**3. Droplet impact erosion**

Thomas and Brunton [14] investigated repeated liquid impacts for several materials. Erosion curves are drawn for each material and then generalised into one curve, which shows the presence of three stages (**Figure 8**). The first stage is the incubation period during which no weight loss occurred, but some plastic or brittle deformation was noted. In stage 2, pits formed and grew by the removal of material. In stage 3, the erosion rate fell down to a lower value. The growth of small depressions (stage 1) into pits was explained by the stress concentrations. Even though the average stress is low, local soft points of materials may account for yielding. At the start, these local disturbances are very rare, so the first depression would appear with some delay. Later on, with the formation of many depressions, the erosion rate would arise. In stage 2, the tangential flow over the roughened surface also greatly influences the erosion phenomenon; work hardening and eventual fracture of the material occur. In stage 3, the rate of erosion declines again since the drop is broken up by the roughened surface; also the impact is no longer normal to the surface. They tried to compare the constant erosion damage with the fatigue mechanism.

#### **3.1. Time dependence of erosion rate**

**Figure 6.** Formation of cavitation at the impact of a jet on a solid surface. From Field et al. [8].

98 Cavitation - Selected Issues

**Figure 7.** Formation of shock wave in a liquid droplet upon impact on a solid surface. From Haller et al [12].

With less intense but repeated impacts, there is no immediate material loss, but randomly disposed dimples gradually develop, and the surface undergoes gradual deformation and work hardening. The material loss may occur through the propagation of fatigue-like cracks that intersect to release erosion fragments. In materials with non-uniform structure, damage will initiate at weak spots. In brittle materials, circumferential cracks may form around the impact site, which are caused by the tensile stress waves propagating outwards along the surface [4].

Heymann (1969) [4] characterised the repetitive impact erosion in five different stages (**Figure 9**) as follows:

**Figure 8.** The development of erosion in a number of materials eroded at an impact velocity of 125 m/s with a water jet diameter of 1.5 mm. (a) Experiment results and (b) three-stage model for erosion process. From Thomas and Brunton [14].

to be loosened, and we have a gradual transition—the acceleration period—from the incubation period to the maximum rate stage. The subsequent decrease in erosion rate is explained by different concepts. Some relate it to the increase in surface area after the surface has roughened, so the more energy is needed to remove the material. Some relate it to the fact that on the eroded surface, peaks and craters tend to decrease the erosion rate as drops falling on the peaks or slopes will result in decrease in impact pressure. Also the liquid retained in the craters is supposed to cushion the impact. Some relate it to the work hardening of the eroded surface [4].

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Erosion can be characterised by its fundamental driving parameters, which help to provide insight into the governing phenomenon. In the following paragraphs, these fundamental parameters have been classified in different groups, and their influences on erosion have been

Many authors give the idea of threshold velocity dependent on the material and also on the droplet size below which no erosion would take place, analogous to the endurance limit in fatigue. However at low-impact velocities, the incubation period becomes so long that no material loss takes place in a reasonable testing time, which may give the appearance of a threshold so this phenomenon is not yet firmly settled. Dependence of erosion on impact velocity can be explained by the simple power law as Erosion~Vn where n is found to be in the

range of 4–5. For brittle materials, exponents as high as 6–9 have been reported [4, 15].

erosion, the effect of the tangential component is more pronounced [4, 15].

Except for any scouring action, erosion depends only on the normal component of the impact velocity; thus, because of the strong dependence on the impact velocity, erosion is reduced strongly as the impacts become more glancing. However, when the surface is roughened by

Ahmad et al. [16] proved experimentally that the erosion of low-pressure steam turbine blades increases with the impacting droplet size. In other words, erosion tends to reduce as the drop size decreases, that is, a given volume of water did less damage if divided into smaller drops even though it implies more impacts on the surface. This is probably due to the fact that in fatigue, the spatial extent of imposed stresses must exceed some characteristic dimension [4]. They showed that the influence of droplet size on the extent of erosion can be presented by a

the common steam turbine blade materials [16]. If the effect of droplet size is combined with that of impact speed, the scale of steam turbine blade erosion may significantly be changed.

impact. They found the value of n in the range of 3.2–3.5 for

**3.8. Factors affecting erosion**

**3.9. Impingement parameters**

summarised.

*3.9.1. Impact velocity*

*3.9.2. Impact angle*

*3.9.3. Droplet size*

simple power law relation Erosion~D<sup>n</sup>

**Figure 9.** Characteristic erosion versus time curves. (A) Incubation stage, (B) acceleration stage, (C) maximum rate stage, (D) deceleration stage and (E) terminal stage. From Heymann (1969).

