ACADEMIC RESEARCH
COOLING OUT
The next step in understanding the laws of nature: Thermal simulation helps
to design a new generation of magnets for the Large Hadron Collider.
By Slawomir Pietrowicz, Associate Professor, Department of Thermodynamics
Wroclaw University of Technology, Wroclaw, Poland
© 2014 ANSYS, INC.
© CERN
P
hysicists and engineers
are addressing some of
the unsolved questions of
physics using the Large
Hadron Collider (LHC), the
world’s largest and highest
energy particle accelerator. The researchers accelerate particles to high levels of
energy and then create collisions between
them. Considered by some to be one
of the great engineering milestones
of mankind, the LHC’s inner triplet of
superconducting quadrupole magnets is
responsible for focusing particle beams
just before the collision point. The current magnets operate at the limits of wellestablished niobium-titanium (Nb-Ti)
technology. Plans are to replace the existing magnets with niobium-tin (Nb3Sn)
magnets that support higher magnetic
fields. Nb3Sn magnets present many
technical challenges, perhaps the greatest being maintaining the component at
the very low temperatures required for
superconducting conditions. Researchers
use ANSYS computational fluid dynamics (CFD) software to simulate thermal
and mass transfer within potential magnet designs as part of the process to optimize the new generation of LHC magnets.
Developing cutting-edge equipment —
such as the LHC, which will expand
our knowledge of the laws of nature —
requires researchers to push the current
limits of simulation.
The LHC lies in a tunnel 17 miles
(27 kilometers) in circumference and
as mean deep as 328 feet (100 meters)
beneath the French–Swiss border near
Geneva, Switzerland. Since going live in
2008, the LHC already has helped to discover two previously unknown particles:
Chi_b (3P) and a large subatomic particle
called a boson that is now suspected to be
the elusive Higgs boson. The accelerator
was instrumental in recovering the first
LHC interconnection
observations of the decay of the BS meson
particle into two muons.
An upgrade to the LHC is planned for
the next few years. The upgraded accelerator will be called the Super Large Hadron
Collider (SLHC). The upgrade aims at
increasing luminosity of the machine by
a factor of 10, providing a better chance
to see rare processes and improving
Developing
cutting-edge
equipment — such
as the Large
Hadron Collider —
requires researchers
to push the limits
of simulation.
statistically marginal measurements.
Accelerator luminosity is a measure of
the number of particles that pass through
a given area each second multiplied by
their opacity or the ability of a detector to
see them.
NEW APPROACHES TO MAGNET
DESIGN
A superconducting magnet is an electromagnet that consists of superconducting
wire coils. These coils must stay at cryogenic temperatures during operation. At
these low temperatures, the electrical
resistance of the coils drops to near zero,
enabling the wire to conduct very large
currents and generate intense magnetic
fields. The proposed upgrade would subject the inner triplet of superconducting
magnets to higher levels of radiation and
heat than they currently are designed to
withstand. The magnets already operate
at the limits of the Nb-Ti alloy technology
that is responsible for their super-conducting properties, so their replacements
ANSYS ADVANTAGE Volume VIII | Issue 1 | 2014
ACADEMIC RESEARCH
are expected to be made of Nb3Sn alloy,
another superconducting material,
which supports higher magnetic fields
and higher temperatures. The greater
expense and unique properties of Nb3Sn
require new approaches to magnet design
and fabrication that present considerable
engineering challenges.
For proper operation of a superconducting magnet, the coils need to be maintained at temperatures below the point at
which the Nb-Ti or Nb3Sn alloys become
superconducting. The difference between
operating and critical temperatures must
be maintained at a certain level for the
conductors to function properly. To facilitate this, the coils are generally covered
with an insulator and immersed in superfluid helium coolant, which occupies
the spaces between them. In the superfluid state, helium has almost zero viscosity and zero entropy; it is subject only
to its own inertia, so it flows without friction through pores and obstructions. This
keeps any viscous heating due to fluid
flow to a minimum. Heat generated in
the coils flows through the insulation
surrounding the coils to the helium. The
speed of heat loss to the helium is governed by the thermal conductivity of the
insulation and the thermal resistance to
the flow of heat across the helium–solid
boundary.
