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# A lattice boltzmann/s n framework for coupled heat transfer and neutron transport problems

#### Kao, Min-Tsung

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## Permalink

https://hdl.handle.net/2142/108130

## Description

- Title
- A lattice boltzmann/s n framework for coupled heat transfer and neutron transport problems
- Author(s)
- Kao, Min-Tsung
- Issue Date
- 2020-04-29
- Director of Research (if dissertation) or Advisor (if thesis)
- Valocchi, Albert J.
- Vanka, Surya Pratap
- Kozlowski, Tomasz

- Doctoral Committee Chair(s)
- Uddin, Rizwan
- Committee Member(s)
- Zhang, Yang
- Department of Study
- Nuclear, Plasma, & Rad Engr
- Discipline
- Nuclear, Plasma, Radiolgc Engr
- Degree Granting Institution
- University of Illinois at Urbana-Champaign
- Degree Name
- Ph.D.
- Degree Level
- Dissertation
- Keyword(s)
- Lattice Boltzmann Method
- Discrete-ordinates Method
- Coupling between neutron transport and heat conduction equations
- Temperature-dependent cross sections
- Temperature-dependent thermal conductivity

- Abstract
- Nuclear reactors are complex, coupled, multi-physics and multi-scale systems. There are usually two approaches — loose coupling and tight coupling — to solve coupled mathematical equations describing a multi-physics system. The major advantage of loose coupling is to allow separately validated codes to perform specific calculations without modifying them. This may be the only approach available when users do not have access to the source codes. One of the disadvantages of loose coupling is data exchange between codes. On the other hand, tight coupling prevents the disadvantages due to data exchange in loose coupling. The goal of this dissertation is to study the coupling between neutron transport and heat conduction equations with temperature-dependent thermal conductivity and temperature-dependent neutron cross sections. The neutron transport equation is solved using the discrete ordinates method (SN ); and the heat conduction equation is solved using the lattice Boltzmann method (LBM). In the SN method, the angle in the integro-differential form of the NTE is discretized. Similarly, the continuous velocity space is discretized in the LBM. Taking advantage of the similarities between the SN and the LBM approaches, a consistent framework to solve tightly coupled NTE using the SN method, and the heat conduction equation using the LBM is developed in this dissertation. A new “two-point interface scheme” is proposed for the heat conduction problems in the LBM to satisfy the continuities of temperature and heat flux at the interface for the multi-region problems. The integrated framework and the two-point interface scheme is applied to simple 1-D, Cartesian geometry, one and two-region heat conduction problems with temperature-independent and temperature-dependent thermal conductivities. Numerical results for the two-region heat conduction problems with temperature-dependent thermal conductivities studied in this dissertation and corresponding CPU times solved using the LBM with the two-point interface scheme are compared against those obtained using simple finite difference methods. Two types of temperature dependence of neutron cross sections are studied in this dissertation. The first one assumes neutrons are in the thermal energy range (near-Maxwellian spectrum), and the fission and the absorption cross sections are inversely proportional to temperature. This type of temperature feedback assumes same correlations for the fission and the absorption cross sections, and is used for the one-way coupled criticality and two-way coupled problems. The second temperature feedback is only used in the two-way coupled problems, and it assumes that the capture cross section is proportional to temperature to mimic Doppler effect. For the one-way coupled, fixed source problems with non-multiplying medium (fission cross section is zero) with the first type of temperature feedback, the magnitude of the minimum temperature-dependent absorption cross section (at the location of maximum temperature), Σa(T(k(T))), can be as much as 30 % lower than its counterpart evaluated at the effective temperature. In addition, the maximum neutron scalar flux is about 15 % higher with temperature dependent absorption cross section, Σa(T(k(T))). Moreover, the peak of the scalar flux moves toward higher temperature region due to the reduction of temperature-dependent absorption cross section at higher temperatures. Furthermore, the drop in absorption cross section at higher temperatures increases neutron diffusion, resulting in spatially more uniform scalar flux distribution. For the one-way coupled, fixed source problems (fission cross section is zero), lower thermal conductivity due to fuel burnup leads to higher temperature. On the contrary, for the two-way coupled simulations (fission cross section is not zero) with the first type of temperature feedback for the fission and the absorption cross sections, a reduction in the thermal conductivity increases the fuel temperature, which is in turn reduced due to negative fuel temperature coefficient of reactivity. For the two-way coupled simulations with the second type of temperature feedback (Doppler effect), an increase in the temperature, due to negative fuel temperature coefficient of reactivity, increases capture cross section; and the scalar flux, power density and thus temperature, are decreased. For the two-way coupled problems using the two types of temperature feedbacks studied in this dissertation, the system can stabilize after small perturbations in the reactor. In both temperature feedback mechanisms, an increase of the surface temperature decreases scalar flux and fission power, which in turn reduces temperature. Thus, the maximum fuel temperature decreases, and the fuel temperature profile becomes more uniform (flat).
- Graduation Semester
- 2020-05
- Type of Resource
- Thesis
- Permalink
- http://hdl.handle.net/2142/108130
- Copyright and License Information
- Copyright 2020 Min-Tsung Kao

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