#### **3.2. Incubation stage A**

During this stage, little or no material loss occurs, although roughening and metallurgical changes take place in the surface. However, the incubation period may not occur if the impact conditions are severe enough.

#### **3.3. Acceleration stage B**

During this stage, the erosion rate increases rapidly to a maximum value. The extent of this maximum erosion rate depends mainly upon the erosive environment and the material erosion resistance.

#### **3.4. Maximum rate stage C**

During this stage, the erosion rate remains constant or nearly so. The continuous material removal from the cumulated pits forms the constant peak of this erosion stage.

#### **3.5. Deceleration stage D**

During this stage, the erosion rate declines to some fraction of the maximum rate (1/2–1/4).

#### **3.6. Terminal stage E**

During this stage, the erosion rate remains constant once again indefinitely. However, some tests do not show this stage.

#### **3.7. Reasons for time dependence**

The incubation and acceleration stages are easy to explain if it is assumed that the erosion results from a fatigue-like failure mechanism. Then many impacts must occur in one area for a fragment to be loosened, and we have a gradual transition—the acceleration period—from the incubation period to the maximum rate stage. The subsequent decrease in erosion rate is explained by different concepts. Some relate it to the increase in surface area after the surface has roughened, so the more energy is needed to remove the material. Some relate it to the fact that on the eroded surface, peaks and craters tend to decrease the erosion rate as drops falling on the peaks or slopes will result in decrease in impact pressure. Also the liquid retained in the craters is supposed to cushion the impact. Some relate it to the work hardening of the eroded surface [4].

#### **3.8. Factors affecting erosion**

Erosion can be characterised by its fundamental driving parameters, which help to provide insight into the governing phenomenon. In the following paragraphs, these fundamental parameters have been classified in different groups, and their influences on erosion have been summarised.

#### **3.9. Impingement parameters**

#### *3.9.1. Impact velocity*

**3.2. Incubation stage A**

100 Cavitation - Selected Issues

conditions are severe enough.

(D) deceleration stage and (E) terminal stage. From Heymann (1969).

**3.3. Acceleration stage B**

**3.4. Maximum rate stage C**

**3.5. Deceleration stage D**

**3.6. Terminal stage E**

tests do not show this stage.

**3.7. Reasons for time dependence**

sion resistance.

During this stage, little or no material loss occurs, although roughening and metallurgical changes take place in the surface. However, the incubation period may not occur if the impact

**Figure 9.** Characteristic erosion versus time curves. (A) Incubation stage, (B) acceleration stage, (C) maximum rate stage,

During this stage, the erosion rate increases rapidly to a maximum value. The extent of this maximum erosion rate depends mainly upon the erosive environment and the material ero-

During this stage, the erosion rate remains constant or nearly so. The continuous material

During this stage, the erosion rate declines to some fraction of the maximum rate (1/2–1/4).

During this stage, the erosion rate remains constant once again indefinitely. However, some

The incubation and acceleration stages are easy to explain if it is assumed that the erosion results from a fatigue-like failure mechanism. Then many impacts must occur in one area for a fragment

removal from the cumulated pits forms the constant peak of this erosion stage.

Many authors give the idea of threshold velocity dependent on the material and also on the droplet size below which no erosion would take place, analogous to the endurance limit in fatigue. However at low-impact velocities, the incubation period becomes so long that no material loss takes place in a reasonable testing time, which may give the appearance of a threshold so this phenomenon is not yet firmly settled. Dependence of erosion on impact velocity can be explained by the simple power law as Erosion~Vn where n is found to be in the range of 4–5. For brittle materials, exponents as high as 6–9 have been reported [4, 15].

#### *3.9.2. Impact angle*

Except for any scouring action, erosion depends only on the normal component of the impact velocity; thus, because of the strong dependence on the impact velocity, erosion is reduced strongly as the impacts become more glancing. However, when the surface is roughened by erosion, the effect of the tangential component is more pronounced [4, 15].

#### *3.9.3. Droplet size*

Ahmad et al. [16] proved experimentally that the erosion of low-pressure steam turbine blades increases with the impacting droplet size. In other words, erosion tends to reduce as the drop size decreases, that is, a given volume of water did less damage if divided into smaller drops even though it implies more impacts on the surface. This is probably due to the fact that in fatigue, the spatial extent of imposed stresses must exceed some characteristic dimension [4]. They showed that the influence of droplet size on the extent of erosion can be presented by a simple power law relation Erosion~D<sup>n</sup> impact. They found the value of n in the range of 3.2–3.5 for the common steam turbine blade materials [16]. If the effect of droplet size is combined with that of impact speed, the scale of steam turbine blade erosion may significantly be changed.

