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Fluids, Volume 4, Issue 2 (June 2019)

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Open AccessArticle
Reynolds Stress Perturbation for Epistemic Uncertainty Quantification of RANS Models Implemented in OpenFOAM
Received: 3 May 2019 / Revised: 16 June 2019 / Accepted: 18 June 2019 / Published: 22 June 2019
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Abstract
Reynolds-averaged Navier-Stokes (RANS) models are widely used for the simulation of engineering problems. The turbulent-viscosity hypothesis is a central assumption to achieve closures in this class of models. This assumption introduces structural or so-called epistemic uncertainty. Estimating that epistemic uncertainty is a promising [...] Read more.
Reynolds-averaged Navier-Stokes (RANS) models are widely used for the simulation of engineering problems. The turbulent-viscosity hypothesis is a central assumption to achieve closures in this class of models. This assumption introduces structural or so-called epistemic uncertainty. Estimating that epistemic uncertainty is a promising approach towards improving the reliability of RANS simulations. In this study, we adopt a methodology to estimate the epistemic uncertainty by perturbing the Reynolds stress tensor. We focus on the perturbation of the turbulent kinetic energy and the eigenvalues separately. We first implement this methodology in the open source package OpenFOAM. Then, we apply this framework to the backward-facing step benchmark case and compare the results with the unperturbed RANS model, available direct numerical simulation data and available experimental data. It is shown that the perturbation of both parameters successfully estimate the region bounding the most accurate results. Full article
(This article belongs to the Special Issue Recent Numerical Advances in Fluid Mechanics)
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Open AccessArticle
Effect of Overburden Height on Hydraulic Fracturing of Concrete-Lined Pressure Tunnels Excavated in Intact Rock: A Numerical Study
Received: 2 June 2019 / Revised: 14 June 2019 / Accepted: 17 June 2019 / Published: 19 June 2019
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Abstract
This study investigated the impact of overburden height on the hydraulic fracturing of a concrete-lined pressure tunnel, excavated in intact rock, under steady-state and transient-state conditions. Moreover, the Norwegian design criterion that only suggests increasing the overburden height as a countermeasure against hydraulic [...] Read more.
This study investigated the impact of overburden height on the hydraulic fracturing of a concrete-lined pressure tunnel, excavated in intact rock, under steady-state and transient-state conditions. Moreover, the Norwegian design criterion that only suggests increasing the overburden height as a countermeasure against hydraulic fracturing was evaluated. The Mohr–Coulomb failure criterion was implemented to investigate failure in the rock elements adjacent to the lining. A pressure tunnel with an inner diameter of 3.6 m was modeled in Abaqus Finite Element Analysis (FEA), using the finite element method (FEM). It was assumed that transient pressures occur inside the tunnel due to control gate closure in a hydroelectric power plant, downstream of the tunnel, in three different closure modes: fast (14 s), normal (18 s), and slow (26 s). For steady-state conditions, the results indicated that resistance to the fracturing of the rock increased with increasing the rock friction angle, as well as the overburden height. However, the influence of the friction angle on the resistance to rock fracture was much larger than that of the overburden height. For transient-state conditions, the results showed that, in fast, normal, and slow control gate closure modes, the required overburden heights to failure were respectively 1.07, 0.8, and 0.67 times the static head of water in the tunnel under a steady-state condition. It was concluded that increasing the height of overburden should not be the absolute solution to prevent hydraulic fracturing in pressure tunnels. Full article
(This article belongs to the Special Issue Recent Numerical Advances in Fluid Mechanics)
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Open AccessArticle
Equation Discovery Using Fast Function Extraction: a Deterministic Symbolic Regression Approach
Received: 27 April 2019 / Revised: 29 May 2019 / Accepted: 12 June 2019 / Published: 15 June 2019
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Abstract
Advances in machine learning (ML) coupled with increased computational power have enabled identification of patterns in data extracted from complex systems. ML algorithms are actively being sought in recovering physical models or mathematical equations from data. This is a highly valuable technique where [...] Read more.
Advances in machine learning (ML) coupled with increased computational power have enabled identification of patterns in data extracted from complex systems. ML algorithms are actively being sought in recovering physical models or mathematical equations from data. This is a highly valuable technique where models cannot be built using physical reasoning alone. In this paper, we investigate the application of fast function extraction (FFX), a fast, scalable, deterministic symbolic regression algorithm to recover partial differential equations (PDEs). FFX identifies active bases among a huge set of candidate basis functions and their corresponding coefficients from recorded snapshot data. This approach uses a sparsity-promoting technique from compressive sensing and sparse optimization called pathwise regularized learning to perform feature selection and parameter estimation. Furthermore, it recovers several models of varying complexity (number of basis terms). FFX finally filters out many identified models using non-dominated sorting and forms a Pareto front consisting of optimal models with respect to minimizing complexity and test accuracy. Numerical experiments are carried out to recover several ubiquitous PDEs such as wave and heat equations among linear PDEs and Burgers, Korteweg–de Vries (KdV), and Kawahara equations among higher-order nonlinear PDEs. Additional simulations are conducted on the same PDEs under noisy conditions to test the robustness of the proposed approach. Full article
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Open AccessFeature PaperArticle
Computation of Kinematic and Magnetic α-Effect and Eddy Diffusivity Tensors by Padé Approximation
Received: 13 May 2019 / Revised: 5 June 2019 / Accepted: 7 June 2019 / Published: 14 June 2019
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Abstract
We present examples of Padé approximations of the α-effect and eddy viscosity/diffusivity tensors in various flows. Expressions for the tensors derived in the framework of the standard multiscale formalism are employed. Algebraically, the simplest case is that of a two-dimensional parity-invariant six-fold [...] Read more.
