METHOD AND SYSTEM FOR TURBINE BUDE CHARACTERIZATION
RELATED APPUCATiONS
[0001] This application cialms the benefit of US Provisional Application No.
60/914,998, filed April 30,2007, which is incorporated herein by reference In its entirety for purposes of each PCT member state and region In which such incorporation by reference Is permitted or otherwise not prohibited.
TECHNICAL FIELD
[0002] The present Invention relates to turbomachinery, and, more
particularly, to characterizing and comparing blade response based on wheel-box testing with fluid (e.g., oil) excitation and on modeling of the fluid excitation, and to characterizing the dynamics of one or more turbine stages, providing for characterization of a stage In terms of natural frequencies, normalized response intensity, and stage modal shape (also referred to as nodal configuration).
BACKGROUND
[0003] Generally, a standard wheel-box test may be used for characterizing
turbine blades; however, such known tests only partially address desires and needs for turbine blade design. For Instance, the output of such tests only provide for measuring the natural frequencies of the system, with poor information about wheei\blade modal forms and forcing excitation. Consequently, standard wheel-box tests allow for only output-output analysis (e.g., the determination of the quality factor).
[0004] Additionally, in such standard wheel-box tests, the excitation is typically
reproduced by means of a gas spray, and thus carmot be performed at too low of an absolute pressure. Further, it may be noted that the excitation forces produced with a gas spray are limited by the vacuum pump flow rate capability. This limit does not allow for using high spray flow rates arid consequently does not allow for high Impulse forces on the blades.
[0005] Consonant with the foregoing, the present inventors are unaware of
any works modeling or characterizing (e.g., quantifying) a gas spray excitation (which excitation is very difficult to model), providing for complex characterization. The difficulties In modeling or characterizing the gas spray excitation (e.g.,

quantifying) also limits standard wheel-box testing; for example, this Inability
prevents designing and/or optimizing the excitation to excite one or more specific
modes (e.g., as may be desired by a customer).
[0006] While software (e.g., LMS. B&K, AGILIS, etc.) is available for
performing post-processing of test-data signals acquired during wheel-box tests and
providing for the characterization of the modal shapes, such post-processing
software represents a specific methodology of characterizing modal shapes and has
various limitations. For instance, such post-processing software do not allow for
closing the loop through the analysis of the excitation.
[0007] in other words, techniques for measuring, analyzing, and/or
characterizing rotating blades (e.g., dynamic characterization of turbine blades) are generally limited to output-output type techniques and, for example, use neither excitation modeling nor input-output methodologies.
SUMMARY OF INVENTION
[0008] Various embodiments of the present invention provide methods and
apparatuses for testing, characterizing, and/or analyzing turbomachinery based on a fluid excitation and quantitative modeling of the fluid excitation. Various embodiments of the present invention additionally or altematively provide methods and apparatuses for testing, characterizing,' and/or analyzing modal shape or nodal configuration of a bladed disk (e.g., a turbine stage) based on a phase analysis of strain signals acquired from a bladed disk subjected to a fluid excitation, wherein the modal shape or nodal configuration corresponds to modes of blades coupled through a disc or shrouding.
[0009] in accordance with some embodiments of the present invention, a
method providing for characterizing a turbine blade, comprises providing at least one turbine blade on a rotor; rotating the rotor, thereby rotating the at least turbine blade; Impinging a liquid onto the turbine blade during rotation of the at least one turbine blade; and providing a quantitative model of the excitation force imparted on the at least one turbine blade by the Impinging liquid. The liquid may be an oil. Impinged as an atomized spray. The impingement of the liquid onto the at least one turbine blade may be controlled according to the quantitative model of the excitation force imparted onto the at least one turbine blade by the liquid. The signals received from sensors that are directly or indirectly coupled to the turbine blades may be processed

