Discrete Phase Model (DPM)
Discrete Phase Model (DPM)
The discrete Phase Model is a subsection of?Multiphase flows. A discrete phase model (DPM) is used when the aim is to investigate the behavior of the particles from a?Lagrangian?view and a discrete perspective. The difference between the Lagrangian and the Eulerian view is that fluid behavior in the Lagrangian view is examined based on particle tracking of a particulate flow, whereas fluid behavior is considered in the Eulerian view based on the assumption of a?finite volume?element in the fluid flow path.
In Discrete Phase Model, the continuous phase is solved using?Navier-Stokes?equations. At the same time, the discrete phase is simulated by tracking a large number of?particles,?bubbles, or?droplets?passing through the calculated continuous flow field. It should be noted that the discrete phase can exchange?momentum,?mass, and?energy?with the?continuous phase. This method can be made much simpler by ignoring the?interaction?of particles (as well as droplets and bubbles) with each other. Of course, this can happen when the discrete phase, even with a large mass, has a much smaller volume (less than 10%) than the continuous phase. After each iteration of the continuous phase calculations, the particle paths are calculated and determined separately.
The dense discrete phase model (DDPM) is a Lagrangian?parcel-based?approach that models particle collisions and uncorrelated translations using the kinetic theory of granular flows (KTGF). This approach has numerous advantages over the established Eulerian two-fluid model (TFM). These include better resolution of particle?clusters?and bubbles, more natural incorporation of particle size distributions and better handling of crossing particle jets/clusters. In this study, results from the DDPM are compared to dedicated experiments and TFM simulations over a wide range of fluidization velocities, particle sizes, and bed loadings. Special attention was given to ensure that the frictional effects typical of such dense particle flows are accounted for. The DDPM proved capable of reproducing the good fit to experiments achieved by the TFM on a significantly coarser mesh.
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The discrete element method (DEM) is an intuitive method in which discrete particles collide and other surfaces during an explicit dynamic simulation. Typically, each DEM particle represents a?separate grain,?tablet,?shot peen, etc. DEM does not apply to situations in which individual particles undergo complex?deformation. Therefore, DEM is, unlike conceptually, more straightforward than the smoothed particle hydrodynamic (SPH) method in which groups of particles collectively model a continuum body. For example, DEM is well-suited for particle mixing applications. In this application, DEM is used to model the initially separated blue and white particles, and rigid finite elements are used to model two mixing augers and the box-shaped container. Another example of using DEM for a mixing application is described in the Mixing of?granular?media in a drum mixer.
The Discrete Phase used to model different types of phenomena, including:
Physical Models
1. Particle Radiation Interaction
The radiation effects must be considered in cases where a high temperature dominates the fluid domain, like in combustion chambers. There are seven radiation models available in ANSYS Fluent. Also, the Particle Radiation Interaction option allows us to consider the radiation effect on the particles. Note that this option is available only when the?P1?or?discrete ordinates?(DO) model is used.
Additionally, two extra material properties must be specified by the user, including?emissivity?and?scattering factor. Plus, the recommended emissivity for ash and coal is?0.5?and?1,?respectively. Moreover, the recommended scattering factor is?0.9?for coal combustion.
2. Thermophoretic Force
In fluid domains with a?high-temperature gradient, the suspended particles tend to move toward the colder area. The force is known as the thermophoretic force, which needs an additional force source term to be considered. The?thermophoretic coefficient?must also be specified. It can be a function of temperature or the default expression of Talbot.
3. Saffman Lift Force
Another force source term should be added to include the Saffman lift force acting on?sub-micron?particles caused by shear stress.
Virtual Mass Force & Pressure Gradient Force
In cases where the?density of both phases is close(density ratio >0.1), additional forces could be added to particle force balance by activating virtual mass and pressure gradient. It has a significant effect in cases like liquid with gaseous bubble flows.
