## Publications

84 results found

Ghebali S, Chernyshenko SI, Leschziner MA, Turbulent skin-friction reduction by wavy surfaces

Direct numerical simulations of fully-developed turbulent channel flows withwavy walls are undertaken. The wavy walls, skewed with respect to the mean flowdirection, are introduced as a means of emulating a Spatial Stokes Layer (SSL)induced by in-plane wall motion. The transverse shear strain above the wavywall is shown to be similar to that of a SSL, thereby affecting the turbulentflow, and leading to a reduction in the turbulent skin-friction drag. Thepressure- and friction-drag levels are carefully quantified for various flowconfigurations, exhibiting a combined maximum overall-drag reduction of about0.5%. The friction-drag reduction is shown to behave approximatelyquadratically for small wave slopes and then linearly for higher slopes, whilstthe pressure-drag penalty increases quadratically. Unlike in the SSL case,there is a region of increased turbulence production over a portion of thewall, above the leeward side of the wave, thus giving rise to a local increasein dissipation. The transverse shear-strain layer is shown to be approximatelyReynolds-number independent when the wave geometry is scaled in wall units.

Lasagna D, Huang D, Tutty O,
et al., Sum-of-Squares approach to feedback controlof laminar wake flows, *Journal of Fluid Mechanics*, ISSN: 1469-7645

Chernyshenko S, 2017, Relationship between the methods of bounding time averages

The problem of finding bounds of time-averaged characteristics of dynamicalsystems, such as for example the bound on the mean energy dissipation rate in aturbulent flow governed by incompressible Navier-Stokes equations, isconsidered. It is shown that both the well-known background flow method ofDoering and Constantin and the direct method proposed by Seis in 2015correspond to the same quadratic storage functional in the framework of theindefinite storage functional method. In particular, a background flow can befound corresponding to the linear functional used in the direct method and viceversa. It is shown that any bound obtained with the background flow method canalso be obtained by the direct method. The reverse is true subject to anadditional constraint. The relative advantages of the three methods arediscussed.

Ghebali S, Chernyshenko SI, Leschziner M, 2017, Can large-scale oblique undulations on a solid wall reduce the turbulent drag?, *Physics of Fluids*, Vol: 29, ISSN: 1070-6631

Direct numerical simulations of fully developed turbulent channel flows with wavy walls are undertaken. The wavy walls, skewed with respect to the mean flow direction, are introduced as a means of emulating a Spatial Stokes Layer (SSL) induced by in-plane wall motion. The transverse shear strain above the wavy wall is shown to be similar to that of a SSL, thereby affecting the turbulent flow and leading to a reduction in the turbulent skin-friction drag. However, some important differences with respect to the SSL case are brought to light too. In particular, the phase variations of the turbulent properties are accentuated and, unlike in the SSL case, there is a region of increased turbulence production over a portion of the wall, above the leeward side of the wave, thus giving rise to a local increase in dissipation. The pressure- and friction-drag levels are carefully quantified for various flow configurations, exhibiting a combined maximum overall-drag reduction of about 0.6%. The friction-drag reduction is shown to behave approximately quadratically for small wave slopes and then linearly for higher slopes, whilst the pressure-drag penalty increases quadratically. The transverse shear-strain layer is shown to be approximately Reynolds-number independent when the wave geometry is scaled in wall units.

Huang D, Jin B, Lasagna D,
et al., 2017, Expensive Control of Long-Time Averages Using Sum of Squares and Its Application to A Laminar Wake Flow, *IEEE Transactions on Control Systems Technology*, ISSN: 1063-6536

This paper presents a nonlinear state-feedback control design approach for long-time average cost control, where the control effort is assumed to be expensive. The approach is based on sum-of-squares and semidefinite programming techniques. It is applicable to dynamical systems whose right-hand side is a polynomial function in the state variables and the controls. The key idea, first described but not implemented by Chernyshenko et al., is that the difficult problem of optimizing a cost function involving long-time averages is replaced by an optimization of the upper bound of the same average. As such, a controller design requires the simultaneous optimization of both the control law and a tunable function, similar to a Lyapunov function. This paper introduces a method resolving the well-known inherent nonconvexity of this kind of optimization. The method is based on the formal assumption that the control is expensive, from which it follows that the optimal control is small. The resulting asymptotic optimization problems are convex. The derivation of all the polynomial coefficients in the controller is given in terms of the solvability conditions of state-dependent linear and bilinear inequalities. The proposed approach is applied to the problem of designing a full-information feedback controller that mitigates vortex shedding in the wake of a circular cylinder in the laminar regime via rotary oscillations. Control results on a reduced-order model of the actuated wake and in direct numerical simulation are reported.

