### Control of Chaotic Flows and Fluid Forces (Previous Part)

Control of Chaotic Flows and Fluid Forces (Previous Part)

**Flow Characteristic**

“Numerical simulations using the LBM were conducted to analyze the flow past two offset square cylinders with a control plate. The was maintained at 150. We are changing and and obsering the results. Where is the distance between the two cylinders and is the distance between the plate and cylinders.

During the whole process we find the different graphs of vorticity contour visulization where solid and dashed lines represents the possitive and negative vortices respatively. We find the values of strouhal number using FFT commant in matlab. Here we discuss only few cases to avoid the repetation.

First we discuss the patteren of vorticity contour visulization by taking and changing the plate distance as , , , and are one by one.

**Effect of , , and at **

Figures 4.6(a-f) to 4.9(a-f) illustrate the influence of gap position between the cylinders when g = 2. For different values of . At (Figures 3.6(a-f)), the flow is fully chaotic and cansiderably merge with each others without any regular pattern. (Figure 3.6(a)). The streamlines further canfinus the chotic nature of flow (Figure 3.6(b)). The drag coefficients of both cylinders are anti-phase in nature and showing same modulations (Figure 3.6(d)).

The chaotic flip-flopping nature can be clearly of both cylinders (Figure 3.6(e,f)). There is a longest peak in the spectra which confines the existence of primay shedding frequency. Furthermore, the minor peaks also confines the existence of secandary cylinder interaction frequencies. Almost the similar kind of flow characterstics observed for (Figure 3.7(a-f)).

As the value of increared from to and , the flow features almost becomes identical for the two offset cylinders and resembles the isolated behavior (Figures 3.8(a-f) and 3.9(a-f)).

The two-rows vortex pattern can be seen behind the upstream control plate. Interestingly, again it becomes modulated as the value of increared from to (Figure 3.9(c)). Furthermore, the lift signals at are sinusoidal and in-phase (figure 3.8(d)). And becomes anit-phas as value increared to (Figure 3.9(d)).

This ensure that the upsteam control plate position is critical and important for flow past effset cylinders. This further confines that at upto is the critical spacing for the upstream control plate.

**Vortes**

Now we consider the case in which the distance of plate remains constant as but we change the gaps between cylinders when and we see that vortices are very clear and close showing the unsteady behavior of fluid. But when we increase the distance, we observe the dispersion of bubbles.

This figure shows non-synchronized wake pattern. At start the antiphase combination occurs, vortex shedding is more complex and shows the merging behaviors. But with increasing the distance between cylinders we get the smooth behaviors.**Streamlines**

On the other hand streamlines visualization for this case presented in figure. With increasing the distance between cylinders streamlines becoming steady for wake pattern with each cylinder which revels the generations of vortices.

**Drad, lift coefficients**

The graphs of time-drag coefficient and time-lift coefficient show periodic behavior with varying amplitude for and . Where shows the modulated signals, which is because the shape and size of vertices are not same

**Strouhal number**

Power spectrum analysis of reveals multiple frequency peaks for and , indicating a complex interaction between the cylinders. Increasing the distance reduces the number of peaks, suggesting a decrease in distortion.

**Flow characteristics**

For this post, the value of is . We are changing from to , and obsering the results, where is the distance between the two cylinders.

The vortex shedding behavior is more complex at downstream and shows merging behavior throughout the computational domain due to minor change in gap and clearly depicts an in-phase separation of flow for both cylinders shown in (Fig 4.19(a)). (Figs 4.19(d) and 4.19(e)) shows periodic detachment and synchronized vortices behind both cylinders produces an oscillating wake on whole computational domain. The flow visualization revealed distinct antiphase and inphase characteristics in the wake of both cylinders.

(Figs 4.20(a-j)) shows the time history analysis for and for fixed at different . Figures 4.20(a-f) show periodic fluctuations in drag coefficient ( ) and lift coefficient ( ). Where shows the modulated signals, which is because the shape and size of the vortices are not same. In (Figs 4.20(g-j) and show sinusoidal behavior with amplitude difference. show periodicity when the distance between the cylinder is high.

Power spectrum analysis reveals multiple, irregular frequencies and a dominant primary vortex shedding. Jet flow interference leads to multiple peaks due to highly modulated signals.

**Conclusions**

Numerical investigations are carried out to examine the effect in the presence of which is the distance between two offsets square cylinders and distance between a controal plate and cylindera, by using Lattice Boltzmann method.

The focus of our current work is to fully analyze the effect of and in different wake patterns. We observed many wake patterns depending on and .

With a fixed Reynolds number (Re) of 150, we varied L from 0.5 to 10 and g from 1 to 5. This generated vortices that exhibited complex behavior downstream, lacking synchronization. The streamlines were also non-synchronized and interfered with each other due to the non-similar vortices. Without an upstream control plate, C_D showed modulation, and we observed distortion in the power spectrum analysis.

We also compare our results with two offset square cylinders without controal plate. The value of increased, both and decreases. As the value of increased, the and values are decresed and finally approaches to the values without upstream control plate.

**Future work**

In future, I wish to implement the proposed method for -dimensional real-world problem. The theoretical development of the method is also in my future goals.

Finally I would like to apply the LBM for the formulation and dimensional two-phase flow problem.