TURBO-MACHINERY STAGE FAMILIES TUNING/CALIBRATION
SYSTEM AND METHOD
BACKGROUND
TECHNICAL FIELD
[0001] Embodiments of the subject matter disclosed herein generally relate
to methods and systems and, more particularly, to mechanisms and techniques for
tuning/calibrating turbo-machinery stage families.
DISCUSSION OF THE BACKGROUND
[0002] One turbo-machinery is a centrifugal compressor. Centrifugal
compressors are usually designed in families intended to cover a specific flow range
and use. Centrifugal compressor can have one or several stages. Each individual
design within the family may be of different size and may have a varying number of
blades in the impeller (e.g., splitter or non-splitter in one or multiple rows), statoric
parts (e.g., return channel with vanes, one or multiple rows with splitter or cascade
vanes or wedge type vanes), a diffuser (e.g., with airfoil of low solidity or cascade or
wedge type with one or multiple rows of vanes or without vanes), and an exit system
(e.g., scroll, collector, deswirl), etc. The individual designs in a family stretch from
low to high design flow coefficients and sometimes from low to high design Mach
numbers. Each family member is defined with one design flow coefficient and
speed, but also with a useable flow range and speed range, as shown in Figure 1.
The family shown in Figure 1 includes four designs, each one with its design speed
line 2 , 4 , 6 , and 8 and several additional speed lines. In total there are twelve speed
lines to be used in the calibration/tuning of the 1-D models with respect to the
polytropic efficiency and head for this specific example. It is noted that all values in
Figure 1 are normalized to a corresponding value at a medium-high design flow rate.
A chosen number of the designs (called test masters and shown as elements 10 in
Figure 2) are selected for testing and then tuned/calibrated to test data. The
tuned/calibrated test masters 10 are saved as database masters, which in turn are
used to populate the design database, which is schematically illustrated in Figure 2.
The other design points 12 are not tested. However, these points are also stored in
the design database and these points correspond to already designed compressors.
When a customer orders a new compressor having the design indicated by point 14
in Figure 2, which does not exist in the design database, the test masters and the
designed points may be used to model the desired compressor, e.g., determine the
design parameters.
[0003] Optimization strategies have been used in recent years for the
aerodynamic and mechanical design of turbo-machine components. In particular,
numerical optimization techniques seem to be one of the most promising tools for the
aerodynamic design of new generation turbomachinery components (Bonaiuti et al.,
"Analysis and Optimization of Transonic Centrifugal Compressor Impellers Using the
Design of Experiments Technique", Journal of Turbomachinery, 128(4), pp. 786-797,
2006, the entire content of which is incorporated herein by reference).
[0004] An aero design cycle of centrifugal compressor stages starts with a
1-D performance prediction and calculation process followed by detailed design,
analyses and tests to validate the prediction. A part of the design process is the 1-D
performance parameters prediction and calculation. This task is carried out with the
help of a 1-D performance prediction tool, which calculates, for example, a polytropic
head, polytropic efficiency, work coefficient etc. of the compressor. The flow models
in the 1-D tool needs to be adjusted by means of so called tuning/calibration
coefficients in order to fit as close as possible to test data. High accuracy and
predictability of the 1-D tool is desired and continuous improvements are performed
to have a better prediction tool with minimal deviation from experiment. Fleet
feedback and reports are effectively utilized in developing correlations for better
predictability.
[0005] Presently, the tuning process of the 1-D tool is a manual process.
This process utilizes data from the tests conducted for different stages together with
a limited, small, number of tuning parameters.
[0006] For example, centrifugal compressors are usually designed in
families intended to cover a specific flow range and use. Figure 3 illustrates families
20, 22, 24, 26, and 28 having different geometric characteristics (represented as
polygons). The graph of Figure 3 classifies the various compressors based on a
design peripheral Mach number versus flow coefficient. The Mach number
represents the speed of the medium (being compressed by the compressor) relative
to speed of sound and the flow coefficient indicates the amount of medium flowing
through the compressor. Individual designs in a family cover a range of flow
coefficients and often multiple speed lines (i.e., different Mach numbers). Each
family member may be characterized by a design flow coefficient and a speed, the
so called design point, but its calibration/tuning parameters are usable in the family
flow range and speed range (a range of several operating points). A database may
be used to store representatives points per families indexed according to flow
coefficients and Mach numbers.
[0007] In addition, tuning/calibration parameters that prove effective for one
particular stage may not be suitable for another stage. The more the performance
indices need to be optimized, the higher the number of iterations required by the
user to reach an acceptable, although not necessarily optimum, level of improvement
with respect to the baseline, where the baseline may be represented by default
tuning/calibration parameter values. The number of tuning/calibration parameters
affects the optimization process as a small increase of the number of
tuning/calibration parameters leads to a rapid increase in the number of iterations
needed.
