Wall roughness height

The equivalent sand-grain roughness height of the wall. 0 is a hydraulically smooth wall; a positive value switches the wall's turbulent-viscosity condition to the rough-wall function, which lowers the log law and raises the wall friction.

Last updated 2026-11-03

Theory

With the wall-function treatment, a smooth wall uses Spalding's law of the wall (nutUSpaldingWallFunction), continuous from the viscous sublayer to the logarithmic region (Spalding, 1961). When $k_s > 0$ the program writes OpenFOAM's nutkRoughWallFunction instead (OpenFOAM user guide, 2026), with the same log-law constants $\kappa = 0.41$ , $E = e^{\kappa B} = 8.43$ ( $B = 5.2$ ) and with $k_s$ and $C_s$ (Roughness constant). That condition divides $E$ by a roughness function of the roughness Reynolds number $k_s^+$ , equation (1), which shifts the logarithmic velocity profile down by $\Delta B$ , equation (2): the wall carries more shear for the same near-wall velocity. Below $k_s^+ \approx 2.25$ the wall behaves as smooth; above about 90 it is fully rough, where $\Delta B = \frac{1}{\kappa}\ln(1 + C_s k_s^+)$ .

The rough-wall function is a log-law wall function, not Spalding's blended law: it assumes the first cell lies in the logarithmic region ( $y^+ \gtrsim 30$ ), and a wall with roughness should be meshed accordingly (Target y+). With the low-Re treatment (Wall treatment) the roughness is not applied (nutLowReWallFunction).

Roughness applies to outer walls and to both sides of internal walls (baffles). It does not affect perforated walls.

Equations

k_s^+ = \frac{u_\tau k_s}{\nu}, \qquad u_\tau = C_\mu^{1/4}\sqrt{k}

(1)

\frac{u}{u_\tau} = \frac{1}{\kappa}\ln\!\left(\frac{E\,y^+}{f_r(k_s^+, C_s)}\right) = \frac{1}{\kappa}\ln y^+ + B - \Delta B, \qquad \Delta B = \frac{1}{\kappa}\ln f_r

(2)

where	meaning	unit
$k_s$	Equivalent sand-grain roughness height (this setting)	m
$k_s^+$	Roughness Reynolds number	-
$u_\tau$	Friction velocity from the wall-cell $k$	m/s
$\nu$	Kinematic viscosity	m²/s
$\kappa, E, B$	Log-law constants 0.41, 8.43, 5.2	-
$f_r$	Roughness function of OpenFOAM's rough-wall condition	-
$\Delta B$	Downward shift of the log law	-

Default and rule

Default: 0 m (smooth wall)
Rule: 0 m (smooth).
Source: The log-law constants ( $\kappa$ 0.41, $B$ 5.2) are the program's choice. The rough-wall condition and its roughness function are OpenFOAM's nutkRoughWallFunction (OpenFOAM user guide, 2026); the exact transitional form of $f_r$ is that of the OpenFOAM implementation and is described here only qualitatively.

Valid range ≥ 0; ignored with the low-Re wall treatment

Typical values

Drawn steel tube about 0.00002-0.00005 m, commercial steel about 0.00005 m, rusted or welded sheet up to about 0.0005 m (indicative handbook values).

Not Spalding

A positive roughness replaces the continuous Spalding wall function by a log-law wall function; a first cell in the viscous or buffer layer then gives a wrong wall shear.

Low-Re treatment

Ignored when the wall is resolved to $y^+ \approx 1$ .

Theory

Equations

Default and rule

Valid range ≥ 0; ignored with the low-Re wall treatment

Related 4

References 2