Assessment of suboptimal control for turbulent skin friction reduction via resolvent analysis

2017 ◽  
Vol 828 ◽  
pp. 496-526 ◽  
Author(s):  
Satoshi Nakashima ◽  
Koji Fukagata ◽  
Mitul Luhar
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
High Gain ◽  
Friction Reduction ◽  
Suboptimal Control ◽  
Navier Stokes ◽  
Spectral Space ◽  
Spanwise Direction ◽  
Linear Superposition ◽  
Control Laws

This paper extends the resolvent analysis of McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to elucidate the drag reduction mechanisms for the suboptimal control laws proposed by Lee, Kim & Choi (J. Fluid Mech., vol. 358, 1998, pp. 245–258). Under the resolvent formulation, the turbulent velocity field is expressed as a linear superposition of propagating modes identified via a gain-based decomposition of the Navier–Stokes equations. This decomposition enables targeted analyses of the effects of suboptimal control on high-gain modes that serve as useful low-order models for dynamically important coherent structures such as the near-wall (NW) cycle or very-large-scale motions. The control laws generate blowing and suction at the wall that is proportional to the fluctuating streamwise (Case ST) or spanwise (Case SP) wall shear stress, with the magnitude of blowing and suction being a design parameter. It is shown that both Case ST and SP can suppress resolvent modes resembling the NW cycle. However, for Case ST, the analysis reveals that control leads to substantial amplification of flow structures that are long in the spanwise direction. Quantitative comparisons show that these predictions are broadly consistent with results obtained in previous direct numerical simulations. Further, the predicted changes in mode structure suggest that suboptimal control can be considered a modified version of opposition control. In addition to the study of modes resembling the NW cycle, this paper also considers modes of varying speed and wavelength to provide insight into the effects of suboptimal control across spectral space.

scholarly journals A framework for studying the effect of compliant surfaces on wall turbulence

2015 ◽  
Vol 768 ◽  
pp. 415-441 ◽  
Author(s):  
M. Luhar ◽  
A. S. Sharma ◽  
B. J. McKeon
Keyword(s):  
Rational Design ◽  
Large Scale ◽  
Stokes Equations ◽  
Positive Influence ◽  
Wall Turbulence ◽  
Navier Stokes ◽  
Spectral Space ◽  
Linear Superposition ◽  
Navier Stokes Equations ◽  
Compliant Surfaces

This paper extends the resolvent formulation proposed by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382) to consider turbulence–compliant wall interactions. Under this formulation, the turbulent velocity field is expressed as a linear superposition of propagating modes, identified via a gain-based decomposition of the Navier–Stokes equations. Compliant surfaces, modelled as a complex wall admittance linking pressure and velocity, affect the gain and structure of these modes. With minimal computation, this framework accurately predicts the emergence of the quasi-two-dimensional propagating waves observed in recent direct numerical simulations. Further, the analysis also enables the rational design of compliant surfaces, with properties optimized to suppress flow structures energetic in wall turbulence. It is shown that walls with unphysical negative damping are required to interact favourably with modes resembling the energetic near-wall cycle, which could explain why previous studies have met with limited success. Positive-damping walls are effective for modes resembling the so-called very-large-scale motions, indicating that compliant surfaces may be better suited for application at higher Reynolds number. Unfortunately, walls that suppress structures energetic in natural turbulence are also predicted to have detrimental effects elsewhere in spectral space. Consistent with previous experiments and simulations, slow-moving spanwise-constant structures are particularly susceptible to further amplification. Mitigating these adverse effects will be central to the development of compliant coatings that have a net positive influence on the flow.

Proposal of control laws for turbulent skin friction reduction based on resolvent analysis

2019 ◽  
Vol 866 ◽  
pp. 810-840 ◽  
Author(s):  
Aika Kawagoe ◽  
Satoshi Nakashima ◽  
Mitul Luhar ◽  
Koji Fukagata
Keyword(s):  
Shear Stress ◽  
Wall Shear Stress ◽  
Drag Reduction ◽  
Skin Friction ◽  
Friction Reduction ◽  
Suboptimal Control ◽  
Spectral Space ◽  
Control Laws ◽  
Wall Shear ◽  
Skin Friction Reduction

This paper evaluates and modifies the so-called suboptimal control technique for turbulent skin friction reduction through a combination of low-order modelling and direct numerical simulation (DNS). In a previous study, Nakashima et al. (J. Fluid Mech., vol. 828, 2017, pp. 496–526) employed resolvent analysis to show that the efficacy of suboptimal control was mixed across spectral space when the streamwise wall shear stress (case ST) was used as a sensor signal, i.e. specific regions of spectral space showed drag increment. This observation suggests that drag reduction may be attained if control is applied selectively in spectral space. DNS results presented in the present study, however, do not show a significant effect on the flow with selective control. A posteriori analyses attribute this lack of efficacy to a much lower actuation amplitude in the simulations compared to model assumptions. Building on these observations, resolvent analysis is used to design and provide a preliminary assessment of modified control laws that also rely on sensing the streamwise wall shear stress. Control performance is then assessed by means of DNS. The proposed control laws generate as much as $10\,\%$ drag reduction, and these results are broadly consistent with resolvent-based predictions. The physical mechanisms leading to drag reduction are assessed via conditional sampling. It is shown that the new control laws effectively suppress the near-wall quasi-streamwise vortices. A physically intuitive explanation is proposed based on a separate evaluation of clockwise and anticlockwise vortices.

