U.S. patent application number 13/880817 was filed with the patent office on 2013-08-29 for radial diffuser vane for centrifugal compressors.
The applicant listed for this patent is Sen Radhakrishnan, Susanne Clary Svensdotter, Libero Tapinassi. Invention is credited to Sen Radhakrishnan, Susanne Clary Svensdotter, Libero Tapinassi.
Application Number | 20130224004 13/880817 |
Document ID | / |
Family ID | 43876985 |
Filed Date | 2013-08-29 |
United States Patent
Application |
20130224004 |
Kind Code |
A1 |
Radhakrishnan; Sen ; et
al. |
August 29, 2013 |
Radial Diffuser Vane for Centrifugal Compressors
Abstract
A turbo machine comprising a rotor assembly comprising at least
one impeller, a bearing connected to the rotor assembly, wherein
the bearing is configured to rotatably support the rotor assembly,
and a stator comprising at least one diffuser connected to an exit
portion of the at least one impeller, wherein the at least one
diffuser comprises a plurality of diffuser vanes, wherein at least
one of the plurality of diffuser vanes comprising a camber line
defined by a function comprising an inflection point.
Inventors: |
Radhakrishnan; Sen;
(Bangalore, IN) ; Svensdotter; Susanne Clary; (Le
Creusot, FR) ; Tapinassi; Libero; (Florence,
IT) |
|
Applicant: |
Name |
City |
State |
Country |
Type |
Radhakrishnan; Sen
Svensdotter; Susanne Clary
Tapinassi; Libero |
Bangalore
Le Creusot
Florence |
|
IN
FR
IT |
|
|
Family ID: |
43876985 |
Appl. No.: |
13/880817 |
Filed: |
August 12, 2010 |
PCT Filed: |
August 12, 2010 |
PCT NO: |
PCT/EP10/61788 |
371 Date: |
April 22, 2013 |
Current U.S.
Class: |
415/191 ;
29/889.2; 415/207 |
Current CPC
Class: |
F04D 29/444 20130101;
Y10T 29/4932 20150115; F01D 9/00 20130101 |
Class at
Publication: |
415/191 ;
29/889.2; 415/207 |
International
Class: |
F01D 9/00 20060101
F01D009/00 |
Claims
1. A turbo machine comprising: a rotor assembly comprising at least
one impeller; a bearing connected to the rotor assembly, wherein
the bearing is configured to rotatably support the rotor assembly;
and a stator comprising at least one diffuser connected to an exit
portion of the at least one impeller, wherein the at least one
diffuser comprises: a plurality of diffuser vanes, wherein at least
one of the plurality of diffuser vanes comprising a camber line
defined by a function comprising an inflection point.
2. The turbo machine of claim 1, wherein the function is
y=ax.sup.3+bx.sup.2+cx+d, where a, b, c and d are constants.
3. The turbo machine of claim 1, wherein the function is one of a
higher order polynomial function, a Sigmoid function, a Gompertz
function, and a Bezier curve.
4. The turbo machine of claim 1, wherein the function is an
exponential function.
5. The turbo machine of claim 1, wherein a portion of the at least
one of the plurality of diffuser vanes disposed near a leading edge
is substantially unloaded when operating at design conditions, and
wherein a load gradually increases to a maximum loading towards a
middle portion of the at least one of the plurality of diffuser
vanes.
6. The turbo machine of claim 1, wherein each of the plurality of
diffuser vanes is attached to one of a hub or shroud.
7. The turbo machine of claim 1, wherein the function is a Bezier
curve.
8. A method of manufacturing a turbo machine, the method
comprising: providing a rotor assembly comprising at least one
impeller; connecting the rotor assembly to a bearing assembly
configured to rotatably support the rotor assembly; and providing a
stator assembly comprising at least one diffuser connected to an
exit portion of the at least one impeller, wherein the at least one
diffuser comprises: a plurality of diffuser vanes, wherein at least
one of the plurality of diffuser vanes comprises a camber line
defined by a function comprising an inflection point.
9. The method of claim 8, wherein the function is
y=ax.sup.3+bx.sup.2+cx+d, where a, b, c and d are constants.
10. The method of claim 8, wherein the function is one of a higher
order polynomial function, a Sigmoid function, a Gompertz function,
and a Bezier curve.
