Reducing Drag of Body by Adding a Plate

. This paper focuses on theoretical investigations of the location of a separation point laminar boundary layer on the surface of a circular cylinder. The investigations were carried out by CFD software FlowSimulation. The displacement of the separation point on the surface of the circular cylinder is achieved by installing a flat plate in front of the cylinder parallel to the flow. It was found that the greatest displacement of the separation point to the back of the cylinder is possible when the chord of the plate equals to a quarter of the diameter of the circular cylinder. The flat plate allows not only to change the position of the separation point but also to reduce the drag by about 25%.


Introduction
The theme of this article is a topical problem of fluid mechanics, as it solved one of the main questions of aerohydrodynamics -the drag reducing. The flow around the cross-section of the cylindrical bodies can be wind loads that act on the rocket launcher on the start table, the wind load acting on a tall building with a round shape and also the load, which act on gas and oil pipelines that lie at the bottom of the seas and rivers. Methods that reduce the drag of the body, through the displacement of the point of boundary layer separation include: suction of blowing gas [1,2], the motion of the wall [3], change the shape of the wall [4,5], the location of the body near the base body [4,6]. In this article we investigated the last of these waysmethod of displacement of the separation point of the laminar boundary layer on the surface of the circular cylinder by installing a flat plate in front of the cylinder parallel to the flow. The object of investigation was a cylinder with a diameter d=62.5 mm that shown in Fig. 1. In front of the cylinder parallel to the stream was installed the flat plate, which had the following characteristics: t=2 mm is the thickness of the plate, с is the chord of the plate in mm. The plate was located near the cylinder under the meridian angle .
T There is a gap h=d/10 between the cylinder and the plate. Due to the existence of the gap, the effect of the confusor is created [7,8]. This effect leads to a separation of the flow from the surface of the cylinder and the separation point moves to the back of the cylinder. In Fig. 1

Method of the study
The position of separation point were made by CFD in the software FlowSimulation, which is an add-on package to SolidWorks [9]. The integration of the Navier-Stokes equations was obtained in the nonstationary formulation [10]    In the software FlowSimulation equations (1) are simulated turbulent, laminar and transitional flow. For the simulation of turbulent flows is used the definition for small-time: the effect of the turbulence on the flow parameters, large-scale temporal changes are taken into account by introducing appropriate time-derivatives. In the result, the equations (1) have additional memberstension Reynolds, to close the system of equations (1) are the transport equation of turbulent kinetic energy and its dissipation in the framework of the k-Z turbulence model. The transition of laminar flow to turbulent flow is simulated by means of the universal wall functions [9].
The degree of the turbulence for all calculations was taken equal 0.8% H , which corresponds to the degree of turbulence of the flow in the wind tunnel of the Samara University.
To solve the problem, the nonstationary model of the physical process is sampled in space and time. To do this, the whole computational domain is covered with grid design and calculated by the method of the finite volumes. The grid block has the shape of parallelepipeds.
The local crushing of the cells shown in Fig. 3.

Figure 3. The grid location near the model
In addition to finding the separation point on the upper surface of the circular cylinder was calculated the drag coefficient. The drag coefficient was calculated not for an isolated cylinder only and for the combination of the cylinder with a flat plate. The calculation was carried out based on the method of pulses. According to the theorem of impulse the change of the momentum equals the impulse of the force acting on the streamlined body. The drag coefficient is determined by the formula (2) [7,8,10] where q is the impact pressure, 1 u is the velocity at plane d 20 behind the body, b a, are the boundaries of integration along the y -axis.