according to the quantitative model. The processing may Include analyzing phase Information from the sensors to determine the modal shape/nodal configuration among a plurality of the at least one turbine blade.
[0010] In some embodiments, a method providing for characterizing at least
one turbine blade comprises modeling the. excitation force imparted onto the at least
one turbine blade by a liquid; and controlling the impingement of the liquid onto the
at least one turbine blade according to the excitation force model. The excitation
force model may provide the excitation force as a function of time and/or provides
the excitation force frequency components or harmonic content.
[0011 ] In some embodiments, a method providing for characterizing at least
one turbine blade comprises processing signals received from sensors directly or
Indirectly coupled to turbine blades mechanically excited by a liquid, wherein the
processing is performed according to a quantitative model of the excitation force
Imparted on the at least one turbine blade by the liquid. The processing may
comprise determining the modal shape/nodal configuration among a plurality of the
turbine blades. The excitation force model may provide the excitation force as a
function of time and/or provides the excitation force frequency components or
harmonic content. ;:
[0012] In some embodiments, a method providing for characterizing at least
one turbine blade comprises processing phase signals received from sensors
directly or indirectly coupled to turbine blades to determine the modal shape/nodal
configuration among a plurality of the turbine blades. The received phase signals
may con-espond to the turbine blades being mechanically excited by a liquid.
[0013] Various embodiments of the present invention also may comprise
relating the response of the turbine blades determined by the modal shape/nodal
configuration analysis with the quantification of the excitation to provide damping
factors associated with at least one modal shape/nodal conflguratbn.
[0014] Various embodiments of the present Invention also comprise at least
one computer-readable medium, and/or a system comprising at least computer-readable medium, wherein the at least one computer-readable medium stores programming that when executed by at least one computer Is operative In the at least one computer Implementing one or more of the methods described above and/or otherwise described and/or claimed herein.

[0015] It will be appreciated by those skilled in the art that the foregoing brief
description and the following detailed description are exemplary and explanatory of the present invention, but are not intended to be restrictive thereof or limiting of the advantages which can be achieved by this Invention. Additionally, It is understood that the foregoing summary of the invention is representative of some embodiments of the invention, and Is neither representative nor inclusive of all subject matter and embodiments within the scope of the present invention. Thus, the accompanying drawings, referred to herein and constituting a part hereof, iliustratis embodiments of this invention, and, together with the detailed description, serve to explain principles of this invention.
BRIEF DESCRIPTION OF THE DRAWINGS
[0016] Aspects, features, and advantages of embodiments of the invention,
both as to structure and operation, will be understood and will become more readily apparent when the invention is considered in the light of the following description made in conjunction with the accompanying drawings, in which like reference numerals designate the same or similar parts throughout the various figures, and wherein:
I [0017] FIG. 1 schematically depicts an Illustrative test set-up for exciting one
or more bladed wheels with a liquid (e.g. oil) during a wheel-box test, In accordance with some embodiments of the present Invention;
[00181 FIGS. 2A-2C schematically depict an illustrative model, in accordance
with some embodiments of the present Invention, for obtaining the force transfenred
; by the impact of the droplets of a spray with a blade of a rotating wheel;
[0019] FIG. 3 schematically depicts the planar development of blades at
different time values, in accordance with some embodiments of the present
invention;
[0020] FIG. 4 depicts an illustrative histogram of impacts in accordance with
» modeling an excitation force, in accordance with some embodiments of the present Invention;
[0021] FIGS. 5A-C shows the force in the V'^'^J reference system for the
illustrative case represented by the histogram of impacts depicted in FIG. 4; in accordance with some embodiments of the present invention;

