two cylinder_edited shahid (2)

117

CHAPTER IV

RESULTS AND DISCUSSIONS

4. 1iNTRODUCTION

The simulations are conducted for five Reynolds numbers of 100, 3900, 10000, 15000 and 22000. The choice of the Reynolds numbers of simulation depends largely on the experimental data available. Reynolds number 100 and 10000 is chosen for validation purpose since experimental data is available. Critical flow parameters, which are time-averaged drag coefficient and fluctuating lift coefficient, have been predicted and some of them calculated values are compared with experimental and previous numerical values.

4.2 VALIDATION CASE FOR A SINGLE CYLINDER WITH RE = 100

In this section, we will discuss the case with Re = 100. For this purpose, we will use Laminar Model. Here, all simulations have done using Hex Grid which contains 190*190*8 number of cells in the x, y and z direction respectively. The overall forces acting on the cylinder are important parameters for practical application of CFD. The time domain data of the drag coefficient is converted into frequency domain by using the Fast Fourier Transform (FFT). Good agreement with the experimental result is observed. The results for pressure, velocity and total pressure is shown below.

(a) Streamlines

(b) Pressure ContourFigure 4.1: Flow characteristics for a Single Cylinder at Re = 100.

Figure 4.2: Time histories drag forces for single cylinder at Re = 100

Figure 4.3: Time histories of lift forces for single cylinder at Re = 100

Figure 4.4: Absolute Pressure plot on five different lines behind the cylinder.

The simulation results of flow past a single cylinder is presented for mean drag coefficients lift coefficient and are compared with the data in literature in Table 4.1. From Table 4.1, we can see that at = 100 Re the results of the present work agree closely with other results. Time histories of lift and drag coefficients for this Reynolds number is shown in Fig.4.2. And also the pressure and streamlines are presented for the mentioned Reynolds number in Fig.4.1 (a), 4.1 (b) and 4.1 (c). As it is evident, vortices are shed periodically from the cylinder and a small vortex street is formed at this Reynolds number. The lift and drag coefficients also oscillate due to the asymmetric pressure distribution occurred by periodic vortex shedding. Figure (4.1 a) shows the velocity streamline of the cylinder with a maximum velocity of 0.003 meter per second. Figure (4.1 b) shows the static pressure contour of the cylinder. For single cylinder with Reynolds number of 100 the value of pressure behind the cylinders is -0.002 pa The maximum static pressure at front of the cylinder is 0.004 Pa. The mean drag co-efficient for this model is found to be 1.27. From figure 4.4 we can observe that the same pressure is in all lines. for laminar cases, the absolute pressure is same as atmosphere pressure =101325pa. The maximum absolute pressure should be same at (x, y) coordinates. 4.2.1 Grid Independency Test

Grid independency is a test in which we observe that no change in result is observed as we go on refining the mesh. In this work a grid independency test is carried for three sizes of mesh. 170*170*8, 190*190*8 and 210*210*8 . These are the number of elements in the x, y and z direction. The value of mean Drag Co-efficient is taken for comparison of the results.

Table 4.1: Grid Independency Test for a single cylinder at Re = 100

Grid typeNumber of cellsMean drag co-efficient

Finer210*210*81.29

Fine190*190*81.27

Standard170*170*81.01

From the above table it can be seen that no significant change is found between the results of 190*190*8 mesh and finer 210*210*8 mesh hence to save the computational time and maintain the accuracy 190*190*8 number of elements are chosen for all further cases. And hence the 190*190*8 number of mesh elements is called as grid independent mesh.

Table 4.2: Comparison of Mean drag Co-efficent or Present results with Literature for single cylinder, Re=100

Number of CylindersPresentDEHKORDI Behzad GhadiriManeghiniDing et alSingha et al

One 1.271.391.371.351.431

The time-dependant variations of lift and drag coefficients for the cylinder at Re =100 are presented in above Figures. From Table 4.1, one can see that at Re =100, the results of present work agree closely with other results, showing an small error in comparison to the data of Dehkordi Behzad, Mittal et al etc. which seems so reasonable.

4.3 VALIDATION CASE FOR A SINGLE CYLINDER WITH RE = 10000

In this section, we will discuss the case with Re = 10000. For this purpose, we will use LES Turbulence Model. Here, all simulations have done using Hex Grid. Table 4.3 shows comparison of mean drag, Cd for present model with experimental data available in literature. The time domain data of the drag coefficient is converted into frequency domain by using the Fast Fourier Transform (FFT). Good agreement with the experimental results is observed. Below figures shows the results of pressure, velocity and streamline pattern etc.

(a) Streamlines

(b) Pressure Contour

Figure 4.5: Flow characteristics for a single cylinder at Re = 10000.

Figure(a): Time histories of drag forces for single cylinder

Figure(b): Time histories of drag forces for single cylinder Figure 4.6: Time histories of lift forces for single cylinder at Re = 10000


The time histories of drag coefficients for the Reynolds number of 10000 are shown in above figures. The simulation results of flow past a single cylinder with higher Reynolds number of 10000 is presented for drag and lifts forces and is compared with the data in literature in Table 4.3. From Table 4.3, we can see that at Re = 10000 the results of the present work agree closely with other results. Time histories of lift and drag coefficients for this Reynolds number is shown in Fig.4.3. As it is evident, in this case also vortices are shed periodically from the cylinder and a vortex street is formed. As can be seen from the streamlines the separation area is reduced in this case as compared to laminar flow, this is due to the tendency of the turbulent flow to remain attached to the wall. The lift and drag coefficients also oscillate due to the asymmetric pressure distribution occurred by periodic vortex shedding. Figure 4.3 shows the velocity streamline of the cylinder with a maximum velocity of 0.44 meter per second. As we can see from the figure that the Stream line pattern in the wake region is turbulent and pair of vortices are found behind the cylinders. Figure 4.3 b shows the static pressure contour of the cylinder. For single cylinder with Reynolds number 10000 the maximum pressure behind the cylinder is -44.46 also the maximum static pressure at front of the cylinder is 33.3 Pa which is much higher compared to laminar flow. From figure 4.7 we can observe that the maximum pressure is on line 2 which is at a distance of 0.015 below the centre of cylinder, the maximum absolute pressure is 101326 Pa. The (x, y) coordinates for maximum absolute pressure is (0.15,-0.05)m respectively.

