Turbulence inlet conditions and wall treatment

With turbulence_model: "k_omega_sst", Vanellus derives the turbulence fields at inlets from the API inputs and applies smooth-wall functions at fluid walls. The rest of the model follows the standard k–ω SST formulation.

Inlet turbulence

For inlet speed \(U\), turbulent intensity \(I\), viscosity ratio \(R_\mu\), fluid density \(\rho\), and dynamic viscosity \(\mu\), Vanellus sets turbulent kinetic energy \(k\) and specific dissipation rate \(\omega\) using

\[ k = \frac{3}{2}(U I)^2, \qquad \omega = \frac{\rho k}{R_\mu \mu}. \]

Here, the API turbulent_intensity is \(I\), supplied as a fraction, and viscosity_ratio is \(R_\mu = \mu_t/\mu\), the ratio of turbulent to molecular dynamic viscosity.

The speed used in these equations depends on the boundary condition:

• velocity_inlet uses its prescribed speed, so its tke and sdr conditions remain fixed;
• ambient_pressure_inlet, fan_inlet, and linked_fan_exhaust use the current volumetric face flux, so Vanellus updates tke and sdr on every SIMPLE iteration; and
• ambient_pressure_inlet_outlet does the same on faces currently carrying inflow and applies zero normal gradients on faces carrying outflow.

Ordinary and flow-rate outlets apply zero normal gradients to tke and sdr. A linked-fan intake is also an outlet from the solved domain, so its turbulence conditions are zero-gradient; the linked exhaust supplies the incoming turbulence.

Wall treatment

At every SIMPLE iteration, Vanellus calculates a dimensionless wall coordinate from the finished mesh and current solution:

\[ y^* = \frac{C_\mu^{1/4}\sqrt{k} y}{\nu}. \]

Here, \(y\) is the distance from the wall to the adjacent cell center and \(\nu\) is the local kinematic viscosity. This is not mesh_settings.target_wall_distance: that setting only guides mesh creation, while \(y^*\) changes with the solved tke field.

Vanellus then applies these wall treatments:

• Momentum: the wall is no-slip. Turbulent viscosity is zero in the viscous branch and follows a smooth-wall log law in the log-law branch.
• Turbulent kinetic energy: tke is zero at the wall. Production in the adjacent cell is zero in the viscous branch and follows the smooth-wall log law in the log-law branch.
• Specific dissipation rate: sdr uses the viscous form close to the wall and the log-law form farther out. Wall-adjacent cell values are imposed by this wall function rather than obtained from the ordinary cell equation.
• Heat transfer: turbulent thermal conductivity uses a Jayatilleke wall function with the fluid Prandtl number and a turbulent Prandtl number of 0.85. It is zero in the thermal viscous branch and follows the thermal log law above its transition point.

The momentum functions use a smooth-wall constant of 5.0; wall roughness is not an API input. For wall-adjacent sdr and turbulent-production values, a cell touching multiple wall faces receives the average of their contributions.

See also

• Flow boundary conditions shows the complete field conditions at each inlet and outlet.
• Mesh resolution and controls explains how target_wall_distance influences the generated mesh.
• Field initialization and starting guesses explains how Vanellus seeds tke and sdr before the first iteration.
• API reference lists the accepted turbulence fields and limits.