particulate-formation type behaviour in Ansys Fluent. The list is by no means exhaustive. Most of this information is summarised from ansys literature.
Discrete Particle Modelling
- I could use literature data to find the concentration and particle size of contaminants
normally present in air that drive heterogeneous nucleation. I could use
this to set up the injection of DPM particles
- I could then define the particle diameter as a variable, and define the growth rate based on:
(size, temperature, partial pressure, mass transfer film resistance) using UDFs.
Advantages:
- Already working with discrete particles; continuation of a theme.
Disadvantages:
- Contaminant concentration is a guess.
- Does not account for transfer to the walls.
- UDFs more complex than they sound: growth will require source terms, will still require a multispecies gas phase,
- I haven’t found a tutorial that covers condensation using DPM. The options for heat & mass
transfer in DPM are “Droplet (heating, evaporation, boiling)”, “Multi-component
(multicomponent evaporation), “Combusting (Heating, de-volatilisation, heterogenous
reaction)”. Condensation is not included in Fluent, and a User Defined Function is required.
Evaporation-Condensation Modelling:
Is available with mixture models and Eulerian multiphase. Option of Lee model or the Thermal Phase Change model.
Lee Model:
The theory guide mentions the Hertz-Knudsen equation. This equation is re-arranged so that the
driving force is defined based on Tsat rather than Psat. The following coefficient is a constant in the
model defined by the user:
mass trans. is defined:
Nb. These equations are for evaporation, but condensation equations are of the same form.
The user guide states “diameter (dh) and accommodation coefficient (B) are usually not very well known, which is why the coefficienct “coeff” must be tuned to experimental data”. Personally, I think this could be problematic because we expect that dh and Tsat change with condensation properties. In this model the user defines “coeff” as a constant and I don’t think it can be defined as a UDF. This model is capable of defining the saturation temperature in terms of total pressure, but it requires a UDF to define saturation temperature in terms of partial pressure.
Advantages:
- Looks simple to implement. Based on a tutorial I tried modelling condensation of pure steam
at ~+100degC and it seemed to give OK results.
Disadvantages:
- Over simplistic, assuming “coeff” and “dh” are const. for condensation from an inert gas like air, we also need saturation as a function of partial pressure.
Thermal Phase Change Model:
Thermal phase change model uses the two resistance model to model heat transfer (which is basically h-values for liquid & vapour phase heat transfer coefficients). The mass transfer is the governed entirely based on the heat transfer process and the overall heat balance. Only works with a Eulerian model. In this model you specify (along with the heat transfer characteristics) the continuous phase and dispersed phase transfer coefficients. According to the user guide these “act as multipliers for the heat transfer coefficients determined for each phase and the default value of 1 is usually appropriate”. This factor doesn’t seem to appear in the equations in the theory guide.
Advantages:
- Some of the literature I have read actually states growth of particles can be heat-transfer limited.
- Seems more appropriate than the Lee model at face value.
Disadvantages:
- Would still require a UDF for saturation in terms of partial pressure.
Soot models:
Three soot models exist in Ansys.
1. One-step model (Khan and Greeves), single transport eqn. for soot mass fr.
2. Two-step model (Tesner) transport eqns for radical nuclei concentration and soot mass fr.
Both models use empirical rate constants for soot formation.
3. Moss-Brookes model, solve transport eqns for soot mass fr. And normalized number density.
Moss-Brookes Hall model – as above for hydrocarbons larger than methane.
In Khan and Reeves model the source term takes a form similar to the Arrhenius equation. You can define the formation const. Cs, the equivalence ratio exponent r, activation temperature E/R. In the Two-step model, nucleation is defined using a simpler Arrhenius-type equation with branching and collision terms included. The rate of soot formation depends on the nucleation rate, but it also involves two empirical constants. The mean particle size is predefined, so this model isn’t actually modelling particle growth. In the Moss-Brookes model the nucleation is dN/dt, the source term for the number density. The mean diameter in this model is used to find the coagulation rate. But dM/dt has a surface growth term – this is the source term in the soot mass fraction equation. So (I’m guessing) if N & M both change separately, then you know the number and you know the mass fraction of particles, so you can work out what the mean particle size must be from these two
values.
Advantages:
- The soot models are built into fluent. Could be faster or easier than writing UDFs
Disadvantages:
- All of the models are highly empirical and application specific to soot formation.
- Adjusting the model parameters might eventually lead to something representative of
another particulate formation in another scenario, but these parameters must be set as
constants and cannot be UDFs, which could be restrictive.
- Possibly wrong tool for the job.
Eulerian wall film:
Eulerian wall film model is relevant as it can be used to model particle capture & inclusion into films. It can model film condensation and evaporation, as well as ice accreditation on aircraft. Can model heat & mass transfer in evaporation & condensation. Solidification, Melting & sublimation possible
through UDFs. Works with DPM and Euler-Euler particle models. The wall film is transient, but it can be used in steady-state flows with the “film time step size”. Using the wall film model with mixture species transport allows us to model mass transfer from an inert gas using partial pressure.
Population Balance Modelling:
Population Balance Modelling applies to Eulerian multiphase models. Nucleation can be specified as constant, or via a UDF. There are five types of population balance model, in two categories:
1. Discrete method:
a. Homogenous discrete
b. Inhomogenous discrete
2. Method of Moments:
a. Standard Method of Moments
b. Quadrature Method of Moments
c. Discrete Quadrature Method of Moments
The Discrete, homogenous model uses Hounslow’s approach for bin discretisation, which uses geometrically increasing bin sizes. Homogenous models have only two phases. Particles share velocities, so it won't model segregation of larger particles by settling or impaction. In the discrete inhomogeneous model the bin sizes are at the discretion of the user. Each bin size is handled as a separate phase, so the computational load is higher, but each bin has its own velocity allowing size separation to be modelled.The method of moments uses the moments of the distribution in place of the distribution itself. The resulting distribution can then be reconstructed from the moments to give the “statistically most probable distribution”. The quadrate method of moments allows breakup & coalescence to be modelled, but similarly to the standard method, describes every particle with a single velocity field. Discrete quadrature method of moments allows for different velocity fields on different particle sizes, nucleation and growth modelling in population balance models.Nucleation is defined as a boundary condition, in the discrete methods, it creates particles at a constant rate in the smallest size bin. Nucleation rate can be defined as a constant or as a UDF. Growth rate in m/s can also be defined as constant or via a UDF. Neither of these are available when using inhomogeneous discrete method. For the Standard method of moments, only size-independent growth is available. You can add mass transfer using species transport options. You have the choice of: none, constant rate, user defined, population balance. In the latter nucleation and growth rates are calculated by the population balance kernels.
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