U.S. patent application number 13/107374 was filed with the patent office on 2012-11-15 for rotor with asymmetric blade spacing.
This patent application is currently assigned to HAMILTON SUNDSTRAND CORPORATION. Invention is credited to Loc Quang Duong, Benjamin E. Fishler, Jay M. Francisco, Xiaolan Hu, Anthony C. Jones, James C. Napier, Nagamany Thayalakhandan, Gao Yang, Bo Zheng.
Application Number | 20120288373 13/107374 |
Document ID | / |
Family ID | 47076517 |
Filed Date | 2012-11-15 |
United States Patent
Application |
20120288373 |
Kind Code |
A1 |
Duong; Loc Quang ; et
al. |
November 15, 2012 |
ROTOR WITH ASYMMETRIC BLADE SPACING
Abstract
A turbine apparatus comprises a rotor with a hub section defined
about a rotational axis and a plurality of blades attached to the
hub section. The plurality of blades comprises a first group having
a first angular spacing in a first circumferential sector of the
rotor, and a second group having a second angular spacing in a
second circumferential sector of the rotor. The first angular
spacing is different from the second angular spacing, and the rotor
blades are asymmetric about the rotational axis.
Inventors: |
Duong; Loc Quang; (San
Diego, CA) ; Hu; Xiaolan; (San Diego, CA) ;
Thayalakhandan; Nagamany; (San Diego, CA) ; Zheng;
Bo; (San Diego, CA) ; Fishler; Benjamin E.;
(San Diego, CA) ; Yang; Gao; (San Diego, CA)
; Jones; Anthony C.; (San Diego, CA) ; Napier;
James C.; (San Diego, CA) ; Francisco; Jay M.;
(Chula Vista, CA) |
Assignee: |
HAMILTON SUNDSTRAND
CORPORATION
Windsor Locks
CT
|
Family ID: |
47076517 |
Appl. No.: |
13/107374 |
Filed: |
May 13, 2011 |
Current U.S.
Class: |
416/185 |
Current CPC
Class: |
F04D 29/284 20130101;
Y02T 50/672 20130101; F01D 5/141 20130101; F04D 29/666 20130101;
F04D 29/30 20130101; F01D 5/16 20130101; Y02T 50/673 20130101; Y02T
50/60 20130101; F01D 5/048 20130101; F05D 2250/30 20130101; F05D
2260/961 20130101 |
Class at
Publication: |
416/185 |
International
Class: |
F01D 5/22 20060101
F01D005/22 |
Claims
1. A turbine apparatus comprising: a rotor having a hub defined
about a rotational axis, the hub having first and second
circumferential sectors; and a plurality of blades attached to the
hub and extending radially therefrom, the plurality of blades
comprising a first group of blades having a first angular spacing
in the first sector and a second group of blades having a second
angular spacing in the second sector; wherein the first angular
spacing is different from the second angular spacing, and the rotor
blades are asymmetric about the rotational axis.
2. The turbine apparatus of claim 1, wherein the plurality of
blades comprises an odd number N of blades, the first group of
blades comprising (N-1)/2 of the N blades and the second group of
blades comprising (N+1)/2 of the N blades.
3. The turbine apparatus of claim 2, wherein the first angular
spacing is approximately 360.degree./(N-1) and the second angular
spacing is approximately 360.degree./(N+1).
4. The turbine apparatus of claim 1, wherein the plurality of
blades comprises an even number N of blades, the first group of
blades comprising N/2-1 of the N blades and the second group of
blades comprising N/2+1 of the N blades.
5. The turbine apparatus of claim 4, wherein the first angular
spacing is approximately 180.degree./(N/2-1) and the second angular
spacing is approximately 180.degree./(N/2+1).
6. The turbine apparatus of claim 1, further comprising a plurality
of splitters attached to the hub section and disposed between the
plurality of blades.
7. The turbine apparatus of claim 6, wherein the plurality of
splitters comprises a first group of splitters having the first
angular spacing in the first circumferential section and a second
set of splitters having the second angular spacing in the second
circumferential section.