Results
According to know data [5] for the circular cylinder the dimensionless coordinate of the separation point is equal , x is the distance along the arc that forms the surface of the isolated cylinder from the stagnation point to the separation point. The tangential stress is zero 0 W W [5,9] in the boundary layer on the body surface in the separation point.
The simulation gave the value of the relative coordinate of the separation point S=0.619 for the isolated circular cylinder. Fig. 4, Fig.5 and Fig. 6 shows the velocity, pressure and tangential stress distributions around the circular cylinder, respectively and marked redpoint the separation point.  To verify the results, dimensionless coordinates of the separation points were calculated for elliptical cylinders with different half-axis relationships a/b. Table 1 shows the calculated values for the position of the separation point on the elliptical cylinder with different half-axis relationships a/b.  7 shows the obtained dimensionless coordinates of the separation point in comparison with other authors. Fig. 7 also shows the experimental results of the drag coefficient of elliptic cylinder vs the degree of compression of the ellipse. The experimental data are corresponding to the Reynolds number Re=10 5 . The experimental results of the drag coefficient C D were taken from work [11]. Theoretical values of the dimensionless coordinates were taken from Chang's book [5], Schlichting [10] and the experimental results of the values S were taken from [12]. The presented values of the dimensionless coordinates S and the drag coefficient C D clearly demonstrate the dependence of these quantities on the degree of compression of the elliptic cylinder. The presented data in this study indicate that the calculated values for the separation points agree with both the theoretical Chang's results [5] and the experimental results [12]. It is clear from these data that the displacement of the dimensionless coordinates of the separation point S to the back of the cylinder leads to a decreasing the drag coefficient C D . This fact was also noted in works [5,10].
Further investigation was only performed for a circular cylinder in the presence of the plate. All the calculated values of drag coefficient obtained for the isolated cylinder and combination of the cylinder with a plate. The size of the slit was chosen to be so that the distance from the plate to the surface of the cylinder was always greater than the thickness of the boundary layer.
The calculation of the separation points for combinations of the cylinder with a plate was made for flat plates with relative chords 25 . 0 с and .

. 0 с
The dimensionless coordinates of the separation points were calculated from the tangential stress distribution of along the upper surface of the circular cylinder and determined by the equality of the tangential stress to zero. Table 2 and Fig. 8 show the results of calculation of the dimensionless coordinates of the separation point S for a circular cylinder in the presence of the plate. Fig. 8 shows the calculating results of the dimensionless coordinates of the separation point S, which were obtained for two plates in comparison with data for the isolated cylinder. The specified values of 0 T deg represent a situation in which the symmetry axis of the plate coincides with the longitudinal axis of abscissa.  The Table 3 shows the calculated values of the drag coefficient for combination of the cylinder with the flat plate.  .9 and Fig.10 show dependencies dimensionless coordinates of separation point S and drag coefficient C D vs meridional angle for combinations of the cylinder with the flat plate for dimensionless cords 0.25 c and 0.5 c . The values were obtained as a result of the numerical simulation, some of the values were taken from the works of the authors [7,8].  As can be seen from the data in Fig. 7-10 obtained results of the dimensionless coordinates S for the combinations of the cylinder with the plate are greater than for an isolated cylinder. Thus, it can be concluded that the separation point is displacing downward towards the back of the cylinder B on the upper surface of the circular cylinder.
According to the results of the books [5,10] and the data presented in Fig. 4, the values C D with increasing coordinates of the separation point S are decreased. It is concluded from the present study that with the increasing value S drag coefficient C D decreases and with decreasing value S drag coefficient C D increases.
Thus, the location of the plate in front of the cylinder allows obtaining the displacement of the separation point to the back of the cylinder B and as a consequence the drag reduction.
According to know data [10][11][12] the drag coefficient of the isolated cylinder is equal to C D ≈1. Therefore, analyzing the results can say, that for the plate 5 . T deg (Fig. 9). For the combinations of the cylinder with the plate with the dimensionless chord 5 . 0 с the separation point gets its highest value S=0.715 at the meridian angle 20 T deg (Fig. 10). The obtained data are shown in Table 4.    when the meridional angle of the installation of the plate is T=12 deg. Fig. 15 shows the pressure distribution around the circular cylinder with the plate 0.5. ñ Fig. 16 shows the tangential stress distribution on the surface of the circular cylinder and marked the red point is the separation point. The theoretical values of the angle of disposition of the separation point measured from the stagnation point s M are given in works [5,10,12]. The results of the calculation angle s M and comparison with the known data are given in Table 5. According to [10], the theoretical value equals

Conclusion
The results in the present investigation demonstrate that the displacement of the separation point on the surface of the circular cylinder to the back of the cylinder is made possible due to the location in front of the cylinder the flat plate. The position of the flat plate was studied parallel to the flow and was established at different meridian angles with respect to the longitudinal axis of the cylinder which parallel to the flow. The results show not only the displacement of the separation point of the boundary layer to the back of the cylinder but also reducing drag coefficient of the circular cylinder which can reach 25%.