U.S. patent number RE34,386 [Application Number 07/651,289] was granted by the patent office on 1993-09-21 for impeller.
This patent grant is currently assigned to National Research Development Corporation. Invention is credited to John F. Davidson, Keshavan Niranjan, Aniruddha B. Pandit.
United States Patent |
RE34,386 |
Davidson , et al. |
September 21, 1993 |
Impeller
Abstract
A rotating impeller for stirring liquids contained in tanks.
Strip-like blades of simple form radiate from a central hub, in
swept-back configuration relative to the direction of rotation. The
blades are angled relative to the hub so as to exert a forward and
downward force upon the liquid as the impeller rotates, and the
blade curvature is such that the area projected upon the liquid by
the solid structure of the rotating blade is less than the
corresponding area that would be projected by an otherwise similar
blade in which imaginary straight lines connected all adjacent
vertices, and any void areas lying within the boundaries of those
imaginary lines had been filled in. The preferred arrangement of
the blades is such that when the impeller is arranged with its axis
vertical, curvature of each blade along its length is such that it
extends away from the hub in a diminishing downward curve, reaches
a lowest point, and then rises again before the blade tip is
reached. In cross-section each blade will typically be straight and
parallel-sided, but may also be slightly curved, of aerofoil
section, etc.
Inventors: |
Davidson; John F. (Cambridge,
GB), Niranjan; Keshavan (Reading, GB),
Pandit; Aniruddha B. (Bombay, IN) |
Assignee: |
National Research Development
Corporation (London, GB2)
|
Family
ID: |
10601288 |
Appl.
No.: |
07/651,289 |
Filed: |
January 25, 1991 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
Issue Date |
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Reissue of: |
73823 |
Jul 15, 1987 |
04799862 |
Jan 24, 1989 |
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Foreign Application Priority Data
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Jul 18, 1986 [GB] |
|
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8617569 |
|
Current U.S.
Class: |
416/242; 261/93;
366/325.92; 366/330.1; 366/330.3; 366/330.4; 366/343; 416/243 |
Current CPC
Class: |
B01F
3/04531 (20130101); B01F 7/00275 (20130101); B01F
7/00341 (20130101); B01F 2003/04673 (20130101); B01F
15/00883 (20130101) |
Current International
Class: |
B01F
15/00 (20060101); B01F 3/04 (20060101); B01F
7/00 (20060101); B01F 005/10 () |
Field of
Search: |
;416/223R,242,243,238,DIG.2 ;366/330,343 |
References Cited
[Referenced By]
U.S. Patent Documents
Foreign Patent Documents
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568738 |
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Jan 1959 |
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CA |
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007396 |
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May 1983 |
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EP |
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2803407 |
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Aug 1979 |
|
DE |
|
806764 |
|
Dec 1958 |
|
GB |
|
1107762 |
|
Mar 1968 |
|
GB |
|
1263165 |
|
Feb 1972 |
|
GB |
|
1528399 |
|
Oct 1978 |
|
GB |
|
2157185 |
|
Oct 1985 |
|
GB |
|
Primary Examiner: Look; Edward K.
Assistant Examiner: Newholm; Therese M.
Attorney, Agent or Firm: Cushman, Darby & Cushman
Claims
We claim:
1. An impeller comprising:
a hub, adapted to rotate in a predetermined direction about an axis
of rotation;
a plurality of blades radiating symmetrically from said hub; each
said blade being of elongated shape and having a longitudinal axis,
the length dimension of said each blade having opposite first and
second ends;
said first end of each said blade being attached to said hub, and
said second end constituting the tip of each said blade;
each said blade being of substantially uniform cross-section
throughout said length;
each blade extending from said hub in a direction wherein said
longitudinal axis thereof extends at an angle to said axis of
rotation of said hub;
in which said longitudinal axis is curved;
and in which each said blade is so disposed relative to said hub
that said curved longitudinal axis results in said blade having a
first and swept-back curvature relative to said predetermined
direction of rotation of said hub and visible when said blade is
viewed in a direction parallel to said axis of rotation, and a
second curvature .Iadd.along its length such that it extends away
from said hub in a diminishing curve in one direction, reaches a
first point, and then curves in an opposite direction before the
tip is reached, said curvatures being .Iaddend.visible when said
blade is viewed in a direction normal to a radius to said axis of
rotation at the point where said blade radiates from said hub.
2. An impeller according to claim 1 in which each said blade is
bent in a continuous curve along its said length.