We present examples of Padé approximations of the α -effect and eddy viscosity/diffusivity tensors in various flows. Expressions for the tensors derived in the framework of the standard multiscale formalism are employed. Algebraically, the simplest case is that of a two-dimensional parity-invariant six-fold rotation-symmetric flow where eddy viscosity is negative, indicating intervals of large-scale instability of the flow. Turning to the kinematic dynamo problem for three-dimensional flows of an incompressible fluid, we explore the application of Padé approximants for the computation of tensors of magnetic α -effect and, for parity-invariant flows, of magnetic eddy diffusivity. We construct Padé approximants of the tensors expanded in power series in the inverse molecular diffusivity 1 / η around 1 / η = 0 . This yields the values of the dominant growth rate to satisfactory accuracy for η , several dozen times smaller than the threshold, above which the power series is convergent. We do computations in Fortran in the standard “double” (real*8) and extended “quadruple” (real*16) precision, and perform symbolic calculations in Mathematica. Full article
(This article belongs to the Special Issue Multiscale Turbulent Transport)
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Open AccessArticle
Interplay of Sensor Quantity, Placement and System Dimension in POD-Based Sparse Reconstruction of Fluid Flows
Received: 5 February 2019 / Revised: 22 May 2019 / Accepted: 10 June 2019 / Published: 13 June 2019
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Abstract
Sparse linear estimation of fluid flows using data-driven proper orthogonal decomposition (POD) basis is systematically explored in this work. Fluid flows are manifestations of nonlinear multiscale partial differential equations (PDE) dynamical systems with inherent scale separation that impact the system dimensionality. Given that [...] Read more.
Sparse linear estimation of fluid flows using data-driven proper orthogonal decomposition (POD) basis is systematically explored in this work. Fluid flows are manifestations of nonlinear multiscale partial differential equations (PDE) dynamical systems with inherent scale separation that impact the system dimensionality. Given that sparse reconstruction is inherently an ill-posed problem, the most successful approaches require the knowledge of the underlying low-dimensional space spanning the manifold in which the system resides. In this paper, we adopt an approach that learns basis from singular value decomposition (SVD) of training data to recover sparse information. This results in a set of four design parameters for sparse recovery, namely, the choice of basis, system dimension required for sufficiently accurate reconstruction, sensor budget and their placement. The choice of design parameters implicitly determines the choice of algorithm as either l 2 minimization reconstruction or sparsity promoting l 1 minimization reconstruction. In this work, we systematically explore the implications of these design parameters on reconstruction accuracy so that practical recommendations can be identified. We observe that greedy-smart sensor placement, particularly interpolation points from the discrete empirical interpolation method (DEIM), provide the best balance of computational complexity and accurate reconstruction. Full article
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Open AccessArticle
Soliton Solution of Schrödinger Equation Using Cubic B-Spline Galerkin Method
Received: 17 April 2019 / Revised: 25 May 2019 / Accepted: 7 June 2019 / Published: 12 June 2019
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Abstract
The non-linear Schrödinger (NLS) equation has often been used as a model equation in the study of quantum states of physical systems. Numerical solution of NLS equation is obtained using cubic B-spline Galerkin method. We have applied the Crank–Nicolson scheme for time discretization [...] Read more.
The non-linear Schrödinger (NLS) equation has often been used as a model equation in the study of quantum states of physical systems. Numerical solution of NLS equation is obtained using cubic B-spline Galerkin method. We have applied the Crank–Nicolson scheme for time discretization and the cubic B-spline basis function for space discretization. Three numerical problems, including single soliton, interaction of two solitons and birth of standing soliton, are demonstrated to evaluate to the performance and accuracy of the method. The error norms and conservation laws are determined and found to be in good agreement with the published results. The obtained results show that the approach is feasible and accurate. The proposed method has almost second order convergence. The linear stability of the method is performed using the Von Neumann method. Full article
(This article belongs to the Special Issue Recent Numerical Advances in Fluid Mechanics)
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Open AccessArticle
Added Mass Effects on a Francis Turbine Runner with Attached Blade Cavitation
Received: 18 May 2019 / Revised: 4 June 2019 / Accepted: 5 June 2019 / Published: 11 June 2019
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Abstract
To have a safe structural design, an analysis of the dynamic behavior of a Francis turbine runner with consideration of the added mass effects of surrounding water is necessary during design phase. Both in design and at off-design operations, large-scale forms of attached [...] Read more.
