A coarse-mesh nodal diffusion method based on response matrix considerations

"March 1977."Originally issued as the 2nd author's Sc. D. thesis, Massachusetts Institute of Technology, Dept. of Nuclear Engineering, 1976"Electric Power Research Institute."Includes bibliographical references (pages 152-155)The overall objective of this thesis is to develop an economical computational method for multidimensional transient analysis of nuclear power reactors. Specifically, the application of nodal methods based on the multigroup diffusion theory approximation to reactors composed of regular arrays of large homogeneous (or homogenized) zones was investigated. A nodal scheme is formulated using the response matrix approach as a conceptual basis. Solutions of equivalent sets of coupled one dimensional problems are used to treat the local multidimensional response problems. Polynomial expansions in conjunction with weighted residual procedures are employed to obtain approximate solutions of the one-dimensional problems. A linear set of nodal equations expressed in terms of nodal average fluxes and interface average partial currents is obtained. Applications to two-dimensional few-group, static and transient problems demonstrate that the nodal scheme can be an order of magnitude more computationally efficient than conventional finite difference methods

Nonlinear methods for solving the diffusion equation

"November, 1976."Also issued as a Ph. D. thesis written by the first author and supervised by the second author, MIT Dept. of Nuclear Engineering, 1977Includes bibliographical references (pages 112-116)This thesis is concerned with methods for the transient solution of the neutron diffusion equations in one or two energy groups. Initially, nonlinear methods for solving the static diffusion equations using the finite element method were investigated. By formulating a new eigenvalue equation, some improvement in the solution efficiency was obtained. However, the transient solution of the diffusion equation using the finite element method was considered to be overly expensive. An analytic method for solving the one-dimensional diffusion equation was then developed. Numerical examples confirmed that this method is exact in one dimension. The method was extended to two dimensions, and results compared employing two different approximations for the transverse leakage. The method based on a flat approximation to the leakage was found to be superior, and it was extended to time-dependent problems. Results of time-dependent test problems show the procedure to be accurate and efficient. Comparisons with conventional finite difference techniques (such as TWIGL or MEKIN) indicate that the scheme can be an order of magnitude more cost effective

A new approach to solving the multimode kinetics equations

Cover reads: By Joe C. Turner [sic], Allan F. HenryAlso issued as a Ph. D. thesis in the Department of Nuclear Engineering, 1972Includes bibliographical references (leaves 95-97)AEC AT(11-1)--305

Finite element synthesis method

Originally presented as the first author's thesis (Ph. D.), M.I.T. Dept. of Nuclear Engineering, 1975Includes bibliographical references (leaves 151-155)AT(11-1)226

Spatial homogenization of diffusion theory parameters

Originally presented as the first author's thesis, (Ph. D.)--in the M.I.T. Dept. of Nuclear Engineering, 1977Includes bibliographical referencesPrepared under ERDA Research ad Development EY-76-S-02-226

Continued development of nodal methods for nuclear reactor analysis

Northeast Utilities Service Company and Pacific Gas & Electric Compan

Development of a three-dimensional two-fluid code with transient neutronic feedback for LWR applications

The development of a three-dimensional coupled neutronics/thermalhydraulics code for LWR safety analysis has been initiated. The transient neutronics code QUANDRY has been joined to the two-fluid thermal-hydraulics code THERMIT with the appropriate feedback mechanisms modeled. A literature review of the existing coupled neutronics/thermal-hydraulics codes is presented. It indicates that all of the known codes have limitations in their neutronic and/or thermal-hydraulic models which limit their generality of application and accuracy. It was also found that a tandem coupling scheme was most often employed and generally performed well. A detailed steady-state and transient coupling scheme based on the tandem technique was devised, taking into account the important operational characteristics of QUANDRY and THERMIT. The two codes were combined and the necessary programming modifications were performed to allow steady-state calculations with feedback. A simple steady-state sample problem was produced for the purpose of testing and debugging the coupled code

TITAN code development for application to a PWR steam line break accident : final report 1983-1984

