Title of Invention

"AN IMPELLER FOR A CENTRIFUGAL PUMP"

Abstract In accordance with the present invention, an impeller for use in a centrifugal pump has at least one vane the radially outer terminal end of which is configured to produce a flow velocity profile that controls and reduces the wear caused by slurry fluid being expelled from the impeller on the inner surface of the pump casing. The impeller vanes of the present invention are generally configured with a radially outwardly extending portion, as compared with ihe conventional straight or concave edge of an impeller vane. The outwardly extending portion may vary in shape, but is selected to produce a flow velocity profile that reduces wear in the pump casing.
Full Text IMPROVED VELOCITY PROFILE IMPELLER VANE
BACKGROUND OF THE INVENTION
Field of the Invention: This invention relates to pump impellers
and specifically relates to an impeller having vanes particularly configured
to selectively determine the velocity profile of the impeller to thereby
selectively modify the wear of the purnp casing when processing slurries.
Description of Related Art: Rotodynamie pumps are used-in-a
variety of industries to process liquids and slurries. The type of fluid
being processed dictates the type and configuration of the pump that is
used in the particular application. That is, pumping clear liquid places
less demand on pumps than does the processing of slurries, which
contain an amount of solids or particulate matter that is abrasive and
degrading to the internal structures of the pump.
Therefore, pump designers and engineers must consider the type
of fluid or slurry that is going to be processed and select or design an
impeller and pump casing that is most suitable to the application. For
example, in the processing of clear liquids (e.g., water), it is typical that
the pump casing is a volute, the shape of which changes in cross
sectional area from the cutwater of the pump to near the outlet of the
pump, and comparatively little wear is observed in the pump casing.
In the processing of slurries however, pump designers must
consider the effect of hydraulic surface geometry not only from the point
of optimizing pump efficiency, but also from the standpoint of minimizing
wear in the pump casing. Thus, it has been typical in slurry pump design
to modify the general volute shape of clear liquid-processing pumps to
provide, for example, wider impeller outlets and casings with parallel
sides.
Another factor that determines wear on the pump casing is the
shape of the impeller vanes. Specifically, the outer edge of the vanes of
the impeller have been demonstrated to significantly effect the flow
velocity of fluid moving through the pump. It has been observed that the
typical vane configuration having a straight outer edge, at or near the
periphery of the shroud, produces a certain fluid velocity that leads to
wear on the pump casing along the sides of the volute.
Thus, it would be advantageous in the art to provide an impeller
having vanes that are specifically designed or configured to produce a
more even wear pattern thus extending the overall wear life of the pump
casing when processing slurries, particularly those with high solids
content and/or particularly abrasive solids content.
BRIEF SUMMARY OF THE INVENTION
In accordance with the present invention, an impeller is provided
having at least one vane that is particularly shaped at the outer terminal
end thereof to produce flow velocities that are less deleterious to wear on
the pump casing when processing slurries. The vane configurations of
the present invention are adaptable for use in any rotodynamic pump
which employs an impeller, but is described and illustrated herein in
connection with use in a centrifugal slurry pump.
The impeller of the present invention comprises at least one vane
which extends from at or near a center point of the i mpeller,
corresponding to the central axis of the pump, and extends radially
outwardly toward the peripheral edge of the impeller where the vane has
a defined outer terminal end. The impeller of the present invention may
have a single shroud (generally known as a semi-open impeller), two
shrouds (generally known as a closed impeller) or may have no shroud
(generally known as an open impeller). The invention is described
herein, however, as having at least one shroud, which is positioned for
orientation toward the drive side of the pump casingi (i.e., opposite the
inlet of the pump).
The outer terminal end of the vanes of the present invention are
configured with a radially outwardly extending portion that generally
defines a convex-like edge of the vane. As used h&rein, the term
"convex" is not meant to be limited to the conventional definition of a
curved surface, but is meant only to convey that the outer terminal edge
of the vane extends radially outwardly relative to the center axis of the
impeller, rather than being straight or curved radially inwardly toward the
center axis of the impeller; however, the outer terminal edge may be any
shape, including but not limited to hemispherical, curvilinear, or
comprised of two or more intersecting lines.
The convex-like outer terminal end of the vanes of the present
