Note: Descriptions are shown in the official language in which they were submitted.
'7(~
This invention relates to a static mixer.
As is known, various types o~ static mixers have been used for mixing
flowable media in an attempt to obtain a homogeneous flow. For example, static
mixers are described in Brauner et al German Patenk 2,3Z8,795 ~May 5, 1977) and
Brauner et al A.S. 2,522,106 ~laid open November 25, 1976) as well as in Schutz
et al United States Patent 4,170,446 granted October 9, 1979. Generally, these
static mixers have mixing devices disposted in tubular casings and have guide
elements which are disposed in layers to form flow channels for the throughput.
As is known, static mixers must be as short as possible in length for
economic and technical reasons. Specifically, the cost of materials and the
~ressure drop are the economic reasons. The overall length should be short for
technical reasons in order to insure that the mixer is of compact construction
and that the residence time of the media in the mixer is short.
It has been previously assumed, in practice, that if a required level
of homogeneity is required, for example, in relation to concentration or tempera-
ture, the mixer elements of a static mixer must have a large number o webs and
the webs must be arranged in a narrow "pack" in order to give a small "mesh"
size. In such cases, the mixer length becomes relatively short. However9 i~
has been found in practice that this advantage is accomplished by a considerable
pressure drop. This requires high pumping forces and, therefore, high energy
costs, Further, the mixer elements have to be very strong. Another difficulty
is that the mixer elements become difficult to clean and become clogged fairly
readily because of deposits which form on the webs.
Accordingly, it has been suggested that the pressure drop could be
decreased by some "loosening-up" of the mixer element structure, i.e., by Usillg
fewer webs and by increasing mesh size. However, the layer ~ormation laws for
determining homogeneity show that such a construction would reduce the layers
produced over a particular mixer length. Thus, the length would have to be in-
-1 ~
Ltïlt~
creased approxImately in the same proport~on as the pressure drop is reduced.
This constructIon has, there~ore, not been used in practice.
Accordingly, it is an obJect of the invcntion to provide a static mixer
with geometric proportions which provide a relatively high mixing quality within
a relatively reduced length and at a relatively low pressure drop.
It is another object of the invention to provide a static mixer which
can operate at low energy levels to produce a mixture of relatively high quality.
Briefly, the invention provides a static mixer which is comprised of a
tubular casing which defines a flow passage having a predetermined diameter along
a longitudinal axis of the passage and at least one mixer element which is dis-
posed in the flow passage. In accordance with the invention, the mixer element
has a length of from 0.75 to 1.5 times the diameter of the 10w passage and is
formed of at least two groups of ~ebs. The webs of each group are disposed in
parallel relation to each other at a predetermined transverse spacing of from
0.2 to Q.4 times the diameter of the flow passage. The webs are also in angular
relation to the axis of the flow passage while being in crossing relation to the
webs of the other group. Also, each web has a maximum web width of from 0.1 to
0.167 times the diameter of the Elow passage.
The surprising knowledge underlying the invention is that if the above-
recited dimensions are observed, the resulting mixer is only slightly longer thana conventional mixer and has an unexpectedly low pressure drop, as is described
hereinafter.
The static mixer can be used particularly for mixing processes of
Newtonian and non-Newtonian liquids.
The tubular casing can be a c~lindrical tube or a tube with a square
cross-section. In the first case, the contour of the webs in the marginal zones
is adapted to the circular cross-section of the cylindrical tube.
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The geGmetry o~ t~e nlixer elements is determined by the dimensional
specI~icat~ons for the relatlonship o~ web width ~ to tube diameter d and the
relatlonship of the ~ransverse between-webs spacing m within each group pairs
to the tube diameter d and the relationship of mixer element length 1 to tube
diameter d. ~or instance, the expression b/d = 0.167 means that six we~s are
distributed over the same tube cross-section, whereas the expression b/d ~ 0.1
indicates that ten webs are distributed over the same tuhe cross-section.
The relationship between the spacing m and the tube diameter d denotes
the web density in the tube - i.e., mesh size along the tube axis and therefore
the total web surface area.
