Using Frozen Beads from a Mixture of Mesitylene and Meta-Xylene with Rupert’s Drop Properties in Cryogenic Neutron Moderators

Abstract

An experimental study was conducted on the feasibility of using frozen beads with the properties of Rupert’s drops—solid frozen beads with enhanced strength made from a mixture of aromatic hydrocarbons—in cryogenic neutron moderators utilizing bead technology. It is demonstrated that the use of a new modification of the dosing device with a high discharge rate (approximately 6 units/s) significantly improves process efficiency. With standard pneumatic transport parameters maintained, it was possible to load solid frozen beads made from a mixture of mesitylene and meta-xylene into the cryogenic moderator chamber. The loading speed increased five-fold, while the beads remained intact during pneumatic transport.

1. Introduction

Pelletized cryogenic moderators based on the aromatic hydrocarbon mesitylene are an effective tool for generating high-intensity cold neutron beams at research neutron sources [1,2,3,4,5].

The finely dispersed, uniform filling of the moderator, located in the immediate vicinity of the source, with solid frozen beads, averaging 3.5–3.9 mm in diameter, enables the attainment of a uniform neutron spectrum throughout the entire volume of its chamber. This is an important parameter for minimizing errors and obtaining reliable results in neutron physics experiment. To achieve this, solid frozen beads transported to the moderator chamber via a pneumatic route with cold helium must possess good mechanical properties (strength, hardness, etc.) and must not collapse. It is also crucial to ensure proper cooling of both the chamber and the pneumatic line of the moderator [6,7,8].

The delivery of the beads to the chamber begins with a dosing device, in which the beads undergo increased mechanical pressure and friction due to constant contact with each other and the metal walls during mixing, especially when a new modification of the dosing device with a high discharge rate (6–8 units/s) is used. Such operating conditions can lead to the formation of fragments due to the complete or partial destruction of the beads, which will subsequently enter the pneumatic transport system.

In addition, during the pneumatic transportation process, as the beads move along the pipeline, they constantly clash with the walls of the steel pipe. As a result of these clashes, fragments can also form. Their accumulation in various sections of the pipeline (especially in the lifting sections and in the chamber itself) can lead to an increase in the hydraulic resistance of the flow, which is inversely proportional to the size of the beads. This, in turn, results in a reduction in flow and an increase in the temperature of the helium.

As a result, the temperature of the beads also increases, which ultimately leads to an increase in temperature throughout the entire volume of the moderator chamber and a decrease in the output of cold neutrons from its surface. In some cases, this can lead to a complete cessation of helium circulation and an emergency stop of the moderator, which is a negative scenario, especially in the context of about the routine operation of a cryogenic moderator at a research reactor at rated power.

Currently, the problem of chipping and destruction of beads is partially solved by the selection of pneumatic transport parameters. However, in this case, there are limitations, as follows: On the one hand, the speed of the beads should not be too low to avoid congestion in the transport line; on the other hand, it should not be too high to prevent their destruction. This restriction hinders the ability to accelerate the loading process of the moderator chamber by increasing the speed of helium or, for example, to make a technological purge by repeatedly increasing its consumption, due to the formation of congestion, etc. Additionally, some beads may still collapse in the dispenser before entering the pneumatic transport system. In this context, the experimental search for ways to manufacture solid beads with initially better strength and impact resistance appears more promising.

According to the physical model under development by the authors of this paper for the fabrication of solid frozen spheres from a mixture of mesitylene and meta-xylene, as described in detail in Section 2.1 of this paper, it is possible to produce beads with the properties of Rupert’s drops by increasing the heat transfer of the beads during the manufacturing process. Compared to conventional materials, Rupert’s drops have increased strength due to the presence of internal mechanical stress [9,10,11]. At the same time, during transportation or due to increased pressure on the beads in the dosing device during actual operation, it is still impossible to exclude the possibility of their spontaneous destruction. The model under development is based on the models presented in the following works [11,12,13].

Therefore, the feasibility of using solid frozen beads of the Rupert’s drop type for loading the moderator chamber needs to be verified experimentally. This was done first with a full-scale testbed and followed by implementation and testing of this technique at the complex of cryogenic moderators of the IBR-2 reactor (JINR, Dubna, Russia).

2. Materials and Methods

2.1. Formation of a Solid Frozen Bead from Mesitylene with the Properties of a Rupert’s Drop

The production of solid frozen beads is carried out using special devices known as mechanical gravity droppers [8].

The process of forming a drop in such a device occurs through drop-formers nozzles located at the lower part of the dropper (Figure 1).