invention generally produces a fluid velocity profile that reduces wear on
the inside surface of the pump casing. The shape of the convex-like
outer-terminal end of the vanes may be^particularly selected to specifically
modify or determine the fluid velocity profile so that, given a particular
type of slurry being processed, the wear on the pump casing can be
controlled and reduced.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS
In the drawings, which illustrate what is currently believed to be the
best mode for carrying out the invention:
FIG. 1 is a representational view in elevation of a centrifugal pump
illustrating a typical volute pump casing;
FIG. 2 is a representational view in cross s ection of the pump
illustrated in FIG. 1, taken at line 2-2;
FIG. 3 is a partial view in cross section of a conventional impeller
vane illustrating the terminal end of the vane, which is a straight edge;
FIG. 4 is a partial view in cross section of another conventional
impeller vane illustrating the terminal end of the vane, which is concave;
FIG. 5 is a schematic representation of the* fluid velocity profile of a
vane having a terminal end as shown in FIG. 3;
FIG. 6 is a schematic representation of the* fluid velocity profile of a
vane having a terminal end as shown in FIG. 4;
FIG. 7 is a schematic representation of the* fluid velocity profile of a
vane configuration of the present invention, the terminal end of which
comprises an outwardly extending edge;
FIG. 8 is a representational view in cross section of a first
embodiment of the present invention;
FIG. 9 is a representational view in cross section of a second
embodiment of the present invention;
FIG. 10 is a representational view in cross section of a third
embodiment of the present invention;
FIG. 11 is a representational view in cross section of a fou rth
embodiment of the present invention;
FIG. 12 is a representational view in cross section of a fifth and
sixth embodiment of the present invention;
FIG. 13 is a representational view:.i_n_crQss_secti_Qn of a ..sixth.,
embodiment of the present invention; and
FIG. 14 is a representational view in cross section of a seventh
embodiment of the present invention.
DETAILED DESCRIPTION OF THE INVENTION
FIG. 1 illustrates representationally a conventional centrifugal
pump 10 comprising an impeller 12 and a pump casing 14. An inlet 16 is
provided through the pump casing 14, which delivers incoming fluid to the
impeller 12. The pump casing 14 that is depicted in FIG. 1 is a volutetype
casing which extends from a cutwater 18 to a discharge 20. As
indicated by the arrows positioned within the pump casing 14 in FIG. 1,
and as further illustrated in the cross section view of FIG. 2, it can be
seen that the cross section area of the pump volute typically increases
from the cutwater 18 of the pump 10 toward the discharge 20 of the pump
As depicted in FIG. 2, as the impeller 12 is rotated by the drive
shaft 22, fluid entering the inlet 16 moves into the impeller 12 and is
expelled outwardly into the volute 24 of the pump casing 14. The
expelled fluid is further moved along the volute 24 of the pump casing 14
from the cutwater 18 to the discharge 20 and encounters a progressively
larger cross sectional area of the pump casing 14, as depicted in FIG. 2.
As further shown representationally in FIG. 1, the impeller 12 of a
conventional pump has at least one vane 30, and usually a plural ity of
vanes 30, which radiates outwardly from a point at or near the center 32
of the impeller 12. As shown more clearly in FIG. 3, for example, the
impeller 12 may have a shroud 34, which is generally formed as a
flattened disk having a center point 32 corresponding to the center axis of
the pump. The vanes 30 extend outwardly from at or near the center 32
of the shroud 34 toward the peripheral edge 36 of the shroud 34 where
the vane 30 terminates. Each vane 30 has a leading face 38 against
which the incoming fluid impacts as the fluid is expelled radially outwardly
toward the volute 24 of the pump casing 14 (FIG. 2).
Again referring to FIGrSrthe-outer terminal end~40 of each vane
30 defines an edge 42, as shown in cross sectional view taken at line Y
through the vane 30. FIG. 3 depicts a first conventional configuration for
a vane 30 which has a straight edge at the outer terminal end 40 of the
vane 30. The straight outer edge 42 of this conventional type of vane 30
is generally co-terminus with the peripheral edge 36 of the shroud 34, as
shown.
FIG. 4 illustrates another conventional configuration of an impeller
vane 30 where the outer edge 44 of the outer terminal end 40 of the vane
30 is concave, as illustrated in the cross section view taken at line X
through the vane 30. That is, the outer edge 44 curves inwardly toward
the center point 32 of the shroud 34 and the center 46 of the outer edge
44 is not co-terminus with the peripheral edge 36 of the shroud 34.
It has been demonstrated that the shape of the terminal end of the
vane effects the flow velocity of fluid exiting the impeller, and thereby
effects the type or pattern of wear that may be experienced in the pump
casing when processing slurries. As depicted in FIG. 5, for example, it
has been shown that a conventional vane having a straight outer edge 42
