Waterjetting 20c - Critical Distances intro

I remember going down the New Orleans just after Hurricane Katrina, and being a member of one of the first inspection teams that drove down the Delta inspecting the damage. One of the things that has remained in my memory was that of driving past one of the large coal piles being stored outside one of the local power stations, and being surprised that – despite the wind and rain – it was still there. Some years previously I had visited several places that had build ultra-ultra-high pressure jet generating devices. (Not sure what else you call a system that produces jet impact pressure that begin to approach 1 million psi). The one that has struck in my memory was visiting the underground test for Dr. Bill Cooley’s water cannon. Built to advance the concept of using high pressure gas to drive a pulse of water at a rock target (this was during the days examining new ways to drive underground tunnels) the device fired a small slug of water through a very carefully designed nozzle to generate a jet measured to produce 500,000 psi on impact.

We stood around and watched as the device was loaded, charged and fired and were, I suppose, a little disappointed at the damage induced around the impact point. Only a small amount of fragments were produced from the shot, and as you can see from the figure above, there was not a lot of evident surface damage from the shots. Actually, for the amount of energy involved, the amount of material removed was quite significant and some of the pieces were several inches in size:

Figure 2. Fragments recovered after a single shot of the cannon.

Later analysis explained why the damage had not been greater. The problem arises because of the way that the pressure is generated to drive the jet. Most of the devices of the time, whether our own, others in the US, the UK or in Russia, used a gas driver to generate the driving pressure, either using smokeless powder (as we did) or storing gas volumes under pressure and then suddenly releasing the accumulated volume to provide the driver.

The problem with this approach is that the driving pressure is not sustained as the water moves down the relatively long nozzle, and the driving pressure on the surface is thus very transient. One recording of such from the UK showed a typical pulse for their unit:

Figure 3. Pressure pulse for the water cannon device developed in the UK.

Dr. Cooley’s cannon had a much shorter and more rapidly decaying pulse, and this was largely the reason that the damage that it induced was not greater. The high impact energy was able to generate large cracks into the surface as the jet penetrated, some of which coalesced with the surface and allowed fragments to release, but the energy pulse was not long enough at the high pressure and with inadequate volume to fill the cracks produced and pressurize them to cause rapid extension and result in larger volume material removal.

The relatively low pressure impact of the rain on the coal in the Gulf, and the high pressure impact on the rock in the test mine both saw the ability of the water to penetrate into the surface layers of the material. But in both cases the impact pressure on the water that permeated into the cracks within that surface was not enough in the secondary phase of the failure process, to sustain internal pressures within the cracks that would lead to large volume material removal.

Now, as I mentioned last time, there are ways to enhance the effect of an impact, by creating secondary surfaces for the rock to break to. The best illustration of this, perhaps is to consider two small (six-inch side) blocks of plexiglas. We drilled a small hole through to the center of each and placed a detonating cap in that hole. We then fired the detonator.

Figure 4. Block of Plexiglas after a detonating cap has been fired in the middle of the block.

Note that the block was big enough to contain the crack damage. But note also that there is very little material removed, because the cracks that were formed by the explosion were contained within the block and did not interact very much. Now consider what happened when we first drilled a circular relief slot around a similar hole and charge. (We based the radius of the cut on the results of the first shot, shown above). After the detonation, this is what we achieved:

Figure 5. Similar bock to figure 4 except that a relief slot was first cut into the block

Note that there are (for those of us interested in driving tunnels) several interesting improvements. Firstly the cracks that radiated out to the walls of the first block now stopped within the central isolated core, and the wall of the excavation is now smooth and undamaged. Secondly the interaction of the radiating cracks within the core all reached the relief slot, and broke the core into fragments that were liberated. And that this also broke to the back of the slot, which was left relatively flat and at the end of the relief slot, so that it would be easy to start a new drilling and breaking operation to deepen the tunnel without having to redrill any damaged zone at the end of the previous excavated section.

But, for the purpose of today’s exercise, note that in the first place – even though there were free surfaces at the edge of the block, they were too far away for the cracks to reach them, and effectively break out the material. It was only when the relief slot was moved closer to the exploding detonator that the central volume was broken out and the effective result that was desired was achieved.

The critical parameter is the correct assessment of the distance over which the interaction between the event and the free surface (or in the case of last time’s discussion between two concurrent jet cuts) will take place.

As I will discuss in later posts, sometimes the distance that is critical to effective jet use is only on the order of fractions of an inch, and if done correctly the result (as above) is impressive, if the distance is too great, then nothing happens. But we’ll talk more about this, in many applications, in the future.

Waterjetting 9b - the effect of standoff distance.