4. Erosion/Accretion
The erosion/accretion physical model is proved by ANSYS Fluent to consider erosion rates on wall boundaries. Also, five erosion models are prepared, including?Generic?Model,?Oka,?Finnie,?Mclaury?and?DNV. Each has specific parameters that need to be set. There are plenty of related products available in MR-CFD?learning products. For instance, check the sedimentation and erosion in a shell and tube heat exchanger.
5. Pressure Dependent Boiling
the moment the particle`s temperature reaches boiling temperature, ANSYS Fluent switches from vaporization (Law 2) to Boiling (Law 3). By enabling pressure dependent boiling option, the switching condition will be changed. Thus, when the?saturation vapor pressure?becomes greater than the domain pressure (Psat>P), the switching occurs. So, the accurate definition of droplet saturation vapor pressure is of the essence.
It needs to be mentioned that the?Temperature Dependent Latent Heat?will automatically be activated. Therefore, defining accurate latent heat for the droplet and evaporating species is important.
6. Two-way Turbulence Coupling
It is not always the continuous phase eddies acting on the discrete phase. In cases where the particle diameter is less than 0.1 turbulent length scale, the?damping?occurs and can produce?turbulence eddies. For larger particles, turbulence kinetic energy is also produced. By enabling two-way turbulence coupling, we can consider the mentioned turbulence effects.
7. DEM Collision – Stochastic Collision and Coalescence
The different coupling models were discussed in?Overview article. In cases where the volume fraction of particles is high, the probable collision of the particles is strongly effective. In other words, the four-way coupling should be hired to simulate the particle-particle interactions as well.
Considering?granular?effects, the?DEM collision?model is appropriate for simulation but requires high computational costs. Due to its complexity, we discuss it later in another article. On the other hand, we`ve got an?alternative choice?provided by ANSYS FLUENT:?Stochastic collision and coalescence. It is appropriate for?low weber number?collisions (We<100) and could result in shattering in high weber collision cases. Moreover, the weber number define as shown:
There is another limitation of the Stochastic collision model. The?DPM iteration interval?is limited to?1?and cannot be increased.
In addition, this model assumes the collision frequency is much less than particle time step size. So defining a large particle time step size leads to inappropriate results and provokes time step independence study.
8. Breakup
The breakup model should be activated in simulations where the droplets breakup is highly probable or is a part of instructions like in sprays.?
Break-up models
The atomization regimes can be divided into four major regimes. The Rayleigh regime, first and second wind-induced, is known as?Primary breakup (Jet breakup). It occurs due to wave instability on the jet surface. The atomization regime is categorized as a?secondary breakup (Droplet breakup).?It causes by hydraulic instabilities and body forces.
Six?breakup models:
?1. TAB (Taylor Analogy Breakup)
According to this model, the breakup works based on the?Taylor analogy?of a?distorting droplet to a spring-mass system. It is an appropriate model in many engineering applications. It Considers the effect of droplet oscillations and distortions. Additionally, It is suitable for?Low weber number injection (?Low-speeded sprays (We<100)).
When the droplet size reaches a?critical value, the parent droplet decomposes into several Child drops. The needed condition for a breakup to occur is defined below.
Where x is the Horizontal distortion of the droplet from a spherical state,???is the constant value equal to
By changing the droplet shape
2. Wave breakup model
In this method, injected liquid breakup process is related to the?relative velocity?between the liquid and gas phases?and is suitable for flows with a?high Weber number (We>100).?The model implies that the breakup period and the ensuing droplet size are related to the Kelvin-Helmholtz instability.?
3. Kelvin-Helmholtz Rayleigh-Taylor breakup model (KHRT)
The KH-RT model Considers the interaction between aerodynamic breakup and instabilities due to droplet acceleration. This model is suitable for?High Weber numbers?and is not recommended for low-pressure sprays.
5 . Stochastic Secondary Droplet (SSD) Model
TAB and Wave breakup models determine the breakup by a?single?diameter scale, whereas?the SSD model considers a random diameter distribution. The likelihood of breakup is independent of the parent droplet size in the SSD model, and the secondary droplet size is selected using an analytical solution of the?Fokker-Planck?equation for the probability distribution.