#### **3.10. Dependence on liquid properties**

Most liquid impact erosion tests have been performed with water at normal atmospheric conditions. However, some tests have been performed with different liquid properties, which show that the erosion varies with approximately the 2nd to 2.5th power of liquid density and the 1/2–3/4 power of the inverse of viscosity. Moreover, a slight increase in erosion is found by an increase in the impacting liquid temperature. This mechanism is explained by the increased shear damage of the target surface, which is caused by the resulting lateral jet flow [4].

with a velocity that is almost equal to the circumferential velocity of the blades. In a modern

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Since the recognition of the erosion phenomenon in the low-pressure stages of steam turbines, many experiments have been designed to study the erosion phenomenon on laboratory scale by simulating the conditions as observed in a real steam turbine. Worthington (1908) was the first who studied liquid-solid impact experimentally by using high-speed photography. The first study about erosion was carried out in a Parsons steam turbine plant in 1925. Honneger [2], Gardner (1932) and de Haller [9] were the pioneers in the experimental study of steam turbine blade erosion. The basic methodology to simulate the droplet impact erosion on a laboratory scale is to arrange a high-speed droplet impact on a target surface. This high-speed droplet impact is, typically, achieved in a rotating test rig where the specimen alone or the specimen and nozzle both rotate in a controlled environment to achieve a predesigned impact speed and number impacts on the target surface [15, 20]. Some scientists achieved this high-speed droplet impact by using some special arrangements where they used a chamber that is closed at the one end by a piston and at the other end by the specimen surface. By operating on the piston, a highspeed jet or a shock wave is produced, which subsequently impacts on the target surface [14, 21]. The materials, which are to be tested in the test rig to find out their erosion resistance, are milled in a cylindrical, rectangular or a button-like shape [15]. Ahmad et al. performed the experiments with blade-like specimens. These specimens experience similar impact angles and impact speeds on their surfaces in the erosion rig as those observed for the corresponding blade spans in the real steam turbine, whereby the erosion process is accelerated by increasing

The test duration is normally motivated by the test intent specification to greatly accelerate the erosion process in such a way that monotonic saturating material loss gradients can be established within a feasible time frame. To quantify the erosion, the weight loss is interpreted with the help of the material density to reflect the volumetric erosion of the material. As a second key figure, the area-specific first-time derivative, i.e. the erosion rate, is derived and evaluated. As the erosion rate reflects the tendency of a material to erode at a given erosive environment, its reciprocal value will reflect the resistivity of the material to erode in terms of time taken by the erosive environment for a given degree of material degradation [15].

As soon as the phenomenon causing the droplet impact erosion has been well understood and agreed amongst the scientific community, different remedial measures have been proposed and implemented to avoid the erosion of steam turbine blades. In the first step, the axial spacing between stator and rotor has been increased. In an increased path between stator and rotor, the droplets are further accelerated and broken up into smaller droplets under the action of steam aerodynamic forces. Moreover, trailing edges of the stator guide vanes are deliberately made thinner. This leads to smaller initial secondary droplets produced from

3600 rpm turbine, the impact speed is estimated to be as high as 700 m/s [15, 19].

**4.1. Quantification of droplet impact erosion**

the droplet impact number [22].

**4.2. Protection against droplet impact erosion**

### **3.11. Correlation with mechanical properties**

It is always desirable to correlate erosion resistance of materials with a single mechanical property. It is found that hardness, resilience, toughness, tensile strength, ductility and the strain energy can affect erosion resistance greatly, but comprehensive knowledge is not yet available in this field [4, 14, 15, 17, 18]. Moreover, a ductile material with more toughness is more erosion resistant. Also annealed materials show greater erosion resistance than the cold-worked materials [14].

#### **3.12. Effects of alloying elements and microstructure**

Improved erosion resistance has been associated with alloying elements such as chromium, manganese and cobalt. The effect of nickel is inconsistent. Fine microstructure is advantageous and so is the ability of the surface layer to become work-hardened as a result of impact-induced deformation. The extremely high erosion resistance of Stellite (cobaltchromium-tungsten alloy) has been explained by a microstructure consisting of small hard carbide particles in a strong but more ductile matrix. Very high erosion resistance has been reported for chromium-manganese steels (about 10% Cr and 12% Mn) that undergo austeniticmartensitic phase transformation under impingement. Simoneau et al. found that low stacking-fault energy is the key to high erosion resistance in austenitic stainless steel as well as cobalt base alloys [4, 15].
