# Boundary condition models

The KFX boundary models consists of 5 different models.

## Wall law of turbulent flow

The k-ε model is used to turbulent time and length scales.  Near walls, k-ε has very strong gradients which demands very fine grid resolution if they should be resolved.  Another approach, which is used in KFX®, is to use flat plate theory of turbulent shear flow, assuming equilibrium between production and destruction of k.  This implies that dissipation of turbulent kinetic energy must be fixed in cells adjacent to walls.  In addition coefficients of heat and momentum transfer from wall are determined by this analysis.

## Modeling wall temperatures

In KFX® a three dimensional and transient conduction model is included.  This model works on solid obstacle cells with solved temperatures.  Different solid construction cells may be used when change in density, specific heat and thermal koduction shall be modelled.
Both the solid construction conduction model and the flow model, needs information about the surface temperature of solids.  For solid construction cells the surface temperature is found by balancing incoming heat flux with heating of the wall cell.  In order to model the high temperature gradient imposed by high, instantaneous heat fluxes, a linear heating model of the wall cells is used.  For surface porosities, which is the plates model in KFX®, focus is to have a transient heat balance for each plate element.  This imply that due to the incoming heat fluxes on both sides, absorbtivity, conductivity, density, specific heat, droplet evaporation and plate thickness, transient temperatures on both sides and the core temperature of the element must be calculated.  A three point conduction formula is used in this model, and the non-linearity in the radiation term is taken care of by a Newton-Rapson formulation.

## Sub grid geometry (Porosity)

Solid objects that are smaller than the local control volume are modeled by a porosity approximation. A solid object is modeled by a combination of surface porosity and volume porosity. A control volume has six surfaces. Each surface can be closed, partly closed or fully open. The surface porosity is zero when a surface is fully closed and one when it is fully open. Control volumes with no obstacles in them have all four porosity values equal to one.

The surface porosity impacts the velocity equations through drag terms. If only a small fraction of a control volume surface is closed by surface porosity, the only link to the turbulence model is through velocity gradients that appear as a consequence of the velocity drag term. If more that 30% of the surface is closed, turbulence energy and dissipation is calculated by the logarithmic law of the wall function. Control volume surfaces that are partly or fully closed are also coupled to the radiation model and the fluid enthalpy equation. The solid surfaces of a control volume are assigned thermal and radiative properties so that solid temperature development can be calculated.

Volume porosity is not linked to solid thermal response, but is coupled to velocity through drag functions. It is also affects the inertia term of the transport equations since a high solid volume fraction leads to a small fluid volume. When a control volume is only solid, it is denoted as an obstacle and treated by manipulating the coefficient matrix for the equation solvers. Temperature development can be calculated within solid obstacles.

## Wind

Profiles of the wind velocity and the related turbulence parameters are distributed throughout the outer surfaces of the calculation domain, according to the wind velocity, wind profile exponent and turbulence intensity given at 10 m above the ground/sea and the surrounding temperature. Pasquil categories of turbulence are predefined.

## Jet inlet

When a high-pressure gas is discharged through an orifice to an ambient pressure much below the exit pressure, an under-expanded jet with a shock structure is created. To resolve the shock structure numerically, it is necessary to perform a detailed compressible simulation. However, for consequence analyses of high-pressure gas leaks, the details of the shock structure is less interesting than the overall gas dispersion. The ComputIT's jet boundary condition method utilizes ideal gas relations and conservation of mass, momentum, and energy to predict the fluid state downstream the shock structure. The calculated exit state may then be used as the jet inlet condition in Kameleon FireEx.

The Hydrocarbon Jet and Spray Calculator (HCJSC) is a tool similar to the ComputIT's jet boundary condition method. However, the HCJSC is not based upon ideal-gas relations, but utilizes an extensive thermodynamic database to incorporate real gas effects. The HCJSC also handles two-phase fluids in a consistent manner. The HCJSC should be chosen over the ComputIT's jet boundary condition method when the hydrocarbon mixture is in the two-phase region and at conditions with very high pressures. In particular, it should be used when the mixture contains large hydrocarbon molecules as these increases the probability of a two-phase fluid. Read more  