Stagnation Inlet

The stagnation inlet boundary is an inlet condition that is well-posed for compressible flows, although it is equally valid for incompressible flows.

The stagnation conditions refer to the conditions in an imaginary plenum, far upstream, in which the flow is completely at rest. For incompressible flows, Bernoulli's equation is used to relate total pressure, static pressure, and velocity magnitude. For compressible ideal-gas flows, isentropic relations are used, and characteristic variables determine the propagation properties of the flow. In compressible flow, the total pressure, total temperature, and flow direction are always used to obtain the inlet flow conditions.

Supersonic Flow

Confusion often arises, however, about the need to specify the static pressure at the inlet, termed supersonic static pressure in Simcenter STAR-CCM+. The characteristics of the flow dictate that when the inlet flow is supersonic, all information comes from upstream conditions, including static pressure. This flow regime is termed hyperbolic, and the situation dictates that supersonic static pressure must be appropriately specified. When the inlet flow is subsonic, the flow regime is termed elliptic, which means that the static pressure is obtained from the downstream flow. In this case, the value that is specified for supersonic static pressure is ignored, and ideally, its value could be left at the default. This is not always advisable, as in some situations the inlet flow can momentarily become supersonic during the simulation iteration. If this occurs, and the supersonic static pressure is improperly specified, the solution might diverge. In these situations, it is recommended that isentropic relations be used to specify a value for supersonic static pressure that corresponds to a slightly supersonic Mach number.

As an example of using isentropic relations to set the supersonic static pressure, consider the isentropic relation for the ratio of static pressure to total pressure in an ideal gas:

Figure 1. EQUATION_DISPLAY

\frac{p_{t}}{p} = {1 + \frac{(γ - 1)}{2} M^{2}}^{γ / (γ - 1)}

(87)

In this relation, $p$ and $p_{t}$ are the absolute static pressure and absolute total pressure, respectively, and $M$ is the Mach number. To obtain the static pressure, one could set $M = 1.02$ for a mildly supersonic flow and use the known total pressure to compute the required value.

For more information, see Stagnation Inlet.

Multiphase Flow

The formulation for multiphase flow is not as well-defined as for single phase flow, as the isentropic relations that relate pressure to temperature do not hold for a multiphase mixture. The same theory is extended to compressible flow, but is expected to break down at high speeds.

The stagnation flow inlet allows you to specify the total pressure of the mixture with the volume fraction per phase at the inlet boundary. For multiphase flow, the total pressure is defined as the sum of the static pressure with the dynamic pressure of each phase weighted with the volume fraction:

Figure 2. EQUATION_DISPLAY

p_{t} = p_{s} + \sum_{k = 1}^{n} \frac{1}{2} α_{k} ρ_{k} v_{k}^{2}

(88)

where $α_{k}$ is the k-phase volume fraction, $ρ_{k}$ is the phase density, and $v_{k}$ is the velocity of the k-phase. This relation is exact for constant density and approximate for compressible and non-isothermal cases.

Applications

The inlet to a simulation of internal flows for which the stagnation conditions are known.

Compatibility

Should be used in combination with pressure outlet boundaries
A stagnation boundary cannot exist in the same continuum as a flow split outlet boundary.