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Topic: Is creating a vortex the best way to achieve the greatest amount of composition and temperature uniformity?

anonymous
I have two round containers in which I would like to create a vortex with the greatest amount of surface area. I would like to use impellors centralized at the bottom of the units, which would provide the greatest amount of mixing/density and thermo linearity in the fluid as well as the least turbulence. The liquid material in each container would have a range of viscosity from that of water (1-5 centipoise) to that of light motor oil -- approximately 200 centipoise). The range of volume in each container would be from approximately 85% full to approximately the top of the impellor blade on the bottom of the container. Dimensions of the first container are: Height- 2.25 meters, Diameter- 2 meters, Volume- approx. 6000 liters Dimensions of second container are: Height- 1 meter, Diameter- 0.5 meter, Volume- approx. 200 liters What size of impellors/drive motor would I need for these containers to cover the range of volumes in each ( from almost full to almost empty) and its distance from the bottom of the container? Is a variable speed drive available with tank level feedback control? Is an impellor blade unit available that can also perform heating operations (say 0 to boiling and beyond) with feedback temperature control from within the tank? If ingredients are added to the containers, will they be mixed/suspended evenly with the liquid volume? What are the pressure considerations if these units are sealed/closed? The tanks are insulated, can you estimate how much power consumption is required? Lastly, do you have a formula to calculate the surface area of a vortex and the impellor size required to produce it-is there a vorticity equation?
  • Avatar Dave Dickey Forum Moderator 302 Posts

    Re: Is creating a vortex the best way to achieve the greatest amount of composition and temperature uniformity?

    The basic statement of the problem is fundamentally incorrect.  Creating a vortex in a cylindrical container is inconsistent with achieving the greatest amount of composition and temperature uniformity.  Vortexing the entire contents of a vessel is about the worst possible way of mixing for uniformity.  A vortex in a cylindrical container effectively will cause solid-body rotation of the fluid, which provides almost no radial or vertical flow, both of which are necessary to accomplish mixing.
     
    The answer to the seventh question provides some insight into the answers to the other parts of the question:
     
    7.    A formula to calculate the impeller size and speed necessary to create a vortex does not exist.  First, a complicated relationship exists between impeller type, size, rotational speed, liquid level coverage, and vortex depth.  Second, such a complicated relationship has little industrial utility.  Any situation showing only circular vortex motion is a sign of poor mixing.  The only situations for which a vortex can be a benefit is in combination with other mixing characteristics associated with axial flow and baffles to achieve vertical and radial mixing motion.  If the only motion fluid motion follows the rotation of the vortex, then any concentration or temperature differences will merely circulate around the vessel.  Some studies of vortexing have been conducted, but the results have not been reduced to a formula.  Most industrial situations benefiting from a surface vortex are tested at full scale and impeller speed or liquid coverage are adjusted to optimize the vortex depth.  At the maximum vortex depth, the amount of surface area can only be about 50% greater than the flat surface area of stationary liquid.
     
    6.    All mixers are 100% efficient.  All of the horsepower applied to the fluid in the vessel will be converted into heat.  Insulated vessels will retain that heat, so an estimate of temperature rise can be derived from the power dissipated.  Note: the power dissipated in the fluid will be lower than the motor power, sometimes by a large amount.
     
    5.    A liquid is an incompressible fluid, by definition.  So pressure should have no effect of vortex formation.  The only pressure consideration would involve any vapor coming off the liquid, possibly as a result of heating.
     
    4.    If ingredients are added to containers with only rotational flow (strong vortexing) mixing and/or suspension will be slow and ineffective.  The rotational motion which forms a vortex is similar to the conditions in a centrifuge, which is designed to separate, not mix, materials of different densities.
     
    3.    Impeller blades designed to disperse gas, typically radial-flow disk impellers and wide-blade hydrofoil impellers, can operate above the boiling point the liquid.  The impellers alone will not provide enough heat for boiling the liquid, because of the high heat of vaporization of liquids.  External heat must be applied to the vessel to effectively raise the temperature.
     
    2.    Liquid level measurement can be difficult, especially with a vortex and changing liquid level.  With good liquid level measurement and a programmed controller, mixer speed could be adjusted.  However, no such special purpose equipment is commercially available as a standard package.
     
    1.    If forming a vortex is sufficient for these applications, then a 0.8 meter diameter pitched-blade turbine operating at 1.13 rps with a 2,200 Watt motor should be sufficient for the 6,000-liter vessel.  For the 200-liter vessel, a 0.4 meter diameter pitched-blade turbine operating at 1.4 rpm with a 380 Watt motor should be sufficient.
     
    The effect of viscosity between 1 and 200 cp will have little if any effect on these applications, since whatever mixing does occur will be turbulent.  The effect of fluid properties on power requirements will be in direct proportion to the fluid density and effectively independent of viscosity for this range of conditions.
     
    The mistake often made in moving from the laboratory to production is that mixing in a glass beaker with a magnetic stir bar can be scaled geometrically.  A glass beaker with a stir bar will mix effectively for two primary reason, small size and large surface to volume ratio.  Small size means that any mixing will occur quickly, simply because of small distances and high rotational speeds.  While the contents appear to simply vortex, even small vibrations of the stir bar can cause secondary flow that will not occur with a shaft-mounted impeller.  In a beaker, the surface area at sides causes sufficient friction to create secondary motion and mixing.  As the process is scaled-up to production, the surface area increases with the vessel diameter squared, while the volume increases as the diameter cubed.  In the large vessel, friction at the wall has almost no effect on the swirling contents and thus adds no effective mixing.
     
