- Email: [email protected]
Rain erosion resistance characterizations
Wear 258 (2005) 545–551
Rain erosion resistance characterizations Link between on-ground experiments and in-flight specifications A. D´eom∗ , R. Gouyon, C. Berne Office National d’Etudes et de Recherches A´erospatiales, 29 Avenue de la, Division Leclerc, 92320 Chˆatillon, France Received 22 December 2003
Abstract With the increasing velocity of vehicles and the fact that the vehicles must fly even in rainy conditions, environmental problems such as rain erosion become more important. Precise specifications are now being set for the rain erosion of materials in the vehicle design. Different attempts have been done to predict the rain erosion resistance of materials from their mechanical properties but this will give only the order of magnitude of the resistance, which is generally insufficient. Thus this resistance must be known more accurately, that is possible only by experiments. To perform this, different apparatus are existing: rotating arms, linear tracks, water jet generators. Each apparatus present advantages and disadvantages. For example, with rotating arms the advantage of using real water droplets is counterbalanced by the disadvantage of the existing tangential force which can affect the measurements. With tracks, very severe vibrations are induced. With water jet generators, there is no tangential force, but the use of a jet instead of a droplet necessitates the knowledge of equivalence laws. Each apparatus has its own characteristics: water droplet diameter, water concentration, which cover a part of possible rain specifications. In-flight specifications are characterized by generally one rain intensity, a time duration, and a droplet diameter distribution. The link between on-ground conditions and in-flight specifications must be established to determine, from the rain erosion resistance measurements performed on specimens of the material, if the structure built with this material will withstand the in-flight rain erosion specifications. We will present the results of our recent studies concerning the possibilities of linking on-ground characterizations obtained with water-jet apparatus to in-flight specifications. © 2004 Elsevier B.V. All rights reserved. Keywords: Rain erosion; On-ground experiments; Water-jet experiments; In-flight specifications
1. Introduction The possibility of in-flight damage due to rain erosion is an important point taken into account since many years. We can see for example Figs. 1 and 2 photographies of rain damaged equipment published in the proceedings of a rain erosion conference dated on 1965 [1]! Since this date, the velocities of the aircrafts and missiles increased largely, what increased dramatically the possibility of erosion damage. Moreover, new equipment such radomes are more sensitive ∗
Corresponding author. Tel.: +33 1 46 73 48 76; fax: +33 1 46 73 48 91. E-mail address: [email protected] (A. D´eom).
0043-1648/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2004.09.053
than before to a very small change of thickness as it can be produced by erosion. These new specifications make necessary new studies in the field. Rain erosion in-flight specifications for a system (aircraft, missile, . . .) are given by a required time of resistance of a part of the system (window, dome, . . .) when it encounters at a given velocity water droplets coming from a rain characterized by its rain intensity in mm/h. Furthermore, this rain is composed of a large number of droplets of different diameters. The distribution in diameter of the droplets is dependent on the intensity of the rain. It is very difficult and expensive to make in-flight experiments to characterize the rain erosion resistance of a system.
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Fig. 1. Rain damaged navigational light of Javelin aircraft.
One of the main reason is the difficulty to measure the characteristics of the rain (distribution of the droplets in diameter and water concentration) and the intrinsic variability of such a meteorological phenomenon. On-ground rain erosion characterizations are more convenient but whatever the apparatus used, whirling arm, water-jet generator, . . . the experiments are made with given diameters or with diameter distributions of the droplets largely different from those of actual rains. Our attempt was to try to link the measurements from an on-ground apparatus: the water generator MIJA with in-flight rain specifications.
Fig. 2. Sandwich type radome of Hawker Hunter after flight in rain.
2. Link between on-ground experiments and in-flight specifications 2.1. Analysis of the distribution of droplets in a natural rain Real rain is characterized by a specific drop diameter distribution which can be described approximately by the formula of Marshall and Palmer: Nd = 8000 exp[−4.1(d/I 0.21 )]
(1)
where Nd is the number of drops per unit of volume and unit of diameter interval δd, d, diameter of the spherical drop (mm), and I intensity of rain (mm/h) The product Nd δd is then the number of drops in 1 m3 of air with a diameter between d and d + δd. Fig. 3 shows the distribution of drops versus drop diameter for rain intensities
Fig. 3. Comparison of drop distribution for rain rates of 100 and 10 mm/h following the Marshall and Palmer law.