[0008] An optimization procedure handling the geometrical design features
of the centrifugal compressors has already been developed (see for example, Omar
et al. "An Aerodynamic Optimization Procedure for Preliminary Design of Centrifugal
compressor stages", GT2008-51 154, ASME Turbo Expo 2010, the entire content of
which is incorporated herein by reference). This optimization procedure is intended
for the preliminary design of the centrifugal compressor stages. An effectiveness of
this optimization algorithm may be limited as the flow models in the 1-D performance
prediction tool needs to be calibrated with test data in order to be able to estimate
the expected flow behavior through the compressor stage. Considering the
dependability of other tools on the predictability of 1-D tool, it may be desirable to
develop an automated optimization algorithm that matches the 1-D tool with respect
to the experiment results.
SUMMARY
[0009] According to one exemplary embodiment, there is a method for
automatically determining a final set of tuning/calibration parameters for designing a
new turbo-machinery. The method includes inputing an initial set of
tuning/calibration parameters; calculating family turbo-machinery quantities based on
the initial set of tuning/calibration parameters; comparing the calculated family turbomachinery
quantities with measured quantities and calculating a first error between
the calculated family quantities and the measured quantities; calculating a second
error between the initial set of tuning/calibration parameters and default values of the
turbo-machine variables; forming a modified objective function that includes both the
first and second errors; during an iterative process, varying the initial set of
tuning/calibration parameters in such a way that the final set of tuning/calibration
parameters is found and the final set of tuning/calibration parameters achieves (1) a
best fit between the family of turbo-machinery quantities and the measured
quantities, and (2) a smooth transition for the final set of tuning/calibration
parameters from one member to another member of the family; and storing in a
database the final set of tuning/calibration parameters for the family.
[0010] According to another exemplary embodiment, there is a design
apparatus for determining a final set of design parameters for a new turbomachinery.
The design apparatus includes an interface configured to input an initial
set of tuning/calibration parameters; and a processor connected to the interface.
The processor is configured to calculate family turbo-machinery quantities based on
the initial set of tuning/calibration parameters; compare the calculated family turbomachinery
quantities with measured quantities and calculate a first error between the
calculated family quantities and the measured quantities; calculate a second error
between the initial set of tuning/calibration parameters and default values of the
turbo-machine variables; form a modified objective function that includes both the
first and second errors; vary, during an iterative process, the initial set of
tuning/calibration parameters in such a way that the final set of tuning/calibration
parameters is found and the final set of tuning/calibration parameters achieves (1) a
best fit between the family of turbo-machinery quantities and the measured
quantities, and (2) a smooth transition for the final set of tuning/calibration
parameters from one member to another member of the family; and store in a
database the final set of tuning/calibration parameters for the family.
[0011] According to yet another exemplary embodiment, there is a computer
readable medium including computer executable instructions, where the instructions,
when executed, implement the method discussed above.
BRIEF DESCRIPTION OF THE DRAWINGS
[0012] The accompanying drawings, which are incorporated in and
constitute a part of the specification, illustrate one or more embodiments and,
together with the description, explain these embodiments. In the drawings:
[0013] Figure 1 is an example of a family to be used for designing another
turbo-machine;
[0014] Figure 2 is a schematic diagram of a family of turbo-machines
categorized by Mach number and flow coefficient;
[0015] Figure 3 is a schematic diagram of multiple families of turbomachines
categorized by Mach number and flow coefficient;
[0016] Figure 4 is a graph illustrating a polytropic efficiency versus flow for a
compressor family;
[0017] Figure 5 is a graph illustrating a polytropic head versus flow for a
compressor family;
[0018] Figure 6 is a flowchart illustrating an algorithm for calculating design
parameters for a new turbo-machinery according to an exemplary embodiment;
[0019] Figure 7 is a graph illustrating measured points of a family of
compressors relative to an estimated curve for the same family according to an
exemplary embodiment;
[0020] Figure 8 is a graph illustrating design point conditions and off-design
conditions for a compressor family according to an exemplary embodiment;
[0021] Figure 9 is a graph illustrating design parameters manually (and for
one family member at a time) and automatically tuned for a compressor family
according to an exemplary embodiment;
[0022] Figure 10 is a graph illustrating an automatically tuned polytropic
efficiency and head versus a manually tuned/calibrated one for a compressor family
member according to an exemplary embodiment;
[0023] Figure 11 is a graph illustrating smoothly tuned design parameters
for a compressor family according to an exemplary embodiment;
[0024] Figure 2 is a schematic diagram of a design apparatus according to
an exemplary embodiment;
[0025] Figure 13 is a flow chart illustrating a method for calculating design
parameters according to an exemplary embodiment; and
[0026] Figure 4 is a schematic diagram of a centrifugal compressor.