To have a safe structural design, an analysis of the dynamic behavior of a Francis turbine runner with consideration of the added mass effects of surrounding water is necessary during design phase. Both in design and at off-design operations, large-scale forms of attached cavitation may appear on runner blades and can change the added mass effects of the surrounding fluid in relation to a single water domain. Consequently, a numerical investigation of the modal response of a Francis runner has been carried out by reproducing the presence of various sizes of leading edge cavitation (LEC) and trailing edge cavitation (TEC). The fluid–structure interaction problem has been solved by means of an acoustic-structural coupling method. The calculated added mass effects with cavitation have been compared with those corresponding to the pure water condition without cavitation. Firstly, a single blade has been investigated to evaluate the level of significance for the proposed cavity shapes and dimensions. Afterwards, based on the results obtained, the complete runner structure has been considered, factoring in similar cavity shapes and locations. The results prove that significant added mass effects are induced on the entire runner by the attached cavitation that increase the natural frequencies of the first modes. Moreover, the added mass effects increase with cavity size and amplitude of blade deformation below the cavity. Full article
(This article belongs to the Special Issue Turbomachinery Flow Analysis)
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Open AccessEditorial
Experimental and Numerical Studies in Biomedical Engineering
Received: 3 June 2019 / Accepted: 5 June 2019 / Published: 6 June 2019
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Abstract
The term “biomedical engineering” refers to the application of the principles and problem-solving techniques of engineering to biology and medicine [...] Full article
(This article belongs to the Special Issue Experimental and Numerical Studies in Biomedical Engineering)
Open AccessFeature PaperArticle
Experimental Observation of Modulational Instability in Crossing Surface Gravity Wavetrains
Received: 3 April 2019 / Revised: 24 May 2019 / Accepted: 30 May 2019 / Published: 4 June 2019
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Abstract
The coupled nonlinear Schrödinger equation (CNLSE) is a wave envelope evolution equation applicable to two crossing, narrow-banded wave systems. Modulational instability (MI), a feature of the nonlinear Schrödinger wave equation, is characterized (to first order) by an exponential growth of sideband components and [...] Read more.
The coupled nonlinear Schrödinger equation (CNLSE) is a wave envelope evolution equation applicable to two crossing, narrow-banded wave systems. Modulational instability (MI), a feature of the nonlinear Schrödinger wave equation, is characterized (to first order) by an exponential growth of sideband components and the formation of distinct wave pulses, often containing extreme waves. Linear stability analysis of the CNLSE shows the effect of crossing angle, θ , on MI, and reveals instabilities between 0 < θ < 35 , 46 < θ < 143 , and 145 < θ < 180 . Herein, the modulational stability of crossing wavetrains seeded with symmetrical sidebands is determined experimentally from tests in a circular wave basin. Experiments were carried out at 12 crossing angles between 0 θ 88 , and strong unidirectional sideband growth was observed. This growth reduced significantly at angles beyond θ 20 , reaching complete stability at θ = 30–40 . We find satisfactory agreement between numerical predictions (using a time-marching CNLSE solver) and experimental measurements for all crossing angles. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics)
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Open AccessFeature PaperArticle
Jovian Vortices and Jets
Received: 16 April 2019 / Revised: 15 May 2019 / Accepted: 16 May 2019 / Published: 3 June 2019
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Abstract
We explore the theory of isolated vortices in strongly sheared, deep zonal flows and the stability of these banded jets, as occur in Jupiter’s atmosphere This is done using the standard 2-layer quasigeostrophic model with the lower layer depth becoming infinite; however, this [...] Read more.
We explore the theory of isolated vortices in strongly sheared, deep zonal flows and the stability of these banded jets, as occur in Jupiter’s atmosphere This is done using the standard 2-layer quasigeostrophic model with the lower layer depth becoming infinite; however, this model differs from the usual layer model because the lower layer is not assumed to be motionless but has a steady configuration of alternating zonal flows. Steady state vortices are obtained by a simulated annealing computational method as generalized to fluid problems with constraints and also used in the used in the context of magnetohydrodynamics. Various cases of vortices with a constant potential vorticity anomaly atop zonal winds and the stability of the underlying winds are considered using a mix of computational and analytical techniques. Full article
(This article belongs to the collection Geophysical Fluid Dynamics)
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Open AccessArticle
Teaching Fluid Mechanics and Thermodynamics Simultaneously through Pipeline Flow Experiments
Received: 12 May 2019 / Revised: 26 May 2019 / Accepted: 28 May 2019 / Published: 1 June 2019
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Abstract
Entropy and entropy generation are abstract and illusive concepts for undergraduate students. In general, students find it difficult to visualize entropy generation in real (irreversible) processes, especially at a mechanistic level. Fluid mechanics laboratory can assist students in making the concepts of entropy [...] Read more.
