OCEAN HYDRODYNAMIC MODEL

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2 Jurnal Teknologi Pengelolaan Limbah (Journal of Waste Management Technology), ISSN Volume 10 Nomor 1 Juli 2007 (Volume 10, Number 1, July, 2007) Pusat Teknologi Limbah Radioaktif (Radioactive Waste Technology Center) OCEAN HYDRODYNAMIC MODEL Chevy Cahyana Radioactive Waste Technology Center - BATAN ABSTRACT Ocean hydrodynamic models are very important for simulate global oceanic circulation. Hydrodynamic model on oceanic system can be used for assess heat dissipation on the ocean and the dispersion of radionuclide that released to the ocean water, and also can be used for ocean climate study. Various computer codes have been developed using hydrodynamic model to simulate many kinds of physical behavior on ocean. Princeton Ocean Model (POM), Oceanic General Circulation Model (OGCM) and Surface water Modeling System (SMS) are some of computer codes that use hydrodynamic model. These computer codes have been implemented for ocean behavior study. Simulation results show insignificant difference compared with observation data. INTRODUCTION Radioactive effluent can be released from stack to the atmosphere system on nuclear facility operation. Radioactive plume that move on the ocean will be deposited into ocean water bodies, and then radioactive effluent will be dispersed in ocean system. On the other side, radioactive waste can be released directly into ocean system (Fig. 1). Radioactive effluent can influence the ocean ecosystem. The utility of ocean water as cooling water of a nuclear facility can discharge warm water as a secondary effluent into the ocean system. The discharge of cooling water with its thermal loads, especially in a chronic release could alter the temperature distribution in a small area such as estuary or coastal water. Addition of such water constitutes a form of pollutants to the ecosystem for the thermal pollutant can cause stressed to the entire ecosystem [1]. Figure 1. The pathway of the radioactive effluent released to ocean water body. The consequences of released of effluent radioactive and warm cooling water to the ocean ecosystem from nuclear facility operation must be assessed deeply and comprehensive. For this reason, the study of radioactive and heat effluent movement must be done. Radioactive effluent dispersion and heat dissipation in the ocean are influenced by ocean water circulation. The hydrodynamic model is used to assess the behavior of ocean water circulation. Hydrodynamic is the scientific study of the motion of fluids, especially non compressible liquids, under the influence of 86

3 Chevy Cahyana : Ocean Hydrodynamic Model internal and external forces. Hydrodynamic includes concepts of momentum, continuity, compression, viscosity, time, turbulence, friction, coriolis, transport, forcing mechanism and Navier-Stokes equation. Various computer codes have been developed using hydrodynamic concepts to assess the behavior of ocean circulation. Some of these computer codes are Princeton Ocean Model (POM), Oceanic General Circulation Model (OGCM) and Surface water Modeling System (SMS). HYDRODYNAMIC CONCEPTS The definition of hydrodynamic is the scientific study of the motion of fluid, especially non compressible liquid, under the influence of internal and external forces. The important forces are gravity, friction and coriolis. Forces are vector, so they have magnitude and direction [2]. Gravity Gravity is the dominant force. The weight of water in the ocean produces pressure. Change in gravity due to the motion of sun and moon relative to earth produces tides, tidal currents and tidal mixing. Buoyancy is the upward or downward force due to gravity acting on a parcel of water that is more or less dense than other water at its level. Friction Friction is the force acting on a body as it moves past another body while in contact with that body. The bodies can be the parcel of water or air. Wind stress is the friction due to wind blowing across the sea surface. It transfers horizontal momentum to the sea, creating currents. Wind blowing over waves on the sea surface causing them to grow into bigger waves. Coriolis force Coriolis force is the dominant pseudo-force influencing motion in a coordinate system fixed to the earth. Pseudo-forces are apparent forces that arise from motion in curvilinear or rotating coordinate system. Coriolis effect is the deflection of wind that moving along the surface of the earth to the right of the direction of travel in the northern hemisphere and to the left of the direction of travel in the southern hemisphere. This effect is caused by the rotation of the earth and is responsible for the direction of the rotation of water masses. As a consequence, currents rotate counter clockwise on the northern hemisphere and clockwise on the southern hemisphere. Hydrodynamic is branch of fluid mechanics. Fluid mechanics used in oceanography are based on Newtonian mechanics modified by our evolving understanding of turbulence. Particular equations on hydrodynamic concepts are constructed from the conservation laws of mass, momentum, angular momentum and energy (table 1). Table 1. Conservation laws leading to basic equation of fluid motion [2] Conservation of mass: Conservation of energy: Conservation of momentum: Conservation of angular momentum: Leads to continuity equation Conservation of heat leads to heat budget Conservation of mechanical energy leads to wave equation Leads to momentum (Navier-Stokes) equation Leads to conservation of vorticity Hydrodynamic includes concepts of momentum, continuity, compression, viscosity, time, turbulence, friction, coriolis, transport, forcing mechanism and Navier-Stokes equation [3]. Momentum Momentum is defined as the product of mass and velocity of an object. In general, the momentum of an object can be conceptually thought of as how difficult it is to stop the object, as determined by multiplying two factors: its inertia (the resistance of an object to being accelerated) and its velocity. The conservation law of momentum states that the total momentum of a closed system of objects (which has no interactions with external agents) is constant. (1) Continuity In fluid dynamics, a continuity equation is an equation of conservation of mass. Its differential form is: 87

