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481

Erosion by Water-hammer.

By S t a n l e y S. Cook, B.A. (Cantab.).

(Communicated by Sir Cliarles Parsons, F.R.S.—Received January 13, 1928.—Revised May 23, 1928.)

[Plate 9.]

Corrosion or erosion of the surfaces of metals under water is in many cases found to be actively promoted by their motion through the water, or by the motion of the water over them. In such cases the relative parts played in the action by corrosion and erosion respectively are not readily distinguished. Even where corrosion products are found the action may still be primarily one of erosion, the latter merely creating the conditions favourable to corrosion. I t may, for example, have the effect of removing a surface layer or protective scale. On the other hand, where corrosion products are not found the process is frequently claimed to be a corrosive one, the only function allowed to erosion being that of removing the products of corrosion as fast as they are formed.

No doubt in some instances this latter point of view is justifiable, but in many cases the reason for attributing the action to corrosion rather than to erosion is merely that the mechanical nature of the cause is not sufficiently apparent, through a failure to recognise the remarkable ability of water and other nearly incompressible fluids, under certain circumstances, to produce momentary pressures far in excess of the yield-point strength of ordinary materials. The object of this note is to show that in many instances a satisfactory mechanical explanation of such action can be advanced by associating it with the phenomenon known as water-hammer, and, in particular, to show that the same principles afford a satisfactory explanation of the impact pressures produced by drops of water impinging on metallic surfaces.

As a member of the Committee appointed by the Admiralty in 1915 to determine the cause of the erosion of propeller blades, the author, in the early

^spring of 1917, investigated the hydrodynamic properties of collapsing cavities in an incompressible fluid, and made calculations of the pressures that might arise from the collapsing vortices of cavitating propellers, which being

, subsequently verified by experimental methods convinced the Committee that the deterioration of propeller blades of cruisers and destroyers by erosion

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482 S. S. Cook.

was caused by water-hammer effects resulting from cavitation.* Two years later, in 1919, with the permission of the Admiralty a paper was read by Sir Charles Parsons and the author at the Spring Meeting of the Institution of Naval Architects, f describing the work of the Committee at considerable length, including the above-mentioned calculations and a description of the experimental apparatus by which they were confirmed.

In recent years, with the higher surface speeds and the high vacua generally adopted in steam turbines the leading edges of the moving blades, especially towards the exhaust end of the turbine, are frequently found eroded. Several attempts have been made to account for this erosion. Experimental investigations have pointed to the impingement of water drops on the surface of the blades as being the cause, but the theoretical treatment has not hitherto led to a satisfactory conclusion. The author has recently succeeded in applying methods similar to those adopted by him in 1917 to the calculations of the impact pressures, and has been able to show that such pressures are amply sufficient to account for the observed erosion.

The investigation of the problem of propeller erosion led the author to consider the case when a spherical cavity, in an incompressible fluid, is suddenly permitted to collapse. Such a condition of things might arise in various ways. For example, a propeller blade might cut across a vortex core in such a way as to isolate a cavity and at the same time destroy the vortex motion. Or a sudden arrest of flow of water in a tube by stoppage of the inlet would, by the momentum of the water, tend to break the continuity of the fluid and create cavities which would immediately afterwards tend to collapse. The work done by the surrounding fluid closing in as the cavity collapses is converted into velocity energy, and since, in an incompressible fluid moving symmetrically towards a fixed point, the velocity varies inversely as the square of the distance from that point, this velocity energy will be found mainly concentrated at the reduced surface of the cavity. I t was shown that the velocity at the surface = \ /§ P (R03 — R3) /R3, where P = the pressure of the surrounding fluid and R 0 and R the initial and final radii of the cavity. Thus for R = 1/20 R0 and P = 1 atmosphere the velocity at the final surface of the cavity = 730 metres per second, and supposing the cavity to collapse finally on a surface with this velocity (we might, for example, consider a hemispherical cavity

* Report of the Propeller Sub-Committee (section III) of the Board of Invention and Research—Erosion of Propellers—September 17, 1917.

t “ Investigations into the Causes of Corrosion or Erosion of Propellers, 4 Transactions of the Institu tion of Naval Architects ’ (1919).



Erosion by Water-hammer. 483

collapsing on to the surface of a propeller blade in the diametral plane) it Avas further shown that the water-hammer pressure thus produced would be as high as 10,000 atmospheres or roughly 65 tons per square inch, the pressure finally reached depending upon the ratio of the initial to the final radius of the cavity, and. therefore, upon the original volume of the cavity and the coarseness of grain of the surface upon which it collapses.

