RADIAL DIFFUSER VANE FOR CENTRIFUGAL COMPRESSORS
The present invention relates generally to compressors and, more specifically, to
diffuser vanes for centrifugal compressors.
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".
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.
More specifically, as shown in the exemplary side-sectional view of Figure 1(a) 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, Figure 1(b) 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.
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 Figure 1(b)) 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 Figure 1(c).
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 Figure 1(d).
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.
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 Figures 2(a) and 2(b). Starting with Figure 2(a), 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.
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.
Figure 2(b) 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, Q) in the circular plane, as:
my + x
Q =
2
m + 1
m = Cot
where,
r0 is the radius of the diffuser vane leading edge radial position, and
a is the angle of absolute velocity at diffuser vane leading edge.
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.
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.
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.
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.
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.
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.
The accompanying drawings illustrate exemplary embodiments, wherein:
Figures 1(a)- 1(d) illustrate background art associated with diffusers used in
centrifugal compressors;
Figures 2(a) and 2(b) show conventional straight camber line and conformal mapped
camber line diffuser blades, respectively;
Figure 3 depicts an exemplary centrifugal compressor in which diffusers
manufactured according to exemplary embodiments can be employed;
Figure 4 illustrates airfoil concepts;
Figure 5 describes beta angles associated with diffuser implementations according to
exemplary embodiments;
Figure 6 depicts a diffuser blade profile having an S-shaped camber line according to
an exemplary embodiment;
Figure 7 is a graph depicting an S-shaped camber line according to an exemplary
embodiment relative to other camber lines;
Figure 8 is a graph depicting an S-shaped camber line and its inflection point
according to an exemplary embodiment;
Figures 9-1 1 are plots depicting simulation results according to exemplary
embodiments;
Figure 12 is a flowchart illustrating a method of manufacturing a turbo machine
according to an exemplary embodiment;
Figure 13 shows a diffuser according to an exemplary embodiment, and
Figure 14 illustrates usage of Bezier curves to define an S-shaped camber line
according to an exemplary embodiment.
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.
To provide some context for the subsequent discussion relating to diffuser blades and
diffuser blade shapes according to the exemplary embodiments, Figure 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.
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 Figure 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.
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 Figure 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.
Figure 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 Figure 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 Figure 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.
According to exemplary embodiments, the camber lines of diffuser vanes are "Sshaped"
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
Figure 6. Although not easy to see in Figure 6, the S-shape of the camber line 602 is
more apparent in Figure 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 xaxis)
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.
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 Figures 2(a) and 2(b) 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= ax3 + bx2 + 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.
Another S-shaped camber line 800 associated with a diffuser blade according to an
exemplary embodiment is illustrated in Figure 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 Figure 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 Figure 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 Db values which are greater
than those associated with a straight camber line shape (and also, therefore, a
conformal mapped camber line as seen in Figure 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.
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 Figures 9-1 1.
Figure 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
of0.3.
The results plotted in Figure 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.
Another simulation, the results of which are plotted in Figures 10 and 11, was
conducted relative to centrifugal compressors employing diffuser blades with
conformal mapped camber lines (functions 1000 and 100), 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. Figure 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 Figure 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.
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).
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 Figure 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.
Exemplary embodiments also include a method of manufacturing a turbo machine
which can be expressed a shown in the flowchart of Figure 12. Therein, at step 1200,
a rotor assembly is provided including at least one impeller. The rotor assembly is
connected, at step 1202, to a bearing assembly which rotatably supports the rotor
assembly. A stator assembly is provided at step 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.
In addition to manufacturing centrifugal compressors with diffuser vanes having Sshaped
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 Sshaped
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. Figure 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.
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:
\ +e
while Gompertz functions take the form of:
y = aέ
Like the above described third order algebraic equations, these exponential equations
also generate functions which have inflection points.
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 Figure 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 (XI, Yl) and (X2, Y2), respectively.
A greater number of control points can be used to define higher order curves having
multiple inflection points.
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.

CLAIMS:
1. A turbo machine comprising:
a rotor assembly including 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 said
impeller,
wherein said at least one diffuser includes:
a plurality of diffuser vanes, at least one of said plurality of diffuser vanes
having a camber line defined by a function having an inflection point.
2. The turbo machine of claim 1, wherein said function is y= ax3 + bx2 + cx +d,
where a, b, c and d are constants.
3. The turbo machine of any preceding claim, wherein said function is one of a
higher order polynomial function, a Sigmoid function, a Gompertz function and a
Bezier curve.
4. The turbo machine of any preceding claim, wherein said function is an
exponential function.
5. The turbo machine of any preceding claim, wherein a portion of the at least
one of said 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 said plurality of
diffuser vanes.
6. The turbo machine of any preceding claim, wherein each of said plurality of
diffuser vanes is attached to one of a hub or shroud.
7. The turbo machine of any preceding claim, wherein said function is a Bezier
Curve.
8. A method of manufacturing a turbo machine comprising:
providing a rotor assembly including at least one impeller;
connecting said rotor assembly to a bearing assembly for rotatably supporting
the rotor assembly; and
providing a stator assembly including at least one diffuser connected to an exit
portion of said impeller,
wherein said at least one diffuser includes:
a plurality of diffuser vanes, at least one of said plurality of diffuser vanes
having a camber line defined by a function having an inflection point.
3 2 9. The method of claim 8, wherein said function is y= ax + bx + cx +d, where a,
b, c and d are constants.
10. The method of claim 8 or claim 9, wherein said function is one of a higher
order polynomial function, a Sigmoid function, a Gompertz function and a Bezier
curve.
1 . The method of any of claims 8 to 10, wherein said function is an exponential
function.
12. The method of any of claims 8 to 11, wherein a portion of the at least one of
said 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 said plurality of
diffuser vanes.
13. The method of any of claims 8 to 12, further comprising:
attaching each of said plurality of diffuser vanes to one of a hub or shroud.
14. The method of any of claims 8 to 13, wherein said function is a Bezier curve.
15. A diffuser comprising:
an inner annular wall;
an outer annular wall;
a plate portion disposed between said inner annular wall and said outer annular
wall; and
a plurality of diffuser vanes disposed on said plate portion, at least one of said
plurality of diffuser vanes having a camber line defined by a function having an
inflection point.
16. The diffuser of claim 15, wherein said function is y= ax + bx + cx +d, where
a, b, c and d are constants.
17. The diffuser of claim 15 or claim 16, wherein said function is one of a higher
order polynomial function, a Sigmoid function, a Gompertz function and a Bezier
curve.
18. The diffuser of any of claims 15 to 17, wherein said function is an exponential
function.
19. The diffuser of any of claims 15 to 18, wherein a portion of the at least one of
said 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 said plurality of
diffuser vanes.
20. The diffuser of any of claims 15 to 19, wherein said function is a Bezier curve.