Moosavi Mehr,Hadi

Analytical Models of two - phase Air - Water flow on chutes and Stepped Spillways

Abstract

In the present thesis, the results of an analytical study of the two-phase flow over stepped spillway and steep chute in the fully developed region are presented. Using two-phase air-water flow assumptions in the advection- diffusion equation, the continuity equation for the air phase is derived. By substituting 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. Since the depth of two-phase flow (D) isn’t clearly determined, three different assumptions for the depth of two-phase flow are used: , and (e.g., 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).

To determine the error and correlation between results of present models and results of Straub and Anderson’s model, Chanson’s model (1994) and experimental results of Chamani and Rajaratnam (1997, 1999), two criterio and are used. These two criterions show that the results of present models for the lower region are in good agreement with analytical and experimental results of Straub and Anderson and the experimental results of Chamani and Rajaratnam (1997, 1999).

Because of the fluctuation and turbulence in the upper region of the two-phase flow, the air concentration is assumed the 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 two-phase flow on chutes are between 44 to 59 percents.