Comparison of flow structures around circular and elliptical cylinders
Sercan Dogan (1), Eyub Canli(2), Muammer Ozgoren(1), Ozgur Solmaz(2) and Gokhan Ozseker(3)
(1)
Department of Mechanical Engineering, Engineering Faculty, Selcuk University, Konya, Turkey
+903322232023 [email protected]
(2)
Department of Mechanical Engineering, Technology Faculty, Selcuk University, Konya, Turkey
(3)
Arcelik A.S. Refrigerator Plant, Eskisehir, Turkey
1. Introduction – Well known geometries are essential in fluid mechanics due to the fact that flow
around these geometries can be foreseen relatively easily. Complex engineering designs can be evaluated
in respect of the well known geometries and some solutions can be developed relatively easily by means
of geometrical assumptions in the basis of similarity context. Therefore reliable data on basic geometries
in fluid mechanics is important. In order to provide better scientific ground for the advanced research,
researchers are still working on these geometries with new measurement techniques such as PIV method
and numerical methods such as computational fluid dynamics (CFD).
Cylinders are one of the most encountered geometries for fluid-structure interaction research as
well as engineering applications containing various structural geometries. Some examples are bridge
abutments, heat exchanger tubes, reactor cores, poles for construction and various machine elements in
rod shapes. At this point an emphasis should be made for the cross section of the cylinder since circle
comes in mind first when a cylinder is mentioned. However in application, there are a lot of different
cylinder geometries which have different cross sections. For instance pipes, especially for the heat
exchangers, have different cross sections and known also as “non-circular conduits”. Underwater vehicles
are other examples having cylindrical shapes with different cross sections comparing to circular
geometry. Among them, ellipse geometry attracts attention because it has a streamline shape yet it can be
act as a very bluff body when its longer diameter is placed across the stream. To evaluate ellipse
cylinders, one should use literature data via Reynolds analogy. In the mean time, Reynolds Number can
be defined according to different dimensions. This study makes a numerical comparison of dimensions
used to define Reynolds number of the flow in case of three cross sections. Two of them are circular cross
sections and the remaining one is an ellipse cross section. The unique part of the comparison is the
dimensions of the ellipse cross section and the ratio between them. The longer diameter of the ellipse
cross section is equal to the diameter of the big circular cross section and the shorter diameter of the
ellipse cross section is equal to the diameter of the short circular cross section and the ratio of larger
diameter to shorter diameter is 3.25 for elliptical cross section.
For the literature survey, there are many studies on the flow characteristics around the circular
cylinders but the comparison of the circular cylinder and other bluff bodies are restricted. Ozgoren [1]
provided a valuable comparison results in the wake region of the circular and square cylinder by PIV and
dye visualization method. Arat [2] investigated flow around elliptical cylinders having different aspect
ratios by means of a PIV setup and revealed streamline topologies. Results were interpreted in respect of
heat transfer mechanisms and further data such as vortex shedding characteristics and shear layer
instability effects were presented for Reynolds number in the range of 1500-10000. A two-dimensional
(2-D) heat transfer analysis was performed in one and two-row tubes and plate fin heat exchangers
(circular and elliptical sections), using experimentally determined heat transfer coefficients from a heat
and mass transfer analogy by Rocha et al. [3]. Aspect ratio for the elliptical cylinder was 0.86 and the
elliptical cylinder was compared to a circular cylinder for the Re=0-1600. Nagarani et al. [4] reported a
numerical and experimental investigation for the comparison of elliptical and circular cylinders. Elliptical
cylinder were found favorable against circular cylinder in respect of better heat transfer performance. In
another study of Ozgoren et al. [5], three dimensional flow characteristics of a cylinder and a sphere
wakes were compared by means of PIV technique for the Reynolds number 5000 and 10000. For further
information about the PIV technique, a detailed information was given by Adrian and Westerweel [6].
There are many studies about bluff bodies in the literature due to having inevitable engineering
applications.
In this study, three cylinders having different cross sections; namely Small Circular Cross
Section (diameter a=20mm), Big Circular Cross Section (diameter D=65mm) and 3.25 aspect ratio of the
Elliptical Cross Section were placed in a 2D computational flow domain in order to investigate flow
characteristics around them for the Reynolds number 6500. Details of the method are given in the next
section. Results are given in graphical form for streamline topology, vorticity contours and turbulent
kinetic energy so that one can make an evaluation for general flow characteristics.
2. Numerical Analysis - In this study, for three cylinders having different cross sections, numerical
analyses were carried via FLUENT and the results were post processed with TECPLOT. Two
dimensional computation domain was preferred prior to the analyses because cylinders yield nearly same
flow structures along their axis and change in their axis can be neglected or in other words no extra effort
is needed for that information. Remaining flow structures data in the plane perpendicular to the cylinder
axis is corresponding to the interests of this study. For modeling that plane, a 2D plane was prepared
containing a solid contour in it. This solid contour i.e. cross section has the shape according to
investigation. For instance it was a circle or ellipse with predefined dimensions. The dimensions and
schematics of the cross sections are provided in Figure 1. Especially rear part of the flow domain should
be satisfactorily long in order to examine unsteady wake region. Transition SST turbulence model was
used during numerical calculations. Further information about transition SST model improvements can be
found [7]. The computational domain and boundary conditions are illustrated in Figure 2. Approximately
543417 number of quad elements used in the mesh net. Minimum value of orthogonal quality was 0.67
and there were approximately 545233 nodes exist in all meshes. Convergence criteria was set to 10 -6 for
continuity, x velocity, y velocity, k, omega and intermit. Nearly 1000 iterations were made before
calculations converge. Steady analysis was selected and second order upwind schemes were selected.
