Waterjetting 31c - Jet interactions and traverse speed

The last post included the idea that, with a jet penetrating to most of its final depth in the first 1/100th of a second, that the best traverse speed that could be used would end up around 50 ft per minute. Actually this is a little low as an estimate, and the reason for this goes back to a picture from another post. On the other hand the speed may be reduced a little, as a way of getting more material out of the target faster.

Figure 1. Jets penetrating through a bed of glass beads. The original image has been duplicated and the two shown together. The darker green is where the water has penetrated between the glass beads.

In the picture shown not only is the water penetrating and cutting down into the bed, it is also, to a small degree, penetrating into the side walls of the hole, and this becomes more evident as the jet reaches toward terminal depth, and the jet coming back starts to interact with the jet entering the hole, giving the bulge in the penetration, as the water starts to reach out further into the material.

While it obviously varies with the material, the side penetration of the jet into the material around, and ahead of the jet means that the material is, to a degree, pre-weakened by that penetration, and becomes easier to cut, so that the best speed for cutting can be slightly increased from the number derived last time.

There is another benefit to this, which the Chinese developed in one of their mining machines, although it also has application in milling and other removal techniques.

The high optimal speed of the jet was developed by oscillating a waterjet nozzle vertically, as the head was traversed, more slowly along the horizontal. Because of the benefits of the oscillation the head cut a wide path through the material to about the same depth as it did when the jet was traversed without oscillation. The volume removed however was roughly an order of magnitude greater.

Figure 2. Slots cut into a soft cement. The two slots are roughly equivalent in depth but the lower one had the nozzle oscillate perpendicular to the traverse direction across the block. (see here)

One can, as a result, remove much more material where a plain waterjet (as opposed to one that carries abrasive or cavitates) is moved across the target surface.

When looking for the best combination of oscillation speed, as a function of the horizontal speed in cases such as those shown in Figure 2, it is important to consider how much of the water has penetrated into the side of the cut, as shown in Figure 1.

The softer the material, and the easier that the jet penetrates into the wall of the slot, then the further apart the two passes can be made. But that inter-cut distance varies also with the speed that the primary cut is being made. If the cut is being made at the most efficient speed to remove material, then the speed will be high so that the rebounding jet does not start interfering with the incoming jet, as is shown in the lower parts of figure 1.

Thus the two adjacent passes should be made close enough that the two layers of darker green around the upper parts of the slot depths in figure 1 just barely overlap. On the other hand if the traverse speed is slowed so that the interaction of the incoming and outgoing jets does occur, with the result driving water into the ribs to the extent shown at the hottom of the holes in figure 1, then the two cuts can be spaced further apart, roughly at the distance shown in the figure. This is because any rib of material between the two cuts is now cut on either side and beneath by the penetration of the water, and will be removed with no additional energy being required.

This is particularly handy in materials that have a lot of joints such as, for example, coal or soil. Here the spacing can be increased significantly.

Figure 3. Slot cut into coal by a nozzle with two orifices (upper left) oscillating vertically on the front of the plow shape shown on the right. The slot is roughly 2-inches wide.

However this does not work as well where the target material is stickier, for example with a clay.

Figure 4. Cuts made into wet clay – to help in visualization the cuts are filled with bentonite (white) to contrast the shape and location with the darker clay that was cut through.

In drier clays and shales, where the material responds in a more brittle way, the rib between the two adjacent cuts may shatter and give the larger volume removal rates required.

Where this is not the case, and where the cutting ability of the two jets can be better estimated then two adjacent jets can be aimed so that they meet within the body of the target.

Figure 5. Waterjet cuts in claystone with the two cuts inclined so that they met at the bottom of the wedge shape shown. The wedge is loose, and can be lifted out of the block by hand.

In this way, by arranging a set of jets into a pattern which will be controlled by the shape of the cut to be made, and over what area, a large volume of material can be removed with the use of the least amount of water.

