# Thermal stratification and circulation of water bodies subjected to thermal discharge

Dissertation

Spring 3-31-1977

## Degree Name

Doctor of Engineering Science in Mechanical Engineering

## Department

Mechanical Engineering

Amir N. Nahavandi

Otto I. Reisman

Jui Sheng Hsieh

Pasquale J. Florio

Rong-Yaw Chen

## Abstract

A three-dimensional analytical model for large water bodies is presented. Time histories and spatial distribution of pressure, velocity and temperature in water bodies, subjected to thermal discharge, are determined employing a digital computer. The dynamic response is obtained for a rectangular water body by applying a finite difference method to the mass, momentum and energy balance equations. These partial differential equations are algebraically manipulated to obtain; 1) three parabolic differential equations integrated temporally to find the horizontal velocity components and temperature; 2) one algebraic integral equation to get the vertical velocity component; 3) one elliptic differential equation integrated spatially to find the pressure; and 4) one differential equation to get the water level. Numerical stability criteria are developed which facilitate the selection of space and time increments for stable numerical integration.

The distinctive feature of this analysis, as compared to previous studies, is the calculation of pressure and water level from equations of motion without simplifying assumptions such as hydrostatic pressure approximation and rigid-lid concept.

The mathematical formulation is verified by applying this analysis to cases where the final steady state flow patterns have been determined analytically or experimentally by others. In particular, the final steady state solution obtained from this dynamic analysis is verified with existing flow measurements of laminar flow development in a square duct. Furthermore, the natural circulation flows developed by this analysis are verified with known flow patterns in partially heated ponds.

The problem of thermal discharge entering a river with known initial velocity and temperature distribution is then analyzed. The time histories of the velocity and temperature distribution as well as the velocity and temperature profiles are obtained. These results provide the values of temperature rise and the rate of temperature rise needed for the assessment of the extent of thermal pollution in water bodies.

COinS