After solution was converged, velocity data belonging to each grid in the computational domain were
used for the calculation of the time-averaged streamline topology and vorticity magnitude. Post
processing software of ANSYS and TECPLOT were utilized to prepare streamline topology graphics,
vorticity magnitude contours and turbulent kinetic energy contours. All data are of steady conditions and
correspond to the time averaged data of experimental work.
Small Circular Cylinder
Ellipse Cylinder
Big Circular Cylinder
Figure 1. Schematics of the 2D models and their dimensions
Figure 2. Mesh structures and boundary conditions of 2D models
3. Results and Discussion – All results given in the present work is extracted from a wider research and
selected for the present comparison purposes. The streamline topology, vorticity contours and turbulent
kinetic energy contours are given in Figure 3 for two different circulars and one elliptical cross section in
a matrix form. The elliptical cylinder acted as a streamlined geometry comparing to the circular cylinder.
Separation point was retarded for the elliptical cylinder as shown that θ in Figure 3 for streamline
topology and the wake was very narrower and shorter than the wake of the circular cylinder. The longer
and narrower fluid-structure interaction around bluff body will yield a better convection heat transfer.
Foci occur in the wake region of circular cylinders and they occupy around three and 2.5 times cylinder
diameter area for small and big cylinders in downstream, respectively. These foci combine and form a
stagnation point for all cylinder cases. On the other hand, the foci and stagnation point exist shorter
distance in the case of the elliptic cylinder case due to the retarded flow separation of the modified ellipse
geometry. The attached flow length of the ellipse is longer than the circular cross section cases which
means better heat transfer convection and reduced pressure losses. These results should be considered for
Reynolds 6500 and the characteristic length for the Reynolds number is diameter of the cross sections.
Vorticity magnitude and turbulent kinetic energy units are 1/s and m2/s2 respectively. Maximum values of
turbulent kinetic energy contours occur as 0.0012 m2/s2 for small and big circular cylinders. However,
this value is smaller than other cylinders for elliptical cross section cylinder and it is as 0.0009 m 2/s2.
Time Averaged Streamline Topology
Time Averaged Vorticity Contours
Time Averaged Kinetic Energy Contours
Figure 3. Comparison of the flow structures of the cylinders
4. Conclusions – Flow characteristics of an elliptical cross section were compared with the circular cross
section having same diameter of the ellipse cross section for the same Reynolds number. It is observed
that curvature and aspect ratio of the bluff body have an important effect in the wake structure and flow
separation. Vortex formation length becomes shorter in the case of the ellipse cross section because of
delaying flow separation and decreasing blockage ratio. Ellipse cross section is very favorable with its
streamlined shape for thermal-fluid, aerodynamics and hydrodynamic applications. The findings from the
CFD analysis are given as follows:



The wake sizes of the circular cross sections are proportional to their diameters. It means that the
normalized ratios of the vortex formation length to cylinder having (65 mm) diameter or ellipse
diameter are approximately same.
Wake of the ellipse cross section is nearly three times smaller than the circular cross section
having the same diameter (20 mm).
Streamline topology have similar shape with two foci and a saddle point.
The obtained results can be used for the interpretation of real world applications and further validation
studies that can be conducted in the future. Some application fields can be heat transfer in heat exchanger,
structures, military vehicles, bridge legs, fluid-structure interaction and sculpture. Experimental study by
PIV or other methods can be done for validation purpose.
Acknowledgment –0582.STZ.2013-2 numbered SANTEZ project, Turkish Ministry of Science Industry
and Technology, Selcuk University Scientific Research Projects Coordinatorship (BAP), Selcuk
University Advanced Technology Research Application Centre and Arcelik A.S. Refrigerator Plant are
acknowledged.
5. References
[1] M. Ozgoren, Flow Measurement and Instrumentation; 17(4) (2006) 225-235.
[2] H.T. Arat, C. Karakuş, A. Koç and E. Baltacıoğlu, 6th International Ege Energy Symposium &
Exhibition; June 28-30, 2012 Izmir, Turkey.
[3] L.A.O. Rocha, F.E.M. Saboya and J.V.C. Vargas, Int. J. Heat and Fluid Flow; 18 (1997) 247–252.
[4] N. Nagarani, K. Mayilsamy and A. Murugesan, European Journal of Scientific Research; 73(2)
(2012) 143-156.
[5] M. Ozgoren, E. Pinar, B. Sahin and H. Akilli, International Journal of Heat and Fluid Flow, 32
(2011) 1138-1146.
[6] R.J. Adrian and J. Westerweel “Particle Image Velocimetry” Cambridge University Press (2010)
[7] Anonymous, 2013, Fluent 14.0 User Guide, Fluent Inc.