Under each nozzle, there is a cell located inside a cryostat filled with a refrigerant (liquid nitrogen), which is designed to freeze each bead separately to prevent them from sticking together, which occurs because of the high adhesion of the beads up to a temperature of 150 K [8]. Each cell produces a bead in 30 s; there are 19 cells in the device. The upper part of the dropper is mounted on top of the cryostat and is filled with a mixture of liquid mesitylene and meta-xylene. The performance of such a gravity dropper is quite low and typically does not exceed 50 mL/h.

It has been experimentally established that to produce beads with the properties of Rupert’s drops, a production speed of approximately 10 s per bead must be achieved. Achieving such a production rate in standard gravitational droppers is made possible by additional heating of liquid nitrogen with a nichrome wire. The wire is installed in the lower part of the cells that separate the beads from one another. The specifications of the heating wire are as follows: length of ~1.8 m, cross-section of ~0.46 mm, current of ~3 A, and voltage of 24 V.

We shall omit the description of the drop formation process and the reverse Leidenfrost effect [12,13] and proceed directly to examining the crystallization stage of beads made from a mixture of mesitylene and meta-xylene.

The duration of cooling of a liquid bead to its melting point is determined as follows [13], and it should be noted that the use of these forms of Equations (1) and (2) is explained in Appendix A:

$$t_2=C_{\mathrm{drop}}·{\displaystyle \frac{{\lambda }^f}{{\mathrm{c}}_{\mathrm{p}}}}{\left(T_{Fr}-T_N\right)}^{{\displaystyle \frac{-3}{4}}}$$

(1)

$$C_{\mathrm{drop}}={\displaystyle \frac{4{\rho }_d{c}_{p}R}{3\eta }}{\left({\displaystyle \frac{9\mu R}{2{\rho }_d{\rho }_{g}g{k}^3{L}^v}}\right)}^{{\displaystyle \frac{1}{4}}},$$

(2)

where $T_N, \mathrm{K}$—liquid nitrogen temperature; $T_{Fr}, \mathrm{K}$—the melting temperature of the mixture of mesitylene and meta-xylene; ${\lambda }^f, {\displaystyle \frac{\mathrm{J}}{\mathrm{kg}}}$—the specific heat of fusion of the mixture of mesitylene and meta-xylene; ${\rho }_d, {\displaystyle \frac{\mathrm{kg}}{{\mathrm{m}}^3}}$—the density of a drop; $c_p, {\displaystyle \frac{\mathrm{J}}{\mathrm{kg}·\mathrm{K}}}$—the specific heat capacity of a drop; $R, \mathrm{m}$—the drop radius; $\eta$—the fraction of the drop surface in contact with the vapor layer; $\mu , \mathrm{Pa}·\sec$—the viscosity of the nitrogen vapor; ${\rho }_g$, ${\displaystyle \frac{\mathrm{kg}}{{\mathrm{m}}^3}}$—the density of the vapor layer; $g$, ${\displaystyle \frac{\mathrm{m}}{{\sec }^2}}$—gravitational acceleration; $k$, ${\displaystyle \frac{\mathrm{W}}{\mathrm{m}·\mathrm{K}}}$—the thermal conductivity coefficient of the liquid nitrogen vapor; $L^v$, ${\displaystyle \frac{\mathrm{J}}{\mathrm{kg}}}$—the specific heat of vaporization of the liquid nitrogen.

The numerical values used in the calculations are provided in

Table A1. Values of physical quantities used in the work.

Physical Quantity	Notation	Value
Surface tension of liquid nitrogen with nitrogen vapor at 77.4 K	$\mathsf{\sigma }$, ${\mathsf{\sigma }}_{\mathrm{l}-\mathrm{s}}$	8.85 mN/m [16]
Surface tension of mesitylene at 230 K	${\mathsf{\sigma }}_{\mathrm{d}-\mathrm{s}}$	30 mN/m [17]
Density of liquid nitrogen at 77.4 K	${\mathsf{\rho }}_{\mathrm{N}}$	806.08 kg/m3 [18]
Density of mesitylene drop at 300 K	${\mathsf{\rho }}_{\mathrm{d}}$	861.12 kg/m3 [17]
Density of nitrogen vapor at 77.4 K	${\mathsf{\rho }}_{\mathrm{g}}$	4.6121 kg/m3 [18]
Viscosity of nitrogen vapor at 77.4 K	$\mathsf{\mu }$	54.440 10−7 Pa · s [18]
Thermal conductivity coefficient of nitrogen vapor over liquid nitrogen at 77.4 K	$\mathrm{k}$	7.1876 mW/m/K [18]
Specific heat capacity of the drop at 300 K	${\mathrm{c}}_{\mathrm{p}}$	1.75 kJ/kg/K [17]
Specific heat capacity of the crystallized drop at 230 K	${{\mathrm{c}}_{\mathrm{p}}}^{\mathrm{s}}$	1.21 kJ/kg/K [19]
Drop radius	R	1.75–2.5 mm
Fraction of the drop’s surface in contact with the vapor layer	$\mathsf{\eta }$	0.5
Gravitational acceleration	$\mathrm{g}$	9.81
Latent heat of vaporization of liquid nitrogen	${\mathrm{L}}^{\mathrm{v}}$	200 kJ/kg [20]
Latent heat of fusion of mesitylene	${\mathsf{\lambda }}^{\mathrm{f}}$	80.12 [21]
Initial temperature of the drop	${\mathrm{T}}_0$	300 K
Temperature of liquid nitrogen	${\mathrm{T}}_{\mathrm{N}}$	77.4
Melting temperature of mesitylene	${\mathrm{T}}_{\mathrm{Fr}}$	228.43 [22]
Leidenfrost temperature of liquid nitrogen	${\mathrm{T}}_{\mathrm{L}}$	126 [23]
Temperature outside the cryostat	${\mathrm{T}}_{\mathrm{out}}$	300 K

