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By Michael R. Ruith and Franklyn J. Kelecy, Fluent Inc.
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The impeller design for the Eckardt Rotor O, showing static
pressure contours on the surfaces of the compressor for a
mass flow rate of 6 kg/s and a rotor speed of 14,000 rpm
CFD has been used extensively over the
past three decades to predict the performance
of compressors for both single
and multiple blade row configurations. Today,
with the power of modern computers, steady-state
solutions are carried out on a routine basis,
and can be considered as part of the design
process. As CFD algorithms and software have
continued to be developed and refined, it remains
essential that validation studies be conducted
in order to ensure that the results are both
sufficiently accurate and can be obtained in
a robust and predictable manner.
Surface mesh on spinner, hub, blade and diffuser for a single
passage with the shroud removed; the meshed volume is
outlined by the blue lines
One of the most widely-used validation
cases for compressors is the study carried out
by Eckardt1,2,3 for a centrifugal compressor
|impeller, also known simply as the Eckardt rotor.
Eckardt published a series of papers in the 1970s
discussing experiments conducted on two 20-
blade centrifugal compressor rotors, known as
Rotor O and Rotor A. The resulting impeller
performance maps as well as the investigation
of local effects have been used extensively over
the years to test the accuracy and robustness
of CFD codes for turbomachinery.
FLUENT 6 has a long history of application
in a variety of industries, including turbomachinery,
and thus has been validated for a wide
range of geometries and flow conditions.
However, validation studies for turbomachinery
have mostly been limited to the calculation
of a single operating point or a speed line.
With the advent of robust and accurate solution
techniques in FLUENT 6.2, it was decided
that a more extensive validation study should
be conducted than had been attempted in the
past. Specifically, it was desired to carry out
a series of calculations for multiple speed lines,
where each speed line was analyzed from choke
to near stall. The Eckardt centrifugal compressor1
was deemed to be well suited for this study
given the availability of data for a wide range
of conditions with which the numerical predictions
could be compared.
The compressor consists of a centrifugal
impeller with 20 radially ending blades,
together with a spinner attached to the hub.
The inner and outer intake diameters are 90
and 280mm, respectively, while the impeller
tip diameter is 400mm. The blade camber lines
have ellipsoidal shapes in cylindrical sections.
The vaneless diffuser has a constant flow area
to radius ratio of two. Experimental tests revealed
that the tangential compressor outlet produced
a severe distortion of the flow field, with a strong
asymmetry of the flow field within the diffuser1.
In an attempt to avoid these effects, Eckardt
placed an additional throttle ring near the outlet
of the diffuser. This ring substantially constrained
the maximum mass flow, causing the
compressor to choke early. However, the distortion
of the flow field in the remaining portion
of the compressor map was reduced to
an insignificant level. This observation is
important because in the present study, the throttle
ring was not modeled, so the choke line defined
in Eckardt’s compressor map is not applicable.
The geometry and mesh were generated
using GAMBIT. Assuming 18-degree rotationally
periodic conditions, only a single blade passage
was modeled. The flow volume extends
from the inflow position 200mm upstream of
the leading edge of the blade, through the blade
passage, and finally into the vaneless diffuser
section to the outlet placed at a radial position
of 350mm. Due to the sharp angle at the
axis, triangular elements were chosen for the
surface mesh on the spinner close to the center.
These were connected to hexahedral elements
in the remainder of the spinner region
through a conformal interface. In order to adequately
resolve the leading edge of the blade
as well as the flow channel, hexahedral elements
and a non-conformal interface were used
for the remainder of the domain. This choice
also permitted a lower total cell count by reducing
the resolution upstream of the rotor. The
final hybrid mesh consisted of approximately
500,000 elements.
Since the stationary shroud and diffuser surfaces
were surfaces of revolution, a single rotating
frame was employed for the entire flow
domain, thus permitting the use of steady-state
modeling procedures. The fluid was assumed
to be air, modeled as an ideal gas. The turbulent
flow was modeled with the realizable
k-e model, using a non-equilibrium, (pressure
gradient sensitized) wall treatment. The
implicit, coupled, density-based solver was used
for the flow calculations, since high subsonic
Mach numbers were expected in the blade passage
(especially close to the trailing edge).