3. An impeller according to claim 2 in which the curvature of the
said continuous curve is uniform along said length.
4. An impeller according to claim 1 in which the said elongated
shape of each said blade presents first and second opposite long
edges of said shape each extending between said first and second
ends, and in which said first and second opposite long edges are
parallel and curved.
5. An impeller according to claim 1 in which the locus of said
attachment of said first end of each said blade to said hub is
substantially linear, said line being inclined to a plane
intersecting the axis of said rotation of said hub at right angles,
whereby if said impeller is rotated in said predetermined direction
about a vertical axis said blades exert a forward and downward
force upon any fluid which they contact. .[.6. An impeller
according to claim 1 in which the orientation of said blades is
such that when said impeller is arranged with its axis of said
rotation vertical, and is viewed in elevation, said curvature of
each blade along its said length is such that said blade extends
away from said hub in a diminishing downward curve, reaches a
lowest point, and then rises again before said
blade tip is reached..]. 7. An impeller according to claim .[.6.].
.Iadd.1 .Iaddend.in which said blade tips, and the locus of
attachment of said first ends of said blades to said hub, lie at
substantially the same
horizontal level when said impeller is so viewed. 8. An impeller
according to claim 1 in which each said blade is twisted along its
length, in the
manner of a marine propeller. 9. An impeller according to claim 1
in which
said cross-section of each said blade is arcuate. 10. An impeller
according to claim 1 in which said cross-section of said blade is
of aerofoil shape.
Description
This invention relates to rotatable impellers for stirring liquids
contained in tanks, and to mixing apparatus comprising tanks fitted
with such impellers. In typical industrial applications, liquid to
be stirred is contained in a cylindrical tank arranged with its
axis vertical, and the depth of the liquid is of the same order as
the diameter of the tank. Stirring is effected by rotating impeller
immersed in the liquid, and mounted on a shaft co-axial with the
tank. Typically the stirring takes place for one or both of two
reasons. Firstly, the liquid may contain particles, which it is
necessary to suspend and distribute homogeneously throughout the
liquid. Secondly, air or other gas may be blown into the liquid,
for instance through a perforated tube which is typically immersed
in the liquid on the tube axis below the impeller, and it is
necessary to achieve good dispersion of the gas within the liquid.
The undesirable effect of gross rotation of the liquid within the
tank by the rotating impeller is often inhibited by vertical
baffles mounted at equal angular intevals around the inner surface
of the cylindrical wall of the tank.
Three impellers, each now regularly in use for the commercial
stirring of liquids, are illustrated in FIGS. 1A and 1B to 3 of the
accompanying diagrammatic drawings. Each such FIG. shows a tank and
the respective impeller in diagrammatic axial section, and FIGS.
1A, 1B and 2A, 2B also include a further underneath plan view of
the impeller along. The axial section gives an impression of the
flow patterns that are set up when the impeller is mounted at the
bottom end of a vertical shaft and rotated within a body of liquid
contained in a cylindrical vessel.
FIG. 1 shows the kind of impeller usually known as a "disk turbine"
or "Rushton impeller", comprising a circular disk 1 with six
paddles 2 mounted at equal spacing around the periphery 3. Each
paddle 2 is a plane rectangular metal sheet coplanar with the axis
of the shaft 4 on which the disk is mounted, and extending both
above and below the disks. In operation the dominant centrifugal
action of the rotating paddles 2 throws the liquid out radially,
generating the two circulation loops 5 and 6 within the liquid
contained within a cylindrical vessel 7. The latter has a circular
base 8 and a side wall 9, and vertical baffles 10 are mounted on
the inner surface of the wall to inhibit gross rotation of the
liquid by the impeller. Where the liquid contains particles, it is
a drawback of this type of impeller that particle pick-up from
close to the base 8 of the vessel is poor, because the circulation
velocity in loop 6 close to the base is low. Also when gas is
injected into the liquid, for instance through a sparging head 11
comprising a perforated ring 12 connected by radial feed conduits
13 to a vertical inlet pipe 14, the gas bubbles tend to enter the
eye of the impeller because of both their buoyancy and the action
of circulation loop 6; this gas then tends to form a gas cavity
behind each paddle 2, so reducing the power transmitted to the
liquid by that paddle. More generally, when any liquid is stirred
by such a paddle intense local turbulence will be generated around
the tips of the paddles in the region indicated by reference 15;
this turbulence has the disadvantage of dissipating much of the
input power. This disadvantage can be diminished by mounting the
plane paddles 2 in sweepback fashion as at 2a, so that they lie at
an acute angle to the tangent 16 to the periphery 3 instead of at
right-angles.
