Friday, September 19, 2014

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).