produces a flow velocity profile where fluid is expelled at a higher velocity
at or near the axial sides 48, 50 of the vane than from the center of the
vane between the axial sides 48, 50. Consequently, a wear pattern in the
pump casing occurs on either side of the volute in a spiral-type pattern.
As demonstrated in FIG. 6, the flow velocity profile produced by a
conventional vane having a concave outer edge 44 is similar to the flow
velocity profile produced by a vane having a straight outer edge 42,
except that a double spike of flow velocity occurs, or is produced, at the
axial ends of the vane. Consequently, a double spiral wear pattern is
observed along the volute of the pump casing when processing slurries
through the pump. In both conventional vane configurations shown in
FIGS. 5 and 6, relatively less wear occurs at the center of the volute of
the pump.
In view of the foregoing, it would be advantageous to provide a
vane configuration having an outer terminal end that is suitably shaped to
produce a-flow velocity profile that results-in-more-controlled and reduced
wear in the volute of the pump casing compared to conventionally known
impeller vanes. The inventors have discovered that a vane 60 having a
generally convex-like outer edge 62, as illustrated, for example, in FIG. 7,
produces a flow velocity profile where the velocities are more evenly
distributed across the volute of the pump casing, thereby resulting in
more even wear of the internal casing surface than what would normally
occur with conventional vane configurations.
FIG. 8 more clearly illustrates that, in general, the impeller vane 60
of the present invention has an outer terminal end 64 defining an outer
terminal edge 62 that is convex-like in shape in that the outer edge 62
includes a radially outwardly extending portion 66 that extends beyond
the peripheral edge 36 of the shroud 34. Thus, the radius Rv of the
outwardly extending portion 66, as measured from the center 32 of the
impeller 34 to the outermost terminus 68 of the vane 60, is greater than
the radius Rs of the shroud 34. As explained more fully below, the shape
of the outwardly extending portion 66 of the terminal end 64 may vary,
and may be specifically selected to produce the desired flow velocity
profile consistent with the pumping requirements of a given application.
FIG. 8, however, illustrates a first embodiment of the invention
where the outer terminal end 64 of the vane 60 has an outwardly
extending portion 66 that has a radius Rv which is greater than the radius
Rs of the shroud 34. The outer edge 62 of the vane 60 is also configured
with a portion 70, 72 on either side of the outwardly extending portion 66
that has a radius RB, which, in this embodiment, is equal to the radius Rs
of the shroud 34. Thus, the vane 60 has a width and the outwardly
extending portion 66 has a width-WP that is less than the width Wv of the
vane 60. It should be noted that in equally suitable alternative
embodiments described more fully below, the width WP of the outwardly
extending portion 66 may be equal to the width Wv of the vane 60.
In the first embodiment of the present invention shown in FIG. 8,
the outwardly extending portion 66 is generally arcuate in shape as
measured from Point A to the terminus 68 of the outwardly extending
portion 66 thence to Point B. Thus, by way of example only, the
outwardly extending portion 66 may have a radius Rc. However, the
arcuate line between Point A, the terminus 68, and Point B need not have
a consistent radius (i.e., an arc). Those of skill in the art, consistent with
the disclosure hereof, will understand that the dimensions of the arcuate
or curvilinear line forming the outwardly extending portion 66 may be
suitably varied to produce a desired flow velocity profile as described.
In an alternative embodiment of the invention shown in FIG. 9, the outer
edge 62 of the vane 60 includes an outwardly extending portion 66 having
a terminus 68 that defines a radius Rv of the vane 60. The outer edge 62
further has a portion 70, 72 on either side of the outwardly extending
portion 66 the radius RB of which is less than the radius Rs of the shroud
34. Further, the radius Rs of the shroud 34 is less than the radius Rv of
the outwardly extending portion 66. The outwardly extending portion 66
is defined between Point A, the terminus 68 of the vane 60, and Point B,
and has a width WP. The width Wp of the outwardly extending portion 66
is less than the width Wv of the vane 60.
In the alternative embodiment of FIG. 9, the outwardly extending
portion 66 is illustrated, by way of example only, as being formed of two
intersecting lines the first line 74 being defined between Point A and the
terminus 68 of the vane 60, and the second line 76 being defined
between the terminus 68 and Point B. This embodiment further serves to
illustrate that the shape of the outwardly extending portion 66 can be
other than an arcuate or curved line, as shown in FIG. 8, and can be
comprised of a plurality of intersecting lines. Again, those of skill in the
art will understand from the disclosure herein that the shape of the outer
edge 62 of the vane 60 may be suitably modified in any variety of ways to
provide a desired flow velocity profile.
