DPM Erosion and Accretion Maps in ANSYS Fluent 2024 R1

#+CATEGORY: cfd

#+TAGS: DPM erosion accretion Finnie Oka wall-impact deposition

#+MATURITY: growing

DPM Erosion and Accretion :: Wall Impact Analysis and Deposition Maps

This page covers the erosion/accretion models available in ANSYS Fluent 2024 R1, wall impact reporting, deposition accounting, and the Finnie and Oka erosion models. Target application: shisha PM2.5 simulation, where erosion is negligible but deposition (tar condensation, particulate sticking) on glass and body surfaces is the primary interest.

Erosion vs. Accretion — Definitions

For shisha PM2.5:

• Erosion is negligible (PM2.5 particles are too small and soft to abrade glass)
• Accretion is the primary concern: tar and particulate deposit on bowl walls, hose, and body surfaces

Fluent treats both under the same /Erosion/Accretion/ model framework. The erosion rate can be set to zero by choosing appropriate material properties.

Activation in Fluent 2024 R1

Access: Models > Discrete Phase > Erosion/Accretion...

Procedure: 1. Open the DPM model dialog 2. In the Physical Models tab, enable /Erosion/Accretion/ 3. Select the Erosion Model:

• Finnie (default, for ductile materials)
• Oka (for brittle materials)
• User-Defined (UDF for custom model)

4. Select the Wall material:

• Ductile (glass, metal -- Finnie model appropriate)
• Brittle (ceramics, ash deposits -- Oka model)

5. Click OK

After activation, Fluent computes erosion/accretion rate on all wall boundaries for every particle impact.

The Finnie Erosion Model

The Finnie model (1960, revised 1995) is the classical erosion model for ductile materials. It describes the erosion rate as a function of particle impact angle.

Erosion rate: $$R_{\text{erosion}} = \sum_p \frac{m_p C_d}{A_{\text{face}}} f(\theta)$$

where:

• $m_p$ = mass flow rate of particle parcel $p$
• $C_d$ = erosion coefficient (material property, kg/kg)
• $A_{\text{face}}$ = area of the wall face
• $f(\theta)$ = angular dependence function

Finnie's angular function (original 1960): $$f(\theta) = \begin{cases} K_1 \sin(2\theta) - 3\sin^2(\theta) & \text{if } \tan\theta < 1/3 \\ \frac{1}{3}\cos^2(\theta) & \text{if } \tan\theta \geq 1/3 \end{cases}$$

where $\theta$ is the impact angle relative to the wall surface and $K_1$ is a material constant (typically $K_1 = 2$).

Finnie's revised angular function (1995): $$f(\theta) = \left(\frac{1}{\epsilon}\right)^{0.5} \left[\sin(2\theta) - \frac{1}{\epsilon}\sin^2(\theta)\right]$$

where $\epsilon$ is the ratio of cutting to plowing efficiency (typically $\epsilon = 3$).

For Fluent's implementation: Fluent uses the form: $$R_{\text{erosion}} = \frac{\sum_p m_p \cdot C \cdot V_p^{n} \cdot f(\theta)}{A_{\text{face}}}$$

where $V_p$ is the particle impact velocity, $n$ is the velocity exponent, and $f(\theta)$ depends on the selected function.

Default Fluent parameters:

*The Oka Erosion Model :PROPERTIES: :ID: cfd_dpm-erosion-accretion--oka :CUSTOM_ID: cfd_dpm-erosion-accretion--oka :END:

The Oka model (2005) is designed for brittle materials and is widely used in industry. It captures the peak erosion at low impact angles typical of brittle fracture.

