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.

Waterjetting 7b - more insight into jet structure

In last week’s post I showed some high-speed photographs of the plain water jets that come from the small diamond and sapphire orifices and that are useful in cutting a wide variety of target materials. Before moving away from the subject of high-speed photography, this post will use results from that technique to talk about why pressure washer nozzles may not work well, and have limited range. From there it will raise the topic of adding abrasive to a waterjet stream.

Most of us, I suspect, by this point in time, have used a pressure washer to do some cleaning, typically around the house or perhaps at a car wash. The jet that comes out of the end of the nozzle is typically a fan-shaped stream that widens as the water moves away from the orifice. This flattening of the jet stream, and the resulting spreading jet is achieved by cutting a groove across the end of the nozzle to intersect either a conic or ball-ended feed channel from the back end of the nozzle.


Figure 1. Schematic of how a fan–generating orifice is often made.

One of the problems with this simple manufacturing process is that the very sharp edge that is produced to give a clean jet leaving the nozzle is very thin at the end. This means that with water that is not that clean (and most folk don’t filter or treat pressure washer water) the edge can wear rapidly. I have noted several designs (and we tested many) where the jet lost its performance within an hour of being installed, particularly with softer metal orifices. And in an earlier post I did show the big difference between the performance of a good fan jet and a bad.

So how do photographs help understand the difference, and explain why you should generally keep a fan jet nozzle within about 4-inches of a surface it you are trying to clean it. That does, however, depend on the cone angle that the jet diverges at, once it leaves the nozzle. We found that a 15-degree angle seemed to work best of the different combinations that we tried. If the jet remained of sufficient power, this would mean that it would clean a swath about half-an inch wide with the nozzle held 2-inches above the surface. At 4-inch standoff it will clean a swath about an inch wide, and at 6 inches, this goes up to over an inch-and-a-half. But that would require that the jet be of good quality, and evenly distributed.


Figure 2. Back-lit flash photograph of a fan jet, at a jet pressure of around 1,000 psi. It is less than 6 inches from the end of the orifice to the rhs of the picture.

In Figure 2, the lack of water on the outer edges of the stream shows that the water is not being evenly distributed over the fan. As the water volume leaves the orifice, the sheet of water begins to spread out into the wider, but thinner, sheet that forms the fan. But as it gets wider it also gets thinner, and, like a balloon, water can only be spread so thin before the sheet begins to break up. As soon as it starts to do so, the surface tension in the water causes it to pull back into roughly circular rings of droplets.


Figure 3. Fan jet breakup from a spreading sheet into rings (or strings) of large droplets that rapidly break down into mist.

These droplets start out as relatively large in size, but they are moving at several hundred feet per second, and as single droplets moving through stationary air the air rapidly breaks them up into smaller droplet sizes, and then into mist, while at the same time slowing the droplets down. The smaller they get the quicker that deceleration occurs. When droplets get below 50 microns in size they become ineffective. (From a study that was done on determining the effect of rain on supersonic aircraft).


Figure 4. Showing the stages of the fan jet breakup from a solid sheet to mist that does little but wet the surface that it strikes.

However, if the nozzle is held just in that short range where the droplets have formed, but have not broken down, then the jet will be more effective than it would have been at any other point along its length. This is because of something that was first discovered when scientists at the Royal Aircraft Establishment-Farnborough and at the Cavendish Lab at Cambridge University were studying what would happen if they flew a Concorde into rain, while it was still going supersonic. (They actually tried this in a heavy rain storm in Asia and found it was a seriously bad idea).

The pressures that can develop under the spherical droplet can exceed twice the water hammer pressure so that the impact pressure on the surface can exceed 20-times the driving pressure supplied by the pump. But the region effected is very small, and the effect diminishes as the surface gets wetter. And the problem, as with all waterjet streams, is that it is very hard to know where that critical half-inch range is. It varies even within the same nozzle design models due to small changes on the edge of the orifice. And as a very rough rule of thumb, a perfect droplet moving at a speed of around 1,000 ft/sec will travel 138 diameters before it is all mist. Most drops aren’t perfect and thus will travel around 30 – 50 diameters and once they turn into mist they will decelerate to having no power in less than quarter-of-an-inch. The implication of this, which we checked with field experiments, is that if you hold a pressure washer nozzle with a fan tip more than 4-6 inches from the target you are largely just wetting the surface, and spending a fair amount of money in creating turbulent air.

This story of jet breakup is a somewhat necessary introduction to two posts that I will be along before long. The first will be to discuss how we can use a different idea for nozzle designs to do a much better job, at greater standoff distances, and I will tie that in with some of the advantages of going to much higher pressure to do the cleaning job.

The other avenue that this discussion opens relates to how we mix abrasive within the mixing chamber of an abrasive nozzle design, and that will come along a little later.

(For those interested in more reading there have been a series of Conferences on Rain Erosion, and then “Erosion by Solid and Liquid Impact” which were held under the aegis of John Field at Cambridge for many years. See, for e.g.. Field, J.E., Lesser, M.B. and Davies, P.N.H., "Theoretical and Experimental Studies of Two-Dimensional Liquid Impact," paper 2, 5th International Conference on Erosion by Liquid and Solid Impact, Cambridge, UK, September, 1979, pp. 2-1 to 2-8. The founding conference was held under the imprimatur of the Royal Society, which devoted a volume to the Proceedings. Phil. Trans. Royal Society, London, Vol. 260A.)