A.1 ASTM - Multiple linear regression fit equations
Based on an extensive international test program with liquid impact
erosion facilities at different research organisations and universities,
and sponsored by ASTM, Heymann9,10 derived a multiple
linear regression fit equation for the incubation life. He presented the
following equation for the incubation period as a function of
impingement conditions of waterdrops and metal surface grade:
\begin{equation}
\log N_{0}=-5.64\log v_{d}-3.12\log d_{d}+\log\text{NOR}+18.94\text{\ \ \ }\left(s=0.21,\ n=31\right)\nonumber \\
\end{equation}With
\(N_{0}\) = “number of specific impacts” for incubation (-),
\(v_{d}\) = impact velocity normal to the target surface (m/s),
\(d_{d}\) = waterdrop diameter (mm).
NOR = ”incubation resistance number” as defined by
Heymann9,10. This is a normalized resistance value for
a certain metal surface grade with respect to stainless steel AISI 316
(NOR = 1) with a hardness of 170 Vickers.
Eq. A-1 is a multi-regression fit equation for results of droplet
impingement erosion tests performed with erosion test facilities at ten
laboratories. All of these have facilities of the type where one or more
specimens are attached to a rotating disc or arm and their circular path
intersects one or more liquid sprays. The drop impact velocity is taken
as the peripheral velocity of the specimen. The tests are performed at
drop impact velocities of 140, 210, and 400 m/s, the drop sizes ranges
from 1.2 to 2.0 mm.
For stainless steel AISI 316 (NOR = 1) and a drop size of 1.8
mm, this multi-regression fit equation (Eq. A-1) results to thenumber of specific impacts for incubation as a function of water
drop impact velocity as shown in Figure A-1. The 2.5 and 97.5 %
confidence limits of the log-normal distribution are given. The used
nominal drop impact velocities in the interlaboratory test program are
also shown.
The number of specific impacts for incubation can be transformed to
incubation period in hours by using the definition for “number of
specific impacts” is given by9,10:
\begin{equation}
N_{0}=\left(\frac{V_{\text{water}}}{A_{e}}\right)\times\left(\frac{A_{d}}{V_{d}}\right)=3600C_{v}v_{d}I_{p}\times\frac{3000}{2d_{d}}=5.4\times 10^{6}\frac{C_{v}v_{d}I_{p}}{d_{d}}\nonumber \\
\end{equation}\(\frac{V_{\text{water}}}{A_{e}}\) = volume of waterdrops impinged per
unit exposed area
\(\frac{A_{d}}{V_{d}}\) = projected area of a waterdrop divided by the
volume of a waterdrop
\(C_{v}\) = volume concentration of water in air (-)
\(I_{p}\) = incubation period (h)
In the whirling arm tests used by Heymann9,10, the
mean volume concentration of water in air, \(C_{v}\) = 1.8 x
10-6 (mean log(\(C_{v}\)) = -5.74, standard deviation
s = 0.44). By way of comparison: for typical rain conditions, rain
intensity Ir = 25.4 mm/h, drop size dd =
1.8 mm, and gravitational drop velocity vg = 6.2
m/s6, the volume concentration of water in air,\(C_{v}\) = 1.1 x 10-6 (log(\(C_{v}\)) = -5.94).
The metals supplied to the laboratories are: Aluminium 1100-O and
6061-T6, Nickel 270, Stainless Steel AISI 316, and Stellite 6B. The
first four metals provided most of the test data; only a few data-points
are included for Stellite 6B. The normalized “incubation resistance
numbers” (NOR) are determined for each of the metals tested,
the numbers are shown in Table A-1. All relevant differences in metal
properties compared to AISI 316 (hardness of 170 HV) are accumulated in
the NOR value of the metal.