8. The turbine apparatus of claim 1, wherein the rotor comprises an
impeller and further comprising a compressor rotor rotationally
coupled to the impeller, the compressor rotor comprising: a
compressor hub defined about the rotational axis, the compressor
hub having a first and second circumferential sectors; a second
plurality of blades attached to the second hub and extending
radially therefrom, the second plurality of blades comprising a
first group of blades having the first angular spacing in the first
sector of the second hub and a second group of blades having the
second angular spacing in the second sector of the second hub.
9. An auxiliary power unit comprising the turbine apparatus of
claim 8, and further comprising a curvic coupling for rotationally
coupling the second rotor to the first rotor.
10. An auxiliary power unit comprising the turbine apparatus of
claim 8, wherein the first rotor is clocked with respect to the
second rotor such that the first plurality of blades is out of
phase with respect to the second plurality of blades.
11. An impeller comprising: a hub section defined about a
rotational axis, the hub section comprising first and second
circumferential sectors; a first set of blades extending radially
from the first sector of the hub section, the first set of blades
having a first angular spacing; and a second set of blades
extending radially from the second sector of the hub section, the
second set of blades having a second angular spacing; wherein the
first angular spacing is different from the second angular spacing,
such that the first and second sets of blades are asymmetric about
the rotational axis.
12. The impeller of claim 11, wherein the first set of blades
comprises an odd number of blades N1 and the first angular spacing
is about 180.degree./N1.
13. The impeller of claim 12, wherein the second set of blades
comprises an even number of blades N1+1 and the second angular
spacing is about 180.degree./(N1+1).
14. The impeller of claim 12, wherein the second set of blades
comprises an odd number of blades N1+2 and the second angular
spacing is about 180.degree./(N1+2).
15. An auxiliary power unit comprising the impeller of claim
11.
16. The auxiliary power unit of claim 15, further comprising a
compressor rotor rotationally coupled to the impeller, the
compressor rotor comprising: a compressor hub defined about the
rotational axis, the compressor hub comprising first and second
circumferential sectors; a third set of blades extending radially
from the first sector of the compressor hub, the third set of
blades having the first angular spacing; a fourth set of blades
extending radially from the second sector of the compressor hub,
the fourth set of blades having the second angular spacing.
17. A turbomachine comprising: a load impeller circumferentially
divided into first and second sectors, the first sector of the load
impeller having a set of blades with a first angular spacing and
the second sector of the load impeller having a set of blades with
a second angular spacing; a power head impeller circumferentially
divided into first and second sectors, the first sector of the
power head impeller having a set of blades with the first angular
spacing and the second sector of the power head impeller having a
set of blades with the second angular spacing; and a rotational
coupling between the load impeller and the power head impeller, the
coupling defining a rotational axis; wherein the first angular
spacing and the second angular spacing are different, such that the
load impeller and the power head impeller are asymmetric about the
rotational axis.
18. The turbomachine of claim 17, wherein the load impeller is
clocked about the rotational axis with respect to the power head
impeller, such that the load impeller is out of rotational phase
with respect to the power head impeller.
19. The turbomachine of claim 17, wherein the load impeller and the
power head impeller each comprise an equal, odd number of blades N,
and wherein the first angular spacing is about 360.degree./(N-1)
and the second angular spacing is about 360.degree./(N+1).
20. The turbomachine of claim 17, wherein the load impeller and the
power head impeller each comprise an equal, even number of blades
N, and wherein the first angular spacing is about
180.degree./(N/2-1) and the second angular spacing is about
180.degree./(N/2+1).
Description
BACKGROUND
[0001] This invention relates generally to turbine and compressor
systems, and specifically to rotor noise reduction. In particular,
the invention concerns noise reduction for compressor rotors,
impellers and other turbomachinery components, including compressor
and impeller rotors for auxiliary power units or APUs.
[0002] Turbine engines are utilized in a wide range of applications
including electrical power generation, aviation, and industrial
heating and cooling. The turbine core is built around a compressor
section in flow series with a combustor and turbine section, with
an upstream inlet and downstream exhaust. The compressor section
compresses air from the inlet, which is mixed which fuel in the
combustor and ignited to generate hot combustion gas. The turbine
section extracts energy from the expanding combustion gas, which is
then discharged through the exhaust. Some of the energy is used to
drive the compressor section, and the excess is delivered in the
form of rotational motion or propulsive thrust, or a combination
thereof.