A. D´eom et al. / Wear 258 (2005) 545–551
547
each diameter can be calculated: Ndr = Nd ×
πDi2 × Vg × t 4
(2)
Table 1 shows an example of calculation of the actual number of drops encountered by a 10 mm diameter surface going through a rain of 100 mm/h rain intensity at 300 m/s during 10 s. The step of diameter δd used for the computation is 0.25 mm. According to Field [2], there is a relation between the diameter of the drop and the velocity for different impacts leading to the same degradation of an infrared material: Fig. 4. Comparison of the volume filled by the drops of different diameters, for both rain rates.
of 100 and 10 mm/h. Fig. 4 shows a comparison of the volume filled with the drops for both rain intensities. Increasing the intensity increases of course the quantity of water impinging on the material but also increases the relative part of large diameter droplets. Palmer’s formula gives for each drop diameter the number of drops contained in 1 m3 of rain. Knowing the diameter Di of the impacted surface, the velocity Vg of the object and the rain exposure duration t, the actual number Ndr of drops of
Vd2 /Vd1 = (d1 /d2 )1/3
(3)
Field quantifies the degradation using the measurement of the damage with a microscope at a perfectly defined magnifying power. We will make the hypothesis that this relation also applies to the damage criterion we are using: a 10% loss of optical transmission. Relation (3) assists in the conversion from a distribution of drops with different diameters but at the same velocity to a distribution of drops with the same diameter, but at different velocities. One can see, Table 1, in column “equivalent 2 mm drop velocity” the result of such a calculation in the case of the use of the water jet generator multiple impact jet apparatus (MIJA).
Table 1 Results of the computation of the equivalent rain erosion experiment, using an apparatus with only one droplet diameter, with an actual rain dmin
dmax
Number of droplets/ m3
Volume filled by the drops (mm3 /m3 )
Actual number of drops
Equivalent 2 mm droplet velocity (m/s)
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 5.25 5.50 5.75 6.00 6.25 6.50
0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 5.25 5.50 5.75 6.00 6.25 6.50 6.75
2000 1355 917 621 421 285 193 131 89 60 41 28 19 13 9 6 4 3 2 1 1 1 0 0 0 0 0
2 37 117 218 314 388 433 451 445 420 384 342 297 254 213 176 144 116 93 74 58 45 35 27 21 16 12
471 319 216 146 99 67 45 31 21 14 9.6 6.5 4.4 3.0 2.0 1.4 0.9 0.6 0.4 0.3 0.2 0.1 0.1 0.1 0.0 0.0 0.0
1 150 189 216 238 256 273 287 300 312 323 334 343 353 362 370 378 386 393 400 407 414 420 427 433 439 444
Total
5122
1459
Number of 2 mm droplets 0 2 9 15 20 22 23 23 21 19 16 14 11 9 7 6 5 4 3 2 2 1 1 1 1 0 0 235
Rain intensity I (mm/h): 100; impacted surface diameter (mm): 10; droplet velocity (m/s): 300; time duration (s): 10; first diameter (mm): 0.00000001; diameter step (mm): 0.25; power velocity dependence: −7.
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Bench MIJA generates successive water jets which hit at a great speed the object for which one needs to measure the resistance to rain erosion. The water jets are sent randomly onto the object so as to simulate the random distribution of water drops in real rain. A full description of MIJA can be found in [3]. Comparative measurements with trials on the whirling arm at SAAB-SCANIA facility help to calibrate MIJA with a more conventional facility and also to give the correlation of the drop speed equivalent to the MIJA jet, for a given drop diameter (in our case 2 mm) [4]. Simulating real rain could be obtained by using MIJA in successive trials with a different number of impacts at different velocities. This fastidious trial can be avoided if one knows the dependence of the degradation on the impact velocity, which is the case if the material has already been characterized by rain erosion measurements at different velocities. Following our know-how, curves of dependence of the rain exposure time to get 10% of transmission loss can generally be written as follow: t0.1 = aV n
(4)
with n the power velocity dependence for the material, which can vary from 3 to 15, depending largely on the material. For a given drop diameter, the number of impacts needed to obtain a given degradation at a given velocity, can be calculated from the number of impacts necessary to get the same degradation at another velocity with the formula: NV2 = NV1 (V2 /V1 )n
(5)
In the case of the example of Table 1, this permits the calculation of the number of impacts to launch with MIJA at 300 m/s for each set of drops at the equivalent 2 mm droplet velocity V.
