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 29d - Fixing an Oops.

There was a story that is told in Mining Engineering classes about a tunnel that collapsed, even after there had been a whole series of tests carried out to make sure that the rock was strong enough before the tunnel excavation was started. In working out why the tunnel had collapsed some questions were raised about the tests made on the rock samples. It turned out that the testing technicians had received the samples and struggled to find good enough quality pieces of rock in the sample from which they could extract the required sample sizes to run the standard strength tests.

When they reported the results of their tests these predicted that the rock would be strong enough to stand, without collapse, for a long enough time for artificial supports to be placed under the rock and to hold it in place. But it was not that strong segment of the rock that failed, rather it was the rather more rotten rock that surrounded it which provided the weakest link in the tunnel wall. That material had been too weak to make into a sample, and the technician had therefore not reported the lack of strength.

Knowing the properties of a target material before starting a job is an important part of correctly forecasting how how long it will take to perform the cutting tasks required and, as a result, how much to charge for the work. And further to ensure that there is no unanticipated cost that will come from the use of the waterjet tool at the parameters planned.

These unintended consequences have, for example arisen in the past when a high-pressure waterjet system was being used to remove damaged concrete from the surface of a bridge. (As with the tunnel we’ll keep the bridge as an unidentified example).

In repairing a bridge deck it is usually required that the top layer of concrete be removed just past the top layer of reinforcing steel (rebar). This allows a good bond between the previous concrete and the repair pour, which also bonds to the rebar giving a repair that will last for some time. (More conventional repairs leave a weakened joint between the repair and the old concrete which fails more rapidly in many cases).

However the waterjet system is only discriminatory to some extent. The jet pressure can be set so that it will only remove damaged concrete, for example, but does not have sufficient pressure to remove healthy (and less cracked) material. But if the material is weaker than expected, or the damage extends further into the deck than was expected, then the waterjet system will continue to remove damaged concrete, even if this means it ends up removing material all the way through the deck. This can be a real problem, given the extra money and time that must now be spent in replacing that additional concrete, and ensuring that full integrity is restored to the deck. This additional cost can be more than the price of the original repair work, and do serious damage to the economic health of the waterjet company. Unfortunately with many of the systems today becoming more and more automated, it requires close attention the machine at all times to ensure that only the required amount of material is removed and no more.

One solution to the problem is, at least initially, the very opposite of what you might think would be the best answer. It is to increase the pressure of the jets removing the material. For a system with the same horsepower as the machine that was being used first, this means that the amount of water used will be less, and the nozzle diameters will, as a result, also shrink in size.

The smaller jet diameters and higher pressures mean that the cutting distance of the jets themselves will become shorter, as the jet decays more rapidly with distance. (To give an extreme example a 1200 psi jet at a diameter of about an inch-and-a-half can throw a jet about 125 ft. At 50,000 psi and at a diameter of about 0.005 inches the range of the jet is usually less than 2 inches*.) Within their effective range, the higher pressure jets will cut much faster, and so it is possible, by mounting the cutting nozzles in an array that spins around a common axis, to rapidly clean a swath of material (say up to 2 ft in width) as the head moves across a traffic lane at an advance rate of roughly 1 pass a minute as it moves up over the bridge. The higher rotational speeds will also restrict the depth to which the jets can cut on a single pass, so that the depth of material removed can be relatively accurately programmed into the machine by adjusting some of the operating controls. (After first finding out what the best parameters will be for THAT bridge concrete in a small test area off the main work site).

There is an additional advantage to using the higher pressures, and that comes with the smaller volumes of water that will be required to take the damaged layer of concrete from the surface. This water will be contaminated by the different fluids that may have soaked into the bridge over time, and by the corrosion products of the deterioration. For these reasons all the debris and water from the demolition operation will have to be collected, removed and properly (and expensively) disposed of. The higher the volume of water then the greater the collection and disposal cost, and the lower water volumes needed with higher pressures will thus carry a lower disposal price.

The example given here is for the removal of damaged concrete from bridge decks and garage floors, but the underlying principle also applies in the milling of pockets into materials of differing composition, where a controlled depth of cut needs to be held, even if the material strength changes.

