This way it was possible to check for the flow fields two-dimensionality in paral- Our overall control strategy is shown in Figure 5.

The control algorithm acts on the estimate of the Mode 1 amplitude only. This design de- cision was made based on our earlier investigations con- trolling a low dimensional model of the flow. This approach was successful in stabilizing back control strategy: the cylinder wake in a 2D CFD simulation Siegel et al da1 This allows the use of plitude of mode 1.

When em- tioning of the cylinder model, as seen in Figure 3. POD, a nonlinear model reduction approach, is also referred to in the literature as the Karhunen-Loeve expansion POD decomposes a unsteady flow field into spatial modes and temporal mode amplitudes, and is an essential com- ponent of our feedback control strategy shown in Figure 5. The desired POD model contains an adequate num- ber of modes to enable modeling of the temporal and spatial characteristics of the large-scale coherent struc- tures inherent in the flow.

This Sirovich16 is employed to generate the basis functions of mode was found to be necessary to obtain an estimate of the POD spatial modes from the PIV measurements.

## Control of three-dimensional phase dynamics in a cylinder wake

Only the U velocity component in the direction of the It is being used to both estimate the effectiveness of the mean flow was used for POD decomposition in this ef- controller, as well as to allow for gain scheduling to ac- fort. This decision was made in order to be able to esti- count for changes in the flow receptivity to forcing in a mate the mode amplitudes based on sensor information, real time fashion.

Additionally, Noack et al. Since the change in mean flow distri- the mean flow greatly improves the ability of the model bution is an important quantity, we chose the U velocity to account for transient effects in the flow field.

## [] Optimal control of circular cylinder wakes using long control horizons

For this, two The answers to the above questions have been addressed different schemes are reported in literature. Most often by Cohen et al. This process involves spatial derivatives of the using just the first mode. Furthermore, feedback based snapshots, which are, particularly in the case of experi- on the first mode alone suppressed all the other modes mental data, inherently sensitive to noise.

Gillies8 used in a four mode POD model, indicating that higher order a simple least squares fit, which we found to be much modes derive from the fundamental modes. In view of more robust. Neither of these methods is very suitable this result, truncation of the POD model took place after for real time implementation, since they require itera- the first four modes, which contain more than For this At this point, it is imperative to note the difference be- reason, the experiment made use of linear stochastic es- tween the number of modes required to reconstruct the timation LSE to estimate the mode amplitudes in real flow and the number of modes required to control the time.

### Suppression of vortex shedding for flow around a circular cylinder using optimal control

LSE is deterministic in terms of computing time, flow. In this effort, we are interested in estimating only while least square fitting is not. Thus LSE is a much enough modes for closed-loop control. On the other hand, better choice for real time implementation. In order to an accurate reconstruction of the velocity field based on compute the LSE transformation matrix that maps the a low-dimensional model may be obtained using between sensor readings onto POD mode amplitude estimates, a modes.

Siegel et al24 have shown that sensor tuating velocity component in the direction of the flow placement schemes that work well for the limit cycle flow as described in Equation 4.

The decomposition of this perform poorly when applied to transient forced or feed- component of the velocity field is as follows: back controlled schemes. In this effort, we re- verted back to the 35 sensor setup first used in the CFD simulations. Shown are the first four modes of the al.

## Drag force on circular cylinder

Solid lines are positive, dashed lines negative isocontours. A comparison of the real time Mode tion error. While there are mi- The objective of this investigation was to explore the ef- nor differences in the peak amplitudes, the phase error fect of fixed and variable phase feedback on the modes between both signals is minimal, even during highly present in the wake as well as their spanwise phase dis- transient flow states.

Typical errors in amplitude are in tribution. Siegel et al24 had suffered from instability over longer Overall, there remains much work to be done in the periods of time, as had the fixed phase runs in the CFD sensor placement and mode estimation areas for tran- simulations. Up to this point it was unclear if this was sient flows. While it is relatively easy to obtain high due to three dimensional effects in the cylinder wake. The controller is activated at time 0s, and subsequently a decrease in Mode 5 amplitude can be ob- The results of initial studies of the effect of linear feed- served.

