MATHEMATICAL MODELING OF A TURBULENT FLOW IN A CENTRIFUGAL SEPARATOR

2021 ◽  
pp. 121-138
Author(s):  
Z.M. Malikov ◽  
◽  
M.E. Madaliev ◽  
Keyword(s):  
Mathematical Modeling ◽  
Turbulent Flow ◽  
Gas Flow ◽  
Stokes Equations ◽  
Solid Phase ◽  
Navier Stokes ◽  
Centrifugal Separator ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Carrier Gas Flow

The numerical results of mathematical modeling of a two-phase axisymmetric swirling turbulent flow in a separation zone of a centrifugal separator are presented. The motion of the carrier gas flow is described by the Reynolds-averaged Navier-Stokes equations. A system of equations is enclosed by the Spalart-Allmaras turbulence model. The study is based on the obtained fields of averaged velocities of the carrier medium, with account for turbulent diffusion. Numerical solution to the problem is implemented using the semi-implicit method for pressure linked equations (SIMPLE). The results obtained when the solid phase effect on the air flow dynamics is taken into account are compared with those obtained when the effect is left out of account. The numerical calculations are validated using the experimental data.

scholarly journals Comparison of turbulence models for two-phase flow in a centrifugal separator

2021 ◽  
Vol 264 ◽  
pp. 01009
Author(s):  
Erkin Madaliev ◽  
Murodil Madaliev ◽  
Kamol Adilov ◽  
Tohir Pulatov
Keyword(s):  
Gas Flow ◽  
Separation Zone ◽  
Solid Phase ◽  
Turbulence Models ◽  
Simple Algorithm ◽  
Phase Flow ◽  
Centrifugal Separator ◽  
Two Phase ◽  
Carrier Gas Flow ◽  
Air Medium

The numerical results of mathematical modeling of a two-phase, axisymmetric swirling turbulent flow in the separation zone of a centrifugal separator are presented. The movement of the carrier gas flow was modeled using RANS, which were closed using the SARC turbulence models, the SST-RC model, and the SSG/LRR-RSM-w2012 model. For the numerical solution of the problem, the SIMPLE algorithm was used. The article compares the results of numerical calculation of turbulence models. The results of a comparison of numerical calculations with allowance for the effect of the solid phase on the dynamics of the air medium and without taking it into account with experimental data are presented.

Parallel Numerical Prediction of Pulverized Coal Particle Flow in Bifurcator-Type Flow Splitters

2003 ◽  
Vol 125 (1) ◽  
pp. 1-6 ◽  
Author(s):  
Th. Frank ◽  
H. Schneider ◽  
K. Bernert ◽  
K. Pachler
Keyword(s):  
Numerical Simulation ◽  
Gas Flow ◽  
Stokes Equations ◽  
Decomposition Methods ◽  
Numerical Approach ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Numerical Effort ◽  
Tracking Model

This paper deals with the numerical simulation of two-phase flows based on the solution of the Navier-Stokes equations with a k−ε turbulence model for the gas phase and a particle tracking model of the disperse phase fulfilling the framework of the Eulerian-Lagrangian (PSI-cell) approach. The numerical procedures for the two phases are based on multigrid and domain decomposition methods applied to a block-structured grid. Due to the enormous numerical effort of such flow simulations the entire solving procedure has been parallelized for computers of MIMD architecture. The paper gives a short description of the applied and developed numerical methods. Furthermore the numerical simulation of a particle laden gas flow through a flow splitter from the area of power engineering is presented as an example for a real world application of the numerical approach.

