scholarly journals Revised partial coupling in fluid–particulate systems

2018 ◽  
Vol 10 (4) ◽  
pp. 215-227
Author(s):  
Husam A Elghannay ◽  
Danesh K Tafti
Keyword(s):  
Void Fraction ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Particle Interaction ◽  
Point Mass ◽  
Mass Force ◽  
Source Terms ◽  
Convergence Behavior ◽  
Full Coupling ◽  
Partial Coupling

Fluid equations in Computational Fluid Dynamics coupled with Discrete Element Method (CFD-DEM) simulations solve the volume-averaged Navier–Stokes equations. Full coupling between the dispersed phase and continuous phase is made by the exchange of source terms as well as the void fraction. The void fraction is calculated from the presence of the particles in the computational fluid cells while the source terms are calculated from the point mass force models of the fluid–particle interaction forces. Dense particulate system with large spatiotemporal variations in the void fraction shows hard convergence behavior. This can impact the robustness of the solver during the time integration process. One option is to use partial coupling by neglecting the explicit effect of void fraction in the fluid momentum equations while retaining its effect on force models. Although the partial coupling is more stable and shows better convergence behavior, the mobility of the particles is found to be reduced as compared to the full-coupling approach. In the current work, we propose a revised partial coupling in which a modified fluid velocity is used in point mass force models to compensate for the omission of the void fraction in the fluid governing equations. The effectiveness of this method is demonstrated in a fluidized bed and in sediment transport simulations. In both cases it is shown that the use of the proposed method gives very good comparisons with the fully coupled simulations while reducing the fluid calculation time by factors ranging from 1.35 to 4.35 depending on the flow conditions. The revised partial coupling is not recommended as a substitute for full coupling in dense systems but as an alternate approach when full coupling leads to numerical difficulties.

Parameter Studies on the Effect of Boundary Conditions in Three-Dimensional Calculations of Bubble Column

2002 ◽  
Author(s):  
E. Bourloutski ◽  
M. Sommerfeld
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Bubble Column ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Fluid Phase ◽  
Time Dependent ◽  
Navier Stokes ◽  
Mass Force ◽  
Source Terms

This paper describes an extension and validation of the Euler/Lagrange approach for three-dimensional time-dependent calculations of the flow in a bubble column. The fluid phase was calculated based on the Euler approach solving the unsteady Reynolds-averaged Navier-Stokes equations in a time-dependent way. The conservation equations were closed using the standard k-ε turbulence model. The coupling between the phases is considered through the momentum source terms and source terms in the k- and ε-equations. The usage of the Consistent term for the k-equation and taking into account an additional dissipation due to the presence of small bubbles yielded a reasonable agreement of the predicted turbulent kinetic energy level with measurements. Bubble motion was calculated by solving the equations of motion taking into account drag force, pressure, added mass force, transverse lift force, buoyancy and gravity. Numerical calculations are presented providing information on the sensitivity of the results on several boundary conditions, such as disturbed aeration. The computational results are validated based on available measurements in a laboratory-scale bubble column.

Modeling of the Vortex-Structure in a Particle-Laden Mixing-Layer

2005 ◽  
Author(s):  
Jens A. Melheim ◽  
Stefan Horender ◽  
Martin Sommerfeld
Keyword(s):  
Vortex Structure ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Mixing Layer ◽  
Equation Model ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Calculated Concentration ◽  
Langevin Model ◽  
Particle Velocities

Numerical calculations of a particle-laden turbulent horizontal mixing-layer based on the Eulerian-Lagrangian approach are presented. Emphasis is given to the determination of the stochastic fluctuating fluid velocity seen by the particles in anisotropic turbulence. The stochastic process for the fluctuating velocity is a “Particle Langevin equation Model”, based on the Simplified Langevin Model. The Reynolds averaged Navier-Stokes equations are closed by the standard k-epsilon turbulence model. The calculated concentration profile and the mean, the root-mean-square (rms) and the cross-correlation terms of the particle velocities are compared with particle image velocimetry (PIV) measurements. The numerical results agree reasonably well with the PIV data for all of the mentioned quantities. The importance of the modeled vortex structure “seen” by the particles is discussed.

scholarly journals Modeling Free Surface Flows Using Stabilized Finite Element Method

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Deepak Garg ◽  
Antonella Longo ◽  
Paolo Papale
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Free Surface ◽  
Numerical Scheme ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Computer Code ◽  
Free Surface Flows ◽  
Surface Flows ◽  
Element Method

This work aims to develop a numerical wave tank for viscous and inviscid flows. The Navier-Stokes equations are solved by time-discontinuous stabilized space-time finite element method. The numerical scheme tracks the free surface location using fluid velocity. A segregated algorithm is proposed to iteratively couple the fluid flow and mesh deformation problems. The numerical scheme and the developed computer code are validated over three free surface problems: solitary wave propagation, the collision between two counter moving waves, and wave damping in a viscous fluid. The benchmark tests demonstrate that the numerical approach is effective and an attractive tool for simulating viscous and inviscid free surface flows.

scholarly journals Calculation Analysis of Pressure Wave Velocity in Gas and Drilling Mud Two-Phase Fluid in Annulus during Drilling Operations