*The word “usually” is used since there are ways of increasing the jet throw to several thousand orifice diameters.

Waterjetting 25b - range with abrasive

In the last post I wrote about the impact of smaller jet diameters, and higher pressures, in truncating the range over which a waterjet is effective. The same is true, to an extent, when one adds abrasive to the water.

Our “green tube” test has been described in earlier posts, where the distance over which particles settle out of the jet provide a measure of how much energy they were given. However it is not that simple to interpret the results from these tests. The reason is that, as with a plain waterjet, the range of the particles is controlled to a degree by the size of the individual grain. Why is this? Well this series tries to keep formulae to a minimum, but one is needed in the answer to that question.

The origin comes from our friend Newton, whose Laws have come down to us over the centuries, and the second of which states:

Force = mass x acceleration

Consider that when an initially stationary particle is sitting in a jet stream, the force being applied to it by that jet is equal to the pressure of the jet, multiplied by the area over which the pressure is applied. If for simplicity we assume that the particle is spherical, then the area over which the pressure is applied (assuming that the particle is centralized within the jet stream) is equal to the pressure multiplied by the cross-sectional area, which is given by the product of the square of the radius multiplied by pi.

On the other hand the mass of the particle is related to the volume, which is in a cubic relationship with the radius. Thus if these two terms are substituted in the equation above, and combining all the non-radial terms into a constant results in an equation where:

Acceleration x radius cubed x constant = pressure x radius squared x constant

Rewriting this gives:

Acceleration = (1/radius) x pressure x constant.

This means that larger particles have smaller accelerations for a given pressure, while smaller ones accelerate faster.

However, and this pertains to the results we saw from the green tube tests, just as the smaller particles are accelerated faster while in the jet stream as it passes through the nozzle assembly, so those smaller particles will decelerate faster when having to travel through the relatively stationary air outside of the nozzle.

Thus if you are, for example, using a smaller jet flow (and smaller jet orifice in consequence) then the normal practice is also to reduce the size of the focusing tube, and – to otherwise keep the system practical – to also reduce the size of the abrasive particles fed into the system.

However, while this gives a better cutting effect immediately under the nozzle (hence the widespread recommendation to restrict the standoff distance between the nozzle and the target to about a quarter-of-an-inch) there is a more rapid decline in the speed of the particles as they move away from the nozzle. The net result is a shorter range for the jet, and a shorter cutting depth in consequence.

There is a small caveat to holding this as an absolute conclusion. Back in the days of the U.S. Bureau of Mines Dr. George Savanick showed that where an abrasive jet could be held within a relatively narrow slot, as it cut down, that the walls of the slot tended to concentrate the jet, and thus extend its range beyond that achieved if the jet were, for the sake of example, just cutting through a piece. Thus, when not through-cutting the part, there will be some extension of the jet range, and this has to be considered when setting the operating parameters for a particular job.

Which brings us back to defining the optimum size of the operating plant required to complete a given job, and a resolution of the optimum parameters for carrying out the job.

As I have noted before, this is not a simple and straightforward choice. Proponents of different operating systems will advocate different solutions based on the units that they are most familiar with. And there are arguments that can be made for different choices. However, in making the choice of the best system to use, one must be aware of the limitations (as well as the benefits) of the different choices that might be available.

Consider that a lower pressure, higher flow rate system might use larger particles, and thus be able to cut through a target plate of a given thickness with better speed than a higher-pressure, lower flow rate alternative. However were the target to be of a thinner stock where the range of the jet is not that critical, then the higher pressure system may well give the better performance (given, inter alia, that it will also use less abrasive and water).

Making a selection as to the better operating system, therefore, requires a clear understanding of the different modes in which the system is likely to be used. Will it be for relatively thin materials, where high precision and narrow cuts are required, but the material need not necessarily be through-cut. Or is the system one where a cut may be required through perhaps 30-inches of reinforced concrete in a reactor (of which more in a later post). In the latter case the lower pressure, higher flow rate jet, with the ability to use larger particles and sustain their velocity further, when further confined by the walls of the cut. The former condition would argue for the use of a higher-pressure, lower-flowrate combination, while the latter (as a generalized statement) would incline more to the lower pressure alternative. (And the terms are relative, since in the latter case we are likely still talking about pressures of around 30,000 psi or higher to achieve the depths of cut within the reinforced concrete.)

