Step right up! Get your free neutrons at ORNL!
By Leigh Soutter
"Free" neutrons are hardly free at all when it comes to money-actually, it takes enormously sophisticated equipment to create them, and only a handful of places on earth do it. Who needs free neutrons, anyway? Developers of advanced materials, new biotechniques, and cold fusion make just a few candidates. Now more than ever, cutting-edge experimentalists like these turn to the High-Flux Isotope Reactor (HFIR) at the Oak Ridge National Laboratory in Oak Ridge, Tennessee, to satisfy their needs. With COMSOL Multiphysics, senior safety analyst Dr. Jim Freels ensures that these powerful neutron streams enter equipment slow, cold, and trouble free.
Figure 1: The major buildings at the High-Flux Isotope Reactor at Oak Ridge National Laboratory showing the new hydrogen cold source (orange) and the new HB-4 beeam tube (dark green). The neutron flux travels down the guide hall of the HB-4 to experimental equipment used by a diversity of visiting researchers.
Right now, the HFIR (Figure 1) is one of the most powerful research reactor facilities in existence. Established in the 1960s, its unique design currently uses moderated nuclear fission to produce free neutrons for researchers and industrial users. The neutrons are termed "free" because they exist outside the nucleus of atoms after reactions break them into subnuclear constituents: protons, electrons, and antineutrinos. Being electrically neutral, the free neutrons penetrate deep because they pass unhindered through electrical fields within atoms and slow primarily when they collide with atomic nuclei. With only one proton and neutron encased in its nucleus, hydrogen makes an excellent refrigerant for the fast-moving free neutrons.
At HFIR, neutron production is most intense in the hot center of the 2-foot diameter reactor core, where rare isotopes such as californium-252 form. HFIR collects whatever free neutrons form outside the core to produce a dense or "bright" flux for scattering studies and other experiments at a new beam facility named HB-4 (Figure 1). When their new low-temperature hydrogen system comes on line to cool the neutrons, the flux coming out of this beam tube to experimental equipment will be as slow and bright as the current best in the world.
"The hydrogen from the new cold source must not only cool the neutrons, it also must cool all of the equipment it passes through," explains Freels. The new hydrogen cold source at HFIR maintains approximately 5 kg of the gas at between 18 and 21 K and circulates it continually in a transfer-line loop. Three variable-speed circulators move the hydrogen from the cold source into the line. The circulators spin fast enough to pump the hydrogen through at 0.074 kg/s. Even though they operate by magnetic levitation, the spinning still generates considerable heat. The pressurizer (Figures 2 and 3) picks up some of this heat while it maintains 14 to 15 bar absolute along the line, a level that prevents subcooled nucleate boiling. When the hydrogen circulates through the moderator vessel at the outer extent of the loop, the neutron beam coming from the reactor passes through it. The free neutrons pass down empty guide halls to experimental equipment, traveling like a dense invisible laser beam. The flowing hydrogen, however, returns from the moderator vessel to the pump module for recirculation.
With the nuclear reactions, the variable-speed circulators, and intrinsic heat leaks, the hydrogen must dissipate 2200 W of heat. "This is where COMSOL Multiphysics comes in: to give us an accurate estimate of the cooling process," he adds. The components of greatest concern have the steepest temperature drops-the pressurizer that receives the heat from the ambient surroundings and the moderator vessel with an outer wall that absorbs a dense neutron flux.
A pressure-volume-temperature balancing act
Figure 2: The pressurizer sits inside a vacuum chamber within the pump module and picks up heat from three variable-speed circulators. For the pressurizer, temperatures drop top to bottom from 300 K to 18 K and inside pressures average between 14 to 15 bar absolute.
The simulations that Freels conducts often involve significant temperature and pressure changes. Typically they include heat transfer in solids with non-isothermal hydrogen flow, at times laminar and at other times turbulent. Complicating the models is the fact that material properties vary strongly with temperature and pressure. Says Freels, "We use COMSOL Multiphysics because it lets us efficiently design one-of-a-kind physics and makes it straightforward to incorporate varying experimental data in our models. Most of the software programs we see require intensive training just to set up even the most artificially simple problems. With COMSOL Multiphysics I could use tools that come standard to solve real problems with real materials right from the start."
A pressurizer (Figure 3), housed within a safety-first pump module, generally interfaces the ambient outside world and the cold cryogenic world within the HFIR. If air and heat leak in and create just the right mixture with hydrogen, a fire or explosion could result. To prevent such a disaster, the pressurizer sits within a vacuum chamber housed inside a safety-first pump module that Freels helped design. The two chambers of the pressurizer stack one above the other and interact through heat-resistive tubing. Near the variable-speed circulators, at the top of the pressurizer, temperatures reach approximately 300 K. The base of the pressurizer connects by a vertical tube to the main transfer line where hydrogen at 18 K moves at 8.1 m/s through a pipe diameter of 1.25 cm. Inside the pressurizer, the hydrogen remains relatively still.
Figure 3: Simulating non-isothermal hydrogen flow and solid conduction reveals temperatures and flow patterns within the important lower pressurizer chamber (a). Simulating conduction alone in the pressurizer yields about the same overall temperature drop (b). Critical to safety, the conductiononly model underpredicts the mass of cold hydrogen in the lower chamber.
"We use COMSOL Multiphysics because it lets us efficiently design one-of-a-kind physics and makes it straightforward to incorporate varying experimental data in our models. Most of the software programs we see require intensive training just to set up even the most artificially simple problems."
