A Complex Analysis Formalism to Explain Fluid Behavior Across Barriers

We analyzed fluid flow over two circular cylinders in a tandem set-up and in an unstaggered configuration using complex analysis. We determined the complex potential using the superposition of doublets. Conformal mapping was used to analyze changes in the angle of attack θa. The flow was visualized using Python to display both streamlines, equipotential lines, and stagnation points. The forces on both cylinders were calculated using Blasius’ theorem. The force between the cylinders in both configurations were found to be proportional to the sum of inverse powers of the separation distance. This verifies the Ground Effect where an aerofoil experiences greater lift as it is closer to the ground. A repulsive force between the cylinders for case 1 and an attractive force between the cylinders for case 2 were observed. The equipotential lines for case 1 and case 2 resemble the electric field lines between two similar and opposite charges, respectively. This tells us that the nature of interaction between the cylinders can be determined by examining the equipotential lines. Results also reveal a shift from a repulsive force to an attractive force for case 1 for an angle of attack, θa ≥ π/4. Thus, the magnitude of the force between any two cylinders can be varied by varying the sepa- ration distance while the nature of the force can be varied by changing the angle of attack