Entropy and entropy generation are abstract and illusive concepts for undergraduate students. In general, students find it difficult to visualize entropy generation in real (irreversible) processes, especially at a mechanistic level. Fluid mechanics laboratory can assist students in making the concepts of entropy and entropy generation more tangible. In flow of real fluids, dissipation of mechanical energy takes place due to friction in fluids. The dissipation of mechanical energy in pipeline flow is reflected in loss of pressure of fluid. The degradation of high quality mechanical energy into low quality frictional heat (internal energy) is simultaneously reflected in the generation of entropy. Thus, experiments involving measurements of pressure gradient as a function of flow rate in pipes offer an opportunity for students to visualize and quantify entropy generation in real processes. In this article, the background in fluid mechanics and thermodynamics relevant to the concepts of mechanical energy dissipation, entropy and entropy generation are reviewed briefly. The link between entropy generation and mechanical energy dissipation in pipe flow experiments is demonstrated both theoretically and experimentally. The rate of entropy generation in pipeline flow of Newtonian fluids is quantified through measurements of pressure gradient as a function of flow rate for a number of test fluids. The factors affecting the rate of entropy generation in pipeline flows are discussed. Full article
(This article belongs to the Special Issue Teaching and Learning of Fluid Mechanics)
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Open AccessArticle
On the Kutta Condition in Compressible Flow over Isolated Airfoils
Received: 10 April 2019 / Revised: 22 May 2019 / Accepted: 27 May 2019 / Published: 1 June 2019
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Abstract
This paper presents a novel and accurate method to implement the Kutta condition in solving subsonic (subcritical) inviscid isentropic compressible flow over isolated airfoils using the stream function equation. The proposed method relies on body-fitted grid generation and solving the stream function equation [...] Read more.
This paper presents a novel and accurate method to implement the Kutta condition in solving subsonic (subcritical) inviscid isentropic compressible flow over isolated airfoils using the stream function equation. The proposed method relies on body-fitted grid generation and solving the stream function equation for compressible flows in computational domain using finite-difference method. An expression is derived for implementing the Kutta condition for the airfoils with both finite angles and cusped trailing edges. A comparison of the results obtained from the proposed numerical method and the results from experimental and other numerical methods reveals that they are in excellent agreement, which confirms the accuracy and correctness of the proposed method. Full article
(This article belongs to the Special Issue Recent Numerical Advances in Fluid Mechanics)
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Open AccessArticle
On Moderate-Rayleigh-Number Convection in an Inclined Porous Layer
Received: 29 April 2019 / Revised: 24 May 2019 / Accepted: 28 May 2019 / Published: 31 May 2019
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Abstract
We investigate the flow structure and dynamics of moderate-Rayleigh-number (Ra) thermal convection in a two-dimensional inclined porous layer. High-resolution numerical simulations confirm the emergence of O(1) aspect-ratio large-scale convective rolls, with one ‘natural’ roll rotating in the [...] Read more.
We investigate the flow structure and dynamics of moderate-Rayleigh-number ( R a ) thermal convection in a two-dimensional inclined porous layer. High-resolution numerical simulations confirm the emergence of O ( 1 ) aspect-ratio large-scale convective rolls, with one ‘natural’ roll rotating in the counterclockwise direction and one ‘antinatural’ roll rotating in the clockwise direction. As the inclination angle ϕ is increased, the background mean shear flow intensifies the natural-roll motion, while suppressing the antinatural-roll motion. Our numerical simulations also reveal—for the first time in single-species porous medium convection—the existence of spatially-localized convective states at large ϕ , which we suggest are enabled by subcritical instability of the base state at sufficiently large inclination angles. To better understand the physics of inclined porous medium convection at different ϕ , we numerically compute steady convective solutions using Newton iteration and then perform secondary stability analysis of these nonlinear states using Floquet theory. Our analysis indicates that the inclination of the porous layer stabilizes the boundary layers of the natural roll, but intensifies the boundary-layer instability of the antinatural roll. These results facilitate physical understanding of the large-scale cellular flows observed in the numerical simulations at different values of ϕ . Full article
(This article belongs to the Special Issue Convective Instability in Porous Media, Volume II)
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Open AccessArticle
Effect of Inclination on Vortex Shedding Frequency Behind a Bent Cylinder: An Experimental Study
Received: 16 May 2019 / Accepted: 29 May 2019 / Published: 31 May 2019
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Abstract
This paper presents experimental results on the vortex shedding frequency measured behind a bent cylinder. Experiments were conducted in a wind tunnel covering Reynolds numbers between 50 and 500, a range of interest for flow sensing, flow control, and energy harvesting applications. The [...] Read more.
This paper presents experimental results on the vortex shedding frequency measured behind a bent cylinder. Experiments were conducted in a wind tunnel covering Reynolds numbers between 50 and 500, a range of interest for flow sensing, flow control, and energy harvesting applications. The bent cylinder comprised a vertical leg always oriented at normal incidence with respect to the free-stream flow, and an inclined leg whose inclination was varied during the tests between 90° and 15°. The bent cylinder was oriented in the wind tunnel with the vertical leg upstream and the inclined leg downstream, and the vortex shedding frequency was measured with hot-wire anemometry at several locations behind the inclined leg. The present bent cylinder design improves upon those previously considered by providing a finer control on the upstream boundary condition acting upon the inclined leg, which in the present design is not affected by the yaw angle of the inclined leg. With the exception of free-end effects, only noticeable for certain inclinations and Reynolds number values, inclination effects were surprisingly not observed, and the frequency of vortex shedding measured behind the inclined leg of the bent cylinder was consistent (within a few percent) with the cross-flow vortex shedding frequency at the same flow velocity. The present results corroborate and significantly extend the limited observations on bent cylinders available in the literature, further highlighting the importance of the upstream boundary condition on the vortex shedding process with inclined cylinders. Full article
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Open AccessArticle
Statistics of Extreme Waves in Coastal Waters: Large Scale Experiments and Advanced Numerical Simulations
Received: 7 February 2019 / Revised: 15 May 2019 / Accepted: 20 May 2019 / Published: 29 May 2019
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Abstract
The formation mechanism of extreme waves in the coastal areas is still an open contemporary problem in fluid mechanics and ocean engineering. Previous studies have shown that the transition of water depth from a deeper to a shallower zone increases the occurrence probability [...] Read more.