The second form of known stirring impeller illustrated in FIG.
112A, 2B is a standard marine propeller 20, with the typical
complement of three blades 21. The blades are of complex but
well-known shape, designed to exert a screw action upon the liquid
and to accelerate it in a downward direction, parallel to the axis
of shaft 4. A single circulation loop 22 is therefore set up within
the liquid, and high velocity in the lower part 23 of the loop
between the impeller 20 and the base 8 promotes good particle
pick-up where particles are present in the liquid. However, if gas
is being introduced through sparging head 11, that gas tends to
bypass much of the liquid because the strong loop 22 carries the
bubbles both outwardly towards the wall 9, and then up that wall
between baffles 10 and straight to the surface 24 of the liquid,
because the circulation in the top part 25 of loop 22 is relatively
weak so that bubbles tend to break the surface rather than remain
within the loop 22.
In the pitched-bladed impeller 30 of FIG. 3, six plane strip-like
blades 31 are mounted at equal angular intervals around the rim 32
of a rotor 33, from which they each extend radially outwards. The
line along which the root of each blade is attached to the rim is
inclined to the vertical, so that as the shaft 4 rotates in the
direction of arrow 34 the forward face of each blade 31 is angled
downwards. In operation the illustrated flow pattern therefore
results; some turbulence in region 35, as in region 15 in FIG. 1,
and two circulation loops 36 and 37 with a particularly vigorous
downward and outward motion 38 at the start of loop 37, due to the
angling of blades 31.
The present invention arises from the search for an impeller
comparably simple in construction with those of FIGS. 1 and 3 but
with improved performance in general, and in particular with less
tendency to generate excessive turbulence immediately outboard of
the tips of the blades of paddles, and with reduced energy
requirement in order to achieve a pre-determined standard of
mixing. In the course of the search, one factor that has become
seen to be of significance is the effective area that is "swept"
through the liquid by each blade or paddle as the impeller rotates.
FIG. 4 is a diagrammatic radial section through one of the paddles
2 of the impeller of FIG. 1. Because the paddle is plane and
rectangular, the area which it sweeps through the liquid as the
impeller spins is simple the area (a.times.b) of the paddle itself.
If the paddle does not lie at right-angles to the local tangent but
is inclined to it, as at 2a in FIG. 1, the area which it sweeps is
diminished, by multiplying the same paddle area (a.times.b) by the
sine of the angle of the inclination. However, we have appreciated
that if the blade has at least one curved side, either by being so
formed or by being bent after formation or both, what is in effect
an enhancement of the swept area can be obtained. In FIG. 5 the
plane rectangular paddle 2 of FIG. 4 is replaced by a plane paddle
40 having four vertices A, B, C, D and fixed to disk 1 so as to be
coplanar with the axis of shaft 4. Opposite sides AD and BC are
straight and vertical while the other two opposite sides AB and CD
are curved and parallel. The area actually sept by paddle 40 as
disk 1 rotates is therefore the area of the four-sides plate ABCD
itself, and will be referred to a the actual swept area. However,
we have found that while the power required to drive an impeller
with such paddles tends to be related to the actual swept area, the
degree of mixing achieved tends to reflect the sum of that actual
area and any further area that can be enclosed by joining adjacent
vertices by a straight line instead of by the curved side of the
solid figure. In FIG. 5, such a further area (shown shaded) is
indicated by reference 41 and is of segmental shape, being bounded
on one side by the curved side AB of the solid plate and on the
other by the imaginary straight line 42 joining vertices A and B.
In the following text, the sum of the actual swept area (in FIG. 5,
the area of the four-sided plate ABCD) and such a further area (in
FIG. 5, the shaded area 41) will be referred to as the total swept
area. It will thus be apparent that the actual swept area
represents the actual area projected upon the fluid by the solid
structure of a rotating blade, while the total swept area
represents the area projected by an otherwise similar blade in
which imaginary lines connect all adjacent vertices, and any void
area lying within the boundaries of those lines have been filled
in.
According to the present invention an impeller comprises a
plurality of blades or paddles radiating symmetrically from a
rotatable hub, in which each blade is of elongated form and is
curved along its length, one end of the length being attached to
the hub and the other constituting the blade tip; in which the
curvature of the blades gives them a swept-back configuration
relative to the direction of rotation of the impeller; and in which
the total swept area, swept by each blade, exceeds the actual swept
area.