4 Jurnal Teknologi Pengelolaan Limbah (Journal of Waste Management Technology), Vol 10 No ISSN (2) Where, ρ is density, t is time, and u is fluid velocity. Compression For liquids, whether the incompressible assumption is valid depends on the fluid properties (specifically the critical pressure and temperature of the fluid) and the flow conditions (how close to the critical pressure the actual flow pressure becomes). The incompressible Navier-Stokes equations can be used to solve incompressible problems. They are simplifications of the Navier-Stokes equations in which the density has been assumed to be constant. Viscosity Viscous problems are those in which fluid friction has significant effects on the solution. The Reynolds number can be used to evaluate whether viscous or inviscid equations are appropriate to the problem. Stokes flow is flow at very low Reynolds numbers, such that inertial forces can be neglected compared to viscous forces. On the contrary, high Reynolds numbers indicate that the inertial forces are more significant than the viscous (friction) forces. Therefore, we may assume the flow to be an inviscid flow, an approximation in which we neglect viscosity at all, compared to inertial terms. This idea can work fairly well when the Reynolds number is high, even if certain problems, such as those involving boundaries, may require that viscosity be included. Transport There are two kinds of transport in hydrodynamic, i.e., diffusion and advection. Diffusion is the movement of particles from an area where their concentration is high to an area that has low concentration (salt through a membrane). Advection is transport in a fluid (sand in a river). HYDRODYNAMIC NUMERICAL MODELING Numerical modeling of hydrodynamic consist of data requirement, conceptual model and method for solve the equation. The key requirements are available data and sufficient information to characterize the type of flow regime expected in the system. Data should be available for a number of areas. The general data requirements for modeling are geographical data, flow and stage, constituent loading, initial condition and data to calibrate the model result against field values. Geographical data describes the system layout. Flow and stage data define the flows crossing boundaries of the system. Constituent loadings define the water quality inputs. Modeling flow is very complex, thus modelers attempt to simplify the system as much as possible whilst still ensuring that the major components are fully represented. The governing equations are, in general, time transient, non-linear and highly complex when flow is turbulent. An additional complication is that the density of the water may vary. Thus the most general case, simulation must also include simultaneous solution for density influencing parameters such as salinity or temperature. When flow is influenced by density variations it is described as stratified. When it is not influenced by density variations it is then described as homogeneous [4]. With the available data and based on the processes of interest a Conceptual Model should be developed. The conceptual model should outline all of the processes of interest at the site and how these will be represented with a numerical model. There are five major types of approaches and approximations that can be applied for different types of flow regimes. Fully three-dimensional flow Three-dimensional flow systems where the hydrostatic assumption applies. Two-dimensional depth averaged flow Two-dimensional laterally averaged flow One-dimensional cross-section averaged flow One dimension model can be applied for upstream sections of rivers where effects of flow variation across the river section can be neglected but where the tidal storage prism of the upstream river requires that it be modeled. Two dimensions model (horizontal plan - vertically averaged) can be applied for shallow areas that are subject to flooding and drying (marshes, wetlands and sand-banks). Three dimensions model can be applied where the processes alter with depth such as in the bay, ocean, deep reservoirs, etc. Almost always were wind is involved. A depth averaged model is never suitable for a wind dominated water body, because in fact water return under neath. This assumption is the reason why three dimensions model is better than two dimensions model. These conditions are described on figure 2 bellow, 88

