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7.5.3 Calculation Procedure at Mass Flow Inlet Boundaries

When mass flow boundary conditions are used for an inlet zone, a velocity is computed for each face in that zone, and this velocity is used to compute the fluxes of all relevant solution variables into the domain. With each iteration, the computed velocity is adjusted so that the correct mass flow value is maintained.

To compute this velocity, your inputs for mass flow rate, flow direction, static pressure, and total temperature are used.

There are two ways to specify the mass flow rate. The first is to specify the total mass flow rate, $\dot{m}$, for the inlet. The second is to specify the mass flux, $\rho v_n$ (mass flow rate per unit area). If a total mass flow rate is specified, FLUENT converts it internally to a uniform mass flux by dividing the mass flow rate by the total inlet area:


 \rho v_n = \frac{\dot{m}}{A} (7.5-1)

If the direct mass flux specification option is used, the mass flux can be varied over the boundary by using profile files or user-defined functions. If the average mass flux is also specified (either explicitly by you or automatically by FLUENT), it is used to correct the specified mass flux profile, as described earlier in this section.

Once the value of $\rho v_n$ at a given face has been determined, the density, $\rho$, at the face must be determined in order to find the normal velocity, $v_n$. The manner in which the density is obtained depends upon whether the fluid is modeled as an ideal gas or not. Each of these cases is examined below.



Flow Calculations at Mass Flow Boundaries for Ideal Gases


If the fluid is an ideal gas, the static temperature and static pressure are required to compute the density:


 p = \rho R T (7.5-2)

If the inlet is supersonic, the static pressure used is the value that has been set as a boundary condition. If the inlet is subsonic, the static pressure is extrapolated from the cells inside the inlet face.

The static temperature at the inlet is computed from the total enthalpy, which is determined from the total temperature that has been set as a boundary condition. The total enthalpy is given by


 h_0 (T_0)= h(T) + \frac{1}{2} v^2 (7.5-3)

where the velocity is related to the mass flow rate given by Equation  7.5-1. Using Equation  7.5-2 to relate density to the (known) static pressure and (unknown) temperature, Equation  7.5-3 can be solved to obtain the static temperature.



Flow Calculations at Mass Flow Boundaries for Incompressible Flows


When you are modeling incompressible flows, the static temperature is equal to the total temperature. The density at the inlet is either constant or readily computed as a function of the temperature and (optionally) the species mass fractions. The velocity is then computed using Equation  7.5-1.



Flux Calculations at Mass Flow Boundaries


To compute the fluxes of all variables at the inlet, the flux velocity, $v_n$, is used along with the inlet value of the variable in question. For example, the flux of mass is $\rho v_n$, and the flux of turbulence kinetic energy is $\rho k v_n$. These fluxes are used as boundary conditions for the corresponding conservation equations during the course of the solution.


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