Each blade may be bent in a continuous curve along its length. Such
curvature may be uniform throughout the length.
The two opposite long edges of the blade may be parallel, and may
be either straight or curved.
Each blade may be attached to the hub along a line inclined to a
plane which intersects the axis of rotation of the hub at
right-angles, the arrangement being such that if the impeller is
rotated about a vertical axis the blades exert a forward and
downward force upon liquid within which the impeller is
rotated.
The arrangement of the blades may be such that when the impeller is
arranged with its axis of rotation vertical, and is viewed in
elevation, the curvature of each blade along its length is such
that it extends away from the hub in a diminishing downward curve,
reaches a lowest point, and then rises again to some extent,
preferably to the same extent, before the top is reached.
The blades may contain further curvatures. For instance a blade may
be twisted to some extent along its length, in the manner of a
marine propeller. A blade may also be slightly curved, rather than
straight, over its depth dimension: in use, some degree of
hydrofoil effect may be set up by the reaction of such a blade with
the fluid around it. The blades may be formed from sheet-form
material and so be of uniform thickness throughout, but the
invention also includes impellers with blades formed from material
of non-uniform thickness, for instance material of a shallow
aerofoil shape when the depth dimension is viewed in cross-section.
The criterion should however be that the maximum thickness of the
blade is very small compared with the depth, which in turn is small
compared with the length.
The invention will now be described, by way of example with
reference to the following further figures of drawings in
which:
FIGS. 1A, 1B, 2A, 2B and 3-5 are illustrations of prior are mixing
impeller;
FIG. 6 is a perspective view of an impeller rotated about a
vertical axis taken from above;
FIG. 7 is another perspective view, but from underneath;
FIG. 8 is a plan view of one from of blade, when first cut from
flat material;
FIG. 9 shows the same blade in elevation, when ready for attachment
to the hub after bending about its long axis;
FIG. 10 is a diagrammatic view of the impeller in vertical
elevation, and includes a part similar to the second parts of FIGS.
1 to 3, diagrammatically illustrating the flow pattern set up in
use by an impeller as shown in FIGS. 6 to 9; and
FIG. 11 is an alternative diagrammatic illustration of how the
shape of the blade of FIGS. 8 and 9 may be determined.
The impeller 49 of FIGS. 6 to 10 comprise six blades 50 extending
outwardly at sixty-degree intervals from a hub 51. A central hole
52 in the hub receives shaft 4 to which the hub will be fixed by
screw means shown diagrammatically at 53 in FIG. 6, and by which
the impeller will be rotated in the direction of arrow 54 in the
same way as the known impellers shown in FIGS. 1 to 3 and already
described.
Each blade 50 is first stamped as a blank from flat metal sheet, to
the four-sided shape shown in FIG. 8. Of the two pairs of opposite
and parallel sides of this four-sided figure, one pair (55,56) are
long and curved and the other pair (57,58) are short and straight.
The imaginary line 59 will be referred to as the long axis of the
blank, and the imaginary line 60 as one of the transverse
axes--that is to say the axes related to the depth dimension of the
blade--and because axis 59 is long compared with axis 60 the blank
may be described as being elongated in shape. To convert it to the
form required of one of the blades 50, the blank is bent along its
long axis 59 as shown in FIG. 9. The short end 57 of the blade is
the end welded, slotted or otherwise attached to the hub so that
the locus of the meeting of the hub and blade is a line 61 (see
FIGS. 6 and 10) which is slanted to the vertical so that the
forward face 62 of each blade (examples of which are best seen in
FIG. 7) is angled downwardly at about 45 degrees to the vertical.
Because line 61 is necessarily curved, the short side 57 of the
blank must be course be reshaped into a corresponding curve before
the blade is actually fixed to the hub. Because the illustrated
blades 50 are stamped from flat sheet and formed as described, the
transverse axes 60 will be straight. However, the blades could as
one alternative be slightly curved over their depth dimensions as
indicated in outline at 68 in FIG. 6, giving rise to some degree of
"hydrofoil" action as each blade moves through the surrounding
fluid in use. As another alternative the invention includes not
only blades of uniform thickness but also thin blades of
non-uniform section, for instance the foil section indicated in
outline at 69.