Making the best use of this combination does require some testing to determine how best to angle the jets so that they meet at the right distance into the target and with sufficient force remaining that they will remove the isolated blocks of material between the two (or more) jet paths. In these cases it is best where the jets are traversed over the surface of the target at a slower than optimal speed, since a small buildup in pressure at the bottom of the common slot will make it easier for the jet to dislodge the wedge of material between the two cuts.

As material gets stronger, however, the benefits of that penetration become less, and to make sure that the material between the two cuts is removed, the two cuts should be aimed so that they will intersect within the cutting depths. With vertical slots the two cuts can be brought quite close, with no interaction between them.

Figure 6. Parallel adjacent cuts in sandstone, where the ribs are not removed by the jet between adjacent passes.

Waterjetting 31b - short pulse lengths and traverse speed

One of the more surprising things that we learned at the beginning of the research into high pressure waterjet action was how quickly a jet will penetrate to almost full depth of penetration, and how slowly it will cut deeper after that. It is a lesson that often escapes even those who work with the technology today.

A series of tests was carried out in which a jet was exposed for very short periods of time to a fixed block of sandstone. The time that the jet hit the rock varied and the results were used to make the following plot:

Figure 1. Average penetration as a function of exposure time, for a continuous jet impacting a static target. (Polyox is polyethylene oxide) (after Brook and Summers )

The experiment was then repeated using a device that would only allow the jet to hit the rock for much shorter periods of time. When these results were plotted, the following graph was obtained.

Figure 2. The depth of penetration into sandstone as a function of time, for very short intervals. (ibid)

The depths achieved with the longer exposure times were therefore occurring within the first 1/100ths of a second, and the penetration that followed that initial impact time was at a much lower rate.

The reason for this had been suggested by earlier work by Leach and Walker at Sheffield who pointed out that once the jet starts into the hole it has no other path to exit rather than to turn around and come out the way it went in. Since the jet is continuing to flow into the hole, the result is that the pressure in the hole will diminish over time.

Figure 3. The effect of hole depth on the pressure developed at the bottom (after Leach and Walker).

It should be mentioned, however, that Leach and Walker built a special stand to make these measurements and the hole was built out of steel, rather than being eroded by a jet. The reason that this is important is that where the target is weaker then the turbulence generated by the jet:rebound will additionally erode the walls of the hole, particularly at the depth where the jet pressure falls to the threshold pressure of the material. At this point the jet begins to enlarge a cavity at the bottom of the hole. The pressure can then rise in the cavity, as the hole walls are reamed and the pressure bulb can cause spallation of the overlying rock. It is also why one has to be careful in the drilling of holes in glass, since a similar series of steps can also arise with abrasive waterjet cutting, and internal pressures within the drilled hole can cause the glass to fracture.

Rehbinder also built a narrow slot to measure pressure drop with depth of the hole, and showed that the rapid decline in pressure with depth that Leach and Walker found, was related to the relative narrowness of the hole, and that when the holes were wider, relative to the jet, that this decline was not as dramatic.

Figure 4. Changes in hole pressure with depth as a function of hole width. (after Rehbinder)

As I have mentioned in a previous post a logical progression is to then pulse the water so that each slug of water has time to leave the hole before the next one arrives. When this is carried out, in our case by building a small interrupting wheel that spun between the nozzle and the target, the jet will continue to penetrate although at a slower rate than that originally achieved.

Figure 5. The penetration of rock with an interrupted jet. (after Brook and Summers)

There have been several attempts since that time to use pulsed jets as a way of improving breakage, with a lower energy cost. This has centered around some form of water cannon, or similar tool, although the main problem – never really resolved – of maintaining a high firing rate without destroying the seals in the supply lines has led to that approach being shelved.

Other developments first led to a pulsation in the feed line to the nozzle, first described by Gene Nebeker of Scientific Associates at the 3rd ISJCT in Chicago in 1976. Although that work continued for a number of years it was never able to achieve commercial reality at the time. Subsequently Dr. Vijay pioneered the approach that led to the formation of VLN Advanced Technologies Inc. Using an ultrasonic method of pulsation, which produces very short duration pulses at a high rate in the stream, the company has developed a market, particularly in removing coatings from surfaces.