Table 4.3: Validation for Mean Drag Co efficient for One Cylinder at Re = 10000.

Number of Cylinder Cd (present)Gopalkrishnan ExperimentalDong, DNS Method

One Cylinder 1.321.1861.143

4.4 VALIDATION CASE FOR TWO SIDE BY SIDE CYLINDERS AT T/D = 2 AND RE = 10000

The study of flow around a single cylinder presented in previous section provides a good insight into better understanding the flow characteristics around two-cylinder geometries. In this section, the results for the simulation of flow around two side-by-side circular cylinders are presented and comparison of these results with other available experimental data is performed for the validation of the solver.

(a) Streamlines

(b) Static Pressure FieldFigure 4.8: Flow characteristics for two side by side cylinders at Re = 10000, T/D = 2

Figure 4.9: Time histories of drag forces for top cylinder at Re = 10000

Figure 4.10: Time histories drag forces for bottom cylinder at Re = 10000

Figure 4.11: Time histories lift forces for top cylinder at Re = 10000

Figure 4.12: Time histories lift forces for bottom cylinder at Re = 10000


From figure 4.13 we can observe that the maximum pressure is on line 3 and which is at a distance of 0.12 m from the centre of cylinder, the maximum Absolute pressure is 101351 Pa. The (x, y) coordinates for maximum absolute pressure is (0.15,0.12)m respectively.

4.4.1 Grid Independency Test

Grid independency is also carried for two cylinders. In this work three sizes of mesh 170*170*8, 190*190*8 and 210*210*8 is chosen. The value of mean Drag Co-efficient is taken for comparison of the results. Table 4.4: Grid Independency test for two cylinder

Grid typeNumber of cellsMean drag co-efficient

Finer210*210*81.36

Fine190*190*81.36

Standard170*170*81.42

From the above table it can be seen that no significant change is found between the results of 190*190*8 mesh and finer 210*210*8 mesh hence to save the computational time and maintain the accuracy 190*190*8 number of elements are chosen for all further cases. And hence the 190*190*8 number of mesh elements are called as grid independent mesh.

Table 4.5: The table shows the Mean Drag Co efficient for Two Cliynder at T/D = 2, Re= 10000

Number of CylindersCylinderCd (Present)Cd (Sarvghad Navid)

Two Cylinder Top 1.411.37

bottom 1.361.37

The time histories of lift and drag coefficients for gaps T / D = 2 are depicted in above Figures. Second cylinder shows low drag which is because of the pressure difference between front and back sides of this cylinder. While the reattachment of these shear layers onto the surface of downstream cylinder and shedding of vortices behind this cylinder are responsible for its oscillations. As was mentioned above, in this case vortices also shed from upstream cylinder which along with the separation of shear layers increases the forces acting on this cylinder. For the downstream cylinder, the impingement of upstream shed-vortices and their combination with some vortices behind downstream cylinder leads to strong oscillations in lift coefficient variations. The mentioned impingement and different shed-vortices with various attributes induce larger oscillating drag coefficients for downstream cylinder. It is seen that the variation of the Reynolds number and transverse gap have significant effects on flow characteristics behind upper and lower cylinders. These changes lead to notable changes from the results obtained for a single cylinder in terms of hydrodynamic forces, wake pattern and vortex shedding from both cylinders.

4.5 RESULTS FOR 25 DIFFERENT CASES CONSIDERED FOR TWO SIDE BY SIDE CYLINDERS

Analysis results of the twenty five Cases are shown in this section, and comparison of the results for pressure forces behind the cylinder is presented. 4.5.1 Discussion for Two Side by Side Cylinder with T/D = 1.5 and Re = 100

The flow behaviour around two side by side cylinders in laminar regime is analysed. The results are shown below.

(a) Streamlines

(b) Static Pressure Field

Figure 4.14: Flow characteristics for two side by side cylinders for T/D =1.5 and Re = 100.

Figure 4.15: Time histories of drag forces for top cylinder at Re = 100and T/D = 1.5

Figure 4.16: Time histories of drag forces for bottom cylinder at Re = 100and T/D = 1.5

Figure 4.17: Time histories of lift forces for top cylinder at Re = 100and T/D = 1.5

Figure 4.18: Time histories of lift forces for bottom cylinder at Re = 100and T/D = 1.5In order to extract the Pressure details behind the cylinders five lines are created as shown in figure below and the values of Pressure are plotted on these lines.

Figure 4.13: 5 Lines created behind the cylinders.

The lines are created in such a way that first line is at a distance of 0.05 m from the cylinder and all other lines are 0.05 m away from each other. The length of the line is taken as 0.30 m, in which 0.15 m is above the central axis and 0.15 is below the central axis. All the two cylinders are symmetry about this axis. The below graph shows the pressure values plotted on these five lines, X-axis gives the length of the line and Y-axis gives the value of the pressure.


The time histories of lift and drag coefficients for the Reynolds number of 100 are shown in above figures. As is evident, the lift and drag coefficients oscillate due to the asymmetric pressure distribution caused by periodic vortex shedding. Figure 4.7 a shows the velocity streamline of the cylinder with a maximum velocity of 0.064 meter per second. As we can see from the figure that the flow separates earlier and a thick wake is found behind the cylinders and negative drag is observed and high mean drag co-efficient is observed. The maximum static pressure at front of the cylinder is 0.004 Pa. From figure 4.19 we can observe that the same absolute pressure is in all lines. for laminar cases, the absolute pressure is same as atmosphere pressure =101325pa. The maximum absolute pressure should be same at all (x,y) coordinates.

