# Boundary conditions

## General boundary conditions

The following inputs are defined using the prefix `bc`:

| Description | Type | Default
--- | --- | --- | ---
regions | Regions used to define boundary conditions. | Strings | None
delp_dir | Direction for specified pressure drop. Note that this direction should also be periodic. | Int | 0
delp | Pressure drop (Pa) | Real | 0
po_no_par_out | Force particles to bounce back rather than exiting at pressure outflows. | Int | 0

The type of the boundary conditions in the BC region must be defined with the prefix `bc`:

| Description | Type | Default
--- | --- | --- | ---
[region_name] | Specify boundary condition type. Options: `pi` - pressure inflow `po` - pressure outflow `mi` - mass inflow `eb` - embedded boundary - for inhomogeneous Dirichlet BCs of temperature or fluid velocity (mass inflow) on the contained EBs | String | None

### Fluid settings

For each boundary condition region, the fluid inputs are defined using the prefix `bc.[region_name].[fluid_name]`:

| Description | Type | Default
--- | --- | --- | ---
volfrac | Volume fraction [required if bc type is `mi`] | Real | 0
density | Fluid density [required if bc type is `mi` or `pi`] | Real | 0
pressure | Fluid pressure [required if bc type is `po' or ``pi`] | Real | 0
temperature | Fluid temperature [required if bc type is `mi` or `pi`] | Real | 0
velocity | Velocity components [required if bc type is `mi` and `volflow` or `massflow` not specified] | Reals | 0 0 0
volflow | Volumetric flow rate [required if bc type is `mi` and `velocity` or `massflow` not specified] | Real | 0
massflow | Mass flow rate [required if bc type is `mi` and `velocity` or `volflow` not specified] | Real | 0
species.[species_name] | Species species_name mass fraction [required if solve_species`=1 and bc type is ``mi` or `pi`] | Real | 0

Note that for a `mi` only one of `velocity` or `volflow` or `massflow` should be specified. Additionally, velocity can be specified as a vector or a scalar, the latter of which is applied normal to the inflow plane, as with volflow and massflow.

Below is an example for specifying boundary conditions for fluid (`fluid`).

    bc.regions = inflow outflow

    bc.inflow = mi
    bc.inflow.fluid.volfrac     =  1.0
    bc.inflow.fluid.density     =  1.0
    bc.inflow.fluid.velocity    =  0.015  0.0  0.0
    bc.inflow.fluid.temperature =  300
    bc.inflow.fluid.species.O2  =  0.0
    bc.inflow.fluid.species.CO  =  0.5
    bc.inflow.fluid.species.CO2 =  0.5

    bc.outflow = po

    bc.outflow.fluid.pressure =  0.0

Below is an example for specifying a normal inflow velocity magnitude for a region eb-flow.

    bc.regions = eb-flow

    bc.eb-flow = eb

    bc.eb-flow.my_fluid.volfrac  = 1.0
    bc.eb-flow.my_fluid.velocity = 0.1

Below is an example where only specific cells are imposed a velocity inflow in the x-direction.

    bc.regions = eb-flow

    bc.eb-flow = eb

    bc.eb-flow.eb.normal_tol = 3.0
    bc.eb-flow.eb.normal =  0.9848  0.0000  0.1736  # 10 deg

    bc.eb-flow.my_fluid.volfrac  = 1.0
    bc.eb-flow.my_fluid.velocity = 0.1  0.0  0.0

### Solids settings

For each inflow boundary condition region, general solids inputs are defined using the prefix `bc.[region_name]`:

| Description | Type | Default
--- | --- | --- | ---
solids | Name of solid type in BC region. Only one solid is allowed in an BC region. | String | None

Warning

Mass inflow boundary conditions, `bc.[region_name] = mi`, only support PIC parcels. EB inflow boundary conditions, `bc.[region_name] = eb`, support DEM particles and PIC parcels.

For inflow boundary conditions , the solid inputs are defined using the prefix `bc.[region_name].[solid_name]`: Note that diameter distributions must define a weighting type, please refer to ReferenceParticleDistributions.

| Description | Type | Default
--- | --- | --- | ---
volfrac | Volume fraction | Real | 0
temperature | Temperature | Real | 0
species.[species_name] | Mass fraction of `species_name` | Real | 0
velocity | Velocity components | Reals | 0 0 0
volflow | Volumetric flow rate. | Real | 0
massflow | Mass flow rate. | Real | 0
diameter | Method to specify particle diameter in the IC region. This is only used for auto-generated particles. Options: `constant` - specified constant `uniform` - uniform distribution `normal` - normal distribution `custom` - user-defined distribution | String | None
type | Distribution weighting. Options: `number-weighted` `volume-weighted` | String | N/A
bins | Number of bins used when discretizing the distribution to approximate the number of particles within an initial condition region. | Int | 64
diameter.constant | Monodisperse (single valued) particle diameter. Required for `constant` distributions. | Real | 0
diameter.mean | Distribution mean. Required for `normal` distributions. | Real | 0
diameter.std | Distribution standard deviation. Required for `normal` distributions. | Real | 0
diameter.min | Minimum diameter to clip distribution. Required for `normal` distributions and `uniform` distributions. | Real | 0
diameter.max | Maximum diameter to clip distribution. Required for `normal` distributions and `uniform` distributions. | Real | 0
diameter.custom | File name that specifies either the cumulative or probability distribution. Required for `custom` distributions. | String | None
density | Method to specify particle density in the IC region. This is only used for auto-generated particles. Options: `constant` - specified constant `uniform` - uniform distribution `normal` - normal distribution `custom` - user-defined distribution | String | None
density.constant | Monodisperse (single valued) particle density. Required for `constant` distributions. | Real | 0
density.mean | Distribution mean. Required for `normal` distributions. | Real | 0
density.std | Distribution standard deviation. Required for `normal` distributions. | Real | 0
density.min | Minimum diameter to clip distribution. Required for `normal` distributions and `uniform` distributions. | Real | 0
density.max | Maximum diameter to clip distribution. Required for `normal` distributions and `uniform` distributions. | Real | 0
density.custom | File name that specifies either the cumulative or probability distribution. Required for `custom` distributions. | String | None

