Development of a Numerical Model to Evaluate the Terrestrial Behavior of Radionuclides

(1)

2019 ⦽ǎႊᔍᖒ⠱ʑྜྷ⦺⫭ ⇹ĥ⦺ᚁݡ⫭ םྙ᫵᧞Ḳ

373 Development of a Numerical Model to Evaluate the Terrestrial Behavior of Radionuclides

Byung-Il Min*, Kihyun Park, Sora Kim, Byung-Mo Yang, Jiyoon Kim, and Kyung-Suk Suh

Korea Atomic Energy Research Institute, 111, Daedeok-daero 989beon-gil, Yuseong-gu, Daejeon, Republic of Korea

*

bimin@kaeri.re.kr

1. Introduction

A numerical model is needed to evaluate the long-term movement of radionuclide to land, river, lake, and ocean after an nuclear accident such as Fukushima accident. In this study, we develop a numerical model using a traditional kinematic wave equation.

2. Wave Equation

2.1 Kinematic Wave Equation

Fluid mechanics is used in various fields, and appropriate governing equations should be used according to the purpose of use. Generally, Saint Venant equation is used to express the flow of the river. The equation is as follows.

డ஺ డ௧൅ డொ డ௫ൌ ݍ ൅ ሺ݅ െ Ȱሻ డ௨ డ௧൅ ݑ డ௨ డ௫൅ ݃ డ௬బ డ௫ ൌ ݃൫ݏ௙െ ݏ଴൯ െ ݍሺ ௨ି௩ ஺ ሻ (1)

The equation (1) may be rewritten in the following form for a ready reference to the various types of wave models that are recognized.

ଵ ௚ డ௨ డ௧൅ ௨ ௚ డ௨ డ௫൅ డ௬బ డ௫ ൅ ൫ݏ௙െ ݏ଴൯ ൌ Ͳ (2)

The unknown parameters for the channel shapes under consideration

D

_k and

mk

being the

unknown functions. The Kinematic Wave equation for the channel flow can be written as given below:

డ஺ డ௧൅

డሺఈೖ஺೘ೖሻ

డ௫ ൌ ݍ (3)

2.2 Kinematic Wave Equation Solution

As illustrated in Fig 1, an overland flow starts from the upstream boundary without any inflow. This water deficit propagates into the downstream reach. The water surface profile is continually being increased until it reaches its equilibrium.

Fig.1. Illustration of one-dimensional Overland Unsteady Flow Profile.

The initial conditions for the Kinematic Wave equation overland flow include the dry bed condition everywhere on the ground before it rains.

ݕሺݐǡ ݔሻ ൌ ݕሺͲǡ ݔሻ ൌ ͲǤͲ

(2)

337744

2019 ⦽ǎႊᔍᖒ⠱ʑྜྷ⦺⫭⇹ĥ⦺ᚁݡ⫭םྙ᫵᧞Ḳ Guo and Urbonas (2009) and Guo et al. (2012) applied watershed shape factor to convert a natural watershed into its equivalent rectangular plane so that the unit-width KW theory can be used to predict overland flow from a given rainfall.

ܮ௪ ܮ ൌ ሺͳǤͷ െ ܣ௠ ܣሻሺ ʹ ߨ_ͺሺ ߨܣ ͺܮଶሻሻ ܺ௪ൌ ஺ ௅ೢ (6)

in which A= watershed area, B= watershed width, Am = larger half area between left and right areas along the waterway through the catchment, L = length of waterway, Xw= length of overland flow, and Lw= width of plane as illustrated in Fig. 2.

Fig. 2. Conversion of Natural Catchment into Kinematic Wave Rectangular Plane.

3. Numerical Results

3OHDVHIROORZWKLV$XWKRU¶V*XLGH The developed numerical model has been applied to the field and will be compared with observation data in future studies.

Fig. 3. Computation results of precipitation and eroded soil weight.

REFERENCES

[1] Guo, J. C.Y. and Urbanos B. (2009). "Conversion of Natural Watershed to Kinematic Wave Cascading Plane," Journal of Hydrologic Engineering, Vol 14, No 8, August, pages 839-846

[2] Guo, James C. Y. Cheng, Jeff, Wright, L.(2012) ³)LHOG7HVWRQ&RQYHUVLRQRI1DWXUDO Watershed LQWR.LQHPDWLF:DYH5HFWDQJXODU3ODQHV´$6&( J. of Hydrologic Engineering, Vol. 17, No. 8, August.