DETAILED DESCRIPTION
[0027] The following description of the exemplary embodiments refers to the
accompanying drawings. The same reference numbers in different drawings identify
the same or similar elements. The following detailed description does not limit the
invention. Instead, the scope of the invention is defined by the appended claims. The
following embodiments are discussed, for simplicity, with regard to the terminology and
structure of centrifugal compressors. However, the embodiments to be discussed next
are not limited to these systems, but may be applied to other systems, for example
other types of compressors or other turbo-machines like steam turbines, gas turbines
etc., that use 1D performance prediction tool for the initial performance prediction.
[0028] Reference throughout the specification to "one embodiment" or "an
embodiment" means that a particular feature, structure, or characteristic described in
connection with an embodiment is included in at least one embodiment of the subject
matter disclosed. Thus, the appearance of the phrases "in one embodiment" or "in an
embodiment" in various places throughout the specification is not necessarily referring
to the same embodiment. Further, the particular features, structures or characteristics
may be combined in any suitable manner in one or more embodiments.
[0029] Some terminology to be used to describe the exemplary
embodiments is discussed next. While the following terms are understood as
defined below, it is noted that those skilled in the art may use similar terms for the
same quantities. Calibration/tuning parameters/variables are coefficients used to
adjust the D flow model in order to fit it as close as possible to test data. Design
variables are variables defining the geometric design of the compressor. Operating
parameters/variables are parameters determining the functioning of the compressor
(e.g., gas quantities, mass flow, rotational speed, pressure ratio, temperature, etc.).
A design point includes a set of flow conditions (e.g., gas quantities, mass flow,
rotational speed, pressure ratio, temperature, etc.) for which the compressor has
been designed. An operating point includes one or several sets of flow conditions at
which the compressor will be used (e.g., gas quantities, mass flow, rotational speed,
pressure ratio, temperature, etc.). The operating point may or may not be the same
as the design point.
[0030] The following quantities are also defined.
[0031] Flow coefficient: f = Q
p u2
[0032] Polytropic efficiency: hr =
r h(G / )
[0033] Polytropic head rise: ,O , = °° 0 = thr
[0034] Work coefficient: t = ' '
[0035] D2 = Impeller blade tip diameter
[0036] g = Gravity constant [m/s2]
[0037] Hoo = Head at stage exit [m]
[0038] Ho = Head at stage inlet [m]
[0039] h0o = Total enthalpy at stage exit [J/kg=m2/s2]
[0040] h0j = Total enthalpy at stage inlet [J/kg=m2/s2]
[0041] Poi = Total pressure at stage inlet [Pa]
[0042] Poo = Total pressure at stage exit [Pa]
[0043] Q = Mass flow [kg/s]
[0044] Toi = Total temperature at stage inlet [K]
[0045] Too = Total temperature at stage exit [K]
[0046] U2 = Impeller blade tip speed [m/s], and
[0047] Y= Ratio of specific heat capacities.
[0048] According to an exemplary embodiment, an optimization algorithm
may interface an optimization tool with a 1-D prediction tool for providing a best
possible solution within given tuning/calibration limits. The automated optimization
algorithm may improve the predictability of the 1-D tool when used for the
development of centrifugal compressor stages or other turbo machines. The 1-D
tuning/calibration parameters are predicted in alignment with the experiment and
then these parameters are used to perform subsequent 2-D and 3-D design phases.
In one application, the optimization algorithm starts with one set of tuning/calibration
parameters. These can be either default values, taken from a similar family of turbomachines
or chosen from within a pre-determined range. The algorithm then
calculates various quantities of the machine and compares two errors (to be
described later). Then, the algorithm re-run the calculations while varying the
tuning/calibration parameters within a pre-determined range until a minimum error is
found. An additional constraint may be imposed on the algorithm and this is that for
all the design operating points included in the optimization, a smoothness between
the tuning/calibration parameters needs to be found. In other words, the optimization
works as a calibration in two dimensions, operating points on one axis and
tuning/calibration parameters on the other. Together they define the performance
result, which is desired to have a minimal deviation from the measured results. At
the same time, each tuning/calibration parameter is desired to be smooth over the
operating points range.
[0049] The 1-D tool is capable of computing, based on a given geometric
outline of a stage of a compressor and operating conditions (e.g., inlet pressure and
temperature, mass flow, rotation speed, gas properties, etc.), quantities such as
polytropic efficiency, polytropic head, work coefficient, pressure ratio, surge, choke
limits, etc. The geometry taken into consideration may include an impeller, a
diffuser, and an exit system but a wide variety of components may be used including,
but not limited to, Inlet Guide Vane, impeller (Splitter or Non Splitter in one or
multiple rows), statoric parts (return channel with vanes (one or multiple rows) with
splitter or cascade vanes or wedge type vanes), diffuser (with airfoil of low solidity or
cascade or wedge type with one or multiple rows of vanes or without vanes), exit
system (scroll, collector, deswirl), etc.
