Particle generator

This problem contains basic test cases for one or more Abaqus elements and features.

This page discusses:

ProductsAbaqus/Explicit

Elements tested

PD3D

Features tested

  • Probability density of generator particles

  • Mass flow rate per inlet area of generated particles

Problem description

The probability density of generator particles and the mass flow rate per inlet area of generated particles are tested for four particle generators, each generating a single particle species. Each particle generator has a single faceted inlet surface with constant dimensions of 7 mm × 7 mm.

Table 1 lists the particle size probability density function (PDF) type and parameters for each particle generator species. The mass flow rate per unit inlet area for each particle generator species is held constant for the duration of the analysis. Particles of all species have a constant entry speed of 1000 mm/s. All generated particles in this problem continue to travel with the entry velocity along the normal direction to the generating inlet facet. Each particle generator can generate a maximum of 20000 particles. Figure 1 presents a view that is normal to the inlet facets showing the generated particles at the end of the analysis.

Figure 1. Four particle generators.

Table 1. Particle generator description.
Particle generator Probability density function Particle size distribution Mass flow rate per unit inlet area
 
PG1 Normal distribution Mean = 0.01 mm 5.0 × 10−8 t/mm2s for 0.02 s
Standard deviation = 0.02 mm
Minimum radius = 0.0005 mm
Maximum radius = 0.05 mm
PG2 Log-normal distribution Mean = 0.25 mm 5.0 × 10−8 t/mm2s for 0.02 s
Standard deviation = 1.0 mm
Minimum radius = 0.0005 mm
Maximum radius = 0.3 mm
PG3 Uniform distribution Minimum radius = 0.0005 mm 5.0 × 10−8 t/mm2s for 0.02 s
Maximum radius = 0.05 mm
PG4 Piecewise linear distribution Minimum radius = 0.0001 mm 5.0 × 10−8 t/mm2s for 0.02 s
Maximum radius = 0.057 mm

Results and discussion

A direct user time increment of 1.0 × 10−4 s was specified for the analysis. Generated and specified PDFs and mass flow rates are compared for particle generators PG1, PG2, PG3, and PG4.

Comparison of generated PDF

The specified normal and the log-normal probability density functions for particle generators PG1 and PG2, respectively, are truncated PDFs. Truncated analytical PDF curves are compared to the generated results for these two cases (see Probability Density Function for more details on truncated PDFs). Figure 2 and Figure 3 show the comparison of generated PDFs with the specified truncated PDF for generators PG1 and PG2, respectively. Figure 4 and Figure 5 show the comparison of generated uniform and piecewise linear PDFs with the corresponding specified PDFs for generators PG3 and PG4, respectively.

The two main factors influencing the agreement between the generated and specified PDF are the rejection of candidate particle sizes during the generation process (see Particle Generator for further details) and the number of particles being generated. The figures show that the generated PDF follows the specified PDF in an average sense in all four cases.

Comparison of generated mass flow rate

Since the inlet area does not change, the mass flow rate (MFR) for this problem is

5.0×10−8⁢ ⁢ t/mm2⁢s×(7⁢   mm×7⁢  mm)=  2.45×10−6⁢ t/s.

Figure 6, Figure 8, and Figure 9 show the comparison of achieved to specified mass flow rates for particle generators PG1, PG3, and PG4, respectively. Particle generators PG1, PG3, and PG4 exhaust the maximum number (20000) of particles and halt generating particles, causing the mass flow rates for these generators to drop to zero at 0.004 s, 0.0085 s, and 0.0138 s, respectively. The achieved mass flow rate closely matched the specified mass flow rate for these three particle generators. Particle generator PG2 generates 8048 particles during the analysis. Figure 7 shows the comparison of achieved to specified mass flow rate for particle generator PG2. Due to the discrete nature of particle generation and larger particle sizes, the achieved mass flow rate matched the specified mass flow rate only in an average sense for particle generator PG2 (see Particle Generator for further details).

Figures

Figure 2. Comparison of generated vs. specified PDF for particle generator 1.

Figure 3. Comparison of generated vs. specified PDF for particle generator 2.

Figure 4. Comparison of generated vs. specified PDF for particle generator 3.

Figure 5. Comparison of generated vs. specified PDF for particle generator 4.

Figure 6. Comparison of achieved vs. specified MFR for particle generator 1.

Figure 7. Comparison of achieved vs. specified MFR for particle generator 2.

Figure 8. Comparison of achieved vs. specified MFR for particle generator 3.

Figure 9. Comparison of achieved vs. specified MFR for particle generator 4.