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APEX Task I Summary Report for FY01 Content I.
1
APEX Task I Summary Report for FY01
Content
I.
Field Characterizations for Near Term Physics Devices (e.g. NSTX and
CMOD)
II.
Design Exploration for CMOD
III.
Design Analysis of NSTX Free Surface Flow Options
IV.
Preliminary Experimental Study of Free Surface Flow Options Applicable to
Near Term Physics Devices
V.
Disruption Analysis
APEX Task I has been aimed at exploring flowing liquid wall options and, within a 5-
year time frame (~2004), operating a flowing liquid wall experiment in an experimental
physics device. The goals of Task I are to help develop and provide liquid wall
technology systems that meet experimental physics device (such as NSTX) conditions
before installation.
I.
Field Characterizations for Near Term Physics Devices (e.g. NSTX and
CMOD)
The poloidal flux distribution in and near the plasma for NSTX and CMOD were
computed obtained from the EQDISK file information. Only two cases were analyzed for
NSTX; a) a high beta (23%) inner wall limiter plasma and b) a low beta lower single null
plasma. A lower single null plasma with modest beta was the only case provided by
CMOD. Since the parameters of a given machine are variable (plasma current, toroidal
field, plasma pressure, etc. may all be varied over a range, while the sign of some values
may also change), the design of a liquid surface module for a device can not be fixed in
one set of conditions but rather to consider a range of operating points to assure the
module is suitable. Additional cases will have to be analyzed before final design of a
module to be placed in either device. Therefore, the field data documented in the APEX
web site should only be used for scoping studies. The poloidal field is calculated from
the vertical (z) and radial (R) gradients of the flux. The radial and vertical fields at the
lower divertor plate in NSTX are shown in Figure 1. Divertor region fields for CMOD
are shown in Figure 2. In addition, field gradients are computed. In general, due to the
small size of C-Mod and NSTX the toroidal field gradients are larger than for DIII-D,
ITER. Poloidal field gradients for NSTX and CMOD are shown in Figures 3 and 4
respectively. Note that poloidal field gradients in excess of 0.1 T/m are evident, whereas
the gradients in the toroidal field exceed 1 T/m because of the small major radius of these
devices.
II.
Design Exploration for CMOD
Novel CMOD divertor concept has been proposed as shown in Figures 3 and 4. In the
proposed concept, the modules form a continuous toroidal array, but would not form a
continuous electrical loop, as there is an electrical break at each current feed. The intent 2
is to provide as close to a toroidally continuous surface as possible, but there is an
insulating break between each module. The module sides could be changed from radial
to a 45 degree angle from radial at the front to facilitate complete coverage if this is
deemed necessary. A current is applied perpendicular to the flow direction in the lithium
channel that provides an electromagnetic propulsion effect, which in turn propels the
liquid around the channel and out nozzles to form jets. Calculations indicate that the
current direction is indeed across the channels and that no current is flowing in the jets
themselves. Preliminary calculations based on 2-D MHD modeling show that a current
of about 100 A is sufficient to provide a jet velocity of about 10 m/s in C-Mod, which has
a toroidal field of around 10 Tesla (the field in CMOD is about 6 Tesla not 10, the current
will probably need to be higher). The wall consists of multiple rows of jets that shadow
each other. The present concept shows two modules attached to one bias electrode but
other combinations are possible.
Although the design can be modified (for example, to raise the jet to a higher elevation to
allow the plasma strike on the jet instead of the solid tile), urgent questions to be
addressed for the proposed self-pumped divertor concept are: (1) will the surface area be
large enough for particle pumping? and, (2) will the stable free jets (about 1-5 mm
diameter and 20 cm tall) form in the proposed region (field gradient effect)? 3) can the
flow former and flow catcher be shielded from plasma heat flux by geometry alone?
III.
Design Analysis of NSTX Free Surface Flow Options
The goal of the analysis is to provide design information for the APEX study in order to
evaluate the feasibility of a fast free lithium surface for particle and heat removal in a
near term physics device. This is accomplished by the development of 3D MHD model.
