The Right ◽  
Dependent Domain

AbstractThe paper discusses a stabilization of a finite element method for the equations of fluid motion in a time-dependent domain. After experimental convergence analysis, the method is applied to simulate a blood flow in the right ventricle of a post-surgery patient with the transposition of the great arteries disorder. The flow domain is reconstructed from a sequence of 4D CT images. The corresponding segmentation and triangulation algorithms are also addressed in brief.

scholarly journals IV. On the dynamical theory of incompressible viscous fluids and the determination of the criterion

1895 ◽  
Vol 186 ◽  
pp. 123-164 ◽  
Keyword(s):  
Singular Solution ◽  
Physical State ◽  
Theoretical Calculations ◽  
Equations Of Motion ◽  
Dynamical Theory ◽  
Viscous Fluids ◽  
Linear Functions ◽  
Incompressible Viscous Fluids ◽  
Theoretical Results

1. The equations of motion of viscous fluid (obtained by grafting on certain terms to the abstract equations of the Eulerian form so as to adapt these equations to the case of fluids subject to stresses depending in some hypothetical manner on the rates of distortion, which equations Navier seems to have first introduced in 1822, and which were much studied by Cauchy and Poisson) were finally shown by St. Venant and Sir Gabriel Stokes, in 1845, to involve no other assumption than that the stresses, other than that of pressure uniform in all directions, are linear functions of the rates of distortion, with a co-efficient depending on the physical state of the fluid. By obtaining a singular solution of these equations as applied to the case of pendulums in steady periodic motion, Sir G. Stokes was able to compare the theoretical results with the numerous experiments that had been recorded, with the result that the theoretical calculations agreed so closely with the experimental determinations as seemingly to prove the truth of the assumption involved. This was also the result of comparing the flow of water through uniform tubes with the flow calculated from a singular solution of the equations so long as the tubes were small and the velocities slow. On the other hand, these results, both theoretical and practical, were directly at variance with common experience as to the resistance encountered by larger bodies moving with higher velocities through water, or by water moving with greater velocities through larger tubes. This discrepancy Sir G. Stokes considered as probably resulting from eddies which rendered the actual motion other than that to which the singular solution referred and not as disproving the assumption.

Surveillance Models of Large-Scale ESP With High Viscosity Fluids and Gas

2012 ◽  
Author(s):  
Lissett Barrios ◽  
Stuart Scott ◽  
Charles Deuel
Keyword(s):  
Large Scale ◽  
Two Phase Flow ◽  
Electrical Current ◽  
High Viscosity ◽  
Viscous Fluids ◽  
Phase Flow ◽  
Centrifugal Pumps ◽  
Operational Parameters ◽  
Two Phase ◽  
Operational Conditions

The paper reports on developmental research on the effects of viscosity and two phases, liquid–gas fluids on ESPs which are multi stage centrifugal pumps for deep bore holes. Multiphase viscous performance in a full-scale Electrical Submersible Pump (ESP) system at Shell’s Gasmer facility has been studied experimentally and theoretically. The main objectives is to predict the operational conditions that cause degradations for high viscosity fluids when operating in high Gas Liquid Radio (GLR) wells to support operation in Shell major Projects. The system studied was a 1025 series tandem WJE 1000. The test was performed using this configuration with ten or more pump stages moving fluids with viscosity from 2 to 200 cP at various speed, intake pressure and Gas Void Fractions (GVF). For safety considerations the injected gas was restricted to nitrogen or air. The ESP system is a central artificial lift method commonly used for medium to high flow rate wells. Multiphase flow and viscous fluids causes problems in pump applications. Viscous fluids and free gas inside an ESP can cause head degradation and gas locking. Substantial attempts have been made to model centrifugal pump performance under gas-liquid viscous applications, however due to the complexity this is still a uncertain problem. The determination of the two-phase flow performance in these harmful conditions in the ESP is fundamental aspects in the surveillance operation. The testing at Shell’s Gasmer facility revealed that the ESP system performed as theoretical over the range of single flowrates and light viscosity oils up to Gas Volume Fractions (GVF) around 25%. The developed correlations predict GVF at the pump intake based on the operational parameters. ESP performance degrades at viscosity higher than 100cp as compared to light oil applications, gas lock condition is observed at gas fraction higher than 45%. Pump flowrate can be obtained from electrical current and boost for all range of GVF and speed. The main technical contributions are the analysis of pump head degradation under two important variables, high viscosity and two-phase flow inside the ESP.

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