[0022] FIG. 6 shows the tangential force transferred to one blade In 360° of
rotation by four nozzles of the same size, unlformly distributed around the
circumference at the same radial location, under the same conditions for the
illustrative case of FIGS. 5A-C, In accordance with some embodiments of the
present Invention;
[0023] FIG. 7 shows the force decomposition for FIG. 6 In terms of Its Fourier
components at different XRevs, In accordance with some embodiments of the
present Invention;
[0024] FIG. 8 shows the 4XRev component of the force as function of the
rotational speed, corresponding to the Illustrative conditions for the Illustrative case
model of FIGS. 6 and 7, In accordance with some embodiments of the present
Invention;
[0025] FIG. 9 is a flowchart depicting illustrative steps for performing tonal
analysis, according to some embodiments of the present invention;
[0026] FIG. 10 shows the LO blade (last stage) Campbell diagram for an
experimental test performed in accordance with some embodiments of the present
Invention;
[0027] FIGS. 11A and 11B show the measured response and normallzed
measured response, respectively, for six different blades at five different crossings
for an experimental test performed In Accordance with some embodiments of the
present invention;
[0028] FIGS. 12A-F show the magnitude of the responses, plotted as
microstrain vs. rpm, for six blades, for an experimental test performed In accordance
with some embodiments of the present Invention;
[0029] FIGS. 12G-L show the respective phase data, plotted as degrees vs.
rpm, for the six blades, con-esponding to the magnitude data of FIGS. 12A-F, for an
experimental test performed In accordance with some embodiments of the present
invention;
[0030] FIG. 13 is a Campbell diagram from which the data of FIGS. 12A-L is
extracted along the 6th engine order, for an experimental test performed In
accordance with some embodiments of the present Invention;
[0031] FIG. 14 shows a polar plot of displacement corresponding to theoretical
blade phases and measured blade phases, corresponding to the data of

FIGS. 12G-L, for an experimental test performed in accordance with some
embodiments of the present Invention;
[0032] FIG. 15 shows a polar plot of displacement corresponding to the
4XRev crossing with the first mode, for an experimental test performed In
accordance with some embodiments of the present invention;
[0033] FIGS. 16A-L depict the magnitude data (microstrain vs. rpm) and the
coHBspondlng phase data (degrees vs. rpm) for six blades for the 5XRev crossing,
for an experimental test performed In accordance with some embodiments of the
present invention; and
[0034] FIGS. 17A-C show polar plots of blade displacements corresponding to
three respective peaks for the measured SXRev crossing data, along with the
theoretical displacements for a 5ND configuration, for an experimental test
performed In accordance with some embodiments of the present Invention.
DESCRIPTION OF EMBODIMENTS OF THE INVENTION
[0035] As will be understood in view of the ensuing description, various
embodiments of the invention relate to experimental testing, and include aspects and embodiments that may be divided, for convenience, into three primary areas: test set-up; excitation analysis/modeling; and post-processing (e.g., phase\tonal analysis). As will be understood, subject matter embraced by the present invention Includes, but is not limited to, embodiments directed to each of these primary areas individually, as well as to embodiments directed to combinations of two or more of these primary areas. More specifically, as will be understood by those sidlled In the art, methods and systems according to embodiments of the present Invention Include Integrating embodiments and/or aspects of all three areas In order to define and characterize the mechanical response of the system (e.g., the turbine blades being tested).
[0036] Additionally, as will be understood by those sidiied in the art in view of
the present disclosure, methods and systems according to embodiments of the ' present invention provide for experimental measurements of the vibration
characteristic parameters (natural frequencies, damping factors associated with each modal shape, etc) on rotating buckets/biades wheels. Methods and systems according to embodiments of the present invention allow for the characterization of the stage in temns of natural frequencies, normalized response Intensity, and stage

