Municipal mixing with reciprocating motion disk

Abstract

A reciprocating motion disk for mixing wastewater in a tank of a treatment plan is optimized for geometry, along with cycling speed and stroke length, to cause effective mixing velocity throughout the tank.

Claims

1. In a wastewater treatment system, a method for mixing liquids or slurries in a wastewater treatment tank, comprising: providing in the wastewater treatment tank a reciprocating mixer disk for mixing the liquids or slurries by cyclical up and down motion of the mixer disk within the tank, the mixer disk comprising a polygonal or essentially circular solid ring with an outer diameter and an inner diameter, the inner diameter of the ring defining a central essentially open area A.sub.open, the solid ring having a closed area A.sub.closed, and the mixer disk having essentially radial struts supporting the solid ring, extending from the solid ring inwardly to a central hub, the solid ring having a width from the outer diameter to the inner diameter, reciprocating the mixer disc in up and down motion at a cycle rate of C cycles per minute, at a stroke length S in inches, and the product of CS(A.sub.open+A.sub.closed)/A.sub.open being in the range of 1530 to 8750.

2. The method of claim 1, wherein said product is in the range of 2000 to about 5000.

3. The method of claim 1, wherein said product is in the range of 2400 to about 3750.

4. The method of claim 1, wherein said outer diameter and said inner diameter of the solid ring define a ratio in a range of 2.0 to 2.5.

5. The method of claim 4, in which the outer diameter and said inner diameter of the solid ring define a ratio in a range of 2.2 to 2.3.

6. The method of claim 1, wherein the disk is operated in reciprocating vertical motion at a peak disk speed in the range of 3 to 5 feet per second.

7. The method of claim 1, wherein a factor A.sub.f is in a range of 0.25 to 0.75, where A.sub.f=A.sub.open/A.sub.x, and A.sub.x is the area of liquid displaced inwardly to the open area as the disk is advanced.

8. The method of claim 7, wherein the factor A.sub.f is in a range of 0.35 to 0.65.

9. The method of claim 7, wherein the factor A.sub.f is about 0.5.

10. The method of claim 1, wherein the disk is operated in reciprocating vertical motion at a peak disk speed in the range of 2 to 6 feet per second.

Description

DESCRIPTION OF THE DRAWINGS

(1) FIG. 1A is a perspective view showing one example of a reciprocating mixer disk geometry.

(2) FIG. 1B is a plan view of the same disk.

(3) FIGS. 2A and 2B are perspective and plan views showing another disk geometry.

(4) FIGS. 3A and 3B are perspective and plan views showing another mixing disk, with a polygonal shape.

(5) FIG. 4 is a diagram with plan and section views showing disk geometry factors, i.e. dimensions.

(6) FIGS. 5-8 are schematic plan views showing a polygonal disk and identifying areas of the disk that can be involved in calculations regarding disk geometry.

DESCRIPTION OF PREFERRED EMBODIMENTS

(7) The drawings illustrate several different general configurations of reciprocating mixer disk to which the principles of the invention can be applied. FIGS. 1A and 1B show one pattern in the form of a mixing disk 10 comprised of an annular ring 12 of closed area that is shown flat, planar but which could be conical if desired, as in some mixer disks of the prior art. The flat ring 12 has outer and inner radii, R.sub.o and R.sub.i respectively, defining a width, W.sub.disk=R.sub.oR.sub.i, closed area 14 (references to closed area herein include only the ring 12). In the center is an open area 16. If the solid ring 12 is sloped, in a conical shape, it is the projected area that is important to the invention, that is, the area that would be seen as the closed area 12 in plan view, such as seen in FIG. 1B.

(8) The mixing disk has a hub 18 to which a reciprocating mixer shaft is attached concentrically, secured into either the hub side seen in FIG. 1A or the opposite side. A series of spokes or struts 20, eight of which are shown in the examples here, secure the closed-area ring 12 to the hub 18. The mixing disk 10, for most purposes according to the invention, is of a large diameter, e.g. four or six feet to seven or eight feet, and can be formed of stainless steel or other corrosion-resistant metal, such as painted steel.

(9) FIGS. 2A and 2B show another design of a mixing disk 22, similar to that of FIG. 1A but with struts 24 secured to the annular disk 12 in a different way, in which the end of each strut is forked with a slot, fitting closely over the thickness of the ring 12. The struts can be welded or otherwise securely affixed to the disk.