scholarly journals Gyrotactic swimmers in turbulence: shape effects and role of the large-scale flow

2018 ◽  
Vol 856 ◽  
Author(s):  
M. Borgnino ◽  
G. Boffetta ◽  
F. De Lillo ◽  
M. Cencini
Keyword(s):  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
Navier Stokes Equations ◽  
Preferential Sampling ◽  
Wide Range ◽  
Shape Effects ◽  
Dilute Suspensions ◽  
Large Scale Flow

We study the dynamics and the statistics of dilute suspensions of gyrotactic swimmers, a model for many aquatic motile microorganisms. By means of extensive numerical simulations of the Navier–Stokes equations at different Reynolds numbers, we investigate preferential sampling and small-scale clustering as a function of the swimming (stability and speed) and shape parameters, considering in particular the limits of spherical and rod-like particles. While spherical swimmers preferentially sample local downwelling flow, for elongated swimmers we observe a transition from downwelling to upwelling regions at sufficiently high swimming speed. The spatial distribution of both spherical and elongated swimmers is found to be fractal at small scales in a wide range of swimming parameters. The direct comparison between the different shapes shows that spherical swimmers are more clusterized at small stability and speed numbers, while for large values of the parameters elongated cells concentrate more. The relevance of our results for phytoplankton swimming in the ocean is briefly discussed.

Reconsideration of spanwise rotating turbulent channel flows via resolvent analysis

2018 ◽  
Vol 861 ◽  
pp. 200-222 ◽  
Author(s):  
Satoshi Nakashima ◽  
Mitul Luhar ◽  
Koji Fukagata
Keyword(s):  
Turbulent Flows ◽  
Stokes Equations ◽  
Turbulent Channel Flow ◽  
Reynolds Numbers ◽  
High Gain ◽  
Spectral Space ◽  
Rotation Rates ◽  
Wide Range ◽  
Effects Of Rotation ◽  
Spanwise Rotation

We study the effect of spanwise rotation in turbulent channel flow at both low and high Reynolds numbers by employing the resolvent formulation proposed by McKeon & Sharma (J. Fluid Mech., vol. 658, 2010, pp. 336–382). Under this formulation, the nonlinear terms in the Navier–Stokes equations are regarded as a forcing that acts upon the remaining linear dynamics to generate the turbulent velocity field in response. A gain-based decomposition of the forcing–response transfer function across spectral space yields models for highly amplified flow structures, or modes. Unlike linear stability analysis, this enables targeted analyses of the effects of rotation on high-gain modes that serve as useful low-order models for dynamically important coherent structures in wall-bounded turbulent flows. The present study examines a wide range of rotation rates. A posteriori comparisons at low Reynolds number ($\mathit{Re}_{\unicode[STIX]{x1D70F}}=180$) demonstrate that the resolvent formulation is able to quantitatively predict the effect of varying spanwise rotation rates on specific classes of flow structure (e.g. the near-wall cycle) as well as energy amplification across spectral space. For fixed inner-normalized rotation number, the effects of rotation at varying friction Reynolds numbers appear to be similar across spectral space, when scaled in outer units. We also consider the effects of rotation on modes with varying speed (i.e. modes that are localized in regions of varying mean shear), and provide suggestions for modelling the nonlinear forcing term.

Rayleigh number scaling in numerical convection

1996 ◽  
Vol 310 ◽  
pp. 139-179 ◽  
Author(s):  
Robert M. Kerr
Keyword(s):  
Boundary Layer ◽  
Rayleigh Number ◽  
Large Scale ◽  
Stokes Equations ◽  
Good Evidence ◽  
Navier Stokes ◽  
Fixed Temperature ◽  
Navier Stokes Equations ◽  
Local Boundary ◽  
Velocity Boundary Layer

Using direct simulations of the incompressible Navier-Stokes equations with rigid upper and lower boundaries at fixed temperature and periodic sidewalls, scaling with respect to Rayleigh number is determined. At large aspect ratio (6:6:1) on meshes up to 288 × 288 × 96, a single scaling regime consistent with the properties of ‘hard’ convective turbulence is found for Pr = 0.7 between Ra = 5 × 104 and Ra = 2 × 107. The properties of this regime include Nu ∼ RaβT with βT = 0.28 ≈ 2/7, exponential temperature distributions in the centre of the cell, and velocity and temperature scales consistent with experimental measurements. Two velocity boundary-layer thicknesses are identified, one outside the thermal boundary layer that scales as Ra−1/7 and the other within it that scales as Ra−3/7. Large-scale shears are not observed; instead, strong local boundary-layer shears are observed in regions between incoming plumes and an outgoing network of buoyant sheets. At the highest Rayleigh number, there is a decade where the energy spectra are close to k−5/3 and temperature variance spectra are noticeably less steep. It is argued that taken together this is good evidence for ‘hard’ turbulence, even if individually each of these properties might have alternative explanations.

