Inlet Boundary Conditions

At an inlet, the inflow conditions can be specified by several different approaches in Simerics-MP: velocity inlet, volumetric flux inlet (specified and resistor-capacitor model), total pressure inlet, and static pressure inlet.

Velocity Inlet

The specified velocity at an inlet is only applicable for flows with constant density in order to have a fixed mass flow rate and thus a unique solution. However, this inflow condition has been extended for variable density flows when the inlet densities are calculated based on the density laws.

In Simerics-MP, the inlet velocity can be determined by specifying cartesian velocity components . The mass flow rate entering a velocity inlet boundary is computed as:

5.64

where is the cell face area at the inlet.

In equation 5.64, the inlet density must be predetermined in order to obtain a physically meaningful solution. For an incompressible flow, it is a known material property as a constant. For a compressible or variable density flow, it is calculated as a function of temperature, pressure, and/or species mass/mole fractions at the inlet:

5.65

where is the inlet mass fraction of the chemical species, whose value is directly specified at the inlet. The inlet static pressure ()and temperature can be either directly specified or computed from the specified total pressure and temperature values.

Other primary variables such as temperature, chemical species, and turbulent kinetic energy and turbulent kinetic energy dissipation rate are specified for the velocity Inlet.

Volumetric Flux Inlet

The boundary condition of volumetric flux inlet assumes that the inflow is normal to the inlet boundary surface, and the volumetric flux is given:

5.66

where ̇ is the inlet volumetric flux, and is the inlet velocity normal to the boundary surface.

From equation 5.66, the inlet velocity value or profile can be determined: In Simerics-MP, two options are available: constant velocity and fully developed velocity profile.

Velocity at the inlet is calculated from the known volumetric flux. Other variables are treated in the same way as the velocity inlet conditions.

It may be noted that in Simerics-MP, the inlet volumetric flux, , can be determined by either user-specified values/profiles, or by one of the Resistor Capacitor Model.

Total Pressure Inlet

With the specified total inlet pressure, predetermined flow direction and all the necessary scalar properties, the inflow conditions can be calculated based on the velocity-pressure relations:

5.67

where is the velocity magnitude; is the specified total inlet pressure; and is calculated static inlet pressure.

For compressible flows of gas, isentropic process is used to obtain relations between static pressure and inlet velocity as discussed above.

Note: Although physically unrealistic, for some specially cases total pressure can also be used for outlet flow conditions.

Static Pressure Inlet

Specifying inlet static pressure alone, in principle, does not provide sufficient information for inflow boundaries. For practical purposes, it is provided in Simerics-MP as an option. If the dynamic head is important, user can specify the velocity in addition to the pressure such that it is included as an added momentum source.

 

Outlet Boundary Conditions

At an outlet, the outflow conditions are specified in a similar way to the inflows. In Simerics-MP, the outlet boundary conditions are velocity outlet, volumetric flux outlet and static pressure outlet.

Velocity Outlet

At a velocity outlet, the velocity at the boundary face is specified, and all the flow scalar variables are assumed to be zero-gradient:

5.68

where is the direction normal to outlet boundary.

Volumetric Flux Outlet

The boundary condition of volumetric flux outlet assumes that the outflow is normal to the outlet boundary surface

5.69

where is the specified outlet velocity, is either the user-specified outlet volumetric flux or computed from one of the options in the Resistor Capacitor model.

With the calculated outlet velocity from equation 5.69, the outlet flow boundary conditions are treated in the same way as the velocity outlet conditions.

Static Pressure Outlet

For a static pressure outlet, it only requires the specification of a static (absolute) pressure at the outlet boundary, while zero-gradient conditions apply for all the other flow quantities. Moreover, the value of the specified static pressure is used only when the flow is subsonic. Should the flow become locally supersonic, the specified pressure will no longer be used, and the outlet pressure is, like all the other flow variables, extrapolated from the pressure values in the adjacent interior cells:

	5.70
	5.71

where is the Mach number at the outlet boundary.

 

Symmetry Boundary Conditions

For symmetry boundaries, the flow conditions imposed are zero-gradients:

5.72

where represents all the flow variables.

 

Wall Boundary Conditions

Wall boundary conditions are used to bound fluid and solid regions. In viscous flows, the no-slip boundary condition is enforced at walls. A wall can be stationary or moving (translation or rotation). Let and represents the velocity tangential and normal to a wall, respectively, we have the non-slip wall boundary condition as:

5.73 5.74

where is specified tangential velocity value such as the local transitional and rotating velocity of the wall surfaces.

A wall can also be rigid (non-deforming wall) or flexible (deforming wall). To model a flexible wall, one of the options in Simerics-MP is the Deformation Model.

For a fluid-to-fluid interface or zone, one of the following models may be applied.

Fan Model

The fan model is a lumped parameter model that can be used to determine the impact of a fan with known characteristics upon some larger flow field. In this model, a fan is assumed to be infinitely thin, and across the fan boundary, there exists a pressure rise which is the function of flow velocity.

In Simerics-MP, the fan is modelled as an interior cell-to-cell interface. It employs user-specified empirical DP-Q Curve to describe the relationship between the pressure rise and volumetric flux (velocity) across the interface. It predicts the amount of flow through the fan, without considering the detailed flow through the fan blades. The detailed description on this interface condition can be found in Resistor Capacitor model and Boundary Conditions.

 

Pressure Jump Model

The pressure jump model assumes discontinuous or different pressures act on either side of an interior cell-to-cell interface. As in the fan model, the DP-Q Curve is specified by users to compute the pressure changes (rise or drop) across an interior flow interface. Again, the detailed description on this interface condition can be found in Resistor Capacitor model and Boundary Conditions.

 

Porous Surfaces

Porous Surfaces can be considered as a special pressure jump model based on the porous media model. It is essentially a 1D simplification of the porous media model available for cell zones. This boundary type assumes a porous medium zone with a finite thickness over which the characteristics of velocity and pressure-drop are defined using the Darcy’s law and/or the inertial loss term:

5.75

where

	Velocity magnitude (m/s).
	Thickness of the porous medium (m).
	Pressure drop across the porous medium zone (Pa).
	Quadratic drag coefficient (1/m).
	Permeability (m2).
	Porosity (specified in the Common module).
	Dynamic viscosity (Pa-s).

It may be pointed out that instead of using the full porous media model, this simpler model is often used for its simplicity and better convergence. Examples of uses for the porous jump surfaces include modelling pressure drops through screens and filters, and modelling radiators when the heat transfer is not concerned.