It then remains to add the number of impacts of 2 mm drops at 300 m/s to be performed by MIJA. 2.2. Experimental validation 2.2.1. Principle Two steps would be necessary in order to verify the previous analysis. The first one would consist in a comparison of the degradation of two samples, the first one exposed at successive trials with different diameters of droplets at the same velocity and the second one exposed to successive trials with MIJA at different velocities. Referring to Table 1, we must compare, at a given velocity of 300 m/s, the degradation of the first sample after 319 impacts of droplets with a diameter between 0.25 and 0.50 mm, followed by 216 impacts of droplets with a diameter between 0.50 and 0.75 mm followed by . . . 1 impact of droplet with a diameter between 4.0 and 4.25 mm with the degradation of the second sample after 319 impacts with MIJA at a velocity of 150 m/s, followed by 216 impacts at a velocity of 189 m/s, followed by . . . 1 impact at a velocity of 378 m/s. This first step which requires experiments either in flight with perfectly known rain parameters or to use an on-ground apparatus in which samples can hit or be hit with spherical water droplets with a diameter changing from 0 to 4 mm at a velocity of 300 m/s has not been performed. The second step consists to compare, always referring to Table 1, the degradation of a sample hit with MIJA with 319 impacts at 150 m/s, followed by 216 impacts at 189 m/s, followed by . . . 1 impact at the velocity 378 m/s, with the degradation of a sample after 235 impacts at 300 m/s. This step can be performed.
Fig. 5. Variation of the normalized transmission in the 3.5–6 m range of the sample of glass 9754 no. 101 with the increase of the normalized cumulative rain exposure time (Ved = 295 m/s).
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Table 2 Calculated distribution of droplets of a natural rain corresponding at a rain intensity of 19.43 mm/h and computation of the number of 2 mm droplets to simulate the erosion of a 12 mm diameter surface of a glass 9754 sample hit at 295 m/s during 30 s dmin
dmax
Number of droplets/ m3
Volume filled by the drops (mm3 /m3 )
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00
0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50
4000 1332 444 148 49 16 5 2 1 0 0 0 0
33 294 454 414 293 178 98 50 24 11 5 2 1
4002 1333 444 148 49 16 5 2 1 0 0 0 0
1859
6000
Total
Actual number of drops
Equivalent 2 mm droplet velocity (m/s)
Number of 2 mm droplets
1 186 234 268 295 318 338 355 372 387 400 413 425
0 26 62 65 49 31 17 9 4 2 1 0 0 267
Rain intensity I (mm/h): 19.43; impacted surface diameter (mm): 12; droplet velocity (m/s): 295; time duration (s): 30; first diameter (mm): 0.00000001; diameter step (mm): 0.5; power velocity dependence: −8.52963315.
2.2.2. Experimental results To perform the experiments, we choose an infrared material also transparent in the visible, in order to follow easily the optical degradation of the material. This material is a glass with the reference 9754. The first step was the measurement of the dependence on velocity of the characteristic optical time t0.1 for this material. Let us remember than t0.1 represents the rain exposure time for which a 10% loss of optical transmission can be observed. The normalized rain exposure time is calculated from the number of impacts N delivered by MIJA using the following relation: tnorm =
106 N (Dg )3 1.5 (Di )2Ved
Table 3 MIJA experiments performed on sample no. 104 to simulate the erosion of a 12 mm diameter surface of a glass 9754 sample hitting at 295 m/s during 30 s a precipitation of 19.43 mm/h intensity Number of impacts to deliver by MIJA
Equivalent 2 mm droplet velocities to generate (m/s)
Equivalent 2 mm drop velocities really generated (m/s)
1333 444 148 49 16 5 2 1
186 234 268 295 318 338 355 372
188 236 270 295 312 328 359 356
(6)
Table 4 Calculated distribution of droplets of a natural rain corresponding at a rain intensity of 19.43 mm/h and computation of the number of 2 mm droplets to simulate the erosion of a 12 mm diameter surface of a glass 9754 sample hit at 450 m/s during 1 s dmin
dmax
Number of droplets/ m3
Volume filled by the drops (mm3 /m3 )
Actual number of drops
Equivalent 2 mm droplet velocity (m/s)
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50
0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75
2000 1154 666 384 222 128 74 43 25 14 8 5 3 2 1
2 32 85 135 165 174 166 147 124 100 78 59 44 32 23
102 59 34 20 11 7 4 2 1 1 0.4 0.2 0.1 0.1 0.0
1 225 283 325 357 385 409 430 450 468 485 500 515 529 542
Total
241
Number of 2 mm droplets 0 0 1 1 2 2 2 1 1 1 1 1 0 0 0 13
Rain intensity I (mm/h): 19.43; impacted surface diameter (mm): 12; droplet velocity (m/s): 450; time duration (s): 1; first diameter (mm): 0.00000001; diameter step (mm): 0.25; power velocity dependence: −8.52963315. with Dg is the equivalent droplet diameter (=2 mm), Di the
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Fig. 6. Front face of sample no. 101 after rain erosion using MIJA (Ved = 295 m/s, number of impacts = 245, tnorm = 30.8 s).
