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7.3.3 Calculation Procedure at Pressure Inlet Boundaries

The treatment of pressure inlet boundary conditions by FLUENT can be described as a loss-free transition from stagnation conditions to the inlet conditions. For incompressible flows, this is accomplished by application of the Bernoulli equation at the inlet boundary. In compressible flows, the equivalent isentropic flow relations for an ideal gas are used.



Incompressible Flow Calculations at Pressure Inlet Boundaries


When flow enters through a pressure inlet boundary, FLUENT uses the boundary condition pressure you input as the total pressure of the fluid at the inlet plane, $p_0$. In incompressible flow , the inlet total pressure and the static pressure, $p_s$, are related to the inlet velocity via Bernoulli's equation:


 p_0= p_s + \frac{1}{2} \rho v^2 (7.3-5)

With the resulting velocity magnitude and the flow direction vector you assigned at the inlet, the velocity components can be computed. The inlet mass flow rate and fluxes of momentum, energy, and species can then be computed as outlined in Section  7.4.3.

For incompressible flows, density at the inlet plane is either constant or calculated as a function of temperature and/or species mass fractions, where the mass fractions are the values you entered as an inlet condition.

If flow exits through a pressure inlet, the total pressure specified is used as the static pressure. For incompressible flows, total temperature is equal to static temperature.



Compressible Flow Calculations at Pressure Inlet Boundaries


In compressible flows , isentropic relations for an ideal gas are applied to relate total pressure, static pressure, and velocity at a pressure inlet boundary. Your input of total pressure, $p'_0$, at the inlet and the static pressure, $p'_s$, in the adjacent fluid cell are thus related as


 \frac{p'_0 + p_{\rm op}}{p'_s + p_{\rm op}} = \left ( 1 + \frac{\gamma - 1}{2} {\rm M}^2 \right )^{\gamma / (\gamma - 1)} (7.3-6)

where


 {\rm M} \equiv \frac{v}{c} = \frac{v}{\sqrt{\gamma R T_s}} (7.3-7)

$c$ = the speed of sound, and $\gamma = c_p/c_{\rm v}$. Note that the operating pressure, $p_{\rm op}$, appears in Equation  7.3-6 because your boundary condition inputs are in terms of pressure relative to the operating pressure. Given $p'_{0}$ and $p'_{s}$, Equations  7.3-6 and  7.3-7 are used to compute the velocity magnitude of the fluid at the inlet plane. Individual velocity components at the inlet are then derived using the direction vector components.

For compressible flow, the density at the inlet plane is defined by the ideal gas law in the form


 \rho = \frac{p_s' + p_{\rm op}}{RT_s} (7.3-8)

The specific gas constant, $R$, is computed from the species mass fractions, $Y_i$, that you defined as boundary conditions at the pressure inlet boundary. The static temperature at the inlet, $T_s$, is computed from your input of total temperature, $T_0$, as


 \frac{T_0}{T_s} = 1 + \frac{\gamma - 1}{2} {\rm M}^2 (7.3-9)


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