• Transactions of the Korean Society of Mechanical Engineers
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• v.7 no.4
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• pp.417-424
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• 1983

This paper presents two methods of obtaining approximate analytic solutions for the temperature distributions and heat flow to two-dimensional transient heat conduction problems in a finite strip with constant thermal properties using the Heat Balance Integral. The methods introduced in this study are as follows; one using the Heat Balance Integral only, and the other successively using the Heat Balance Integral and an exact analytic method. Both methods are applicable to a large number of the two-dimensional unsteady conduction problems in finite regions such as extended surfaces with uniform thickness, but in this paper only solutions for the unsteady problems in a finite strip with boundary condition at the base expressed in terms of step function are provided as an illustration. Results obtained by both methods are compared with those by the exact two-dimensional transient analysis. It is found that both approximate methods generate small time solutions, which can not be obtained easily by any exact analytic method for small values of Fourier numbers. In the case of applying the successive use of the Heat Balance Integral and Laplace transforms, the analysis shows good agreement with the exact solutions for any Fourier number in the range of Biot numbers less than 0.5.

• The Magazine of the Society of Air-Conditioning and Refrigerating Engineers of Korea
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• v.11 no.3
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• pp.1-8
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• 1982

When exact analytical solutions to certain type of heat conduction problems are quite cumbersome or not obtainable, it is important to introduce approximate analytical methods which are simple and useful compared with numerical methods. In this study, therefore, the Heat Balance Integral Method is applied to analysis of steady-state conduction in a straight fin of trapezoidal profile, and the two-dimensional temperature distribution in the fin and the approximate fin efficiency are obtained. Results are compared with those by the one- dimensional analysis and two-dimensional numerical analysis for a wide range of Biot numbers. It is shown that the two-dimensional temperature distribution obtained by the integral method is in good agreement with that by the finite element method at Biot numbers for which the result by the one-dimensional analysis is unreliable.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.9
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• pp.2404-2412
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• 1994

A mathematical model has been developed for predicting kinematic, thermal, and solidification histories of atomized droplets during flight. Liquid droplet convective cooling, recalescence, equilibrium-state solidification, and solid-phase cooling were taken into account in the analysis of the solidification process. The spherical shell model was adopted where the heterogeneous nucleation is initiated from the whole surface of a droplet. The growth rate of the solid-liquid interface was determined from the theory of crystal growth kinetics with undercooling caused by the rapid solidification. The solid fraction after recalescence was obtained by using the integral method. The thermal responses of atomized droplets to gas velocity, particle size variation, and degree of undercooling were investigated through the parametric studies. It is possible to evaluate the solid fraction of the droplet according to flight distance and time in terms of a dimensionless parameter derived from the overall energy balance of the system. It is also found that the solid fraction at the end of recalescence is not dependent on the droplet size and nozzle exit velocity but on the degree of subcooling.

• 유체기계공업학회:학술대회논문집
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• 2003.12a
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• pp.161-166
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• 2003

It is the common features of the integral reactors that the main components of the RCS are installed within the reactor vessel, and so there are no any flow pipes connecting the coolant pumps or steam generators. Due to no any flow pipes, it is impossible to measure the differential pressure at the RCS of the integral reactors, and it also makes impossible measure the flow-rate of the reactor coolant. As a alternative method, the method by the measurement of coolant pump power has been introduced in this study. Up to now, we did not found out a precedent which the coolant pump power is used for the real-time flow-rate calculation at normal operation of the commercial nuclear power plants. The objective of the study is to embody the real-time flow-rate calculation method by the measurement of coolant pump power in an integral reactor. As a result of the study, we could theoretically reason that the capacity-head curve and capacity-shaft power curve around the rated capacity with the high specific-speeded axial flow pumps have each diagonally steep incline but show the similar shape. Also, we could confirm the above theoretical reasoning from the measured result of the pump motor inputs, So, it has been concluded that it is possible to calculate the real-time flow-rate by the measurement of pump motor inputs. In addition, the compensation for a above new method can be made by HBM being now used in the commercial nuclear power plants.

• Nuclear Engineering and Technology
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• v.49 no.5
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• pp.905-913
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• 2017

Advanced reactor designs often feature longer operating cycles between refueling and new concepts of operation beyond traditional baseload electricity production. Owing to this increased complexity, traditional proportional-integral control may not be sufficient across all potential operating regimes. The prototypical advanced reactor (PAR) design features two independent reactor modules, each connected to a single dedicated steam generator that feeds a common balance of plant for electricity generation and process heat applications. In the current research, the PAR is expected to operate in a load-following manner to produce electricity to meet grid demand over a 24-hour period. Over the operational lifetime of the PAR system, primary and intermediate sodium pumps are expected to degrade in performance. The independent operation of the two reactor modules in the PAR may allow the system to continue operating under degraded pump performance by shifting the power production between reactor modules in order to meet overall load demands. This paper proposes a Takagi-Sugeno (T-S) fuzzy logic-based power distribution system. Two T-S fuzzy power distribution controllers have been designed and tested. Simulation shows that the devised T-S fuzzy controllers provide improved performance over traditional controls during daily load-following operation under different levels of pump degradation.