The formation mechanism of extreme waves in the coastal areas is still an open contemporary problem in fluid mechanics and ocean engineering. Previous studies have shown that the transition of water depth from a deeper to a shallower zone increases the occurrence probability of large waves. Indeed, more efforts are required to improve the understanding of extreme wave statistics variations in such conditions. To achieve this goal, large scale experiments of unidirectional irregular waves propagating over a variable bottom profile considering different transition water depths were performed. The validation of two highly nonlinear numerical models was performed for one representative case. The collected data were examined and interpreted by using spectral or bispectral analysis as well as statistical analysis. The higher probability of occurrence of large waves was confirmed by the statistical distributions built from the measured free surface elevation time series as well as by the local maximum values of skewness and kurtosis around the end of the slope. Strong second-order nonlinear effects were highlighted as waves propagate into the shallower region. A significant amount of wave energy was transmitted to low-frequency modes. Based on the experimental data, we conclude that the formation of extreme waves is mainly related to the second-order effect, which is also responsible for the generation of long waves. It is shown that higher-order nonlinearities are negligible in these sets of experiments. Several existing models for wave height distributions were compared and analysed. It appears that the generalised Boccotti’s distribution can predict the exceedance of large wave heights with good confidence. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics)
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Open AccessArticle
Lubrication Approximation for Fluids with Shear-Dependent Viscosity
Received: 30 April 2019 / Revised: 16 May 2019 / Accepted: 20 May 2019 / Published: 28 May 2019
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Abstract
We present dimensionally reduced Reynolds type equations for steady lubricating flows of incompressible non-Newtonian fluids with shear-dependent viscosity by employing a rigorous perturbation analysis on the governing equations of motion. Our analysis shows that, depending on the strength of the power-law character of [...] Read more.
We present dimensionally reduced Reynolds type equations for steady lubricating flows of incompressible non-Newtonian fluids with shear-dependent viscosity by employing a rigorous perturbation analysis on the governing equations of motion. Our analysis shows that, depending on the strength of the power-law character of the fluid, the novel equation can either present itself as a higher-order correction to the classical Reynolds equation or as a completely new nonlinear Reynolds type equation. Both equations are applied to two classic problems: the flow between a rolling rigid cylinder and a rigid plane and the flow in an eccentric journal bearing. Full article
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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Open AccessArticle
A 3D Numerical Study of Interface Effects Influencing Viscous Gravity Currents in a Parabolic Fissure, with Implications for Modeling with 1D Nonlinear Diffusion Equations
Received: 15 December 2018 / Revised: 14 May 2019 / Accepted: 22 May 2019 / Published: 28 May 2019
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Abstract
Although one-dimensional non-linear diffusion equations are commonly used to model flow dynamics in aquifers and fissures, they disregard multiple effects of real-life flows. Similarity analysis may allow further analytical reduction of these equations, but it is often difficult to provide applicable initial and [...] Read more.
Although one-dimensional non-linear diffusion equations are commonly used to model flow dynamics in aquifers and fissures, they disregard multiple effects of real-life flows. Similarity analysis may allow further analytical reduction of these equations, but it is often difficult to provide applicable initial and boundary conditions in practice, or know the magnitude of effects neglected by the 1D model. Furthermore, when multiple simplifying assumptions are made, the sources of discrepancy between modeled and observed data are difficult to identify. We derive one such model of viscous flow in a parabolic fissure from first principals. The parabolic fissure is formed by extruding an upward opening parabola in a horizontal direction. In this setting, permeability is a power law function of height, resulting in a generalized Boussinesq equation. To gauge the effects neglected by this model, 3D Navier-Stokes multiphase flow simulations are conducted for the same geometry. Parameter variations are performed to assess the nature of errors induced by applying the 1D model to a realistic scenario, where the initial and boundary conditions can not be matched exactly. Numerical simulations reveal an undercutting effect observed in laboratory experiments, but not modeled when the Dupuit-Forchheimer assumption is applied. By selectively controlling the effects placed on the free surface in 3D simulations, we are able to demonstrate that free surface slope is the primary driver of the undercutting effect. A consistent lag and overshoot flow regime is observed in the 3D simulations as compared to the 1D model, based on the choice of initial condition. This implies that the undercutting effect is partially induced by the initial condition. Additionally, the presented numerical evidence shows that some of the flow behavior unaccounted for in the 1D model scales with the 1D model parameters. Full article
(This article belongs to the Special Issue Advances in Experimental and Computational Rheology)
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Open AccessArticle
Quantum Mechanical and Optical Analogies in Surface Gravity Water Waves
Received: 14 February 2019 / Revised: 1 April 2019 / Accepted: 26 April 2019 / Published: 27 May 2019
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Abstract
We present the theoretical models and review the most recent results of a class of experiments in the field of surface gravity waves. These experiments serve as demonstration of an analogy to a broad variety of phenomena in optics and quantum mechanics. In [...] Read more.