Table 4.6: The table shows the Mean Drag Co efficient for T/D=1.5 and Re = 100.

Number of CylindersCylinderCd

Two CylinderTop 1.81

bottom1.80

4.5.2 Discussion for Two Side by Side Cylinder with T/D = 1.5 and Re = 3900

The flow behaviour around two side by side cylinders with Reynolds number of 3900 is analysed. The results are shown below.Chang pic ___ I change it

(a) Streamlines

(b) Static Pressure FieldFigure 4.20: Flow characteristics for two side by side cylinder at Re = 3900, T/D = 1.5

Figure 4.21: Time histories of drag forces for top cylinder at Re = 100and T/D = 2

Figure 4.22: Time histories of drag forces for bottom cylinder at Re = 3900and T/D = 2



Figure 4.25: Absolute Pressure plot on the five lines behind the cylinders.

The time histories of lift and drag coefficients for the Reynolds number of 3900 are shown in above figures. As is evident, the lift and drag coefficients oscillate due to the asymmetric pressure distribution caused by periodic vortex shedding. Figure 4.11 shows the velocity streamline of the cylinder with a maximum velocity of 0.4912 meter per second. The separation area in this case is less compared to previous laminar case of Re =100. No negative drag is observed and mean drag is less compared to previous case. The maximum static pressure at front of the cylinder is 5.5 Pa. From figure 4.25 we can observe that the maximum Absolute pressure is on line 4 and 5 which is at a distance of -0.12 m to 0.15 from the centre of cylinder, the maximum pressure is 101326 Pa. The (x, y) coordinates for maximum absolute pressure is (0.25,0.15)m respectively.

Table 4.7: The table shows the Mean drag co efficient for Re=3900, T/D =1.5.


Two Cylinder Top 1.296

Bottom 1.08

4.5.3 Discussion for Two Side by Side Cylinder with T/D = 1.5 and Re = 10000

The flow behaviour around two side by side cylinders with Reynolds number of 10000 is analysed. The results are shown below.

(a) Streamlines

(b) Static Pressure ContourFigure 4.26: Flow characteristics for two side by side cylinder at Re = 10000, T/D = 1.5

Figure 4.27: Time histories of drag forces for top cylinder at Re = 10000 and T/D = 1.5

Figure 4.28: Time histories of drag forces for bottom cylinder at Re = 10000 and T/D = 1.5

Figure 4.29: Time histories of lift forces for top cylinder at Re = 10000 and T/D = 1.5

Figure 4.30: Time histories of lift forces for bottom cylinder cylinder at Re = 10000 and T/D = 1.5

Figure 4.31: Plots of Absolute Pressure on five lines behind the cylinders.

The time histories of lift and drag coefficients for the Reynolds number of 10000 are shown in above figures. Velocity streamline of the cylinder shows a maximum velocity of 0.4912 meter per second. The separation zone in this case is much smaller compared to previous cases and due to turbulence a pair of vortices is formed behind the cylinder. The maximum static pressure in front of the cylinder is 27 Pa. From figure (4.31) we can observe that the maximum Absolute pressure is on line 5, the maximum pressure is 101324 Pa and is -0.15 m below and below the central axis. The (x, y) coordinates for maximum absolute pressure is (0.25,-0.15) m respectively.

Table 4.8: The table shows the Mean Drag Co efficient for Re=10000, T/D = 1.5.



Bottom1.51

4.5.4 Discussion of the Case with T/D=1.5 and Re = 15000


(a) Streamlines


Figure 4.32: Flow characteristics for two side by side cylinder at Re = 15000, T/D = 1.5


Figure 4.34: Time histories of drag forces for bottom cylinder at Re = 15000 and T/D = 2

Figure 4.35: Time histories of lift forces for top cylinder at Re = 15000 and T/D = 2

Figure 4.36: Time histories of lift forces for bottom cylinder at Re = 15000and T/D = 2

Figure 4.37: Plots of Absolute Pressure on five lines behind the cylinders

The time histories of lift and drag coefficients for the Reynolds number of 15000 are shown in above figures. Figure 4.17 shows the velocity streamline of the cylinder with a maximum velocity of 0.6585 meter per second. Small recirculation zone is observed behind the cylinder and hen flow gets reattached and uniform. The maximum static pressure at front of the cylinder is 80.7 Pa and minimum is -267 Pa. From figure 4.37 we can observe that the maximum pressure is on line 3 maximum Absolute pressure is 101326Pa and is nearly same for all the points on the line. The (x, y) coordinates for maximum absolute pressure is (0.15,0)m respectively.

Table 4.9: The table shows the Mean drag co efficient for Re=15000, T/D=1.5.



bottom 1.228

4.5.5 Discussion of the Case with T/D = 1.5, Re = 22000


(a) Streamlines






Figure 4.42: Time histories of lift forces for bottom cylinder at Re = 22000and T/D = 1.5

Figure 4.43: Plots of Absoloute Pressure on five lines behind the cylinders The time histories of lift and drag coefficients for the Reynolds number of 22000 are shown in above figures. Velocity streamline shows a maximum velocity of 1.098 meter per second. In this case also the separation area is narrower but higher vortices are formed. The maximum static pressure at front of the cylinder is 179 Pa. From figure 4.44 we can observe that the maximum Absolute pressure is on line 3, the maximum pressure is 101326Pa and is -0.15 m below the central axis. The (x, y) coordinates for maximum absolute pressure is (0.2,-0.15)m respectively.

Table 4.10: The table shows the Mean drag co efficient for T/D = 1.5 and Re=22000



bottom 1.474

From all the five Reynolds number considered for T/D = 1.5 it is found that the maximum pressure behind the cylinders is observed for Re of 22000 on line 1 behind the cylinder.

4.6 DISCUSSION OF THE TWO SIDE BY SIDE CYLINDER FOR T/D=2

Five cases with five different Reynolds number is analyzed for L/D ratio of 2 and the results are presented below.

