Theory

Layer $i$ (1 at the wall) is $r$ times thicker than layer $i-1$ , equation (1), so the stack is a geometric series. The mesher is given the ratio as expansionRatio together with either the first layer (firstLayerThickness, curvature sizing with the wall function) or the last layer (finalLayerThickness, uniform sizing and low-Re), both relative to the size of the cell just outside the layers (OpenFOAM user guide, 2026).

A larger ratio reaches a given stack thickness with fewer layers but makes a larger jump in cell size inside the boundary layer; a ratio of 1 gives layers of equal thickness. With curvature sizing the ratio also decides how many of the auto layers fit within 0.8 of the wall cell (see Number of prism layers): with a first layer of 0.075 wall cells, 6 layers make 0.74 wall cells at $r = 1.2$ .

The size jump from the outermost layer to the cell outside is also governed by $r$ indirectly: with the last-layer form the outermost layer is 0.5 (wall function) or 0.1 (low-Re) of that cell by construction.

Equations

t_i = t_1\,r^{\,i-1}, \qquad \delta = \sum_{i=1}^{n} t_i = t_1\,\frac{r^{n} - 1}{r - 1} \quad (r \ne 1), \qquad \delta = n\,t_1 \quad (r = 1)

(1)

where	meaning	unit
$t_i$	Thickness of layer $i$ , 1 at the wall	m
$t_1$	First-layer thickness	m
$r$	Expansion ratio	-
$n$	Number of layers	-
$\delta$	Thickness of the stack	m

Default and rule

Default: auto: 1.2 (wall function), 1.15 (low-Re)Computed by the program
Rule: Auto, changed together with the wall treatment: 1.2 with the wall function, 1.15 with low-Re (gentler, because twelve layers have to fit into a thinner stack). A typed value is used as typed.
Source: The values 1.2 and 1.15 are the program's defaults; they are not derived from a measurement or a published correlation. The stack thickness is the geometric series of equation (1), as the program computes it.

Valid range no check by the program; values a little above 1

Values

The program does not limit the value. Values a little above 1 are usual; 1 gives equal layers.

Stack too thick

A larger ratio, or more layers, makes a thicker stack. With curvature sizing on auto the number of layers is reduced to fit; a typed number of layers is not, and gets a warning.

Not measured

Neither 1.2 nor 1.15 was compared with other ratios on a real muffler.

References 1

OpenCFD Ltd. (2026). OpenFOAM user guide. openfoam.com. Web page

Theory

Equations

Default and rule

Valid range no check by the program; values a little above 1

Related 3

References 1