Much is written about having to make absolute choices in cutting, but in many cases it is only a matter of relative performance, with systems across a range of parameters being able to effectively achieve the goal. The selection of which system to use should focus more on the normal range of materials that one is expected to cut in the normal course of operations. (And slicing though parts of a nuclear reactor is not normal in most aspects of this business).

Waterjetting 25a - choosing jet parameters for range.

The range over which a waterjet is able to cut material can widely quite significantly, depending on a wide range of factors, including abrasive content. An earlier post described the way in which students in a waterjet class were shown some of the difficulties in assessing risks arising from the use of a waterjet, and the range over which it was dangerous. Simplistically the students first cut along a plywood panel to see how far from the nozzle the jet would remove wood.

Figure 1. By slightly tilting the 4-ft wide panel and then having students move the jet past the board along the left-hand edge, a measure of the range of the jet could be obtained.

However, after the students had decided that, for the 10,000 psi 0.03-inch diameter jet, the cutting range was about ¾ of the way across the width (i.e. 3 ft) they were then tasked to pass the jet, as fast as they could, over a piece of pork that was at least a foot further away from where they estimated the distance that the jet stopped cutting.

Figure 2. A piece of pork after being “sliced” by a 10,000 psi waterjet.

The pork was typically cut to a depth of over an inch, grooving into the bone at a distance that the student had previously decided was “safe.” It was pointed out to the class that the pork was a good simulator for human flesh.

The point of the demonstration was fairly obvious, but it does highlight that the distance at which a jet stops cutting one material because of insufficient energy, may still be quite a distance closer than that critical distance for other softer materials.

In one of the earlier scientific papers on waterjet cutting Leach and Walker plotted the drop in jet pressure from two different nozzle shapes, against the distance from the nozzle.

Figure 3. Decline in jet pressure with distance from the nozzle (Leach and Walker)

With poorer nozzle designs and in cutting many harder materials the critical distance at which the jet pressure falls below half the original pressure, and thus in many materials stops cutting, is at around 125 nozzle diameters. For a 0.03-inch diameter jet, cutting a distance of 36 inches takes the range to 1,200 diameters. And while that range is partly because we have significantly improved the fluid flow into the nozzle it relates, as noted, also to the strength of the material being cut.

One reason to mention this is that I have seen, both in photos and real life, people foolish enough to hold their hands in front of a 40,000 psi waterjet, as an illustration of the safety of the tool at even a short range. (Typically they were using jets of around 0.006 inches diameter with the hand about a foot from the nozzle). A slight increase in nozzle diameter, undetected by the operator, or a change in fluid content (such as by adding a long-chain polymer (such as Superwater) could extend the range of the jet several-fold, so that the unsuspecting operator might lose several fingers before realizing the change in conditions.

An earlier post described the work of Clark Barker and Bruce Selberg, who demonstrated that an increase in polish of the inner surfaces and a smooth transition path into the orifice could extend the cutting range of a jet in harder materials from 125 diameters to over 2,000.

Achieving a smooth flow path to the orifice is critical to superior performance, though – as I have mentioned before – it was at one time surprising to me how many contractors did not even have the nozzle insert mating with the end of the supply pipe. Rather, with the nozzle insert held in a holder, they just turned the latter until it was tight, not always achieving contact between the back of the nozzle insert and the pipe. In addition there have been many cases I have seen where the nozzle insert inlet diameter differs from that of the internal diameter of the connecting pipe Again this will interfere with performance away from the nozzle.

Assuming, however, that one has stabilized the flow into the nozzle, and that it is of the right shape, how can one increase the jet throw distance further? The obvious, and wrong, answer is to up the pressure that is driving the jet.

Why is this the wrong answer? Well, if one considers what happens when a jet shoots out into the air, as one can see in a high-speed flash photograph:

Figure 4. Flash photograph (exposure at about one-millionth of a second) of a high speed waterjet showing the structure.

