
Research Article


Impact of a Splitter Plate on Flow and Heat Transfer Around Circular Cylinder at Low Reynolds Numbers 

Seyed Esmail Razavi,
Vahid Farhangmehr
and
Farzad Barar



ABSTRACT

In the current investigation, the effect of a splitter plate length on flow induced forces and heat transfer behavior of circular cylinder at low Reynolds numbers (20<=Re<=1000) was studied using a finite volume methodology on triangular unstructured grid. A significant reduction in the drag coefficient as well as the average Nusselt number was observed in the presence of splitter plate implying stabilization of the wake region and accordingly reduction of the vortex shedding. However, the conductive heat transfer was increased as a result of the extra heat transfer area generated by splitter plate, upon which the overall heat transfer of the system was improved.





INTRODUCTION
Experiments and numerical simulations reported by a large number of researchers
have shown that the flow and heat transfer characteristics of the separated
flows downstream of circular cylinder can be greatly influenced if a splitter
plate is placed along the centerline of the wake (Nakamura et al., 1994;
Boisaubert and Texier, 1998; Kawai, 1990; Roshko, 1954). Splitter plate can
alter or even suppress regular vortex shedding from cylinder and hence affect
the flowinduced forces as well as the heat transfer characteristics. Roshko
(1954) studied the effect of splitter plate on the wake of circular cylinder
at Reynolds number of 1.54×10^{4}. This researcher showed that a splitter
plate with 5D (diameter of cylinder) length suppressed the regular vortex shedding
and also reduced the pressure drag of the cylinder to ~ 63% of that of the plain
cylinder. However, when a 1.14D length splitter plate moved to down stream forming
a gap, complicated changes in base pressure and Strouhal number of cylinder
were observed. To study the influence of splitter plate length (0≤l_{sp}≤7)
on drag and vortex shedding in the range (10^{4}≤Re≤5x10^{4}),
(Apelt et al., 1973; Apelt and West, 1975) carried out experiments with
two combinations, i.e., a circular cylinder and a normal flat plate (fixed separation
point) both of which connected with a splitter plate and showed that the short
splitter plate (l_{sp}≤2) significantly changed the characteristics
of downstream flow from the circular cylinder and from the normal plate. They,
however, showed that the splitter plates longer than 2D decreased the drag and
progressively slowed down the vortex shedding at l_{sp} = 3D
and l_{sp} = 5D for the flat plate and the circular cylinder,
respectively. Beyond these splitter plate lengths, it was reported that no further
changes occurred, the drag coefficient remained constant and the vortex shedding
decreased (Apelt et al., 1973; Apelt and West, 1975). Further Anderson
and Szewczyk (1997) conducted experiments in an atmospheric wind tunnel to study
near wake of circular cylinder at subcritical Reynolds numbers (2700≤Re≤46000).
They found that a basemounted splitter plate appeared to be responsible for
the modification of the formation region characteristics without disrupting
usual VonKarman street. Their results provide an explanation for the nonlinearity
in the relationship between shedding frequency and the chord length of the splitter
plate. Sparrow and Kang (1985) performed experimental investigation on longitudinally
finned cross flow tube banks looking at the heat transfer and pressure drop
characteristics and showed that a high degree of heat transfer enhancement can
be obtained by attaching integral wake splitters at the rear of the tubes. The
effectiveness of a flat plate placed on the stagnation line of a square cylinder
was studied upon changing the position and the width of the plate (Mahbub Alam
et al., 2006), who reported that the optimum width of the plate for suppressing
fluid forces was approximately 1/10 of the cylinder width. Tiwari et al.
(2005) carried out a numerical simulation of flow and heat transfer around a
circular cylinder with splitter plate in the channel. They found that splitter
plate caused a reduction in the size of the wake zone in comparison with the
wake of circular cylinder, where the narrowing of the wake zone reduced convective
heat transfer but splitter plate increased the area for conduction heat transfer.
Taking all together, there was an improvement in heat transfer characteristic
of circular tube in comparison with plain cylinder. All these interesting findings
led us to pursue the effect of splitter plate length on the flow induced forces,
the average Nusselt number and the overall heat transfer of circular cylinder
in the range of 20≤Re≤1000, where this range was recruited to address
such interesting impacts on cylinder using finite volume methodology with unstructured
triangular grid.
MATERIALS AND METHODS
Problem statement: The computational domain for the mentioned problem
is shown in Fig. 1. At law Reynolds numbers (20≤Re≤1000),
different chord lengths of the splitter plate
were considered for the study
of flow structure and heat transfer behavior, where, D is cylinder diameter
and L is splitter plate length. Splitter plate thickness was taken to 0.1D.
Water was used as the working fluid and Prandtl number in each cell was computed
using third order polynomial.
Grid generation: Schematic representation of 2D computational domain
and the grid used was demonstrated in Fig. 1. The grid was
generated by means of Watson's incremental algorithm that possesses a preliminary
procedure for generation of an initial grid produced by the frontal approach.
After construction of the final mesh, a Laplace filter was used to smooth the
distribution of the grid points. This latter method were shown to involve movement
of each node to the central area of the neighboring cells (Thompson et al.,
1999).
Governing equations and solution algorithm: The two dimensional laminar
incompressible equations of continuity, NavierStokes and energy were used for
simulation of flow and heat transfer of circular cylinder with a splitter plate.
Pressure field obtained by artificial compressibility technique (Chorin, 1976).
We employed Jameson's cell centered five stage timestepping scheme for unstructured
grid with convergence acceleration techniques such as local time stepping and
implicit residual smoothing (Jameson, 1986). Governing equations in nondimensional
form were as follow:
The variables in Eq. 1 were shown as nondimensionalized,
Eq. 2, where asterisk indicates physical variable.
No slip and constant temperature conditions were applied to solid boundary.
The inflow and outflow conditions were applied to far field boundary 1 and
24, respectively.