[0003] The compressor and turbine sections each include a number of
rotor blade and stator vane airfoils, which are arranged in a
series of alternating blade and vane stages. In large-scale
engines, two, three or more sections may be coaxially arranged into
high, low and intermediate pressure spools, which can rotate at
different speeds, and in different directions.
[0004] In ground-based industrial gas turbines, the output or power
shaft is coupled to an external load such as an electrical
generator, or to a pump, blower or other rotary apparatus. In
aviation applications, the low-spool is coupled to a propeller
(turboprop engines) or a propulsion fan (turbofan engines), or to a
helicopter rotor or rotary wing (turboshaft engines). Depending on
configuration, the coupling may include a gearbox for independent
speed control of the fan or output shaft, with respect to the low
spool.
[0005] Auxiliary power units incorporate smaller-scale (typically
one-spool) gas turbine engines, and are used to generate electrical
power and run or various auxiliary and accessory systems. In
aviation applications, APUs generate electrical power and supply
cabin air while the aircraft is on the ground, and provide
compressed air to the bleed system for main engine startup.
Depending on configuration, APUs can also be employed as in-flight
power sources for air conditioning and other environmental control
systems, and provide independent or emergency backup power for
hydraulics, pneumatics, avionics and flight control.
[0006] In each of these applications, the compressor and turbine
rotors operate at high speeds. As portions of the blades reach
transonic and supersonic velocities, they generate shock waves at
the blade passing frequency (BPF), the "pure tone" frequency at
which individual blades pass a given fixed point in space.
[0007] As a result, gas turbine engines are complex noise sources,
and the compressor rotor is a principal noise source. In APUs and
other impeller-type rotor applications, the noise is dominated by a
discrete tone associated mainly with the BPF, which exceeds the
broadband noise portion of the acoustic spectrum. The noise
intensity is also a function of aero-acoustic-mechanical
interactions between the rotor blades and the working fluid, with
multiple tones occurring at harmonics of the engine shaft frequency
or engine order. Acoustic energy also shifts and redistributes away
from the BPF as the shock fronts propagate away from the rotor and
into the far field, resulting in a multi-tone noise spectrum with a
characteristic "buzz-saw" like sound quality.
SUMMARY
[0008] A turbine apparatus comprises a rotor with a hub section and
a plurality of blades. The hub section is defined about a
rotational axis, and is divided into first and second
circumferential sectors. The blades are attached to the hub
section, extending radially outward.
[0009] Blades in the first sector have a first angular spacing, and
blades in the second sector have a second angular spacing. The
first angular spacing is different from the second angular spacing,
so that the blades are asymmetric about the rotational axis of the
rotor.
BRIEF DESCRIPTION OF THE DRAWINGS
[0010] FIG. 1 is a cross-sectional view of a turbomachine with
asymmetric rotor blade spacing.
[0011] FIG. 2A is a perspective view of a rotor with asymmetric
blade spacing, in an even blade number embodiment.
[0012] FIG. 2B is a perspective view of a rotor with asymmetric
blade spacing, in an odd blade number embodiment.
[0013] FIG. 3 is a frequency spectrum plot for a turbomachine
rotor.
[0014] FIG. 4A is a velocity field contour plot for a rotor with
symmetric blade spacing.
[0015] FIG. 4B is a velocity field contour plot for a rotor with
asymmetric blade spacing.
DETAILED DESCRIPTION
[0016] FIG. 1 is a cross-sectional view of turbomachine 10 with
asymmetric rotor blade spacing. In this particular embodiment,
turbomachine 10 comprises an auxiliary power unit with inlet plenum
12, curvic coupling or shaft 14, load impeller 16 and power head
impeller 18. Load impeller 16 and power head impeller 18 co-rotate
about turbine axis A, coupled by curvic coupling 14. Load impeller
16 and power head impeller 18 have asymmetric blade spacing to
reduce pressure pulsations and vibrations, increasing service life
and lowering the environmental noise profile of turbomachine
10.