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
Yuanhua Lin ◽  
Xiangwei Kong ◽  
Yijie Qiu ◽  
Qiji Yuan
Keyword(s):  
Wave Velocity ◽  
Void Fraction ◽  
Pressure Wave ◽  
Angular Frequency ◽  
Mass Force ◽  
Virtual Mass ◽  
Drilling Mud ◽  
Influx Rate ◽  
Drilling Operations ◽  
Well Depth

Investigation of propagation characteristics of a pressure wave is of great significance to the solution of the transient pressure problem caused by unsteady operations during management pressure drilling operations. With consideration of the important factors such as virtual mass force, drag force, angular frequency, gas influx rate, pressure, temperature, and well depth, a united wave velocity model has been proposed based on pressure gradient equations in drilling operations, gas-liquid two-fluid model, the gas-drilling mud equations of state, and small perturbation theory. Solved by adopting the Runge-Kutta method, calculation results indicate that the wave velocity and void fraction have different values with respect to well depth. In the annulus, the drop of pressure causes an increase in void fraction along the flow direction. The void fraction increases first slightly and then sharply; correspondingly the wave velocity first gradually decreases and then slightly increases. In general, the wave velocity tends to increase with the increase in back pressure and the decrease of gas influx rate and angular frequency, significantly in low range. Taking the virtual mass force into account, the dispersion characteristic of the pressure wave weakens obviously, especially at the position close to the wellhead.

scholarly journals Mathematical Model for the Electrokinetic Instability of Electrolyte Flow

2019 ◽  
Vol 224 ◽  
pp. 02003
Author(s):  
Andrey Shobukhov
Keyword(s):  
Electric Potential ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Fluid Velocity ◽  
Steady State Solution ◽  
Stability Loss ◽  
Navier Stokes ◽  
Ion Distribution ◽  
Navier Stokes Equations ◽  
Dilute Aqueous Solution

We study a one-dimensional model of the dilute aqueous solution of KCl in the electric field. Our model is based on a set of Nernst-Planck-Poisson equations and includes the incompressible fluid velocity as a parameter. We demonstrate instability of the linear electric potential variation for the uniform ion distribution and compare analytical results with numerical solutions. The developed model successfully describes the stability loss of the steady state solution and demonstrates the emerging of spatially non-uniform distribution of the electric potential. However, this model should be generalized by accounting for the convective movement via the addition of the Navier-Stokes equations in order to substantially extend its application field.

scholarly journals Higher-order dissipation in the theory of homogeneous isotropic turbulence

2016 ◽  
Vol 803 ◽  
pp. 250-274 ◽  
Author(s):  
Norbert Peters ◽  
Jonas Boschung ◽  
Michael Gauding ◽  
Jens Henrik Goebbert ◽  
Reginald J. Hill ◽  
...  
Keyword(s):  
Source Term ◽  
Isotropic Turbulence ◽  
Stokes Equations ◽  
Higher Order ◽  
Distribution Functions ◽  
Order Structure ◽  
Source Terms ◽  
Homogeneous Isotropic Turbulence ◽  
Higher Order Moments ◽  
Even Order

The two-point theory of homogeneous isotropic turbulence is extended to source terms appearing in the equations for higher-order structure functions. For this, transport equations for these source terms are derived. We focus on the trace of the resulting equations, which is of particular interest because it is invariant and therefore independent of the coordinate system. In the trace of the even-order source term equation, we discover the higher-order moments of the dissipation distribution, and the individual even-order source term equations contain the higher-order moments of the longitudinal, transverse and mixed dissipation distribution functions. This shows for the first time that dissipation fluctuations, on which most of the phenomenological intermittency models are based, are contained in the Navier–Stokes equations. Noticeably, we also find the volume-averaged dissipation $\unicode[STIX]{x1D700}_{r}$ used by Kolmogorov (J. Fluid Mech., vol. 13, 1962, pp. 82–85) in the resulting system of equations, because it is related to dissipation correlations.

scholarly journals Body-force modeling for aerodynamic analysis of air intake – fan interactions

2016 ◽  
Vol 26 (7) ◽  
pp. 2048-2065 ◽  
Author(s):  
William Thollet ◽  
Guillaume Dufour ◽  
Xavier Carbonneau ◽  
Florian Blanc
Keyword(s):  
Body Force ◽  
Stokes Equations ◽  
The Body ◽  
Test Case ◽  
Force Model ◽  
Strong Impact ◽  
Analytic Model ◽  
Source Terms ◽  
Content Type ◽  
Air Intake

Purpose The purpose of this paper is to explore a methodology that allows to represent turbomachinery rotating parts by replacing the blades with a body force field. The objective is to capture interactions between a fan and an air intake at reduced cost, as compared to full annulus unsteady computations. Design/methodology/approach The blade effects on the flow are taken into account by adding source terms to the Navier-Stokes equations. These source terms give the proper amount of flow turning, entropy, and blockage to the flow. Two different approaches are compared: the source terms can be computed using an analytic model, or they can directly be extracted from RANS computations with the blade’s geometry. Findings The methodology is first applied to an isolated rotor test case, which allows to show that blockage effects have a strong impact on the performance of the rotor. It is also found that the analytic body force model underestimates the mass flow in the blade row for choked conditions. Finally, the body force approach is used to capture the coupling between a fan and an air intake at high angle of attacks. A comparison with full annulus unsteady computations shows that the model adequately captures the potential effects of the fan on the air intake. Originality/value To the authors’ knowledge, it is the first time that the analytic model used in this paper is combined with the blockage source terms. Furthermore, the capability of the model to deal with flows in choked conditions was never assessed.