The mechanisms of target failure are different from those achieved with the more conventional, longer pulsed systems, where the length of the individual jet slugs allows more pressurization of cracks within the target. That kinetic energy allows the jets to operate under water, however shorter pulsation lengths (similar in some ways to rain) are attenuated where there is a layer of water on the surface particularly when this is confined, and Brunton and Rochester found that some of the advantages of the technique (including the ability to generate water hammer pressures are diminished when that layer is thicker.

However, if a waterjet penetrates to close to its maximum penetration within a period of around 0.01 seconds, and the jet is cutting a hole that is roughly three times the diameter of the orifice, then it is logical to suggest that after that residence time the nozzle should move further down the sample. If the jet is roughly 0.033 inches in diameter then the nozzle should move roughly 0.1 inches in 0.01 seconds or roughly 10 inches per second, or 50 ft. per minute. Lab studies have shown that shown that speeds in this range are most efficient where plain waterjets are used in cutting. Because abrasive waterjets penetrate material in a different way the best cutting speed for that technology is much slower.

The topic will continue in the next post, since it is often difficult to persuade operators how fast they should be moving tools to get them to be most efficient.

Leach S. J. and Walker G. L. “Some aspects of rock cutting by high speed water jets”. Phil. Trans. R. Soc. 260A, 295-308 (1966).
Nebeker E.B. and Rodriguez S.E. “Percussive water jets for rock cutting,” paper B1, 3rd ISJCT, BHRA, Chicago, May 1976.
Brunton, J.H., Rochester, M.C., "Erosion of Solid Surfaces by the Impact of Liquid Drops," In Erosion-Treatise on Materials Science and Technology, ed Preece, pp. 185 - 248.
Rehbinder, G., "Some Aspects of the Mechanism of Erosion of Rock with a High Speed Water Jet," paper E1, 3rd International Symposium on Jet Cutting Technology, May, 1976, Chicago, IL, pp. E1-1 - E1-20.

Waterjetting 31a - Changing Jet Pressure, Diameter and Exposure

A high-pressure waterjet will penetrate into a material by penetrating into small cracks in the surface and pressurizing those cracks, so that they grow and join together freeing material. This mechanism changes where one moves to add abrasive, but that discussion will come later.

The larger the cracks in the material, then the lower the pressure needed to penetrate into the crack, and to then cause it to grow. Large grained, weakly bonded material, such as for example soil, can, as a result be washed apart by pressures as low as those caused by a heavy rain. As the material becomes more cohesive (think initially of a heavy clay) then the amount of force required to grow the fissures is greater, while the crack lengths are usually smaller. This means that the jet pressure will have to be higher for the same volume of material to be removed.

As one moves from soils to rocks and other materials will increasingly smaller grain size, so the pressure required to cut into the material must be increased. Initially we call the pressure at which the jet starts to dig a hole the initial pressure or threshold pressure of the material.

The way to find out its value is to point the jet at right angles to the jet and begin to raise the jet pressure. When the jet has not enough pressure to penetrate and grow cracks in the target, then it will flow along the surface after impact. However when the jet starts to drill a hole into the target, then the water going into that hole has only one way out – back the way it came, and now the jet comes back along the axis of the jet. (Hitting the operator if the lance is hand-held and this is partly why you need personal protective equipment).

Generally that pressure is not enough to give an economic removal rate and the jet pressure should be raised significantly above the threshold to reach that level. All other things being equal (such as nozzle diameter, standoff distance and traverse speed) then as the jet pressure is raised the depth of the cut will increase in proportion, as will the volume of material removed. This is the case whether the pump providing the water is an intensifier system (usually at higher pressure) or a triplex or similar pump. The main difference in the plot is because of the difference in the diameter of the cutting jets. Berea sandstone is a “standard” rock that has been used in many cutting tests over the decades because of its relatively uniform structure and strength. The uniaxial compressive strength of the sandstone is around 5,000 psi.

