Volume 23
http://acousticalsociety.org/
169th Meeting of the Acoustical Society of America
Pittsburgh, PA
18-22 May 2015
Physical Acoustics: Paper 1pPA7
Understanding the fluid dynamics associated with
macro scale ultrasonic separators
Kedar C. Chitale
FloDesign Sonics Inc., Wilbraham, MA, [email protected]
Bart Lipkens
Department of Mechanical Engineering, Western New England University, Springfield, MA,
[email protected]
Walter Presz, Jr.
FloDesign Sonics Inc., Wilbraham, MA, [email protected]
Olivier Desjardins
Department of Mechanical and Aerospace Engineering, Cornell University, Ithaca, NY,
[email protected]
Acoustic standing wave fields are widely used in MEMS applications to separate micron sized particles
from fluids. However, the use and understanding of macro scale ultrasonic separators are still limited and
challenging. New macro-scale, ultrasonic separators are presented that use multidimensional standing
waves to trap and generate tightly packed clusters of suspended particles which continuously grow and
drop out of a flowing fluid mixture. Typical flow Reynolds numbers are less than 50, particle
concentrations up to 20% and ultrasonic standing wave fields at frequencies of 1-3 MHz and acoustic
pressure amplitudes of about 1 MPa. At such small Reynolds numbers the flow is dominated by shear
forces and the drag on clumps of particles is significantly lower than Stokes’ drag on a single particle.
The fluid dynamics associated with these systems is extremely complex due to the coupling between the
fluid flow field, suspended particles, and acoustic radiation forces. This work discusses the key physics
involved and explains our current understanding of operation of macro scale acoustic separators. The
status of CFD (Computational Fluid Dynamics) efforts to predict the flow fields and particle clustering in
such systems is presented and compared to experimental results.
Published by the Acoustical Society of America
© 2015 Acoustical Society of America [DOI: 10.1121/2.0000070]
Received 18 June 2015; Published 29 July 2015
Proceedings of Meetings on Acoustics, Vol. 23 045004 (2015)
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K. C. Chitale et al.
Understanding the fluid dynamics associated with macro scale ultrasonic separators
INTRODUCTION
Ultrasonic separators use acoustic standing waves to separate dispersed particles from a fluid medium.
MEMS (Micro Electro Mechanical System) ultrasonic separators have been widely researched and
developed for applications such as cell sorting and size differentiation. Most of these systems rely on using
half or quarter wavelength acoustic chambers which at frequencies of a few MegaHertz are typically less
than a millimeter in thickness, and operate at very slow flow rates, e.g. µL/min. Such systems are not
scalable since they benefit from extremely low Reynolds number, laminar flow operation, and require
minimal fluid dynamic optimization. New macro-scale, ultrasonic separators [4-7], wherein a
multidimensional standing wave generates tightly packed clusters of suspended fluid or particulate which
continuously drop out of a flowing fluid mixture due to gravity forces are quite different. These systems
are much larger with high flowrates that require significant fluid dynamic optimization to function properly.
Figure 1 presents such an acoustic wave separator system. Typical flow Reynolds numbers are less than 50,
particle concentrations up to 20%, ultrasonic standing wave fields at frequencies of 1-3 MHz and acoustic
pressure amplitudes of about 1 MPa. The system shown has a 3”x3”x3” acoustic chamber and the acoustic
standing wave field is setup inside the cube with a 2 MHz PZT-8 transducer. This system operates
continuously at near 90% clarification for a 1.5% yeast mixture with flowrates of about 270 ml/min, and a
packed cell mass of >50% in the concentrated cell stream.
Clarified
fluid
Pump in
Pump out
Cell-fluid
mixture
Concentrated
cells
Acoustic chamber
FIGURE 1. An acoustic wave separator system which takes a cell-fluid mixture as input and outputs
clarified fluid and concentrated cells
The same system has been operated effectively for the clarification of protein from a CHO cell/protein
mixture. Such applications are important in the advancement of the pharmaceutical industry. For these
applications, multiphase effects become important at relatively low volume fractions, and play a dominant
role in the operation. A complete understanding of the mixture distribution throughout the acoustic standing
wave section, particle trapping and clustering, and gravitational separation of particles from the carrier fluid
is key to system optimization. The fluid dynamics associated with macro-scale ultrasonic acoustic
separators is discussed in the following sections.
MULTI-DIMENSIONAL ACOUSTIC STANDING WAVE
New macro-scale, ultrasonic separators work by using multidimensional standing waves to generate