5) Madabhushi Breakup model
In brief, Madabhushi is a combination of the?wave?model and Plich and Erdman’s breakup theory. The droplets inject with a constant diameter, the same as jet diameter. After forming a liquid column, a primary breakup occurs at column breakup time (tcb). C0?is the column breakup time constant, ug?is the gas velocity of the crossflow, rhol?& rhog?are liquid and gas density, respectively.
6. Schmehl Breakup model
Schmehl’s breakup model is a new complex model considering three different breakup regimes. It has a specific governing equation for each regime. In addition, the distinguish criteria is the local weber number previously described in the article.?
Droplet Evaporation V.s Multi-component Evaporation
The evaporation process should be studied from two different aspects;?Heat transfer?and?mass transfer.?Wherever there is a temperature gradient between droplet and ambient, heat transfers from the higher temperature to below. Therefore, as the droplets inject into the hot domain, the heat transfer begins, and the droplet’s temperature increases until it reaches vaporization temperature. Note that the saturation vapor pressure at the droplet’s surface rises due to higher temperatures. The concentration gradient of evaporative species between the droplet’s surface and its environment controls mass transfer.
Compared to the droplet evaporation model, the multi-component evaporation model is more comprehensive and closer to the actual liquid evaporation because real liquid consists of multiple species, each with its specific properties. Naturally, the light components vaporize first and leave the heavier components, which take longer to vaporize. By employing a multi-component model in Ansys Fluent software, we can define several species and their components. Still, it also requires accurate input parameters, including partial pressure, mass fraction of each component, etc.
Parcel Concept
Parcel?in?ANSYS Fluent?software is defined as a?group of monologue particles?with?similar properties?such as diameter, velocity, position, shape, etc. The parcel’s properties are considered the same as particles. In another view, each parcel represents a fraction of the total mass flow rate.
Parcel concept is related to the?computational cost?as it is costly to calculate the trajectory of every particle in the flow domain. It should be noted that since the particles have similar properties in each cell (there are unique properties there), the parcels assumption is entirely correct. Generally,?the more parcels are used, the more accuracy and convergence of the solution but also the higher the computational cost.
There are?four methods?to define parcels in Ansys Fluent software:
while??is the mass flow rate of particles,???Is the particle mass, and is the time step size.
Drag Law Models
Totally, there are?fourteen drag law models?
Discrete phase B.C
In discrete phase simulations, the interaction between particles and walls is essential to significantly predict a particle’s fate because wall impingement may cause a?secondary breakup, splashing, leaving the domain, etc. It is handled by boundary conditions available in the?Boundary Cond Type?drop-down list under discrete phase model conditions shown in the figure.
1. Reflect B.C
the particle?rebounds after collision?with the boundary. Thus, the?momentum change?is defined by the coefficient of restitution: (n: velocity in the normal direction to the wall, 2: represent velocity after collision, 1: represent velocity before the collision)
2. Trap B.C
By applying the trap model to the DPM boundary condition type of a wall, the trajectory calculations are?terminated after the collision, and the fate of the particle is counted as trapped. Furthermore, the?entire mass is converted to the vapor phase?in a droplet evaporation simulation. Check the figure below.
3.Escape
If the DPM boundary condition type is set to escape the model, the?particle vanishes?after it encounters the boundary. Ansys Fluent sets the inlet’s and outlet’s DPM boundary conditions to escape type by default.
4.Wall-jet
Theoretically, the wall-jet model is based on the Naber-Reitz theory, which defines velocities and directions by resulting momentum flux in a non-viscous jet. It is used when the?wall film isn’t of the essence?or cannot be formed, like on?hot walls.
4.Wall-film
There are Four probable scenarios depending on impact energy and wall temperature. The following equation is the definition of?impact energy:
E: Impact energy,?rho?: liquid density,?Vr?: relative velocity of the particle in the frame of the impinging wall Vr2=(Vp-Vw)2, D: droplet diameter,?Sigma: surface tension of the liquid,?h0?:
The four scenarios consists of?Stick, Rebound, Spread and Splash.
E<16: sticking
16<E<57.7: Spread
E>57.7: splashing