11. The method of claim 8, wherein the function is an exponential
function.
12. The method of claim 8, wherein a portion of the at least one of
the plurality of diffuser vanes disposed near a leading edge is
substantially unloaded when operating at design conditions and
wherein a load gradually increases to a maximum loading towards a
middle portion of the at least one of the plurality of diffuser
vanes.
13. The method of claim 8, further comprising: attaching each of
the plurality of diffuser vanes to one of a hub or shroud.
14. The method of claim 8, wherein the function is a Bezier
curve.
15. A diffuser comprising: an inner annular wall; an outer annular
wall; a plate portion disposed between the inner annular wall and
the outer annular wall; and a plurality of diffuser vanes disposed
on the plate portion, wherein at least one of the plurality of
diffuser vanes comprises a camber line defined by a function
comprising an inflection point.
16. The diffuser of claim 15, wherein the function is
y=ax.sup.3+bx.sup.2+cx+d, where a, b, c and d are constants.
17. The diffuser of claim 15, wherein the function is one of a
higher order polynomial function, a Sigmoid function, a Gompertz
function, and a Bezier curve.
18. The diffuser of claim 15, wherein the function is an
exponential function.
19. The diffuser of claim 15, wherein a portion of the at least one
of the plurality of diffuser vanes disposed near a leading edge is
substantially unloaded when operating at design conditions, and
wherein a load gradually increases to a maximum loading towards a
middle portion of the at least one of the plurality of diffuser
vanes.
20. The diffuser of claim 15, wherein the function is a Bezier
curve.
Description
CROSS-REFERENCE TO RELATED APPLICATION
[0001] This is a national stage application under 35 U.S.C.
.sctn.371(c), PCT application number PCT/EP2010/061788 filed on
Aug. 12, 2010, the disclosure of which is hereby incorporated in
its entirety by reference herein.
BACKGROUND OF THE INVENTION
[0002] Embodiments of the present invention relate generally to
compressors and, more specifically, to diffuser vanes for
centrifugal compressors.
[0003] A compressor is a machine which accelerates gas particles
to, ultimately, increase the pressure of a compressible fluid,
e.g., a gas, through the use of mechanical energy. Compressors are
used in a number of different applications, including operating as
an initial stage of a gas turbine engine. Among the various types
of compressors are the so-called centrifugal compressors, in which
mechanical energy operates on gas input to the compressor by way of
centrifugal acceleration, e.g., by rotating a centrifugal impeller
(sometimes also called a "rotor") by which the compressible fluid
is passing. More generally, centrifugal compressors can be said to
be part of a class of machinery known as "turbo machines" or "turbo
rotating machines".
[0004] Centrifugal compressors can be fitted with a single
impeller, i.e., a single stage configuration, or with a plurality
of impellers in series, in which case they are frequently referred
to as multistage compressors. Each of the stages of a centrifugal
compressor typically includes an inlet conduit (inducer section)
for gas to be compressed, an impeller which is capable of imparting
kinetic energy to the input gas and a diffuser which converts the
kinetic energy of the gas leaving the rotor/impeller into pressure
energy.
[0005] More specifically, as shown in the exemplary side-sectional
view of FIG. 1A taken along the axis of a compressor in the
direction of the process gas flow, a centrifugal compressor stage
100 includes an impeller 102 attached to a rotor 104 followed by a
diffuser 106 and a return channel or exit scroll 108. The diffuser
106 collects the high velocity fluid from the impeller 102's exit
and allows the fluid to slow down, thereby converting the dynamic
pressure to a static pressure. To provide another perspective of
this structure, FIG. 1B shows a cross-sectional view of the
compressor stage 100 taken along the other axis, i.e.,
perpendicular to the direction of the process gas flow. Therein,
the rotor 104 is seen in the center of the Figure surrounded by an
impeller 102 having a number of impeller blades 114. The impeller
blades 114 can be connected, on one end, to a hub portion 116 of
the impeller 112, and on the other end to a shroud portion 118 of
the impeller 102.
