Grazing velocity

Selects where the grazing velocity $V_\infty$ of the grazing correction comes from: the solved velocity in the core of the tube next to each wall face (CFD), or one Mach number for the whole wall (Grazing Mach number (flow)).

Last updated 2026-11-03

Theory

Rogers and Hersh define the grazing velocity as the free-stream velocity past the orifice, outside the wall boundary layer (Rogers and Hersh, 1975). The velocity ON the perforated wall is not that: the cyclic baffle face averages the fast tube side with the slow chamber side, which would lower $V_\infty$ and therefore $K$ .

With "CFD, tube core":

At each $K$ evaluation the solver writes two extra velocity samples, at a distance $\delta$ from the wall along each side's own face normal (equation 1): one inside the tube and one in the chamber.
Each wall face takes the tangential speed of the nearest sample point on each side, and the faster side is used as $V_\infty$ , equation (2).
The tube radius comes from a cylinder fit to the exported wall surface; when the wall is not tube-shaped, $\delta = 5$ mm.
If the core samples are missing, the wall's own tangential velocity is used and the K record says so (the grazing speed, and therefore $K$ , is then low).

With "Mach number", $V_\infty$ is the typed Mach number times the speed of sound at the material temperature, the same for every face.

Equations

\delta = 0.5\,R_{tube} \quad (5\ \text{mm when the wall is not tube-shaped})

(1)

V_{\infty,f} = \max\left(\lvert\mathbf{U}_{t}\rvert_{a,f},\ \lvert\mathbf{U}_{t}\rvert_{b,f}\right) \quad \text{(CFD)}, \qquad V_\infty = M\,c(T) \quad \text{(Mach)}

(2)

where	meaning	unit
$\delta$	Distance of the core samples from the wall	m
$R_{tube}$	Radius of the tube fitted to its surface	m
$\lvert\mathbf{U}_t\rvert_{a,f}, \lvert\mathbf{U}_t\rvert_{b,f}$	Tangential speed at the sample of side a / b nearest to face $f$	m/s
$M$	Typed grazing Mach number	-
$c(T)$	Speed of sound at the material temperature	m/s

Default and rule

Default: CFD, tube core
Rule: CFD, tube core.
Source: The definition of $V_\infty$ : (Rogers and Hersh, 1975). The core sampling is the program's way of obtaining that free-stream velocity, because the face value on the baffle includes the slow chamber side. Sampling uses OpenFOAM's surfaces function object (patchInternalField, offsetMode normal) (OpenFOAM user guide, 2026).

Valid range CFD, tube core | Mach number

When to use Mach

When the solved core flow is not representative (for example a check of the model at a known grazing speed), or for a quick comparison.

Mach and temperature

The Mach option uses the speed of sound at the Material step's temperature, not the local gas temperature of a compressible run.

Theory

Equations

Default and rule

Valid range CFD, tube core | Mach number

Related 3

References 2