Instability and Transition of a Plane Bubble Plume

2002 ◽  
Author(s):  
Ophe´lie Caballina ◽  
Eric Climent ◽  
Jan Dusˇek
Keyword(s):  
Stokes Equations ◽  
Fluid Layer ◽  
Fluid Velocity ◽  
Continuous Phase ◽  
Collective Effects ◽  
Recent Experimental Data ◽  
Fluid Viscosity ◽  
Bubble Plume ◽  
Carrier Fluid ◽  
Bubble Cloud

When bubbles are continuously released from a located source at the bottom of a fluid layer initially at rest, a plume is produced. The motion of the carrier fluid is initiated and driven by buoyancy of the bubble cloud. In the present study, a detailed analysis of the bubble plume transition is investigated. The continuous phase flow is obtained by direct numerical resolution of Navier-Stokes equations forced by the presence of bubbles. Collective effects induced by the presence of bubbles are modelled by a spatio-temporal distribution of momentum. Time evolution of the dispersed phase is solved by lagrangian tracking of all the bubbles. Focused on the description of plume transition, several configurations (plume widths, fluid viscosity, injection rate) are investigated. During the laminar ascension of the plume, fluid velocity profiles can be non-dimensionalised on a single auto-similar evolution. Dimensional analysis provides a prediction of the limit rising velocity of the plume top. This prediction has been confirmed by our numerical simulations. Furthermore, our first results point out the symmetry breaking induced by plume instability which appears beyond a critical transition height. Various data show that the Grashof number based on injection conditions is the key parameter to predict the transition of the plume. Our results agree very well with recent experimental data. Comparison with experiments on thermal plumes in air shows that the bubble plume is more unstable. This feature should be related to the lack of diffusion in the lagrangian transport of density gradient by the bubble cloud and to the slip velocity between the two phases.

Fluid Flow and Lateral Fluid Dispersion in Bounded Granular Beds

2002 ◽  
Author(s):  
Azita Soleymani ◽  
Eveliina Takasuo ◽  
Piroz Zamankhan ◽  
William Polashenski
Keyword(s):  
Reynolds Number ◽  
Porous Media ◽  
Numerical Solutions ◽  
Stokes Equations ◽  
Numerical Study ◽  
Fluid Velocity ◽  
Three Dimensional ◽  
Numerical Results ◽  
Transition To Turbulence ◽  
Wide Range

Results are presented from a numerical study examining the flow of a viscous, incompressible fluid through random packing of nonoverlapping spheres at moderate Reynolds numbers (based on pore permeability and interstitial fluid velocity), spanning a wide range of flow conditions for porous media. By using a laminar model including inertial terms and assuming rough walls, numerical solutions of the Navier-Stokes equations in three-dimensional porous packed beds resulted in dimensionless pressure drops in excellent agreement with those reported in a previous study (Fand et al., 1987). This observation suggests that no transition to turbulence could occur in the range of Reynolds number studied. For flows in the Forchheimer regime, numerical results are presented of the lateral dispersivity of solute continuously injected into a three-dimensional bounded granular bed at moderate Peclet numbers. Lateral fluid dispersion coefficients are calculated by comparing the concentration profiles obtained from numerical and analytical methods. Comparing the present numerical results with data available in the literature, no evidence has been found to support the speculations by others for a transition from laminar to turbulent regimes in porous media at a critical Reynolds number.

Lift, drag and added mass of a hemispherical bubble sliding and growing on a wall in a viscous linear shear flow

2008 ◽  
Vol 366 (1873) ◽  
pp. 2233-2248 ◽  
Author(s):  
Dominique Legendre ◽  
Catherine Colin ◽  
Typhaine Coquard
Keyword(s):  
Shear Flow ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Added Mass ◽  
Unsteady Motion ◽  
Navier Stokes ◽  
Mass Force ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Linear Shear

The three-dimensional flow around a hemispherical bubble sliding and growing on a wall in a viscous linear shear flow is studied numerically by solving the full Navier–Stokes equations in a boundary-fitted domain. The main goal of the present study is to provide a complete description of the forces experienced by the bubble (drag, lift and added mass) over a wide range of sliding and shear Reynolds numbers (0.01≤ Re b , Re α ≤2000) and shear rate (0≤ Sr ≤5). The drag and lift forces are computed successively for the following situations: an immobile bubble in a linear shear flow; a bubble sliding on the wall in a fluid at rest; and a bubble sliding in a linear shear flow. The added-mass force is studied by considering an unsteady motion relative to the wall or a time-dependent radius.

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