Turbulence Modeling Resource

Defining Boundary Conditions for RANS Turbulence Models

For RANS turbulence models, the inflow boundary conditions are often specified as nondimensional variables. For example, the inflow value of the $ \tilde{\nu} $ variable in the SA model can be set with a nondimensional value of $ \tilde{\nu}/\nu_r = 3$, where $ \nu_r $ is some reference viscosity. Similarly, the boundary condition for turbulent kinetic energy can be expressed using a turbulence intensity, defined as: $$ I = \sqrt{\frac{2 k}{3 u_r^2}}. $$ where $ u_r $ is a reference velocity. An intensity can be specified at the inflow boundary condition, which then is combined with a reference velocity to give a value for $k$. Alternately, the boundary condition for $k$ can be specified using the reference velocity directly as $k/u_r^2$. Similar nondimensional boundary conditions exist for $\varepsilon$, $\omega$, etc.

All of these approaches require some reference condition to nondimensionalize the turbulent variables. This choice may be implicit in a nondimensional CFD code, where the reference conditions are assumed and no dimensional quantities are present. For simple external flows, the choice of reference conditions is straightforward: the freestream conditions are used as the "reference" condition.

The situation grows more complicated for internal flows, jets, or mixing layers. In a planar mixing layer there is a low-speed inflow and a high-speed inflow. Which velocity should be used for the reference velocity, the low-speed or the high-speed? Should the different inlet conditions use different reference velocities? If a single reference velocity is specified, the two sides of the mixing layer will have different turbulence intensities. This can have unintended and surprising consequences.

Consider the following example: The boundary condition on $k$ could be specified as some small value of $ k/u_r^2 = C$, where $C$ is a small constant. This nondimensional value of $k$ could then imposed with a single reference velocity for all boundaries. If a high velocity is selected as a the reference velocity, $ u_r = u_{\mathrm{high}} $, a low-speed inflow with velocity $ u_{\mathrm{low}} $ would then have the inflow value of $ k/u_{\mathrm{low}}^2 = C u_{\mathrm{high}}^2/u_{\mathrm{low}}^2 $. If $ u_{\mathrm{high}} / u_{\mathrm{low}} $ is large, the turbulence intensity at the low-speed inflow can also be large even if C is small.

There are two common approaches in CFD codes:

A single reference condition is specified. For external flows, this is commonly the freestream state. For wind-tunnel simulations, this may be the conditions in the test section.
Each inflow boundary defines its reference conditions separately.

These two different approaches should be kept in mind when performing code-to-code comparisons. Different codes may be imposing different boundary conditions on the turbulent variables, even if density, velocity, or temperature are identical. This has been seen in validation cases where a full wind tunnel is modeled with a converging-diverging nozzle and a test section. Two different CFD codes may specify the inflow differently:

Code #1 may specify the turbulent BCs using the conditions in the test section.
Code #2 may specify the turbulent BCs using the conditions at the inflow plane, upstream of the converging-diverging nozzle.

These two approaches may lead to very different predictions for the turbulent quantities in the test section.

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Page Curators: Christopher Rumsey, Ethan Vogel, Clark Pederson
Last Updated: 07/14/2026