    This question is based on several common misconceptions about how mixing takes place and the effect of a vortex.  The best assumption is that the presence of a vortex is an indication of poor mixing.

    The answers by this expert are based on the best available interpretation of the information provided.  The consequences of the application of this information are the responsibility of the user.  If clarification is needed, please submit a further question.


     

    EDITOR'S NOTE: The questioner offered additional information, to which our expert offered this additional advice:

        This question and answer are quite different, once the objective of the mixing is clear.  The need for a vortex, based on this description is still irrelevant.  The amount of additional surface area provided by a vortex is inconsequential by comparison with the surface renewal provided by turbulent mixing.
     
    1)  The following are recommendations for the mixers:
     
    First container - Height 2.25 meters, Diameter 1.5 meters top and bottom, 2 meters center, barrel shaped, 4 baffles 0.15 meters wide, contoured to vessel shape, mounted about 0.01 meters off the wall.
    Impeller - pitched-blade turbine, 4 blades, 45 degree angle, pumping downward 0.6 meters in diameter, 0.12 meter wide blades, 0.1 meters off the bottom.  Rotational speed 2.08 rps (125 rpm) with a 3.7 kW motor.
     
    Second container - Height 1 meter, Diameter 0.5 meters top and bottom, 0.6 meters center, barrel shaped, 4 baffles 0.04 meters wide, contoured to vessel shape, mounted about 0.005 meters off the wall.
    Impeller - pitched-blade turbine, 4 blades, 45 degree angle, pumping downward 0.25 meters in diameter, 0.05 meter wide blades, 0.04 meters off the bottom. Rotational speed 5.8 rps (350 rpm) with a 0.75 kW motor.
     
    2)    No known variable speed drive specifically programmed for liquid level feedback control.  A programmed logic controller (PLC) with a liquid level sensor could be programmed to provide a form of feedback control.  Control logic would have be developed to match surface motion and mixing intensity.  Manual adjustment or incremental adjustment to liquid level could be more practical.
     
    3)    Baffle recommendation is included in the answer to question 1).  Standard baffles are 4 at 90 degrees around the vessel, approximately 1/12 the tank diameter and spaced a small distance from the vessel wall.

     

  • Avatar Philip Goh Community Member 1 Post

    Re: Is creating a vortex the best way to achieve the greatest amount of composition and temperature uniformity?

    Thank you Mr Dave for a detailed explanation. I was about to build a 2.4m depth x 1.8m dia cylindrical tank with a rotary mixer, 50 rpm propeller mounted at the bottom center, to mix water with some chemicals and thanks for this article, I now know vortex at the center will not mix well. I would like to ask a few questions for your kind expert recommendations: 1) If I were to mount the rotary propeller at one side, say offset from one wall instead of the center, would this mix well? Would vortex cease to exist, knowing vortex is bad? 2) If instead of circular cylindrical shape, would a rectangular shape solve the mixing problem, ie mix better than circular? 3) Would using two level propellers, one close to bottom and one close to top shaped differently would create better mix and hinder vortex formation? 4) I plan to use PVC tanks, can PVC Baffles at the sides works as may be easier to make or must I use stainless steel blades? Grateful for your insights and advise.
  • Avatar Dave Dickey Forum Moderator 302 Posts

    Re: Is creating a vortex the best way to achieve the greatest amount of composition and temperature uniformity?

    The answers to these questions may depend as much on available equipment and supplier capabilities as the technical requirements for good mixing. Some process requirements may make one or more of the possible answers better than the others. Knowing that the propeller speed is 50 rpm is less than half the story. The propeller diameter has a greater effect on mixing intensity and power requirements than the rotational speed, although both are important factors.

    1. If the propeller were mounted off-center, such as near the bottom half-way between the center and the side wall of the tank, the vortex would not be as strong as if the propeller were at the center. Depending on the mixing intensity the vortex could be more or less of a problem. Without baffles in the tank a vortex is likely to form. Any off-set mounting will limit the maximum mixing intensity to less than what would be possible with a center-mounted mixer in a baffled tank.

    2. If the tank had a square cross-section a vortex would not be as strong as if the tank were a cylinder. However, a tank with a square cross-section would not be as effective as a cylindrical tank with baffles.

    3. Using two level propellers may improve the mixing in a tank, because the tank is taller than the diameter, but the number and location of the propellers will not eliminate the vortex. In fact, the impeller near the liquid surface is likely to create a vortex and draw air into the process. Air may cause foaming and reduce the mixing efficiency.

    4. Using PVC tanks is not a problem, the absence of baffles with a center mounted mixer is the problem. If you can have PVC baffles added to your tank, the material of construction is not problem.

    Your process will probably work best if you have two propellers at different levels in the tank. The bottom one should not be at the bottom of the tank, but one-half to one propeller diameter off the bottom. The upper propeller should be positioned approximately half way between the bottom propeller and the liquid surface, but at least one propeller diameter above the bottom propeller. The tank needs to have four, vertical baffles evenly spaced around the tank, each about one-twelfth of the tank diameter wide.

    The answers by this expert are based on the best available interpretation of the information provided.  The consequences of the application of this information are the responsibility of the user.  If clarification is needed, please submit a further question.