Fantuzzi G, Goluskin D, Huang D,
et al., 2016, Bounds for Deterministic and Stochastic Dynamical Systems using Sum-of-Squares Optimization, *SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS*, Vol: 15, Pages: 1962-1988, ISSN: 1536-0040

Fantuzzi G, Goluskin D, Huang D,
et al., 2016, Bounds for Deterministic and Stochastic Dynamical Systems using Sum-of-Squares Optimization, *SIAM Journal on Applied Dynamical Systems*, Vol: 15, Pages: 1962-1988

Huang D, Chernyshenko S, 2016, LONG-TIME AVERAGE COST CONTROL OF POLYNOMIAL SYSTEMS: A SUM-OF-SQUARES-BASED SMALL-FEEDBACK APPROACH, 8th ASME Annual Dynamic Systems and Control Conference (DSCC 2015), Publisher: AMER SOC MECHANICAL ENGINEERS

Lasagna D, Huang D, Tutty OR,
et al., 2016, Sum-of-squares approach to feedback control of laminar wake flows, *JOURNAL OF FLUID MECHANICS*, Vol: 809, Pages: 628-663, ISSN: 0022-1120

Lasagna D, Huang D, Tutty OR, et al., 2016, Controlling Fluid Flows with Positive Polynomials, 35th Chinese Control Conference (CCC), Publisher: IEEE, Pages: 1301-1306, ISSN: 2161-2927

Lasagna D, Tutty OR, Chernyshenko S, 2016, Flow regimes in a simplified Taylor-Couette-type flow model, *EUROPEAN JOURNAL OF MECHANICS B-FLUIDS*, Vol: 57, Pages: 176-191, ISSN: 0997-7546

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- Citations: 1

Zhang C, Chernyshenko SI, 2016, Quasisteady quasihomogeneous description of the scale interactions in near-wall turbulence, *PHYSICAL REVIEW FLUIDS*, Vol: 1, ISSN: 2469-990X

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- Citations: 4

Huang D, Chernyshenko S, 2015, Low-order State-feedback Controller Design for Long-time Average Cost Control of Fluid Flow Systems: A Sum-of-squares Approach, 34th Chinese Control Conference (CCC), Publisher: IEEE, Pages: 2479-2484, ISSN: 2161-2927

Huang D, Chernyshenko S, 2015, Long-time Average Cost Control of Stochastic Systems Using Sum of Squares of Polynomials, 34th Chinese Control Conference (CCC), Publisher: IEEE, Pages: 2344-2349, ISSN: 2161-2927

Huang D, Chernyshenko S, Goulart P,
et al., 2015, Sum-of-squares of polynomials approach to nonlinear stability of fluid flows: an example of application, *PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES*, Vol: 471, ISSN: 1364-5021

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- Citations: 5

Huang D, Chernyshenko S, Lasagna D, et al., 2015, Long-time Average Cost Control of Polynomial Systems: A Sum of Squares Approach, European Control Conference (ECC), Publisher: IEEE, Pages: 3244-3249

Chernyshenko SI, Goulart P, Huang D,
et al., 2014, Polynomial sum of squares in fluid dynamics: a review with a look ahead, *PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES*, Vol: 372, ISSN: 1364-503X

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- Citations: 9

Blesbois O, Chernyshenko SI, Touber E,
et al., 2013, Pattern prediction by linear analysis of turbulent flow with drag reduction by wall oscillation, *JOURNAL OF FLUID MECHANICS*, Vol: 724, Pages: 607-641, ISSN: 0022-1120

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- Citations: 11

Chernyshenko S, 2013, Drag reduction by a solid wall emulating spanwise oscillations. Part 1

A new idea for turbulent skin-friction reduction is proposed, wherein theshape of the solid wall is designed to create the spanwise pressure gradientacting similarly to the well-known method of drag reduction by in-planespanwise wall motion. Estimates based on the assumption of similarity with dragreduction effect of in-plane wall motion suggest that drag reduction of about2.4% can be achieved in the flow past a wavy wall, with the crests forming anangle of about 38 degrees with the main flow direction, and the wave period inthe main flow direction equal to about 1500 wall units. The required height ofthe wall waves have to be adjusted to achieve the same intensity of thespanwise motion as that created by an in-plane moving wall of the samewavelength and with peak wall velocity equal to 2 wall units. Further researchis being conducted in order to determine this height. Suggestions are made forfurther research on confirming the feasibility of the proposed method and onoptimising the wall shape.