Numerical Modeling of Evolution of Boundary Between Incompressible Gas and Liquid in Two-Dimensional Region

2006 ◽  
Vol 4 ◽  
pp. 224-236
Author(s):  
A.S. Topolnikov
Keyword(s):  
Numerical Modeling ◽  
Interphase Boundary ◽  
Incompressible Liquid ◽  
Stokes Equations ◽  
Numerical Code ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Incompressible Media ◽  
Good Agreement

The paper is devoted to numerical modeling of Navier–Stokes equations for incompressible media in the case, when there exist gas and liquid inside the rectangular calculation region, which are separated by interphase boundary. The set of equations for incompressible liquid accounting for viscous, gravitational and surface (capillary) forces is solved by finite-difference scheme on the spaced grid, for description of interphase boundary the ideology of Level Set Method is used. By developed numerical code the set of hydrodynamic problems is solved, which describe the motion of two-phase incompressible media with interphase boundary. As a result of numerical simulation the solutions are obtained, which are in good agreement with existing analytical and experimental solutions.

TRIGGERING OF DETONATION PROCESSES IN PROPULSION CHAMBER

2021 ◽  
Vol 14 (2) ◽  
pp. 40-45
Author(s):  
D. V. VORONIN ◽  
Keyword(s):  
Thermal Conductivity ◽  
Numerical Modeling ◽  
Gas Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Chemically Reacting ◽  
Plane Disk ◽  
And Diffusion

The Navier-Stokes equations have been used for numerical modeling of chemically reacting gas flow in the propulsion chamber. The chamber represents an axially symmetrical plane disk. Fuel and oxidant were fed into the chamber separately at some angle to the inflow surface and not parallel one to another to ensure better mixing of species. The model is based on conservation laws of mass, momentum, and energy for nonsteady two-dimensional compressible gas flow in the case of axial symmetry. The processes of viscosity, thermal conductivity, turbulence, and diffusion of species have been taken into account. The possibility of detonation mode of combustion of the mixture in the chamber was numerically demonstrated. The detonation triggering depends on the values of angles between fuel and oxidizer jets. This type of the propulsion chamber is effective because of the absence of stagnation zones and good mixing of species before burning.

NUMERICAL SIMULATION OF ISOTHERMAL AND THERMAL TWO-PHASE FLOWS USING PHASE-FIELD MODELING

2007 ◽  
Vol 18 (04) ◽  
pp. 536-545 ◽  
Author(s):  
NAOKI TAKADA ◽  
AKIO TOMIYAMA
Keyword(s):  
Phase Field ◽  
Stokes Equations ◽  
Density Ratio ◽  
Navier Stokes ◽  
Phase Field Modeling ◽  
Two Phase Flows ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Field Modeling ◽  
High Density Ratio

For interface-tracking simulation of two-phase flows in various micro-fluidics devices, we examined the applicability of two versions of computational fluid dynamics method, NS-PFM, combining Navier-Stokes equations with phase-field modeling for interface based on the van der Waals-Cahn-Hilliard free-energy theory. Through the numerical simulations, the following major findings were obtained: (1) The first version of NS-PFM gives good predictions of interfacial shapes and motions in an incompressible, isothermal two-phase fluid with high density ratio on solid surface with heterogeneous wettability. (2) The second version successfully captures liquid-vapor motions with heat and mass transfer across interfaces in phase change of a non-ideal fluid around the critical point.

Computational analysis of turbulent flow through an eccentric annulus under different temperature conditions

2018 ◽  
Vol 28 (9) ◽  
pp. 2189-2207 ◽  
Author(s):  
Erman Ulker ◽  
Sıla Ovgu Korkut ◽  
Mehmet Sorgun
Keyword(s):  
Turbulent Flow ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Content Type ◽  
Non Linear ◽  
Fully Developed Turbulent Flow ◽  
Effects Of Temperature ◽  
Eccentric Annuli ◽  
Pipe Rotation