When the HFIR shuts down for regular maintenance or during a power outage, the hydrogen in the transfer line essentially shrinks, which sucks some of the gas from the pressurizer into the transfer line. If the hydrogen in the pressurizer is too hot, it heats up the mass already in the transfer line. The mixing lowers the density, which could trip the variable-speed circulators or unnecessarily damage other loop components. Sufficient hydrogen at temperatures below 33 K in the lower chamber of the pressurizer prevents such disruptions.
Freels uses COMSOL Multiphysics to determine if the pressurizer will contain enough hydrogen at a sufficiently low temperature to prevent trouble when the HFIR shuts off. His models combine the Non-Isothermal Flow and the Convection and Conduction application modes for the hydrogen, with the Thin-Conductive Shell application mode for the pressurizer walls. He handles the nonlinear changes in the hydrogen properties by importing experimental data with COMSOL Multiphysics' automatic interpolation feature. He uses cubic spline or linear interpolation and reads in experimental data through text files. With the data, COMSOL finds the right material value at each iteration step. As Freels explains, "Simply using the interpolation functions, it was very easy to set up these nonlinear material properties in the provided tables."
A major boost in computational efficiency came from using shell elements for the thin walls of the pressurizer. Representing the pressurizer walls with a thin 3D layer would require an enormous quantity of tiny elements. COMSOL Multiphysics´ shell elements model physics along a boundary instead of across it. In Freel´s case, the walls of the pressurizer became 2D surfaces represented by a relatively coarse mesh.
Freels also combined the parametric solver with solver scripting to set up an iterative-relaxation scheme. By automatically integrating the density of the gas in the lower chamber, his model determines if the mass of hydrogen in the cold lower chamber is enough to ensure the HFIR operates safely.
The second time around...flexibility and ease of use
Figure 4: Neutrons coming from the reactor pass straight through the moderator vessel walls before they travel down the HB-4 guide hall. The hydrogen that cools the flux enters the moderator vessel through a narrow inlet, expands, turns 180°, picks up 2.7 kW of heat from the striking neutrons, recompresses and exits in the reverse direction.
When Freels started using COMSOL Multiphysics, he already had an HFIR pressurizer model built on conduction alone, but he needed to model non-isothermal turbulence in the moderator vessel. He started with a few examples in the model library and then tackled a problem he knew inside out: the conduction-only model of the HFIR pressurizer (Figure 3b). He reports enthusiastically, "Building the model was amazingly easy. I created the 3D pressurizer geometry in the user interface with the built-in CAD tools. I then parameterized the model using intuitive type-it-in expressions. The temperatures I got from that first model matched my results from the different simulations with other packages including Abaqus, Nastran, and our own Heating program. The COMSOL Multiphysics model gave as good or better results and took a lot less effort."
It's easy to see why Freels completely tossed out his early conduction-only work once he added the non-isothermal flow and the nonlinear material properties to his model. This showed that slow buoyant recirculation actually produces much more cold hydrogen than predicted with conduction alone. As Freels notes, "We are validating the non-isothermal simulation results by comparing them with results from a testing program that includes temperature sensors on the pressurizer walls. These simulations potentially circumvent tremendous trouble and definitely saved us a pressurizer redesign. I wish we had done it with COMSOL Multiphysics from the start."
Figure 5: Freels sets up his non-isothermal turbulence models and matches the results to test data from literature. Shown are temperatures at a heated wall obtained with the simulation and NASA data (squares) from a rocket engine test.
The moderator vessel gets its name because hydrogen passing inside it "moderates" or lowers the temperature of the neutron flux that crosses through it. It is a pouch-shaped aluminum flow-through bend at the outer end of the transfer loop, just at the entry of HB-4 (Figure 4). The outer wall of the vessel heats when it absorbs free neutrons, so the hydrogen inside picks up approximately 2.7 kW of heat. The temperature rise is enough to trigger nonlinear hydrogen behavior along the boundary layers near the aluminum walls. Even when the reactor shuts down for maintenance, it remains so hot that flowing hydrogen is required to cool it (Figure 5).
While modeling non-isothermal turbulent flow with nonlinear material properties is understandably tricky, Freels can still build his simulations straight from the COMSOL Multiphysics user interface. His models couple the k-e Turbulence application mode with the Convection and Conduction application mode, and he adds an extra equation to account for the non-isothermal effects. Figure 5 shows his match to NASA test data for a similar case-a rocket jet engine with heating on a side wall.
Commenting on his experience with the software, Freels says, "COMSOL Multiphysics modeling is amazingly easy, especially when you consider how hard it is to use other software. Once I sorted out the non-isothermal turbulence strategy, I had the models up and running in pretty short order. The project wound up contracting outside experts to build the same Fluent and CFX models since it just takes too long to set up even simple problems with them. For instance, we found that interfacing experimental material properties with Fluent required a separate coding development. But in COMSOL Multiphysics, we did it all from the graphical interface."
User Profile: Dr. Jim Freels
Dr. Jim Freels, a nuclear engineer with a mathematical science background, is no beginner to numerical modeling. He wrote his own finite-element code for computational fluid dynamics during PhD research at the University of Tennessee, Knoxville, with Dr. A. J. Baker as his advisor. He's managed a wide variety of scientific software programs beginning with his work at SAIC (Oak Ridge, TN), Technology for Energy Corporation (Knoxville, TN), and during his 14-year career at Oak Ridge National Laboratory.
Commenting on the necessity for the modeling described in this article, Freels says, "When it comes to safety at ORNL, a single analysis is very rarely acceptable. In our extensive review process, we check all analyses against other codes capable of performing similar calculations."
Read the research paper at:
www.comsol.com/academic/papers/1780