(10) FIGS. 3A and 3B show a different design wherein the closed area annular mixing disk 12a is polygonal rather than circular, in this case octagonal. The formula for optimum area applies no matter the shape selected, so long as a closed generally ring-shaped area surrounds an open central area. Here, as seen in FIG. 3B, the closed area 12a is defined by eight trapezoid shapes. The area of each segment is defined by the width, W.sub.disk, times the average length of major sides, shown as L.sub.1 for the outer length and L.sub.2 for the inner length of the segment. This area can also be calculated using the radii R.sub.o and R.sub.i and the number of sides, which defines the segment angle involved. The open area 16a of the polygonal mixer disk 24 is simply calculated as the area of an octagon (in this example), made up of eight triangles. The spokes 20 may or may not be included, as explained further below. The hub 18 area may also be included or not as discussed below.

(11) In all these different geometries, the sum of the projected closed area and the open area is divided by the open area to form the ratio of interest, basically the ratio of the entire area within the disk's outer diameter, to the open area, or area of the circle or polygon inward of the closed annular ring. This ratio is multiplied by frequency in CPM and stroke length in inches.

(12) As noted above, the numerical value resulting from this calculation should be in the range of about 1530 to about 8750. This results in a mixer disk design with a greater ratio of projected closed area to total, overall area, as compared to mixer disks of the prior art.

(13) More specifically, the above design number is preferably between about 2000 to 5000, and more preferably, one mixer disk design has the above numerical value in the range of about 2400 to about 3750. As an example, this would correspond to a circular mixer disk reciprocating at 30 CPM with a stroke of 20 inches, and a ratio of outer disk radius, R.sub.o to inner ring radius R.sub.i of 2.0 to 2.5 (ratio of squares being 4.0 to 6.25).

(14) Testing was conducted in a liquid-filled tank, with mixing disks reciprocated in the tank as stated above, and with R.sub.o/R.sub.i ratios in a range between 1.5 and 2.5. Average velocities of liquid movement were measured within the tank, and it was found that for velocities of one inch per second, two inches per second, and three inches per second, a strong correlation was found between the percentage of tank volume being at each of these average velocities and the ratio of outer radius R.sub.o to inner radius R.sub.i. Ratios of 2.0 to 2.5 (squared range 4.0 to 6.25) were found very effective, with radius ratios of 2.2 to 2.3 being most effective. The ratio range of 2.0 to 2.25 corresponds to a range of 2904 to 3038 for the calculated design factor number described above.

(15) FIGS. 4 through 8 are diagrams showing disk geometry factors and relationships of various areas. The following definitions apply in those drawings:

(16) Velocity Definitions: VM=maximum disk velocity VU=disk velocity upper limit=e.g. 43.982 in/s (24 stroke @ 35 CPM) VL=disk velocity lower limit=e.g. 7.854 in/s (6 stroke @ 25 CPM) VM range (VLVMVU)

(17) Polygon Definitions: n=(number of equal length sides) R.sub.i=inner perpendicular distance from polygon center to side R.sub.o=outer perpendicular distance from polygon center to side R.sub.x=x perpendicular distance from polygon center to side X.sub.f=disk width displacement factor (0.20xf0.40)

(18) Area Definitions: A.sub.hs=area occupied by hub and spokes A.sub.open (area open)=A.sub.iA.sub.hs A.sub.closed (area closed)=A.sub.oA.sub.i A.sub.x=(area displaced thru A.sub.open) A.sub.do (area displaced away from A.sub.open)=A.sub.oA.sub.x A.sub.f=A.sub.open/A.sub.x(0.35af0.65), broadly 0.25 to 0.75

(19) In the example below the number of polygonal sides is assumed at one million, i.e. essentially infinite, in effect circular. Dimensions are assumed for the purpose of this example. In the example the area occupied by the disk hub and spokes A.sub.hs is subtracted out of the full area within the inner polygon to calculate the true open area. However, all of this hub and spokes area can be ignored, as noted above, and as assumed relative to the claims. That is, the open area can be more approximately calculated by simply using the entire polygonal or circular area inward of the solid annulus.