[0017] Inlet plenum 12 divides into load inlet 20 for load impeller
16 (on the left in FIG. 1) and power head inlet 22 for power head
impeller 18 (on the right, facing load impeller 16). Air (or
another compressible fluid) is drawn through inlet 20 to load
impeller 16, which compresses the fluid for a bleed air system or
pneumatic reservoir, or for another compressed fluid supply.
[0018] Inlet 22 provides air to power head impeller 18, which
compresses the air for the combustor section of turbomachine 10. A
turbine rotor extracts rotational energy from the expanding
combustion gas, driving power head impeller 18 and load impeller 16
via shaft 14. Depending on embodiment, shaft 14 is also coupled to
a gearbox, generator or other accessory device.
[0019] Impellers 16 and 18 rotate at high speed, generating shock
waves at the blade passing frequency. In order to reduce vibrations
and lower the characteristic buzz saw noise output profile, rotors
16 and 18 have asymmetric blade spacing. This reduces acoustic
energy at the BPF, shifting energy to other engine orders and
frequencies.
[0020] In dual-rotor embodiments, load impeller 16 and power head
impeller 18 have the same number of blades, and load impeller 16 is
clocked or rotated on curvic coupling 14 with respect to power head
impeller 18. As a result, the load impeller blades rotate out of
phase with the power head blades, further reducing noise and
vibration effects as described below.
[0021] FIG. 2A is a perspective view of rotor 30 for a
turbomachine, with asymmetric blade spacing. In this particular
embodiment, rotor 30 comprises a load impeller or power head
impeller for an auxiliary power unit. Alternatively, rotor 30
comprises an impeller, compressor rotor or a turbine rotor for an
APU, turbofan, turboprop or turboshaft engine, or another bladed
turbomachine component such as a rotor for a pump, blower or
turbine.
[0022] Rotor 30 comprises frustoconical hub section 32 with
alternating main (long) blades 34 and splitter (short) blades 36.
Alternatively, rotor 30 is referred to as a drum or rotor disk (or
disc), and hub section 32 may have a generally conical, cylindrical
or barrel shape.
[0023] In impeller and compressor embodiments, rotor 30 is
typically formed of a strong, lightweight metal such as titanium,
or a similar alloy. In turbine embodiments, rotor 30 is formed of
high-temperature materials such as nickel, cobalt and iron-based
alloys or superalloys. Alternatively, rotor 30 is formed from a
range of other materials including aluminum, brass and other
metals, or from graphite, polymers and composite materials.
[0024] Depending on embodiment, blades 34 and splitters 36 (if
present) may be integrally formed with hub section 32, for example
by molding or by machining a single casting or forging.
Alternatively, blades 34 and splitters 36 are separately formed,
and attached to hub section 32 by welding, or using a mechanical
attachment at the root.
[0025] As shown in FIG. 2A, rotor 30 comprises an even number of
main blades 34 and splitters 36, for example sixteen. Main blades
34 are circumferentially spaced around rotor 30, extending radially
from hub section 32 and axially along rotational axis A. Splitters
36 are interspersed between main blades 34.
[0026] Main blades 34 are divided into first 180.degree. sector 38A
comprising seven blades 34 with first inter-blade spacing
S1.apprxeq.25.7.degree., and second 180.degree. sector 38B
comprising nine blades 34 with second inter-blade spacing
S2.apprxeq.20.0.degree.. First blade spacing S1 is thus different
from second blade spacing S2, in order to reduce vibrations and
lower the buzz-saw noise profile by shifting acoustic energy out of
the blade passing frequency.
[0027] Blade spacing is an angular measurement, extending
circumferentially about axis A between the centers or middles of
adjacent main blades 34, across splitters 36. In general, the
angular separation remains constant, while the actual separation
distance between blades 34 varies in the radial direction (that is,
away from hub section 32, perpendicular to the rotational axis).
Alternatively, angular spacing S1 and S2 differ primarily in the
transonic and supersonic regions of blades 34, where the shock
waves form. In these embodiments, angular spacing S1 and S2 are
defined at a particular span height, for example 90% span height,
or at the blade tip (100% span height).