FIG. 10 shows best the relationship between the total and actual
swept areas which are swept by the blades 50. In the enlarged
detail of the FIG., showing the blade (50a) lying most nearly at
right-angles to the direction from which the view is taken, it is
clear that the actual swept area, represented by the structure of
the blade itself which is shown shaded, is less than the total
swept area which includes also the area above the top edge 55a of
the blade but below the imaginary line 63 joining vertices 64 and
65 which preferably (and as shown) lie in the same horizontal
plane. From this FIG. it is also apparent that due to the curvature
of long axis 59 of the blade, and the angling of the line 61 along
which the root of the blade is attached to the hub 51, each blade
slopes downwardly away from its attachment to the hub 51 but
reaches a lowest level (70, 71) and is rising again as the blade
tip (short side 58) is approached. It will be noted that with such
geometry the centre of gravity of the blade lies higher, and thus
closer to the level of the root line 61, than would be the case if
the blade sloped downwards continuously from root to tip, and thus
promotes better mechanical balance and strength.
FIG. 10 also indicates the typical flow pattern which an impeller
according to the invention sets up in use. Like the pitched-bladed
impeller 30 of FIG. 3, impeller 49 sets up two strong and
beneficial circulation loops 36 and 37. However, the curvature of
each blade along its long axis 59 results in each blade being swept
back in relation to the direction of rotation of the impeller which
is indicated by arrow 54. In the case of the impeller actually
illustrated in FIGS. 6 to 10, the extent of the sweepback is such
that at the tip 58 of each blade the long axis 59 makes an angle
.alpha. of about forty-five degrees to the radial line 66 joining
that tip to the axis of shaft 4, as is best shown in FIG. 6. This
sweepback has an advantage comparable to that of the alternative,
angles arrangement of paddle (2a) in FIG. 1, namely that the
reaction of the paddle against the fluid imparts to that fluid an
element of motion that is not aligned with the motion of the blade
itself, so reducing the absolute velocity relative to the container
that is imparted to the fluid. This reduction of the absolute
velocity reduces the dissipation of energy near the impeller--that
is to say the energy wasted in regions 15 and 35 in FIGS. 1 and
3--so that more of the input power goes into the loops 36, 37 thus
giving better mixing. In general the impeller illustrated in FIGS.
6 to 10 generates a combination of downward and radial motion
appropriate for mixing. When gas is introduced to the vessel 7 of
FIG. 10, for instance by sparge pipe 11 as before, the turbulent
wake which formed behind each paddle or blade of the known
impellers of FIGS. 1 and 3 is largely avoided; the shape and
mounting of the blades of the impeller according to the invention
promotes a smooth flow pattern over each blade so that when gas is
injected below the impeller that is less tendency to form gas
cavities behind the impeller blades. Compared with the ship's
propeller shown in FIG. 2A, 2B, the impeller of FIGS. 6 to 10 has
the potential advantages of better bubble distribution when gas is
injected, due to greater radial liquid velocities in lops 36 and
37, and better particle distribution due to the combination of
better upward liquid velocities near to the base of the tank, and
higher radial velocities in the upper part of the tank at the crest
of loop 36.
An experiment was performed to compare the blending efficiency of
an impeller according to the invention, as shown in FIGS. 6 to 10,
with that of the three known impellers shown in FIGS. 1 to 3 and
also the modified version of FIGS. 1 in which the paddles (2a) are
swept back at forty-five degrees. The following dimensions were
common to all five experiments:
tank diameter: 0.3 m
liquid depth: 0.3 m
impeller diameter (D): 0.1 m
height of impeller above bottom of tank: 0.1 m
gross rotation of the fluid within the tank was inhibited by four
vertical baffles 10, each of height 0.3 m and width 0.1 m, equally
spaced around the inner face of the cylindrical side wall 9. In the
experiments a tracer was injected into the liquid and the
concentration of the tracer was measured as a function of time at a
fixed point int he liquid. If stirring is continued indefinitely,
ultimately the concentration reaches a steady value c when mixing
is complete. A mixing time N.sub..theta. is defined as the time
taken to reach a concentration within the range 1.05 c to 0-.95 c,
i.e. a concentration when c varies from its ultimate value by no
more than 5%. N.sub..theta. is found to be constant for a given
impeller/ vessel combination, and its value is a measure of the
effectiveness of the impeller, small values being better than
large. The following table records not only N.sub..theta., and the
energy (in Joules) expended in 10 seconds of operation using each
impeller, but also the power number N.sub.p =P/.rho.N.sup.3
D.sup.5, P being the power to drive the impeller, .rho. the liquid
density and N the speed of rotation. For high values of Reynolds
number ND.sup.2 /.mu., .mu. being the liquid viscosity, the power
number is constant. A low value of power number is desirable to
minimise driving power.