Also, the fluctuating von Karman Modes 1 and 2 back on the global wake flow field were presented by show a slight increase in oscillation amplitude. The flow Siegel et al They were based on a 7 sensor estimate of visualization shown in Figure 12 shows a random phase the flow state, which did not yield accurate Mode 5 am- distribution across the span at the time when the con- plitudes. We therefore repeated the study with the present troller is activated, and a fixed spanwise phase at the end 35 sensor setup described above.

The results in terms of of the run. This behavior is very much identical to the Mode 5 amplitude are shown in Figure 9. Mode 5 pro- open loop lock-in behavior shown in Figures 6 and 7.

- Treat Yourself: 70 Classic Snacks You Loved as a Kid and Still Love Today!
- Creeping flow around a bubble!
- Piv measurement!
- Baseball: The Peoples Game?

The shedding exhibits strong phase jumps, and ultimately returns to a drag value close to the unforced flow as evidenced by the amplitude of Mode 5. This that increase the vortex shedding intensity. While all increase is coincident with a decrease in the vortex shed- cases where the vortex shedding is reduced, develop ding, as can be seen in both the Mode 1 and 2 ampli- strong spanwise phase variations.

Clearly, the controller tudes, as well as the flow visualization shown in Figure is able to weaken the vortex shedding in the measure- 16 bottom left. This phase tom right. Clearly, the behavior of the first phase locked variation does contaminate the measurement plane after flow is very similar if not identical to the fixed phase some time, though, and consequently leads to the phase feedback with the same phase angle. This demonstrates jumps observed in the mode estimates.

### Publications

In order to investigate this, we Mode 1 conducted the variable phase feedback runs detailed be- Mode 2 low. Top left, 10s, top right, 20s, bottom left, 30s, bottom right Effects of the SJ pair on the cylinder wake are investigated in a systematical way, with the focus placed on the SJ's momentum coefficient, frequency and position. In the second configuration, the same cylinder is allowed to oscillate in the cross-flow direction under the excitation of asymmetrically shedding vortices as well as the constraint of a spring.

It is well demonstrated that this one-dimensional VIV of the cylinder can be successfully suppressed by the use of SJ control. Due to stronger vortex shedding induced by increased relative motion between the cylinder and its surrounding flow, however, not all the cases that perform complete wake suppression on the fixed cylinder are able to completely suppress the VIVs of the oscillating cylinder.

Through the present study, details about SJ-controlled flow around the cylinder and in the wake are also revealed. View full-text via PolyU eLinks. The analysis of an ill-posed problem using multi-scale resolution and second-order adjoint techniques Aleksey K. Alekseev , Ionel Michael Navon. Sensitivities, adjoints and flow optimization Max Gunzburger.

Tokumaru , Paul E. A general framework for robust control in fluid mechanics Thomas R. Bewley , Roger Temam , Mohammed Ziane. Metcalfe , Babak Bagheri. Flow control : passive, active, and reactive flow management Mohamed Gad-el-Hak. Numerical study of vortex shedding from a rotating cylinder immersed in a uniform ow Aeld.

- Drawing Cylinder In Webgl.
- Machine Intelligence and Knowledge Engineering for Robotic Applications.
- Love, Lust & Faking It: The Naked Truth About Sex, Lies, and True Romance.
- References;
- Creeping flow around a bubble.

MH Chou. Optimal control of the unsteady Navierâ€”Stokes equations.

- Control techniques in flow past a cylinder- A Review - IOPscience.
- The Alchemyst (The Secrets of the Immortal Nicholas Flamel, Book 1)!
- Shadowing and Surveillance: A Complete Guidebook!
- Control techniques in flow past a cylinder- A Review!
- Log in to Wiley Online Library.
- Submission history.
- Swipe to navigate through the articles of this issue.

Related Papers.