modal shape (nodal configuration). In addition, it will be appreciated In view of the present disclosure that tests according to embodiments of the present Invention may be performed In a relatively early phase of the design development, since It does not require the entire flowpath hardware.
[0037] FIG. 1 schematically depicts an Illustrative test set-up for exciting one
or more bladed wheels (e.g., a compressor\turbine blade wheel) with a liquid (e.g.
oil) during a wheel-box test, In accordance with some embodiments of the present
Invention. More specifically, the depicted embodiment Includes a chamber 100 In
which three bladed wheels 102a, 102b, 102c (e.g., turbine stages, each comprising a
number of turbine blades mechanically coupled to a common shroud) are mounted
on a rotor shaft 122 that is driven by motor drive 112. Chamber 100 may be
evacuated to a desired pressure by vacuum pump 110, which Is communicably
coupled to computer 106. By way of example, a test may be performed at very low
absolute pressure (e.g., on the order of 10 mbar) In chamber/bunker 100 by control
of vacuum pump 100, thus increasing dhe measured signal-to-noise ratio.
[0038] One or more of the bladed wheels 102a, 102b, 102c each includes at
least a plurality of blades that each includes one or more strain gauges,
schematically depicted as gauges 120, mounted thereon. The strain gauge signals
are communicably coupled (link not shown for clarity) to a communication interface
104, which Is mounted toward an end of shaft 122 and is communicably coupled to
computer 106. (While communicable cormections are depicted by lines, such lines
schematically depict a communication link, which may be implemented by a
conductive cormection (e.g., a cable, bus, etc.) and/or by a wireless cormection (e.g.,
telemetry), and may provide for unidirectional or bidirectional signal communication,
depending on the implementation and functional requirements.
[0039] The system Includes a plurality of controllable nozzles 103 disposed
about one or more of the bladed wheels 102a, 102b, 102c (e.g., turbine stages) for directing fluid onto the blades of one ol- more of the bladed wheels 102a, 102b, 102c. For ease of understanding, only two nozzles 103 are schematically depicted as being directed on each stage/disk. In accordance with various embodiments of the present invention, as will be further understood In view of the excitation model presented herelnbelow, nozzles 103 are implemented as atomizing type nozzles. Each of the nozzles 103 may be configured or mounted such that Its orientation and/or position relative to the blades and bladed wheels Is adjustable, so that the

nozzle may direct fluid onto the blades from various circumferential and/or radial positions relative to the blade disc, and from various angles relative to the blade surface. Each nozzle 103 is coupled to a fluid supply (not shown) and Is separately controllable by computer 106 (e.g., by means of a controllable valve to throttle and gate the fluid flow, an adjustable pin to adjust the nozzle aperture/armulus, etc.) to control the fluid emission parameters (ie.g., spray mass flow, pressure, heat, etc.). For clarity of exposition, positional/orientation control as well as fluid emission parameter control by computer 106 Is schematically depicted by computer 106 being communicably coupled to a manlfold/feedthrough 105, which is coupled to nozzles 103.
[0040] As Indicated above, computer 106 is communicably coupled for
controlling and/or receiving signals (e.g., signals from strain sensors 102a, various
sensors for monitoring other parameters/conditions and/or for feedback control, etc.)
from vacuum pump 110, motor drive 112, nozzles 103, and gauges 120 via Interface
104. Computer 106 may store acquired test data sets on storage medium 107.
Computer 106 is also operable for executing software to provide program control of
testing operations including. In accordance with some embodiments, controlling
nozzles 103 to provide desired forcing excitations as determined In accordance with
a model of the fluid excitation. Computer 106 may also be operable to perform
analysis or other post-acquisition processing of the acquired test data, such as
performing tonal analysis In accordance with some embodiments of the present
Invention. It will be understood, however, that such post-processing, as well as other
modeling (e.g. excitaWon modeling) or pre-test analysis or data generation (e.g., for
generating desired excitation signals) may be implemented offline by one or more
other computers that may not be useable for testing.
[0041] in accordance with some embodiments of the present Invention, a
wheel Is excited by Impingement of a certain number of (e.g., one or more) oil spray jets (e.g., nozzles 103 In the test set-up of FIG. 1). Once the blade, rotating at the rotational speed, comes In contact with the oil, It accelerates each oil droplet of the spray along its rotational direction. In this way, the momentum variation Impressed on the oil droplet has the effect to transfer a certain momentum to the blade and so exciting it. As indicated above, the oil spray (e.g., emitted through a nozzle) may be located In one or more different circumferential locations (which may be adjustable)

