Atmospheric Wall Function - Boundary Condition

Atmospheric Wall Function - Boundary Condition   Description

Atmospheric Wall Function is a boundary condition used for the turbulent viscosity \(\nu_t\) at the wall in atmospheric boundary layer simulations. It is a specialized condition, designed to represent the effects of turbulence at the ground level in simulations of atmospheric flows, typically within the context of Large Eddy Simulations (LES) or Reynolds-Averaged Navier-Stokes (RANS) simulations.

Unlike other rough wall functions available in SimFlow, where roughness is typically characterized by the diameter of sand grains, this approach does not assume homogeneous conditions. Instead, it considers a much larger scale of roughness, represented by the roughness length, denoted as \(z_0\). This roughness length is the height at which the logarithmic wind profile theoretically reaches zero.

Atmospheric Wall Function - Boundary Condition   Understanding Atmospheric Wall Function

The calculations of turbulent viscosity \(\nu_t\) are based on turbulent kinetic energy \(k\):

\[\nu_{t_w} = \nu_w \left( \frac{y^+ \kappa}{\ln \left( \max \left( E^\prime, 1 + 10^{-4} \right) \right) } - 1 \right)\]
\[u^* = C_\mu^{1/4} \sqrt{k}\]
\[y^+ = \frac{u^* y}{\nu_w}\]
\[E^\prime = \frac{y + z_0}{z_0}\]
\[u = \frac{u^*}{\kappa} \ln \left(\frac{z + z_0}{z_0}\right)\]
where:
  • \(\nu_{t_{w}}\) - Turbulent Viscosity at the Wall \([m^2/s]\)
  • \(\nu_t\) - Kinematic Viscosity of Fluid Near the Wall \([m^2/s]\)
  • \(y^+\) - Non-Dimensional Wall Distance (Wall Units) \([-]\)
  • \(\kappa\) - von Kármán Constant \([-]\)
  • \(u^*\) - Friction Velocity \([m/s]\)
  • \(C_\mu\) - Empirical Model Constant \([-]\)
  • \(k\) - Turbulent Kinetic Energy \([m²/s²]\)
  • \(z_0\) - Surface Roughness Length \([m]\)
  • \(E^\prime\) - Dimensionless Roughness Parameter \([-]\)

Atmospheric Wall Function - Boundary Condition   Application & Physical Interpretation

Atmospheric Wall Function is applied at the ground or terrain boundary in atmospheric simulations where the flow interacts with the Earth’s surface.

Atmospheric Wall Function in Wind Comfort applications

Example applications: Wind around Buildings Analysis

These types of simulations can be solved using the simpleFoam (solver). Atmospheric Wall Function is applied together with other turbulent quantities on the walls in order to model the Atmospheric Boundary Layer (ABL).

Example Boundary Conditions set for Wind Comfort applications
PhysicsPressureVelocityk\(\epsilon\)\(\nu_t\)

Ground

Zero Gradient

Atmospheric Inlet

Standard Wall Function

Standard Wall Function

Atmospheric Wall Function

Example usage of Atmospheric Wall Function for Wind Comfort applications in SimFlow
ValidationDescription

Wind Analysis

SimFlow validation case with detailed description of wind comfort CFD analysis

Atmospheric Wall Function - Boundary Condition   Atmospheric Wall Function in SimFlow

To define Atmospheric Wall Function on the wall boundary, the proper option must be selected from the drop-down menu in the Turbulence tab - Figure 1. Please note that the Turbulence tab will be visible only if the turbulence equations are activated (Turbulence panel).

Atmospheric Wall Function in SimFlow
Figure 1. Atmospheric Wall Function in SimFlow

Atmospheric Wall Function - Boundary Condition   Atmospheric Wall Function - Alternatives

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

Boundary ConditionDescription

Rough Wall Function

to model the effects of surface roughness on turbulent flow near walls, based on sand-grain diameter and velocity calculations

Rough Wall Function (k)

to model the effects of surface roughness on turbulent flow near walls, based on sand-grain diameter and turbulent kinetic energy calculations