### Mathematical Modeling of Pressure on Cylindrical Ellipse using Side-by-Side Conﬁguration

Chairul Imron, Mahmud Yunus

#### Abstract

The application of the concept of fluid is often used to solve problems in the daily life. One of them is the problem of fluid around an elliptical cylinder. This study aims to solve the problems of the fluid around two elliptical cylinder configuration with side-by-side using the Navier-Stokes equations. Navier-Stokes equations–incompressible, viscous and unsteady-are solved using finite difference method staggered grid and SIMPLE (Semi Implicit Method for Pressure-Linked Equation) algorithms. Finite difference method is used to complete the grid arrangement, whereas the SIMPLE algorithm is used to obtain components of velocity and pressure value. Results of this study are the pressure value based on fluid flow profile and a mathematical model which received an elliptical cylinder pressure. Profile of fluid flow is simulated by varying the Reynolds number of 100, 1000, 7000, and 10000 as well as variations in the distance between the cylinder with a ratio of 2 <= S/a <= 6 where L is the distance between the cylinder and a is the minor axis of the cylinder ellipse. Then the pressure is calculated based on the value of the received cylinder pressure components. After obtaining the pressure value, then we create a mathematical model of the stresses imposed on the elliptical cylinder.

#### Keywords

Drag coefﬁcient; Navier-Stokes equations; passive control

PDF

#### References

S. Singha and K. Sinhamahapatra, “Flow past a circular cylinder between parallel walls at low Reynolds numbers,” Ocean Engineering, vol. 37, no. 8-9, pp. 757–769, 2010.

H. Sarvghad-Moghaddam, N. Nooredin, and B. Ghadiri-Dehkordi, “Numerical simulation of flow over two side-by-side circular cylinders,” Journal of Hydrodynamics, Ser. B, vol. 23, no. 6, pp. 792–805, 2011.

C. Imron, B. Widodo, and T. Yuwono, “Numerical simulation of fluid flow around circular and I-shape cylinder in a tandem configuration,” Applied Mathematical Sciences, vol. 7, no. 114, pp. 5657–5666, 2013.

D. Z. Noor, M.-J. Chern, and T.-L. Horng, “An immersed boundary method to solve fluid–solid interaction problems,” Computational Mechanics, vol. 44, no. 4, pp. 447–453, 2009.

A. L. E. Silva, A. Silveira-Neto, and J. Damasceno, “Numerical simulation of two-dimensional flows over a circular cylinder using the immersed boundary method,” Journal of Computational Physics, vol. 189, no. 2, pp. 351–370, 2003.

DOI: http://dx.doi.org/10.12962/j24775401.v1i1.1474

### Refbacks

• There are currently no refbacks.

View My Stats 