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.