[0006] Of more interest for the present application is the diffuser
section 106. Vaned diffusers 106 (i.e., those diffusers having a
circumferential array of airfoils (diffuser blades 110) along the
flow passage as best seen in FIG. 1B) are employed to achieve
higher stage efficiency by directing the highly tangential fluid
flow at the impeller exit to be more radial towards the diffuser
exit. By way of contrast, some centrifugal compressors have
vaneless diffuser sections 120, as shown in FIG. 1C. Making the
fluid flow more radial inside the diffuser 106 by using vanes
reduces the distance taken by the fluid to travel through the
diffuser 106. This concept is illustrated by the flow arrows in the
centrifugal pump illustrated in FIG. 1D.
[0007] Reducing the distance taken by the fluid reduces the
friction losses associated with the travel of the process fluid and
thereby increases the efficiency of compressors which use vaned
diffusers relative to compressors using vaneless diffusers. On the
other hand, centrifugal compressor stages employing vaned diffusers
106 are also known for their reduced operating range as compared to
their vaneless counterparts.
[0008] The operating range of a centrifugal compressor 100
including a vaned diffuser 106 is determined based, at least in
part, on the shape of the diffuser blades 110 which are employed.
The shape of a diffuser blade (or more generally any airfoil) can
be expressed by its camber line, (i.e., a line drawn halfway
between the upper surface of the diffuser blade and the lower
surface of the diffuser blade), and the thickness distribution
along the camber line. Two previously used diffuser blade shapes
are shown in FIGS. 2A and 2B. Starting with FIG. 2A, a diffuser
blade 200 having a straight camber line 202, i.e., a camber line
with no change in slope, drawn as a dotted line between the upper
diffuser blade surface 204 and the lower diffuser blade surface 206
is illustrated.
[0009] Employing diffuser blades 200 having a straight camber line
in a centrifugal compressor is problematic because, for example,
the leading edge of the diffuser vane with that shape is relatively
highly loaded and the compressor has a relatively low stall
limit.
[0010] FIG. 2B shows an alternative diffuser blade 208 having a
different shape which is referred to as a conformal mapped blade
camber. Shown by dotted line 210, between its upper surface 212 and
lower surface 214, the conformal mapped blade camber line can be
defined, e.g., using coordinates of the camber line of an airfoil
in the rectangular plane (x, y), and polar coordinates (r, .theta.)
in the circular plane, as:
r = r 0 .times. [ ( mx - y ) / ( m 2 + 1 ) ] ##EQU00001## .theta. =
my + x m 2 + 1 ##EQU00001.2## m = Cot .alpha. 3 ##EQU00001.3##
where, r.sub.o is the radius of the diffuser vane leading edge
radial position, and .alpha..sub.3 is the angle of absolute
velocity at diffuser vane leading edge.
[0011] This diffuser blade shape also results in certain drawbacks
when employed as part of a diffuser in a centrifugal compressor.
For example, employing diffuser blades 208 having a conformal
mapped camber line in a centrifugal compressor is problematic
because the trailing edge of the diffuser vane with that shape is
relatively highly loaded and the compressor has a relatively low
choke limit.
[0012] Accordingly, it would be desirable to design and provide
diffuser blades having shapes which improve the performance of
centrifugal compressors and which address the aforementioned
drawbacks of existing diffuser blade shapes.
BRIEF SUMMARY OF THE INVENTION
[0013] Various devices, systems and methods according to exemplary
embodiments of the present invention provide diffusers, e.g., as
part of a turbo machine, with diffuser vanes having S-shaped camber
lines. Such S-shaped camber lines are defined by functions having
an inflection point along their length, or a portion of such
curves. Using diffuser vanes having such shapes results in, among
other things, an operational characteristic wherein a portion of
the diffuser vanes disposed near a leading edge is substantially
unloaded when operating at design conditions and wherein the load
gradually increases to a maximum loading value towards a middle
portion of the diffuser vanes.
[0014] According to an exemplary embodiment, a turbo machine
includes a rotor assembly having at least one impeller, a bearing
connected to, and for rotatably supporting, the rotor assembly, and
a stator including at least one diffuser connected to an exit
portion of the impeller, wherein the at least one diffuser includes
a plurality of diffuser vanes, at least one of the plurality of
diffuser vanes having a camber line defined by a function having an
inflection point.
[0015] According to another exemplary embodiment, a method of
manufacturing a turbo machine includes providing a rotor assembly
including at least one impeller, connecting the rotor assembly to a
bearing assembly to rotatably support the rotor assembly, and
providing a stator assembly including at least one diffuser
connected to an exit portion of the impeller, wherein the at least
one diffuser includes a plurality of diffuser vanes, at least one
of the plurality of diffuser vanes having a camber line defined by
a function having an inflection point.