[0028] In these embodiments, rotor 30 and hub 32 are divided into
two equal circumferential sectors 38A and 38B, with different
numbers of blades N1 and N2. Each sector occupies half the rotor
circle (that is, 180.degree. in circumferential angle),
corresponding to blade spacing S1=180.degree./N1 and
S2=180.degree./N2, respectively.
[0029] For even numbers of blades N, first sector 38A comprises
N1=N/2-1 or fewer blades 34 (and splitters 36), and second sector
38B comprises N2=N/2+1 or more blades 34 (and splitters 36). The
angular spacing is defined for each of the adjacent blade pairs in
the corresponding groups of blades. Blades at the periphery of each
sector will have a larger spacing on one side (e.g., toward sector
38A), and a smaller blade spacing on the other side (e.g., toward
sector 38B).
[0030] In these even-bladed embodiments, the numbers of blades N1
and N2 in sectors 38A and 38B differ by an even number. In the
nominal or first-order embodiment, therefore, N1=N/2-1 and
N2=N/2+1, with a blade difference of N2-N1=2. In this embodiment,
the blade spacing is:
S 1 ( even ) = 180 .degree. N / 2 - 1 , and [ 1 ] S 2 ( even ) =
180 .degree. N / 2 + 1 . [ 2 ] ##EQU00001##
[0031] In other (higher-order shift) embodiments, the blade numbers
may differ by four, six or more, and the blade spacing varies
accordingly. It is also possible to divide even numbers of blades
and splitters into two equal sets of N1=N2=N/2 blades each, and
define unequal circumferential sectors of different angular sizes.
In these embodiments, one set of blades occupies more than
180.degree. of the rotor circumference and the other set of blades
occupies less than 180.degree., and the blade spacing varies
accordingly.
[0032] Splitters 36 are also divided into groups 38A and 38B.
Typically, the spacing between adjacent blades 34 and splitters 36
is half the inter-blade spacing, so the inter-splitter spacing in
each sector is substantially equal to inter-blade spacing S1 and
S2, respectively. Alternatively, splitters 36 are shifted with
respect to blades 34, and the inter-blade and inter-splitter
spacing vary.
[0033] Asymmetric, non-uniform blade spacing goes against the
general teachings and common-sense wisdom in the art, which is that
blades and splitters should be symmetrically arranged to reduce
imbalance. In general, balance is maintained by machining or
milling hub section 32 to compensate for mass redistribution due to
different blade spacing S1 and S2. Material may either be added or
removed, for example on a balance land or balance rim, or along the
impeller bore or the back-face of frustoconical portion hub section
32. Alternatively, balance is maintained by drilling or shaping
holes in rotor 30, by adding or adjusting balance weights, or via
intentional run-out or offset or altering the curvic pitch
diameter.
[0034] While the angular spacing between blades varies, however,
blades 34 may be characterized by a substantially identical
geometric profile. In particular, blades 34 of FIG. 2A all have
substantially the same mass and stiffness matrix, yielding
substantially the same eigenvalues, natural vibration frequencies
and corresponding mode shapes. This contrasts with blade mistuning
techniques, in which individual blades have different geometric
profiles, different mass and stiffness matrices, and different
eigenvalues and natural frequencies.
[0035] FIG. 2B is a perspective view of alternate rotor 30 for a
turbomachine, with asymmetric blade spacing. Rotor 30 comprises hub
section 32, main blades 34 and splitters 36.
[0036] For odd numbers of blades N, as shown in FIG. 2B, first
sector 38A comprises (N-1)/2 or fewer blades 34 (and splitters 36),
and second sector 38B comprises (N+1)/2 or more blades 34 (and
splitters 36). In this case, the difference in blade number is odd.
For the nominal or first-order case N1=(N-1)/2 and N2=(N1+1)/2
(that is, N2-N1=1), the corresponding blade spacing is:
S 1 ( odd ) = 360 .degree. N - 1 , and [ 3 ] S 2 ( odd ) = 360
.degree. N + 1 . [ 4 ] ##EQU00002##
[0037] In one particular embodiment, rotor 30 comprises fifteen
main blades 34 and fifteen splitters 36, as shown in FIG. 2B. First
sector 38A comprises seven blades 34 with angular spacing
S1.apprxeq.25.7.degree., and second sector 38B comprises eight
blades 34 with angular spacing S2.apprxeq.25.0.degree.. First blade
spacing S1 is thus larger than second blade spacing S2, and the
blades are asymmetric about the rotor axis.
