.FCSys.Species.Fluid

Information

Fixed assumptions:

1. The gradient of material current is uniform in the direction of the current.
2. The normal translational force on pairs of boundaries is split equally between the boundaries. This includes the body, shear (transverse translational transport), and exchange forces due to intermolecular drag and transfer during chemical reactions and phase change. It excludes the thermodynamic, dynamic (advective normal translational transport), and nonequilibrium (irreversible compression) pressures. It also excludes transient effects since translational momentum is stored at the boundaries (not in the subregion).
3. Nonequilibrium pressure is included in the thermodynamic states at the boundaries. In particular, the specific enthalpy at a boundary is a function of the temperature and the sum of the thermodynamic and nonequilibrium pressures at the boundary (and a possible artifact of dynamic pressure; see the first note regarding parameters). The rate of advection of energy is the product of this specific enthalpy and the material current.

Notes regarding the parameters:

1. If approxVelocity is true, then the normal velocities at the boundaries are calculated from the boundary currents assuming that the density is uniform. This avoids nonlinear systems of equations, but it introduces an artifact of the dynamic pressure into the thermodynamic states at the boundaries. The extra pressure is m Ṅ_i² (v - v_i)/A′, where m is the specific mass, v is the specific volume in the subregion, v_i is the specific volume at the boundary, Ṅ_i is the boundary current, and A′ is the available cross-sectional area. This affects the energy balance via the specific enthalpy at the boundaries.
2. If consTransX, consTransY, or consTransZ is ConsTrans.steady, then the derivative of translational momentum at and normal to the boundaries (proportional to ∂Ṅ_i/∂t) is treated as zero and removed from the translational momentum balances/material transport equations at the corresponding boundaries.
3. If consRot is true, then rotational momentum is conserved without storage (i.e., steady). This means that the shear forces are mapped so that there is no net torque around any rotational axis that has all its boundaries included (i.e., all the boundaries around the perimeter). Rotational momentum is not exchanged among species or directly transported (i.e., uniform or shaft rotation).
4. Upstream discretization is applied by default. The central difference scheme may be used by setting upstreamX, upstreamY, and upstreamZ to true. The typical diffusion properties are such that the Péclet number for the upstream discretization of pressure will be much less (factor of 1/10,000) than the Péclet numbers for translational and thermal transport. Therefore, it may appear that pressure is not advected with the material transport stream.
5. The indices of the translational Nusselt number (Nu_Φ) correspond to the orientation of the translational momentum that is transported, not the axes of material transport.
6. The default thermal Nusselt number is one, which represents pure conduction through the gas. Use 3.66 for internal flow where the boundaries are uniform in temperature or 48/11 (approximately 4.36) if the heat flux is uniform [Incropera2002].

Translational momentum and thermal energy are advected as material is exchanged due to phase change and reactions. This occurs at the velocity (φ) and the specific entropy-temperature product (sT) of the reactants (source configurations), where the reactant/product designation depends on the current conditions.

The advective exchange is modeled via a stream connector (Chemical). The rate of advection of translational momentum is the product of the velocity of the source (φ) and the mass flow rate (Ṁ or mṄ). The rate of thermal advection is the specific entropy-temperature product of the source (sT) times the rate of material exchange (Ṅ). If there are multiple sources, then their contributions are additive. If there are multiple sinks, then translational momentum is split on a mass basis and the thermal stream is split on a particle-number basis.

For more information, please see the Species model.