Purpose The purpose of this paper is to solve Navier–Stokes equations including the effects of temperature and inner pipe rotation for fully developed turbulent flow in eccentric annuli by using finite difference scheme with fixing non-linear terms. Design/methodology/approach A mathematical model is proposed for fully developed turbulent flow including the effects of temperature and inner pipe rotation in eccentric annuli. Obtained equation is solved numerically via central difference approximation. In this process, the non-linear term is frozen. In so doing, the non-linear equation can be considered as a linear one. Findings The convergence analysis is studied before using the method to the proposed momentum equation. It reflects that the method approaches to the exact solution of the equation. The numerical solution of the mathematical model shows that pressure gradient can be predicted with a good accuracy when it is compared with experimental data collected from experiments conducted at Izmir Katip Celebi University Flow Loop. Originality/value The originality of this work is that Navier–Stokes equations including temperature and inner pipe rotation effects for fully developed turbulent flow in eccentric annuli are solved numerically by a finite difference method with frozen non-linear terms.

scholarly journals A ternary Cahn–Hilliard–Navier–Stokes model for two-phase flow with precipitation and dissolution

2020 ◽  
pp. 1-35
Author(s):  
Christian Rohde ◽  
Lars von Wolff
Keyword(s):  
Phase Field ◽  
Stokes Equations ◽  
Solid Phase ◽  
Immiscible Fluids ◽  
Sharp Interface ◽  
Ion Concentration ◽  
Navier Stokes ◽  
Interface Model ◽  
Sharp Interface Model ◽  
Two Phase

We consider the incompressible flow of two immiscible fluids in the presence of a solid phase that undergoes changes in time due to precipitation and dissolution effects. Based on a seminal sharp interface model a phase-field approach is suggested that couples the Navier–Stokes equations and the solid’s ion concentration transport equation with the Cahn–Hilliard evolution for the phase fields. The model is shown to preserve the fundamental conservation constraints and to obey the second law of thermodynamics for a novel free energy formulation. An extended analysis for vanishing interfacial width reveals that in this limit the sharp interface model is recovered, including all relevant transmission conditions. Notably, the new phase-field model is able to realize Navier-slip conditions for solid–fluid interfaces in the limit.

scholarly journals Do the Volume-of-Fluid and the Two-Phase Euler Compete for Modeling a Spillway Aerator?

Water ◽  
2021 ◽  
Vol 13 (21) ◽  
pp. 3092
Author(s):  
Lourenço Sassetti Mendes ◽  
Javier L. Lara ◽  
Maria Teresa Viseu
Keyword(s):  
Stokes Equations ◽  
Cost Benefit ◽  
Volume Of Fluid ◽  
Navier Stokes ◽  
Type Model ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Entrained Air ◽  
Computational Resources ◽  
Mesh Convergence

Spillway design is key to the effective and safe operation of dams. Typically, the flow is characterized by high velocity, high levels of turbulence, and aeration. In the last two decades, advances in computational fluid dynamics (CFD) made available several numerical tools to aid hydraulic structures engineers. The most frequent approach is to solve the Reynolds-averaged Navier–Stokes equations using an Euler type model combined with the volume-of-fluid (VoF) method. Regardless of a few applications, the complete two-phase Euler is still considered to demand exorbitant computational resources. An assessment is performed in a spillway offset aerator, comparing the two-phase volume-of-fluid (TPVoF) with the complete two-phase Euler (CTPE). Both models are included in the OpenFOAM® toolbox. As expected, the TPVoF results depend highly on the mesh, not showing convergence in the maximum chute bottom pressure and the lower-nappe aeration, tending to null aeration as resolution increases. The CTPE combined with the k–ω SST Sato turbulence model exhibits the most accurate results and mesh convergence in the lower-nappe aeration. Surprisingly, intermediate mesh resolutions are sufficient to surpass the TPVoF performance with reasonable calculation efforts. Moreover, compressibility, flow bulking, and several entrained air effects in the flow are comprehended. Despite not reproducing all aspects of the flow with acceptable accuracy, the complete two-phase Euler demonstrated an efficient cost-benefit performance and high value in spillway aerated flows. Nonetheless, further developments are expected to enhance the efficiency and stability of this model.

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