Theory

The loss coefficient of a perforated tube can span decades as the ratio of hole to grazing velocity falls, so it is relaxed geometrically rather than linearly, equation (1). The relaxed value is what is compared with the 2 % restart threshold and what is written into the solver (K check interval).

Through the grazing correlations $K \propto r^{-2n}$ with $n$ = 0.47 or 0.534: in log space $K$ changes about half as fast as the velocity ratio, and the plain update ( $\alpha_K = 1$ ) converges in the validation runs; relaxing it only adds checks and restarts.

Equations

K = K_{old}^{\,1-\alpha_K}\,K_{target}^{\,\alpha_K}

(1)

where	meaning	unit
$K_{old}$	Loss coefficient in use	-
$K_{target}$	Newly evaluated loss coefficient	-
$\alpha_K$	Relaxation factor (this setting)	-

Default and rule

Default: 1.0
Rule: 1.0 (no relaxation).
Source: The default of 1.0 is based on a validation run of a two-baffle test muffler: with a log slope of $K(r)$ of about 0.47 the plain update converges, and relaxation only multiplies the restarts. Grazing correlations: (Rogers and Hersh, 1975).

Valid range 0 < α_K ≤ 1

Values

Above 0, at most 1.

Small values

Below about 0.5 each check moves $K$ only partly, so more checks exceed 2 % and more restarts disturb the solution.

References 1

Rogers, T. and Hersh, A. S. (1975). The effect of grazing flow on the steady state resistance of square-edged orifices. 2nd Aeroacoustics Conference, AIAA Paper 75-493. DOI 10.2514/6.1975-493

Theory

Equations

Default and rule

Valid range 0 < α_K ≤ 1

Related 3

References 1