As the jet travels through the air, so the relatively stationary air around the jet strips off, and decelerates, the jet in layers starting from the outside. These show up as backward pointing stringers flowing out from the main jet stream. As the outer layers are peeled off (as with stripping the layers from an onion) so the remaining diameter gets less until, as in the picture above, there is no jet left.

Consider that with a higher driving pressure that there is a greater differential between the air speed and that of the jet, and obviously the stripping action will occur more rapidly, reducing the overall range of the jet.

Now consider if, instead of putting that additional power into pressure/jet velocity one were, instead to put it into additional flow. Then there are more layers of the jet to strip away, and the differential is not as great. As a result, when one compares the performance of two jets one gets:

Figure 5. Comparing the performance of two jets.

Notice in this case that relatively close to the nozzle the two jets, cut to roughly the same depth, and in this range the higher pressure, smaller jet has advantages in that the thrust it applies to the holding tool is less, and the total amount of water used is also less (roughly 4.3 gpm rather than 7.3 gpm). However if one is cutting at a greater standoff distance between the wall and the target, then at about 4 ft from the nozzle (1000 diameters of the larger, 1500 diameters of the smaller) the lower pressured, higher flow rate jet becomes more effective.

This relative change in nozzle effectiveness with pressure and diameter was also reported from results at lower pressure when developing nozles for cutting coal in Germany.

Figure 6. Comparing the pressure profiles of jets at two different diameters and pressures, as a function of distance from the nozzle.(Benedum et al)

Note that here, again, at about 8 m from the nozzles, both jets are producing about the same impact pressure, while closer to the nozzle the smaller (blue line) jet has a better profile (at 0.78 inch diameter, and 1,300 psi) than the larger (black line) jet (at 1-inch diameter, and 1,000 psi). But at greater distances the lower pressure, larger diameter jet becomes more effective.

There is, in short, significant benefit to determining, before one starts, what the objective is and over what range the jet is expected to cut, since both will help decide what set of jet operating conditions will give the better result.

References Leach, S.J., and Walker, G.L., "Some Aspects of Rock Cutting by High Speed Water Jets," Phil. Trans. Royal Society, London, Vol. 260A, pp. 295 - 308.
Barker, C.R. and Selberg, B.P., "Water Jet Nozzle Performance Tests", paper A1, 4th International Symposium on Jet Cutting Technology, Canterbury, UK, April, 1978.
Benedum, W., Harzer, H., and Maurer, H., "The Development and Performance of two Hydromechanical Large Scale workings in the West German Coal Mining Industry," paper J2, Proc. 2nd Int. Symp. Jet Cutting Tech., BHRA.

Waterjetting 16c - Optimal AFR and cutting curves

The discussion on surface quality which forms this month’s topic has, to date, focused on linear cutting since this has been the simplest way of explaining some of the factors that go into choosing an optimum abrasive feed rate (AFR) for a system. Along the way, however, I have pointed out that the internal design of an abrasive nozzle has a considerable impact on the relative performance of different systems.

If, for example, the internal geometry is such that there is not an optimal transition of energy between the high-pressure waterjet stream and the abrasive particles, then trying to draw conclusions over the influence of some of the operational parameters, such as pressure, can lead to false conclusions. The optimal AFR changes with the relative sizes of the waterjet orifice, the location of the abrasive feed line, the length of the mixing chamber and the geometry of the focusing tube. These parameters are generally held fixed since most folk buy only one cutting head design, and tend to stick with it once purchased. However, as I pointed out at the beginning of this blog, there is a considerable difference between the performance of different abrasive cutting heads.

Figure 1. Comparison of the relative cutting performance of twelve different abrasive nozzle designs, when operated otherwise at the same pressures, water flow rates and AFR.

The best design, for the particular waterjet and AFR parameters that were tested in generating Figure 1, was 24% more effective than the average performance of the nozzle designs tested. This is indicative that the design was more efficient in accelerating the abrasive to a higher velocity than the competing designs. Those designs were tested at a number of pressures and AFR values to ensure that the conclusions held within the range of test – and they did. But as the pressures and AFR values change so there is a change in the optimal design with consequences on the optimal AFR as it relates to the operating pressure of the system.