diameter of the impacted surface, and Ved equivalent droplet velocity (m/s). One can see for example in Fig. 5 the decrease of the normalized transmission of a 9754 glass sample with the increase of the cumulative normalized rain exposure time for the velocity of 295 m/s. t0.1norm is found equal to 30.8 s. Fig. 6 shows a picture of the eroded front face of the sample at the end of the trial. Three velocities were used to determine the dependence of t0.1norm on velocity: 246, 295 and 349 m/s (Fig. 7). The power velocity dependence is found equal to −8.53. Let us calculate the distribution of droplets of an actual rain for the parameters used in one of the previous experiments: I = 19.43 mm/h, Di = 12 mm, Ved = 295 m/s and for a time of exposition to the rain equal to the duration of the test, about 30 s (Table 2). From the previous calculation, the experiment to perform with MIJA to verify if one can replace several successive trials at different velocities by one experiment at a unique velocity, can be deduced. One can see Table 3 the trials to realize and the experiments really performed with MIJA on sample no. 104. A little discrepancy can be observed between
Fig. 7. Dependence on velocity of the characteristic optical time for glass 9754.
Fig. 8. Front face of sample no. 104 after experiments using MIJA with successive trials at different velocities to simulate 30 s of erosion at 295 m/s in a 19.43 mm/h rain intensity.
the velocities to perform and the velocities really performed, particularly for the experiments with a small number of hits. Fig. 8 shows a photography of the front face of sample no. 104 at the end of the experiment. The degradation of the sample in the visible range is comparable to the degradation of sample no. 101 tested at the unique velocity of 295 m/s. The loss of transmission of sample no. 104 is equal to 8%, which is very comparable to the 10% loss of transmission of sample no. 101. The replacement of the characterization at different velocities being successful at 295 m/s, that is to say for a velocity in the middle range of the characterization of the power dependence on velocity we used, it was interesting to test the method for a higher velocity. Let us consider the velocity of 450 m/s. Considering the power velocity dependence of the material, we could obtained a 10% loss of transmission in 0.93 s corresponding to about 18 MIJA impacts. Table 4
Fig. 9. Front face of sample no. 106 after experiments using MIJA with successive trials at different velocities to simulate 1 s of erosion at 450 m/s in a 19.43 mm/h rain intensity.
A. D´eom et al. / Wear 258 (2005) 545–551
shows the results of the computation of the number of 2 mm droplets to perform with MIJA and the corresponding droplet distribution of a natural rain. Fig. 9 shows a photography of the front face of sample no. 106 hit with the method of the successive trials at different velocities. A loss of optical transmission equal to 6–7%, instead of 10% was measured at the end of the experiment. This little discrepancy can come from the extrapolation to high velocities of the power velocity dependence of the characteristic optical time. Effectively, an experiment at the velocity of 450 m/s gives a value of 2.1 s instead of 0.93 s for t0.1norm obtained for 26 impacts instead 18.
3. Conclusions There are not too many difficulties in performing rain erosion tests when the goal of the experiments is only the comparison of one material to another. The difficulties are largely increasing when the objective of the experiments is to compare the resistance of the materials to given flight require-
551
ments. Supposing the influence of droplet diameter follows the Field law, we experimentally show that it is possible to simulate the action of the droplets of different diameter of a natural rain by the action of droplets with a unique diameter as produced by the water jet generator MIJA. MIJA can be a very useful tool to characterize the rain erosion resistance of materials within in-flight requirements.
References [1] A.A. Fyall, in: A.A. Fyall, R.B. King (Eds.), Proceedings of the Rain Erosion Conference held at Meersburg, West Germany, 5th–7th May, Royal Aircraft Establishment, Farnborough, UK, 1965. [2] R.J. Hand, J.E. Field, D. Townsend, J. Appl. Phys. 70 (11) (1991) 7111–7118. [3] C. Seward, J. Pickles, J.E. Field, Window and Dome Technologies and Materials II, Proceedings of the SPIE’s 1990 Tech. Symposium, vol. 1326, 1990, pp. 280–290. [4] A. D´eom, D. Balageas, Proceedings of the 8th European Electromagnetic Structures Conference, Nottingham, 6–7 September, 1995, pp. 87–94, TP ONERA1995-169.