tightly packed clusters of suspended fluid or particulate which continuously grow and drop out of a flowing
fluid mixture due to gravity. The flow in such systems is typically perpendicular to the primary direction
of the standing wave. Figure 2 shows a general picture of an acoustic separator system showing the working
mechanism. A fluid with particulate in suspension, continuously flows into an acoustic chamber where a
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K. C. Chitale et al.
Understanding the fluid dynamics associated with macro scale ultrasonic separators
piezoelectric transducer and reflector system are designed to generate a multi-dimensional acoustic standing
wave perpendicular to the flowing medium. The acoustic radiation forces on the particulate cause
particulate trapping, clustering and continuous drop out due to gravity as shown in Fig. 2. Figure 3 shows
a series of time-sequenced photographs of yeast movement in a multi-dimensional, acoustic standing wave.
FIGURE 2. Schematic of an acoustic separator system
The lighter color represents high yeast concentration. Figure 3(a) represents a uniform yeast mixture as it
enters the acoustic chamber. As the mixture flows through the acoustic chamber, particles in suspension
experience a strong axial force component in the direction of the standing wave. Since this acoustic force
is perpendicular to the drag force, it quickly moves the particles to pressure nodal planes or antinodal planes
(i.e. depending on the contrast factor of the particle) as shown in Fig. 3(b). The lateral acoustic radiation
force, which is in the flow direction, acts to move the particles towards each other resulting in an
agglomeration or clustering as seen in Fig. 3(c). The lateral acoustic radiation force component also acts to
stop and trap the particles, by overcoming Stokes’ drag, for such clusters of particles to continually grow
and then drop out of the mixture due to gravity. Therefore, the magnitudes of axial and lateral forces are
important.
(a)
(b)
(c)
FIGURE 3. Movement of yeast particles inside an acoustic standing wave in a stationary system. (a)
t=0 s, uniform distribution of yeast particles (b) t=0.01 s, particles move to nodal planes by action of
axial radiation forces (c) t= 0.1 sec, particles form clusters (white) by action of lateral radiation forces.
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K. C. Chitale et al.
Understanding the fluid dynamics associated with macro scale ultrasonic separators
The multi-dimensional acoustic standing wave needed for such operation is obtained by driving a
transducer at a frequency that both generates the acoustic chamber standing wave and excites a fundamental
3D vibration mode of the transducer crystal as shown schematically in Fig. 4 (a). The figure shows crystal
vibration patterns by exciting it at a frequency close to one of its natural frequencies of vibration. The plate
(b)
(a)
FIGURE 4. (a) 3D vibration pattern of crystal, (b) Multi-dimensional wave causing particle clustering
at nine specific locations within the trapping planes, photo taken from glass reflector
3D mode of vibration of the crystal is carried by the acoustic standing wave across the fluid in the chamber
all the way to the reflector and back, resulting in a multi-dimensional standing wave. Three dimensional
force gradients are generated in every nodal plane of the standing wave. These three dimensional force
gradients stop the particles and move them to cluster locations in the plane. Multiple particle clusters are
formed along lines in the axial direction of the standing wave as shown in the photograph of an operating
system in Fig. 4(b).
Figure 5 shows a free body diagram of a particle in suspension while in the acoustic chamber. The X
direction is the axial direction of the acoustic standing wave. The flow through the acoustic chamber, as
described in this paper, is in a lateral or Y direction. Due to this, strong lateral acoustic radiation forces are
needed to stop and trap the particles with respect to the flow by overcoming the viscous drag force. In
addition, lateral forces are responsible for creating tightly packed clusters of particles. Therefore, particle
separation depends on generating a multi-dimensional standing wave that can overcome the particle drag
force as the mixture flows through the acoustic chamber and generate tightly packed clusters that fall out
due to gravity. There are several formulations for radiation pressure experienced by a sphere inside an
acoustic field [1, 2]. Gor’kov’s model [1] is for a single particle in a standing wave and assumes that the
particle size is much less than the wavelength of the standing wave (Rp<<λ). This model cannot be used for
particle clusters, which are encountered in the described macro system, with size comparable to the
wavelength of the standing wave. A more complex and complete model for acoustic radiation forces
presented by Ilinskii and Zabolotskaya [2], which is not limited by particle size, was used.