[0050] For each component type, the user may be requested to provide the
geometrical data defining its outline (e.g., meridional and blade-to-blade). These
parameters may be provided to an input file. The results of the calculation may be
stored in an output file in which the results may be presented in modules repeated
for all design and off-design conditions. By applying the prediction tool to this
geometry, the associated performance parameters can be extracted from the
corresponding output file.
[0051] An experimental validation of the prediction tool for an existing stage
design indicates the relevance of family tuning/calibration. For example, Figure 4
shows a comparison between predicted values (lines 30) and tested values (points
32). Normalized polytropic efficiency is plotted versus the flow coefficient normalized
by the design flow coefficient of medium flow coefficient stage. Figure 5 shows a
similar comparison for a polytropic head versus the flow coefficient normalized by the
design flow coefficient of medium flow coefficient stage. It can be seen from Figures
4 and 5 that family tuning/calibration does not necessarily mean an optimal
tuning/calibration for all the individual family members as an objective is to find an
optimal overall match.
[0052] In the traditional tuning/calibration, the main effort is put on the
design point, which is tuned mainly with two factors related to the efficiency and the
impeller exit flow angle. The intention in the traditional tuning is to match the
polytropic efficiency and head as close as possible. Impeller inlet loss models are
then modified, by means of two coefficients working on the inlet flow, to improve
choke and stall limits. All these steps are performed individually for each design flow
coefficient stage. The shape of the performance curve is not necessarily followed.
[0053] Variations in speed ratio for each design flow coefficient are usually
not tuned/calibrated but only checked. Once all designs have been tuned/calibrated,
the resulting parameters are compared and some of them are adjusted. It is desired
to have a smooth development parameter value with design flow coefficients within
the family. In one application, three additional tuning/calibration parameters were
used (associated with flow separation, flow blockage and critical Mach number) in
order to also tune/calibrate the shape of the performance curves. However, such a
manual tuning/calibration process, for example, for a family with six members and
seven tuning parameters takes nearly two months when performed by an
experienced engineer. Even then it is not certain that the true optimal
calibration/tuning has been achieved, since a manual tuning/calibration is performed
only until an acceptably good match has been found.
[0054] According to an exemplary embodiment, a novel optimization
algorithm (from here on referred to as "the optimizer") is capable of tuning/calibrating
the entire centrifugal compressor stage family with 'n' number of speed lines in both
design and off-design conditions in one run. The optimizer may handle all the
centrifugal compressor stage types and masters of different mass flows having the
same design peripheral Mach number. Input details for the optimizer may be files
defining the stage parameters and corresponding experimental data for all the
stages that are to be tuned/calibrated. The optimizer is flexible enough to be used
both for the tuning/calibration of a single stage and for the entire centrifugal
compressor stage family including "n" number of stages (called masters) that are
tested and their performance stored in a database. The optimizer can handle any
number of tuning/calibration variables during one run. One objective of the optimizer
is "minimizing" an RMS (root mean square) value of an error between test and
predicted values. The error as stated here may include two components, a first
component indicating how far a predicted/calculated point deviates from
experimental data (the Error component), and a second component indicating how
much the calibration/tuning variable/parameter deviates from a default value as
specified by the user (the Devi component). The default values may be found in
open literature or in in-house design practices.
[0055] The two error components may be weighted with variable weights by
means of a W_devi factor as specified by the user. Also, each test point may be
given an individual weight by the user, so that for example, the design point can be
heavier weighted that the other points. One advantage of this algorithm that aids in
accurate optimization is that each point may be handled individually.
[0056] Figure 6 is a diagram illustrating the optimization process according
to an exemplary embodiment. In step 40, an objective function (to be discussed
later) and constraints are defined based on user input values. A modified objective
function (OFMOD) is calculated. The modified objective function is discussed in
more details later. Then, in the optimization loop 42, the optimizer determines in
step 44 an initial/new set of tuning/calibration parameters. Conditions associated
with the initial set of tuning/calibration parameters are also discussed later. The
algorithm uses the 1-D prediction tool in step 46 to predict the performance (i.e.,
quantities as polytropic head, polytropic efficiency and work coefficient) of the
compressor by using the new set of tuning/calibration variables. This step may
involve calculating the two error components. The performance of the compressor is
checked and a new objective function value is computed in step 48. Then, the
algorithm may be repeated using a different set of tuning/calibration variables until a
desired final set is achieved. The final set of tuning/calibration variables achieves (1)
a best fit between the family of turbo-machinery quantities and measured quantities,
and (2) a smooth transition for the final set of tuning/calibration parameters from one
member to another member of the family. A summary 50 of the analysis may be
presented to the user.