Erosion rate: $$R_{\text{erosion}} = \sum_p \frac{m_p}{A_{\text{face}}} \cdot g(V_p) \cdot h(\theta)$$

Velocity dependence: $$g(V_p) = \left(\frac{V_p}{V_0}\right)^{n_1} \cdot \left(\frac{H_v}{H_{v0}}\right)^{-n_2}$$

where:

• $V_0 = 100$ m/s (reference velocity)
• $H_v$ = Vickers hardness of the target material
• $H_{v0} = 1$ GPa (reference hardness)
• $n_1, n_2$ = material-dependent exponents

Angular dependence: $$h(\theta) = (\sin\theta)^{n_1} \cdot \left[1 + H_v (1 - \sin\theta)\right]^{n_3}$$

where $n_1, n_3$ are fitted parameters.

Fluent's Oka parameters (defaults):

Which model for shisha glass? The Finnie model is appropriate for glass surfaces (ductile behavior at the scale of PM2.5 impacts). The Oka model is more appropriate for ceramic bowl materials or if you study ash deposition.

For pure deposition tracking (tar/particulate sticking without material removal), set the erosion constant $C = 0$ and use the accretion rate: $$R_{\text{accretion}} = \sum_{p \in \text{trap}} \frac{m_p}{A_{\text{face}}}$$

This simply computes the mass flux of trapped particles per unit wall area.

Reporting Erosion/Accretion

Contour visualization: 1. Graphics and Animations > Contours > Settings... 2. Contours of: DPM > Erosion Rate (or Accretion Rate) 3. Surfaces: select wall zones 4. Display

The erosion rate contour shows the spatial distribution of material loss (or gain) on wall surfaces.

Surface-integrated report: 1. Reports > Discrete Phase > Erosion... 2. Select wall zones 3. Fluent reports:

• Maximum erosion rate (kg/m^2.s)
• Average erosion rate over the wall
• Total eroded mass (kg/s)

TUI: ``` report/dpm/erosion <wall-zone-1> <wall-zone-2> ```

Wall impact details: For detailed per-impact data (useful for understanding deposition patterns): 1. Reports > Discrete Phase > Impacts... 2. Select wall zones 3. Fluent reports:

• Number of impacts
• Impact velocity (mean, max)
• Impact angle (mean, max)
• Particle diameter at impact
• Total mass of impacting particles

TUI: ``` report/dpm/impacts <wall-zone> ```

Time-Dependent Deposition (Transient DPM)

For transient simulations, the deposition accumulates over time. Fluent tracks cumulative deposition on each wall face.

Setup: 1. Enable /Erosion/Accretion/ model 2. Enable Unsteady Particle Tracking 3. Run transient DPM with multiple time steps 4. Fluent accumulates deposition mass on each wall face

Post-processing cumulative deposition: 1. Graphics and Animations > Contours > Settings... 2. Contours of: DPM > DPM Deposition 3. This shows the cumulative mass per unit area deposited on each wall over all time steps

Deposition rate vs. cumulative mass:

For shisha simulation (puff-by-puff), the cumulative deposition after multiple puffs shows where tar accumulates over a session.

Deposition vs. Reflection — Boundary Condition Impact

The DPM boundary condition on walls determines whether particles are tracked for deposition:

For shisha PM2.5:

• Glass body: trap is appropriate (tar condenses and sticks)
• Bowl inner surface: trap (particulate deposits)
• Hose interior: trap or semi-reflect (depends on humidity/temperature)

The semi-reflect model: For more realistic deposition modeling, use a sticking probability: 1. Boundary Conditions > Wall Zone > DPM tab 2. Set BC Type to reflect 3. Enable Sticking Probability 4. Set probability = $p$ (0 to 1, where 0 = always bounce, 1 = always stick) 5. Fluent uses a Monte Carlo approach: each impact is tested against the probability

TUI: ``` define/boundary-conditions/dpm <zone-name> ; Set reflecting BC with sticking probability > type reflect > sticking-probability 0.5 ```

See Also

• DPM Post-Processing Guide
• DPM Boundary Conditions
• DPM Physical Models
• DPM Concentration Fields
• Shisha PM2.5 DPM Case Study