Chernyshenko S, Huang D, Goulart P, et al., 2013, Nonlinear Stability Analysis of Fluid Flow using Sum of Squares of Polynomials, 11th International Conference of Numerical Analysis and Applied Mathematics (ICNAAM), Publisher: AMER INST PHYSICS, Pages: 265-268, ISSN: 0094-243X

Mathis R, Marusic I, Chernyshenko SI,
et al., 2013, Estimating wall-shear-stress fluctuations given an outer region input, *JOURNAL OF FLUID MECHANICS*, Vol: 715, Pages: 163-180, ISSN: 0022-1120

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- Citations: 33

Vodop'yanov IS, Nikitin NV, Chernyshenko SI, 2013, Turbulent drag reduction by spanwise oscillations of a ribbed surface, *FLUID DYNAMICS*, Vol: 48, Pages: 461-470, ISSN: 0015-4628

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- Citations: 1

Chernyshenko SI, Marusic I, Mathis R, 2012, Quasi-steady description of modulation effects in wall turbulence

A theoretical description of the phenomenon of modulation of near-wallturbulence by large scale structures is investigated. The description given issimple in that the effect of large-scale structures is limited to aquasi-steady response of the near-wall turbulence to slow large-scalefluctuations of the skin friction. The most natural and compact form ofexpressing this mechanism is given by the usual Reynolds-number-independentrepresentation of the total skin friction and velocity, scaled in wallvariables, where the mean quantities are replaced by large-scalelow-pass-filtered fluctuating components. The theory is rewritten in terms offuctuations via a universal mean velocity and random mean square fluctuationvelocity profiles of the small-scales and then linearised assuming that thelarge-scale fluctuations are small as compared to the mean components. Thisallows us to express the superposition and modulation coefficients of theempirical predictive models of the skin friction and streamwise fluctuatingvelocity given respectively by Marusic et al. (13th Eur. Turb. Conf., 2011) andMathis et al. (J. Fluid Mech. 2011, vol. 681, pp. 537-566). It is found thatthe theoretical quantities agree well with experimentally determinedcoefficients.

Duque-Daza CA, Baig MF, Lockerby DA,
et al., 2012, Modelling turbulent skin-friction control using linearized Navier-Stokes equations, *JOURNAL OF FLUID MECHANICS*, Vol: 702, Pages: 403-414, ISSN: 0022-1120

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- Citations: 15

Goulart PJ, Chernyshenko S, 2012, Global stability analysis of fluid flows using sum-of-squares, *PHYSICA D-NONLINEAR PHENOMENA*, Vol: 241, Pages: 692-704, ISSN: 0167-2789

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- Citations: 14

Booker CD, Zhang X, Chernyshenko SI, 2011, Large-Scale Vortex Generation Modeling, *JOURNAL OF FLUIDS ENGINEERING-TRANSACTIONS OF THE ASME*, Vol: 133, ISSN: 0098-2202

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- Citations: 1

Daque CA, Baig MF, Lockerby DA, et al., 2011, Modelling turbulent skin-friction control using linearised Navier-Stokes equations, 13th European Turbulence Conference (ETC), Publisher: IOP PUBLISHING LTD, ISSN: 1742-6588

Wang HL, Nikitin NV, Chernyshenko SI, 2011, Identification of a Laminar-Turbulent Interface in Partially Turbulent Flow, *FLUID DYNAMICS*, Vol: 46, Pages: 911-916, ISSN: 0015-4628

Goulart PJ, Chernyshenko SI, 2010, Stability Analysis of Fluid Flows Using Sum-of-Squares, *2010 AMERICAN CONTROL CONFERENCE*, Pages: 2971-2976, ISSN: 0743-1619

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- Citations: 2

Goulart PJ, Chernyshenko SI, 2010, Stability analysis of fluid flows using sum-of-squares, Pages: 2971-2976

In this paper we present a new method for assessing the stability of finite-dimensional approximations to the Navier-Stokes equation for fluid flows. Approximations to the Navier-Stokes equation typically take the form of a set of linear ODEs with an additional bilinear term that conserves the total energy of the system state. We suggest a structured method for generating Lyapunov functions using sum-of-squares optimization that exploits this energy conservation property. We provide a numerical example demonstrating the use of this technique to assess the stability of a model of a shear flow between infinite parallel plates. © 2010 AACC.

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