[0038] Asymmetric blade spacing reduces the level of rotor and
blade vibrations due to aero-mechanical coupling, and lowers the
sound intensity and environmental impact of the acoustic field
generated. In particular, asymmetric blade spacing reduces impeller
tone noise at the BPF by reducing the Lighthill turbulence stress
tensor, as compared to a rotor with a symmetric distribution of the
same blade count.
[0039] Asymmetric blade spacing also reduces the amplitude of
aerodynamic pressure oscillations experienced by the diffuser
vanes, maintaining vane integrity by reducing resonance effects at
the natural vibration frequencies. In particular, asymmetric blade
spacing reduces the amplitude of pressure excitations though
harmonic effects, decreasing the likelihood of high cycle fatigue
(HCF) damage or failure, which can occur when cyclic stresses
exceed the endurance limits of the vane material. Vibration effects
are further reduced by out of phase synchronization of multiple
rotors, as further described below.
[0040] FIG. 3 is a frequency spectrum plot for a turbine rotor.
Frequency is given along the horizontal axis, with magnitude along
the vertical, both in arbitrary units. Frequency peaks are labeled
by engine order (EO).
[0041] Sources of rotor vibration can be traced to two main
categories or types: mechanical and aerodynamic. Mechanical causes
are related to dynamic characteristics of the rotor, and are
influenced by a number of factors including unbalance, bearing
support misalignment, shaft run out, and damaged or rubbing parts.
Aerodynamic causes are related to pressure pulsations at discrete
multiples of the rotor rotational frequency and number of blades
(i.e., multiples of the BPF). Aerodynamic sources originate in
disturbances generated by blades 34, which are transmitted to rotor
30.
[0042] In the rotor frequency spectrum, the first engine order
(1EO) represents the effect of rotor imbalance. The second, third,
fourth, sixth, eighth and other harmonics are due to mechanical
factors, as described above. A rotor or impeller with sixteen main
blades, for example, will exhibit dynamic effects characterized by
the second (2EO), fourth (4EO) and eighth engine orders (8EO), due
to the common factors of two, four and eight. A rotor or impeller
with fifteen main blades will exhibit dynamic effects characterized
by the third (3EO) and fifth engine orders (5EO), due to the common
factors of three and five.
[0043] The acoustic field is described by an inhomogeneous wave
equation, which can be derived from the Navier-Stokes equations.
Using Einstein notation:
.differential. 2 .rho. .differential. t 2 - c 0 2 .gradient. 2
.rho. = .differential. 2 T ij .differential. x i .differential. x j
, [ 5 ] ##EQU00003##
where .rho. is the air or fluid density, c.sub.0 is the ambient
sound speed and T.sub.ij is the Lighthill turbulence stress tensor.
Sound (noise) generation is attributed to the right hand side of
this equation.
[0044] The Lighthill stress tensor is further defined by:
T.sub.ij=.rho.v.sub.iv.sub.j-.sigma..sub.ij+(p-c.sub.0.sup.2p).delta..su-
b.ij, [6]
with velocity components v.sub.i and v.sub.j, viscous stress
contribution .sigma..sub.ij and pressure p. The term
.rho.v.sub.iv.sub.j is the Reynolds stress tensor, representing
unsteady convention of flow. Viscous stress tensor .sigma..sub.ij
represents the sound generated by shear, and pressure p is
incorporated into the non-linear acoustic or sound generation term
(p-c.sub.0.sup.2.rho.), with Kronecker delta .delta..sub.ij defined
to be one for i=j and zero for i.noteq.j.
[0045] Bladed turbine components generate pressure pulsations with
a strong discrete component at the blade passing frequency, for
example at a BPF corresponding to 15EO or 16EO, depending on the
blade count. For a rotor having dynamic characteristics expressed
in harmonics of the engine order, the BPF amplitude will in general
influence rotor stability.
