Assessment of a Particle Bed Based Beam Stop Page: 2 of 3
This article is part of the collection entitled: Office of Scientific & Technical Information Technical Reports and was provided to UNT Digital Library by the UNT Libraries Government Documents Department.
Extracted Text
The following text was automatically extracted from the image on this page using optical character recognition software:
where, Nu is the Nusselt number hdl,/k, h is the heat
transfer coefficient, k is the thermal conductivity and Pr
is the Prandtl number.
The film temerature drop can be estimated from the
following relationship,
AT= P IhA
Where, P is the power per unit volume of bed, A is the
heat transfer area per unit volume of the packed bed
(A = 6(1- e)/dp for spheres). Based on the above
relationships it can be shown that for a bed of randomly
packed particles the pressure drop and film temperature
drop vary approximately in the following ways, as
functions of particle diameter and velocity only,
Ap ~ V2/dp - AT- dp514N34
where, Ap is the pressure drop across the packed bed,
and AT is the film temperature drop between coolant
and particle surface. The above relationships indicate
that it is not possible to simultaneously minimize both
the pressure drop and film temperature drop, and thus a
compromise is required. In the case of gas cooled
targets the ambient pressure is generally increased in
order to increase the coolant density, which in turn
implies a reduction in the coolant velocity for a given
power extraction requirement and thus a reduction in the
bed pressure drop. The compromise in this case must
thus be extended to include the ambient pressure. In the
case of water-cooling the avoidance of boiling in the
bed is the primary criterion, and thus the particle surface
temperature must be below the saturation temperature at
all points within the bed. This comment also applies to
other liquid coolants. However, in the case of liquid
metals the probability of boiling is much lower, and
pressure is generally not of concern. Thus an
appropriate particle diameter must be chosen to result in
an acceptable film drop and particle surface
temperature. Finally, in the case of liquid metal coolants
the pressure (both ambient and pressure drop) and film
drop are not of primary concern, but the mixed mean
outlet temperature will be. It is desirable to keep this
temperature within practical limits in order to guarantee
that the target will have a reasonably long life, while
operating in the implied radiation environment. In
addition, the entire outlet duct network will have to
operate at the elevated temperature.
2.2 Thermal Shock Considerations
In combination with the thermal considerations
discussed above, the promise of a packed particle
scheme in absorbing and diffusing an undiluted beam is
explored. What the particle bed promises is the
attenuation of stress wave generated in the "heated"zone and propagating outward. Borrowing the concept
from the study of the dynamic response of saturated
porous media where, in bulk terms, stress waves
attenuate more due to sharing of energy between the
solid and fluid phases as well as frictional effects
between the particles making up the solid skeleton, it is
anticipated that the thermal stresses experienced by the
packed bed outside the heated zone are' reduced
significantly when compared to a solid volume. While
the benefit of the packed bed can be realized in the
larger scale, the survivability of the bed particles
intercepting the incoming beam will depend almost
entirely on three parameters, namely, the particle
diameter, the beam spot size relative to the diameter and
the pulse structure.
The relation between the pulse length and the particle
diameter has been dicussed in length in [1]. It is
analytically shown that the ratio tpuise/tvel, where tpeise is
the pulse length and ttmve is the time it takes the sound
to traverse the particle diameter, controls the level of
dynamic stress in the particle that follows the initial
thermal stress of same magnitude within the heated
zone. Thus, if the deposition of energy in the particle is
"slower" than the sound propagation, the dynamic stress
is reduced. Thus, a choice of particle size can be made
based on the pulse length while considering the effects
of the previous section regarding the heat transfer
requirements.
This study also investigated the relationship between the
beam spot size and the diameter of the particle.
Specifically, for the applicable case in which the beam
spot radius is smaller than that of the diameter, the
ability of the particle to dynamically relax from the
initial quasi-static thermal stress state depends on the
ratio of the two radii.
Figure 1 depicts an idealized arrangement of packed bed
particles with the central element intercepting the beam.
Shown in Figure 2 are the radial stresses in the central
particle for two ratios of beam spot radius to particle
radius while the particle is not in contact with the
surrounding bed. Based on the stress amplitudes which
indicate that the center of the particle experiences the
same stress at the end of the pulse, the subsequent stress
wave field is quite different. Indeed, the particle sees
less stress as a result of the stress wave propagation and
reflection.
Figure 3 depicts various times of the thermal stress
propagation in the particle arrangement of Fig. 1 by
considering the non-linear surface contact between the
particles but ignoring the possible contribution of the
fluid in the "porous" structure. The latter is expected to
be of significance when a liquid metal playing the role
of coolant. In such case, the liquid will absorb a potion
of the beam, heat-up and induce its own pressure waves
plus, due to its high acoustic impedance, will allow for
stress waves to propagate outward through its interface
Upcoming Pages
Here’s what’s next.
Search Inside
This article can be searched. Note: Results may vary based on the legibility of text within the document.
Tools / Downloads
Get a copy of this page or view the extracted text.
Citing and Sharing
Basic information for referencing this web page. We also provide extended guidance on usage rights, references, copying or embedding.
Reference the current page of this Article.
Simos, N.; Ludewig, H.; Montanez, P. & Todosow, M. Assessment of a Particle Bed Based Beam Stop, article, June 3, 2002; Upton, New York. (https://digital.library.unt.edu/ark:/67531/metadc741739/m1/2/: accessed March 29, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.