4.6.1 Discussion of the Two Side by Side Cylinder for T/D=2 and Re = 100


(a) Streamlines

(b) Static Pressure FieldFigure 4.45: Flow characteristics for two side by side cylinder at Re = 100, T/D = 2

Figure 4.46: Time histories of drag forces for top cylinder at Re = 100 and T/D = 2



Figure 4.49: Time histories of lift forces for bottom cylinder at Re = 100 and T/D = 2

Figure 4.50: Absolute Pressure plots on five lines behind the cylinder.

The time histories of lift and drag coefficients for the Reynolds number of 100 are shown in above figures. Velocity streamline shows a maximum velocity of 0.06327 meter per second. Due to earlier separation the separation area is larger and a higher value of drag is observed. The maximum static pressure at front of the cylinder is 0.001 Pa. and the minimum static pressure behind the cylinder is -0.00856. From figure 4.50 we can observe that the maximum Absolute pressure at all line should be same, because of laminar flow. the maximum Absolute pressure is 101325 Pa The absolute pressure should be same at all (x, y) coordinates.

Table 4.11: The table shows the mean drag co efficient for TD =2 and Re = 100.



bottom 1.689

4.6.2 Discussion of the Two Side by Side Cylinder for L/D=2 and Re = 3900


(a) Streamlines




Figure 4.54: Time histories of lift forces for top cylinder at Re = 3900and T/D = 2



The time histories of lift and drag coefficients for the Reynolds number of 3900 are shown in above figures. The velocity streamline of the cylinder shows maximum velocity of 0.1629 meter per second. The flow remains attached and hence lower mean drag is observed. The maximum static pressure at front of the cylinder is 5.127 Pa. From figure 4.56 we can observe that the maximum Absolute pressure is on line 4 and 5, the maximum Absolute pressure is 101325 Pa and is -0.15 m to 0.01 below and above the central axis. The (x, y) coordinates for maximum absolute pressure is (0.3,-0.15) m respectively.

Table 4.12: The table shows the Mean drag co efficient for T/D =2 and Re =3900.



bottom 1.154



(a) Streamlines


Figure 4.57: Flow characteristics for two side by side cylinders at Re = 10000, T/D = 2






The time histories of lift and drag coefficients for the Reynolds number of 10000 are shown in above figures. The maximum velocity is 0.477 meter per second. Pair of vortices is formed behind the cylinder. Drag increases as the flow time increases. The maximum static pressure at front of the cylinder is 62.360 Pa. From figure 4.62 we can observe that the maximum Absolute pressure is on line 3, the maximum absolute pressure is 101351pa and 0.12 m above the central axis.The (x, y) coordinates for maximum absolute pressure is (0.15,0.12)m respectively.

Table 4.13: The table shows the Mean drag co efficient for T/D=2 and Re = 10000



bottom 1.36



(a) Streamlines


Figure 4.63: Flow characteristics for two side by side cylinder at Re = 15000, T/D = 2






The time histories of lift and drag coefficients for the Reynolds number of 15000 are shown in above figures. The maximum velocity in between the two cylinders is 0.6933 meter per second. Flow pattern is more uniform and small separation zone is observed. The maximum static pressure at front of the cylinder is 82.27 Pa. From figure 4.68 we can observe that the maximum Absolute pressure is on line 2, the maximum absolute pressure is 101330 Pa and is near to the central axis. The (x, y) coordinates for maximum absolute pressure is (0.1,-0.02)m respectively.

Table 4.14: The table shows the Mean drag co efficient for T/D =2 and Re =15000



bottom 1.363

4.6.5 Discussion of the Two Side by Side Cylinder for T/D=2 and Re = 22000The flow behaviour around two side by side cylinders with Reynolds number of 22000 is analysed. The results are shown below.

(a) Streamlines


Figure 4.69: Flow characteristics for two side by side cylinder at Re = 22000, T/D = 2 Figure 4.70: Time histories of drag forces for top cylinder at Re = 22000and T/D = 2

Figure 4.71: Time histories of drag forces for bottom cylinder at Re = 22000and T/D = 2 Figure 4.72: Time histories of lift forces for top cylinder at Re = 22000and T/D = 2



The time histories of lift and drag coefficients for the Reynolds number of 22000 are shown in above figures. The maximum velocity in between the two cylinders is 1.033 meter per second. Pair of periodic vortices is formed behind the cylinder. The maximum static pressure at front of the cylinder is 183.4 Pa. From figure 4.74 we can observe that the maximum Absolute pressure is on line 2, the maximum absolute pressure is 101345 Pa and is - 0.12 m below the central axis. The absolute pressure maximum at (x, y) coordinates is (0.1,-0.12)m respectivelyThe (x, y) coordinates for maximum absolute pressure is (0.1,-0.12)m respectively. Table 4.15: The table shows the Mean drag co efficient for T/D= 2 and Re=22000.



bottom 1.363

4.7DISCUSSION FOR TWO SIDE BY SIDE CYLINDER WITH L/D=2.5 CASEFive cases with different Reynolds number are considered and results are shown below4.7.1 Discussion of the Two Side By Side Cylinder with L/D=2.5 and Re = 100

The flow behaviour around two side by side cylinders with a Reynolds number of 100 is analysed. The results are shown below.

(a) Streamlines







Figure 4.80: Plots of Absolute Pressure on five lines behind the cylinders.

The time histories of lift and drag coefficients for the Reynolds number of 100 are shown in above figures. Figure 4.39 shows the velocity streamline of the cylinder with a maximum velocity of 0.003395 m/s in between and above and below the two cylinders. Negative lift co-efficient is found for the Bottom Cylinder and higher values of drag is observed for both the cylinders with bottom cylinder having higher drag compared to top cylinder. The maximum static pressure at front of the cylinder is 0.006526 Pa. From figure 4.80 pressure plot we can observe that the maximum absolute pressure is on all line should be same. because of laminar flow. The absolute pressure same at all (x, y) coordinates.

