7.5 Friction Optimization
481
wide range of particle–wall friction is tested to reveal the rules about the flow pattern
conversion in a specific pebble bed. Quantitative criteria are defined to evaluate the
flow patterns in the pebble bed. The efficient way of friction control for different
parts of the pebble bed is proposed for practical engineering. The Discrete Element
Method (DEM) is employed here to carry out simulations.
It is validated through a series of three-dimensional DEM simulations that reducing friction is helpful to create the uniform and consistent flow field required by
nuclear engineering. The particle–wall friction poses a decisive impact on flow patterns, and the particle–particle friction usually plays a secondary role. The relation
between particle–wall friction and flow pattern conversion is also concluded. Moreover, new criteria are created to describe flow patterns quantitatively according to
crucial issues in HTGR like stagnant zone, radial uniformity, and flow sequence. Last
but not least, it is proven that the friction control of the hopper part is more important
than that of the cylindrical part in practical pebble beds, so reducing friction between
pebbles and hopper surface is the engineering priority.
7.5.1 Numerical Setup
The discrete element method is utilized here too. For the current simulation, the longitudinal section of the three-dimensional cylindrical pebble bed with a contraction
bottom is depicted in Fig. 7.32a. The bed with 1 m total height and 0.8 m cylinder
diameter has a 0.12 m diameter discharge hole at the bottom center. It consists of
two parts—bin and hopper. About 230,000 pebbles with an equal diameter of 12 mm
are needed to fill up the bed and form the initial random packing state. When the
recirculating process starts, the discharging rate at the discharge hole is set to match
the loading rate at the top, so that the total number of pebbles existing in the bed
would remain constant. In the simulation, a trick is utilized to realize the controlled
discharge process: once a pebble is loaded into the bed at the top, another pebble
staying at the discharge hole would vanish automatically. This means that the discharging rate is determined by the loading rate, which is much easier to be set to a
fixed value.
However, based on the above setup, the simulation is time-consuming due to the
computational complexity of the discrete element method. The simulation adopts
two strategies to speed up simulation [23]: reducing the space and softening the
particles. As shown in Fig. 7.33 the actual simulation domain is a 45
◦ wedge with
cyclic boundary conditions at the wedge boundaries (refer to Fig. 7.32b). In this way,
the number of calculated pebbles decreases to one-eighth of the sum (about 30,000),
cutting down calculation amount and simulation time significantly. In addition, simulation time step t is controlled by the binary contact time t bc . For the simulation
accuracy, time step t is required to be a small fraction of t bc . t bc is related to particle
stiffness: the stiffer the particles are, the shorter the t bc and t become, and the longer
the simulation time gets. Particle stiffness is determined by Young’s modulus (E) of
particles according to the contact model defined in DEM. Currently, the linear spring
481
wide range of particle–wall friction is tested to reveal the rules about the flow pattern
conversion in a specific pebble bed. Quantitative criteria are defined to evaluate the
flow patterns in the pebble bed. The efficient way of friction control for different
parts of the pebble bed is proposed for practical engineering. The Discrete Element
Method (DEM) is employed here to carry out simulations.
It is validated through a series of three-dimensional DEM simulations that reducing friction is helpful to create the uniform and consistent flow field required by
nuclear engineering. The particle–wall friction poses a decisive impact on flow patterns, and the particle–particle friction usually plays a secondary role. The relation
between particle–wall friction and flow pattern conversion is also concluded. Moreover, new criteria are created to describe flow patterns quantitatively according to
crucial issues in HTGR like stagnant zone, radial uniformity, and flow sequence. Last
but not least, it is proven that the friction control of the hopper part is more important
than that of the cylindrical part in practical pebble beds, so reducing friction between
pebbles and hopper surface is the engineering priority.
7.5.1 Numerical Setup
The discrete element method is utilized here too. For the current simulation, the longitudinal section of the three-dimensional cylindrical pebble bed with a contraction
bottom is depicted in Fig. 7.32a. The bed with 1 m total height and 0.8 m cylinder
diameter has a 0.12 m diameter discharge hole at the bottom center. It consists of
two parts—bin and hopper. About 230,000 pebbles with an equal diameter of 12 mm
are needed to fill up the bed and form the initial random packing state. When the
recirculating process starts, the discharging rate at the discharge hole is set to match
the loading rate at the top, so that the total number of pebbles existing in the bed
would remain constant. In the simulation, a trick is utilized to realize the controlled
discharge process: once a pebble is loaded into the bed at the top, another pebble
staying at the discharge hole would vanish automatically. This means that the discharging rate is determined by the loading rate, which is much easier to be set to a
fixed value.
However, based on the above setup, the simulation is time-consuming due to the
computational complexity of the discrete element method. The simulation adopts
two strategies to speed up simulation [23]: reducing the space and softening the
particles. As shown in Fig. 7.33 the actual simulation domain is a 45
◦ wedge with
cyclic boundary conditions at the wedge boundaries (refer to Fig. 7.32b). In this way,
the number of calculated pebbles decreases to one-eighth of the sum (about 30,000),
cutting down calculation amount and simulation time significantly. In addition, simulation time step t is controlled by the binary contact time t bc . For the simulation
accuracy, time step t is required to be a small fraction of t bc . t bc is related to particle
stiffness: the stiffer the particles are, the shorter the t bc and t become, and the longer
the simulation time gets. Particle stiffness is determined by Young’s modulus (E) of
particles according to the contact model defined in DEM. Currently, the linear spring