I f
and may be located in such a way to transfer momentum at any radial section of the blade.
[0042] As may be appreciated, such a test set-up as shown in FIG. 1 allows
for having very high signal-to-nolse ratios. For Instance, as may be appreciated, a
high signal-to-noise ratio is provided by using a liquid (e.g., oil), which, compared to
a gas, provides much higher forces (e.g., the liquid is associated with a much higher
mass or density (e.g., at the same volume flow rate) compared to a gas; also,
compared to a gas. a liquid has a much lower divergence from the nozzle).
[0043] Various embodiments of the present invention provide for
characterizing the excitation in the case of a liquid (e.g., oil) spray. As understood,
embodiments of the present Invention include methods for characterizing such a
liquid (e.g., oil) excitation, such as representing such an excitation In terms of a force
as a function of time and/or In terms of frequency components (e.g, harmonic
content of the excitation). The ensuing description sets forth an Illustrative model for
characterizing the excitation force in accordance with some embodiments of the
present invention, and those skilled In the art will understand that that aspects and
embodiments of the present Invention, including embodiments directed to the
excitation analysis/modeling itself as well as embodiments employing the excitation
force characterization (e.g., in terms of time dependence and/or frequency
components) are not limited to this particular illustrative model.
[0044] FIGS. 2A-2C schematically depicts an illustrative model, In accordance
with some embodiments of the present invention, for obtaining the force transfenred by the Impact of the droplets of a spray 209 emitted by nozzle 203 with a blade of wheel 201 rotating at N revolutions per minute (rpm).
[0045] In this model, a blade (e.g., blade 205) Is modeled by a plane of nonmal
n( '^rjW^j",) of equation! ;> . •

[0046] FIG. 2A schematically depicts what may be referred to as the planar
development of the section of the blades (e.g., blades 205 and 207, also referred to in the drawings as Blade 1 and Blade 2, respectively) row at constant radius /; equal
to the radius at which the nozzle 203 Is positioned. In this plane 4 is the point of Intersection of the line describing the blade and the line describing the plane

tangential to the blade's edges in axiai direction (^r^). Since the blade is rotating, the point Po moves with a velocity Vg in the tangential direction (S):

[0047] A simplified model, which those skilled in the art will understand as
being suitable for many implementations, considers the spray as a whole of droplets
ejected from the nozzle. Each droplet exits the nozzle with an axiai velocity V^:
[0048] When the droplet reaches the plane of blades edges its velocity is:

[0049] From this point the droplet enters the area of possible impacts with the
blade. In this illustrative embodiment of a spray impact model, the case of a type H (hollow cone) nozzle is represented. The intersection of the spray pattem with the plane ^Cg is schematically depicted In FIG. 2A from the sez. AA perspective, and In
FIG. 2C in the TTS plane (showing the spray pattem Intersection having an armular shape of width s, mean radius Rext, and extending to radius Rext)- The analysis of the impact considers the droplets moving from this plane into the area of possible impact. If one droplet is at a given axial distance / from the plane ^g, it will reach the plane in a time

[0050] The droplet position D can be identified with its radial and curvilinear
coordinates (R and (p) on the plane ^^ together with its axial distance from jvg, I. Each droplet can be identified In the blade system as follows:

or alternatively, given equation (6), as follows:


[0051] in considering the occurrence of an impact event between a droplet
and a blade, the total time T fertile possible Impacts to take place is considered. This time, 7, Is simply the time needec^ for the blade to cover a distance equal to the sum of blade pitch and the total spray impression dimension on the plane icg:

[0052] The time /' needed by each droplet to reach the plane jcg is then
randomly chosen in the interval [0,T]. While the droplet travels from its initial position to the plane JIB , also the base point 4 of the plane representing the blade, moves tangentlaily as follows:
where P^ is the Initial position of P^:

[0053] At the instant f the drop^ stands on the plane jig and its coordinates
are then:

[0054] At this point, counting the time f" from the instant when the droplet
leaves the plane ;T^ , the droplet position is given by:

while the base point PQ becomes:

[0055] The condition for impact is finally represented by equation (1) with
P = D:

[0056] Substituting equations (12) and (13) Into equation (14), the equation for
the impact time t" is:


[0057] Inverting equation (16), it Is possible to find the time elapsed from the
Instant when the droplet enters the area of possible impacts and the Impact itself