In such a case the final act of erosion is due to water-hammer, the concentration merely having the effect of increasing the velocity in the final stage of collapse and making the water-hammer more intense. The pressure due to this water-hammer is determined as follows :—

The pressure generated on an element of surface at its first encounter with water moving at a finite velocity is different from that produced by the steady impact of a moving stream of water at the same velocity. If a moving column of water is suddenly arrested by a fixed surface, without any interposing gas to cushion the blow, there is a sudden arrest of the front layer of the impinging column. The pressure generated by the blow in such a case is only limited by the fact that both solids and fluids possess a slight degree of compressibility, so that the velocity energy of the front layer of the column is converted on impact into potential energy. If V be the velocity of the column of water the kinetic energy of a layer of thickness and unit area of section is |pV2A/q \\There p is the density of the fluid. After impact the velocity energy of this layer is destroyed and replaced by potential energy of amount Sp2 Ah ([3 being the compressibility). The equivalence of these two amounts of energy gives p = \T\ / p/[3 as the pressure instantaneously set up in the front layer of the column. Thus the pressure generated in this simple case of a water-hammer blow is \ \ / p/8. Since for \\rater p = 1 and B = approximately 1/20,000 per atmosphere of pressure, a velocity of only 10 metres per second will, on sudden arrest, give rise in this way to a pressure of 140 atmospheres.

I t will be seen that for low velocities the momentary pressure caused in this manner is much greater than the steady pressure due to the momentum of a jet of fluid at the same velocity. The latter is pV2, and will only have the same value as the water-hammer pressure when pY2 = V \ / p/fl or V = 1 /\/p p , that is to say, when the velocity is equal to the velocity of sound in the fluid in question. For velocities much lower than this, the water-hammer pressure will greatly exceed that due to an impinging jet, for example, at 250 metres per second, or about one-sixth of the velocity of sound in water, the water- hammer pressure will be six times as great as that arising from the momentum of a jet of water steadily impinging at the same \7elocity.

2 l 2



484 S. S. Cook.

I t should be noted, too, that the water-hammer pressure induced by a suddenly arrested column of water is independent of the length of the column. I t follows that drops of water, however minute, will at the first moment of impact produce the same water-hammer effect as large volumes of water, the only difference being in the area of attack and the duration. The duration will depend upon the length of the column, being the time required for the shock wave to travel to the end of the column and back again to the surface of impact. For example, if the column is 1 metre in length the pressure endures for about one seven-hundredth part of a second.

The above considerations show that arising from the mechanical properties of nearly incompressible fluids water-hammer on small areas is a powerful factor contributing to erosion, and that where the conditions are such that cavities may form in the water and subsequently collapse in the neighbourhood of metallic surfaces, there is then the possibility of much higher velocities in the water locally than are normal to the general conditions, and, in addition, the certainty that wherever such high velocities are destroyed by the interposition of a surface, intense momentary pressures will be set up by the water- hammer effect above referred to.

Rapid erosion of the same character as on propeller blades, frequently encountered on the runners, casings and liners of centrifugal pumps, screw pumps and hydraulic turbines, can also be satisfactorily accounted for in this manner.

In the same way the erosion of steam turbine blades may be attributed to the water-hammer of drops of water impinging on the surface of the blades in a high vacuum. On the outer portion of the moving blades at the exhaust end the leading edges are found to be thickly honeycombed with minute indentations of conical shape of varying depths and are sometimes completely perforated, the action occurring on the convex surface of the blade, that is to say, on the side towards which the blade is moving. I t occurs chiefly at peripheral speeds in excess of about 120 metres per second, and is of increasing intensity as the speed is increased.

This erosion is attributed to drops of water arising from condensation of the steam by expansion, which drops moving at a lower velocity are overtaken by the rotating blade. I t has already been pointed out that the water-hammer pressure due to the impact of a drop is the same as for a larger volume, depending only upon the velocity. The water-hammer pressure calculated as above is 12 tons per square inch for a speed of 120 metres per second and 30 tons per square inch for a speed of 300 metres per second, so that it will be seen to be of the same order as the yield-point strength of materials usually employed-




Many experiments have been carried out with the object of producing such erosion of turbine blades under controlled conditions.* They have, however, employed either high-pressure steam jets impinging directly on blades or bars of metal, or water jets upon revolving test pieces or blades, and are not, therefore, representative of the conditions prevailing in the exhaust-end blading of turbines. Jets were doubtless employed from the point of view that a jet would be more destructive than isolated drops, but the foregoing investigations of the water-hammer effect of drops indicates that a large number of small drops is likely to be the more destructive. Further, there is the possibility of some of the drops being of irregular shape, with the effects referred to below.

In order to investigate the erosion produced by a multitude of minute drops impacting on metal at high velocity, the following experiment has been made : The apparatus consisted of a ring of turbine blades mounted on a shaft and rotated at a high speed within a cylindrical casing. At two diametrically opposed points in one end wall of this casing two sprayers of the White ” oil-fuel burner type were used to project a fine spray of water across the moving blades. The blades were widely separated in the circumferential direction to give the spray access to their surfaces. This was necessary because on account of the high speed of motion of the blades which made the relative direction of impingement of the water drops nearly circumferential. The bladed rotor thus represented an exhaust-end element of a steam turbine from which two out of every three blades were removed. The rotor was 12 inches diameter and the blades 4 inches high. The axes of the water sprayers were situated at a distance of 8 inches from the axis of the rotor.

The apparatus was run for 18| hours at a speed of 8800 revolutions per minute, so that the speed of impact varied from 140 metres per second at the roots of the blades to 233 metres per second at the tips. By the formula given on p. 483 the corresponding water-hammer pressures are 12-4 tons per square inch to 20-7 tons per square inch.