Without an awareness of these inter-related parameters it is possible to draw erroneous conclusions about the best choice of cutting parameters for a given operation. The situation becomes even more complex where the paths being cut are no longer straight but involve complex contour cutting, and where there are requirements for zero taper and high surface quality on the cut faces of the part being generated.

One solution to the problem is to accept the limitations of the system, and cut the part at a constant speed, slow enough that the jet cuts through the piece on first contact with the abrasive stream over the length of the cut. (In other words after the abrasive bounces away from the initial contact plane along the cut it does not meet any more material before it exits from the bottom of the cut). At a pressure of 40,000 psi the cutting speed to achieve these requirements over an half-inch thick titanium target lies at around 0.3 inches per minute.

Figure 2. Change in cut face taper angle with traverse speed at a cutting pressure of 40,000 psi.

However as the pressure of the jet is increased the cutting speed to sustain that quality cut goes up significantly, so that there is a significant benefit to the increased pressure. But the optimization to achieve this is geared to ensuring that the optimal abrasive feed rate has been selected, for a given nozzle design and waterjet pressures. Without a short series of tests to ensure that the system is being run at this optimal condition it is not possible to accurately state how a system can best be used.

I have described, in an earlier post, how such a simple test can be run. It should be stressed, however, that the selection of an optimal AFR for a nozzle is based on the nozzle geometry and the operating pressure of the system. That selection will provide the best cutting jet and this jet will have different capabilities in different target materials. Composite materials will cut at a different optimal speed depending on the material type and thickness, and these values will differ when metals, or ceramic materials are being cut. But, as a general rule, the selection of the best cutting conditions are first established by knowing the thickness and type of material to be cut. This should then produce, based on tested performance tables, recommendations for the cutting speeds at different pressures, where the cutting pressure in turn defines the optimal abrasive feed rate. Based on an assessment of the different categories of cost of an individual operation one can then decide which set of conditions would provide the most economical and acceptable answer to providing the quality of cut required.

In some cases it may be that the cutting head can be tilted so that, particularly with straight cuts, the part being isolated will have a perpendicular edge, while the scrap piece will have a tapered edge at twice the normal angle. For example under the conditions illustrated in figure 2 tilting the nozzle by only one degree will allow cutting at 4 ipm rather than 0.3 ipm, a 12-fold gain in performance, depending on the assurance of the quality of the surface being sustained.

As mentioned earlier this option becomes more difficult as the part being cut acquires contours. At higher pressures the angle of the cutting face curve is reduced, but in thicker parts there is often a slight displacement backwards (a rooster tail as it is sometimes called) from the top edge of the cut to the bottom. When the nozzle comes to cutting around a curve that backward projection at the bottom of the cut can pull the cut edge away from vertical unless the cutting head is adjusted to ensure that this difference is minimized to the levels acceptable to the customer. Most commonly this is achieved by slowing the head speed according to the radius of the curve, with sharper turns being made at slower speeds. Some adjustment in the angle of the head can also be made, but this requires a more advanced method of control and programming in developing the cutting path for the head.

Note: Because of the season this site will be Dark next week, so let me take the opportunity of wishes the readers of the waterjetting series all the Compliments of the Season, and with hopes that you have a Prosperous and Happy New Year.

Waterjetting 1c - Volume flow, horsepower and thrust tables

Over the course of my career there is one table that I have used, for one reason or another, just about every week. Most folk will not likely need it nearly that often, but it contains some information that can be handy, if it is suddenly needed.

The table provides the relationship between the pressure of a waterjet system, the size of the nozzle that the water is fed through, and the resulting flow rate that is being used, the horsepower of the jet, and the thrust that the jet will exert back on the equipment/person holding the nozzle.

It is a very straightforward set of calculations, and I will build the table in two parts. The first will be a line-by-line explanation of how the calculations are made, and what the basis is, and then I will provide a tabular format (which is the one that I use) from which values can be read off. Because this is built in Excel the values on the edges of the table are changeable, to fit your own particular set of needs. Construction of the tables will be given through a series of 30 steps.

I am going to write about the parts that make up a system to deliver water under pressure in later articles, and so some things that will be explained then are going to be just stated at this point. The first of these comes when one considers nozzle size.

