Below are some eclectic notes on DPM I thought would be worth uploading. The section begins with DPM basics and goes on to discuss stiff DPM type problems. Please excuse the non-standard referencing and abruptness. the bulk of this info is simply re-constituted from the Ansys literature. The 2nd half of the post looks briefly at how heat transfer is modelled for the particles.
Source: http://www3.nd.edu/~gtryggva/CFD-Course2010/2010-Lecture-19.pdf
The most important equation for Euler-Lagrange models is:
The force balance is usually something like this:
Drag + gravity & buoyancy + other forces (lift, added mass, pressure… thermophoresis?)
When the effect of the particles on the fluid is not considered, this is known as one-way coupling. The DPM source terms are not included in the flow calculations, and DPM is applied as a post-processing technique.
When the effect of the particles on the fluid is considered, this is known as two-way coupling. The DPM source terms are included in the flow calculations. In this case, the particles need to be iterated with the flow. The DPM underrelaxation factor defines how many iterations are required for the source terms to take full effect on the flow. This is described by the graph below, you can see the default DPM URF = 0.5 takes about 10 iterations to update the source term, 10 iterations is the default setting for the “number of continuous phase iterations per DPM iteration” in Fluent.
The default URFs are fine for simple cases. For more complex cases default URF can be too aggressive. Effect of URF is highly non-linear. You can increase the number of stochastic tries for turbulence random walk models in order to even out the particle’s effect on the flow. Underrelax the species and energy to start-up the solution (recommends 0.9 for each) then once solution is stable, attempt to increase these to 1.
Source: fluent lectures – combustion 15.0_L4_DPM.
Often the convergence problem is related to high source terms generated in certain cells. Try increasing stochastic tries, and increase the number of gas-phase iterations per DPM iteration. Energy, radiation and ‘mixture fraction’ (species) should have residuals less than e-6.
Node based averaging spreads the load of a DPM source into neighbouring cells. Good for reducing grid dependency, and improving convergence in steady-state sims. “Enable Node-Based Averaging”.
Source term linearization can be combined with node based averaging for simulations without mass transfer. Must be done with caution - see below.
Source: Ansys Fluent lectures – multiphase -15.0 – DPM.
Solution strategies for steady flows in DPM
Closer coupling between the dispersed and continuous flow.
Increase underrelaxation factor for discrete phase
Decrease number of continuous phase calculations between trajectory calculations
Lower the underrelaxation factors for the continuous phase
Decoupling between dispersed and continuous flow.
Lower the underrelaxation factor for discrete phase
Increase number of continuous phase calculations between trajectory calculations
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DPM Switching Laws
When modelling droplet evaporation, it is advised to always inject particles at a temperature a few degrees below their vaporisation temperature in order to improve stability.
When modelling heat transfer in DPM, irrespective of inert, droplet, or multicomponent particles, DPM switching laws are active. an example of switching laws progressing for a combusting particle:, in order of increasing temperature of particle
inert heating law
drying (water removal) - (evap, boil, inert heating)
...
devolatilisation
combustion
inert heating
Inert heating or cooling: Law one, Law six.
Law one: apply when the particle temperature is less than the defined vaporisation temperature.
Tp < Tvap.
Law six: apply when the volatile fraction fv0 of the particle has been consumed (think this applies to coal combustion models etc). “Equation is saying: activate inert heating when the particle mass has dropped to that of the non-volatiles only”.
The “Inert Heating Law” is a simple single-film equation, with radiation heat transfer added-on.
,h = convective heat transfer coefficient. W/m2. Found by Ranz-Marshall correlation.
Droplet Vaporisation: Law Two
Applies between the vaporisation temperature and boiling pt temperature (or until the volatiles are completely gone).
The “diffusion controlled model” is just a single-film mass transfer law, which assumes the particle Temperature = equilibrium vapour concentration at the particle surface, and that raoult’s law applies in the bulk. Mass transfer resistance is found using the “Sherwood number correlation” which is just the Ranz-Marshall correlation with Heat/Mass Transfer Analogy applied (the one where you just replace dimensionless numbers).
Defining boiling point and latent heat
This is a Hess’s law-style enthalpy balance to extrapolate the latent heat at the boiling down to the vaporisation temperature. This is only active when “temperature dependent latent heat” is selected in the discrete phase model dialogue box.
(P-1 or DO, radiation modelling) when Radiation modelling is OFF, therefore the problem can’t be anything to do with radiation terms.
“temperature dependent latent heat” is off, therefore the problem can’t be anything to do with hess’s law-style calc.
Enthalpy balance for DPM source: P 494, Ansys theory guide
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Linearize source terms: this option linearizes DPM source terms for momentum, energy and species w.r.t. cell variable φ. SDPM = Sconst + Slin φ . Increases numerical stability for steady flows. Transient flows => longer time steps and larger URFs (+ve).
Have to be careful when used in conjunction with average DPM source terms, combining the two for vapourising particles can lead to numerical instabilities and unphysical results for gas temperature.