ADAPTING THE PROBLEM TO CFD
The thermal performance of superconducting magnets cannot be accurately
simulated with off-the-shelf CFD software
because solving the flow of a superfluid
requires six (scalar) equations with independent variables — such as pressure,
temperature, density and two velocity
fields — as opposed to the three equations
used for conventional fluids. Several
researchers have developed custom software to predict thermal performance of
superconducting magnets. However, due
to convergence limitations and numerical instability, these codes are generally
limited to one- or two-dimensional systems with a small number of elements.
Designing a practical Nb3Sn magnet
requires a three-dimensional simulation
with millions of elements.
In the European Union, the development of advanced magnet technology is
currently being coordinated through the
High Field Magnet (HFM) program of the
European Coordination for Accelerator
© 2014 ANSYS, INC.
Model of Fresca2: a) general view with boundary conditions; b) details of geometry and
mesh; c) cross section along z-direction through solid and helium domains
a) Computational domain with boundary conditions for validation model; b) details
of mesh for validation model
Validation of the numerical model against an analytical solution for turbulent heat flux was
done in a 2-D domain with symmetry boundary conditions for all surfaces parallel to the
X–Y plane. The geometry consists of two rectangular domains: a solid domain representing
the insulation layer and a fluid domain representing the superfluid helium.
Research and Development (EuCARD).
EuCARD researchers addressed these challenges, simplifying the original two-fluid
model by making several assumptions
that reduce the system of equations to the
point that they could be implemented in a
commercial CFD code. The group selected
ANSYS CFX because of its excellent scripting capabilities and the researchers’ experience in obtaining excellent correlation
to physical tests with the software. Using
ANSYS CFD and FORTRAN™, researchers added terms to the Navier–Stokes and
energy equations to account for superfluid
properties. A simplified CFD model of a
solid and fluid domain was generated and
compared to the turbulent heat transfer
equation. Error in the heat flux predicted
by the model was at 1.7 percent or lower
throughout the computational domain [1].
ANSYS ADVANTAGE Volume VIII | Issue 1 | 2014
ACADEMIC RESEARCH
Streamlines and velocity field for a) total velocity; b) superfluid; c) normal fluid components
SIMULATING A REALISTIC Nb3Sn
MAGNET DESIGN
Researchers then modeled the proposed
Fresca2 Nb3Sn magnet design. The Nb3Sn
magnet structure is cylindrical, and the
conductors are symmetrical, so the calculation was reduced to a quarter model. The
mesh for the geometry had 2 million hexahedral elements and about 2.5 million
nodes. Researchers applied both a thermal resistance with a bath temperature of
1.9 K at the external boundaries and symmetry conditions to the internal boundaries. They set the initial pressure at 101.3
kPa. The heat load on each conductor in
the magnet generated by alternating current losses is about 0.2 W for the whole
coil. Researchers first modeled the magnet without superfluid helium to evaluate
thermal performance in a worst-case situation. The calculations were carried out for
steady-state and transient heat and mass
transfer. This model took about two hours
to solve on a single computing node.
The team performed another analysis
with superfluid helium inside the magnet.
This model took about 10 days to solve due
to complexity added by the superfluid
terms. Adding superfluid helium to the
model lowered temperatures by about
17 percent. The maximum temperature increase in the coil was predicted to
be 0.193 K, which is well below the target temperature of 5.8 K. The simulation
provided the temperature distribution in
the magnet, as well as velocity contours
and streamlines for the total, superfluid
and normal fluid velocity components.
ANSYS CFD has demonstrated its ability to
accurately predict heat and mass transfer
processes in the Nb3Sn magnet and will
help produce the detailed design for the
next-generation magnet in the SLHC.
© 2014 ANSYS, INC.
Cross section and horizontal section of proposed Fresca2 magnet design. Superfluid helium
occupies about 4.67 percent of the total magnet structure volume, filling the space between
the yoke and vertical pad inter-laminations and the spaces between horizontal and vertical
pads and iron yoke.
Temperature profiles along symmetry axis of validation model show close correlation
between CFD and physical testing.
Temperature contour field for bath
temperature of 1.9 K
Reference
[1] Pietrowicz S.; Baudouy B. Numerical
Study of the Thermal Behavior of an Nb3Sn
High Field Magnet in He II. Cryogenics,
2013, V53, pp. 72–77.
ANSYS ADVANTAGE Volume VIII | Issue 1 | 2014