A nozzle, at its most basic, is a hole of a fixed size. Under just the force of gravity flow is quite low, and to get more water to flow through that hole some pressure must be applied to the water. The very simple relationship between the pressure at which the water is pushed, and the resulting speed of the water is given by the equation:

Speed (ft/sec) = 12.5 x square root of pressure (in psi)

Please note that water starts to compress significantly at about 15,000 psi. For the sake of this initial set of tabulations I am going to neglect that issue, though it will come up at some future date.

1. Since pressure is a value that is often chosen by the operator, the value for pressure is entered into cell c3. For this example, a value of 10,000 is used. (These come from the first system that I worked with, back in Leeds in 1965).

2. The equation to determine the velocity of the water is entered into cell c4 as

[ =12.5*sqrt(c3)].

Because the units need to be consistent going through the calculation, inches will be used initially. So the initial velocity value is multiplied by 12.

3. To convert into inches/second, the value in cell c4 is multiplied by 12 in cell c5 using the equation:

[ = 12*c4]

4. Nozzle diameter is the exit diameter of the nozzle, and this is sometimes referred to as the orifice diameter. This is a selected value and is entered into cell c6. I am using 0.04 inches in the initial example.

The cross-sectional area of the orifice is given by the equation:

Cross-sectional area = π x (radius) squared

5. Orifice cross-sectional area is calculated in cell c7, by entering the equation:

[ = 3.1412*((c6/2)^2)]

As water flows through a hole, the stream does not flow out of the hole at the same diameter as the hole. As the flow enters the hole it necks down to a slightly smaller diameter, which is a function of the nozzle shape, among other things. The reduction is known as the Coefficient of Discharge for the nozzle, and is a specific value for an individual orifice that can vary from a value as low as 0.61 to a high of around 0.95 or better. This is an input value, based usually on a manufacturer’s statement.

6. Enter a coefficient of discharge value, I have used a value of 0.81, in cell c8.

7. Calculate the effective area of flow by entering the equation into cell c9.

[ = c7*c8]

By multiplying the area of the flow by the velocity (the length of the water column that flows through the orifice in a second) then the volume of water that flows through the orifice in a second is calculated.

7. Calculate the volume flow each second, by entering the following into cell c10:

[ = c9*c5]

The volume flow rate is normally required in gallons/minute, and the conversion is to multiply by 60 (to convert from seconds to a minute) and then dividing by 231 (the number of cubic inches in a gallon).

8. The calculation is made in cell c11.

[ = c10*60/231]

Computers calculate to a high number of decimal values, and to keep this in normal perspective I usually trim this to show either one or two decimal points. The value shown should therefore be 3.97 gallons/minute, and the table to date should look like this:

Figure 1. The basic steps in calculating the volume flow of water through a nozzle.

There are two other values that are useful to calculate. The first is the horsepower that is being used in the jet. This calculation is a straightforward multiplication of the pressure of the jet (in psi) and the flow rate (in gpm) divided by 1714.

9. Enter into cell c14 the equation:

[=c11*c3/1714]

The other equation that is often useful to calculate (particularly where lances are being held-held in cleaning operations) is the reaction thrust that comes back from the nozzle. Some years ago we validated in the laboratory that this value can be calculated from the equation:

Thrust = 0.052 x flow (gpm) x square root of pressure (psi)

10. Enter into cell c 16 the equation:

[ =0.052*c11*sqrt(c3)]

This gives the basic form for the calculation of the basic values that are most useful.

Figure 2. The initial individual values calculated for the flow.

(You might want to SAVE at this point).

However most of the time I want to do some comparisons and so instead of carrying out a single calculation I would like to see the values in a table.

To make the table I use the same basic equations that are given in the steps above, but I lay out a table of values for pressure and nozzle diameter, which I will step through for those who are less familiar with some of the features of Excel.

The first step is to enter the values that are going to be most useful. In a general table this starts with the pressure that might be used to clean the siding of a house.

11. Insert pressure values starting with 1,500 psi in cell b23, and continuing along the row to that which is used for some of the more intricate cutting of metal, at 90,000 psi, which is in cell L23.

