5,575 research outputs found
On the structure and origin of pressure fluctuations in wall turbulence: predictions based on the resolvent analysis
No full textWe generate predictions for the fluctuating pressure field in turbulent pipe flow by re-formulating the resolvent analysis of McKeon & Sharma (2010) in terms of the so-called primitive variables. Under this analysis, the nonlinear convective terms in the Fourier-transformed Navier-Stokes equations are treated as a forcing that is mapped to a velocity and pressure response by the resolvent of the linearized Navier-Stokes operator. At each wavenumber-frequency combination, the turbulent velocity and pressure field are represented by the most-amplified (rank-1) response modes, identified via a singular value decomposition of the resolvent. We show that these rank-1 response modes reconcile many of the key relationships between the velocity field, coherent structure (i.e., hairpin vortices), and the high-amplitude wall-pressure events observed in previous experiment and DNS. A Green’s function representation shows that the pressure fields obtained under this analysis correspond primarily to the fast pressure contribution arising from the linear interaction between the mean shear and the turbulent wall-normal velocity. Recovering the slow pressure requires an explicit treatment of the nonlinear interactions between the Fourier response modes. By considering the velocity and pressure fields associated with the triadically-consistent mode combination studied by Sharma & McKeon (2013), we identify the possibility of an apparent amplitude modulation effect in the pressure field, similar to that observed for the streamwise velocity field. However, unlike the streamwise velocity, for which the large scales of the flow are in phase with the envelope of the small-scale activity close to the wall, we expect there to be a ?/2 phase difference between the large scale wall-pressure and the envelope of the small-scale activity. Finally, we generate spectral predictions based on a rank-1 model assuming broadband forcing across all wavenumber-frequency combinations. Despite the significant simplifying assumptions, this approach reproduces trends observed in previous DNS for the wavenumber spectra of velocity and pressure, and for the scale-dependence of wall-pressure propagation speed
Opposition control within the resolvent analysis framework
No full textThis paper extends the resolvent analysis of McKeon & Sharma (2010) to consider flow control techniques that employ linear control laws, focusing on opposition control (Choi et al. 1994) as an example. Under this formulation, the velocity field for turbulent pipe flow is decomposed into a series of highly amplified (rank-1) response modes, identified from a gain analysis of the Fourier-transformed Navier-Stokes equations. These rank-1 velocity responses represent propagating structures of given streamwise/spanwise wavelength and temporal frequency, whose wall-normal footprint depends on the phase speed of the mode. Opposition control, introduced via the boundary condition on wall-normal velocity, affects the amplification characteristics (and wall-normal structure) of these response modes; a decrease in gain indicates mode suppression, which leads to a decrease in the drag contribution from that mode. With basic assumptions, this rank-1 model reproduces trends observed in previous DNS and LES, without requiring high-performance computing facilities. Further, a wavenumber-frequency breakdown of control explains the deterioration of opposition control performance with increasing sensor elevation and Reynolds number. It is shown that slower-moving modes localized near the wall (i.e. attached modes) are suppressed by opposition control. Faster-moving detached modes, which are more energetic at higher Reynolds number and more likely to be detected by sensors far from the wall, are further amplified. These faster-moving modes require a phase lag between sensor and actuator velocity for suppression. Thus, the effectiveness of opposition control is determined by a trade-off between the modes detected by the sensor. However, it may be possible to develop control strategies optimized for individual modes. A brief exploration of such mode-optimized control suggests the potential for significant performance improvement
On coherent structure in wall turbulence
No full textA new theory of coherent structure in wall turbulence is presented. The theory is the first to predict packets of hairpin vortices and other structure in turbulence, and their dynamics, based on an analysis of the Navier-Stokes equations, under an assumption of a turbulent mean profile. The assumption of the turbulent mean acts as a restriction on the class of possible structures. It is shown that the coherent structure is a manifestation of essentially low-dimensional flow dynamics, arising from a critical layer mechanism. Using the decomposition presented in McKeon & Sharma (J. Fluid Mech, 658, 2010), complex coherent structure is recreated from minimal superpositions of response modes predicted by the analysis, which take the form of radially-varying travelling waves. By way of example, simple combinations of these modes are offered that predicts hairpins and modulated hairpin packets. The phase interaction also predicts important skewness and correlation results known in the literature. It is also shown that the very large scale motions act to organise hairpin-like structures such that they co-locate with areas of low streamwise momentum, by a mechanism of locally varying the shear profile. The relationship between Taylor's hypothesis and coherence is discussed and both are shown to be the consequence of the localisation of the response modes around the critical layer. A pleasing link is made to the classical laminar inviscid theory, whereby the essential mechanism underlying the hairpin vortex is captured by two obliquely interacting Kelvin-Stuart (cat's eye) vortices. Evidence for the theory is presented based on comparison to observations of structure reported in the experimental, transitional flow and turbulent flow numerical simulation literature
Model reduction of turbulent fluid flows using the supply rate
No full textA method for finding reduced-order approximations of turbulent flow models is presented. The method preserves bounds on the production of turbulent energy in the sense of the L2 norm of perturbations from a notional laminar profile. This is achieved by decomposing the Navier–Stokes system into a feedback arrangement between the linearized system and the remaining, normally neglected, nonlinear part. The linear system is reduced using a method similar to balanced truncation, but preserving bounds on the supply rate. The method involves balancing two algebraic Riccati equations. The bounds are then used to derive bounds on the turbulent energy production. An example of the application of the procedure to flow through a long straight pipe is presented. Comparison shows that the new method approximates the supply rate at least as well as, or better than, canonical balanced truncation