Table 4.16: The table shows the Mean drag co efficient for T/D = 2.5 and Re =100.


Two CylinderTop1.588

bottom1.594

4.7.2 Discussion of the Two Side by Side Cylinder with T/D=2.5 and Re = 3900


(a) Streamlines


Figure 4.81: Flow characteristics for two side by side cylinders at Re = 3900, T/D = 2.5





Figure 4.86: Absolute Pressure plots on five lines behind the cylinders.

The time histories of lift and drag coefficients for the Reynolds number of 3900 are shown in above figures. Figure shows the velocity streamline of the cylinder with a maximum velocity of 0.1595 meter per second in between the two cylinders, narrow separation region is found compared to the previous case. The maximum static pressure at front of the cylinder is 5.7 Pa. From Figure 4.86 we can observe that the maximum absolute pressure is on line 5 and 3 the maximum absolute pressure is 101325Pa and is at 0.15 m to -0.15 above and below the central axis. The (x, y) coordinates for maximum absolute pressure is (0.15,0.15)m respectively.

Table 4.17: The table shows the Mean drag co efficient for T/D =2.5 and Re = 3900. Number of CylindersCylinderCd


bottom 0.941

4.7.3 Discussion of the Two Side by Side Cylinder with L/D=2.5 and Re = 10000


(a) Streamline






Figure 4.91: Time histories of lift forces for bottom cylinder at Re = 10000 and T/D = 2.5


The time histories of lift and drag coefficients for the Reynolds number of 10000 are shown in above figures. The maximum velocity of 0.4792 m/s is found above the bottom cylinder. Pair of vortices are formed behind the cylinders. The maximum static pressure at front of the cylinder is 57.12 Pa. From Figure 4.92 pressure plot we can observe that the maximum Absolute pressure is 101337 Pa on line 2 which is at a distance of 0.1 m from the centre of cylinder. The absolute pressure maximum at (x, y) coordinates is (0.1,-0.15)m respectively.The (x, y) coordinates for maximum absolute pressure is (0.1,-0.15)m respectively.

Table 4.18: The table shows the Mean drag co efficient for T/D = 2.5 and Re = 10000



bottom 1.35

4.7.4 Discussion of the Two Side By Side Cylinder with T/D=2.5 and Re = 15000


(a) Streamlines


Figure 4.93: Flow characteristics for two side by side cylinders at Re = 15000, T/D = 2.5






The time histories of lift and drag coefficients for the Reynolds number of 15000 are shown in above figures. The maximum velocity of 0.6487 m/s is formed between the two cylinders. The maximum static pressure at front of the cylinder is 83.72 Pa. From Figure 4.98 pressure plot we can observe that the maximum Absolute pressure is on line 2 which is at a distance of 0.05 m and -0.05m from the centre of cylinder and. The maximum Absolute pressure on line 2 is 101337 Pa. The (x, y) coordinates for maximum absolute pressure is (0.1,-0.05)m respectively.




bottom 1.144

4.7.5 Discussion of the Two Side By Side Cylinder with T/D=2.5 and Re = 22000


(a) Streamlines

(b) Static Pressure FieldFigure 4.99: Flow characteristics for two side by side cylinders at Re = 22000, T/D = 2.5




Figure 4.103: Time histories of lift forces for bottom cylinder at Re = 22000 and T/D = 2.5

Figure 4.104: Absolute Pressure plot on five lines behind the two cylinders

The time histories of lift and drag coefficients for the Reynolds number of 22000 are shown in above figures. The maximum velocity of 0.8890 m/s is formed between the two cylinders, the flow is attached and a small separation region is observed. The maximum static pressure at front of the cylinder is 714 Pa. From Figure 4.104 we can observe that the maximum Absolute pressure is on line 1. The maximum Absolute pressure is 101600 Pa and is near to the central axis. The (x, y) coordinates for maximum absolute pressure is (0.05,0.02)m respectively.




bottom 1.594

4.8DISCUSSION FOR THE TWO SIDE BY SIDE CYLINDER WITH L/D=3 CASE

CFD analysis for two side by side cylinders with a gap of 3 is considered and analysis is done for five different Reynolds number and results are presented here.

4.8.1 Discussion for the Two Side by Side Cylinder with T/D=3 and Re = 100


(a) Streamlines



Figure 4.106: Time histories of drag forces for top cylinder at Re = 100 and T/D = 3.Figure 4.107: Time histories of drag forces for bottom cylinder at Re = 100 and T/D = 3



Figure 4.110: Absolute Pressure plot on five lines behind the two cylinders.

The time histories of lift and drag coefficients for the Reynolds number of 22000 are shown in above figures. The maximum velocity of 0.0083 m/s is observed between the two cylinders, even though there is a separation region but it is found to be much narrower than the previous T/D Ration with Reynolds number of 100. The maximum static pressure at front of the cylinder is 0.000037 Pa. From Figure 4.110 we can observe that the maximum Absolute pressure is on all lines should be same. because of laminar flow. The maximum absolute pressure is 101325pa. The absolute pressure maximum same at all (x, y) coordinates

Table 4.21: The table shows the Mean drag co efficient for T/D =3 and Re = 100.


Two CylinderTop1.787

bottom1.759

4.8.2 Discussion for the Two Side by Side Cylinder with T/D=3 case Re = 3900The flow behaviour around two side by side cylinders with Reynolds number of 3900 is analysed. The results are shown below.

(a) Streamlines







The time histories of lift and drag coefficients for the Reynolds number of 3900 are shown in above figures. The maximum velocity of 0.155 m/s is observed in between the cylinders and small separation region is observed. The maximum static pressure at front of the cylinder is 9.9 Pa. From Figure 4.115 we can observe that the maximum Absolute pressure is on line 1. The maximum absolute pressure is 101401 Pa and is 0.15 meter below the central axis. The absolute pressure maximum at (x, y) coordinates is (0.05,-0.15)m respectively.

