Chapter 19. Discrete Phase Models - afs.enea.it

1 Chapter 19. Discrete Phase Models This Chapter describes the Lagrangian Discrete Phase capabilities avail- able in FLUENT and how to use them. Information is organized into the following sections: Section : Overview and Limitations of the Discrete Phase Mod- els Section : Trajectory Calculations Section : Heat and Mass Transfer Calculations Section : Spray Models Section : Coupling Between the Discrete and Continuous Phases Section : Overview of Using the Discrete Phase Models Section : Discrete Phase Model Options Section : Unsteady Particle Tracking Section : Setting Initial Conditions for the Discrete Phase Section : Setting Boundary Conditions for the Discrete Phase Section : Setting Material Properties for the Discrete Phase Section : Calculation Procedures for the Discrete Phase Section : Postprocessing for the Discrete Phase c Fluent Inc.

2 December 3, 2001 19-1. Discrete Phase Models Overview and Limitations of the Discrete Phase Models Introduction In addition to solving transport equations for the continuous Phase , FLU- ENT allows you to simulate a Discrete second Phase in a Lagrangian frame of reference. This second Phase consists of spherical particles (which may be taken to represent droplets or bubbles) dispersed in the continuous Phase . FLUENT computes the trajectories of these Discrete Phase en- tities, as well as heat and mass transfer to/from them. The coupling between the phases and its impact on both the Discrete Phase trajecto- ries and the continuous Phase flow can be included. FLUENT provides the following Discrete Phase modeling options: Calculation of the Discrete Phase trajectory using a Lagrangian formulation that includes the Discrete Phase inertia, hydrodynamic drag, and the force of gravity, for both steady and unsteady flows Prediction of the effects of turbulence on the dispersion of particles due to turbulent eddies present in the continuous Phase Heating/cooling of the Discrete Phase Vaporization and boiling of liquid droplets Combusting particles, including volatile evolution and char com- bustion to simulate coal combustion Optional coupling of the continuous Phase flow field prediction to the Discrete Phase calculations Droplet breakup and coalescence These modeling capabilities allow FLUENT to simulate a wide range of Discrete Phase problems including particle separation and classifica- tion, spray drying, aerosol dispersion, bubble stirring of liquids.

3 Liquid fuel combustion, and coal combustion. The physical equations used for these Discrete Phase calculations are described in Sections , and 19-2 c Fluent Inc. December 3, 2001. Overview and Limitations of the Discrete Phase Models instructions for setup, solution, and postprocessing are provided in Sec- tions Particles in Turbulent Flows The dispersion of particles due to turbulence in the fluid Phase can be predicted using the stochastic tracking model or the particle cloud model (see Section ). The stochastic tracking (random walk) model in- cludes the effect of instantaneous turbulent velocity fluctuations on the particle trajectories through the use of stochastic methods (see Sec- tion ). The particle cloud model tracks the statistical evolution of a cloud of particles about a mean trajectory (see Section ). The concentration of particles within the cloud is represented by a Gaus- sian probability density function (PDF) about the mean trajectory.

4 In both Models , the particles have no direct impact on the generation or dissipation of turbulence in the continuous Phase . Limitations Limitation on the Particle Volume Fraction The Discrete Phase formulation used by FLUENT contains the assumption that the second Phase is sufficiently dilute that particle-particle interac- tions and the effects of the particle volume fraction on the gas Phase are negligible. In practice, these issues imply that the Discrete Phase must be present at a fairly low volume fraction, usually less than 10 12%. Note that the mass loading of the Discrete Phase may greatly exceed 10 12%: you may solve problems in which the mass flow of the Discrete Phase equals or exceeds that of the continuous Phase . See Chapters 18 and 20. for information about when you might want to use one of the general multiphase Models instead of the Discrete Phase model.

5 Limitation on Modeling Continuous Suspensions of Particles The steady-particle Lagrangian Discrete Phase model described in this Chapter is suited for flows in which particle streams are injected into a continuous Phase flow with a well-defined entrance and exit condition. c Fluent Inc. December 3, 2001 19-3. Discrete Phase Models The Lagrangian model does not effectively model flows in which par- ticles are suspended indefinitely in the continuum, as occurs in solid suspensions within closed systems such as stirred tanks, mixing vessels, or fluidized beds. The unsteady-particle Discrete Phase model, however, is capable of modeling continuous suspensions of particles. See Chap- ters 18 and 20 for information about when you might want to use one of the general multiphase Models instead of the Discrete Phase Models . Limitations on Using the Discrete Phase Model with Other FLUENT Models The following restrictions exist on the use of other Models with the dis- crete Phase model: Streamwise periodic flow (either specified mass flow rate or spec- ified pressure drop) cannot be modeled when the Discrete Phase model is used.