(20) TABLE-US-00001 CALCULATING DISK GEOMETRY - OPEN AREA METHOD n := 1000000 number of equal length polygon sides (3 n ) when n = the disk is circular in shape R.sub.i := 22 .Math. in inner distance from polygon center to side R.sub.o := 42 .Math. in outer distance from polygon center to side A.sub.hs := 176.715 in.sup.2 area occupied by disk hub and spokes W.sub.disk := R.sub.o R.sub.i = 20 .Math. in disk width between inner and outer polygons $A_i:=n.Math.R_i^2.Math.\tan \left(\frac{}{n}\right)=1520.53{\mathrm{in}}^2$ area inner polygon $A_o:=n.Math.R_o^2.Math.\tan \left(\frac{}{n}\right)=5541.77{\mathrm{in}}^2$ area outer polygon A.sub.open := A.sub.i A.sub.hs = 1343.82 in.sup.2 open area allowing fluid passage A.sub.closed := A.sub.o A.sub.i = 4021.21 in.sup.2 closed area displacing fluid a.sub.f := 0.559 0.35 a.sub.f 0.65 disk area displaced thru open area factor range $A_x:=\frac{A_{\mathrm{open}}}{a_f}=2.404{10}^3.Math.{\mathrm{in}}^2$ area displaced thru open area $R_x:=\sqrt{A_x.Math.{\left(n.Math.\tan \left(\frac{}{n}\right)\right)}^{-1}}=27.66\mathrm{in}$ displaced distance from polygon center to side A.sub.do := A.sub.o A.sub.x = 3137.81 in.sup.2 area displaced away from open area X := R.sub.x R.sub.i = 5.662 in offset distance from inner polygon $x_f:=\frac{X}{W_{\mathrm{disk}}}=0.830.20x_{f}0.40$ approximate disk width displacement factor range A.sub.i_infinite_sides := .Math. R.sub.i.sup.2 = 1520.53 in.sup.2 area outer polygon with infinite sides (circular) A.sub.o_infinite_sides := .Math. R.sub.o.sup.2 = 5541.77 in.sup.2 area inner polygon with infinite sides (circular) A.sub.x_infinite_sides := .Math. R.sub.x.sup.2 = 2403.96 in.sup.2 area displaced with infinite sides (circular) thru open area A.sub.open = 1.344 10.sup.3 .Math. in.sup.2 A.sub.x A.sub.open = 1.06 10.sup.3 .Math. in.sup.2 A.sub.closed = 1.617 10.sup.3 .Math. in.sup.2

(21) FIG. 7, as well as FIG. 4, demonstrates the effect of the disk moving through liquid. As the disk moves, the volume of liquid directly in the path of the disk annulus is divided between that which enters the opening (along with liquid in the path of the opening) and liquid that flows outwardly, to clear the outer edge of the disk. The sectional view in FIG. 4 shows this, as does the plan view, and denotes the radius from center to the division point as R.sub.x. This is the displaced distance from the polygon center. Similarly, A.sub.x is the area displaced through the open area of the disk, as denoted in FIG. 7. The value of R.sub.x is dependent on disk velocity.

(22) The formulas and sample calculations above reflect that the behavior of liquid flow and liquid velocity in the tank induced by the movement of the disk is relatively complex. However, the formula given above, which involves CPM, stroke length, area enclosed and area open, and the ranges given for the resulting number calculated, are effective if the area occupied by the hub and spokes is simply ignored. That is, open area is simply considered as the full area defined within the inner part R.sub.i of the disk.

(23) As noted above, the velocity of movement of the disk has an effect on how much liquid in the disk's path is drawn into and through the opening, i.e. area A.sub.x. The factor A.sub.f is defined as A.sub.open/A.sub.x, and preferably is in the range of 0.25 to 0.75, more preferably 0.35 to 0.65. Typically A.sub. will be about 0.5, plus or minus 10%.

(24) Linear motion reciprocating mixers with mixing disk meeting the above criteria produce a high velocity through the central opening and mix liquids such as municipal wastewater treatment sludge (particularly in anaerobic digestion) more efficiently than with prior art mixing disks. It should be understood, however, that the invention applies to mixing disks for other liquids and slurries as well, in a wide range of viscosities and densities.

(25) The above described preferred embodiments are intended to illustrate the principles of the invention, but not to limit its scope. Other embodiments and variations to these preferred embodiments will be apparent to those skilled in the art and may be made without departing from the spirit and scope of the invention.