Lumped kinetic molecular method

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

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Lumped Kinetic Molecular Method

ProductsAbaqus/Explicit

Features tested

This section provides basic verification tests to define:

  • Particle generators
  • Fluid cavities
  • Discrete sections
  • Gas species used for particle generators
  • Fluid inflator properties used with particle generators

Problem description

This verification problem uses the lumped kinetic molecular (LKM) method. The mass, average pressure, and average temperature of the generated gas are verified against the uniform pressure method (UPM).

Model
The tank is in the shape of a rectangular box and is meshed using membrane elements. Boundary conditions are applied to all the nodes to make the tank rigid. A particle generator is defined inside the box. The inlet of the particle generator is positioned close to one end of the tank. The tank is initially empty.
Gas material
The particle generator generates gas particles with properties of air. The molecular weight of the gas is 2.897 × 10–6 tonnes/mol, and its heat capacity at constant pressure is 31829.339 J/K mol. To model 2 × 10–7 tonnes of the gas, 200,000 lumped particles are used. The gas is generated at a constant rate of 4 × 10–5 tonnes/sec at a temperature of 100K. The particle generator stops generating at 0.005 seconds.
Boundary conditions
The tank is held rigid until 0.006 seconds. After the gas reaches an equilibrium state, the wall behind the particle generator inlet is held fixed while the side walls are stretched such that the final volume of the tank is 1.5 times its original volume. The stretching of the box stops at 0.009 seconds, and the volume of the tank stays constant to the end of the analysis.

Results and discussion

The generated gas undergoes the following four phases during this test:

  • the initial generation phase,
  • a static pressure phase,
  • an adiabatic expansion phase,
  • and the final static equilibrium phase.
The generated gas reaches an equilibrium state around 0.006 seconds. As the tank is stretched, the gas undergoes adiabatic expansion. Since the mass of the gas stays unchanged during the expansion phase, the pressure and temperature both decrease. The gas once again reaches an equilibrium state after expansion stops at 0.009 seconds.

Figure 1 compares the generated gas mass for the LKM method with the generated mass using the UPM. The four phases in this test can be seen in Figure 2, which compares the average gas pressure in the LKM analysis with the gas pressure obtained from a corresponding UPM analysis. The results from the two methods show close agreement. Figure 3 compares the average gas temperature from the LKM solution with that obtained from the UPM.

Figures

Figure 1. Comparison of generated gas mass.

Figure 2. Comparison of average gas pressure.

Figure 3. Comparison of average gas temperature.