VVF10 - Oxygen-nitrogen gas mixture

Description

This test case examines the oxygen-nitrogen O₂ − N₂ gas mixture properties for various gas volume fractions at ambient temperature and pressure. The figure below illustrates the initial stage where two gases are completely segregated: the heavy gas O₂ occupies the upper part, the light gas N₂ occupies the lower part.

Geometry

The geometry is a cube, 100 mm in length, shown in the following figure.

The cube is partitioned along the height, H, to give two sections, corresponding to the volume fraction of two different gases. Six models for different O₂ and N₂ volume fractions were developed, listed in the following table.

Simulation Model

This model uses Advanced Thermal-Flow solution type.

The mesh is made of tetrahedral elements.

The gases are modeled using the oxygen and nitrogen from the default material library properties: mass density, dynamic viscosity, and specific heat vary with temperature.

Oxygen gas, O₂:

• Molar mass: 0.032 kg
• Specific gas constant: 259.8 J/kg·K

Nitrogen Gas N₂:

• Molar mass: 0.028 kg
• Specific gas constant: 296.8 J/kg·K

The following boundary conditions are applied:

• Initial Conditions constraint: oxygen O₂ mass fraction from table above
• Initial Conditions constraint: nitrogen N₂ mass fraction from table above

The following solution options are set:

• Turbulence Model:None (Laminar Flow), Buoyancy check box selected
• Solution Type: Transient (0 to 250 seconds)
• Ambient Conditions: Pressure = 0.101351 N/mm² (MPa), fluid temperature = 25.02 ºC

The following solver parameters are set:

• 3D Flow Solver: Time Step = 0.1 s
• 3D Flow Solver: Maximum Residuals = 1e-6
• 3D Flow Solver: Buoyancy Model: Full with Hydrostatic Pressure

Theory

The theory described by Poling [17] is used as a basis of comparison between the solver results and the theory. The mixture density is computed as:

where:

• R_O2 and R_N2 are the specific gas constants of oxygen and nitrogen, respectively.
• T is the gas mixture temperature.
• P_O2 and P_N2 are the partial pressure of oxygen and nitrogen, respectively.

The partial pressure exerted by a gas of the mixture is defined as:

where:

• N_n is the number of moles of a gas in the mixture.
• R is the universal gas constant.
• V is the volume of the mixture equal to 0.001 m².

Mass fraction of nitrogen in the mixture is calculated as follows:

where:

• X_N2 and X_O2 are the volume fractions of nitrogen and oxygen, respectively
• ρ_N2 and ρ_O2 are the densities of nitrogen and oxygen, respectively.

Results

The mixture density as a function of percentage of nitrogen and oxygen is presented in the following figure.

Computed mass fractions for nitrogen N₂ are compared with the theoretical values in the following table. All the errors are under 0.5%.