# Mathematical Modelling of the Thermal Process in the Aquatic Environment with Considering the Hydrometeorological Condition at the Reservoir-Cooler by Using Parallel Technologies

Alibek Issakhov (al-Farabi Kazakh National University, Kazakhstan)
DOI: 10.4018/978-1-4666-9755-3.ch010
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## Abstract

This paper presents the mathematical model of the thermal power plant in reservoir under different hydrometeorological conditions, which is solved by three dimensional Navier - Stokes and temperature equations for an incompressible fluid in a stratified medium. A numerical method based on the projection method, which divides the problem into four stages. At the first stage it is assumed that the transfer of momentum occurs only by convection and diffusion. Intermediate velocity field is solved by fractional steps method. At the second stage, three-dimensional Poisson equation is solved by the Fourier method in combination with tridiagonal matrix method (Thomas algorithm). At the third stage it is expected that the transfer is only due to the pressure gradient. Finally stage equation for temperature solved like momentum equation with fractional step method. To increase the order of approximation compact scheme was used. Then qualitatively and quantitatively approximate the basic laws of the hydrothermal processes depending on different hydrometeorological conditions are determined.
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## Introduction

Environment - the basis of human life, as mineral resources and energy are produced from them. Moreover they are the basis of modern civilization. However, the current generation of energy cause appreciable harm to the environment, worsening living conditions. The basis of the same energy - are the various types of power plants. But power generation in thermal power plants (TPP), hydro power plant (HPP) and nuclear power plants (NPP) is associated with adverse effects on the environment. The problem of the interaction of energy and the environment has taken on new features, extending the influence of the vast territory, most of the rivers and lakes, the huge volumes of the atmosphere and hydrosphere.

With the increasing use of coastal waters for the economic and social needs the vulnerability of coastal waters due to the harmful effects of excess concentration of natural substances is elevating too. Pollution associated with the release of industrial products, etc. require special attention and management of coastal waters. Chemical plants and power plants use the coastal water in large quantities for cooling and throw away the water in the environment with higher temperature.

The circulation system of cold water from thermal power plant Kilakap is modeled in the paper (Suryaman et al., 2012). It was built and is operating since 2006, which uses the water of the Indian Ocean as a cooling unit. The water passing through the condenser, is poured back into the ocean through the drainage system. The discharged water temperature is higher than the ocean’s water temperature. It is important that poured warm water from drainage circulating did not get back into the water absorbent cooling system, otherwise the temperature of water absorbent will be growing, in turn causing a temperature increase in the water absorbent and drainage. Any rise in temperature water absorbent reduces cooling efficiency (capacitors), which eventually leads to a decrease in overall plant efficiency. The heated water interacts with the natural conditions of the sea or rivers, affecting aquatic life. When the heat acts as a contaminant this is called thermal pollution. The temperature rise affects various physical and chemical properties of the sea water such as density, viscosity, dissolved oxygen, salinity, turbidity, aquatic flora. Physical and chemical properties’ change directly affects to the lives of marine organisms. Some sea creatures can counteract to a rise in temperature, but not all of them.

The effect of the discharged water depends on the volume and temperature of discharged water, seawater temperatures (near the drain) and on the circulation of the flow around the drain. Heat transfer in coastal waters is part of the physical properties that depends on the tides and ebbs, water depth, sea waves, river flows, salinity, heat source, coastal structures.

Interconnected numerical model is built in the paper (Ali, Fieldhouse & Talbot, 2011). A three-dimensional temperature distribution of hot water thrown to standing water is modeled in the work above. This model is the relationship with the natural experiment, which was carried out on the one side of the British Channel. The thermal camera is used, as a source of shallow and stagnant water. The result of artificial experiment was 10 times smaller, which was held in the laboratory. This model is used for calculating the temperature distribution in the channel when using water as a coolant channel for environmental purposes instead of the use of conventional capacitors. After the use of water as the coolant it is returned again into the channel as a hot thermal dome discharged from the tube end.

The model shows the heat-proportioned profile of the jet, which resets the thermal plume discharging horizontally into shallow and still receiving water.

A mathematical model and numerical simulation to verify operation of the circuit water and thermal circulation is used in the paper (Beckers & Van Ormelingen, 1995). It was imposed by the developer of energy-station seaport Zeebrugge in Belgium, on the North Sea coast. Particular attention was paid to the water cooling, as the classical method of cooling the released warm water in the main river was impossible because the internal port (harbor) Zeebrugge, where the station was actually planned is not supplied with water from the river. This inner reservoir filled with sea water is cut off from the outer harbor and the sea with two gateways (barriers).

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