[0016] According to another exemplary embodiment, a diffuser
includes an inner annular wall, an outer annular wall, a plate
portion disposed between the inner annular wall and the outer
annular wall, and a plurality of diffuser vanes disposed on the
plate portion, at least one of the plurality of diffuser vanes
having a camber line defined by a function having an inflection
point.
BRIEF DESCRIPTION OF THE DRAWINGS
[0017] The accompanying drawings illustrate exemplary embodiments,
wherein:
[0018] FIGS. 1A, 1B, 1C, and 1D illustrate background art
associated with diffusers used in centrifugal compressors;
[0019] FIGS. 2A and 2B show conventional straight camber line and
conformal mapped camber line diffuser blades, respectively;
[0020] FIG. 3 depicts an exemplary centrifugal compressor in which
diffusers manufactured according to exemplary embodiments of the
present invention can be employed;
[0021] FIG. 4 illustrates airfoil concepts according to exemplary
embodiments of the present invention;
[0022] FIG. 5 describes beta angles associated with diffuser
implementations according to exemplary embodiments of the present
invention;
[0023] FIG. 6 depicts a diffuser blade profile having an S-shaped
camber line according to an exemplary embodiment of the present
invention;
[0024] FIG. 7 is a graph depicting an S-shaped camber line
according to an exemplary embodiment of the present invention
relative to other camber lines;
[0025] FIG. 8 is a graph depicting an S-shaped camber line and its
inflection point according to an exemplary embodiment of the
present invention;
[0026] FIGS. 9, 10 and 11 are plots depicting simulation results
according to exemplary embodiments of the present invention;
[0027] FIG. 12 is a flowchart illustrating a method of
manufacturing a turbo machine according to an exemplary embodiment
of the present invention;
[0028] FIG. 13 shows a diffuser according to an exemplary
embodiment of the present invention; and
[0029] FIG. 14 illustrates usage of Bezier curves to define an
S-shaped camber line according to an exemplary embodiment of the
present invention.
DETAILED DESCRIPTION OF EXEMPLARY EMBODIMENTS OF THE INVENTION
[0030] The following detailed description of the exemplary
embodiments refers to the accompanying drawings. The same reference
numbers in different drawings identify the same or similar
elements. Also, the following detailed description does not limit
the invention. Instead, the scope of the invention is defined by
the appended claims.
[0031] To provide some context for the subsequent discussion
relating to diffuser blades and diffuser blade shapes according to
the exemplary embodiments, FIG. 3 schematically illustrates an
exemplary multistage, centrifugal compressor 300 in which such
diffuser blades may be employed. Therein, the compressor 300
includes a box or housing (stator) 302 within which is mounted a
rotating compressor shaft 304 that is provided with a plurality of
centrifugal rotors or impellers 306. The rotor assembly 308
includes the shaft 304 and rotors 306 and is supported radially and
axially through bearings 310 which are disposed on either side of
the rotor assembly 308.
[0032] The multistage centrifugal compressor 300 operates to take
an input process gas from duct inlet 312, to accelerate the process
gas particles through operation of the rotor assembly 308, and to
subsequently deliver the process gas through various interstage
ducts 314 (which include diffusers and diffuser blades described
below) at an output pressure which is higher than its input
pressure. The process gas may, for example, be any one of
atmospheric air, carbon dioxide, hydrogen sulfide, butane, methane,
ethane, propane, natural gas, or a combination thereof. Between the
impellers 306 and the bearings 310, sealing systems (not shown) are
provided to prevent the process gas from flowing to the bearings
310. The housing 302 is configured so as to cover both the bearings
310 and the sealing systems, so as to prevent the escape of gas
from the centrifugal compressor 300. Those skilled in the art will
appreciate that the centrifugal compressor 300 illustrated in FIG.
3 is purely exemplary and that the diffusers and diffuser blades
described below can be used in other compressors, e.g., in-line,
back-to-back, axial compressors, centrifugal pumps, turbines, turbo
expanders, etc.