The blades were of five different materials as given below :—

Material of blades. Elastic limit. Tons/sq. inch. Condition after test.

1

1. “ Heela A.T.V.” steel ............... 51 Unattacked.2. Tungsten steel 40 Rusted and slightly eroded.3. 44 Staybrite ” steel 16 Considerably eroded.4. Monel metal 18 Considerably eroded.5. Mild steel.... 16 Etched as by sand blast.

* ‘ Biown Boveri Review ’ (Dec., 1924, April, 1927).



486 S. S. Cook.

The fine sprays of water playing on the mild steel blades had a peculiar effect. For about \ inch across, the blades had the appearance of having been sandblasted, while the remaining parts were rusted. If the erosion be taken as indicated by the raggedness of the blade inlet edge, then the mild steel blades were not eroded as much as the “ Staybrite ” steel or " Monel ” blades.

Fig. 1 (Plate 9) is a photograph of the rotor after test, the blade at the top and the one to the left of it are of “ Monel ” metal, the next two to the right are of “ Staybrite” steel, whilst the next two to the left are of mild steel sheathed with “ Hecla ” steel on their leading edges.

As has been stated, erosion only occurs on the moving blade. From this it is apparent that it is not due to such drops of water as are carried in the main stream of the steam through the blade passages. Such drops, in fact, issuing from the blades with the same speed as the steam would not be overtaken by the moving blades. I t must therefore be attributed to drops of water swept off the fixed blades into the path of the moving blades. Also it is found that erosion occurs most markedly on that part of the moving blade which is immediately opposite to a binding strip of the fixed blades, indicating that drops are blown off the binding strips.

Minute drops of water assume a practically spherical shape on account of surface tension, but drops formed in the manner suggested may be of moderate dimensions, and under these circumstances a slight departure from spherical shape may be expected. With drops of irregular shape, or even if there are minute surfaces of irregularities on the blades themselves, there is the possibility of the isolation of small empty spaces between the drop and the blade at the moment of impact, in which case the behaviour subsequent to impact would be that of a collapsing cavity with the final generation of much higher water-hammer pressures.

Fig. 2 illustrates the progress towards final collapse after impingement, as it might be conjectured to take place with a drop of this character. In the final stages the concentration of the motion towards the centre of collapse at A will produce high velocities at the surface of the entrapped cavity, and finally water-hammer at A.

Further, when a conical depression has once been formed it is clear that it will be rapidly deepened by drops that may strike directly into it or over its mouth, since concentration will then have its full effect in producing a high final velocity.

Another example of what is usually described as corrosion, but is possibl}’ capable in part of a mechanical explanation, is the pitting of condenser tubes.



Cook.hoy. Soc. Proc., A, vol. 1 19; p i 9̂

F ig. 1.

(Facing p. 486.)



In a recent paper by Sir Charles Parsons to the Institution of Naval Architects* some investigations are described in regard to the cause of pitting of condenser


F ig. 2.—Impact of irregularly shaped drop of water against a fixed surface. Successive stages of deformation after impact, showing cavity enclosed a t middle of front and rapidly collapsing. The successive contours of this cavity are necessitated by the constancy of volume of the fluid.

tubes, which go to show that irregularity of flow and vortex motion in the water box of a surface condenser may cause considerable variations of flow through the tubes, the flow through a tube being momentarily checked when a vortex in the box moves across its mouth, with consequent breakages of continuity of the water near the inlet end of the tube and subsequent collapse of the cavities so created, producing water-hammer effects. These experiments are at present under continuation.

Whilst it is generally held that occluded gases play an important part in the pitting of brass condenser tubes, and certainly there are in most cases distinct

^evidence of corrosion, oxidation and dezincification being found to have occurred near the pits, the causes just mentioned are sufficient to account for pitting of a purely mechanical nature, and it may be that occluded gases compressed

* “ Some Investigations into the Cause of Erosion of the Tubes of Surface Condensers ” (April, 1927).



488 Erosion by Water-hammer.

to a high pressure and possibly to a high temperature at the final collapse of a cavity are brought to a state of high chemical activity so that both corrosion and erosion result from the same causes.

The late Lord Rayleigh discussed the case* in which a spherical cavity, instead of being vacuous, contains a small amount of gas, in which case the velocity of the boundary comes again to zero before complete collapse, the whole of the energy of collapse having been converted into the pressure energy of this imprisoned gas. The final volume is shown to be extremely small when the initial pressure of the gas is only a small fraction of that of the surrounding fluid. I t was, however, assumed that the compression of this gas would take place isothermally, whereas, in the last stages of the compression at any rate, the interval of time during which it takes place being usually extremely small, compression is probably adiabatic, and a high temperature will be reached as well as a high pressure.

I t will be seen from the examples mentioned that the phenomenon of water- hammer and the formation and collapse of cavities in water intensifying the water-hammer in the manner described furnish ample material for the explanation of both corrosion and erosion of metallic surfaces exposed in various ways to such conditions.

* ‘ Phil. Mag.,’ vol. 34, p. 94 (1917).



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