Figure 1. The effect of raising jet pressure on the depth of cut achieved in Berea Sandstone with the cuts made at a speed of 12 inches/minute.

This leads into consideration of the second important parameter, that of the flow rate of the jet, which is mainly defined by the diameter of the orifice through which the jet is formed. The flow volume of water is controlled both by the jet pressure (the higher the pressure the faster the water flows out of the nozzle) and by the diameter of the jet. When one is cutting with water alone then it is often better to have higher flow rates at lower pressure rather than the converse. The reason for this is that larger diameter jets hit more flaws on the surface than smaller ones, and the larger the area that is under attack then the greater the likelihood of larger cracks being present and allowing greater volumes of material to be removed. (There are statistical and mathematical justifications for this, but I will forgo going through that math).

When carrying out rough calculations on relative cutting performance over the years we have assumed that the relationship between the depth of cut and the diameter of the orifice is a power relationship with an exponent of 1.5. When comparing the data for Berea sandstone which we obtained as we changed jet diameters we found the following:

Figure 2. The effect of increasing jet diameter on the depth of cut achieved in Berea Sandstone with the cuts made at a speed of 12 inches/minute.

The exponents are not quite at 1.5, but using that value gives a fairly close initial estimate as to the performance that we can achieve.

Part of the problem in seeking a correlation between the jet cutting performance and the nozzle diameter is that the cutting range of the jet changes quite quickly with a change in nozzle diameter. And while we often use a first rough estimate that the jet throw is 125 – 150 diameters in reality the jet performance changes over that range, as the structure of the jet itself changes.

One way of showing this is to show how the cut depth varies when the target surface is at different distances from the nozzle, a value we often call the stand-off distance. In this case the rock is a sandstone, and similar to that used above, but the tests are made with the jet firing at the rock for different lengths of time, rather than traversing over it.

Figure 3. The effect of increasing exposure time and standoff distance on the depth of hole achieved in Sandstone.

Note that there is a relatively rapid drop in cutting performance as the target is moved away from the nozzle, which had a diameter of around 1 mm (0.04 inches). But the plot also shows that the cutting depth drops away very rapidly with time. After half-a-second the jet has cut roughly half an inch deep when the target is half an inch (12.5 mm) from the nozzle, but after doubling the exposure to a second the jet has only increased the depth of cut to 0.6 inches (15 mm) and with the time of exposure increased to five seconds the depth only increases to around 0.7 inches (17.5 mm).

This will be the topic for the next post, where the effect on the speed of cutting is the subject.

Waterjetting 30d - Applying cavitation damage

Much of the work that we carry out with high pressure waterjets requires that they cut with precision and, in consequence much of the focus has been on controlling the stream of the jet to obtain the tightly constrained cutting action that produces this result.

Yet two of the larger growth sectors of the industry, the sub-divisions that have now been given the titles “hydro-demolition” and “hydro-excavation” don’t have that focus. Rather they seek to remove critical volumes of material, generally to some specific depth, but with less concern over the edges of the hole that is being created (provided water doesn’t penetrate the edge materials).

Depth of cut control is a little more of a challenge using an abrasive waterjet system since I have seen AWJ cuts that penetrated through feet of reinforced concrete and have mentioned the problem that new owners of systems sometimes run into when they run the nozzle for too long in a fixed position over a target and discover that the jet has not only cut the material, but also penetrated through the bottom of the holding tank, and put a hole into the underlying concrete floor.

Precisely controlling depth then becomes a matter of controlling the length of time the jet cuts on a surface, and to get to a fixed depth that will also depend on the amount of abrasive in the water, the jet pressure and the distance from the nozzle to the surface. It can also, to a degree, be controlled by the pressure of the surrounding fluid, although that is an interaction with the driving pressure that can become a little more complex.

In the last post I mentioned that when cavitation is formed around the outside of a jet cutting down through water which is itself pressurized (perhaps only because the jet is under a significant depth as water, such as for example a diver cutting apart an oil platform in the North Sea) then the damage from the cavitation bubble collapse occurs most intensely over a short distance from the nozzle. That distance changes with the cavitation number (simplistically the ratio of the pressure in the water around the jet to the pressure driving the jet itself), the volume flow and in a secondary relationship to the surrounding fluid pressure as well as other factors.