Uf

FD

FAy

FAx
Transducer

g

FA

FB
Reflector
Y
Z
X
FIGURE 5. Forces on a particle inside a standing wave
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K. C. Chitale et al.
Understanding the fluid dynamics associated with macro scale ultrasonic separators
All these forces assume a spherical particle shape. These forces include acoustic radiation force (Eq. 1),
viscous drag force (Eq. 2), and buoyancy or gravity force (Eq. 3), as given by following equations.

nmax n

FAz  iKk 2  

(n  m  1)(n  m)!
An*  An1  2 An* An1 anm* anm1  c.c.
(
2
n
1
)(
2
n
3
)(
n
m
)!



n 0 m   n



FD  6 f R P U f  U P


4
FB   RP3  p   f g
3


… (1)
… (2)
… (3)
Detailed description of Eq. (1) can be found in [3] and is beyond the scope of this paper. Both gravity
and acoustic forces are proportional to particle volume, or the cube of the radius and Stokes’ drag force is
proportional to the radius. Figure 6 presents the different forces acting on the particles in suspension as a
function of particle size. Two particle sizes are of particular interest, Rc1 and Rc2. Rc1, shown in Fig. 6, is a
typical particle size where acoustophoretic separation devices are used. At this size, the acoustic radiation
force and Stokes’ drag force are almost equal in magnitude. The gravity force is much smaller and can be
neglected. Rc2 on Fig. 6 represents a particle size where the acoustic forces drop off dramatically, and
gravity forces are significantly larger than drag forces. If one assumes a particle cluster can be approximated
by a single, spherical shape surrounding the cluster, then the cluster of size Rc2 will naturally drop out of
suspension due to gravity forces. But for this to happen, the lateral component of the acoustic radiation
force has to be the same order of magnitude as the particle cluster drag. Only then, can the acoustic radiation
forces stop the particles and allow the clusters to grow as described. This raises questions on the physics of
clustering, and how the macro-scale system works.
Rc2
Rc1
FIGURE 6. Acoustic radiation force, drag force and gravity force versus particle cluster size
CLUSTERING AND AGGREGATION
One of the major, observed features of our acoustic filtration method is the ability to clump or cluster
dispersed particles. These clusters form because of low flow Reynolds numbers (i.e. of order 1), based on
the particle diameter. At such low Reynolds numbers, inertial forces become negligible and viscous forces
are dominant throughout the flow. As a result, the forces which act on the clusters are very much different
than Stokes’ drag on a single particle. When the particles are spaced closely, high shear forces prevent any
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K. C. Chitale et al.
Understanding the fluid dynamics associated with macro scale ultrasonic separators
significant flow between the particles. The flow resistance around the clusters is much lower than the shear
resistance through the cluster, and the fluid trapped between the particles in the cluster is approximately
stationary. Stated differently, the fluid flows around a particle cluster rather than through it.
A theoretical model for this shielding effect was
developed and is given by Eq. (4), which gives an
approximate ratio of the drag force on a particle
cluster over the sum of the drag forces on all
d
D
individual particles (Stokes’) inside the cluster.
FD 1  d 
  
