3.2.16. Fuel Spreading Submodel

The VULCAN/KAMELEON fire code includes a model which represents the spreading of fuel on a non-absorbing substrate. This feature allows the simulation of fires resulting from fuel spills. Various correlations (Mansfield and Linley [76]) and global, quasi-steady-state, algebraic models (Cline and Koenig [77]; Magnoli [78]) have been developed to determine the size of a circular pool fire resulting from a fuel spill. Since these models are global in nature, and do not include the effects of complex geometries resulting from obstacles, they will not be included as submodel options. The following quantities are required:

$\rho_{fuel}$ , the density of the liquid fuel,

$\mu_{fuel}$ , the viscosity of the liquid fuel,

$Q_{release}$ , the volumetric flow of fuel released by the spill,

$A_s$ , the surface area of the element,

$\gamma$ , the surface tension coefficient of the liquid fuel.

The fuel boundary condition submodel generates the following output:

$h$ , the depth of fuel (m).

The following assumptions are invoked as part of the fuel spreading model presently in VULCAN.

The fuel is sufficiently thin for inertial forces to be neglected as compared to shear forces.

The velocity components in the fuel are always horizontal.

The substrate is smooth, horizontal and non-absorbing.

The flow is laminar.

The interface between the fuel and air at the front of the spreading fuel is parabolic.

The shear stress is zero at the top of the film.

Given the preceding assumptions, the spread of fuel is driven by the difference between hydrostatic pressure due to variations in fuel depth. The transport can then be represented by

(3.502) ${{\partial h} \over {\partial t}} = {{\partial} \over {\partial x_j}} \left( {{\rho_{fuel} g h^3} \over {3 \mu_{fuel}}} \right) {{\partial h} \over {\partial x_j}} + S .$

(3.502) is solved explicitly to track the fuel thickness along the flat surface. Boundary conditions and source terms are defined as follows to represent various physical features.

Drains - The depth of fuel is set equal to zero for cells occupied by drains. The volume of fuel transported into the drain cell is removed via a negative source term. occupied by drains. The volume of fuel transported into the drain cell is removed via a negative source term.

Obstacles - The fuel depth and the gradient of the fuel depth is set equal to zero at the interface between obstacles and surrounding cells.

Release Locations - The source term is defined by the volumetric flow of released fuel divided by the surface area of the element (i.e. $Q_{release}/A_s$ ).

The fuel will spread up until the hydrostatic pressure gradient is balanced by surface tension forces. Subject to the preceding assumptions, the minimum fuel depth is given by

(3.503) $h_{min} = \sqrt{{2 s} \over {\rho_{fuel} g}} ,$

where $s$ is the coefficient of surface tension for the fuel. The reduction in fuel depth due to the vaporization of fuel is calculated by the same technique used to define the fuel vapor boundary condition for pool fires.