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Title:  A lattice boltzmann/s n framework for coupled heat transfer and neutron transport problems 
Author(s):  Kao, MinTsung 
Director of Research:  Valocchi, Albert J.; Vanka, Surya Pratap; Kozlowski, Tomasz 
Doctoral Committee Chair(s):  Uddin, Rizwan 
Doctoral Committee Member(s):  Zhang, Yang 
Department / Program:  Nuclear, Plasma, & Rad Engr 
Discipline:  Nuclear, Plasma, Radiolgc Engr 
Degree Granting Institution:  University of Illinois at UrbanaChampaign 
Degree:  Ph.D. 
Genre:  Dissertation 
Subject(s):  Lattice Boltzmann Method
Discreteordinates Method Coupling between neutron transport and heat conduction equations Temperaturedependent cross sections Temperaturedependent thermal conductivity 
Abstract:  Nuclear reactors are complex, coupled, multiphysics and multiscale systems. There are usually two approaches — loose coupling and tight coupling — to solve coupled mathematical equations describing a multiphysics 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 temperaturedependent thermal conductivity and temperaturedependent 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 integrodifferential 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 “twopoint 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 multiregion problems. The integrated framework and the twopoint interface scheme is applied to simple 1D, Cartesian geometry, one and tworegion heat conduction problems with temperatureindependent and temperaturedependent thermal conductivities. Numerical results for the tworegion heat conduction problems with temperaturedependent thermal conductivities studied in this dissertation and corresponding CPU times solved using the LBM with the twopoint 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 (nearMaxwellian 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 oneway coupled criticality and twoway coupled problems. The second temperature feedback is only used in the twoway coupled problems, and it assumes that the capture cross section is proportional to temperature to mimic Doppler effect. For the oneway coupled, fixed source problems with nonmultiplying medium (fission cross section is zero) with the first type of temperature feedback, the magnitude of the minimum temperaturedependent 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 temperaturedependent 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 oneway 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 twoway 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 twoway 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 twoway 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). 
Issue Date:  20200429 
Type:  Thesis 
URI:  http://hdl.handle.net/2142/108130 
Rights Information:  Copyright 2020 MinTsung Kao 
Date Available in IDEALS:  20200826 
Date Deposited:  202005 
This item appears in the following Collection(s)

Graduate Dissertations and Theses at Illinois
Graduate Theses and Dissertations at Illinois