The relati~nship between the mixer elemènt length 1 and tube diameter
d gives the length of a mixer element.
These and other ob~ects and advantages of the invention will become more
apparent from the following detailed description taken in conjunction with the
drawings wherein:
Figure 1 illustrates a longitudinal sectional view of a static mixer
constructed in accordance with the invention; and
Figure 2 diagrammatically illustrates the mixing quality o various
embodiments of the invention against relative mixer le~gth.
Referring to Figure 1, the static mixer is comprised of a tubular cas-
ing 1, for example, of circular cross-sectional shape and a plurality of mixer
elements 2, 3, 4, 5 which are disposed within the casing 1 in consecutive rela-
tion. As indicated, the casing 1 defines a flow passage of predetermined diame-
ter ~d) while the mixer elements 2 - 5 are disposed in 90 relation to each other
along the longitudinal axis of the casing 1.
Each mixer element 2 - 5 is comprised of criss-crossing groups 6, 7
of ~ebs. The webs of each group are disposed in parallel relation to each other
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at a predetermined transverse spacing (m). As indicated, each group comprises
webs 6'aJ 6"a, 6"'a-6'd, 6"d, 6"'d and 7'a, 7"a, 7"'a-7'd, 7"d, 7"'d. The
webs 6, 7 are disposed in angular relation to the axis of flow passage in the
casing 1 at an angle Cl, with the angle of inclination o the webs of group 6 be-
ing of opposite sign to that of the webs of group 7. As illustrated, the angle
c~ is 45.
Each mixer element comprises three interleaved plate pairs 6'a-6'd,
7'a-7'd; 6"a-6"d, 7"a-7"d; and 6"'a-6"'d, 7"'a-7"'d, the webs of group 6 ex-
tending through gaps between the webs of group 7 to cross the same while the
webs of group 7 extend through gaps between the webs of group 6 to cross the
same.
As, shown, each plate pair consists of eight webs, the webs of each
plate being coplanar ~cf. 6'la-6"d of element 3 and 7" 'a-7" 'd of element 5 in
Figure l). However, the webs 6'a-6'd, 7'a-7'd and so on, instead of being co-
planar, can be offset from one another stepwise. As described in British Patent
1,597,150 Gerhard Schutz, published September 3, 1981, the webs of a single mixer
element can be joined together at their contact places as a whole in a single
working step by electric resistance welding.
As illustrated, each mixer element 2 - 5 is oE the same length 1.
Referring to Figure 2, five embodiments (I - V) of static mixers were
compared Eor measured pressure drop and relative mixer length ~l/d). As illus-
trated, the variation coefficient ~/x is plotted along the ordinate while the
relative mixer length L/d of the entire mixer, comprising a number of mixer ele-
ments is plotted along abscissa. ~ denotes the measured standard deviation from
the measured means concentration x of a tracer in a mixture produced in a static
mixer. The standard deviation ~ from the calculated means value x of the homo-
geneity of ingredients for mixing which a mixer provides can be found, e.g., by
means of electrical conductivity measurements (cf. Chem.-Ing. Techn~ 51 ~1979),
7~61
Nr. 5, pp. 353 - 354).
The formal equation~ r
Zo
is used ~or the pressure drop A P as found by measurements in static mixers in
the case of laminar flow. "~" is *he pressure drop multiple and represents the
ratio of the pressure drop in a static mixer to the empty casing at the same
viscosity ~ , ~ repr0sents the ~low velocity, L the length of the casing and d
the diameter of the tube.
The following table gives the geometric data for mixer. types I - V.
Type ~ m/d lld ~_
I 0.08 0.15 1.63 45
I~ 0.1 0.2 0.75 45
III 0.125 0.3 1. 45
IV ~.167 0.4 1.5 45
V ~ ~ 0 ~ ~ ~ 45
The construction of khe Type I mixer is similar to those described
in German A.S. 2,328,795 and 2,522,106.
The characteristic curves ~/x = f ~L/d~ for Types f - V are plot~ed
in the diagram o Figure 2. ~,/x = 10 2 means that the standard deviation rom
the mean value is 1% and the mixture can be considered to be homogeneous.