One of the problems with relying on photographs is that they are sometimes not of the quality that one would wish. This has happened with today’s topic, where the pictures are old, smaller and in poorer condition than I had remembered. However, with your indulgence, I am going to step through them. I do apologize for their poor quality, however.

The topic is the way in which a waterjet first attacks a target. I have mentioned different parts of this process in the past. But in this post I want to show that it matters where the target is, relative to the nozzle, because the structure of the jet itself changes with that distance, which I call the standoff distance between the jet orifice and the initial target surface.


Figure 1. The break-up pattern of a waterjet (Yanaida K. “Flow Characteristics of Waterjets,” 2nd BHRA Conf. 1974, paper A2.)

As I mentioned last time when the target is close to the nozzle, then the erosion pattern can, in the first few seconds of contact, be seen to be like a butterfly in pattern. The central part of the target, under the jet, is not eroded, but there is severe erosion around the edges of the jet diameter, where a grain will see high differential pressures across its width, and will be subject to high lateral jet flows.


Figure 2. Damage pattern around the impact point of a 10,000 psi pressure, 0.04 inch diameter jet on aluminum, target close to the nozzle.

As the nozzle is moved away from the target surface, however, that pattern of erosion changes. As the jet structure picture shows, the central zone at the initial pressure reduces in radius, and there is an intermediate zone of rapidly diminishing pressure, with an outer shroud of fine droplets. The effect on the impacted target is that there continues to be a small zone with no erosion in the center, and that erosion is still concentrated around this zone, in that of high differential pressure, which now encroaches on that central sector.


Figure 3. Erosion of an aluminum target with the nozzle 2-inches above the surface, 10,000 psi jet through a 0.04 inch diameter orifice.

That central small plateau is reduced to a very small point by the 3-inch standoff, which is where the jet reaches the end of the distance where the pressure remains constant over the central section. Thus, by a 4-inch standoff the central section, though still present, is being eroded.


Figure 4. Erosion of an aluminum target with the nozzle 4-inches above the surface, 10,000 psi jet through a 0.04 inch diameter orifice.

As the nozzle is moved further back from the surface, that central promontory disappears at around a six-inch standoff. It is interesting to note that at this point the cavity is starting to get noticeably deeper.


Figure 5. Erosion of an aluminum target with the nozzle 6-inches above the surface, 10,000 psi jet through a 0.04 inch diameter orifice. (The lower of the two circular damage patterns was caused through experimental conditions and should be ignored). The presence of a central mound can barely be discerned.

By this time the central section of the jet is beginning to break down into, initially short strings, that very rapidly break into droplets. The damage pattern that results shows a cavity that is slightly increasing both in diameter and depth.


Figure 6. Erosion of an aluminum target with the nozzle 8-inches above the surface, 10,000 psi jet through a 0.04 inch diameter orifice.

By this time the jet is continuing as a series of relatively large droplets, still holding a central structure, though surrounded by a rapidly decelerating cloud of mist.


Figure 7. Erosion of an aluminum target with the nozzle 10-inches above the surface, 10,000 psi jet through a 0.04 inch diameter orifice.

It is one of the interesting oddities of the jet cutting business that the amount of material that is eroded from the target is a maximum at this distance.

However, and this was the subject of great debate back at the time that it was first presented, the ability to control the droplet size, and condition as a function of distance, and the reality that in most applications the target must be cut to depth meant that this has a very limited application. It can be used, if the droplets are generated properly, and used within the relatively narrow window that they exist, to improve surface erosion of material.

However, as Mike Rochester found when he studied this, back at Cambridge in the early 1970’s, the presence of a layer of water on the surface, and as the hole deepens this is almost always there, rapidly diminishes the effect.


Figure 8. The effect of a layer of water in diminishing the “droplet impact” effect in erosion of a surface. (After M.C. Rochester, J.H.Brunton “High Speed Impact of Liquid Jets on Solids” First BHRA Symp Jet Cutting Tech, April `972, Coventry UK, paper A1.)

There are ways of getting around this problem, but the presence of water in the cavity that the jet has produced can also lead to problems, and these will be the topic of the next two posts.

Waterjetting 9a - the instant of contact

Plain high-pressure waterjets penetrate into material in a different way than that which occurs when abrasive is used to make cutting easier. And even with abrasive there are different ways in which the target will react depending on how brittle that it is. In this next segment I will write just about the stages that occur as water alone cuts into a target.

In its simplest form consider first a spherical drop of water, moving at very high speed, which suddenly strikes a flat surface.


Figure 1. Droplet striking a flat surface

As the droplet impacts the surface, but can’t penetrate it, so the water that comes into contact with the surface tries to flow away along the surface, to get out of the way of the volume of water striking the surface behind it.

