Как выбрать гостиницу для кошек
14 декабря, 2021
The following definitions are used:
• ps = density of the pebble base material
• pp = pebble density
• Pp = total pebble porosity = average fraction of porosity within (macroscopic, single) pebble volume
• Ppb = pebble-bed density = ratio of pebble-bed mass mpb to pebble-bed volume Vpb
• g = packing factor = ratio of pebble volume to pebble-bed volume
The quantities are connected by
ppb mpb/Vpb (1 Pp)psg [1 ]
In literature, the term ‘fraction of theoretical density’ is also used. This term is identical to (1—Pp). The pebble-bed density ppb is often named ‘apparent’ or ‘tap’ density. The pebble-bed density ppb is an important quantity for nuclear calculations as these require the specific density of lithium and other constituents as inputs. In pebble-bed engineering, the packing factor g (generally given in percentage) is the characteristic quantity.
The packing factor is influenced by the following parameters: filling procedure, pebble shape, surface roughness diameter d, diameter distribution, and container (cavity) dimensions: height H, diameter D.
Fillingprocedure. The selection of an optimum procedure is not trivial, especially for larger mock-ups: filling should be assisted by vibration in such a way that a particle flow within the cavity is prevented or, in case of too small vibration energies, friction forces between pebbles and walls can be overcome.
Pebble shape and surface roughness: ceramic breeder pebble shapes are almost spherical, partly with indentations (melting, spraying processes) or egg-like (extrusion, spheronization, sintering processes). The pebbles originating from melting have a smoother surface than the others. The packing factor is influenced by the surface roughness but negligibly by the pebble shape.
Diameter distribution: The diameter d is of influence with respect to the cavity dimensions, discussed later. Ideally, the packing factor increases with increasing diameter distribution; see, for example, McGeary.87
However, sedimentation during the filling is a critical issue.
For blanket pebble beds, two groups are of interest: (1) Pebble beds with a relatively small d variation: for example, Li2TiO3 pebbles with a nominal diameter of 1 mm ranging from 0.8 to 1.2 mm and Li4SiO4 pebbles ranging from 0.25 to 0.63 mm. Production costs generally favor a wider spread, which is not detrimental in respect to the packing factor, at least for the diameter ranges cited earlier. Packing factors in the range of 63-66% are reached; (2) Binary beds: here, large pebbles, dl, and small pebbles, ds, are used, with ds« 0.1dl. First, the large pebbles are vibrated in the cavity. Then the pebbles are fixed in their position, for example, by a sieve in the filling pipe, to avoid sedimentation during the following pouring in ofthe small pebbles, which fill the spaces between the large pebbles. Packing factors of about 82% were obtained for beryllium beds with dl« 2 mm, ds« 0.2 mm.94 Critical issues are (1) the stability of such pebble packing structure during thermal cycles in the blanket and (2) the buildup of large stresses due to irradiation-induced swelling causing pebble degradation, leading to fracture.
Diameter d, bed height H, diameter D: For finite cavities, there exist two characteristic ratios: H/d and D/d. The reason why g depends on H/d and D/d is the existence of two different characteristic pebble packing structures as demonstrated by
tomography experiments101,105,106: in the pebble
bulk, there is no preferential direction of contacts between pebbles, whereas at the wall, a zone with a thickness of about 4d exists, where regular packing structures are observed and contact zones are no longer homogeneously distributed.
Figure 17 shows tomography results106 for a cylindrical container (D = 49 mm, H= 50 mm) filled with spherical pebbles (d = 2.3 mm). Distinct pebble layers close to the walls can be clearly seen in Figure 17(a) where the positions of the pebble centers are plotted in a horizontal plane (left) and a vertical plane (right).
Figure 17(a) shows axial void fraction distributions. The degree of regularity is largest for the pebbles in contact with the wall and decreases with increasing wall distance. The regularity is most expressed for pebbles in contact with plane walls (D = 1); here, large isles with a dense hexagonal pebble arrangement are observed; see Reimann et al}05 The average packing factor of a plane wall zone is about equal to the bulk packing factor if the bed height is sufficiently large for the two wall zones
|
|
|
|
|
|
|
|
|
|
A disadvantage of a large pebble diameter is also the smaller heat transfer coefficient, as outlined below.
The blanket modules will probably be filled with pebbles through small pipes, as schematically shown in Figure 18. For simple cubic cavities, a homogeneous filling was achieved only by carefully vibrating the container in different tilted positions.97,100
The filling of a TBM mock-up using glass balls for the beryllium pebble beds was investigated by Abou-Sena eta/.,107 by varying the number and positions of the filling pipes. The best results were obtained by using a single filling pipe close to the box corner and, keeping the filling pipe at the highest position, tilting the box around two axes. Here, a packing factor of 63.6% was achieved, which is considered to be very close to the maximum obtainable value.
In the HELICHETTA experiment (see Dell’Orco et a/.108,109) where elongated pebble-bed cavities (10 x 100 x 480 mm3) were filled through a pipe at the top (largest dimension orientated vertically), packing factors of 60% and 62% were achieved for Li2TiO3 pebbles with diameters between 0.8 and
1.2 mm, and 0.6 and 0.8 mm, respectively. For Li4SiO4 pebbles with d between 0.25 and 0.63, the packing factor was more than 64%.