Table 4.22: The table shows the Mean drag co efficient for T/D = 3 and Re =3900



bottom 1.09

4.8.3 Discussion for the Two Side by Side Cylinder with T/D=3 case Re = 10000 The flow behaviour around two side by side cylinders with Reynolds number of 10000 is analysed. The results are shown below.

(a) Streamlines







The time histories of lift and drag coefficients for the Reynolds number of 10000 are shown in above figures. The maximum velocity of 0.517 m/s is observed a little behind the two cylinders, no separation is found and the flow remains attached to the cylinders but a pair of vortices are observed. The maximum static pressure at front of the cylinder is 19.9 Pa. From Figure 4.121 we can observe that the maximum Absolute pressure is on line 1. The maximum absolute pressure is 101401.5 Pa and is 0.1 meter below the central axis; next peak pressure of 40 Pa on line 2 and is at 0.12 meter above and below the central axis. The absolute pressure maximum at (x, y) coordinates is (0.05,0.12)m respectively.

Table 4.23: The table shows the Mean drag co efficient for T/D = 3 and Re=10000.Number of CylindersCylinderCd


bottom 1.12



(a) Streamlines







The time histories of lift and drag coefficients for the Reynolds number of 15000 are shown in above figures. The maximum velocity of 0.65 m/s is observed between the cylinders, small separation region is found but the flow remains uniform. The maximum static pressure at front of the cylinder is 81 Pa. From Figure 4.127 we can observe that the maximum absolute pressure is on line 2. The maximum absolute pressure is 101335 Pa and is 0.05 meter above and below. The absolute pressure maximum at (x, y) coordinates is (0.1,-0.05)m respectively.

Table 4.24: The table shows the drag co efficient for T/D = 3 and Re = 15000



bottom1.143

4.8.5 Discussion for the Two Side by Side Cylinder with L/D=3 case Re = 22000


(a) Streamlines





Figure 4.131. Time histories of lift forces for top cylinder at Re = 22000 and T/D = 3


Figure 4.133: Absolute Pressure plot on five lines behind the two cylinders.

The time histories of lift and drag coefficients for the Reynolds number of 15000 are shown in above figures. The maximum velocity of 0.98 m/s is observed below the top and bottom cylinder. The maximum static pressure at front of the cylinder is 100 Pa. From Figure 4.133 we can observe that the maximum absolute pressure is on line 1, 2, 3 and 4. The maximum absolute pressure is nearly 101350 Pa and is nearly same for all the three lines and is at distance of 0.15 m above the central axis. The absolute pressure maximum at (x, y) coordinates is (0.1,0.15)m respectively. Table 4.25: The table shows the Mean drag co efficient for T/D = 3 and Re = 22000



bottom 1.049

4.9. DISCUSSION FOR THE TWO CYLINDER WITH T/D=4 CASE



(a) Streamlines


Figure 4.134: Flow characteristics for two side by side cylinders at Re = 100, T/D = 4 Figure 4.135: Time histories of drag forces for top cylinder at Re = 100 and T/D = 4




Figure 4.139: Absolute Pressure plot on five lines behind the two cylindersThe time histories of lift and drag coefficients for the Reynolds number of 100 are shown in above figures. The maximum velocity of 0.0144 m/s is observed and a long separation region is observed due to earlier separation and low Reynolds number. The maximum static pressure at front of the cylinder is 0 Pa. From Figure 4.139 we can observe that the maximum pressure is on all lines should be same. because of laminar flow. The maximum absolute pressure is 101325 Pa. The absolute pressure maximum same at all (x, y) coordinates.

Table 4.26: The table shows the Mean drag co efficient for T/D = 4 and Re = 100



bottom 1.488



(a) Streamlines



\Figure 4.142: Time histories of drag forces for bottom cylinder at Re = 3900 and T/D = 4 Figure 4.143: Time histories of lift forces for top cylinder at Re = 3900 and T/D = 4



The time histories of lift and drag coefficients for the Reynolds number of 3900 are shown in above figures. The maximum velocity of 0.0157 m/s is observed behind the two cylinders and a small separation region is observed The maximum static pressure at front of the cylinder is 7.11 Pa. From Figure 5.39 we can observe that the maximum absolute pressure is on line 2, 3 4 and 5 should be same. The maximum absolute pressure is 101325Pa and is -0.03 meter below and 0.1 below the central axis. The absolute pressure maximum at (x, y) coordinates is (0.1,0.1)m respectively.




bottom 1.08



(a) Streamlines


Figure 4.146: Flow characteristics for two side by side cylinders at Re = 10000, T/D = 4 Figure 4.147: Time histories of drag forces for top cylinder at Re = 10000 and T/D = 4

Figure 4.148: Time histories of drag forces for bottom cylinder at Re = 10000 and T/D = 4 Figure 4.149: Time histories of lift forces for top cylinder at Re = 10000 and T/D = 4


Figure 4.151: Absolute Pressure plot of all lines five lines behind the cylinders.

The time histories of lift and drag coefficients for the Reynolds number of 10000 are shown in above figures. The maximum velocity of 0.493 m/s is observed in between the two cylinders and a small separation region with a pair of vortices is observed. The maximum static pressure at front of the cylinder is 32 Pa. From Figure 4.151 we can observe that the maximum absolute pressure is on line 3. The maximum absolute pressure is 101327 Pa and -0.07 meter below the central axis. The absolute pressure maximum at (x, y) coordinates is (0.15,-0.07)m respectively.




bottom 0.946



(a) Streamlines




Figure 4.154: Time histories of drag forces for bottom cylinder at Re = 15000 and T/D = 4 Figure 4.155: Time histories of lift forces for top cylinder at Re = 15000 and T/D = 4


Figure 4.157: Absolute Pressure plots on five lines behind the two cylinders

The time histories of lift and drag coefficients for the Reynolds number of 15000 are shown in above figures. The maximum velocity of 0.637 m/s is observed behind the cylinders with a small separation region. The maximum static pressure at front of the cylinder is 81 Pa. From Figure 4.157 we can observe that the maximum absolute pressure is on line 2. The maximum absolute pressure is 101330 Pa and is 0.1 to 0.07 meter below the central axis. The absolute pressure maximum at (x, y) coordinates is (0.1,0.07)m respectively.




bottom 1.013



(a) Streamlines






Figure 4.163: Absolute Pressure plots on five lines behind the two cylinders.