[0057] Figure 7 illustrates in more details how one of the error component is
calculated. S 1 and S2 are distances between two adjacent points representing
members of the same family. An integrated correction factor 'p' accounts for the
uneven distribution of points and is given by p = (s1 + s2)/2. A distance 'd' is defined
as the normal distance between test data 62 and a prediction curve 60. For
example, if two points (xO, yO) and (x1 , y1) are present on the prediction curve 60
and one test point is between these two points and above them, the distance d is
defined as d = [(y0-y1)(x2) + (x1-x0)(y2) + (x0y1-y0x1)]/sqrt[(x1-x0) 2 + (y1-y0) 2].
Other definitions for the distance d may be used. The error is given by:
error
where n denotes the total number of test data, "* " denotes the multiplication
operation, and w is the weight specified by the designer. If points 62 are farther
away, the values of s 1 and s2 are greater and hence the contribution of the p value
to the error Error is higher compared to points that are located near to one another.
For the first and the last point, the p value may be equal to either s 1 or s2 alone. In
this way, the optimizer handles evenly the uneven distribution of data points
effectively. The optimizer is also capable of handling variable weights for individual
points for the experimental data as defined by the user in the test data input file.
[0058] According to an exemplary embodiment, design and off design
conditions may be handled separately by assigning them to different groups. The
design point is the point having the characteristics intended for a certain compressor,
e.g., speed 10,000 rpm at the intended mass flow. Off design points are points
around the design point, e.g., varying mass flow but at the same speed, and points
with both varying mass flow and speed. The design point 70 and other points on a
desired speed curve 72 may be categorized into three groups: group 1 defined by
parameters corresponding to flow ratio between (1+/- x) , group 2 defined by
parameters corresponding to flow ratio below (1- x) , and group 3 defined by
parameters corresponding to flow ratio above (1+ x) . If two off design speed lines
are considered, assume for speeds 'x' and 'y then parameters corresponding to
flow ratio (1+ x) of x and y are assigned to Group 4 and (1- x) to Group 5. This
separation of the parameters indicates that each group can be considered
individually depending on the requirement and user specification. Figure 8 illustrates
the above groups. Figure 8 also shows the design point 70, the design speed curve
72, and the off-design speed curves 74.
[0059] According to an exemplary embodiment, the optimizer is configured
to tune any number of tuning/calibration variables as specified by the user and any
number of speed lines in one run. When changing the parameters, the optimizer is
determining a smooth evolution of the parameters by, for example, defining a
polynomial function (linear or quadratic or nth order) across these parameters for the
entire family. This novel feature allows the optimizer to more accurately determine
tuning/calibration parameters for a new compressor. Also, the optimizer is
determining a smooth evolution of the tuning/calibration parameters as close as
possible to the default values by normalizing these values by the user specified
bounds of the tuning/calibration variables and these normalized results are assigned
to a specific factor. A deviation is calculated as the sum of all these factors. By
minimizing the RMS value of the total Error and Devi, the tuning/calibration variables
are tuned/calibrated as close as possible to the default criteria. In one application,
the user may choose to relax the Devi factor in order to allow the tuning/calibration
parameters to deviate more from the default values.
[0060] Figure 9 shows the behavior of tuning/calibration parameters
(efficiency correlation factor Q) calculated with the novel optimizer and manually for
two different families F 1 and F2. Family F 1 calculation was performed with four
masters and a quadratic parameter fit and Family F2 used three test masters and a
linear parameter fit. Curve 80 indicates the manual calculation for Family F 1 and
curve 82 indicates the optimizer calculation for the same family. Curve 84 indicates
the manual calculation for family F2 and curve 86 indicates the optimizer calculation
for the same family. Figure 9 illustrates the smooth evolution of the tuning/calibration
parameter resulting from the family tuning/calibration performed by the optimizer
versus the one that was manually tuned/calibrated. In addition, the optimizer
performed family tuned/calibrated parameter is also closer to the default values than
the manually tuned/calibrated parameter.
[0061] In an exemplary embodiment, the algorithm of the optimizer may
start with a differential evolution (DE) genetic algorithm step, followed by a step that
utilizes a simplex-based optimization algorithm (e.g., AMOEBA, Wang, L , and
Beeson, D., 2003, "Non-Gradient Based Methods for probabilistic analysis", 44th
AIAA/ASME/ASCE/AHS structures, structural dynamics, and materials conference,
AIAA 2003-1782, the entire disclosure of which is incorporated herein by reference).
The first step may involve a genetic algorithm (GA) method because of its
robustness and global search capabilities. The second step may be based on the
AMOEBA method, which is a local optimization method. This second step is used to
expedite the process of arriving at a final optimum design once the most promising
part of the design space is identified using the first GA-based step.
