Fixed Value - Boundary Condition

The image depicts a 2D computational fluid dynamics simulation domain. In this example, the boundary condition on the left boundary patch is set to a constant velocity of 1 m/s along the channel’s axis. As the flow field develops within the domain along the flow direction, the value changes near the wall but remains constant at the entrance boundary.

It is worth noting that on the border we can define not only a single constant value, but also a profile that varies along the boundary. The Fixed Value ensures that the specified value or profile remains unchanged throughout the simulation.

The above animation demonstrates the Fixed Value used in a transient simulation. The left and right domain boundaries are at fixed temperatures set to 300K and 400K, respectively, while the bottom and top boundaries are insulated. The temperature profile maintains the fixed temperatures at the sides as time progresses.

The generic inlet flux \(J\) is the sum of diffusive and advective flux:

Fick’s law typically describes the diffusive flux and the total inlet flux can be described as:

where \(D\) is the diffusion coefficient and \(\phi\) is the transported scalar.

This equation implicates the interesting consequence. When the Fixed Gradient boundary condition is applied, only the diffusive part is controlled, but not the advective flux. Hence, the total flux will not be equal to the prescribed fixed gradient. The same applies when Fixed Value is used. In such a case, the advective flux will be defined but not the diffusive one.

In case of typical heat transfer problem, when Fixed Gradient is applied to the wall, the advective flux disappears (zero velocity at the wall) and the prescribed fixed gradient on the wall is proportional to the total heat flux. This, however, is not true when we have an inlet into the domain, with a specified velocity. It is important to understand that the total flux includes advective and diffusive terms. Misunderstanding might appear for so-called convective inlet boundary condition.

Let’s assume that we want to prescribe velocity and a scalar value \(\phi\) (for example, gas component concentration) at the inlet. Assuming a steady state solution, we would expect to get the same total mass flux associated with the given gas component exiting the domain. However, it is important to remember that the total flux takes the advective and diffusive components:

Therefore, the diffusive flux might also increase the concentration entering the fluid domain. The effect of increased concentration will be even higher with decreasing velocity at the inlet. As long as the inlet velocity is significant, the diffusive flux can be neglected, because inlet values quickly reach the first cell, making the gradient very low and convective flux dominates.

Example applications: car, aircraft aerodynamics, wind tunnel experiment

These types of simulations can be solved using the simpleFoam (solver) This solver has two basic independent variables: pressure and velocity. Additionally, turbulence-related variables can be defined. The Fixed Value can be applied to the domain inlet to represent a constant inlet velocity. It can also be applied to the domain outlet to simulate a constant pressure outflow, such as atmospheric pressure.

Example applications: free surface flows, ship hull calculations, sloshing, ship hydrodynamics, wave impact on structures

Problems that require resolving the sharp interface between two fluids, such as water and air, can be calculated using the interFoam (solver) The phase fraction, represented by \(\alpha\), differentiates between the fluids. The Fixed Value is typically used to define the fixed level of the first phase at the entry to the domain. For example, this boundary condition can be employed to set the constant water level in a pipe inlet.

Example applications: room ventilation, room heating, electronic cooling, atmospheric flows

The Fixed Value defines the temperature at a given boundary. This may represent, for example, the temperature of a hot radiator or the inlet temperature of air in a ventilation system.

Example applications: industrial furnaces, jet engines, chemical process industry (chemically reacting foams)

The reactingFoam (solver) can be applied for chemically reacting flows that involve heat transfer and chemical reactions with the combustion. In this application, the Fixed Value defines, for example, the constant gas composition at a given boundary.

When a scalar value is defined, such as pressure or temperature, only a single value needs to be specified. In the example below, a constant temperature is set at the inlet of the domain.

In the case of a vector field, the user must specify three components in the major directions: x, y, and z. Example below illustrates how the Fixed Value is applied to the inlet boundary.

The Fixed Value is a primitive boundary condition, that effectively applies a solution value to the domain boundary, and later on this value is maintained throughout the simulation. However, since it directly imposes the solution and maintains it throughout the simulation, users might take advantage of the initial condition patching to overwrite values in a specified boundary region.

This feature can be used, for example, to define non-uniform concentration at the inlet, where the user wants to have a non-zero concentration only in the center of the inlet patch and a zero concentration on the rest of the patch. In such a scenario, we would define the Fixed Value with concentration equal to 0, and then patch only the center of the inlet patch (marked using a geometry) with the desired concentration value.

The patching operation is available in Patch Initialization.