Fd   D 
2
… (4)
Where ϕ is the concentration of small spheres inside
the big cluster, FD is the drag force on the big cluster
of diameter D, and Fd is the Stokes’ drag force on a
single sphere of diameter d. This is a simplified model which assumes that fluid inside the cluster is
approximately stationary. This model shows that the drag of particle clusters is much smaller than the sum
of the Stokes’ drag of all the particles contained in the cluster. This model was compared to CFD
(Computational Fluid Dynamics) results and is presented in Fig. 8. The CFD model consists of an assembly
of 27 spheres suspended inside a moving fluid. Inter-sphere distance is varied equivalent to different
concentrations of the assembly. Figure 8 shows the results of the CFD model compared to that of theoretical
model above. Drag forces on representative particles inside the assembly of spheres are plotted such as
particle facing the flow directly, particle in the middle of the cluster, particle facing away from the flow etc.
The Reynolds number based on particle size and chamber velocity is 0.01, which is comparable to macroscale acoustic separator systems. The theoretical model agrees very well with computation at all
concentrations, and verifies the assumptions made. The CFD particle cube shape is seen to provide a flow
blockage very similar to that of a larger, spherical particle as seen by the color coded results for flow
velocity. The results show that drag on particles inside a cluster can be 1/10 of the Stokes’ drag, and even
FIGURE 7. Sketch of a typical tightly packed
cluster of particles
FIGURE 8. Normalized drag for clusters of
spheres vs. concentration
FIGURE 9. 27 sphere assembly used in
simulations and velocity prediction
less at high concentrations. This means once particles are trapped and clumped it becomes easier to hold
them together. Also, as particles are brought in planes by axial radiation forces, drag on individual particles
is reduced and the lateral force required to stop and trap particles becomes lower. This is an important result
which explains the excellent trapping seen even with high flow velocities in macroscale separators.
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K. C. Chitale et al.
Understanding the fluid dynamics associated with macro scale ultrasonic separators
Particle Cluster Shape Optimization
The particle clusters that are formed due to acoustic radiation forces, drop into a collection chamber due to
gravity forces. For the best operation of the system, at maximum flow rate, the particle cluster drop velocity
has to be optimized. This raises a question as to the optimal shape of particle clusters. What shapes give us
the lowest drag and therefore the highest terminal drop velocity? At low Reynolds numbers (Re~1)
cylindrical shapes are seen to have significantly lower drag coefficients than spheres [8]. Furthermore, a
cylinder can carry significantly more particles for a given projected area. This means a cylindrical particle
cluster will have higher gravity forces and lower resistance drag than a spherical particle cluster. A
cylindrical particle cluster will drop out of the fluid faster than spherical clusters. Therefore, it is important
to choose an electrical signal drive frequency and shape for the acoustophoretic separation system that gives
the best cylindrical-like cluster generation for drop out. The cylindrical-like clusters are caused by driving
λ/2
D
FIGURE 9. Cylindrical clusters formed inside the acoustic chamber, in a “hockey puck” configuration
where λ is the wavelength of the standing wave
the crystal near its natural vibration mode causing lines of low pressure nodes through the standing wave
in the axial direction, unlike the traditional collection planes of dispersed particles [9]. Figure 9 illustrates
the hockey puck pattern configuration of cylindrical clusters seen in macro scale ultrasonic separators. Tests
have shown that four to sixteen cylindrical like particle clusters per square inch of crystal provide superior
separation and gravity collection performance. The axial acoustic forces associated with the standing wave
will keep the cylindrical clusters intact, meaning the hockey puck shapes are retained even when the clusters
are falling. This assures rapid dropping with high terminal velocities. The cluster terminal velocity (VD) is
obtained by equating the cluster drag and gravity forces, assuming the lateral acoustic force is negligible
when they start dropping, which is supported by Eq. (1). The resulting equation for a cylindrical cluster is
presented in Eq. (5). This prediction is a first order approximation, and assumes the following: the
cylindrical cluster falls as a cylinder, the lateral dimension of the cluster is directly related to the lateral and
axial radiation force ratio, and the thickness of the hockey puck cluster is primarily determined by the
acoustic standing wave frequency. These assumption were primarily developed through experimental
observation. Analytical predictions using Eq. (5) were compared to experimentally observed values from
video data, and both methods predict a drop out velocity on the order of 1 cm/sec. This is significantly
faster when compared to chamber flow velocities. As a result, the mixture flow through velocity in the
acoustic chamber, for a uniformly distributed flow, should have minimal detrimental effects on cluster drop
velocities.
 p
 D
C DVD2   
 1 g