Rain erosion resistance characterizations Link between on-ground experiments and in-flight specifications A. D´eom∗ , R. Gouyon, C. Berne Office National d’Etudes et de Recherches A´erospatiales, 29 Avenue de la, Division Leclerc, 92320 Chˆatillon, France Received 22 December 2003
Abstract With the increasing velocity of vehicles and the fact that the vehicles must fly even in rainy conditions, environmental problems such as rain erosion become more important. Precise specifications are now being set for the rain erosion of materials in the vehicle design. Different attempts have been done to predict the rain erosion resistance of materials from their mechanical properties but this will give only the order of magnitude of the resistance, which is generally insufficient. Thus this resistance must be known more accurately, that is possible only by experiments. To perform this, different apparatus are existing: rotating arms, linear tracks, water jet generators. Each apparatus present advantages and disadvantages. For example, with rotating arms the advantage of using real water droplets is counterbalanced by the disadvantage of the existing tangential force which can affect the measurements. With tracks, very severe vibrations are induced. With water jet generators, there is no tangential force, but the use of a jet instead of a droplet necessitates the knowledge of equivalence laws. Each apparatus has its own characteristics: water droplet diameter, water concentration, which cover a part of possible rain specifications. In-flight specifications are characterized by generally one rain intensity, a time duration, and a droplet diameter distribution. The link between on-ground conditions and in-flight specifications must be established to determine, from the rain erosion resistance measurements performed on specimens of the material, if the structure built with this material will withstand the in-flight rain erosion specifications. We will present the results of our recent studies concerning the possibilities of linking on-ground characterizations obtained with water-jet apparatus to in-flight specifications. © 2004 Elsevier B.V. All rights reserved. Keywords: Rain erosion; On-ground experiments; Water-jet experiments; In-flight specifications
1. Introduction The possibility of in-flight damage due to rain erosion is an important point taken into account since many years. We can see for example Figs. 1 and 2 photographies of rain damaged equipment published in the proceedings of a rain erosion conference dated on 1965 [1]! Since this date, the velocities of the aircrafts and missiles increased largely, what increased dramatically the possibility of erosion damage. Moreover, new equipment such radomes are more sensitive ∗
Corresponding author. Tel.: +33 1 46 73 48 76; fax: +33 1 46 73 48 91. E-mail address: [email protected] (A. D´eom).
0043-1648/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.wear.2004.09.053
than before to a very small change of thickness as it can be produced by erosion. These new specifications make necessary new studies in the field. Rain erosion in-flight specifications for a system (aircraft, missile, . . .) are given by a required time of resistance of a part of the system (window, dome, . . .) when it encounters at a given velocity water droplets coming from a rain characterized by its rain intensity in mm/h. Furthermore, this rain is composed of a large number of droplets of different diameters. The distribution in diameter of the droplets is dependent on the intensity of the rain. It is very difficult and expensive to make in-flight experiments to characterize the rain erosion resistance of a system.
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A. D´eom et al. / Wear 258 (2005) 545–551
Fig. 1. Rain damaged navigational light of Javelin aircraft.
One of the main reason is the difficulty to measure the characteristics of the rain (distribution of the droplets in diameter and water concentration) and the intrinsic variability of such a meteorological phenomenon. On-ground rain erosion characterizations are more convenient but whatever the apparatus used, whirling arm, water-jet generator, . . . the experiments are made with given diameters or with diameter distributions of the droplets largely different from those of actual rains. Our attempt was to try to link the measurements from an on-ground apparatus: the water generator MIJA with in-flight rain specifications.
Fig. 2. Sandwich type radome of Hawker Hunter after flight in rain.
2. Link between on-ground experiments and in-flight specifications 2.1. Analysis of the distribution of droplets in a natural rain Real rain is characterized by a specific drop diameter distribution which can be described approximately by the formula of Marshall and Palmer: Nd = 8000 exp[−4.1(d/I 0.21 )]
(1)
where Nd is the number of drops per unit of volume and unit of diameter interval δd, d, diameter of the spherical drop (mm), and I intensity of rain (mm/h) The product Nd δd is then the number of drops in 1 m3 of air with a diameter between d and d + δd. Fig. 3 shows the distribution of drops versus drop diameter for rain intensities
Fig. 3. Comparison of drop distribution for rain rates of 100 and 10 mm/h following the Marshall and Palmer law.