We present the theoretical models and review the most recent results of a class of experiments in the field of surface gravity waves. These experiments serve as demonstration of an analogy to a broad variety of phenomena in optics and quantum mechanics. In particular, experiments involving Airy water-wave packets were carried out. The Airy wave packets have attracted tremendous attention in optics and quantum mechanics owing to their unique properties, spanning from an ability to propagate along parabolic trajectories without spreading, and to accumulating a phase that scales with the cubic power of time. Non-dispersive Cosine-Gauss wave packets and self-similar Hermite-Gauss wave packets, also well known in the field of optics and quantum mechanics, were recently studied using surface gravity waves as well. These wave packets demonstrated self-healing properties in water wave pulses as well, preserving their width despite being dispersive. Finally, this new approach also allows to observe diffractive focusing from a temporal slit with finite width. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics)
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Open AccessArticle
The Effect of Internal and External Heating on the Free Convective Flow of a Bingham Fluid in a Vertical Porous Channel
Received: 14 April 2019 / Revised: 10 May 2019 / Accepted: 16 May 2019 / Published: 24 May 2019
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Abstract
We study the steady free convective flow of a Bingham fluid in a porous channel where heat is supplied by both differential heating of the sidewalls and by means of a uniform internal heat generation. The detailed temperature profile is governing by an [...] Read more.
We study the steady free convective flow of a Bingham fluid in a porous channel where heat is supplied by both differential heating of the sidewalls and by means of a uniform internal heat generation. The detailed temperature profile is governing by an external and an internal Darcy-Rayleigh number. The presence of the Bingham fluid is characterised by means of a body force threshold as given by the Rees-Bingham number. The resulting flow field may then exhibit between two and four yield surfaces depending on the balance of magnitudes of the three nondimensional parameters. Some indication is given of how the locations of the yield surfaces evolve with the relative strength of the Darcy-Rayleigh numbers and the Rees-Bingham number. Finally, parameter space is delimited into those regions within which the different types of flow and stagnation patterns arise. Full article
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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Open AccessArticle
Three-Dimensional Simulation of Fluid–Structure Interaction Problems Using Monolithic Semi-Implicit Algorithm
Received: 17 March 2019 / Revised: 27 April 2019 / Accepted: 13 May 2019 / Published: 22 May 2019
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Abstract
A monolithic semi-implicit method is presented for three-dimensional simulation of fluid–structure interaction problems. The updated Lagrangian framework is used for the structure modeled by linear elasticity equation and, for the fluid governed by the Navier–Stokes equations, we employ the Arbitrary Lagrangian Eulerian method. [...] Read more.
A monolithic semi-implicit method is presented for three-dimensional simulation of fluid–structure interaction problems. The updated Lagrangian framework is used for the structure modeled by linear elasticity equation and, for the fluid governed by the Navier–Stokes equations, we employ the Arbitrary Lagrangian Eulerian method. We use a global mesh for the fluid–structure domain where the fluid–structure interface is an interior boundary. The continuity of velocity at the interface is automatically satisfied by using globally continuous finite element for the velocity in the fluid–structure mesh. The method is fast because we solve only a linear system at each time step. Three-dimensional numerical tests are presented. Full article
(This article belongs to the Special Issue Recent Numerical Advances in Fluid Mechanics)
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Open AccessFeature PaperArticle
On the Interaction of Side-By-Side Circular Cylinders in Viscoplastic Fluids
Received: 12 April 2019 / Revised: 15 May 2019 / Accepted: 17 May 2019 / Published: 21 May 2019
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Abstract
In this paper, the static interaction of a train of three cylinders in a Bingham fluid is studied numerically using Computational Fluid Dynamics. The variation of drag forces for the cylinders in several configurations is investigated. Positions of the particles in relation to [...] Read more.
In this paper, the static interaction of a train of three cylinders in a Bingham fluid is studied numerically using Computational Fluid Dynamics. The variation of drag forces for the cylinders in several configurations is investigated. Positions of the particles in relation to the reference particle are recognized by the separation distance between the cylinders. A steady state field is considered, with Bingham numbers between 5 and 150. Several separation distances (d) were considered, such that 2.0Dd ≤ 6.0D where D is the cylinder diameter. The Reynolds number was chosen in the range of 5 ≤ Re ≤ 40. In particular, the effect of the separation distance, Reynolds number and Bingham number on the shape and size of the unyielded regions was investigated. The functional dependence of this region and the drag coefficient is explored. The present results reveal the significant influence of the gap between the cylinders on the drag force and the shape of the unyielded regions surrounding the cylinders. It was found that there are several configurations in which the drag forces over the first and the third cylinders are almost equal depending on variation of the Bi, Re and the separation distance. Full article
(This article belongs to the Special Issue Recent Advances in Mechanics of Non-Newtonian Fluids)
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Open AccessArticle
Baropycnal Work: A Mechanism for Energy Transfer across Scales
Received: 5 April 2019 / Revised: 9 May 2019 / Accepted: 13 May 2019 / Published: 18 May 2019
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Abstract
The role of baroclinicity, which arises from the misalignment of pressure and density gradients, is well-known in the vorticity equation, yet its role in the kinetic energy budget has never been obvious. Here, we show that baroclinicity appears naturally in the kinetic energy [...] Read more.