The latter impact of chamber pressure on the cutting range of the jet can be demonstrated with a Lichtarowicz cell, which allows one to see the jet as it cuts through surrounding fluid to the jet, and where, by adjusting the chamber fluid pressure the jet and cavitation cloud length can be extended to and beyond the sample, or reduced so that the jet barely reaches the target.

Figure 1. Backlit picture showing the cavitation bubbles forming and hitting the target.

The problem with generating this type of cavitation cloud as a means of drilling forward is that the bubbles are on the outside of the jet, and so as the jet hits and flows across the surface it protects the surface from the bubbles which flow on the outside of the lateral action.

The bubbles need to be confined against the target surface, and this is easier to do where the bubbles are formed in the center of the jet. The ways of doing this were discussed in an earlier post but can be summarized as being either by creating a turbulent swirl in the jet, or by placing a flat-ended probe into the jet stream.

Figure 2. Methods of creating cavitation bubbles in the center of a jet. (After Johnson et al)

Of these two methods, that using the central probe is more effective over greater distances, since the jet remains relatively coherent, while the swirling jet tends to broaden and lose energy after much shorter distances.

Tests of the central probe device showed that it could very quickly drill a hole more than 18 inches deep – at which point, unfortunately, the probe within the nozzle was itself destroyed by the cavitation action.

These tests were, however, carried out with nozzles with orifice diameters on the order of 0.04 inches, with the probe diameter being roughly half of that. Such designs are difficult to make and then align – ensuring that the probe is centered within the orifice throat, as shown.

In contrast with abrasive waterjet damage, the damage from an individual event is not as critically affected by the particle size nor by the main jet velocity. The collapsing pressure jet from a cavity collapse is at around 1 million psi – as Dr. Al Ellis theorized and we were able to confirm at Missouri S&T. This occurs with relatively little control by the surrounding fluid, or originating jet (which instead is more influential in controlling the intensity of cavitation generation and the location of the collapse).

This means that it is quite possible to use larger jet streams and still achieve quite destructive effects. In Johnson’s early paper on the topic he was using a jet pressure of 1,600 psi and able to drill through blocks of granite. The best advance rate that he could achieve at that time was around 3.5 inches/hour – which is not a practical value for commercial operations.

And unfortunately, for a while, this led us to be distracted into seeking higher and higher operating pressures to drive the jet, forgetting that this did not really change the bubble collapse pressure. It was only later, when we followed Dr. Lichtarowicz’ advice that we started adjusting the back pressure in the system and then we began to achieve useful material removal rates (on the order of cubic inches per minute).

However we did not carry out tests at larger flow rates, where we know, from the evidence at the Tarbela High Dam that much greater volumes of material may be removed, even at relatively low operating pressures.

At the Boulder Dam in the United States cavitation generated a cavity some 100 ft long and roughly 25 ft wide cutting into the rock wall to a depth of 40 ft. along the spillway during the course of a season, as reported by Warnock.

As a result of these tests it is clear that there is a considerable development potential for the practical use of cavitation – at significantly higher production rates than achieved to date, and over the wide spectrum of minerals (since the high destructive pressures exceed those necessary to disintegrate all natural materials).

It will be interesting to see when interest in the topic regenerates.

Johnson, Kohl, Thiruvengadam and Conn “Tunneling, Fracturing, Drilling and Mining with High-Speed Waterjets Utilizing Cavitation Damage.” First ISJCT
Benjamin T.B. and Ellis A.T. “The Collapse of Cavitation Bubbles and the Pressures Thereby Produced against Solid Boundaries,’ Proc. Royal Society (London), A262, pp.221-240.
Wanock J.E. “Experiences in the Bureau of Reclamation,” Cavitation in Hydraulic Structures – a Symposium, ASCE vol 71, no 7, p 1053. (Sept. 1945)