A. D´eom et al. / Wear 258 (2005) 545–551
547
each diameter can be calculated: Ndr = Nd ×
πDi2 × Vg × t 4
(2)
Table 1 shows an example of calculation of the actual number of drops encountered by a 10 mm diameter surface going through a rain of 100 mm/h rain intensity at 300 m/s during 10 s. The step of diameter δd used for the computation is 0.25 mm. According to Field [2], there is a relation between the diameter of the drop and the velocity for different impacts leading to the same degradation of an infrared material: Fig. 4. Comparison of the volume filled by the drops of different diameters, for both rain rates.
of 100 and 10 mm/h. Fig. 4 shows a comparison of the volume filled with the drops for both rain intensities. Increasing the intensity increases of course the quantity of water impinging on the material but also increases the relative part of large diameter droplets. Palmer’s formula gives for each drop diameter the number of drops contained in 1 m3 of rain. Knowing the diameter Di of the impacted surface, the velocity Vg of the object and the rain exposure duration t, the actual number Ndr of drops of
Vd2 /Vd1 = (d1 /d2 )1/3
(3)
Field quantifies the degradation using the measurement of the damage with a microscope at a perfectly defined magnifying power. We will make the hypothesis that this relation also applies to the damage criterion we are using: a 10% loss of optical transmission. Relation (3) assists in the conversion from a distribution of drops with different diameters but at the same velocity to a distribution of drops with the same diameter, but at different velocities. One can see, Table 1, in column “equivalent 2 mm drop velocity” the result of such a calculation in the case of the use of the water jet generator multiple impact jet apparatus (MIJA).
Table 1 Results of the computation of the equivalent rain erosion experiment, using an apparatus with only one droplet diameter, with an actual rain dmin
dmax
Number of droplets/ m3
Volume filled by the drops (mm3 /m3 )
Actual number of drops
Equivalent 2 mm droplet velocity (m/s)
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 5.25 5.50 5.75 6.00 6.25 6.50
0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75 4.00 4.25 4.50 4.75 5.00 5.25 5.50 5.75 6.00 6.25 6.50 6.75
2000 1355 917 621 421 285 193 131 89 60 41 28 19 13 9 6 4 3 2 1 1 1 0 0 0 0 0
2 37 117 218 314 388 433 451 445 420 384 342 297 254 213 176 144 116 93 74 58 45 35 27 21 16 12
471 319 216 146 99 67 45 31 21 14 9.6 6.5 4.4 3.0 2.0 1.4 0.9 0.6 0.4 0.3 0.2 0.1 0.1 0.1 0.0 0.0 0.0
1 150 189 216 238 256 273 287 300 312 323 334 343 353 362 370 378 386 393 400 407 414 420 427 433 439 444
Total
5122
1459
Number of 2 mm droplets 0 2 9 15 20 22 23 23 21 19 16 14 11 9 7 6 5 4 3 2 2 1 1 1 1 0 0 235
Rain intensity I (mm/h): 100; impacted surface diameter (mm): 10; droplet velocity (m/s): 300; time duration (s): 10; first diameter (mm): 0.00000001; diameter step (mm): 0.25; power velocity dependence: −7.
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Bench MIJA generates successive water jets which hit at a great speed the object for which one needs to measure the resistance to rain erosion. The water jets are sent randomly onto the object so as to simulate the random distribution of water drops in real rain. A full description of MIJA can be found in [3]. Comparative measurements with trials on the whirling arm at SAAB-SCANIA facility help to calibrate MIJA with a more conventional facility and also to give the correlation of the drop speed equivalent to the MIJA jet, for a given drop diameter (in our case 2 mm) [4]. Simulating real rain could be obtained by using MIJA in successive trials with a different number of impacts at different velocities. This fastidious trial can be avoided if one knows the dependence of the degradation on the impact velocity, which is the case if the material has already been characterized by rain erosion measurements at different velocities. Following our know-how, curves of dependence of the rain exposure time to get 10% of transmission loss can generally be written as follow: t0.1 = aV n
(4)
with n the power velocity dependence for the material, which can vary from 3 to 15, depending largely on the material. For a given drop diameter, the number of impacts needed to obtain a given degradation at a given velocity, can be calculated from the number of impacts necessary to get the same degradation at another velocity with the formula: NV2 = NV1 (V2 /V1 )n
(5)
In the case of the example of Table 1, this permits the calculation of the number of impacts to launch with MIJA at 300 m/s for each set of drops at the equivalent 2 mm droplet velocity V.
