Atmospheric Inlet - Boundary Conditions

Atmospheric Inlet is a specialised boundary condition for prescribing an atmospheric boundary-layer (ABL) inflow, primarily in Computational Fluid Dynamics (CFD) simulations of environmental and meteorological flows.

The ABL occupies the lowest part of the troposphere, where surface effects dominate. In CFD, we often need fully developed velocity and turbulence profiles at the inlet to reproduce this layer faithfully.

Typical use-cases include:

The Atmospheric Inlet boundary condition imposes log-law, ground-normal profiles for velocity and turbulence quantities in a homogeneous, two-dimensional, dry-air, neutral and equilibrium ABL.

It can be applied to the velocity field and to turbulence variables \(k\), \(\epsilon\) and \(\omega\):

\(u = \frac{u^{*}}{\kappa} \cdot ln( \frac{z - d + z_0}{z_0})\)
\(v=w=0\)

\(k = \frac{(u^{*})^2}{\sqrt{(C_{\mu})}} \cdot \sqrt{C_1 ln(\frac{z - d + z_0}{z_0}) + C_2}\)

\(\epsilon = \frac{(u^{*})^3}{\kappa (z - d + z_0)} \cdot \sqrt{C_1 ln(\frac{z - d + z_0}{z_0}) + C_2}\)

\(\omega = \frac{u^{*}}{\kappa \sqrt{C_{\mu}}} \cdot \frac{1}{z - d + z_0}\)

\(u^{*} = \frac{u_{ref} \kappa}{ln(\frac{z_{ref}+z_0}{z_0})}\)

where:

\(u\) - ground-normal streamwise flow speed profile [\(m/s\)]
\(v\) - spanwise flow speed profile [\(m/s\)]
\(w\) - ground-normal flow speed [\(m/s\)]
\(k\) - Ground-normal turbulent kinetic energy (TKE) profile [\(m^2/s^2\)]
\(\epsilon\) - Ground-normal turbulent kinetic energy (TKE) dissipation rateprofile [\(m^2/s^3\)]
\(\omega\) - Ground-normal specific dissipation rate profile [\(m^2/s^3\)]
\(u^{*}\) - friction velocity [\(m/s\)]
\(\kappa\) - von Karman constant [-]
\(C_\mu\) - model constant [-]
\(z\) - Ground-normal coordinate component [m]
\(d\) - Ground-normal displacement height [m]
\(z_0\) - Aerodynamic roughness length [m]
\(u_{ref}\) - Reference mean streamwise wind speed at \(z_{ref}\) [m/s]
\(z_{ref}\) - Reference height being used in \(u^{∗}\) estimations [m]
\(C_1\) - curve fitting coefficient for profiles [-]
\(C_2\) - curve fitting coefficient for profiles [-]

Atmospheric Inlet is used whenever the domain’s upstream boundary should deliver a fully-developed, neutral atmospheric boundary layer, e.g. wind-comfort studies around buildings, pollutant dispersion over terrain, or vehicle aerodynamics in a cross-wind. Instead of letting the flow build up inside the mesh (which is slow and mesh-dependent), the correct log-law velocity profile is prescribed, matching turbulence levels right at the inlet, so the solution downstream starts from physically realistic wind conditions.

To define Atmospheric Inlet in SimFlow in the boundary condition tap, for velocity or turbulent properties the proper option must be selected from the drop-down menu - Figure 1.

The following parameters must be defined:
Flow Dir. - direction of the air flow
Vertical Dir. - vertical direction (perpendicular to the ground)
\(U_{ref}\) - reference velocity
\(z_{ref}\) - reference height
\(z_{0}\) - roughness height
\(z_{ground}\) - ground location

In this section, we propose boundary conditions that are alternative to Atmospheric Inlet. While they may fulfill similar purposes, they might be better suited for a specific application and provide a better approximation of physical world conditions.