[0033] Turning now to the discussion of diffusers and diffuser
blade shapes, a brief discussion of airfoils and airfoil
terminology will assist the reader to better understand the
exemplary embodiments. Looking at FIG. 4, a generic airfoil 400 has
a leading edge (LE) 402 and a trailing edge (TE) 404, the leading
edge 402 being the end of the airfoil which first contacts the
fluid and which thereby separates the fluid into upper and lower
streams, and the trailing edge 404 being the other end of the
airfoil where the fluid streams converge. The chord line 406 is a
straight line between the LE 402 and TE 404, while the mean camber
line 408 (also sometimes called simply "the camber line") is
disposed midway between an upper surface 410 of the airfoil 400 and
a lower surface 412 of the airfoil 400. An airfoil 400 can have a
point of maximum thickness 414 which may be located at a
predetermined distance from the leading edge 402. Varying these
(and other) parameters associated with the airfoil 400 will result
in varying aerodynamic performance.
[0034] FIG. 5 illustrates some additional terminology which is
relevant for the usage of airfoils as diffuser blades 500 in a
diffuser section 502 of a centrifugal compressor 300. Camber lines
can, for example, be plotted as a function of beta angles (or
change in beta angles) across the length of a diffuser blade 500.
For example, the orientation of the diffuser blades 500, as well as
their shape, defines inlet and outlet beta angles relative to the
leading and trailing edges, respectively, of the diffuser blades
500. More specifically, as shown in FIG. 5, the inlet and outlet
beta angles are defined relative to (1) radii 504, 506 associated
with circles or arcs, and representing the position of the leading
edge and the trailing edge, drawn through (from the axis of
rotation of shaft 104) and (2) the projections (tangent to the
blade camber line) 508, 510 associated with the instantaneous
curvature at the point of interest. Although shown in FIG. 5 only
for the inlet and outlet points on the diffuser blade 500, the beta
angles of the metallic diffuser vanes 500 can also be computed for
any point between the leading and trailing edges and are used to
plot the camber lines as a function of the distribution of beta
angles as described below.
[0035] According to exemplary embodiments, the camber lines of
diffuser vanes are "5-shaped" which results in, among other things,
more balanced loading between the leading and trailing edges of the
vane as compared to the earlier described diffuser vane shapes and
associated camber lines. An example of a diffuser vane 600 having
an S-shaped camber line 602 according to an exemplary embodiment is
provided as FIG. 6. Although not easy to see in FIG. 6, the S-shape
of the camber line 602 is more apparent in FIG. 7 which shows the
S-shaped camber line 602 as a function of the beta angle across the
length of the vane 600 from the leading edge (0 on the x-axis) to
the trailing edge (100 on the x-axis). For comparative purposes, a
straight camber line 700 and conformal mapped camber line 702 are
also illustrated on the same plot.
[0036] Although described generally as "S-shaped" camber lines
herein, diffuser blades or vanes according to these exemplary
embodiments have camber lines which are more specifically defined
by, for example, at least third order algebraic equations or
functions. By way of contrast, the conventional diffuser vanes
described above with respect to FIGS. 2A and 2B have camber lines
which are defined linearly or by quadratic equations, i.e., first
and second order equations. Thus camber lines 602 associated with
diffuser blades 600 according to some exemplary embodiments can be
defined by functions of the form:
y=ax.sup.3+bx.sup.2+cx+d
where a, b, c and d are constants. As will be discussed below,
however, camber lines associated with diffuser blades according to
other exemplary embodiments may be described by other types of
functions.
[0037] Another S-shaped camber line 800 associated with a diffuser
blade according to an exemplary embodiment is illustrated in FIG.
8. Therein, the change in beta angle is plotted across the length
of the diffuser blade revealing again the s-shape characteristic of
the camber line. A characteristic of third order equations is that
they possess an inflection point 802, i.e., a point in the function
or graph wherein the curvature (second derivative) changes signs.