But in the early stages of the impact (see inset) the edges of the droplet ahead of that lateral flow are coming down onto the surface faster than the water can move that is trying to escape. In this range of activity the distance that the edge of the droplet must travel, L, remains smaller than the distance, D, that the water must move to escape.

This instantly traps the water and with confinement comes a very rapid increase in pressure along the edge of the drop. This pressure also acts on the target surface, so that it is pushed down a little. This pressure was first measured by John Field at the Cavendish Lab in Cambridge, UK, who found that it could exceed three times the water hammer pressure that the water might otherwise exert.

For those not that familiar with the term, the water hammer pressure is also sometimes called the hydraulic shock pressure, and it can occur when a valve is suddenly closed in a feed line, and this sends a shock or pressure wave back up the line. (This is what can sometimes cause banging in feed pipes). Often there is a small air cushion built into water lines to act as a sponge, when such a shock occurs, since otherwise the repetitive shocks can cause parts to fail.

This becomes more of a problem with higher pressures because the equation for the pressure that is generated is given by the equation:

Pressure = fluid density x impact velocity x sound speed in the fluid

Compare this with the impact pressure when a shock is not generated:

Pressure = 0.5 x fluid density x (impact velocity)^2

As a very rough rule of thumb, the speed of sound in water is roughly 4,800 ft per second.

If a waterjet is driven out of a nozzle at a pressure of 40,000 psi then the speed at which it is moving can be roughly calculated as:

Jet velocity (ft/sec) = 12 x Square root (Pressure)

The jet velocity, to a first approximation, is thus 12 x 200 = 2,400 ft/sec.

The Water Hammer Pressure is thus 2 x (4,800/2,400) = 2 x 2 = 4 times the pressure exerted by the water more conventionally. Since that driving pressure was, in this case, 40,000 psi, then the water hammer pressure would be 160,000 psi. With the multiplier that Dr. Field found, this can take that pressure up to around 500,000 psi for that instant of contact.

It is, however, only applied to the target at that instant of impact, and where there is the spherical end of the drop to cause the pressure accumulation across the face.

It does, however, cause a very high lateral jet to shoot out of the jet, at about the point that the droplet curvature no longer provides confinement (at about 1/3 of the droplet diameter measured radially from the center of contact).

John Brunton, also at the Cavendish, has provided photographs of the damage done in that instant of contact.


Figure 2. Droplet impact damage on a sheet of Plexiglas (Brunton “High Speed Liquid Impact” Proc Royal Soc London, 1965. P 79 - 85.)

Part of the damage comes from the high lateral velocity of the released water running into the wall of material not compressed under the generated pressure. Mike Rochester found that the diameter of this ring crack closely followed the diameter of the nozzle from which the droplet was released.


Figure 3. Relative size of the ring crack to that of the originating nozzle (jet head) ( M.C. Rochester, J.H.Brunton “High Speed Impact of Liquid Jets on Solids” First BHRA symp Jet Cutting Tech, April `972, Coventry UK, paper A1.)

In our case, however, the jet is not a single droplet, but rather, at least close to the nozzle, a steady stream with the pressure constant across the diameter.

Thus, in the microseconds after the first impact, as the jet continues to flow down onto the target, so it is flowing out across the damaged zone created by that first impact. The resulting pattern of erosion, which we captured in aluminum, changes as the target moves away from the nozzle. Close to the nozzle the wear pattern looks like this:


Figure 4. Damage pattern around the impact point of a jet on aluminum, target close to the nozzle.

The pattern, close to the nozzle, shows that directly under the jet the pressure is relatively even on the surface of the metal. With no differential pressure across the grain boundaries in that region, the metal is uniformly compressed, and suffers no erosion. At the edges of the jet, however, there is not only the original ring crack damage created on the instant of impact, but also there is a differential pressure along the edges of the jet, which helps to dislodge those initial grains, and provide crack loci for the water to exploit and remove material as it moves away from the original contact surface. The greatest portion of the damage, at this point lies outside the edges of the impacting jet as the laterally flowing jet erodes material as the jet continues to flow.

As the target is moved further from the nozzle, the pressure profile changes from one with a constant pressure over the jet, to one where the central constant pressure region starts to decline in size. Rehbinder calculated the two components of the pressure in the target at the beginning of this erosion process at that point and provided the following mathematical plot.


Figure 5. Impact pressures calculated for the pressure into the target and that along it, during waterjet flow. (Rehbinder, G., "Erosion Resistance of Rock," paper E1, 4th International Symposium on Jet Cutting Technology, Canterbury, UK, April, 1978, pp. E1-1 - E1-10.)

The result of this change in the pressure profile of the jet as it moves away from the nozzle can be seen in the change in the erosion patterns of the jet as it strikes an aluminum target, and that will be the topic for the next post.