MODELING AND DYNAMIC SIMULATION OF GRAVITATIONAL FLOW IN ATMOSPHERIC TANKS
Leonardo de Souza Leal
Engenheiro Químico | Engenheiro de Seguran?a do Trabalho | Mestre em Computa??o Numérica | Black Belt em Melhoria Contínua
Mathematical Modeling
In this article is developed the mathematical modeling of the dynamic gravitational flow in atmospheric tanks.
The models were obtained from the mass and momentum balances (equations (1) and (2)).
From equation (1) we get the equation (3), and by equation (2) considering the forces acting at the pipe outlet (hydraulic and friction force) we get equation (4).
The Equations (5) and (6) are expressions for friction factor. If Re > 4000 is used the Colebrook-White equation (equation 5) or if Re < 4000 is used the equation 6.
the nomenclature used is:
Numerical Method
Equations (3) and (4) are solved simultaneously by the Euler Integration Method.
Equation (5) is solved by the Successive Approximation Method.
Example: The equations were implemented in EXCEL VBA and solved numerically by the numerical methods previously mentioned. The data are inserted in the yellow cells and the RUN button performs the simulation. The procedure is:
Results:
Comparison with AFT Fathom 5.0 Software
We performed some simulations shown in the following tables, considering different input conditions. The results were compared with the results obtained by AFT Software Fathom 5.0, observing a good agreement between these results.
Download link to spreadsheet:
https://drive.google.com/open?id=0B0ClBxIeH9j2WjY4cWVPMVQwc28