It then remains to add the number of impacts of 2 mm drops at 300 m/s to be performed by MIJA. 2.2. Experimental validation 2.2.1. Principle Two steps would be necessary in order to verify the previous analysis. The first one would consist in a comparison of the degradation of two samples, the first one exposed at successive trials with different diameters of droplets at the same velocity and the second one exposed to successive trials with MIJA at different velocities. Referring to Table 1, we must compare, at a given velocity of 300 m/s, the degradation of the first sample after 319 impacts of droplets with a diameter between 0.25 and 0.50 mm, followed by 216 impacts of droplets with a diameter between 0.50 and 0.75 mm followed by . . . 1 impact of droplet with a diameter between 4.0 and 4.25 mm with the degradation of the second sample after 319 impacts with MIJA at a velocity of 150 m/s, followed by 216 impacts at a velocity of 189 m/s, followed by . . . 1 impact at a velocity of 378 m/s. This first step which requires experiments either in flight with perfectly known rain parameters or to use an on-ground apparatus in which samples can hit or be hit with spherical water droplets with a diameter changing from 0 to 4 mm at a velocity of 300 m/s has not been performed. The second step consists to compare, always referring to Table 1, the degradation of a sample hit with MIJA with 319 impacts at 150 m/s, followed by 216 impacts at 189 m/s, followed by . . . 1 impact at the velocity 378 m/s, with the degradation of a sample after 235 impacts at 300 m/s. This step can be performed.
Fig. 5. Variation of the normalized transmission in the 3.5–6 m range of the sample of glass 9754 no. 101 with the increase of the normalized cumulative rain exposure time (Ved = 295 m/s).
A. D´eom et al. / Wear 258 (2005) 545–551
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Table 2 Calculated distribution of droplets of a natural rain corresponding at a rain intensity of 19.43 mm/h and computation of the number of 2 mm droplets to simulate the erosion of a 12 mm diameter surface of a glass 9754 sample hit at 295 m/s during 30 s dmin
dmax
Number of droplets/ m3
Volume filled by the drops (mm3 /m3 )
0.00 0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00
0.50 1.00 1.50 2.00 2.50 3.00 3.50 4.00 4.50 5.00 5.50 6.00 6.50
4000 1332 444 148 49 16 5 2 1 0 0 0 0
33 294 454 414 293 178 98 50 24 11 5 2 1
4002 1333 444 148 49 16 5 2 1 0 0 0 0
1859
6000
Total
Actual number of drops
Equivalent 2 mm droplet velocity (m/s)
Number of 2 mm droplets
1 186 234 268 295 318 338 355 372 387 400 413 425
0 26 62 65 49 31 17 9 4 2 1 0 0 267
Rain intensity I (mm/h): 19.43; impacted surface diameter (mm): 12; droplet velocity (m/s): 295; time duration (s): 30; first diameter (mm): 0.00000001; diameter step (mm): 0.5; power velocity dependence: −8.52963315.
2.2.2. Experimental results To perform the experiments, we choose an infrared material also transparent in the visible, in order to follow easily the optical degradation of the material. This material is a glass with the reference 9754. The first step was the measurement of the dependence on velocity of the characteristic optical time t0.1 for this material. Let us remember than t0.1 represents the rain exposure time for which a 10% loss of optical transmission can be observed. The normalized rain exposure time is calculated from the number of impacts N delivered by MIJA using the following relation: tnorm =
106 N (Dg )3 1.5 (Di )2Ved
Table 3 MIJA experiments performed on sample no. 104 to simulate the erosion of a 12 mm diameter surface of a glass 9754 sample hitting at 295 m/s during 30 s a precipitation of 19.43 mm/h intensity Number of impacts to deliver by MIJA
Equivalent 2 mm droplet velocities to generate (m/s)
Equivalent 2 mm drop velocities really generated (m/s)
1333 444 148 49 16 5 2 1
186 234 268 295 318 338 355 372
188 236 270 295 312 328 359 356
(6)
Table 4 Calculated distribution of droplets of a natural rain corresponding at a rain intensity of 19.43 mm/h and computation of the number of 2 mm droplets to simulate the erosion of a 12 mm diameter surface of a glass 9754 sample hit at 450 m/s during 1 s dmin
dmax
Number of droplets/ m3
Volume filled by the drops (mm3 /m3 )
Actual number of drops
Equivalent 2 mm droplet velocity (m/s)
0.00 0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50
0.25 0.50 0.75 1.00 1.25 1.50 1.75 2.00 2.25 2.50 2.75 3.00 3.25 3.50 3.75
2000 1154 666 384 222 128 74 43 25 14 8 5 3 2 1
2 32 85 135 165 174 166 147 124 100 78 59 44 32 23
102 59 34 20 11 7 4 2 1 1 0.4 0.2 0.1 0.1 0.0
1 225 283 325 357 385 409 430 450 468 485 500 515 529 542
Total
241
Number of 2 mm droplets 0 0 1 1 2 2 2 1 1 1 1 1 0 0 0 13
Rain intensity I (mm/h): 19.43; impacted surface diameter (mm): 12; droplet velocity (m/s): 450; time duration (s): 1; first diameter (mm): 0.00000001; diameter step (mm): 0.25; power velocity dependence: −8.52963315. with Dg is the equivalent droplet diameter (=2 mm), Di the
550
A. D´eom et al. / Wear 258 (2005) 545–551
Fig. 6. Front face of sample no. 101 after rain erosion using MIJA (Ved = 295 m/s, number of impacts = 245, tnorm = 30.8 s).