The time histories of lift and drag coefficients for the Reynolds number of 22000 are shown in above figures. The maximum velocity of 1.005 m/s is observed a little far behind the two cylinders with a pair o vortices. The maximum static pressure at front of the cylinder is 167 Pa. From Figure 4.163 we can observe that the maximum absolute pressure is on line 3. The maximum absolute pressure is 101351 Pa and is 0.01 to 0.05 above the central axis and 0.1 meter, 0.15 meter below the central axis. The absolute pressure maximum at (x, y) coordinates is (0.15,0.02)m respectively.




bottom 1.19

In all the above cases considered in this project it is observed that the flow remains attached to the cylinder for higher value of Reynolds number and low mean drag is observed in case of higher Reynolds number compared to lower Reynolds number. For energy harvesting using the flow energy it is observed that for cases with higher Reynolds number we get a higher value of pressure which is suitable for piezoelectric energy conversion. Some more conclusions are drawn in the fifth chapter along with recommendations.

CHAPTER V

CONCLUSION AND FUTURE WORKS

5.1 CONCLUSIONS

In this project, a scheme based on control-volume method has been used to simulate the flow over one and two side by side cylinders in laminar and turbulent flows. Different Reynolds numbers of 100, 3900, 10000, 15000 and 2.2*104 were used in order to investigate the effect of various parameters on flow characteristics and hydrodynamic forces acting on the bodies. The most important conclusions of the numerical simulation of flow over one and two side by side cylinders in laminar and turbulent flow regime are summarized as follows.

1. At low Reynolds number the upstream cylinder shed no vortices. The boundary layer is laminar boundary layer with small vortices.

2. At high Reynolds number the separated upstream shear layers reattach alternatively to the top and bottom surfaces of the downstream cylinder, i.e., one shear layer reattaches to one surface while the other one just involves the other surface.

3. For a single cylinder with Re 10000 the Drag Co-Efficient is found to be 1.32 and small separation is found after the cylinder and then flow oscillations are found which were not much seen in Laminar Case.

4. For two cylinder it is found that the mean drag co-efficient reduces as the gap between the two cylinders increases.

5. Also, it is found that the drag is more for laminar cases for all the gaps compared to turbulent cases.

6. The mean drag co-efficient is always less for bottom cylinder compared to top cylinder, this may be due to wake from the top cylinder.

7. When we compare the value of pressure behind the one and two cylinder it is found that the value of pressure behind the one cylinder is less compared to the value of pressure behind the two cylinders with higher T/D of 2, 2.5, 3 and 4. Whereas the value of pressure behind the single cylinder is found to be higher compared with T/D ratio of 1.5. for single cylinder with Reynolds number of 100 the value of pressure behind the cylinders is -0.002 pa whereas in two cylinder with T/D =1.5 and reynolds number 100 the value or pressure is -2.518e^-4 and for T/D = 2, 2.5, 3 and 4 the value is 0.00135, 0.0014, 0.0075 and 0.0002 Pa respectively. For single cylinder with Reynolds number 10000 the maximum pressure behind the cylinder is -44.46 Pa and for T/D = 1.5, 2, 2.5,3 and the high pressure value is -5 Pa, -5 P, 11 Pa, 80 Pa and 5 pa respectively8. For the pressure values behind the cylinders the lines were created and the values of pressure were plotted and following conclusions are made.

It is found that the pressure value increases as the Reynolds number of the flow increases, hence for 22000 Reynolds number the pressure behind the cylinders is found to be maximum.

Most of the models the pressure values are found to be maximum either on line 1 or line 5. Line 1 is at a distance of 0.05 m from the cylinder and line 5 is at distance of 0.25 meter from the cylinder.

From all the models considered it is found that the model with L/D = 3 and for a Reynolds number of 3900 the value of pressure is 85 Pa which is maximum from all the cases considered. This value is found on line 1 which is 0.05 m away from the centre of the cylinder. And this peak value occurred at 0.15 m below the centre axis which is a symmetric axis between the two cylinders.

Next peak value is observed for T/D = 3 and Reynolds number of 10000, the value is 80 Pa on line 1 and is 0.1 m below the central axis. For T/D = 2.5 also the peak value 28 Pa is observed on line 1. In T/D = 4 the peak value 30 Pa is observed on line 1, 2 and 3

The above mentioned models with corresponding positions are suitable to install piezoelectric sensor to generate the piezoelectricity by harvesting the mechanical energy from the flow.

Finally, it is important to mention that the implemented solver is sufficiently applicable for simulation of flow over complex geometries such as two circular cylinders. Also, the presented results can be a good basis for prediction of structural responses in the two side-by-side circular cylinders.

5.2 future works

The following recommendations are provided which can be considered in future analysis.

1. In this project flow around two circular cylinders is considered, in future flow over Square shape, Elliptical shape, drop shape etc. type of geometry can be taken for flow behind these geometry and calculation of pressure, vortices behind the cylinders.2. Flow can be sent at different angle of attack to observe the difference in drag, pressure. 3. CFD analysis by considering the piezoelectric effect can be performed and result validated with these pressures. 4. Large Eddy Simulation turbulence model is used in this project which is itself a complex and computationally sensitive models but direct numerical Simulation (DNS) turbulence model can be used which solves the equation directly without modelling the smaller eddies.

REFERENCES

Abarbanel, S. S. 2010. Secondary frequencies in the wake of a circular cylinder with vortex shedding. Hampton, Va.: National Aeronautics and Space Administration, Langley Research Center.