The illustrated embodiments of the impeller vane of the present
invention depict a terminus 68 of the vane 60 which is centered relative to
the width Wv of the vane 60. However, it should be noted that the
terminus 68 may be located other than at the centerline 80 of the vane 60
and of the width Wv as may be dictated by or required to achieve the
desired flow velocity profile.
FIGS. 8 and 9 depict alternative embodiments of the invention
where the vane radius Rv is a representational view in cross section of a
fifth embodiment of the present invention is greater than either the shroud
radius Rs and/or the base radius RB. FIGS. 10 and 11 illustrate other
alternative embodiment of the invention. FIG. 10, for example, illustrates
an alternative embodiment where the vane radius Rv is slightly less than
the shroud radius Rs, and both the vane radius Rv and shroud radius Rs
are greater than the base radius RB.
Yet another alternative is illustrated in FIG. 11 where the radius RV
of the vane 60 and the radius Rs of the shroud 34 are substantially equal,
and both are greater than the base radius RB of the vane 60. Both of the
embodiments illustrated in FIGS. 10 and 11 achieve a desired flow
velocity that produces less wear on the volute of the pump casing. It
should be noted that the convex-like outwardly extending portion 66
shown in FIGS. 10 and 11 is depicted as a hemispherical shape by way
of example only, and other suitable convex-like shapes or dimensions are
appropriate and/or useful.
Further, as noted previously, the position of Point A and Point B,
which define the opposing axial ends of the outwardly extending portion
66, may be located anywhere from nearer the center line 80 (FIGS. 8 and
.9) of the vane 60 to the axial ends 82, 84 of the vane 60 as depicted in
FIG. 12. Hence, the distance D between Point A and Point B may be
from D=WV to about D=Wv/3, and Point A and Point B may be equally or
unequally distanced from the centerline 80 of the vane 60.
Referring again to the embodiment of the invention shown in FIG.
12, the axial ends of the outwardly extending portion 66, defined as Point
A and Point B, extend to the axial ends 82, 84 of the vane 60. As such,
the illustrated embodiment of FIG. 12 does not have side portions (70,
71) as in the embodiments of FIGS. 8-11, but the axial ends (Point A,
Point B) of the outwardly extending portion 66 may be viewed as defining
the base radius RB of the vane 60. Thus, in a fifth embodiment of the
invention shown in FIG. 12, the radius Rv of the vane 60, defined from the
center axis 32 of the impeller to the terminus 68 of the vane 60, is.great.er.
than the radius Rs of the shroud 34, and the base radius RB is equal to
the shroud radius Rs.
In a sixth alternative embodiment also shown in FIG. 12 in
phantom line, the shroud 34 may extend beyond the base radius RB of
the vane 60 a selected distance so that the peripheral edge 36' of the
impeller extends to a radius Rs'. The radius Rv of the vane 60 is,
therefore, greater than RB and Rs'.
In a seventh alternative embodiment shown in FIG. 13, the
terminus 68 of the vane 60 may not extend to the peripheral edge 36 of
the shroud 34. Therefore, in this embodiment, the outwardly extending
portion 66 of the vane 60 does not extend beyond the shroud 34, but still
advantageously effects the flow velocity profile of the impeller. In the
embodiment of FIG. 13, the radius Rv of the vane 60 is greater than the
base radius RB, but less than the radius Rs of the shroud 34.
In still another alternative embodiment of the invention shown in
FIG. 14, the terminus 68 of the vane 60 extends to a point substantially
equal to the peripheral edge 36 of the shroud 34 such that the radius Rv
of the vane 60 and radius Rs of the shroud 34 are equal, or substantially
so, and the base radius RB is less than either the radius Rv of the vane or
the radius Rs of the shroud. Again, although the convex-like edge of the
embodiments illustrated in FIGS. 12-14 is arcuate, the outwardly
extending portion 66 may be any suitable shape as previously described.
Regardless of the shape of the outwardly extending portion 66 of
. the vane 60 as illustrated and described previously, the area of the shape
may preferably be between about 30% to about 85% of the area defined
by WV(RV-RB). The following table illustrates by way of example only,
some of the possible dimension ranges of the variables described herein,
but is not meant to be an exhaustive definition of the ranges.
Minimum
1.02RB
0.2
RB
Maximum
1.15RB
1
1.15RB
Preferable
1.06RB
0.65
1.05RB
The impeller vanes of the present invention are configured to
provide a selected flow velocity profile which controls and/or reduces wear
on the pump casing caused by fluid slurry being expelled from the impeller
toward the casing. The impeller vanes may be adapted for use in virtually
any type, size or variety of rotodynamic pump. Those of skill in the art,
conferring with the disclosure herein, will understand the changes and
adaptations that may be made to employ the impeller vanes in various
pumps to produce the desired flow velocity profile. Hence, reference
herein to specific details or embodiments of the invention are byway of illustration only and not by way of limitation.