. The calculations show that for an average droplet diameter of 3.7 mm, the theoretical value of t2 is approximately 16 s (Figure 2).

As the heat exchange intensity between the drop and liquid nitrogen increases, the process of bead formation is no longer quasistatic [13]. Therefore, Formula (1) cannot be applied to describe the crystallization process. In this case, crystallization begins at the outer region of the droplet, which is in direct contact with the vapor “cushion” (nitrogen vapor). Thus, the change in the density of the outer layer is inversely proportional to the heat transfer intensity of the outer layer of the droplet. This correlation is observed experimentally through a decrease in the number of droplets with a diameter of less than 3.6 mm and an increase in the number of droplets with a diameter greater than 3.9 mm.

In this case, the liquid inside the solid shell solidifies with increasing density (

Table A2. Density of mesitylene at different temperatures.

Temperature, K	Density, kg/m³
20	1.08 [24]
290	869 [25]
295	865 [25]
300	861.12 [17]
308.15	852.94 [17]
313.15	848.82 [17]

), resulting in a mechanical stress gradient and the formation of a cylindrical or spherical cavity with a base radius of about 1 mm and a height of approximately 2 mm, similar to what is observed in Rupert’s drops (Figure 3) [10,11,14]. The formation of a cavity is possible when the mechanical stress decreases in proportion to the growth of the defect from which it is formed [15].

Moreover, the nature of the destruction of the solid beads under external impact or, in rare cases, spontaneous destruction into small fragments with a high variety of shapes (Figure 4). As well as the presence of light dispersion inside the bead, this indicates that the beads, frozen within 10 s using a gravitational dropper from the mixture of mesitylene and meta-xylene, exhibit the properties of Rupert’s drops [9,10,11,14].

Preliminary experiments have shown that Rupert’s drops, made from a liquid mixture of mesitylene and meta-xylene, pre-cooled to 230 K, but with the same refrigerant parameters in the gravitational dropper, have nearly a twice as smaller cavity size. This behavior of the cavity is also confirmed by Rupert’s drop studies conducted by other authors on different substances at various temperatures [11,14]. Since the beads made using the new method exhibit the properties of Rupert’s drops, we believe that they also possess enhanced strength compared to ordinary beads. This is because the increased strength of Rupert’s drops is an important property that arises because of mechanical stresses inside the drops [11]. Similar mechanical stresses occur inside beads with Rupert’s drop properties, and therefore, their strength is also increased.

Using the proposed method for producing beads with Rupert’s drop properties, the beads were produced, and the parameters of the proposed method are presented in

Table 1. Parameters for the production of beads from a 280 mL mixture.

	Standard Method	Optimized Method
		1 Bead in 10 s	1 Bead in 7 s
Production time, h	6	3	2
Frequency of liquid nitrogen addition, times/h	1	3	3
Defective beads with a diameter greater than 3.9 mm	<2.5%	<8.5%	<12.5%
Defective beads with a diameter less than 3.6 mm	<2.5%	<1.5%	<0.5%

.

2.2. Experimental Setup for Loading the Moderator Chamber with Frozen Beads Exhibiting Rupert’s Drop Properties, Using a Modified Dosing Device with a High Unloading Rate

The aim of modifying the dosing device is to increase the unloading speed of the beads from the dispenser and enhance the bead storage volume, which in turn increases the speed of bead loading into the moderator chamber using the pneumatic transport system. Increasing the storage volume allows for the beads to be loaded into the dispenser once, instead of three times as with a standard dispenser. This makes it possible to clean the helium in the pipeline only once, as the contamination of the coolant in the pipeline occurs during the loading of the beads into the dosing device [8].

