Mass Flow Inlet

You can use the mass flow inlet boundary to specify the known mass flow rate or the mass flux (mass flow rate per unit area) at a boundary. This boundary condition is designed primarily for specifying mass flow inward across the boundary, but also works for specifying mass flowing outward. Mass flow inlet is available for both compressible and incompressible flow regimes.

Boundary Inputs

For a mass flow inlet boundary, you specify the following variables:


Inputs	Incompressible Equation of State	Compressible Equation of State
total mass flow rate ${\dot{m}}_{total, s p e c}$ or mass flux ${\dot{m}}_{s p e c}^{''}$	✓	✓
supersonic static pressure $P_{s, s p e c}^{\sup}$		✓
total temperature $T_{t, s p e c}$	✓	✓
inflow direction $θ_{s p e c}$	✓	✓

You specify the inflow direction as normal to the boundary, as individual angle components, or directly as flow direction angles. Flow conditions are specified relative to the flow condition's reference frame, which can be either the laboratory, the region, or the local reference frame.

Computed Values

For a mass flow inlet boundary, Simcenter STAR-CCM+ computes the following values at the boundary faces:

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

When you specify the total mass flow rate for the inlet, Simcenter STAR-CCM+ distributes it over all faces of the boundary and calculates a uniform mass flow rate on each face of the boundary:

Figure 1. EQUATION_DISPLAY

\dot{m} = {\dot{m}}_{total, s p e c} \frac{| a |}{A}

(785)

where:

$a$ is the outward pointing face area vector.
$A$ is the total area of the boundary.

When you specify mass flux, the mass flow rate at each face is calculated as:

Figure 2. EQUATION_DISPLAY

\dot{m} = {\dot{m}}_{s p e c}^{''} \cdot | a |

(786)

The static pressure at the boundary is extrapolated from the interior of the domain:

Figure 3. EQUATION_DISPLAY

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

(787)

Compressible Equation of State

When the inflow is supersonic, the static pressure is updated with the specified supersonic static pressure at the boundary:

Figure 4. EQUATION_DISPLAY

P_{s} = P_{s, s p e c}^{\sup}

(788)

The static temperature at the boundary is calculated based on flow conditions:

Inflow

Under inflow conditions, that is, mass flow rate $\dot{m} \geq 0$ , the static temperature at the boundary, $T_{s}$ , is computed by using the total enthalpy (temperature) relation:

Figure 5. EQUATION_DISPLAY

H_{t} = H_{s} + \frac{{| v |}^{2}}{2}, C_{p} T_{t, s p e c} = C_{p} T_{s} + \frac{{| v |}^{2}}{2}

(789)

where $H_{t}$ is the total enthalpy, $H_{s}$ is the static enthalpy, and $C_{p}$ is the specific heat.

This yields a quadratic equation that is solved for $T_{s}$ :

Figure 6. EQUATION_DISPLAY

T_{s} = T_{t, s p e c} - \frac{{(ρ | v |)}^{2}}{2 C_{p}} \cdot {(\frac{R T_{s}}{P_{s}})}^{2}

(790)

where:

Figure 7. EQUATION_DISPLAY

ρ | v | = \frac{\dot{m}}{| θ_{s p e c} \cdot a |}

(791)

Outflow

Under outflow conditions, that is, mass flux $\dot{m} < 0$ , $T_{s}$ is extrapolated from the interior of the domain:

Figure 8. EQUATION_DISPLAY

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

(792)

The fluid density is updated from the equation of state by using the now known boundary values for static pressure $P_{s}$ and static temperature $T_{s}$ :

Figure 9. EQUATION_DISPLAY

\begin{matrix} ρ & = & ρ (P_{s}, T_{s}) \end{matrix}

(793)

The velocity vector at the boundary face is calculated as:

Figure 10. EQUATION_DISPLAY

v = \frac{\dot{m}}{ρ (θ_{s p e c} \cdot a)} θ_{s p e c}

(794)

With the velocity from Eqn. (794), the total enthalpy at the boundary is given by:

Figure 11. EQUATION_DISPLAY

\begin{matrix} H_{t} & = & H_{s} (P_{s}, T_{s}) + \frac{{| v |}^{2}}{2} \end{matrix}

(795)

where the static enthalpy $H_{s}$ is calculated based on the equation of state.

Incompressible Equation of State

The velocity vector is calculated from the mass flux as:

Figure 12. EQUATION_DISPLAY

v = \frac{\dot{m}}{ρ (θ_{s p e c} \cdot a)} θ_{s p e c}

(796)

where the density at the boundary is updated from the equation of state by using the static temperature from the previous iteration:

Figure 13. EQUATION_DISPLAY

\begin{matrix} ρ & = & ρ (T_{s}^{*}) \end{matrix}

(797)

Then, the static temperature at the boundary is recomputed based on flow conditions:

Inflow: Under inflow conditions, that is, mass flow rate $\dot{m} \geq 0$; Figure 14. EQUATION_DISPLAY

$T_{s} = T_{t, s p e c} - \frac{{| v |}^{2}}{2 C_{p}}$
(798)
Outflow: Under outflow conditions, that is, mass flow rate $\dot{m} < 0$ , $T_{s}$ is extrapolated from the interior of the domain:; Figure 15. EQUATION_DISPLAY

$T_{s} = T_{s}^{e x t}$
(799)

The total enthalpy is given by:

Figure 16. EQUATION_DISPLAY

H_{t} = H_{s} (P_{s}, T_{s}) + \frac{{| v |}^{2}}{2}

(800)

where the static enthalpy $H_{s}$ is calculated based on the equation of state.