 4
 f

Proceedings of Meetings on Acoustics, Vol. 23 045004 (2015)
…(5)
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K. C. Chitale et al.
Understanding the fluid dynamics associated with macro scale ultrasonic separators
INLET FLOW
To get the best efficiency out of the acoustic system, a uniform distribution of particles is required in the
acoustic chamber, i.e., mixture should be spread across the entire acoustic chamber. The flow velocities
should be nearly constant to allow particle trapping. However, when working with suspensions of volume
fraction greater than 1%, uniform flow is difficult to achieve. Working with particles with higher density
than water, like cells, and the inlet flow in the horizontal direction, the particles tend to cause the mixture
to “fall down” before reaching the acoustic chamber which is filled with predominantly clarified fluid. This
was evident in the horizontal assembly shown in Fig. 10, where a diffuser inlet was used in an effort to get
lower linear velocities in the acoustic chamber. The figure shows the mixture dropping before entering the
acoustic chamber. The mixture has a higher density than the clarified fluid. Therefore, the fluid mixture
(a)
(b)
(c)
FIGURE 10. 3% yeast suspension flowing horizontally in a diffuser, inlet Re=250, (a) shows flow
developed with yeast suspension dropping down, (b) displays CFD predictions of a similar setup
plotting volume fraction of yeast particles, (c) shows velocities obtained through CFD at a vertical slice
confirming 10 times larger speed near the bottom wall than for uniform flow.
drops dramatically (i.e. at a particle Reynolds number of ~1, inertial effects are negligible and gravity forces
on the fluid become dominant). The drop results in the mixture flowing through the bottom of the chamber
in the horizontal direction at very high velocities driven by gravity forces. The lower density, clarified fluid
is pushed to the chamber top and flows backwards towards the inlet entrance due to conservation of mass
flow. This means that any particle clusters formed on top in the acoustic chamber will not fill and drop. It
also means the lower clusters will be disrupted by extremely high flow velocities. Also, the peak flow
velocities are 10 times higher than what would be expected if particles were uniformly distributed. This in
turn increases local drag on particles and makes them harder to trap. At such low Reynolds numbers and
significant differences in density, inlet wall shapes cannot solve this problem. The mixture flowing
horizontally will not follow inlet contouring as a result of gravity forces being dominant on the fluid.
Figure 11 presents a symmetrical, dual dump, plenum inlet configuration designed to eliminate these
flow problems. A slot, or lines of holes, are placed above the chamber bottom in the plate separating the
dump plenum and acoustic chamber. Mixture flows into the two plenums as shown, and then enters the
acoustic chamber through the slots. The plenum is used to eliminate flow pulsations and flow non-
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K. C. Chitale et al.
Understanding the fluid dynamics associated with macro scale ultrasonic separators
uniformities. The slots are designed to bring the heavier mixture flow into the acoustic chamber above the
Flow out
Line of
symmetry
Plenum
Streamlines
Flow
in
Flow
in
Flow slots
Flow slots
(b)
(a)
Concentrate out
(c)
FIGURE 11. (a) Picture of an experimental setup, (b) Sketch detailing idea behind flow symmetry
and uniformity, (c) CFD predictions of volume fraction of cells showing near uniform rise of cells in
the chamber
chamber bottom, but below the first row of nodal clusters. This minimizes any collector disturbances set
up by the inflow. The acoustic chamber flow direction is up, and opposes gravity. The system is symmetric
about the symmetry line or plane shown. The symmetry line or plane is aligned with gravity forces. Both
the flow outlet and collector outlet are aligned with the line or plane of symmetry, and the gravity direction.
The steady flow streamlines have to be mirror images about the symmetry line or plane. This symmetry is
extremely important since it assures minimal non-uniformities, minimal circulation, and minimal collector
disturbance. It also maximizes gravity forces in the inlet flow distribution and the particle collection
process. The heavy mixture will come in near the chamber bottom, spread out across the chamber due to
gravity forces, and will fill the chamber with near uniform velocity from bottom to top. Figure 11(c)
presents CFD results for low Reynolds number flow into the dual inlet chamber showing symmetric
streamlines and possibility of uniform flow in this arrangement. Uniform velocity provides the best
separation and collection results since the lateral acoustic forces have to overcome particle drags if the
clusters are to grow and continuously drop out of the chamber. A uniform flow velocity in the chamber