12. The discharge coefficient value is set just above the table in cell c21. I am using a value of 0.81. since this is a common value to all calculations in this table, it is put in a place where it is easy to find and change where needed.

13. Nozzle diameter values are also input as a column down from A24 to A35. I have used values from 0.005 inches to 0.1 inches to cover the range of likely interest, though these can be changed, after all the tables are in place. (Those following along might use the values I provide to create the table, after which use your own values for pressure and nozzle diameter, and don’t forget to change the coefficient of discharge.)

The result, at this point should look like this:

Table 3. Basic structure of the flow calculation table

14. Now, in cell b24 (or the relevant cell in your table) enter the following equation, which combines all the different stages outlined above into one single step.

(=$C$21*(3.1412*60*(A24/2)^2*12*12.5*SQRT($B$23))/231)

The $ sign means that the location after the sign is a constant. It can be selected by highlighting the location in the equation (c21) and then pressing the command and T keys at the same time.

15. Now select the column of values that run from b24 to l24, and then use the Fill Right command under the Edit command in the menu. This will give a series of numbers in the shaded squared that can be ignored for the minute, since we are now going to go through and change some of the values.

16. Go to c24 and change the B24 to A24. Change the $B$23 to $C$23. Tab to D24 and repeat (i.e. change the C24 to A24 and $B$23 to $D$23), and continue doing this along the row, ending in cell L24 changing the K24 to L24, and $B$23 to $L$23). (This is just correcting the calculation to using the right nozzle diameter, and the right pressure values). The table should now look like this:

Table 4. The flow table with the first row completed.

And now take advantage of the power of the table.

17. Select the cells from B24 to L35, and then go to Edit -> Fill Down. The table should be filled in. (You might want to SAVE at this point).

Table 5. Full flow table.

The next step is to create the table for the fluid horsepower contained in the jet.

Because all the calculations tie back to one another from now forward, I am going to use a copy function for the pressure and nozzle diameter values, so that if these values are changed in the above table, they will also change in the dependant tables which follow.

The first step then is to insert the pressure and nozzle diameter values.

18. Go to cell A40 and enter

[=A23)

19. Select row 40 cells A40 through L40. Use the EDIT -> Fill Right command to copy the pressure values into the new table.

20. Select column A cells A41 through A52. Use the EDIT -> Fill Down command to copy the nozzle diameter values into the new table.

21. In cell B41 enter the equation: [=B23*B24/1714] select the B23 and press command T which will change the equation to: [=$B$23*A24/1714)

22. Select the B row from B41 to B52 and use the EDIT -> Fill Down command to generate the first column.

23. Go back to the values in cell B41 and remove the $$ signs from $B$23, hit return and remove the $$ signs from $B$23 in cell B42. Continue down the column removing $$ signs from the cells. The numbers in the cells should not change as you go down.

24. Select the cells from B41 to L52. Enter EDIT -> Fill Right. The second table will generate. While the cells are still selected reduce the number of decimal places to 2. SAVE the file. You have just generated the fluid horsepower table, which should look like this.

Figure 6. Fluid horsepower table.

We will now use the same technique to calculate reaction force.

25. In cell A57 enter [=A23]

26. Select cells A57 to L57. Enter EDIT -> Fill Right, to enter the pressure values at the top of the table.

27. Select cells A57 to A52. Enter EDIT -> Fill Down, to enter the nozzle values along the left-hand side of the table.

28. In cell B58 enter the equation for reaction force in terms of pressure and flow.

[=0.052*B24*sqrt(B23)]

29. Select the cells B58 to L58 and enter EDIT - > Fill Right.

30. Enter cell B58 and select the term B23. Press the command key and T at the same time, which will change this from B23 to $B$23. Tab and repeat this for the C23 term in cell C58, for the D23 term in cell D58 and so across the row ending with changing L23 in cell L58 to $L$58.

31. Select cells B58 to L69. Enter EDIT -> Fill Down. The table should be complete. It should look like this:

Table 7. Reaction Force calculation table.

Congratulations, you now have your own table, and by changing the pressure, nozzle diameter and discharge coefficient values along the flow volume table the charts can be tailored for your own conditions.