5 Chevy Cahyana : Ocean Hydrodynamic Model Figure 2. A comparison between 2D and 3D model [4]. Many predictive computer codes for studying the dispersion of radionuclide from land base source have been developed. Compartmental and hydrodynamic model have been applied to describe the dispersion of radioactive contaminant and to predict long term radiological impacts on global, regional and local scales. Special dispersion model have been based on the oceanic general circulation model (OGCM), originally developed for climate studies, which have been used to trace released of radioactive contaminant in the world ocean. Various techniques have been developed to describe the circulation of water in the world ocean using hydrographic data. Sarmento and Bryan (1982) developed a robust diagnostic model, in which the observed water temperature and salinity data were smoothed so the model was less sensitive to noise. This approach was further developed by Fujio and Imasato (1991), who applied the robust diagnostic model to the Pacific Ocean. The model reproduced the Pacific circulation well, even in the deep ocean [5]. The distribution of temperature on ocean water modeling consists of hydrodynamic equation and advection-diffusion equation has been developed by Blumberg and Mellor using continuity and momentum equations below [6]. Continuity equation, η t UD V D = 0 x y Momentum equation, 2 UD U D UV D ~ Fx t x y V D UV D V D ~ Fy t x y where respectively, D = H η, V 1 D 2 0 f V D f UD η gd x η gd x = < wu(0) > < wu( 1) > = < wv(0) > < wv( 1) > U, is mean current velocity on x (east-west) and y (north-south) axis U = U dσ and V = 1 1 D 0 1 V dσ, t is time, H is depth, η is surface elevation about mean sea level, g is acceleration due to gravity and f is Coriolis parameter. Difussifity in x and y axis are, ~ U U V F x = H 2AM H AM x x y y x ~ V U V F y = H 2AM H AM y y x y x where: A M is horizontal difussivity coefficient. Wind stresses at the surface are not considered. Bottom friction in both axis are given by [6], 89

6 Jurnal Teknologi Pengelolaan Limbah (Journal of Waste Management Technology), Vol 10 No ISSN < wu( 1) >= C U z 2 2 U V D 2 2 C V U V < wv( 1) >= z D where: C z is bottom friction coefficient. The two dimensional advection-diffusion equation for distribution of temperature on ocean surface is given by, ( T ) u( T ) v( T ) ( T ) ( T ) J = A A t x y D x D y ρ C H p Where u and v are vertically mean current speed determined from hydrodynamic model. HYDRODYNAMIC MODEL IMPLEMENTATIONS Various computer codes have been developed using hydrodynamic model to simulate many kinds of physical behavior on ocean. Nakano and Povinec used Oceanic General Circulation Model for assessment of the distribution of 137 Cs in the world ocean. Purba used hydrodynamic equation for simulate the water motion and advection-diffusion equation of heat for predict temperature distribution. The governing equation of motion and heat were solved numerically with finite difference methods by using Princeton Ocean Model. Implementation of OGCM for the Assessment of the Distribution of 137 Cs in the World Ocean [5] Nakano applied a modified version of the robust diagnostic OGCM to assess the distribution of 137 Cs in the world ocean. The model covers the world ocean with real topography and divides it horizontally into 2 0 x 2 0 grids and vertically into 15 levels. It covers the area from 79 0 S to 75 0 N, with the exception of the Arctic Ocean, which is not included in the model. The model consists of equation of motion, continuity, state, advection and diffusion. Based on the annual average hydrographic data and wind stress data of IRI/LDEO, the annually averaged velocity fields were determined diagnostically [5]. Figure3. Comparison of the calculated vertical profiles with the observed data. 90