[0062] The GA method randomly generates the tuning/calibration variables.
Therefore, the initial set of tuning/calibration variables are needed only for
performance normalization. This random process of tuning/calibration variable
generation may result in "unphysical-computations" which may cause the prediction
tool to halt or crash. To resolve this issue, the optimization problem has been
structured with higher penalty values for such situations thus ensuring the algorithm
to be executed smoothly. Finally, the procedure may implement features such as
removing any freezing run as a last resort to avoid any premature halt of the
optimization process.
[0063] A modified objective function (OFMOD) is defined as the RMS value
of the total error Error between predicted and experiment as well as the deviation
Devi of the tuning/calibration variables from the default. More specifically, OFMOD
is given by:
OFMOD = Error +W_ devi *devi ,
where Error and Devi have been introduced above. The objective function OF is
defined as Minimize(OFMOD).
[0064] In one simulation performed by the inventors, seven tuning
parameters were used to tune one set of four masters and one set with three
masters, each with three speed lines. The variations in design were such that the
largest design flow coefficient was approximately three times the smallest design
flow coefficient. The optimization was performed for polytropic efficiency and head.
The design point was given a 20 times weight compared to the off-design points and
a devi factor of 5:1 . The CPU time needed was approximately one week per set of
masters comparative to two months for the traditional tuning.
[0065] The optimization algorithm was tested for standard centrifugal
compressor stage family masters. The optimization process used seven
tuning/calibration parameters to tune the four masters, three masters with three
speed lines and one master with four speed lines. An initial set of tuning/calibration
parameters may include either one set of default parameter values or
tuning/calibration parameter values of other turbo-machineries from a similar family
as the new turbo-machinery, or modified tuning/calibration parameter values with an
allowed deviation from the default parameter values. Parameters that were
tuned/calibrated in this particular case include but are not limited to two coefficients
on the inlet flow, one coefficient in the impeller exit flow angle, a critical Mach
number, one coefficient on the flow separation, one efficiency coefficient and one
blockage coefficient. This also includes other performance tuning/calibration
coefficients at the impeller (Splitter or Non Splitter in one or multiple rows), diffuser
(with airfoil of low solidity or cascade or wedge type with one or multiple rows of
vanes or without vanes) and return channel (one or multiple rows with splitter or
cascade vanes or wedge type vanes), exit system (scroll, collector, deswirl) in a
single or multi stage compressor configurations for a single stage master or for the
entire compressor stage master families.
[0066] The modified objective function value represents the cumulative error
considering all the masters and all the speed lines and the optimization algorithm
was executed with the objective of minimizing the OFMOD and tuning/calibrating all
the seven parameters simultaneously. An initial tuning/calibration was based on
differential evolution type genetic algorithm for global optimization followed by a
simplex-based procedure for capturing the local optimum solution. This procedure
was able to reduce the objective function value by almost 80% compared to the
baseline, the baseline being the default values of the tuning/calibration parameters.
[0067] Figure 10 illustrates the results of one of the four masters
tuned/calibrated with respect to measured values at design speed. Values were
normalized with respect to a baseline design point value in order to show the
existence of differences between predicted and experimental values. It is noted that
traditional values 90 are further away from experimental data values 92 than the
optimized values 94. Also, it is noted that the curve shape of the optimized curves
94 better fit the test data than the traditional ones.
[0068] Figure 1 shows that various tuning/calibration parameters 100 of the
compressor family have a smooth evolution from member to member of the family
after the novel optimizer has been applied. The parameter curves 100 shown in
Figure 1 contrast to the manual tuning/calibration results illustrated by curves 80
and 84 in Figure 9. By achieving this high grade of smoothness, the novel optimizer
produces a better database of compressors points and thus, when a new
compressor is ordered by a customer, the interpolation process for calculating the
characteristics of the new compressor produce better and more accurate results.
The characteristic of a curve of being smooth may be described in terms of its first
derivative. For example, consider that a tuning/calibration parameter for the entire
family is described by curve 100 in Figure 11. Curve 100 is considered to be smooth
if a first derivative of the considered tuning/calibration parameter with regard to the
flow coefficient for the entire family is continuous. It is noted that Figure 11 shows
points 102 that correspond to the master designs, i.e., those machines that have
been tested and curve 100 represents the considered design parameter for the
entire family. Thus, when a client desires a new turbo-machinery having a desired
flow coefficient indicated by reference number 104, an operator of the database that
includes curve 102 is able to quickly identify one or more design parameters 106 that
correspond to the desired turbo-machinery.
