Outlet

The outlet boundary represents an outflow condition where no backflow occurs. You apply the outlet boundary at locations of the computational domain where the flow is directed outwards only. As such, the outflow conditions are not prescribed, but they are determined by the flow upstream of the outlet boundary. You can place more than one outlet boundary in your computational domain.

The distribution of variables on the outlet boundary is obtained by extrapolating the values from the cell that is adjacent to the outlet boundary. Ideally, the flow is aligned with and does not vary in the extrapolated flow direction. Therefore, care must be taken where you locate the outlet boundary. You are advised to place the outlet boundary condition where this assumption is met, that is, where you have a fully developed flow profile.

In addition to the extrapolation procedure, a second calculation step is performed to determine the mass flow at the outlet. Simcenter STAR-CCM+ provides the following options to set the mass flow:

Split Ratio—applies the fraction of the total outflow leaving at the respective outlet boundary. Simcenter STAR-CCM+ then calculates the mass flow at these boundaries such as to satisfy overall continuity.
Mass Flow Rate—explicitly defines the mass flow rate at the outlet boundary.
Corrected Mass Flow Rate—explicitly defines the corrected mass flow rate at the outlet boundary.

Either way, to obtain the correct mass flow through an outlet boundary, the velocities are corrected.

If you encounter recirculation through an outlet boundary, that is, inflow into the domain, problems can occur. Recirculation through an outlet boundary can cause convergence problems or it can render the obtained solution inaccurate. Simcenter STAR-CCM+ detects recirculation through an outlet boundary and corrects the mass flux accordingly. If results are produced even though the assumptions for an application of the outlet boundary condition are not fulfilled, you are advised to review them for validity. Alternatively, the location of the boundary condition can be changed, for example through extrusion of the mesh, or the usage of a pressure outlet boundary condition is more appropriate.

The outlet boundary condition is valid for incompressible and (subsonic) compressible flows—it is not valid for transonic and supersonic flows, with the exception of the Corrected Mass Flow Rate option used with the Coupled solver. Additionally, the following limitations apply:

Do not use the outlet boundary with Split Ratio (where mass flux is calculated) in combination with a pressure outlet or stagnation inlet boundary condition. Otherwise, the flow is indeterminate.
Combine an outlet boundary, with Mass Flow Rate or Corrected Mass Flow Rate as the Mass Flow Specification, with at least one other pressure-type boundary (such as an outlet boundary with Split Ratio or a pressure outlet) or a stagnation inlet.
Do not mix split ratio boundaries with the mass flow rate boundaries in one simulation.

Boundary Inputs

For an outlet boundary, you specify the following variables:


Inputs	Incompressible Equation of State	Compressible Equation of State
For Split Ratio: split ratio $f_{i, s p e c}$	✓	✓
For Mass Flow Rates: mass flow rate ${\dot{m}}_{i, s p e c}$	✓	✓

Computed Values

For an outlet boundary, Simcenter STAR-CCM+ computes the following values at the boundary faces:

velocity $v$
static pressure $P_{s}$
static temperature $T_{s}$

Incompressible and Compressible Equation of State

The face value of velocity at an outlet boundary is computed as:

Figure 1. EQUATION_DISPLAY

v = v^{e x t} + \frac{x_{i}}{ρ} n

(823)

where:

ext indicates that the value is extrapolated from the adjacent cell.
$ρ$ is the density, computed at the boundary face.
$n = a / | a |$ with $a$ being the outward pointing face area vector.

$x_{i}$ is the boundary mass-flux correction factor that is computed for outlet boundary depending on the mass flow rate option:

Split Ratios

For specified split ratios, the boundary mass-flux correction factor is calculated as:

Figure 2. EQUATION_DISPLAY

x_{i} = - \frac{f_{i, s p e c}}{\sum_{j = 1}^{n outlets} f_{j, s p e c}} \frac{({\dot{m}}_{in} - {\dot{m}}_{i, out}^{*})}{\sum_{outlet i faces} | a |}

(824)

${\dot{m}}_{in}$ is the total inlet flow defined as:

Figure 3. EQUATION_DISPLAY

{\dot{m}}_{in} = \sum_{non-outlet faces}^{} ρ (v \cdot a)

(825)

${\dot{m}}_{i, o u t}$ is the outlet mass flow rate through outlet boundary i computed as:

Figure 4. EQUATION_DISPLAY

{\dot{m}}_{i, o u t} = \sum_{outlet i faces}^{} ρ max (v^{e x t} \cdot a, 0)

(826)

Mass Flow Rate

For mass flow rates, the boundary mass-flux correction factor is calculated as:

Figure 5. EQUATION_DISPLAY

x_{i} = \frac{({\dot{m}}_{i, s p e c} - {\dot{m}}_{i, t o t a l})}{\sum_{outlet i faces} | a |}

(827)

${\dot{m}}_{i, t o t a l}$ is the total mass flow rate through outlet boundary i computed as:

Figure 6. EQUATION_DISPLAY

{\dot{m}}_{i, t o t a l} = \sum_{outlet i faces}^{} ρ (v^{e x t} \cdot a)

(828)

Corrected Mass Flow Rate

For corrected mass flow rates, the boundary mass-flux correction factor is calculated as:

Figure 7. EQUATION_DISPLAY

x_{i} = \frac{{\dot{m}}_{i, calc} - {\dot{m}}_{i, total}}{\sum_{outlet i face} | a |}

(829)

where ${\dot{m}}_{i, total}$ is the total mass flow rate through the outlet boundary as given by Eqn. (828) and ${\dot{m}}_{i, calc}$ is the total desired mass flow rate through the outlet boundary $i$ computed from the user-specified corrected mass flow rate ${\dot{m}}_{i, spec}$ , as:

Figure 8. EQUATION_DISPLAY

{\dot{m}}_{i, calc} = {\dot{m}}_{i, spec} \frac{P_{t, outlet} / P_{ref}}{\sqrt{T_{t, outlet} / T_{ref}}}

(830)

where:

$P_{t, outlet}$ and $T_{t, outlet}$ are the mass-flow averaged total absolute pressure and temperature at the outlet boundary $i$ .
$P_{ref}$ and $T_{ref}$ are the user-specified reference absolute pressure and temperature.

In the presence of any reversed flow at the outlet boundary $i$ , $P_{t, outlet}$ and $T_{t, outlet}$ are computed as area-averaged quantities.

The boundary face values for static pressure and static temperature are extrapolated from the adjacent cell:

Figure 9. EQUATION_DISPLAY

P_{s} = P_{s}^{e x t}

(831)

Figure 10. EQUATION_DISPLAY

T_{s} = T_{s}^{e x t}

(832)