6 Adaptive time stepping cannot be used with the Discrete Phase model. Only non-reacting particles can be included when the premixed combustion model is used. When multiple reference frames are used in conjunction with the Discrete Phase model, the display of particle tracks will not, by de- fault, be meaningful. Similarly, coupled Discrete - Phase calculations are not meaningful. An alternative approach for particle tracking and coupled Discrete - Phase calculations with multiple reference frames is to track parti- cles based on absolute velocity instead of relative velocity. To make this change, use the define/ Models /dpm/tracking/track-in- absolute-frame text command. Note, however, that tracking par- ticles based on absolute velocity may result in incorrect particle- wall interaction. The particle injection velocities (specified in the Set Injection Prop- erties panel) are defined relative to the frame of reference in which the particles are tracked.

7 By default, the injection velocities are 19-4 c Fluent Inc. December 3, 2001. Overview and Limitations of the Discrete Phase Models specified relative to the local reference frame. If you enable the track-in-absolute-frame option, the injection velocities are spec- ified relative to the absolute frame. Overview of Discrete Phase Modeling Procedures You can include a Discrete Phase in your FLUENT model by defining the initial position, velocity, size, and temperature of individual parti- cles. These initial conditions, along with your inputs defining the phys- ical properties of the Discrete Phase , are used to initiate trajectory and heat/mass transfer calculations. The trajectory and heat/mass transfer calculations are based on the force balance on the particle and on the convective/radiative heat and mass transfer from the particle, using the local continuous Phase conditions as the particle moves through the flow.

8 The predicted trajectories and the associated heat and mass transfer can be viewed graphically and/or alphanumerically. You can use FLUENT to predict the Discrete Phase patterns based on a fixed continuous Phase flow field (an uncoupled approach), or you can include the effect of the Discrete Phase on the continuum (a coupled approach). In the coupled approach, the continuous Phase flow pattern is impacted by the Discrete Phase (and vice versa), and you can alternate calculations of the continuous Phase and Discrete Phase equations until a converged coupled solution is achieved. See Section for details. Outline of Steady-State Problem Setup and Solution Procedure The general procedure for setting up and solving a steady-state Discrete - Phase problem is outlined below: 1. Solve the continuous- Phase flow. 2. Create the Discrete - Phase injections.

9 3. Solve the coupled flow, if desired. 4. Track the Discrete - Phase injections, using plots or reports. c Fluent Inc. December 3, 2001 19-5. Discrete Phase Models Outline of Unsteady Problem Setup and Solution Procedure The general procedure for setting up and solving an unsteady Discrete - Phase problem is outlined below: 1. Create the Discrete - Phase injections. 2. Initialize the flow field. 3. Advance the solution in time by taking the desired number of time steps. Particle positions will be updated as the solution advances in time. If you are solving an uncoupled flow, the particle position will be updated at the end of each time step. For a coupled calculation, the positions are iterated on within each time step. Trajectory Calculations Equations of Motion for Particles Particle Force Balance FLUENT predicts the trajectory of a Discrete Phase particle (or droplet or bubble) by integrating the force balance on the particle, which is written in a Lagrangian reference frame.

10 This force balance equates the particle inertia with the forces acting on the particle, and can be written (for the x direction in Cartesian coordinates) as dup gx ( p ). = FD (u up ) + + Fx ( ). dt p where FD (u up ) is the drag force per unit particle mass and 18 CD Re FD = ( ). p d2p 24. Here, u is the fluid Phase velocity, up is the particle velocity, is the molecular viscosity of the fluid, is the fluid density, p is the density of 19-6 c Fluent Inc. December 3, 2001. Trajectory Calculations the particle, and dp is the particle diameter. Re is the relative Reynolds number, which is defined as dp |up u|. Re ( ).. The drag coefficient, CD , can be taken from either a2 a3. CD = a1 + + ( ). Re Re2. where a1 , a2 , and a3 are constants that apply for smooth spherical par- ticles over several ranges of Re given by Morsi and Alexander [163], or 24 b3 Re CD = 1 + b1 Reb2 + ( ).