By way of contrast, camber line functions associated with
conventional designs do not have inflection points, as shown by the
straight camber line and conformal map camber line which are also
plotted in FIG. 8. It should be noted that the entirety of the
S-shaped curves described herein need not be used in generating
diffuser blades according to exemplary embodiments, i.e., the
curves can be cutoff and still provide the benefits described
herein. For example, the part of the curve shown in FIG. 8 from 0.6
to 1 on the x-axis could be used to shape a diffuser blade
according to an exemplary embodiment. Among other things, this
provides for diffuser shapes having camber lines according to some
exemplary embodiments with .DELTA..beta. values which are greater
than those associated with a straight camber line shape (and also,
therefore, a conformal mapped camber line as seen in FIG. 8). Thus
it will be appreciated by those skilled in the art that the phrase
"diffuser vanes having a camber line defined by a function having
an inflection point" includes diffuser vanes having shapes defined
by a cutoff version of such functions, e.g., including those where
the inflection point defined by the function has been cutoff.
[0038] By employing S-shaped diffuser vanes as described above, the
result is an unloading of the portion of the blade near to the
leading edge at design conditions and a gradual load increase to a
maximum loading towards the blade middle portion. An unloaded
leading edge according to exemplary embodiments will suffer less
flow separation at lower flow rates, thereby increasing the left
operating limit of the compressor. These benefits associated with
exemplary embodiments are shown by various simulation results
described below and illustrated in FIGS. 9-11.
[0039] FIG. 9 illustrates results associated with two simulations
carried out for (1) a vaned diffuser with a straight camber line,
plotted as lines 910, 912 and (2) a vaned diffuser with an S-shaped
profile (based on a Sigmoid function as described below) according
to these exemplary embodiments, shown by lines 900 and 902. The
turbulence model used in the simulation was the Wilcox k-w
turbulence model, with a computational domain consisting of one
impeller blade passage (inducer, one full-length blade and one
splitter blade in case of splitter impeller), and one diffuser
blade passage. The diffuser vanes in this simulation were designed
as low solidity vanes. The interface between the rotating domain
and the non-rotating domain in this simulation was specified as 50%
of the distance between the impeller trailing edge and the diffuser
vane leading edge. Computations associated with this simulation
were carried out with total pressure and total temperature
specified at inlet and mass flow rate specified at outlet. All
external walls were assumed adiabatic and leakage flow through the
impeller seals is assumed negligible and was not modeled. The
impeller upstream was simulated as having a design flow coefficient
of 0.0206 and peripheral Mach number of 0.3.
[0040] The results plotted in FIG. 9 show about a 0.5 point
increase in efficiency at the design point of the centrifugal
compressor and about a 2 point increase in efficiency near the left
hand side of the graph, i.e., at 75% flow. This result tends to
confirm the conclusion mentioned above that exemplary embodiments
increase the stall limit for centrifugal compressors. A fall in the
efficiency on the right hand side of the graph relative to a
centrifugal compressor simulated with diffuser vanes having a
straight camber line is also noted.
[0041] Another simulation, the results of which are plotted in
FIGS. 10 and 11, was conducted relative to centrifugal compressors
employing diffuser blades with conformal mapped camber lines
(functions 1000 and 1100), straight camber lines (functions 1004,
1104), and vaneless diffusers (functions 1006, 1106), with an
exemplary S-shaped camber line result plotted as functions 1002 and
1102. FIG. 10 illustrates the higher overall efficiency of the
exemplary embodiments. More specifically, this comparison shows
that, for example, this exemplary embodiment had an efficiency
improvement of about 1.5 points on the left hand side of the
operating range relative to the centrifugal compressor employing
the straight camber line diffusers, albeit a slightly lower
efficiency than the conformal mapped camber line compressor.
Additionally, on the right hand side of the graph in FIG. 10, it
can be seen that the S-shaped camber according to exemplary
embodiments performed much better in terms of efficiency than the
conformal mapped camber, and only slightly below the straight
camber.
[0042] To summarize, some of the efficiency benefits and advantages
associated with using diffuser vanes or blades having S-shaped
camber lines in centrifugal compressors include: higher efficiency
toward the left (lower) operating range, thereby increasing the
stall limit of the compressor, better or comparable efficiency at
the design point relative to other designs and lower efficiency
towards the choke limit relative to some designs (i.e., except
conformal mapped camber line designs).
[0043] This simulation also showed a higher polytropic head raise
for the S-shaped camber line diffuser according to an exemplary
embodiment relative to the straight camber line diffuser and
vaneless diffuser as shown in FIG. 11. Therein, it can be seen that
a head raise of 6.5% was measured for the S-shaped camber line
diffuser function 1102 according to an exemplary embodiment
relative to a 5.2% head raise for the straight camber line diffuser
function 1104 and 6.2% head raise for the vaneless diffuser. The
conformal mapped diffuser function 1100 shows a just slightly
better head raise than that of the exemplary embodiment 1102.
