Defining area leak using :mix option

Using the :mix option allows users to define a leak with a different fuel concentration than the default value used in FLACS. This is useful when a specific leak within a simulation needs to deviate from the standard concentration assumptions.

Why Use the :mix Option?

In FLACS, a leak typically uses ER0 to define the fuel concentration at its source. The simulation assumes that all leaks use this value unless specified otherwise. However, in some cases, a particular leak may need a different fuel concentration. The :mix option allows users to adjust the concentration of a specific leak by defining it as a combination of the ER0 and ER9 streams.

FLACS defines two streams:

• stream 0 represents the fuel stream.

• stream 9 represents the air stream

By default, the equivalence ratio for each stream is set so:

• ER0 = 1.0e+30, representing pure fuel.

• ER9 = 0.0, representing pure air.

The default assumption is that a leak has a concentration equal to ER0. The :mix option enables a user to modify this for an individual leak.

Example Setup

An area leak is defined by setting the Leak options parameter as follows:

mix 0.6,:AreaLeak(profile=Uniform,shape=Elliptic)

This configuration specifies that the released gas mixture consists of:

• 60% (by mass fraction) stream 0 composition

• 40% stream 9 composition

Log File Output

When running the simulation, the log file provides details about the leak setup. Example log output:

Leakage number 1, generating new cl-file

Fixed mass flow = 2.000 [kg/s], velocity = 151.850 [m/s]

Creating area leak 1

Applying area leak string: 1 "!J+X:mix 0.6,:AreaLeak(profile=Uniform)"

Checking area leak bounds: 1

... area leak crosses 0 symmetry planes

... area leak visible symmetrical part is COMPLETE

# LEAKAGE 1 I,J,K: 4 7 7 !J+X:mix 0.6,:AreaLeak(profile=Uniform)

Creating CGNS file

# LEAKAGE 1 STARTED

Understanding the Mixture Concentration

For the default dispersion values (ER0 = 1.0e+30, ER9 = 0.0):

• The mass fraction of fuel in stream 0 is 1.0 (100%)

• The mass fraction of fuel in stream 9 is 0.0 (0%)

• The resulting fuel mass fraction in the leak is:

  (0.6 × 1.0) + (0.4 × 0.0) = 0.6 (60%)

But what happens if ER0, ER9, or the mix value Change? If ER0, ER9, or the mix value are different, the fuel concentration in the leak changes and a more detailed calculation is required. For example:

Example Case: Methane, ER0 = 9, ER9 = 1, mix = 0.7

Step 1: Understanding the Constants Used

To perform these calculations, we use fundamental constants that describe the composition of air and the combustion properties of the fuel.

Molar Masses of Fuel and Oxygen

• g/mol → This is the molar mass of methane (CH₄). Different fuels will have different molar masses.

• g/mol → This is the molar mass of oxygen (O₂).

Stoichiometric Oxygen-to-Fuel Ratio

• → This is the stoichiometric mole ratio of oxygen to fuel. It tells us how many moles of oxygen are required to completely react with one mole of fuel.

  For methane (CH₄): This reaction requires 2 moles of oxygen per 1 mole of methane, so

Composition of Air

• → This is the mass fraction of oxygen in air (i.e., 23.2% of air is oxygen by mass).

• → This is the mass fraction of nitrogen in air (i.e., 76.8% of air is nitrogen by mass).

  These values represent the standard atmospheric composition.

Step 2: Compute the Stoichiometric Mass Ratio

The stoichiometric mass ratio defines how much oxygen mass is required per unit mass of fuel. It is calculated as:

​

Substituting the known values:

So, for every 1 kg of fuel, 3.992 kg of oxygen is required for complete combustion.

Step 3: Compute the Stoichiometric Air-to-Fuel Mass Ratio

This ratio tells us how much total air mass (oxygen + nitrogen) is required per unit mass of fuel.

Substituting the values:

So, for every 1 kg of fuel, we need 17.206 kg of air (including both oxygen and nitrogen).

Step 4: Compute the Fuel Mass Fractions

For a given equivalence ratio , the fuel mass fraction is given by:

Compute the Fuel Mass Fraction for stream 0 (ER0=9)

​So, when ER0 = 9, the fuel mass fraction is 0.3435 (34.35%).

Compute the Fuel Mass Fraction for stream 9 (ER9=1)

So, when ER9 = 1, the fuel mass fraction is 0.0550 (5.50%).

Step 5: Compute the Final Fuel Mass Fraction in the Leak

The final fuel mass fraction in the leak is computed as:

Substituting the values:

Final Answer

• Fuel mass fraction for stream 0: 0.3435 (34.35%)

• Fuel mass fraction for stream 9: 0.0550 (5.50%)

• Resulting fuel mass fraction in the leak: 0.257 (25.7%)

Key Takeaways

• In FLACS, leaks typically assume the fuel concentration at the source is defined by ER0.

• The :mix option allows an individual leak to have a different concentration by blending ER0 and ER9.

• The final fuel concentration depends on the mass fractions specified in the :mix option.