Resolvent analysis of laminar and turbulent rectangular duct flows

Lopez-Doriga, Barbara; Dawson, Scott T. M.; Vinuesa, Ricardo

doi:10.2514/6.2022-3334

Cited by 3 publications

(2 citation statements)

References 44 publications

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“…This work focuses on turbulent flows through a square duct. This flow configuration has been the subject of a number of prior investigations [17][18][19][20][21][22][23][24][25][26]. One characteristic feature that distinguishes such flows from infinitely-wide channel flow is the presence of secondary mean flow components perpendicular to the direction of the bulk flow [27,28], which typically features a pair of counter-rotating streamwise vortices in each corner, and therefore increases the streamwise velocity near the corner.…”

Section: Introductionmentioning

confidence: 99%

Linear and nonlinear Granger causality analysis of turbulent duct flows

Lopez-Doriga,

Atzori,

Vinuesa

et al. 2024

J. Phys.: Conf. Ser.

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This research focuses on the identification and causality analysis of coherent structures that arise in turbulent flows in square and rectangular ducts. Coherent structures are first identified from direct numerical simulation data via proper orthogonal decomposition (POD), both by using all velocity components, and after separating the streamwise and secondary components of the flow. The causal relations between the mode coefficients are analysed using pairwise-conditional Granger causality analysis. We also formulate a nonlinear Granger causality analysis that can account for nonlinear interactions between modes. Focusing on streamwise-constant structures within a duct of short streamwise extent, we show that the causal relationships are highly sensitive to whether the mode coefficients or their squared values are considered, whether nonlinear effects are explicitly accounted for, and whether streamwise and secondary flow structures are separated prior to causality analyses. We leverage these sensitivities to determine that linear mechanisms underpin causal relationships between modes that share the same symmetry or anti-symmetry properties about the corner bisector, while nonlinear effects govern the causal interactions between symmetric and antisymmetric modes. In all cases, we find that the secondary flow fluctuations (manifesting as streamwise vorticial structures) are the primary cause of both the presence and movement of near-wall streaks towards and away from the duct corners.

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Section: Introductionmentioning

confidence: 99%

Linear and nonlinear Granger causality analysis of turbulent duct flows

Lopez-Doriga,

Atzori,

Vinuesa

et al. 2024

J. Phys.: Conf. Ser.

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“…Lopez-Doriga et al [30] analyze the laminar and turbulent flows across rectangular ducts with high resolvability.…”

Section: Introductionmentioning

confidence: 99%

Hydrodynamics of Incompressible Creeping Couple Stress Fluid Through a Uniformly Porous Channel in Presence of Darcy Resistance: Exact Solution and Physical Insights Using the Inverse Method Approach

Ishaq,

Fatima,

Afzal

et al. 2023

Preprint

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The current study examines the features of a two-dimensional steady incompressible flow of creeping couple stress fluid across a permeable channel with uniform reabsorption. The mathematical model that governs this flow is composed of linear partial differential equations and homogeneous boundary constraints. The Inverse method approach, an analytical technique, is used to find solutions to the problem. By converting the momentum equations to stream functions, the inverse approach helps derive all the relevant physical quantities, including the longitudinal and transverse velocities, fractional reabsorption, leakage flux, axial pressure, volume flow rate, and mean pressure. Using MATLAB software, the dependent functions such as stream function, pressure, and volume flow are evaluated for different parameter values. The findings indicate that the longitudinal velocity is affected by the initial flow rate, while the transverse velocity shows no change in its profile. The streamlines become more straight and identical as the flow rate increases. Backward flow occurs at the end of the slit due to the porosity parameter. However, the initial flow rate does not impact the transverse velocity of the fluid in the permeable channel. This study fully describes a mathematical foundation for understanding fluid movement across permeable boundaries, which have practical applications in areas such as gaseous diffusion, filtration, and biological mechanisms.

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Sparse space–time resolvent analysis for statistically stationary and time-varying flows

Lopez-Doriga,

Ballouz,

Bae

et al. 2024

J. Fluid Mech.

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Resolvent analysis provides a framework to predict coherent spatio-temporal structures of the largest linear energy amplification, through a singular value decomposition (SVD) of the resolvent operator, obtained by linearising the Navier–Stokes equations about a known turbulent mean velocity profile. Resolvent analysis utilizes a Fourier decomposition in time, which has thus far limited its application to statistically stationary or time-periodic flows. This work develops a variant of resolvent analysis applicable to time-evolving flows, and proposes a variant that identifies spatio-temporally sparse structures, applicable to either stationary or time-varying mean velocity profiles. Spatio-temporal resolvent analysis is formulated through the incorporation of the temporal dimension to the numerical domain via a discrete time-differentiation operator. Sparsity (which manifests in localisation) is achieved through the addition of an $l_1$ -norm penalisation term to the optimisation associated with the SVD. This modified optimisation problem can be formulated as a nonlinear eigenproblem and solved via an inverse power method. We first showcase the implementation of the sparse analysis on a statistically stationary turbulent channel flow, and demonstrate that the sparse variant can identify aspects of the physics not directly evident from standard resolvent analysis. This is followed by applying the sparse space–time formulation on systems that are time varying: a time-periodic turbulent Stokes boundary layer and then a turbulent channel flow with a sudden imposition of a lateral pressure gradient, with the original streamwise pressure gradient unchanged. We present results demonstrating how the sparsity-promoting variant can either change the quantitative structure of the leading space–time modes to increase their sparsity, or identify entirely different linear amplification mechanisms compared with non-sparse resolvent analysis.

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Resolvent analysis of laminar and turbulent rectangular duct flows

Cited by 3 publications

References 44 publications

Linear and nonlinear Granger causality analysis of turbulent duct flows

Linear and nonlinear Granger causality analysis of turbulent duct flows

Hydrodynamics of Incompressible Creeping Couple Stress Fluid Through a Uniformly Porous Channel in Presence of Darcy Resistance: Exact Solution and Physical Insights Using the Inverse Method Approach

Sparse space–time resolvent analysis for statistically stationary and time-varying flows

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