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Job Record #17946
TitleDynamic Feedback and POD-based Control of Turbulence
CategoryPhD Studentship
EmployerBen-Gurion University, Dept. Mech. Engng.
LocationIsrael, Beer-Sheva
InternationalYes, international applications are welcome
Closure Date* None *
Dynamic Feedback and POD-based Control of Turbulence in Pipe Flow (under the ISF 
grant October 2022- September 2025 
by Alexander Yakhot Shai Arogeti
Scientific Abstract
The objectives of this proposal are inspired by the four publications. Eckhardt et 
al. (2007) suggested a concept that the coexistence of laminar and turbulent 
regimes, discovered experimentally and in numerical simulations, means that the 
turbulent state is a chaotic saddle. This is consistent with the fact that most 
known solutions appear in saddle-node bifurcations, that is, arise in pairs. 
Willis et al. (2017) introduced a simple, elegant controlling scheme for 
stabilizing solutions at a lower energy branch, thereby preventing laminarization. 
Hof et al. (2010) introduced a forcing term into the Navier–Stokes equations to 
reduce inflection points in the velocity profile, which leads to a flattening the 
velocity profile. It acts as a simple control mechanism preventing the energy 
transfer from the mean flow into turbulent eddies. Modares et al. (2015) developed 
a data-driven approach, the Off-Policy Reinforcement Learning (OPRL) design. The 
control process under consideration is governed by the Navier-Stokes equations, 
i.e., by the “unknown dynamics” using the control design terminology. Therefore, 
we presume that OPRL versions tailored to the turbulence transition control 
problem are of interest.

The research proposal is formulated in the following Tasks:

Task 1. Dynamic feedback control of transition to turbulence formulated in wall 
units. In this Task, new dynamic feedback control schemes are introduced.

Task 2. Optimal control of transition to turbulence using model-free design 
techniques. In this Task, new
(a) observables are examined, (b) a quadratic cost function is defined

Task 3. POD-based control of transition to turbulence in pipe flow. In this Task, 
a new approach to prevent the energy extraction from the mean flow into large-
scale structures is developed. Specifically, the window POD, (WPOD, Grinberg et 
al., 2014) is applied to attenuate the radial cross-plane motion.

The significance of the proposed research is in developing state-of-the-art 
methods, which integrate computational fluid dynamics (CFD) and turbulence 
control. Numerical simulations are performed using the spectral finite-difference 
CFD code (Willis, 2017).

B. Eckhardt, T. M. Schneider, B. Hof, and J. Westerweel. Turbulence transition in 
pipe flow. Annu. Rev. Fluid Mech., 39:447-469, 2007.

A. R. Willis, Y. Duguet, O. Omel’chenko, and M. Wolfrum. Surfing the edge: using 
feedback control to find nonlinear solutions. J. Fluid Mech., 831:579-591, 2017.

B. Hof, A. de Lozar, M. Avila, X. Tu, and T. Schneider. Eliminating turbulence in 
spatially intermittent flows. Science, 327:1491-1494, 2010.

H. Modares, F. L. Lewis, and Z.-P. Jiang. H1 tracking control of completely 
unknown continuous-time systems via Off-Policy Reinforcement Learning. IEEE Trans. 
Neural Netw. Learn. Sys., 26:2550-2562, 201

L. Grinberg, M. Deng, G. E. Karniadakis, and A. Yakhot. Window Proper Orthogonal 
Decomposition: Application to Continuum and Atomistic Data. In Quarteroni A. and 
Rozza G., editors, Reduced Order Methods for Modeling and Computational Reduction. 
MSA - Modeling, Simulation and Applications, vol. 9. Springer, Cham., 2014. 
Published online, 

Contact Information:
Please mention the CFD Jobs Database, record #17946 when responding to this ad.
NameAlex Yakhot, Shai Arogeti,
Email ApplicationYes
Record Data:
Last Modified10:34:43, Monday, September 12, 2022

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