Recently I was involved in a discussion with some folks from Chevron about the effects of viscosity on centrifugal pump performance. Here are some excerpts from our discussion:
"The Hydraulic Institute recently published a new standard to account for the effects of viscosity of centrifugal pump performance," said Sergio D. Castellanos (Field Technical Support, Chevron Pipeline Company, Western Technical Services, Bakersfield, CA). "Prior to this method, viscosity corrections were done using viscosity correction charts. I thought some of you might be interested in this new standard. Perhaps someone has already looked into it and can provide feedback?"
"Thanks for the heads up," responded Ed Ashbridge. "Let me know what you think about it."
"The new method is much easier to use because it calculates the viscosity corrections automatically by using the formulas provided," explained Sergio. "There is no more need to "eyeball" from charts, so the new method is more accurate. The standard also provides a nice background description of the method, along with its limitations, and pump types and pump design characteristics for which procedure is applicable.
"With the new method," he continued, "the efficiency corrections are less severe as viscosity increases (hence less horsepower), but the flow and head capacity corrections are a bit more severe. I would say the differences between both methods are significant. I have a question for everyone. What is a pump with an essentially radial discharge? And can I assume that crudes or refined products behave as Newtonian fluids? These are some of the conditions in order to use the new method."
"I pulled out my old fluid mechanics book to bone up on Newtonian fluids," said Charles Lyon. "I won't quote the definition entirely, but a key statement is "The viscosity is a function only of the condition of the fluid, particularly its temperature." Water, oil, gasoline, alcohol, and even glycerine are given as examples of Newtonian fluids. Examples of non-Newtonian fluids given are slurries, suspensions, gels and colloids. I would feel comfortable with the assumption for crude and refined products, but I must ask at what point (low temperature) does heavy crude stop behaving like a Newtonian fluid? I believe that, at all pumpable temperatures, crude (San Ardo or San Ard/KLM blend) is a Newtonian fluid.
"The radial discharge question is a bit tougher," remarked Charles. "I believe this refers to a typical end suction or open face impeller where the fluid is discharged perpendicular to the shaft centerline or suction direction. Perhaps the method does not work for axial flow centrifugals (turbine pumps) where the impeller side walls are angled beyond 90-deg and/or propeller type pumps. I have asked Dr. Nelik for his insights on all of this." -
"Most fluids are Newtonian," I replied, "e.g. their viscosity is constant with their shear rate. Shear rate is the relative stress imposed on a fluid by that moving fluid. Consider, for example, a 10-in OD closed impeller, with 0.010-in radial clearance between the wear rings, which are each 5-in diameter. If the impeller rotates 3600-rpm, then the metal peripheral velocity is 78 ft/sec (you can calculate this). The fluid in direct contact with the ring is spinning at the same velocity, according to a so-called "no-slip" condition. The stationary ring is 0.010-in away from the movement, so the gradient of velocity is (78 - 0) ÷ (0.010 ÷ 12) = 94,300 ft/sec/ft = 94,300 1/sec. This is the shear rate.
"For an open impeller," I continued, "the distance (du - see Figure 1) is between the spinning impeller open vane and the casing wall. Though the peripheral velocity changes (it is less at 5-in when compared to the OD of, say, 10-in), an average value can be estimated by calculating similar to the above equation. The shear rate will also be similar.
Figure 1.
"Shear-sensitive fluids do not act like this," I added. "Glue, for example, gets "gooked-up." It is not typically pumped by centrifugal pumps, however, but by gear pumps, where the shear rate still applies: in a clearance between the spinning gear and the wall, the clearance will typically range around 0.005-in. A shear rate such as this, however, is usually not an issue because the amount of product in the clearance is small, and the overall "dilution" by the gooked-up, damaged fluid is negligible.
"But this does matter in certain cases," I warned. "For example, if the fluid pumped by a gear pump is an emulsion deposited on a Kodak film, even minor imperfections may cause specks and blemishes that damage the film strip. Similar concerns apply to pumping food stuffs, such as cherries or applies, where the pumps require a gentle pumping action with low shear. Progressive cavity pumps are best for these applications.
"Returning back to centrifugals," I said, "the gap between the impeller wall and casing wall is big - perhaps 0.5-in or so, thus the shear rate in this example is (78 - 0) ÷ (0.5 ÷12) = 1870 1/sec. Now for Newtonian fluids, viscosity does not depend upon the shear rate. If your pumped oil has 300 cSt viscosity, for example, it stays so with a 3600-rpm or 1800-rpm pump: shear rate changes, but viscosity is still 300 cSt. But for some, fluid viscosity itself changes either up, or down (as shown in Figure 1) and such fluids are called Dilatent or Thixotropic. This effects their degradation and may have an effect, and usually does, on power.
"Power is force times speed," I stated. "Force is stress times area. Stress is viscosity times shear rate, so here we are. For diletent fluids, shear stress always rises as both viscosity and shear rate increase, but for thixotropic fluids it can go either way: shear rate may not increase as fast as the decrease in viscosity, and the product (stress) can increase, decrease, or stay about the same. It all depends on a specific fluid being pumps.
"Usually, however, shear stress decreases," I concluded. "This means that power to the pump also decreases with shear rate. In other words, fluid is first viscous, but once it starts moving it becomes less viscous; it takes less power to pump it. It is common to neglect the driver rating (too small): it seizes per viscosity of the fluid in motion, but the motors keep tripping upon start-up because more power is necessary to get things going. Ketchup is a good example - this is why you shake the bottle like crazy at the restraint, to get it flowing. But once it flows, it does so quickly - and all over your shirt!"
For our monthly quiz to readers, name three so-called "dilatent" fluids and get a prize!