CLAIMS
What is claimed is:
1. An impeller for a centrifugal pump, comprising at least one
vane extending radially in length from a central axis of the impeller to an
outer peripheral edge of said impeller, said at least one vane having an
outer terminal end at or near said peripheral edge of said impeller, said
outer terminal end-having an outwardly extending portion being convex--
like in shape.
2. The impeller of claim 1 further comprising at least one
shroud having a peripheral edge defining said peripheral edge of said
impeller, said at least one vane extending outwardly from said shroud.
3. The impeller of claim 2 wherein said outwardly extending
portion has a terminus and a radius Rv measured from said central axis of
said impeller to said terminus, and wherein said shroud has a radius Rs,
measured from said central axis to said peripheral edge, wherein Rv is
equal to or greater than Rs.
4. The impeller of claim 3 wherein said outer terminal end of
said at least one vane further comprises a portion having a radius RB,.
where RB is less than or equal to Rs.
5. The impeller of claim 4 wherein said outwardly extending
portion is arcuate in shape.
6. The impeller of claim 4 wherein said outwardly extending
portion has an outer edge which is formed by the intersection of at least
two lines.
7. The impeller of claim 4 wherein said at least one vane has a
width Wv and wherein said outwardly extending portion has a width Wp,
where Wp is less than or equal to Wv.
8. The impeller of claim 7 wherein the area of said outwardly
extending portion is from about 30% to about 85% the area defined by
WV(RV-RB).
9. The impeller of claim 1 wherein said outwardly extending
portion has an outer edge that is curved or arcuate.
10. The impeller of claim 1 wherein said outwardly extending
portion has an outer edge formed by the intersection of at least two lines.
11. An impeller for a rotodynamic pump, comprising:
a shroud having a central axis and a peripheral edge radially spaced from
said central axis, said shroud having a radius Rs;
at least one vane extending axially outwardly from said shroud and
extending radially from at or near said central axis to said peripheral
edge, said vane having an outer terminal end positioned at or near
said peripheral edge, wherein said outer terminal end comprises an
outwardly extending portion having a radius Rv measured from said
central axis to a terminus of said outwardly extending portion; and
wherein Rv is equal to or greater than Rs.
12. The impeller of claim 11 further comprising a second shroud
positioned parallel to and spaced from said shroud and wherein said at
least one vane extends between said spaced apart shrouds.
13. The impeller of claim 11 wherein said outer terminal end of
said at least one vane further comprises a portion having a radius RB,
wherein RB is equal to Rs.
14. The impeller of claim 11 wherein said outer terminal end of
said at least one vane further comprises a portion having a radius RB,
wherein RB is less than Rs.
15. The impeller of claim 11 wherein said outwardly extending
portion is convex-like in shape.
16. The impeller of claim 11 wherein said outwardly extending
portion has an outer edge which is curved.
47- The impeller of Claim 11 wherein said outwardly extending
portion has an outer edge comprised of at least two intersecting lines.
18. The impeller of claim 11 wherein said at least one va ne has
a width Wv, and wherein the shape of said outwardly extending portion is
from about 30% to about 85% of the area defined by WV(RV-RS).
19. The impeller of claim 13 wherein said at least one vane has
a width Wv, and wherein the shape of said outwardly extending portion is
from about 30% to about 85% the area defined by WV(RV-RB).
20. The impeller of claim 19 wherein said outwardly extending
portion has an outer edge which is shaped to produce a flow velocity
profile selected to reduce wear in a pump casing.
21. The impeller of claim 2 wherein said at least one shroud has
a radius Rs measured from said central axis to said peripheral edge, and
wherein said outwardly extending portion has a terminus and a rad ius Rv
measured from said central axis of said impeller to said terminus a nd said
outwardly extending portion has axial ends defining a radius RB measured
from said at least one axial end to said central axis, wherein RB is less
than Rv and Rs, and Rv is less than Rs.