## Transient boundary conditions

Velocity, temperature, and pressure boundary conditions may also be specified as a function of time simply by adding a new column. The time value is entered in the new first column. We can make the mi boundary condition above time-dependent by replacing:

    bc.inflow.fluid.velocity    =  0.0  0.0    0.0  0.0
    bc.inflow.fluid.velocity    =  3.0  0.015  0.0  0.0

    bc.inflow.fluid.temperature =  0.0  300
    bc.inflow.fluid.temperature =  2.99 300
    bc.inflow.fluid.temperature =  3.0  500
    bc.inflow.fluid.temperature =  4.0  500
    bc.inflow.fluid.temperature =  4.01 300

In the above example, the inflow velocity is accelerated from zero to its final value over a period of three seconds. Linear interpolation is used in between discrete time values and held constant at the last time value. The temperature sees an abrupt spike from 300 up to 500 at t = 3s and then back down again after 4s. Note that the timestep is not adjusted to sync with transient BCs.

## Thermal boundary conditions

Boundary conditions can be applied to embedded boundaries (EBs). For example, a constant wall temperature can be imposed on the entire EB or restricted to a specific region.

To apply a boundary condition to only a portion of an EB, a face normal vector and tolerance can be specified. This allows the condition to be applied only to EB faces whose normals align with the specified direction within a given angular tolerance. The following inputs are defined using the prefix `bc.[region_name].eb`:

| Description | Type | Default
--- | --- | --- | ---
normal | [Optional] Specifies the target face normal direction. Only EB faces whose normals are parallel (within the specified tolerance) will have the boundary condition applied. | Reals | 0 0 0
normal_tol | [Optional] Angular tolerance (in degrees) used with `eb.normal` to select EB faces. A value of 0 requires exact alignment. | Real | 0

The following table lists the thermal boundary condition options that can be applied to embedded boundaries (EBs), with inputs defined using the prefix `bc.[region_name].eb`.

| Description | Type | Default
--- | --- | --- | ---
temperature | Specify a wall temperature model for the embedded boundary. Options: `adiabatic` - no heat flux through the wall `constant` - impose a constant temperature along the EB. `CHT-1D` - compute a temperature for the wall using the 1D conjugate heat transfer model. | String | adiabatic
temperature.constant | Constant wall temperature. A valid is required for `constant` EB temperature model. | Real | None

The conjugate heat transfer model approximates heat transfer through the embedded boundary using one-dimensional, steady-state conduction. The external environment is treated as a thermal reservoir with a constant temperature in both space and time. This approach is illustrated in Fig. 9, where heat flows through a series of thermal resistances: from the fluid to the inner wall surface, through the wall, and finally to the environment. The direction of heat transfer—into or out of the system—is governed by the temperature gradient between the fluid and the surroundings.

Fig. 9 Schematic of the conjugate heat transfer boundary condition.

An effective resistance is calculated based on the convective heat transfer coefficient between the fluid and wall, \(h_{int}\), conduction through the wall with thickness \(L_w\) and thermal conductivity \(\kappa_w\), and convective heat transfer from the exterior wall to the environment \(h_{ext}\).

\[R_{eff} = \left( \frac{1}{h_{int}} + \frac{L_w}{\kappa_w} + \frac{1}{h_{ext}} \right)^{-1}\]

The interior wall temperature is determined by balancing the heat flux contributions from internal convection, wall conduction, and external convection, resulting in a closed-form expression based on the effective thermal resistance of the system.

\[T_{w,int} = T_f - \frac{1}{h_{int}}\left[ \frac{T_f - T_{\infty}}{R_{eff}} \right]\]

The model settings are defined using the prefix `bc.[region_name].eb.temperature.CHT-1D`:

| Description | Type | Default
--- | --- | --- | ---
T_env | Environment temperature | Real | None
h_int | Heat Transfer Coefficient (fluid–wall, internal) Specifies the convective heat transfer coefficient [W/m² K] between the fluid and adjacent solid walls (EBs) located within the interior of the computational domain. | Real | None
h_ext | Heat Transfer Coefficient (wall-environment, external) Specifies the convective heat transfer coefficient [W/m² K] between the wall and the external environment. | Real | None
wall.conductivity | The thermal conductivity of the wall. | Real | None
wall.thickness | Wall thickness. | Real | None
phase_averaged_temperature | Use a phase averaged temperature for simulations containing particles. The phase averaged temperature is computed as the volume fraction weighted sum of the fluid and averaged particle temperatures. \(T = \varepsilon_f T_f + (1-\varepsilon_f) \overline{T}_p\) The averaged particle temperature is computed by depositing the volume-averaged particle temperature to the grid. \(\overline{T}_p = \left( {\sum_p^{N_p} T_p V_p} \right) / \left( {\sum_p^{N_p} V_p} \right)\) | Bool | false

Below is an example for specifying a constant temperature boundary condition in the `hot-walls` region.

    bc.regions = hot-wall

    bc.hot-walls = eb
    bc.hot-walls.eb.temperature = constant
    bc.hot-walls.eb.temperature.constant = 800