The role of baroclinicity, which arises from the misalignment of pressure and density gradients, is well-known in the vorticity equation, yet its role in the kinetic energy budget has never been obvious. Here, we show that baroclinicity appears naturally in the kinetic energy budget after carrying out the appropriate scale decomposition. Strain generation by pressure and density gradients, both barotropic and baroclinic, also results from our analysis. These two processes underlie the recently identified mechanism of “baropycnal work”, which can transfer energy across scales in variable density flows. As such, baropycnal work is markedly distinct from pressure-dilatation into which the former is implicitly lumped in Large Eddy Simulations. We provide numerical evidence from 1024 3 direct numerical simulations of compressible turbulence. The data shows excellent pointwise agreement between baropycnal work and the nonlinear model we derive, supporting our interpretation of how it operates. Full article
(This article belongs to the Special Issue Multiscale Turbulent Transport)
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Open AccessArticle
Time-Reversal Analogy by Nonlinear Acoustic–Gravity Wave Triad Resonance
Received: 13 April 2019 / Revised: 30 April 2019 / Accepted: 13 May 2019 / Published: 17 May 2019
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Abstract
Time reversal of free-surface water (gravity) waves due to a sudden change in the effective gravity has been extensively studied in recent years. Here, we show that an analogy to time-reversal can be obtained using nonlinear acoustic-gravity wave theory. More specifically, we present [...] Read more.
Time reversal of free-surface water (gravity) waves due to a sudden change in the effective gravity has been extensively studied in recent years. Here, we show that an analogy to time-reversal can be obtained using nonlinear acoustic-gravity wave theory. More specifically, we present a mathematical model for the evolution of a time-reversed gravity wave packet from a nonlinear resonant triad perspective. We show that the sudden appearance of an acoustic mode in analogy to a sudden vertical oscillation of the liquid film, can resonate effectively with the original gravity wave packet causing energy pumping into an oppositely propagating (time-reversed) surface gravity wave of an almost identical shape. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics)
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Open AccessArticle
Computational Optimization of Adaptive Hybrid Darrieus Turbine: Part 1
Received: 17 April 2019 / Revised: 10 May 2019 / Accepted: 16 May 2019 / Published: 17 May 2019
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Abstract
Darrieus-type Vertical Axis Wind Turbines (VAWT) are promising for small scale decentralized power generation because of their unique advantages such as simple design, insensitive to wind direction, reliability, and ease of maintenance. Despite these positive aspects, poor self-starting capability and low efficiency in [...] Read more.
Darrieus-type Vertical Axis Wind Turbines (VAWT) are promising for small scale decentralized power generation because of their unique advantages such as simple design, insensitive to wind direction, reliability, and ease of maintenance. Despite these positive aspects, poor self-starting capability and low efficiency in weak and unsteady winds deteriorate further development. Adaptive Hybrid Darrieus Turbine (AHDT) was proposed by the author in the past study as a potential solution to enhance low wind speed characteristics. The objective of the current research is to optimize the parameters of AHDT. AHDT integrates a dynamically varying Savonius rotor with a Darrieus rotor. A fully detailed 2D numerical study employing Reynold-Averaged Navier Stokes (RANS) is carried out to investigate the impact of the Darrieus rotor diameter (DR) on the Savonius rotor (DT) with regard to hybrid turbine performance. The power coefficient of the Darrieus rotor is evaluated when the Savonius rotor is in the closed condition (cylinder) of various diameters. The influence of Reynolds number (Re) on the torque coefficient is examined. Power loss of 58.3% and 25% is reported for DR/DT ratio of 1.5 and 2 respectively for AHDT with solidity 0.5 at 9 m/s. The flow interaction between the Savonius rotor in closed configuration reveals the formation of von Karman vortices that interact with Darrieus blades resulting in flow detachment. An optimum diametrical ratio (DR/DT) of 3 is found to yield the maximum power coefficient of the Darrieus rotor. Full article
(This article belongs to the Special Issue Flow-based Optimization of Products or Devices)
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Open AccessArticle
Near-Wall Flow in Cerebral Aneurysms
Received: 16 March 2019 / Revised: 10 April 2019 / Accepted: 18 April 2019 / Published: 16 May 2019
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Abstract
The region where the vascular lumen meets the surrounding endothelium cell layer, hence the interface region between haemodynamics and cell tissue, is of primary importance in the physiological functions of the cardiovascular system. The functions include mass transport to/from the blood and tissue, [...] Read more.
The region where the vascular lumen meets the surrounding endothelium cell layer, hence the interface region between haemodynamics and cell tissue, is of primary importance in the physiological functions of the cardiovascular system. The functions include mass transport to/from the blood and tissue, and signalling via mechanotransduction, which are primary functions of the cardiovascular system and abnormalities in these functions are known to affect disease formation and vascular remodelling. This region is denoted by the near-wall region in the present work, and we outline simple yet effective numerical recipes to analyse the near-wall flow field. Computational haemodynamics solutions are presented for six patient specific cerebral aneurysms, at three instances in the cardiac cycle: peak systole, end systole (taken as dicrotic notch) and end diastole. A sensitivity study, based on Newtonian and non-Newtonian rheological models, and different flow rate profiles, is effected for a selection of aneurysm cases. The near-wall flow field is described by the wall shear stress (WSS) and the divergence of wall shear stress (WSSdiv), as descriptors of tangential and normal velocity components, respectively, as well as the wall shear stress critical points. Relations between near-wall and free-stream flow fields are discussed. Full article
(This article belongs to the Special Issue Cardiovascular Flows)
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Open AccessArticle
Numerical Optimization of a Stall Margin Enhancing Recirculation Channel for an Axial Compressor
Received: 13 February 2019 / Revised: 22 March 2019 / Accepted: 26 April 2019 / Published: 11 May 2019
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Abstract
A proof of concept is provided by computational fluid dynamic simulations of a new recirculating type casing treatment. This treatment aims at extending the stable operating range of highly loaded axial compressors, so to improve the safety of sorties of high-speed, high-performance aircraft [...] Read more.