[0069] A design apparatus 0 for determining a set of tuning/calibration
parameters for designing a new turbo-machinery is next described with regard to
Figure 12. The design apparatus 110 may include an interface 112 configured to
input operating parameters of other turbo-machineries from a same family as the
new turbo-machinery. For example, the interface 112 may be a keyboard, a mouse,
a scanner, etc. Interface 112 is connected to a processor or dedicated circuitry
(analog or digital) 114. Processor 114 may include various functional blocks. For
example, processor 14 may include a first block 16 that is configured to calculate
family turbo-machinery quantities based on the operating parameters received from
interface 1 2. A calculation block 1 8 is configured to compare the calculated family
turbo-machinery quantities with measured quantities and to calculate a first error
(Error) between the calculated family quantities and the measured quantities. The
same calculation block 118 may be configured to also calculate a second error
(Devi) between tuning/calibration turbo-machine variables and default values of the
turbo-machine variables. A logic block 120 is configured to form a modified objective
function that includes both the first and second errors. The logic block 120 or
another block is configured to determine the set of tuning/calibration parameters for
the family to be smooth from one member to another member based on minimizing
the modified objective function. The results of this operation may be stored in a
database located in a memory 122. The memory may communicate with the
processor 14 or may be located inside processor 114. A display unit 124 may be
attached to the processor 114 and may be configured to display the
tuning/calibration parameters. In one application, the design apparatus 110 may be
a dedicated workstation that is configured to perform specific steps as discussed
next.
[0070] According to an exemplary embodiment, illustrated in Figure 13,
there is a method for automatically determining a final set of tuning/calibration
parameters for designing a new turbo-machinery. The method includes a step 1300
of inputing an initial set of tuning/calibration parameters; a step 1302 of calculating
family turbo-machinery quantities based on the initial set of tuning/calibration
parameters; a step 1304 of comparing the calculated family turbo-machinery
quantities with measured quantities and calculating a first error between the
calculated family quantities and the measured quantities; a step 1306 of calculating a
second error between the initial set of tuning/calibration parameters and default
values of the turbo-machine variables; a step 1308 of forming a modified objective
function that includes both the first and second errors; a step 1310 of varying, during
an iterative process, the initial set of tuning/calibration parameters in such a way that
the final set of tuning/calibration parameters is found and the final set of
tuning/calibration parameters achieves (1) a best fit between the family of turbomachinery
quantities and the measured quantities, and (2) a smooth transition for
the final set of tuning/calibration parameters from one member to another member of
the family; and a step 1312 of storing in a database the final set of tuning/calibration
parameters for the family.
[0071] The above described method may be implemented in the design
apparatus 110 show in Figure 12. The design apparatus 12 may calculate
tuning/calibration parameters for a centrifugal compressor. An exemplary centrifugal
compressor is shown in Figure 14. Centrifugal compressor 140 may include an
impeller 142, a diffuser 144, an exit system 146, and an Inlet Guide Vane device
148.
[0072] The disclosed exemplary embodiments provide a system and a
method for automatically determining a set of tuning/calibration parameters for
designing a new turbo-machinery. It should be understood that this description is not
intended to limit the invention. On the contrary, the exemplary embodiments are
intended to cover alternatives, modifications and equivalents, which are included in
the spirit and scope of the invention as defined by the appended claims. Further, in
the detailed description of the exemplary embodiments, numerous specific details
are set forth in order to provide a comprehensive understanding of the claimed
invention. However, one skilled in the art would understand that various
embodiments may be practiced without such specific details.
[0073] Although the features and elements of the present exemplary
embodiments are described in the embodiments in particular combinations, each
feature or element can be used alone without the other features and elements of the
embodiments or in various combinations with or without other features and elements
disclosed herein.
[0074] This written description uses examples of the subject matter disclosed
to enable any person skilled in the art to practice the same, including making and using
any devices or systems and performing any incorporated methods. The patentable
scope of the subject matter is defined by the claims, and may include other examples
that occur to those skilled in the art. Such other examples are intended to be within the
scope of the claims.

CLAIMS:
1. A method for automatically determining a final set of tuning/calibration
parameters for designing a new turbo-machinery, the method comprising:
inputing an initial set of tuning/calibration parameters;
calculating family turbo-machinery quantities based on the initial set of
tuning/calibration parameters;
comparing the calculated family turbo-machinery quantities with measured
quantities and calculating a first error between the calculated family quantities and
the measured quantities;
calculating a second error between the initial set of tuning/calibration
parameters and default values of the turbo-machine variables;
forming a modified objective function that includes both the first and second
errors;
during an iterative process, varying the initial set of tuning/calibration
parameters in such a way that the final set of tuning/calibration parameters is found
and the final set of tuning/calibration parameters achieves (1) a best fit between the
family of turbo-machinery quantities and the measured quantities, and (2) a smooth
transition for the final set of tuning/calibration parameters from one member to
another member of the family; and
storing in a database the final set of tuning/calibration parameters for the
family.
