The design of a centrifugal compressor, as any other industrial
equipment, is a specific process that involves a variety of disciplines.
The most relevant aspect is the level of interconnection between the
various technical features, to the point that iterative design processes are
on the agenda of every engineer and designer. These processes can be
implemented within the single component of the design’s characteristic
or within the same project.
The incredible scenario of available software helps creating easy
connections and data exchange and is also automating most of the
iterative processes.
Optimization is a now growing process supporting design activities. An
interesting perspective offered by optimization is the possibility, within
the same analysis, to connect various design aspects into a single “box”
to achieve a unique objective. This objective is actually shared by all
the technical features involved and that are represented by the different
engineering disciplines.
Several different centrifugal compressor challenges can be faced during
design. Nevertheless, the dimension of the problem can be easily reduced
through proper evaluation of subsystems and interfaces among them.
Once a design objective is identified, it is possible to use optimization
techniques to speed up the gathering of information.
For example it is possible to minimize/maximize each stage independently
and then moving on to the optimization of the assembly. RSM (response
surface methods) can be used to get the design space behavior (i.e.
stress distribution under different loads) or compressor maps. Another
interesting approach is the statistical one, which allows an appreciation
of the impact that one design parameter change can have on the others.
At the beginning of the design activity, identifying the objectives and
the interaction between the stages/components of interests becomes
relevant in order to establish the correct routine and prioritization of
analyses needed.
As when building a house, the foundations can be defined as the design
process (see Fig. 1): it is possible to add a brick (functional block) at
each step. The various optimizations phase can be connected one
another in order to pass information and to refine the entire design. In the
compressor stage design, the process identified is useful to decide the
parameters that contribute to the important design features: efficiency,
reliability, manufacturability, range of functioning and cost.
The workflow also presents connections with other design aspects: the
Multidisciplinary block, not expanded in this case, can be integrated with
any of the green ones, to any level of detail.
Breaking down the process to the ground level allows the optimization
of each component individually, so that when the full machine is put
together the optimization can be done on the process and interfaces,
eventually taking care of refining the components’ design.
In Fig. 2 a workflow is represented dedicated to identifying the best
possible diffuser within a stage design (that includes an inlet, an impeller and a diffuser). The design has been segmented to study and define
some of the diffuser’s parameters. modeFRONTIER is the software used
to perform the optimization task. In the software workflow two main nodes
are present (where a node identify a software and/or process phase and/
or activity). The first node (Concepts NREC) manages design variables
and second one (Ansys) is used to run computational fluid dynamics
(CFX in the specific). In the first optimization the variable to optimize is
just one. It is the first block needed to build the full process.
PilOPT has been chosen as the algorithm to find the optimum even
if it is a single variable problem because it is a simple design space
with few input variables. This algorithm allows the quick search of the
best solution. With these results it is possible to launch a statistical
analysis to fully understand the impact
of each input variable on the output one.
It is then the designer’s choice whether
to refine the optimization by choosing a
Simplex algorithm taking into account
statistical results, or to move on to the next
design step, maybe integrating the stress
evaluation and the definition of the best
fillet radii around the vane.
This process can be followed for each and
every variable and/or component used
to design a multistage compressor. At this point, the structure of the
workflow can be the same as Fig. 2, where the geometrical and the Ansys
node include multiple stages. The optimization process can follow the
same criteria in order to maximize and/or minimize the relevant variables.
In case of a complex workflow or a long computational time, the RSM
(Response Surface Method) can improve to speed up the process. Before
accessing to this tool, it is fundamental to have a reasonable number of
DOE (Design of Experiments) or test cases to use as database. RSM is
very powerful but potentially dangerous. It calculates the results based
only on the amount of historical data it has, so it is important that this
history includes all the areas of the design space (so algorithms which
scan the entire design space are preferable for generating the test cases).
For example, a 2 stage-compressor with 1 output and 9 input variables
using an algorithm that generates 1665 cases needs 8325 hours of
computational time running on 48 CPUs. With RSM and a reasonable
number of DOE solutions, the entire space can be scanned and calculated
in 2 minutes and 5.5 seconds.
At this point, a judgment has to be made in the results evaluation. Good
engineering practice and final design objective guide the selection of
results of interest and, if needed, the decision to run the full case. From an entire workflow perspective, RSM helps managing large or complex
system, allowing the designer to gather the necessary information in a
reduced amount of time, which is valuable from both project and timeto-
market perspective.
RSM can have another interesting use, due to its own features. It allows
the calculation of a large design space anchored to a good database
and can be used to generate maps. It is sufficient to define the problem
(correct inputs, output and supporting variables), run DOE or collect test
data, then train and run RSM. The result table includes all the necessary
information to create maps as happens during a standard CFX simulation.
Starting from a complex model the possibility to run in few minutes (i.e.
example above) has allowed the generation of a
pressure-power map (see Fig. 3), that is used
to verify the entire range of operation of the new
design.
This methodology can be successfully used to
analyze the design space in any context, but it is
interesting when physical quantities are among
the input variables because it is possible
to observe trends for certain phenomena. It
is possible to characterize the compressor
characteristic curve at different pressure, or
inlet conditions, early in design phase in order to change and manage
properly the geometrical design variables. For example, the search
of stall or surge limits before running a transient analysis of the entire
stage can be conducted observing the results of the RSM. The amount
of data available allows the selection of critical areas, and supports the
possibility to vary some parameters in order to evaluate the impact of
changes before final simulation and design assessment are conducted.
Using all the optimization techniques illustrated the designer has the
freedom to investigate alternative solutions minimizing the computational
cost, including inputs coming from different disciplines (like cost) that
typically are known at the end of the design process, and to evaluate a
design space broader than what was used to. The tools used in the design
process can support the various design goals provide that geometrical
and physical quantities are in a parametric a process is defined
and input/output variables are defined.