Considering that at any given point in time the velocity field of the main hydrodynamic
quantity can be directly relating with the main electromagnetic one (the magnetic field)
without any interference it is possible to build a MHD module into an existing CFD code
(FLOW-3D [1] in this case), which has a verified Navier-Stokes solver for turbulent,
free surface flows. The MHD effect is reflected in an additional term of Lorentz force in
the momentum equation at each time step. In the present model, the MHD Lorentz force
caused by the induced current is derived from the Amperes law by solving the induced
magnetic field equations.
The flow of an electrically conducting fluid under the influence of an external magnetic
field is governed by the following equations which express the conservation of mass and
momentum,
),
(
Re
1
)
.
(
B
j
N
V
p
V
V
t
V
×
+ + = +
(1)
0
=
V
(2)
together with the induced magnetic field equation and the conservation for the magnetic
field under the classical MHD assumptions [2-3], 3
0
)
1
(
)
(
=
× × +
×
×
B
B
V
t
B
m
µ
(3)
0
=
B
(4)
where the magnetic field
B
includes both the applied
)
(
o
B
and induced
)
'
(B
fields. Two
important features are utilized in the developed numerical method to obtain convergent
solutions. First, a penalty factor is introduced in order to force the local divergence free
condition of the magnetic fields. The second is that we extend the insulating wall
thickness to ensure that the induced magnetic field at its boundaries is null. Numerically,
the induction equation is discretized according to the central difference scheme, in which
the induced magnetic field is specified at the cell center. The resulting set of algebraic
equations are then solved iteratively using the Gause-Siedel technique applying boundary
conditions at each time step.
The calculated results of the lithium fluid flow along the NSTX outboard midplane
proceeding from a uniform, inlet of 10m/s and an initial film thickness of 2 mm is shown
in Figure 7. As shown, much of the solid substrate has been left bare due to the fluid
being pushed and spilling over one side of the chute. This feature of spilling over one
side of the chute is the result of the poloidal (x direction) return current induced by the
surface normal field gradient interacting with the toroidal field and can-not be shown
with a 2D model. In order to overcome the phenomena in which the fluid is pushed to one
side, leaving a bare zone, the center axis of the chute is titled 30 degrees away from the
surface normal plane. This allows the flow to closely align with the field line, and
reduces the magnitude and its effect of the surface normal field observed by the fluid. As
a result (as shown in Figures 8 and 9), the undesired feature associated with the spanwise
Lorentz force is eliminated, while no bare spot remains in this modified design. The low
velocity magnitudes observed at the downstream can be resolved by increasing the inlet
velocity (a velocity of ~10 m/s is desired from the surface heat flux removal point of
view).
IV. Preliminary Experimental Study of Free Surface Flow Options Applicable to
Near Term Physics Devices
Preliminary jet experiments using GaInSn under the effects of transverse field and
transverse field gradient have been conducted in the M-Tor facility. The free jet proceeds
out of a 5 mm circular nozzle, passes through a constant field and then an abrupt field
gradient before leaving the coils. The toroidal field increases as the current passing
through the coils increases. The M-Tor facility gives about 0.6 T at the inboard when it is
run at the maximum current of 3400 A. To achieve higher field, a flux concentrator has
been placed in the M-Tor to alter local flux distribution and produce a stronger field in
the experimental area. The flux concentrator can also be shaped to provide a similar field
gradient as seen in NSTX or CMOD. One of the task for year 02 is to design the flux
concentrator to generate a prototypical field gradient. A permanent magnet system has
been designed to allow similar experiments on flowing lithium in the LIMITS device at
Sandia. 4
In this preliminary set of experiments, the maximum transverse (toroidal) field was about
0.93 T, while the maximum field gradient was 33 T/m. As observed, the turbulent
circular GaInSn jet was strongly laminarlized when it passed through the field. The
laminarized jet reflected back and forth (in radial direction) as it proceeded through the
gradient region. Although video (documented in the APEX Web site under Task 1
conference call) has been taken to record jets global behavior with respect to MHD
effect, better diagnostics to accuratel