At open boundaries, we need provide boundary conditions for the variables solved by the transport equations described in Basic Governing Equations. For flows in general, these include density, species density, flow velocity, and the specific internal energy of the fluid. Boundary conditions for these variables are necessary to solve the transport equations in Conservation Equations for Turbulent Reacting Flow.
To specify fluid density at the boundaries, in certain situations, user may specify the value of the fluid density directly. For gas flows, the specified density can be in the form of static or total density. The static density is the density in the thermodynamic sense. The total density, or the "stagnation" density, is the density when the gas is at its stagnation state. The way to convert the total density into static density is described in Conversion of Total Quantities to Static Quantities for Gas.
One can also specify pressure and let Ansys Forte compute the fluid density based on thermodynamic relations. If no pressure gradient is assumed at the boundary, pressure in the ghost cell is set equal to the pressure in the interior and the neighboring fluid cell. If pressure is specified by the user, it can be in the form of static pressure or total pressure. Total pressure is converted to static pressure as described in either Conversion of Total Quantities to Static Quantities for Gas or Conversion of Total Quantities to Static Quantities for Two-phase Fluid, depending on the actual fluid compositions at the inlet.
To compute density using pressure, one also needs information about the fluid temperature. The inflow temperature can be directly specified or calculated by assuming that the mixture reaches the current pressure by going through an isentropic process from a reference state. If temperature is specified at the inlet, it can be in the form of static temperature or total temperature. Similarly, total temperature is converted to static temperature as described in the following subsections. With both pressure and temperature known in the ghost cell, the Equation-of-State (Equation 2–7 for gas, Equation 11–1, Equation 11–3, and Equation 11–5 for two-phase) is used to compute density.
Alternatively, for gas mixtures, if isentropic relations are assumed, the following equation is used to compute density:
 | (3–23) |
where 
is the ratio of specific heats, 
and 
are the density and pressure in the ghost cell,
and 
are the density and pressure at the reference state, respectively.
The reference state is taken as the initial thermodynamic state of the fluid region
adjacent to the open boundary. This isentropic relation uses ideal gas assumption
and is valid only when the fluid mixture is gas. In this case, temperature in the
ghost cell is obtained by the Equation-of-State (Equation 2–7).
Having determined the fluid density, the species density at the open boundary can be readily computed knowing the species compositions, which are specified as user input.
Specific internal energy needs to be computed in the ghost cells to calculate convection of energy across the boundary. Temperature in the ghost cell is needed to compute the specific internal energy (see Equation 2–8 for gas, and Equation 11–2, Equation 11–4, Equation 11–6 for two-phase). As mentioned above, in certain situations, temperature is directly specified by the user, and a conversion is done when the total temperature rather than static temperature is specified. In other situations, temperature is obtained from isentropic relations and Equation-of-State.
Flow velocity at the open boundary is another important boundary condition. Its treatment varies depending on the specific types of boundaries. At Velocity or Mass Flow Rate Inflow Boundaries, flow velocity is specified by the user, either explicitly or implicitly. At Continuative Outflow Boundaries, flow velocities at the boundary are set equal to the average of those on the neighboring interior/fluid vertices. At Pressure Inflow Boundaries and Pressure Outflow Boundaries, flow velocity is computed by the flow solver based on the pressure gradient across the boundary.
If turbulence (Turbulence Models) is considered, boundary conditions should be provided for certain turbulence-related variables. These include the specific turbulent kinetic energy (or turbulent intensity), and turbulence length scale (or dissipation rate). The specified turbulence parameters are assumed to be constant; these values can be set to be the same as the initial values of the neighboring fluid region.
If the Method of Moment soot model (Method of Moments) is used, boundary conditions should be provided for the surface composition and dispersed phase parameters.
Total density, total pressure and total temperature are defined when the fluid
is stagnant. They are sometimes referred as "stagnation" or "reservoir" values.
If the fluid is brought to motion isentropically, its thermodynamic states are
denoted as "static" or "thermodynamic" quantities, and they are related to the
stagnation values by the energy conservation equation under a constant entropy
constraint. For gas flows, these relations are simplified by the assumption of
perfect gas. Specifically, the relation between total pressure
(
) and static pressure (
) is:
 | (3–24) |
In which 
is the Mach number, 
is the flow velocity magnitude, and 
is the speed of sound in the gas. The relation between total
density (
) and static density (
) is:
 | (3–25) |
The relation between total temperature (
) and static temperature (
) is:
 | (3–26) |
The static pressure, density, and temperature are the fluid's thermodynamic
states at flow velocity 
. They are needed in the ghost cells adjacent to the inlet
boundary. If user specifies total quantities, they are converted to the static
quantities using these relations.
This case is considered when the Eulerian two-phase flow model (Eulerian Two-Phase Models) is used. For two-phase fluid, we employ the isentropic energy equation to relate the total quantities and static quantities. Specifically, the following two equations are considered:
 | (3–27) |
 | (3–28) |
in which 
is the specific total enthalpy, 
is the specific total entropy, 
and 
are the specific enthalpy and entropy when the fluid is at
velocity magnitude 
. The specific enthalpy (and entropy) of the two-phase fluid
mixture is the mass-average of each phase's specific enthalpy (and entropy),
like the treatment of specific internal energy in Equation 11–2.
Assuming that the flow velocity (
) is known at the boundary, and if user specifies any two out
of four variables in Equation 3–27 and Equation 3–28, i.e., total temperature
(
), total pressure (
), static temperature (
) and static pressure (
), the other two variables are obtained by solving these two
equations simultaneously. Once the static temperature and static pressure are
available, static density is calculated by the thermodynamic Equation-of-State
(Equation 11–1, Equation 11–3, and Equation 11–5 ).
For liquid, the correlations of enthalpy and entropy with respect to temperature are in complex function forms. As a result, iterations are needed to solve for the unknowns in Equation 3–27 and Equation 3–28.
The method presented in this section does not allow conversion of total density into static density. So, specification of total density is not supported in Eulerian two-phase flow simulations.