### 1.9.1. Inlet (Subsonic)

#### 1.9.1.1. Mass and Momentum

##### 1.9.1.1.1. Normal Speed in

The magnitude of the inlet velocity is specified and the direction is taken to be normal to the boundary. The direction constraint requires that the flow direction, , is parallel to the boundary surface normal, which is calculated at each element face on the inlet boundary.

##### 1.9.1.1.2. Cartesian Velocity Components

The boundary velocity components are specified, with a non-zero resultant into the domain.

| (1–192)

##### 1.9.1.1.3. Cylindrical Velocity Components

In this case the velocity boundary condition is specified in a local cylindrical coordinate system. Only the axial direction of the local coordinate system must be given and the components of velocity in the r, theta and z directions are automatically transformed by the CFX-Solver into Cartesian velocity components. So, in this case you would specify:

| (1–193)

and the solver will compute the rotation matrix that transforms these components from the cylindrical components to the Cartesian components such that the boundary condition is the same as if Cartesian components were specified:

| (1–194)

For details, see Cylindrical Velocity Components in the CFX-Solver Modeling Guide.

##### 1.9.1.1.4. Total Pressure

The Total Pressure, , is specified at an inlet boundary condition and the CFX-Solver computes the static pressure needed to properly close the boundary condition. For rotating frames of reference one usually specifies the stationary frame total pressure instead.

The direction constraint for the Normal To Boundary option is the same as that for the Normal Speed In option. Alternatively, the direction vector can be specified explicitly in terms of its three components. In both cases, the boundary mass flow is an implicit result of the flow simulation.

##### 1.9.1.1.5. Mass Flow Rate

The boundary mass flow rate is specified along with a direction component. If the flow direction is specified as normal to the boundary, a uniform mass influx is assumed to exist over the entire boundary. Also, if the flow direction is set using Cartesian or cylindrical components, the component normal to the boundary condition is ignored and, again, a uniform mass influx is assumed. The mass influx is calculated using:

| (1–195)

where

| (1–196)

is the integrated boundary surface area at a given mesh resolution. The area varies with mesh resolution because the resolution determines how well resolved the boundary surfaces are. The value of is held constant over the entire boundary surface.

#### 1.9.1.2. Turbulence

For the - turbulence model and Reynolds stress models, the inlet turbulence quantities, and , are either specified directly or calculated using expressions that scale the distribution at the inlet according to the turbulence intensity, , where:

| (1–197)

The inlet flows of and involve advection and diffusion.

| (1–198)

| (1–199)

The advection flows are evaluated using the computed inlet values of and :

| (1–200)

| (1–201)

The diffusion flows are assumed to be negligible compared to advection, and are equated to zero.

##### 1.9.1.2.1. Default Intensity and Autocompute Length Scale

When default inlet turbulence intensity is selected, the value is set to:

| (1–202)

which is an approximate value for internal pipe flow. The inlet turbulence energy is calculated using:

| (1–203)

and the turbulence dissipation calculated using:

| (1–204)

where:

| (1–205)

where is the turbulence intensity factor at the boundary condition. The default value of is 1000.

##### 1.9.1.2.2. Intensity and Autocompute Length Scale

The turbulence intensity is specified directly and the distributions of and at the inlet calculated using the same relationships as the `Default Intensity and Autocompute Length Scale` option.

##### 1.9.1.2.3. Intensity and Length Scale

The turbulence intensity and length scale are both specified. The turbulence kinetic energy and dissipation are calculated using:

| (1–206)

and

| (1–207)

##### 1.9.1.2.4. k and Epsilon

Both and are specified directly:

| (1–208)

and

| (1–209)

When the Reynolds stress model is employed, the Inlet boundary conditions are specified with the same turbulence options as those for the - model. Additionally, the stress tensors are extracted using the computed value of . This is done by assuming the Inlet boundary to be isotropic with respect to the Reynolds stresses, such that the normal stress components are:

| (1–210)

and the shear stress components are equal to zero:

| (1–211)

#### 1.9.1.3. Heat Transfer

##### 1.9.1.3.1. Static Temperature

The inlet static temperature is specified:

| (1–212)

The inlet energy flow involves advection and diffusion.

| (1–213)

The energy flow by advection is a function of the specific total enthalpy, :

| (1–214)

where is computed from the specific static enthalpy, , and the inlet boundary velocity:

| (1–215)

The static enthalpy is computed using the specified value of , the boundary values of and , and the thermodynamic relationship for for the given fluid. The evaluation of depends upon the nature of the mass and momentum specification for the boundary condition.

The Inlet energy flow by diffusion is assumed to be negligible compared to advection, and equated to zero.

##### 1.9.1.3.2. Total Temperature

The boundary advection and diffusion terms for specified total temperature are evaluated in exactly the same way as specified static temperature, except that the static temperature is dynamically computed from the definition of total temperature:

| (1–216)

which for a fluid with constant heat capacity is:

| (1–217)

Additional information on the treatment of variable specific heat is available in Ideal Gas Equation of State.

#### 1.9.1.4. Additional Variables

The value of the Additional Variable is specified explicitly at an inlet:

| (1–218)

The inlet flow of involves advection and diffusion:

| (1–219)

and the advection quantity is evaluated using the specified value of :

| (1–220)

The inlet flow by diffusion is assumed to be negligible compared to advection, and set to zero.

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