[0046] In a rotor with asymmetric blade spacing, the periodic and
cyclic pressure field characteristics are reduced by the
introduction of two blade sectors having different numbers of
blades N1 and N2, with different angular spacing S1 and S2. The
pressure function is expressed in terms of a Fourier series of in
the BPF frequency:
P(t)=P.sub.0+.alpha..sub.1 sin(1EO.times.t+.alpha..sub.1)+ . . .
+.alpha..sub.N sin [(N)EO.times.t+.alpha..sub.N]+ . . . [7]
The coefficients a.sub.n represent the relative amplitudes of the
sine function at each engine order, and at relative phase
.alpha..sub.n. Index n runs from n=1 for first engine order 1EO,
through harmonics of order n=N and above.
[0047] In an odd-numbered asymmetric configuration with N1=(N-1)/2
blades at spacing S1 and N2=(N+1)/2 blades at spacing S2, there are
substantial contributions to engine orders 2N1=N-1 and 2N2=N+1:
P ( t ) = P 0 + b 1 sin ( 1 E 0 .times. t + .beta. 1 ) + + b N - 1
sin [ ( N - 1 ) EO .times. t + .beta. N - 1 ] + b N sin [ ( N ) EO
.times. t + .beta. N ] + b N + 1 sin [ ( N + 1 ) EO .times. t +
.beta. N + 1 ] + [ 8 ] ##EQU00004##
In particular, the asymmetric configuration possesses the following
aerodynamic pressure amplitude characteristics:
a N - 1 ( asymmetric ) < 1 1 + b N - 1 ( symmetric ) , [ 9 A ] a
N ( asymmetric ) < 1 1 + b N ( symmetric ) , and [ 9 B ] a N + 1
( asymmetric ) < 1 1 + b N + 1 ( symmetric ) . [ 9 C ]
##EQU00005##
The difference or amplitude reduction coefficient (c) is about
thirty percent (30%) or more (that is, .epsilon..gtoreq.0.30).
Conversely, therefore, unmodified (symmetric) amplitudes b.sub.N-1,
b.sub.N and b.sub.N+1 are at least 30% greater than modified
(asymmetric) amplitudes a.sub.N-1, a.sub.N and a.sub.N+1.
[0048] For the case of a fifteen blade (fifteen splitter) rotor
divided into two groups or sectors of seven and eight blades,
respectively, the first sector of seven blades generates a BPF
pressure signal at engine order 14EO (i.e., 2.times.7), and the
second sector of eight blades generates a BPF pressure signal at
engine order 16EO (i.e., 2.times.8). This gives:
a 14 < 1 1 + .times. b 14 , [ 10 A ] a 15 < 1 1 + .times. b
15 , and [ 10 B ] a 16 < 1 1 + .times. b 16 . [ 10 C ]
##EQU00006##
[0049] The reduction factor is at least 30% in these engine orders,
as described above.
[0050] For even blade counts N, the rotor is divided into a first
sector with N1=N/2-1 blades at spacing S1, and a second sector with
N2=N/2+1 blades at spacing S2. Asymmetric contributions appear at
engine orders (N-2)EO and (N+2)EO:
P(t)=P.sub.0+b.sub.1 sin(1EO.times.t+.beta..sub.1)+ . . .
+b.sub.N-2 sin [(N-1)EO.times.t+.beta..sub.N-2]+ . . . +b.sub.N sin
[(N)EO.times.t+.beta..sub.N]+ . . . +b.sub.N+2 sin
[(N+1)EO.times.t+.beta..sub.N+2]+ . . . [11]
Amplitude reduction is again at least 30%, giving:
a N - 2 ( asymmetric ) < 1 1 + b N - 2 ( symmetric ) , [ 12 A ]
a N ( asymmetric ) < 1 1 + b N ( symmetric ) , and [ 12 B ] a N
+ 2 ( asymmetric ) < 1 1 + b N + 2 ( symmetric ) . [ 12 C ]
##EQU00007##
[0051] For a sixteen-blade rotor divided into sectors of seven and
nine blades, respectively, the first sector generates an excitation
BPF at engine order 14EO (2.times.7 blades), and the second sector
generates an excitation BPF at engine order 18EO (2.times.9
blades). Thus
a 14 < 1 1 + .times. b 14 , [ 13 A ] a 16 < 1 1 + .times. b
16 , and [ 13 B ] a 18 < 1 1 + .times. b 18 . [ 13 C ]
##EQU00008##
[0052] In a turbomachine with two or more rotors, each rotor
contributes to the total pressure amplitude. For co-rotating load
and power head impellers having the same number of blades N, for
example, the net pressure signal is:
P ( t ) = P 0 + c 1 sin ( 1 EO .times. t + .beta. 1 ) + + c N sin [
( N ) EO .times. t + .beta. N ] + + d 1 sin ( 1 EO .times. t +
.gamma. 1 ) + + d N sin [ ( N ) EO .times. t + .gamma. N ] + [ 14 ]
##EQU00009##
Primary (first) engine order 1EO is defined by the blade passing
frequency, which depends on blade number N and angular frequency
w:
1EO.ident.BPF=N.omega.. [15]
For asymmetric blade spacing at odd blade numbers N, "side-band"
harmonic contributions appear at engine orders (N.+-.1)EO. For even
blade numbers N, contributions appear at engine orders
(N.+-.2)EO.