______________________________________ mixing Power Energy in
Joules time Number required for (N.sub..theta.) (N.sub..rho.) 10
seconds mixing ______________________________________ 1. Impeller
of FIG. 1 42 5.5 33.22 with 6 radial paddles as shown at 2. 2.
Impeller of FIG. 1, 38.6 2.6 14.95 with 6 swept-back paddles as
shown at 2a. 3. Marine propeller 52.6 0.80 11.65 (3 blades) as
shown in FIG. 2. 4. Pitch-bladed impeller 41.2 1.2 8.38 (6 blades)
as shown in FIG. 3. 5. Impeller according to 33.5 1.16 4.16 the
invention (6 blades) as shown in FIGS. 6 to 10.
______________________________________
The point at which tracer was introduced, the volume and
concentration of the tracer and other relevant parameters were the
same in all the experiments which gave rise to the results
tabulated above: the type of impeller used was the only apparently
significant variable. In these experiments the impeller according
to the invention thus gave the best reading for mixing time, by far
the best reading for energy consumption, and came a close second to
the marine propeller of FIG. 2A, 2B on power number.
FIG. 11 illustrates the form of a blade as so far described by
imagining it to be cut from a sheet metal tube 70 of diameter 0.7D,
D being as before the diameter of the impeller. The blade is
generated by cutting out a piece of the tube wall, double hatched
in FIG. 11. The boundary of the blade is as before defined by the
four lines AB, BC, CD and DA. AB and CD are straight lines AB, BC,
CD and DA. AB and CD are straight lines parallel to the axis 71 of
the tube, and 0.35D apart. The curve AD is generated by the
intersection of an imaginary cylinder 72 of radius 0.475D with the
tube 70, the axis 73 of cylinder 72 being at right angles to axis
71. The curve BC is generated in the same way as the curve AD, but
the intersecting cylinder 72 is displaced downwards, in the
elevation be a distance of 0.2D. The curvature of the long axis 59
is of course now the curvature (radius 0.35D) of the wall of tube
70.
The effect on impeller performance of the curvatures just discussed
will now be considered. The curvature of the long axis 59 of the
blade is altered by increasing or decreasing the radius of tube 70
of FIG. 11, and affects angle .alpha. of FIG. 6. Reducing the
radius increases .alpha. which reduces the strength of the
circulation loops 36 and 37 in FIG. 10. Increasing the radius
decreases .alpha. and leads to high swirl, i.e. rotation of the
liquid around the axis of the impeller in its direction of
rotation: such swirl dissipates energy by impact on the baffles 10
FIG. 1. A suitable compromise between the conflicting requirements
of (i) strong circulation loops, and (ii) low swirl, is obtained by
having .alpha. about 45.degree..
As to the curvatures of the long blade sides 55 and 56, the "total
swept area" as described and illustrated earlier in this
specification is also represented by the sum of the single hatched
and double hatched areas in FIG. 11. When the blades are mounted on
the hub, the liquid stirred by motion of the blades is proportional
to the "total swept area" because liquid passing through the single
hatched area subsequently passes over the blade near the corner D,
D being at the outer periphery when the blade is mounted on the
hub.
As already noted, mixing effect is approximately proportional to
the total swept area, whereas the power is approximately
proportional to the swept area, i.e. the double hatched are on FIG.
11. From this it follows that it is desirable to maximise the total
swept area by increasing the curvatures 55 and 56, say be reducing
the radius of intersecting cylinder 72 to 0.4D or 0.3D. However, if
the curves AD and BC are too strongly curved, i.e. have too small a
radius of curvature, this leads to an unsatisfactory design: the
centre of gravity of the blades could be below the hub 51. Also the
lowest point of curve BC will be much below the hub level, which
will increase the circulation strength of the loop 37 and reduce
the circulation strength of loop 36 of FIG. 10, adversely affecting
the mixing performance. A suitable compromise is to choose the
radius of curvature of blade sides 55 and 56 (AD and BC in FIG. 11)
so that, when viewed from a point on the hub axis 67 (FIG. 6),
those sides appear as approximately straight lines.
* * * * *