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