Fig. 1: 
Schematic representation of the computational domain and boundaries 

Fig. 2: 
Drag coefficient for plain cylinder 

Fig. 3: 
The average Nusselt number for plain cylinder 
Since no substantial data were available for circular cylinder with splitter
plate, results of the plain cylinder were utilized for verification of the methodology
used for computational assessment of the circular cylinder with splitter plate.
The drag coefficient and average Nusselt number for circular cylinder were compared
to the data obtained from other researchers’ works as shown in Fig.
2 and 3, respectively.
RESULTS AND DISCUSSION
Vortex structures: At Reynolds 40, adding a splitter plate with length
caused slight increase in symmetric vortices length (Fig. 4A). However, when splitter plate length increased up to
two other symmetric vortices
were observed (Fig. 4B). Interestingly, the longer splitter plates were found to prevent the interaction
of separated shear layers with each other, as a result of which the length of
bubbles decreased and the shorter vortices formed on the splitter plate surface
(Fig. 4C, D).
At Reynolds 100, the shear layers were stabilized in response to the splitter
length increases; where the vortex structures also displayed a streamlined status
up to the 3D length of the splitter plate (Fig. 5AC),
after which the vortex shedding was completely suppressed (Fig.
5D). At Reynolds 1000, the secondary vortices were observed near the splitter
surface which clearly indicates an increase in heat transfer (Fig.
6).
Drag forces: The effect of splitter plate length on the drag forces
is shown in Fig. 7. At low Reynolds numbers (Re≤40), adding
a splitter plate longer than 2D increased the friction drag (Fig.
7A). However, the pressure drag remained almost constant (Fig.
7B), at which the overall drag was increased (Fig. 7C).
At the greater Reynolds numbers (Re≥100), reduced shear layers strength caused
a faint reduction in the friction drag (Fig. 7A). Splitter
plate streamlined the flow around the cylinder, by which the wake region was
stabilized and accordingly the pressure drag was decreased (Fig.
7B). Hence, both the pressure and the friction drag were found to decrease
and significant reduction was observed in total drag.
Heat transfer characteristics: Figure 8 shows that
the average Nusselt number decreased in response to increases in the splitter
length. The overall heat transfer in case of circular cylinder with splitter
plate was compared to that of plain cylinder (Fig. 9). The
ratio of overall heat transfer of circular tube with splitter plate to plain
cylinder
at all Reynolds revealed significant enhancement of heat transfer, nevertheless
there existed an exception in the case of
which resulted in an equal heat transfer from cylinder with splitter plate
and plain cylinder at Reynolds (Re≥100). As Reynolds increased up to 100, we observed reduction in the overall heat
transfer ratio, in which it reached the minimum level at Reynolds 100 (Fig.
9). It appears that, at this Reynolds, the splitter plate length has no
influence on the heat transfer ratio.

Fig. 4: 
Stramline at Re=40 with splitter plate of length.(A):0, (B):0.5D, (C):D,
(D):3D 

Fig. 5: 
Instantaneous Vorticity Contours at Re=100 for cylinder with splitter
plate of length.(A):0, (B):0.5D, (C):D, (D):3D 

Fig. 6: 
Instantaneous Vorticity Contours at Re=1000 for cylinder with
splitter plate of length.(A):0, (B):0.5D, (C):D, (D):3D 

Fig. 7: 
Effect of splitter plate length on drag forces. (A): friction drag, (B):
pressure drag, (C): overall drag. Re: Reynolds No., Cv, Cp and Cd: Coefficients
of drag 

Fig. 8: 
Effect of splitter plate length on average Nusselt number. Re: Reynolds
No., Nu: Nusselt No 

Fig. 9: 
Overall heat transfer ratio of circular cylinder with splitter plate to
plain cylinder 
This clearly indicates that the resultant reduction of the convective heat
transfer can cancel the increased conductive heat transfer out, at which point
the heat transfer ratio is almost one. However, when Reynolds number was increased
up to 1000, a progressive increase was seen in the overall heat transfer. Upon our simulation, a reduction was seen for the size of the wake zone in
comparison with the wake of a circular tube (Fig. 5, 6).
Given that the reduction of the size of the wake zone caused decreased convective
heat transfer from the tube surface, hence a reduction was expected to occur
in the average Nusselt number as seen in our data (Fig. 8).
It should be evoked that the splitter plate created a streamlined extension
of the circular tube which results in an enhancement of the heat transfer from
the tube surface; nonetheless it appears that such phenomenon is due to an increased
conduction area. Similar findings have already been reported (Sparrow and Kang,
1985; Tiwari et al., 2005), whose works support our heat transfer results
despite their different undertaken geometrical configurations.
CONCLUSION
So far, particular attention has been devoted to study the impacts of the chord length of the splitter plate on the drag coefficient variations, the vortex structure and the heat transfer characteristics. Little is known about such of note heat transfer and fluid dynamics. Thus, to tackle such issue by means of numerical simulation, a splitter plate was placed on the wake centerline to optimize the characteristics of the wake downstream of a circular cylinder. We found that the splitter plate streamlined the flow around the cylinder and accordingly decreased the pressure drag causing a significant reduction in overall drag. The heat transfer was decreased from the cylinder surface, while placing the splitter plate increased the total heat transfer.

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