[0058] The total time for each droplet under conslderatbn to impact the blade
is then:
[0059] The position of the Impacted droplet3,„ Is given by substitution of
equation (16) into equation (12).
[0060] Clearly, In this illustrative model, not all the impacts are possible or
have interest. l\/lore specifically, in this illustrative embodiment, the impacts of
Interest are those occurring In the blade charmel between the first and the second
blade at time t\ as represented in FIG. 3, which schematically depicts the planar
development of blade 205 and blade 207 et times Q,t\f + f[0061] The situation in the other charmel will then be equal. This condition is
verified when the following is true:

[0062] Moreover the radial and axial coordinates of the point of impact must
be such that the impact occurs physically on the blade:

where a is the axial length of the blade while r„^ is the tip radius.
[0063] In acconjance with this illustrative model according to some
embodiments of the present Invention, the droplets are all assumed to have the same diameter. This diameter is talceia eqiiai to the Soutem-mean diameter ^j^. As known to those skilled in the art, different correlations are available on literature. For purposes of the illustrative model presented herein In accordance with some embodiments of the present invention, the conrelation from Hiroyasu and Kadota is

used (see, e.g., H. Hiroyasu and T. Kadota, "Fuel Droplet Size Distribution In Diesel Combustion Chamber." SAE Paper 740715 (1974)):

where d^^ '^ ^^ \^^' A is a geometrical constant depending on the nozzle (equal to 18.82 for a 28 Gal nozzle for which modeling resuite aria presented herein for purposes of Illustration and by way of example), Ap Is the mean effective pressure
differential across the nozzle (MPa), p„ is the ambient air density (kg/m^), and Q
(mm^/s) is the volumetric flow rate. It will be understood by those sidlled in that art that while the correlation proposed was developed for dlesel Injectors, It is more than sufficient for many modeling Implementations in accordance with various
t
embodiments of the present invention.
[0064] The mass of each droplet Is then:

[0065] The mass flow rate m (which is well known from characterization of the
nozzle) is linked to the time T and the total number M of droplet ejected in that time by the following relation:

from which:

[0066] The droplets are assum^ to have a given distribution in radial
direction and coherent distribution in circumferential and axial directions as explained in the appendix. If ntg is the number of particles In the radial direction, the number of particles in circumferential m^ and axial directions m, are:


where R„^ and s are respectively the mean radius and width of the spray pattern on the plane ^g. Consequently the total number of droplets considered is:

[0067] Inverting equation (26), once Wj, Is known (clearly rounding at the
nearest Integer), m^and m^are also known by equations (24) and (25).
[0068] Summarizing, the droplet travels with velocity F^ spreading from the
nozzle. In the meanwhile, the blade travels In the tangential direction with velocity Vg. Accordingly, at the impact the relative velocity between the blade and the droplet is:

[0069] DesJardin et ai. fomiulated, based on energy conservation principles,
an impact model for a droplet impinging on a surface. {See, e.g., "A Droplet Impact
Model for Agent Transport in Engine Nacelles," Proceedings of the 12**' Halon
Options Technical Working Conference (HOTWC), NIST SP 984, pp. 1-12 (2002)).
One of the results of their work Is a criterion to analyze the behavior of the droplet
after the impact. After impact the droplet can either rebound or stick to the surface.
In particular, refem'ng to DesJardin et al. for additional details, the criterion
essentially states that, If the surface energy of the at-impad state (where the droplet
is assumed to be spread at the surface in a roughly pancake shape) is less than the
energy dissipated during impact, then the droplet sticks to the surface.
[0070] Considering DesJardin et ai.'s analysis in cormection with the droplet
a
characteristics predicted by the previous presented model and the blade velocities typically encountered in a typical wheel box test, for such conditions, generally rebounding does not occur. Accordingly, under such conditions, because the impact can be analyzed like a complete inelastic impact, it Is easier (e.g., than under conditions that include incomplete Inelastic impacts) to compute the forces developing In the impact.

[0071] Each of the M droplets under consideration impacts the blade after a
given time (equation (17)). These times can be collected in a histogram in order to have the number of impacts N happening In a certain Interval of time [/,/+