MORE ON POWER

The amount of power that a piece of equipment can sink to the premix gives a good measure as to its effectiveness. Here is a test setup to determine comparative energy input in dispersers.

Abstract:
The amount of power that a piece of equipment can sink to the premix gives a good measure as to its effectiveness. Here is a test setup to determine comparative energy input in dispersers.

Detail: [By: Mark Drukenbrod]

The way things transmit power from one body to another has been a source of endless fascination many of us since we saw our first Van De Graaff generator as a child. Then, like most post-pubescent American males, most of us apply the intuitive power transmission laws learned in childhood to our first car. It might have been a junker, but we were going to make it the fastest junker in town. So we go to college, or learn a trade, and some quirk of fate neatly deposits us in the paint or ink industries. Here, most of us encounter our first high speed disperser...a formidable beast engineered to put a lot of horsepower into a little tank with just about the strangest looking blade we've ever seen. It seems impossible for that 15" diameter saw toothed dispersion blade to transfer all the power that the 15 HP motor has to offer, but somehow it does. This column will attempt to define the how and why of this transfer and how to accurately predict the amount of power you need to mix in a particular batch. There will be experiments that you can duplicate, graphs that you can use to interpolate, and a gem or two of mixer lore along the way, so let's get started.

The Setup First, a word or two about my test setup, and why we chose to use the equipment that we used. The disperser itself was a 15 HP Myers model 775 with a standard Speed Selector variable speed drive. I chose the Myers because I knew it well, knew it was well built and up to absorbing the level of punishment that I would be dishing out on a continuous basis in the lab here at CB Mills. After I got the disperser, I did some things that help he in a lab setting, but which should not be attempted in a production setting. Since it was necessary that I be capable of mixing anywhere between 20 and 300 gallons, I needed additional speed controls, since I would be mounting blades between 8" and 15" in diameter. To accomplish this, I had a current sensing variable frequency drive installed, along with a digital tachometer that had a math function built in, allowing me to alternatively display shaft rpm or disk peripheral speed. This setup is nifty, but voids the manufacturer's motor warranty, so I do not recommend it to you.

As we can all surmise, the dispersion disk belongs to the general classification of turbines, since the material enters the disk on the shaft axis, is moved from the center to the periphery of the disk radially, and is flung off the disk tangentially into the bulk of the material in the batch. Both the diameter of the disk and the height of the vanes influence the amount of power the disk will use, with all other conditions being controlled. On the product side, the important characteristics of the material that control dissipation are rheology, tank size, and tank shape. The standard vane size impeller is designed to provide the highest discharge velocities without breaking the bank as far as power is concerned. High-vane blades increase the discharge volume at the expense of extra power dissipation. The vanes do a large proportion of the pumping in the tank, while it is thought that most of the dispersion work is done on the flat disk surface. Vane heights range from 0.02 to 0.05 of the disk diameter, and most manufacturers fall in the exact center of this range for their standard blades. People's ideas of optimum disk velocity range from 3000 to 7000 fpm, although as the blades spin faster and faster, power consumption increases logarithmically with speed. Through empirical interpolation over the years, we have found that the best dispersions are done in a speed range between 4500 - 5400 fpm, at which point the blade's secondary energy dissipation (heat) is controllable (and a minority of the total power dissipated. The data was collected from the Myers, operating on 460V, three phase power, fused at 25 amperes. For all of the data collection, I used Myers type high speed blades, with a vane height of 0.035 of the total diameter, punched alternatively up and down out of the outside diameter of the blade, providing an attack angle to impart fluid flow roughly 40 degrees form a true tangent of the blade. True shaft rpm of the mixer was variable (for purposes of keeping the motor intact) between 250 and 7000 rpm, in order to achieve our target 4500-5400 fpm on a wide variety of blade diameters.

The list of variables controlled were:
a) tank diameter: 24"
b) no baffles
c) tank/impeller diameter: 0.36
d) blade placement 1.0 diameters above tank bottom
e) viscosity range: 1cps-40,000cps
f) batch load: 1.3 tank diameters
g) material density 56 - 125 Kg/m3

From this we can assume that a typical run would be with an 8" blade in a 24" diameter tank, filled to 31 inches, with the blade 8" above the tank floor.

Results and calculations:
As we still have a belt-based variable speed drive on the mixer, it was necessary to identify the power loss of the transmission, subtracting it from the input power to give us the delivered, or net power. These numbers were provided by the drive manufacturer. In the graphing of this information, we learned something that we suspected, but did not know for sure. At high energy levels, the transmission transmits about 85% of the power from the motor to the mixing shaft. These numbers reduce in efficiency as the load decreases, bottoming out at about 50% for light loads. Granted, this is not really a problem, since the load does not require the transmission of the entire amount that the drive can deliver anyway. We found the empirical data to fit the mathematical models of mixer operation as used by the rest of the mixer industry (low speed mixers). These mathematical models are derived from the general laws of fluid flow, and the general resistance model for relative motion between a fluid and a spinning impeller. All of these calculations boil down to a Power number, which is one of those pesky dimensionless numbers, related to another similarly pesky and dimensionless number, the Reynolds number. Since both of these equations contain superfluous factors such as constants to adjust for shape and attack angle along with vane swept area and aspect ratio, the equations were reintegrated and simplified to the following:

Power number:
where: p is power in ft/lbs.
gc is the acceleration of gravity (32 ft/sec2)
n is shaft revolutions per sec.
d is impeller diameter in feet
r is the material density in lbs./ft3

The Reynolds number (Re) is:
where: n is shaft revolutions per sec.
d is impeller diameter in feet
r is material density in lbs/ft3
h is viscosity in centipoises

Results:
Coming Soon!