Heat Pollution by Large Buildings and the Effects upon Astrometric Observations

1991 ◽  
Vol 112 ◽  
pp. 326-326
Author(s):  
James A. Hughes ◽  
Calvin A. Kodres
Keyword(s):  
Real Estate ◽  
Boundary Conditions ◽  
Large Scale ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Real Estate Development ◽  
Atmospheric Effects ◽  
Navier Stokes Equations ◽  
Naval Observatory ◽  
The U.S

ABSTRACTRecent, large scale, real estate development near the U.S. Naval Observatory has led to an investigation of the systematic atmospheric effects which heat from large buildings can cause. Results show that non-negligible slopes of the atmospheric layers can be induced which cause a surprisingly large anomalous refraction. The Navier-Stokes equations were numerically integrated using the appropriate boundary conditions and the resulting isopycnic tilts using the appropriate boundary conditions and the resulting isopycnic tilts charted. Rays were then essentially traced through the perturbed atmosphere to determine the magnitude of the anomalous refraction.

An efficient method for predicting zero-lift or boundary-layer drag including aeroelastic effects for the design environment

2015 ◽  
Vol 119 (1221) ◽  
pp. 1451-1460
Author(s):  
J. A. Camberos ◽  
R. M. Kolonay ◽  
F. E. Eastep ◽  
R. F. Taylor
Keyword(s):  
Boundary Layer ◽  
Stokes Equations ◽  
Near Field ◽  
Field Method ◽  
Navier Stokes ◽  
Spanwise Direction ◽  
Design Environment ◽  
Navier Stokes Equations ◽  
Induced Drag ◽  
Flight Regimes

AbstractOne of the aerospace design engineer’s goals aims to reduce drag for increased aircraft performance, in terms of range, endurance, or speed in the various flight regimes. To accomplish this, the designer must have rapid and accurate techniques for computing drag. At subsonic Mach numbers drag is primarily a sum of lift-induced drag and zero-lift drag. While lift-induced drag is easily and efficiently determined by a far field method, using the Trefftz plane analysis, the same cannot be said of zero-lift drag. Zero-lift drag (CD,0) usually requires consideration of the Navier-Stokes equations, the solution of which is as yet unknown except by using approximate numerical techniques with computational fluid dynamics (CFD). The approximate calculation of zero-lift drag from CFD is normally computed with so-called near-field techniques, which can be inaccurate and too time consuming for consideration in the design environment. This paper presents a technique to calculate zero-lift and boundary-layer drag in the subsonic regime that includes aeroelastic effects and is suitable for the design environment. The technique loosely couples a two-dimensional aerofoil boundary-layer model with a 3D aeroelastic solver to compute zero-lift drag. We show results for a rectangular wing (baseline), a swept wing, and a tapered wing. Then compare with a rectangular wing with variable thickness and camber, thinning out from the root to tip (spanwise direction), thus demonstrating the practicality of the technique and its utility for rapid conceptual design.

Fine Structure of Vortex Sheet Rollup by Viscous and Inviscid Simulation

1991 ◽  
Vol 113 (1) ◽  
pp. 31-36 ◽  
Author(s):  
G. Tryggvason ◽  
W. J. A. Dahm ◽  
K. Sbeih
Keyword(s):  
Reynolds Number ◽  
High Reynolds Number ◽  
Large Scale ◽  
Stokes Equations ◽  
Flow Region ◽  
Vortex Sheet ◽  
Navier Stokes ◽  
Vortex Sheets ◽  
Limiting Behavior ◽  
High Reynolds

Numerical simulations of the large amplitude stage of the Kelvin-Helmholtz instability of a relatively thin vorticity layer are discussed. At high Reynolds number, the effect of viscosity is commonly neglected and the thin layer is modeled as a vortex sheet separating one potential flow region from another. Since such vortex sheets are susceptible to a short wavelength instability, as well as singularity formation, it is necessary to provide an artificial “regularization” for long time calculations. We examine the effect of this regularization by comparing vortex sheet calculations with fully viscous finite difference calculations of the Navier-Stokes equations. In particular, we compare the limiting behavior of the viscous simulations for high Reynolds numbers and small initial layer thickness with the limiting solution for the roll-up of an inviscid vortex sheet. Results show that the inviscid regularization effectively reproduces many of the features associated with the thickness of viscous vorticity layers with increasing Reynolds number, though the simplified dynamics of the inviscid model allows it to accurately simulate only the large scale features of the vorticity field. Our results also show that the limiting solution of zero regularization for the inviscid model and high Reynolds number and zero initial thickness for the viscous simulations appear to be the same.

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