Session: 01-07-02 Industrial Fluid Mechanics

Paper Number: 65703

Start Time: August 12th, 10:50 AM

65703 - A Unified Theory for the Pressure Change of Sudden Expansions and Contractions Based on the Momentum Balance 

A new momentum-based approach to calculate the pressure loss of turbulent flows through sudden contractions and orifices is presented. While for sudden expansions the loss coefficient is derived with the aid of the momentum balance (known as the Borda-Carnot equation), all other hydraulic structures are mathematically described using the energy conservation with empirically determined loss coefficients. It will be shown that the proposed approach yields loss coefficients for sudden contractions and orifices straightforward without the use of empirical coefficients.

The integral momentum balance applied to flows through sudden contractions and orifices requires physical coefficients, which are the momentum coefficient and the pressure coefficient. These coefficients account for the inhomogeneous distribution of the velocity and the pressure over the cross-sections. By using a set of numerical simulations with different settings for the area ratio and the discharge, the dependency of the obtained coefficients on the area ratio or the discharge is expressed by simple mathematical functions. Together with these physical coefficients, the momentum balance allows for an analytical calculation of the pressure loss. The predicted pressure loss of a sudden contraction shows good agreement with experimental results and the classical parameterization of Idelchik. The expressions found for the sudden contraction can directly be applied to the momentum balance for the pressure loss of orifices. But in the case of an orifice, an additional physical coefficient is required. Again, the predicted pressure loss shows good agreement with literature numbers. Physically speaking, the orifice is an extension of the sudden contraction.

The proposed approach shows that the momentum balance is also capable of predicting the pressure loss of flows through sudden contractions and orifices without the use of empirical correction coefficients.

Presenting Author: Sebastian Mueller Bundeswehr University Munich

Authors:

Sebastian Mueller Bundeswehr University Munich
Andreas Malcherek Bundeswehr University Munich