diameter of the impacted surface, and Ved equivalent droplet velocity (m/s). One can see for example in Fig. 5 the decrease of the normalized transmission of a 9754 glass sample with the increase of the cumulative normalized rain exposure time for the velocity of 295 m/s. t0.1norm is found equal to 30.8 s. Fig. 6 shows a picture of the eroded front face of the sample at the end of the trial. Three velocities were used to determine the dependence of t0.1norm on velocity: 246, 295 and 349 m/s (Fig. 7). The power velocity dependence is found equal to −8.53. Let us calculate the distribution of droplets of an actual rain for the parameters used in one of the previous experiments: I = 19.43 mm/h, Di = 12 mm, Ved = 295 m/s and for a time of exposition to the rain equal to the duration of the test, about 30 s (Table 2). From the previous calculation, the experiment to perform with MIJA to verify if one can replace several successive trials at different velocities by one experiment at a unique velocity, can be deduced. One can see Table 3 the trials to realize and the experiments really performed with MIJA on sample no. 104. A little discrepancy can be observed between
Fig. 7. Dependence on velocity of the characteristic optical time for glass 9754.
Fig. 8. Front face of sample no. 104 after experiments using MIJA with successive trials at different velocities to simulate 30 s of erosion at 295 m/s in a 19.43 mm/h rain intensity.
the velocities to perform and the velocities really performed, particularly for the experiments with a small number of hits. Fig. 8 shows a photography of the front face of sample no. 104 at the end of the experiment. The degradation of the sample in the visible range is comparable to the degradation of sample no. 101 tested at the unique velocity of 295 m/s. The loss of transmission of sample no. 104 is equal to 8%, which is very comparable to the 10% loss of transmission of sample no. 101. The replacement of the characterization at different velocities being successful at 295 m/s, that is to say for a velocity in the middle range of the characterization of the power dependence on velocity we used, it was interesting to test the method for a higher velocity. Let us consider the velocity of 450 m/s. Considering the power velocity dependence of the material, we could obtained a 10% loss of transmission in 0.93 s corresponding to about 18 MIJA impacts. Table 4
Fig. 9. Front face of sample no. 106 after experiments using MIJA with successive trials at different velocities to simulate 1 s of erosion at 450 m/s in a 19.43 mm/h rain intensity.
A. D´eom et al. / Wear 258 (2005) 545–551
shows the results of the computation of the number of 2 mm droplets to perform with MIJA and the corresponding droplet distribution of a natural rain. Fig. 9 shows a photography of the front face of sample no. 106 hit with the method of the successive trials at different velocities. A loss of optical transmission equal to 6–7%, instead of 10% was measured at the end of the experiment. This little discrepancy can come from the extrapolation to high velocities of the power velocity dependence of the characteristic optical time. Effectively, an experiment at the velocity of 450 m/s gives a value of 2.1 s instead of 0.93 s for t0.1norm obtained for 26 impacts instead 18.
3. Conclusions There are not too many difficulties in performing rain erosion tests when the goal of the experiments is only the comparison of one material to another. The difficulties are largely increasing when the objective of the experiments is to compare the resistance of the materials to given flight require-
551
ments. Supposing the influence of droplet diameter follows the Field law, we experimentally show that it is possible to simulate the action of the droplets of different diameter of a natural rain by the action of droplets with a unique diameter as produced by the water jet generator MIJA. MIJA can be a very useful tool to characterize the rain erosion resistance of materials within in-flight requirements.
References [1] A.A. Fyall, in: A.A. Fyall, R.B. King (Eds.), Proceedings of the Rain Erosion Conference held at Meersburg, West Germany, 5th–7th May, Royal Aircraft Establishment, Farnborough, UK, 1965. [2] R.J. Hand, J.E. Field, D. Townsend, J. Appl. Phys. 70 (11) (1991) 7111–7118. [3] C. Seward, J. Pickles, J.E. Field, Window and Dome Technologies and Materials II, Proceedings of the SPIE’s 1990 Tech. Symposium, vol. 1326, 1990, pp. 280–290. [4] A. D´eom, D. Balageas, Proceedings of the 8th European Electromagnetic Structures Conference, Nottingham, 6–7 September, 1995, pp. 87–94, TP ONERA1995-169.