Anderson, D. John,. (1995). Computational fluid dynamics , First edition. Printed in Singapore by (a.d.john 1995)

Aradag, S. 2009. Unsteady turbulent vortex structure downstream of a three dimensional cylinder. J. of Thermal Science and Technology 29(1): 91-98.

Berselli, L. C., Iliescu, T. & Layton, W. J. 2005. Mathematics of Large Eddy Simulation of Turbulent Flows. Springer.

Deng, j., An-lu, R & Wen-qu, C. 2005. Numerical simulation of flow-induced vibration on two circular cylinders in tandem arrangement. Journal of Hydrodynamics, Ser. B, 17(6): 660-666.

Deardorff, J. W. 1970. A Numerical Study of Three-Dimensional Turbulent Channel Flow at Large Reynolds Numbers. Journal of Fluid Mechanics 41(02): 453-480.

Devaud, C., J. Weisinger, D. Johnson & E. Weckman 2009. Experimental and numerical characterization of the flowfield in the largescale UW live fire research facility. International journal for numerical methods in fluids 60(5): 539-564.

Dehkordi, B. G., H. S. Moghaddam & H. H. Jafari 2011. Numerical simulation of flow over two circular cylinders in tandem arrangement. Journal of Hydrodynamics, Ser. B 23(1): 114-126.

Elsenaar, A. 2005. Reynolds number effects in transonic flow. Neuilly sur Seine, France: AGARD.

Franke, J. & W. Frank 2002. Large eddy simulation of the flow past a circular cylinder at ReD=3900. Journal of Wind Engineering and Industrial Aerodynamics 90:11911206.

Foden, G. 2010. Turbulence. New York: Alfred A. Knopf.

Grinstein, F. F. 2007. Implicit large eddy simulation: computing turbulent fluid dynamics. Cambridge: Cambridge University Press.

Guang-wang, L., R. An-lu & C. Wen-qu 2004. An ALE method for vortex-induced vibrations of an elastic circular cylinder [J]. Acta Aerodynamica Sinica 3: 008.

John, V. & M. Roland 2007. Simulations of the turbulent channel flow at Re= 180 with projectionbased finite element variational multiscale methods. International Journal for Numerical Methods in Fluids 55(5): 407-429.

Kang, S. 2003. Characteristics of flow over two circular cylinders in a side-by-side arrangement at low Reynolds numbers. Physics of Fluids (1994-present) 15(9): 2486-2498.

Kadanoff, L. P. 2009. Phases of Matter and Phase Transitions; From Mean Field Theory to Critical Phenomena. J. Phys.: Cond. Matt 12: 1496.

Kennedy, L. A. 2013. Advanced Thermodynamics Engineering, Kalyan Annamalai, Ishwar K. Puri, Milind A. Jog. Crc Press, Taylor and Francis Group (2011). Elsevier.

Kim, C. & A. Conlisk 1990. Flow induced vibration and noise by a pair of tandem cylinders due to buffeting. Journal of Fluids and Structures 4(5): 471-493.

Kolmogorov. Nikolaevich, A. 1941. The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Proceedings of the USSR .

Obed, S., G. Jagadeesh & K. Kontis 2012. Micro-blast waves using detonation transmission tubing. 28th International Symposium on Shock Waves. pp. 1035-1040.Ouvrard, H., B. Koobus, A. Dervieux & M. V. Salvetti 2010. Classical and variational multiscale LES of the flow around a circular cylinder on unstructured grids. Computers & Fluids 39(7): 1083-1094.

Patel, Y. 2010. Numerical investigation of flow past a circular cylinder and in a staggered tube bundle using various turbulence models.

Posdziech, O. & R. Grundmann 2007. A systematic approach to the numerical calculation of fundamental quantities of the two-dimensional flow over a circular cylinder. Journal of Fluids and Structures 23(3): 479-499

Rogallo, R. S. & Moin, P. 1984. Numerical Simulation of Turbulent Flows Annual Review of Fluid Mechanics .16: 99-137.

Sagaut, P. 2006. Large eddy simulation for incompressible flows an introduction (III Ed.). Berlin: Springer-Verlag.

Shyy, W., Lian, Y., Tang, J., Viieru, D. & Liu, H. 2008. Aerodynamics of Low Reynolds Number Flyers. Cambridge University Press New York.

Siegwarth, J. D. 2008. Vortex shedding flow meter performance at high flow velocities. Gaithersburg, MD: U.S. Dept. of Commerce, National Bureau of Standards.Sarvghad-Moghaddam, H., N. Nooredin & B. Ghadiri-Dehkordi 2011. Numerical simulation of flow over two side-by-side circular cylinders. Journal of Hydrodynamics, Ser. B 23(6): 792-805.

Smetana, F. O. 2006. A Theoretical and experimental study of gas flow through cloth over a range of pressures and temperatures. Ft. Belvoir: Defense Technical Information Center.

Uga, K. C., M. Min, T. Lee & P. F. Fischer 2013. Spectral-element discontinuous Galerkin lattice Boltzmann simulation of flow past two cylinders in tandem with an exponential time integrator. Computers & Mathematics with Applications 65(2): 239-251.

Xie, L. 2014. Advanced Engineering and Technology. Boca Raton: CRC Press.

Webb, R. L. & N. Kim 2005. Enhanced Heat Transfer. Taylor and Francis, NY.

Weinstein, L. A., M. R. Cacan, P. So & P. K. Wright 2012. Vortex shedding induced energy harvesting from piezoelectric materials in heating, ventilation and air conditioning flows. Smart Materials and Structures 21(4): 045003.

Williamson, C. 1985. Evolution of a Single Wake Behind a Pair of Bluff Bodies. Journal of Fluid Mechanics 159(1-18.

Zdravkovich, M. M. 1970. The effects of interference between circular cylinders in cross flow . Journal of Fluids and Structures 1(2): 239-261

two cylinder_edited shahid (2)

Documents