2. The method of Claim 1, wherein the initial set of tuning/calibration parameters
includes either one set of default parameter values or tuning/calibration parameter
values of other turbo-machineries from a similar family as the new turbo-machinery,
or modified tuning/calibration parameter values with an allowed deviation from the
default parameter values.
3. The method of Claim 1 or Claim 2, wherein a tuning/calibration parameter is
smooth when a first derivative of the tuning/calibration parameter relative to a flow
coefficient is continuous for the entire family.
4. The method of any preceding Claim, wherein the measured quantities are
measured for existing turbo-machineries of the family.
5. The method of any preceding Claim, wherein the first error is a root mean
squared (RMS) of a sum of normal distances between (i) each calculated family
turbo-machinery quantity and (ii) a corresponding measured quantity.
6 . The method of any preceding Claim, wherein the second error is weighted
when added to the first error.
7 . The method of any preceding Claim, wherein the final set of tuning/calibration
parameters includes one or more of two coefficients on an inlet flow, one coefficient
of an impeller exit flow angle, a critical Mach number, one coefficient on a flow
separation, one efficiency coefficient and one blockage coefficient.
8. The method of any preceding Claim, wherein the new turbo-machinery is a
centrifugal compressor having plural stages, an impeller, a diffuser, and an exit
system.
9. The method of any preceding Claim, wherein the turbo-machinery quantities
include one or more of a polytropic efficiency, polytropic head, work coefficient,
pressure ratio, surge, and choke limits.
0. The method of any preceding Claim, further comprising:
applying a differential evolution genetic algorithm for minimizing the modified
objective function.
1. The method of Claim 10, further comprising:
randomly generating the initial set of tuning/calibration parameters.
12. The method of Claim 10, further comprising:
applying a simplex-based optimization method for minimizing the modified
objective function.
13. The method of any preceding Claim, further comprising:
using a set of tuning/calibration parameters of the family to determine the final
set of tuning/calibration parameters for the new turbo-machinery.
14. The method of any preceding Claim, further comprising:
determining the final set of tuning/calibration parameters for a design point
and off-design conditions.
15. A design apparatus for determining a final set of tuning/calibration parameters
for a new turbo-machinery, the design apparatus comprising:
an interface configured to input an initial set of tuning/calibration parameters;
and
a processor connected to the interface and configured to,
calculate family turbo-machinery quantities based on the initial set of
tuning/calibration parameters;
compare the calculated family turbo-machinery quantities with measured
quantities and calculate a first error between the calculated family quantities and the
measured quantities;
calculate a second error between the initial set of tuning/calibration
parameters and default values of the turbo-machine variables;
form a modified objective function that includes both the first and second
errors;
during an iterative process, vary the initial set of tuning/calibration parameters
in such a way that the final set of tuning/calibration parameters is found and the final
set of tuning/calibration parameters achieves (1) a best fit between the family of
turbo-machinery quantities and the measured quantities, and (2) a smooth transition
for the final set of tuning/calibration parameters from one member to another
member of the family; and
store in a database the final set of tuning/calibration parameters for the family.
16. The design apparatus of Claim 15, wherein the initial set of tuning/calibration
parameters includes either one set of default parameter values or tuning/calibration
parameter values of other turbo-machineries from a similar family as the new turbomachinery,
or modified tuning/calibration parameter values with an allowed deviation
from the default parameter values
17. The design apparatus of Claim 15 or Claim 16, wherein a tuning/calibration
parameter is smooth when a first derivative of the tuning/calibration parameter
relative to a flow coefficient is continuous for the entire family.
18. The design apparatus of any of Claims 15 to 17, wherein the measured
quantities are measured for existing turbo-machineries of the family.
19. The design apparatus of any of Claims 15 to 18, wherein the first error is a
root mean squared of a sum of normal distances between (i) each calculated family
turbo-machinery quantity and (ii) a corresponding measured quantity.
20. A computer readable medium including computer executable instructions,
wherein the instructions, when executed, implement a method for automatically
determining a final set of tuning/calibration parameters for a new turbo-machinery,
the method comprising:
inputing an initial set of tuning/calibration parameters;
calculating family turbo-machinery quantities based on the initial set of
tuning/calibration parameters;
comparing the calculated family turbo-machinery quantities with measured
quantities and calculating a first error between the calculated family quantities and
the measured quantities;
calculating a second error between the initial set of tuning/calibration
parameters and default values of the turbo-machine variables;
forming a modified objective function that includes both the first and second
errors;
during an iterative process, varying the initial set of tuning/calibration
parameters in such a way that the final set of tuning/calibration parameters is found
and the final set of tuning/calibration parameters achieves (1) a best fit between the
family of turbo-machinery quantities and the measured quantities, and (2) a smooth
transition for the final set of tuning/calibration parameters from one member to
another member of the family; and
storing in a database the final set of tuning/calibration parameters for the
family.