As the main goal of the present investigation
was to reproduce the entire
compressor map of the Eckardt rotor
from choke to surge, the specification
of inlet and outlet boundary conditions
required some additional attention. For
compressors, the total pressure, total
temperature, mass flow, and flow angles
are typically known for the inlet of the
machine, whereas the outlet static pressure
is unknown and a desired result
of the simulation. However, a well-posed
inlet and outlet boundary condition set
for compressible flows requires knowing
the total conditions and flow angles
at the inlet and a static pressure at the
outlet. To resolve this problem, two
approaches were adopted to cover the
range of compressor operating conditions.
For the higher flowrates (up
to choke), a conventional pressure inlet
was used in conjunction with a pressure
outlet augmented with the “mass
flow outlet” option. The mass flow outlet
adjusts the exit pressure such that
a target mass flow rate (prescribed by
the user) is obtained at convergence.
At lower mass flow rates (near the
approximate surge point), a mass flow
inlet (with a mass flux profile prescribed
using a user-defined function) paired
with a conventional pressure outlet was
used. This approach permitted stable
solutions to be obtained at much lower
flowrates than was possible with the
traditional pressure inlet.
The solutions were initialized using
the unstructured “full approximation
scheme”, or FAS, initialization algorithm
which has been recently implemented
in FLUENT 6.2. This procedure makes
use of a series of coarse grid levels (based
on multigrid groupings) upon which
flow solutions are obtained, starting from
the coarsest mesh, interpolating the
solution to the next finest mesh, and
so on until the finest level is reached.
Calculations initialized in this manner
can employ much higher Courant numbers
than usual, thereby reducing the
number of (fine grid) iterations
required to reach convergence.
Moreover, as the solutions on the coarse
meshes are inexpensive, the amount
of CPU time required to perform FAS
is relatively small. In the present
study, the FAS initialization capability
provided a speed increase of about a
factor of five for most cases.
Comparison of the experimentally (blue) and numerically (red) obtained compressor map, showing good agreement between the plotted surge and choke lines with the throttle ring; the difference is greater in the choke region without the throttle ring
Vectors of relative velocity, colored by the local Mach number for choke
condition at n = 16,000 rpm; the perspective view, showing the corner
between blade suction side (left) and shroud (right) illustrates strong flow
separation, in line with experimental results
Three sets of speed line calculations
were performed to examine the flow
through the compressor at rotational
speeds of 12,000, 14,000, and 16,000
rpm. The flow rate was varied from choke
to surge for each speed. Both the total
pressure ratio across the impeller and
the isentropic efficiency were used to
assess the results. A comparison of the
present computations with the compressor
map reported by Eckardt1 show
that the CFD results are in good agreement
with the Eckardt compressor map.
It should be noted that since the Eckardt
experiments were performed using a
throttle ring in the diffuser, the choke
point for the numerical simulations
extends beyond the experimental
choke point indicated in the plot.
These results demonstrate that
modern CFD codes can be employed
to study complex flows in turbomachinery
over a wide range of operating
conditions. Moreover, the efficiency
and robustness of these kinds of calculations
can be significantly enhanced
through techniques like FAS initialization
and the mass flow outlet boundary
condition.
References:
- D. Eckardt, Instantaneous Measurements
in the Jet-Wake Discharge Flow of a
Centrifugal Compressor Impeller. J. Eng.
Power, 337, 1975.
- D. Eckardt, Detailed Flow Investigations
Within a High-Speed Centrifugal
Compressor Impeller. Trans. ASME,
September, 1976.
- D. Eckardt, Flow Field Analysis of Radial
and Backswept Centrifugal Compressor
Impellers Part I: Flow Measurements using
a Laser Velocimeter. In Performance
Prediction of Centrifugal Pumps
and Compressors, edited by S.
Gopalakrishnan, P. Cooper, C. Grennan,
and J. Switzer, ASME, 1980.
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