The table below gives measured values of relative mixer length for
/x = 10 2 and the associated pressure drop multiples z for types I - V.
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Type L/d
I 8 go
II 9 50
III 10 35
IV 14 20
V 30 15
It can ~e gathered from the foregoing data that the relative mixer
lengths ~or Types II, III and IV are not much greater than for Type I, but the
pressure drop multiple o~ Types II, III and IV can ~e reduced considerably below
t~e pressure drop ~Or Type I.
It will also be apparent that the pressure drop reduction is not in
approximately the same relationshlp as the increase in relative mixer length as
has previously been assumed but is much stronger and more pronounced.
A comparison of the results ~or Type V with the results for Types
lQ II - I~ shows that a substantial reduction of the pressure drop multiple is
linked with a substantial increase in relati~e mixer length; the increase of L/d
and the decrease of z as compared with Type I are in approximately the same re-
lationship.
The interesting feature in a comparison o~ the mixing devices with one
another is the pressure drop/throughput ~or the same quality of mixing. Pressure
drop, throughput and relative mixer length are interconnected by way of the
specific power requirement W which is a dimensionless characteristic of a mixer
~cf. e.g., E. Dolling: "Zur Darstellung von Mischvorga'ngen in hochviskosen
FlUssigkeiten'', Dissertation, Techn. Hochschule Aachen/Germany/1971 and H.
2Q Brunemann and G. gohn: "Statische Mischer~', Aufbereitungstechnik, 1972, 1, pp.
16 - 231.
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1~'7'`~0~
T~e spcci~fic p~er r~qu~rement ~ is de~ned ~y the formula:
~ 32 ~ dL 2
in which h p V denotes the power requirement, ~ denotes vlscosity and V denotes
volume flo~.
For a glven quality of mixing~ W is lowest for the technically optimal
mixing device.
The following table gives the observed values of specific power require-
ment W for mixing devic0s for which mixer elements of Types I - V are used.
Type W
I 184 320
II 129 600
III 112 000
IV 125 440
V 460 800
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As the ta~le shows, a device having mixer elements III can be considered to be
the technically optimal mixing device, although the diferences from devices
having mixer element Types II and IV are so slight that the three Types II, III
and IV can be regarded as virtually equivalent. HoweverJ th~ speciic power
requirement W differs considerably for types I and V and can therefore be con-
sidered unsuitable for the purposes~ the invention.
The surprising knowledge underlying the invention is based on the fact
that the difference in mixing efficiency of the mixer element types I - V is
much less than predicted by the well known layer formation law ~H. Brunemann ancl
G. John Chemie-Ing.-Techn. 43 (1971 Nr. 6, pages 347 - 354~):
N = a
'7'~
N denotes the number of layers formed, a denotes the number of
channels in an elemen-t, i.e. in the case a = d/b, and N denotes
the number of mixer elements. In case of constant L/d ra-tio of
the elements it is also possible to write the above equation as:
N = (d/b)k (L/d)
where d = diameter of the tube
b = web width
k = a constant factor
L = length of the casing
The following table gives once again a comparison of the
mixing efficiency and the pressure drop of the element types I - V,
based on measured values ~ and as calculated according to the
layer formation law.
The comparison is given relative to -type I:
I 1~ 1` ~1 .
I 90 124,3,108 lO-2 1 1 l
II 50 lO1.108 1.~.10 4.3 1.8 1.8
III 35 81~.7.10 2.8.~10 25 ~2.8 2 6
IV 20 61.7.10 7,3.10 253 7.3 4.5
V 16 4~6.6.104 ~ 65l5 36 5.6
As it can be seen in the above table, the layer forma-tion law
predicts much more reduced eEficiency than demonstrated by the
invention if fewer webs are used. The content of the invention
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77(~61
is therefore that this prejudice has been overcome.
Thus, the mixer according -to -the invention should have
a length (l) of from 0.75 to 1.5 times the diameter (d) of the
flow passage of the casing l, a web spacing (m) of from 0.2 to
0.4 times -the diameter (d) and a maximum web width (b) of from
0.1 to 0.167 times the diameter (d).
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