[0044] Exemplary embodiments also include a method of manufacturing
a turbo machine which can be expressed a shown in the flowchart of
FIG. 12. Therein, a rotor assembly is provided including at least
one impeller 1200. The rotor assembly is connected 1202 to a
bearing assembly which rotatably supports the rotor assembly. A
stator assembly is provided 1204 including at least one diffuser
connected to an exit portion of the impeller, wherein the at least
one diffuser includes a plurality of diffuser vanes, at least one
of the plurality of diffuser vanes having a camber line defined by
a function having an inflection point.
[0045] In addition to manufacturing centrifugal compressors with
diffuser vanes having S-shaped camber lines according to these
various exemplary embodiments, it may further be desirable to
retrofit existing centrifugal compressors having vaneless diffusers
or diffusers with differently shaped diffuser vanes, with diffusers
having S-shaped camber lines according to the exemplary embodiments
to, for example, increase efficiency relative to vaneless diffusers
or reduce the loss of range associated with existing vaned
diffusers. Thus exemplary embodiments further contemplate the
manufacture of diffusers themselves for retrofitting and/or repair
of existing compressors. FIG. 13 illustrates an exemplary diffuser
1300 including an inner annular wall 1302, an outer annular wall
1304, a plate portion 1306 disposed between the inner annular wall
1302 and the outer annular wall 1304, and a plurality of diffuser
vanes 1308 disposed on the plate portion 1306. One or more of the
diffuser vanes or blades 1308 have an S-shaped camber line, i.e.,
defined by a function having an inflection point. The diffuser 1300
can be a high solidity airfoil diffuser or a low solidity airfoil
diffuser. According to some exemplary embodiments, the S-shaped
diffuser vanes discussed herein can be employed with diffusers 1300
which have more than 10 vanes 1308.
[0046] As mentioned above, third order algebraic equations can be
used to define camber lines according to some exemplary
embodiments. However other types of equations, e.g., exponential
equations, can also be used to define camber lines according to
exemplary embodiments. For example, Sigmoid functions or Gompertz
functions can also be used to define camber lines according to
exemplary embodiments. Sigmoid functions, also known as logistic
functions, can be expressed as:
Y = 1 1 + - x ##EQU00002##
while Gompertz functions take the form of:
y=ae.sup.[-be.sup.(-cx).sup.]
Like the above described third order algebraic equations, these
exponential equations also generate functions which have inflection
points.
[0047] Additionally, higher order polynomial functions, e.g.,
fourth order or higher, can also be used to obtain the same
s-shape. Moreover, according to other exemplary embodiments, more
complicated shapes (with multiple inflection points) can be custom
designed for a particular application. One way to define such
generalized curves is through Bezier Curves. A Bezier curve forming
the s-shape of camber lines according to exemplary embodiments can
be described as shown in FIG. 14. Therein, the shape of the camber
line is defined by the values of co-ordinates of the control points
1401 and 1402 having coordinates (X1, Y1) and (X2, Y2),
respectively. A greater number of control points can be used to
define higher order curves having multiple inflection points.
[0048] Devices, systems and methods according to exemplary
embodiments provide diffusers, e.g., as part of a turbo machine
300, with diffuser vanes having S-shaped camber lines 408. Such
S-shaped camber lines 408 are defined by functions having an
inflection point. Using diffuser vanes 400 having such shapes
results in, among other things, an operation characteristic wherein
a portion of the diffuser vanes 400 disposed near a leading edge
402 is substantially unloaded when operating at design conditions
and wherein the load gradually increases to a maximum loading value
towards a middle portion of the diffuser vanes.
[0049] The above-described exemplary embodiments are intended to be
illustrative in all respects, rather than restrictive, of the
present invention. Thus the present invention is capable of many
variations in detailed implementation that can be derived from the
description contained herein by a person skilled in the art. All
such variations and modifications are considered to be within the
scope and spirit of the present invention as defined by the
following claims. No element, act, or instruction used in the
description of the present application should be construed as
critical or essential to the invention unless explicitly described
as such. Also, as used herein, the article "a" is intended to
include one or more items.
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