2007 M.Sc. Graduated MousaviMehr Seyyed Hadi
Analytical Models of TwoPhase AirWater flow on Chutes
Student Name 


Supervisor 
Mohammad Reza Chamani Hamid Reza Safavi 

Advisor 
Mohammad Karim Beirami 

Date  20070804  
 

Keywords  Twophase flow Airwater Chute Air concentration Energy loss 
Abstract
In the present thesis, the results of an analytical study of the twophase flow over stepped spillway and steep chute in the fully developed region are presented. Using twophase airwater flow assumptions in the advectiondiffusion equation, the continuity equation for the air phase is derived. By substituting the velocity distribution equation proposed by Chiu (1988) in the continuity equation and applying boundary conditions, three models are proposed for the distribution of air concentration in the fully developed region. Three different assumptions for the depth of twophase flow are used: D = y90, y95, and y99; e.g., D = y90 is the depth of flow at which the air concentration is 90 %). Similar to the Straub & Anderson’s study (1958), the cross section of flow is divided in two regions (upper and lower). The results of the present models for the lower region are in good agreement with analytical and experimental results of Straub and Anderson (1958) and the experimental results of Chamani and Rajaratnam (1997). Because of the fluctuation and turbulence in the upper region of the twophase flow, the air concentration is assumed to follow an exponential distribution. The maximum error between the results of the proposed distribution for the upper region and the experimental results is 2 %. Using the air concentration distribution in the relative energy loss equation proposed by Chamani and Rajaratnam for stepped spillways, the relative energy losses for the twophase flow on chutes are between 44 to 59 percents.