Modification of the TITAN computer code which enables it to be applied to a PWR steam line break accident has been accomplished. The code now has the capability of simulating an asymmetric inlet coolant temperature transient by employing different temperature transient forcing functions for different core inlet regions. Up to ten regions of the core can be considered and each region can have at most 50 channels. A total inlet coolant mass flow rate boundary condition option has been added to the code. Flow/coolant temperature transient and control rod transient can be simulated simultaneously by the code as necessary for a steam line break accident simulation. Also, the transient restart capability has been fixed which allows users to change core conditions during a transient calculation for various purposes. All these modifications have been tested by a ten-channel test calculation.Three steam line break accident simulations (YA-1, YA-2, and YA-3) with different pressure forcing functions have been performed. Each simulation included both closed and open-channel calculations. The steady-state results show that a 1-D thermalhydraulic analysis gives accurate results.Case YA-1 employed a pressure forcing function taken from a Yankee Atomic report. No boiling during the whole calculation was observed. Also, no significant difference between closed and open-channel calculations was found.Case YA-2 employed a reduced pressure forcing function with constant pressure after 45 seconds (because of the limitation of W-3 correlation data base). Boiling was observed around 42 seconds after the beginning of the transient. The MCHFR dropped to a value below 6 after boiling. The MCHFR went back to a high value ("30) at 50 seconds for the open-channel calculation while the MCHFR for the closed-channel case still remained below 6. The open-channel model provided a better condition of flow mixing among channels.Case YW-3 had the same pressure forcing function as that of case YA-2 except the pressure kept decreasing after 45 seconds. The MCHFR was about equal for open-and closed-channels. It is concluded that the closed-channel calculations may produce conservative core power values, but the effect on MCHFR is not always conservative

PWR steam line break accident.

A steam line break accident is one of the possible severe abnormal transients in a pressurized water reactor. It is required to present an analysis of a steam line break accident in the Final Safety Analysis Report (FSAR) of a nuclear power reactor. Only simple one-dimensional core simulations are currently applied to such accident analysis. However, the asymmetric characteristics of a steam break accident may require more detailed local information in order to determine the potential fuel damage resulting from the transient. TITAN, a coupled (neutronics and thermal-hydraulics) code with state-of-the-art neutronics and thermal-hydraulics models, is therefore modified and applied to steam line break accident simulations.The capabilities that are added to the code for a steam line break analysis include multiregion core inlet temperature forcing function, total inlet coolant flow rate boundary condition, total inlet coolant flow rate transient simulation capability, boron tracking equations, flow/coolant temperature transient plus control rod transient option, and one-dimensional, fully implicit numerical scheme.for thermal-hydraulics calculations. The modifications to TITAN are tested with a ten-channel PWR model. For inlet coolant temperature transients (one of the transients involved in a steam line break accident) test calculations lead to the conclusion that there is no significant difference between the results of closed- and open-channel calculations until boiling occurs.A ten-channel model with two partially inserted control rods is employed for the transient simulations. Steady state conditions are obtained first by both open- and closed-channel calculations. Results show that cross flow between channels is insignificant. Thus, the onedimensional, fully implicit numerical scheme for the thermal-hydraulics equations is useful to speed up the calculations. More than half of the computational effort is saved by using this scheme compared to the semi-implicit numerical scheme.Two extreme situations relevant to a steam line break accident are investigated: (1) Significant boiling due to severe depressurization when no return to power exists. (2) Return to power with no boiling because of high coolant temperature feedback coefficients. It is concluded that even after boiling occurs, the global parameters, such as total power and assembly power, still show no significant difference between the closed- and open-channel calcualtions. However, the local parameters, such as nodal power, void fraction and MDNBR, reveal differences between the two calculations. Results show that the open-channel calculation predicts lower MDNBR values as compared with the results of closed-channel calculation in a vapor generation process, since the coolant is driven away from of the hot spots. On the other hand, during a vapor condensation process, closed-channel calculations predict lower MDNBR results, since no cross flow is allowed to accelerated the condensation process.A closed-channel, uniform inlet coolant temperature transient calculation is performed. The results verify the necessity for a three-dimensional calculation of the accident simulations, since no boiling was predicted by-the one-dimensional calculation throughout the simulation period