[0053] Frequency-compatible rotors have the same number of blades
N, divided into similar sets of blades N1 and N2 with similar blade
spacing S1 and S2, giving the same BPF excitation frequencies. In
order to shift the two contributions out of phase, one rotor is
clocked or rotated about by an angle of 360.degree./2N about the
engine axis. This yields:
.gamma..sub.n=.beta..sub.n=.pi.. [16]
[0054] In general, two signals of the same frequency having the
same amplitude facing each other (or counter-propagating) can be
canceled or negated by placing them out of phase (or in destructive
interference). The magnitude or amount of the phase shift is a
function of wavelength and the distance between of the two sources.
Mechanically, the phase shift is accomplished via the shaft or
linkage connecting the two impellers to the rotor assembly. For
curvic couplings, for example, the curvic "teeth" structures
(castellations or notches) are typically aligned at either end, and
the angular offset is accomplished by rotating one of the impeller
rotors with respect to the teeth.
[0055] In one particular embodiment, the curvic coupling has 2N
notches or curvic teeth (that is, twice the blade number). In this
embodiment, one of the impellers is rotated by one tooth or notch,
producing an angular offset of 360.degree./2N to generate the
required phase shift. Alternatively, the impeller is rotated by an
odd number of teeth.
[0056] In principle, equally loaded rotors will have substantially
similar amplitude coefficients c.sub.n and d.sub.n, and the net
pressure field may approach zero at some points. In practice,
however, the rotors are not always the same size, and do not
experience the same loading, so the amplitudes are different. In
addition, the relative phase shift varies by location, generating a
standing wave pattern in (at least) the near and intermediate
fields.
[0057] These effects are addressed by controlling tip clearance,
housing eccentricity, rotor run-out and blade stiffness to produce
rotors with substantially equivalent impendence. This further
minimizes the net pressure signal, including the far field region
where environmental effects are a concern.
[0058] FIG. 4A is a velocity field plot for rotor 30 with symmetric
spacing of blades 34 and splitters 36 about hub 32, and FIG. 4B is
plot for asymmetric spacing. Both plots are taken at 95% blade
span, with the Mach contours shown in arbitrary units.
[0059] Flow separation zones FZ correspond to low Mach numbers of
about M.ltoreq.0.30 or M.ltoreq.0.15, and are associated with
acoustic source strength. Comparing FIG. 4A to FIG. 4B, flow
separation for asymmetric blade spacing (FIG. 4B) is weaker than
for the symmetric case (FIG. 4A), and flow separation zones FZ are
reduced in size. Thus, for the same blade count, asymmetric blade
spacing (FIG. 4B) induces relatively lower sound intensity than
symmetric blade spacing (FIG. 4A).
[0060] While this invention has been described with reference to
exemplary embodiments, it will be understood by those skilled in
the art that various changes may be made and equivalents may be
substituted for elements thereof without departing from the spirit
and scope of the invention. In addition, modifications may be made
to adapt a particular situation or material to the teachings of the
invention, without departing from the essential scope thereof.
Therefore, the invention is not limited to the particular
embodiments disclosed herein, but includes all embodiments falling
within the scope of the appended claims.
* * * * *