Documents:

5219-delnp-2006-Abstract-(06-01-2014).pdf

5219-delnp-2006-Abstract-(10-06-2013).pdf

5219-delnp-2006-abstract.pdf

5219-delnp-2006-Claims-(06-01-2014).pdf

5219-delnp-2006-Claims-(10-06-2013).pdf

5219-delnp-2006-claims.pdf

5219-delnp-2006-Correspondence Others-(06-01-2014).pdf

5219-delnp-2006-Correspondence Others-(15-10-2013).pdf

5219-delnp-2006-Correspondence Others-(18-04-2012).pdf

5219-DELNP-2006-Correspondence Others-(20-10-2011).pdf

5219-delnp-2006-Correspondence-Others-(10-06-2013).pdf

5219-DELNP-2006-Correspondence-Others-(12-10-2010).pdf

5219-delnp-2006-correspondence-others-1.pdf

5219-delnp-2006-correspondence-others.pdf

5219-delnp-2006-description (complete).pdf

5219-delnp-2006-Description(Complete)-(10-06-2013).pdf

5219-delnp-2006-drawings.pdf

5219-delnp-2006-form-1.pdf

5219-delnp-2006-Form-13-(06-01-2014).pdf

5219-delnp-2006-form-18.pdf

5219-delnp-2006-Form-2-(06-01-2014).pdf

5219-delnp-2006-Form-2-(10-06-2013).pdf

5219-delnp-2006-form-2.pdf

5219-DELNP-2006-Form-3-(12-10-2010).pdf

5219-delnp-2006-Form-3-(15-10-2013).pdf

5219-delnp-2006-Form-3-(18-04-2012).pdf

5219-DELNP-2006-Form-3-(20-10-2011).pdf

5219-delnp-2006-form-3.pdf

5219-delnp-2006-Form-5-(10-06-2013).pdf

5219-delnp-2006-form-5.pdf

5219-delnp-2006-gpa.pdf

5219-delnp-2006-pct-237.pdf

5219-delnp-2006-pct-301.pdf

5219-delnp-2006-pct-304.pdf

5219-delnp-2006-pct-308.pdf

5219-delnp-2006-pct-311.pdf

5219-delnp-2006-pct-402.pdf

5219-delnp-2006-Petition-137-(10-06-2013).pdf


Patent Number 259106
Indian Patent Application Number 5219/DELNP/2006
PG Journal Number 09/2014
Publication Date 28-Feb-2014
Grant Date 25-Feb-2014
Date of Filing 11-Sep-2006
Name of Patentee WEIR SLURRY GROUP, INC.
Applicant Address 2701 SOUTH STOUGHTON ROAD, MADISON, WI 53716, U.S.A.
Inventors:
# Inventor's Name Inventor's Address
1 CRAIG IAN WALKER 18A GLADYS AVENUE, FRENCHS FOREST, NSW 2086, AUSTRALIA
2 ALEKSANDER SERGEEVICH ROUDNEV 808 BROOK STREET, DE FOREST, WI 53532, USA.
PCT International Classification Number B63H 1/16
PCT International Application Number PCT/US2005/010830
PCT International Filing date 2005-03-30
PCT Conventions:
# PCT Application Number Date of Convention Priority Country
1 10/814,427 2004-03-31 U.S.A.