Predicting structural and statistical features of wall turbulence
No full textThe majority of practical flows, particularly those flows in applications of importance to transport, distribution and climate, are turbulent and as a result experience complex three-dimensional motion with increased drag comparedwith the smoother, laminar condition. In this study, we describe the development of a simple model that predicts important structural and scaling features of wall turbulence. We show that a simple linear superposition of modes derived from a forcing-response analysis of the Navier-Stokes equations can be used to reconcile certain key statistical and structural descriptions of wall turbulence. The computationally cheap approach explains and predicts vortical structures and velocity statistics of turbulent flows that have previously been identified only in experiments or by direct numerical simulation. In particular, we propose an economical explanation for the meandering appearance of very large scale motions observed in turbulent pipe flow, and likewise demonstrate that hairpin vortices are predicted by the model. This new capability has clear implications for modeling, simulation and control of a ubiquitous class of wall flows
Efficient grid-based Bayesian estimation of nonlinear low-dimensional systems with sparse non-Gaussian PDFs
No full textBayesian estimation strategies represent the most fundamental formulation of the state estimation problem available, and apply readily to nonlinear systems with non-Gaussian uncertainties. The present paper introduces a novel method for implementing grid-based Bayesian estimation which largely sidesteps the severe computational expense that has prevented the widespread use of such methods. The method represents the evolution of the probability density function (PDF) in phase space, px(x?,t),discretized on a fixed Cartesian grid over all of phase space, and consists of two main steps: (i) between measurement times, px(x?,t) is evolved via numerical discretization of the Kolmogorov forward equation, using a Godunov method with second-order corner transport upwind correction and a total variation diminishing flux limiter; (ii) at measurement times, px(x?,t) is updated via Bayes’ theorem. Computational economy is achieved by exploiting the localized nature of px(x?,t). An ordered list of cells with non-negligible probability, as well as their immediate neighbors, is created and updated, and the PDF evolution is tracked only on these active cells
Estimation of unsteady aerodynamic forces using pointwise velocity data
No full textA novel method to estimate unsteady aerodynamic force coefficients from pointwise velocity measurements is presented. As opposed to other existing methodologies, time-resolved full velocity fields are not required. The methodology is based on a resolvent-based reduced-order model which requires the mean flow to obtain physical flow structures and pointwise measurement to calibrate their amplitudes. A computationally affordable time-stepping methodology to obtain resolvent modes in non-trivial flow domains is introduced and compared with previous existing matrix-free and matrix-forming strategies. The technique is applied to the unsteady flow around an inclined square cylinder at low Reynolds number. The potential of the methodology is demonstrated through good agreement between the fluctuating pressure distribution on the cylinder and the temporal evolution of the unsteady lift and drag coefficients predicted by the model and those computed by direct numerical simulatio
On the design of optimal compliant walls for turbulence control
No full textThis paper employs the resolvent framework to consider the design of compliant walls for turbulent skin friction reduction. Specifically, the effects of simple spring–damper walls are contrasted with the effects of more complex walls incorporating tension, stiffness and anisotropy. In addition, varying mass ratios are tested to provide insight into differences between aerodynamic and hydrodynamic applications. Despite the differing physical responses, all the walls tested exhibit some important common features. First, the effect of the walls (positive or negative) is the greatest at conditions close to resonance, with sharp transitions in performance across the resonant frequency or phase speed. Second, compliant walls are predicted to have a more pronounced effect on slower moving structures because such structures generally have larger wall-pressure signatures. Third, two-dimensional (spanwise constant) structures are particularly susceptible to further amplification. These features are consistent with many previous experiments and simulations, suggesting that mitigating the rise of such two-dimensional structures is essential to designing performance-improving walls. For instance, it is shown that further amplification of such large-scale two-dimensional structures explains why the optimal anisotropic walls identified in previous direct numerical simulations only led to drag reduction in very small domains. The above observations are used to develop design and methodology guidelines for future research on compliant walls
On using Directional Information for Parameter Space Decomposition in Ellipse Detection
No full textIn this paper we use the parametric polar representation to extend the application of edge directional information from circle to ellipse extraction. As a result we obtain a mapping which decomposes the parameter space required for ellipse extraction into two independent sub-spaces and one final histogram accumulator. The mapping includes the tangent of the angle of the first and second directional derivatives. These tangents are computed by considering edge direction at two border points. We show that the use of gradient information for parameter space decomposition avoids the intensive point labelling imposed by geometric constraints used by other approaches
Scaling and interaction of self-similar modes in models of high-Reynolds number wall turbulence
No full textPrevious work has established the usefulness of the resolvent operator that maps the terms nonlinear in the turbulent fluctuations to the fluctuations themselves. Further work has described the selfsimilarity of the resolvent arising from that of the mean velocity profile. The orthogonal modes provided by the resolvent analysis describe the wall-normal coherence of the motions and inherit that self-similarity. In this contribution, we present the implications of this similarity for the nonlinear interaction between modes with different scales and wall-normal locations. By considering the nonlinear interactions between modes, it is shown that much of the turbulence scaling behaviour in the logarithmic region can be determined from a single arbitrarily chosen reference plane. Thus, the geometric scaling of the modes is impressed upon the nonlinear interaction between modes. Implications of these observations on the self-sustaining mechanisms of wall turbulence,modelling and simulation are outlined
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