assures that maximum flowrate separation and collection are attained when acoustic forces start to get
overwhelmed by flow drag forces somewhere in the acoustic chamber.
ADVANCED CFD MODELING
The CFD modeling already presented in this paper
makes strong assumptions on the mixture of particles
and fluid. While it is very useful to know bulk
properties of flow predicted by this model, the effect
of acoustic forces, particle clustering, and feedback
from the particle phase on the fluid phase can be
challenging to incorporate in that framework. These
phenomena were modeled with a high fidelity EulerLagrange computational framework in the NGA code
[10], a low-Mach number parallel flow solver. In
order to resolve the relevant length scales associated
Proceedings of Meetings on Acoustics, Vol. 23 045004 (2015)
FIGURE 12. Entering particles get into planes
due to strong axial force (viewed from outlet)
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K. C. Chitale et al.
t=2s
Understanding the fluid dynamics associated with macro scale ultrasonic separators
t=4s
t=6s
t=8s
FIGURE 13. Particles get trapped and start clustering in several locations (viewed from reflector)
with acoustophoretic particle-laden flows while remaining computationally tractable, a mesoscale
formulation based on volume filtering is employed [11]. This description explicitly captures the physics
associated with length scales larger than the individual particles and models the processes at particle scale.
Two-way coupling includes momentum exchange between both phases and the effect of volumetric
obstruction of the fluid by particles. Particle collisions are accounted for using a soft-sphere model. A 3D
simulated, multi-dimensional standing wave acoustic field is generated from COMSOL calculations for a
1”x1” 2 MHz crystal. Depth of water chamber is limited to 0.25” to reduce computational time. That
acoustic field is then read into the NGA solver, and is used to provide the acoustophoretic force on the
particles using Gor’kov’s model [1]. Figure 12 shows particles moving into planes as they enter into the
acoustic field, which is caused by the strong axial forces. Figure 13 shows views at different times with
axial direction of acoustics into the paper. The CFD model naturally captures the clustering of the particles.
This shows significant promise for future system optimization and to improve flow field understanding.
CONCLUDING REMARKS
New macro-scale, ultrasonic separators effectively use multidimensional standing waves to generate
tightly packed clusters of suspended fluid or particulate which continuously grow and drop out of a flowing
fluid mixture. The clusters of particles continuously separate out due to gravity as the lateral acoustic
radiation forces, generated by the multi-dimensional standing wave, cause the clusters to grow rapidly in
size. Typical flow Reynolds numbers for macro-scale separators are less than 50, particle concentrations
up to 20%, ultrasonic standing wave field frequencies of 1-3MHz and acoustic pressure amplitudes of about
1MPa. At such low Reynolds numbers the flow is dominated by shear forces, and the drag on clusters of
particles is significantly lower than the sum of Stokes drag on the particles contained in the clusters. This
allows particle trapping and clustering even at high system flow rates. Therefore, such systems have
numerous potential applications including water purification, cell filtration and the clarification of protein
from a CHO cell/protein mixture. For these applications, multiphase effects also become important at
relatively low volume fractions, and play a dominant role in the system operation. Therefore, vertical flow
direction through the acoustic standing wave along with system symmetry is recommended. This minimizes
flow disturbances set up by gravity or inlet flows. This is important since a uniform velocity distribution
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K. C. Chitale et al.
Understanding the fluid dynamics associated with macro scale ultrasonic separators
through the acoustic standing wave provides maximum system flow rates. Also, low Reynolds number flow
physics show that multi-dimensional standing waves that generate cylindrical particle clusters are critical
to good system performance. Cylindrical particle clusters will drop out faster and carry more particles per
frontal area than other shaped clusters. Preliminary results from advanced CFD simulations show
significant promise for further optimization of macro-scale, ultrasonic separators.
ACKNOWLEDGMENTS
For computational resources, the project used the Computational Cloud for Data Driven Biology at the
Massachusetts Green High Performance Computing Center, with financial support from the Massachusetts
Life Sciences Center. (http://www.mghpcc.org/resources/computer-systems-at-the-mghpcc/c3ddb/)
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