7 Chevy Cahyana : Ocean Hydrodynamic Model Implementation of POM for the Simulation of Temperature Distribution [1] Cooling water from electrical power plant at Pemaron, Buleleng, Bali has to be discharged to the nearby coastal water. In order to lower the temperature of the cooling water before it reaches the natural coastal water, the warm water is directed into a cooling canal. The model has to predict water temperature distribution on the cooling canal. Input to the canal is cooling water from the plant, while warm water from the other end of the canal initiate warm water temperature distribution on the coastal water. Model simulation is run for chase with and without wind, during day and night time, using air temperature of 30 0 C and 26 0 C, respectively. Simulation is run until steady state condition reach. Ambient temperature is determined from field measurement which is about 29 0 C in average. The temperature of cooling water discharge continuously into the canal is 37 0 C. In the model, the temperature difference (ΔT) is 8 0 C. Model to simulate distribution of temperature at coastal water consists of hydrodynamic and advection-diffusion of heat equations. Hydrodynamic model which simulate water motion is 2-dimension vertically integrated and has been used in Princeton Ocean Model developed by Blumberg and Mellor. Simulations in canal are run with the design: length of canal is 1000 m and 2000 m, current speed is 1.3 m/sec, water depth is 0.45 m, wind speed is 3.1 m/sec, air temperature is 30 o C, solar radiation is watt/m 2, the relative air humidity is 80% and temperature difference (ΔT) is 3.2 o C. Results of simulation find that the temperature drops over 1000 m and 2000 m length are 0.22 o C (ΔT = 2.98 o C) and 0.44 o C (ΔT =2.76 o C), respectively. Validation of the model is done in 1000m-long cooling canal of Suralaya Power Plant in Banten showed a moderately good results where model predicts a drops of temperature of 0.54 o C while field measurements is 0.77 o C. So, there is about % inaccuracy of the model. Simulations in costal water of Pemaron Beach, Buleleng, Bali, are run with model design grid resolution of 20m x 20m, temperature difference (ΔT) at canal outlet is 2.98 o C and time run for 14 days. There 4 scenarios: cooling water enters as a discharge and no discharge (cooling water drop from pipe above sea water) and at condition ebb and flood spring tide. The distributions of surface temperature with no discharge and with discharge both during flood and ebb spring are given in Figures 6, 7, 8 and 9, respectively. The figures show that during flood spring tide with no discharge temperature difference (ΔT) of 1 o C and 0.1 o C are distributed at radius of 30 m and 80 m, respectively and with discharge radius of distribution for the same temperature difference (ΔT) is 50m and 150 m, respectively. During ebb spring tide with no discharge temperature difference (ΔT) of 1 o C and 0.1 o C are distributed at radius of 30 m and 80 m, respectively and with discharge radius of distribution for the same temperature difference (ΔT) is 50m and 150 m, respectively. No difference between ebb and flood tide. 91

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9 Chevy Cahyana : Ocean Hydrodynamic Model Figure 4. Surface temperature distribution at coastal water of Bontang Bay, East Kalimantan [1] CONCLUSION On the operation of nuclear facilities, radioactive and heat effluent can be released to the ocean water body. The consequences of the release of the effluent to man and to environment must be assessed. Hydrodynamic model can be used for study of radioactive and heat effluent movement in the ocean water body. The simulation of radioactive and heat effluent movement can be used for predict the impact of pollutant to man and to the environment, so the best preventive action can be done. Various computer codes have been developed using hydrodynamic concepts to assess the physical behaviors of the ocean. These computer codes can help the researchers to assess the impact of the released of radioactive effluent to man and to the environment. REFERENCES 1. Purba, M (2004). Distribution of Temperature and Salinity in the Ocean. Proceeding of the Seminar on the Development of Marine Radioecology in Indonesia. Jakarta. 2. Stewart, R. H (2002). Introduction to Physical Oceanography, Department of Oceanography. Texas A&M University. 3. Glamore, W.C (2007) Hydrodynamics, Water Research Laboratory, School of Civil and Environmental Engineering, University of South Wales. 4. Glamore, W.C (2007).Numerical Modeling, Water Research Laboratory, School of Civil and Environmental Engineering, University of South Wales. 5. Nakano, M., Povinec, P. P(2003) Oceanic General Circulation Model for the Assessment of the Distribution of 137 Cs in the World Ocean. Deep-Sea Research Part II. Pergamon. 6. Mellor, G. L (2003) Users Guide for a Three Dimensional, Primitive Equation, Numerical Ocean Model. Princeton University. Princeton, NJ. 93