The modified dosing device with high unloading speed (Figure 5) is a cylindrical cryostat, insulated with multilayer high-vacuum thermal insulation, a heat shield, and a bellows connection to reduce heat transfer from the surrounding environment. Inside the cryostat, there is a 1.4 L bead storage container, which is connected at the bottom to the pneumatic transport pipeline of the cryogenic moderator. The container is also equipped with thermodiodes at the upper and lower parts to monitor the temperature during operation. The operating temperatures are achieved by connecting the dosing device to the pneumatic transport system, which is linked to the cryogenic installation. The operating temperature range of the modified dosing device is similar to that of the standard dosing device [8].

At the bottom of the container there is a disk with six holes, which is rotated by a metal shaft connected to a stepper motor. The loaded beads are located on the disk with holes and enter the pneumatic transport pipeline as the disk rotates. The rotation speed of the disk can vary from 0.5 to 1000 rpm. Visual monitoring of the beads is facilitated by a special viewing window and a light guide (Figure 5 and Figure 6). Significant differences from the standard dosing device [8] include an increased volume of the container for storing the beads, the presence of LED backlighting, and an observation window.

The parameters of the pneumatic transport system during the experiments remained unchanged. The new dosing device was tested under conditions similar to the standard dosing device, except for the increased number of beads. In the modified dosing device, 1 L of beads was used, compared to 330 mL of beads in the standard dosing device. The unloading of beads into the pneumatic transport pipeline was carried out at a rate of approximately 6 beads per second, with the disk rotating at about 4 rpm in pulse mode. The speed of the beads moving through the pneumatic line from the dispenser to the chamber was 2.5–3 m/s, with a helium flow rate of 11–14 m/s (mass flow rate of 1.5–2 g/s). The temperature of the helium during loading was 80 K, while during operation, after the full loading of the moderator chamber, it dropped to 16 K. During the experiments, two complete loadings of the full-scale test stand chamber (Figure 7) were performed, as well as five complete loadings of the chambers of the cryogenic moderators of the IBR-2 research fast reactor (JINR, Dubna, Russia) with frozen beads exhibiting Rupert’s drop properties, with each loading consisting of 1 L or approximately 27,000 beads. The first loading was carried out in 3 stages with a mixed batch of beads, approximately 330 mL of the “regular” beads and approximately 660 mL of the beads with Rupert’s drop properties. Each loading was performed in batches of about 330 mL of beads.

The integrity of the beads was monitored through visual observation of the beads in the test stand chamber during loading. During the experiments, temperature, mass flow rate, and helium flow velocity were also monitored.

As a result of a series of experiments, the following was established:

• The time for fully loading the moderator chamber of the test stand using the modified dosing device with high unloading speed was 1.2 h, which is 5 times faster compared to the standard dosing device. No differences were found in the temperature, mass flow rate, or helium flow rate in the pneumatic transport system compared to the standard dosing device;
• Using standard pneumatic transport parameters, a total of ~6.7 L or approximately 180,000 frozen beads made from a mixture of mesitylene and meta-xylene with Rupert’s drop properties were successfully loaded into the moderator chambers. No fragments of frozen beads were found during the experiment.

3. Results

• During pneumatic transportation of the beads with properties of Rupert’s drops, the effect of spontaneous destruction was not observed. Thus, such beads can be subjected to more intensive mechanical impact, which allows for faster loading times by increasing the gas velocity or the mass flow rate of helium in the pneumatic transport pipeline.
• The use of a modified dosing device for loading frozen beads with properties resembling Rupert’s drops into the chamber of a pelletized cryogenic moderator reduces the loading time by a factor of five.

4. Conclusions

Theoretical and experimental studies on the formation of solid frozen beads from a mixture of mesitylene and meta-xylene with Rupert’s drop properties have significant practical implications for the operation of bead-based cryogenic moderators at research neutron sources. These studies focus on producing frozen beads with Rupert’s drop properties that exhibit improved strength compared to conventional beads obtained in standard gravitational droppers. The use of such enhanced beads, made from a mixture of mesitylene and meta-xylene, along with a modified dosing device with high unloading speed, allows for a significant reduction in the time required to load the bead chamber of a cryogenic moderator. In the future, by increasing the unloading speed of the beads from the dosing device and the transporting gas velocity by 2–3 times, without the risk of destroying the strong beads, the loading time can be reduced to approximately 20 min. This will bring us closer to the development of a rapid material exchange system in the chamber, enabling the creation of a universal cryogenic moderator based on hydrocarbons, for use at research neutron sources of any intensity.