modelSpecies

Information

All of the details below are pertinent to the Fluid model (and the derived Ion model) which inherits from this model. Only some of the details apply to the Solid model because it excludes the transport and exchange of material.

This model is based on the following fixed assumptions:

1. All boundaries are rectangular.
2. The material is orthorhombic. This implies that a gradient which induces diffusion along an axis does not induce diffusion along axes orthogonal to it [Bejan2006, pp. 691–692].
3. The coordinate system (x, y, z) is aligned with the principle axes of transport. For example, if the material is stratified, then the layers must be parallel to one of the planes in the rectilinear grid.
4. The effective transport lengths (kL) are common to material, translational, and thermal transport.
5. There is no radiative heat transfer (or it must be linearized and added to the thermal conductance).
6. Rotational momentum is not stored or transfered.

Figure 1 shows how instances of Species models are connected within a Subregion. A single species in a single phase is called a configuration. The generalized resistances (R) affect the force and rates of chemical exchange and heat flow associated with differences in activity, velocity, and temperature (respectively) between each configuration and a common node. These exchange processes are diffusive. Each resistor generates heat in the Species instance that contains it.

Figure 1: Exchange of a quantity (material, translational momentum, or thermal energy) among configurations (A, B, and C) within a subregion.

Figure 2 shows how a configuration is connected between neighboring instances of a Subregion. Material, translational momentum, and thermal energy are transported by both advection and diffusion. Upstream discretization is applied if it is enabled via the upstreamX, etc. parameters. Like for exchange, the transport resistances are inside the Species model.

Figure 2: Transport of a quantity associated with the same configuration between subregions (1 and 2).

The Species instances within a Phase are combined by Dalton's law of partial pressures (see the Dalton connector), as shown in Figure 3a. The pressures are additive, and each species is assumed to exist at the total extensive volume of the phase. Within a Subregion, the Phases are combined by Amagat's law of partial volumes (see the Amagat connector), as shown in Figure 3b. The volumes are additive, and each species is assumed to exist at the total pressure in the subregion.

a: Pressures of species (A, B, and C) are additive within a phase.	b: Volumes of phases (I, II, and III) are additive within a subregion.
Figure 3: Methods of attributing pressure and volume.

Notes regarding the parameters:

1. The effective transport lengths (kL) may be different that the geometric lengths along the transport axes due to tortouisity. The tortouisity may be anisotropic.
2. If the interval for chemical exchange (τ′), mobility (μ), thermal independity (ν), fluidity (η), or thermal resistivity (θ) is zero, then it should usually be set as final so that index reduction may be performed. If two configurations are connected through their intra, inter, or boundaries connectors and both have zero generalized resistivities for a quantity, then index reduction [Mattsson1993] is necessary.
3. Even if an initialization parameter is not selected for explicit use, it may be used a guess value.
4. If ConsThermo.IC is used for a state (via consMaterial or consEnergy), then the associated initial condition (IC) will be applied forever instead of the corresponding conservation equation.
5. If consEnergy is ConsThermo.steady, then NT∂s/∂t + Mφ∂φ/∂t is treated as zero and removed from the energy balance.
6. If a transport axis is not included (via the outer inclTrans[:] parameter which maps to {inclTransX, inclTransY, inclTransZ} in the Subregion model), then the associated pair of boundaries is removed from the model.
7. The start values of the initial conditions for pressure and temperature (p_IC and T_IC) are the global default pressure and temperature (via the outer instance of the Environment model). The start values of the initial conditions for other intensive properties (ρ_IC, h_IC, and g_IC) are related to the initial pressure and temperature by the characteristics of the species. The start value of the initial condition for the extensive volume (V_IC) is the volume of the subregion. The start value for particle number (N_IC) is related to it via the material characteristics and the initial pressure and temperature. In order to apply other values for any of these initial conditions, it may be necessary to do so before translating the model.

In the boundaries connector array, the transverse translational flow (mΦdot) is only the force due to diffusion. Translational advection is calculated from the current and the velocity. The thermal flow (Q̇) is only the rate of heat transfer due to diffusion. The advection of thermal energy is determined from the current and the thermodynamic state at the boundary.

For the variables that relate to transport, the first index is the axis and the second index is the side. The sides are ordered from negative to positive, according to the Side enumeration. Velocity and force are additionally indexed by the orientation of the momentum with respect to the boundary. The orientations are ordered following the normal axis in Cartesian space, according to the Orient enumeration.

Parameters

Connectors

Components

Contents

Name	Description
Data