A proof of concept is provided by computational fluid dynamic simulations of a new recirculating type casing treatment. This treatment aims at extending the stable operating range of highly loaded axial compressors, so to improve the safety of sorties of high-speed, high-performance aircraft powered by high specific thrust engines. This casing treatment, featuring an axisymmetric recirculation channel, is evaluated on the NASA rotor 37 test case by steady and unsteady Reynolds Averaged Navier Stokes (RANS) simulations, using the realizable k-ε model. Flow blockage at the recirculation channel outlet was mitigated by chamfering the exit of the recirculation channel inner wall. The channel axial location from the rotor blade tip leading edge was optimized parametrically over the range −4.6% to 47.6% of the rotor tip axial chord c z . Locating the channel at 18.2% c z provided the best stall margin gain of approximately 5.5% compared to the untreated rotor. No rotor adiabatic efficiency was lost by the application of this casing treatment. The investigation into the flow structure with the recirculating channel gave a good insight into how the new casing treatment generates this benefit. The combination of stall margin gain at no rotor adiabatic efficiency loss makes this design attractive for applications to high-speed gas turbine engines. Full article
(This article belongs to the Special Issue Turbomachinery Flow Analysis)
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Open AccessArticle
An Experimental and Computational Study on Inverted Flag Dynamics for Simultaneous Wind–Solar Energy Harvesting
Received: 12 April 2019 / Revised: 1 May 2019 / Accepted: 8 May 2019 / Published: 11 May 2019
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Abstract
This paper presents results from experiments and simplified numerical simulations on the flow-induced dynamics and power generation of inverted flags that combine flexible piezoelectric strips with photovoltaic cells to simultaneously harvest kinetic wind energy and solar radiant energy. Experiments were conducted in a [...] Read more.
This paper presents results from experiments and simplified numerical simulations on the flow-induced dynamics and power generation of inverted flags that combine flexible piezoelectric strips with photovoltaic cells to simultaneously harvest kinetic wind energy and solar radiant energy. Experiments were conducted in a wind tunnel under controlled wind excitation and light exposure, focusing in particular on the dynamics and power generation of the inverted flag harvester. Numerical simulations were carried out using a lattice-Boltzmann fluid solver coupled with a finite element structural solver via the immersed-boundary method, focusing in particular on minimizing the simulation run time. The power generated during the tests shows that the proposed inverted flag harvester is a promising concept, capable of producing enough power (on the order of 1 mW) to supply low-power electronic devices in a range of applications where distributed power generation is needed. Notwithstanding key simplifications implemented in the numerical model to achieve a fast execution, simulations and measurements are in good agreement, confirming that the lattice-Boltzmann method is a viable and time-effective alternative to classic Navier–Stokes-based solvers when dealing with strongly coupled fluid–structure interaction problems characterized by large structural displacements. Full article
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Open AccessArticle
Radial Imbibition in Paper under Temperature Differences
Received: 21 March 2019 / Revised: 23 April 2019 / Accepted: 5 May 2019 / Published: 11 May 2019
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Abstract
Spontaneous radial imbibition into thin circular samples of porous material when they have been subjected to radial temperature differences was analyzed theoretically and experimentally. The use of the Darcy equation allowed us to take into account temperature variations in the dynamic viscosity and [...] Read more.
Spontaneous radial imbibition into thin circular samples of porous material when they have been subjected to radial temperature differences was analyzed theoretically and experimentally. The use of the Darcy equation allowed us to take into account temperature variations in the dynamic viscosity and surface tension in order to find the one-dimensional equation for the imbibition fronts. Experiments using blotting paper showed a good fit between the experimental data and theoretical profiles through the estimation of a single parameter. Full article
(This article belongs to the Special Issue Free surface flows)
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Open AccessArticle
Smart Proxy Modeling of SACROC CO2-EOR
Received: 26 February 2019 / Revised: 17 April 2019 / Accepted: 26 April 2019 / Published: 3 May 2019
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Abstract
Large CO2-enhanced oil recovery (EOR) projects usually contain an abundance of geological and good performance data. While this volume of data leads to robust models, it often results in difficult to manage, slow-running numerical flow models. To dramatically reduce the numerical [...] Read more.
Large CO2-enhanced oil recovery (EOR) projects usually contain an abundance of geological and good performance data. While this volume of data leads to robust models, it often results in difficult to manage, slow-running numerical flow models. To dramatically reduce the numerical run-times associated with the traditional simulation techniques, this work investigated the feasibility of using artificial intelligence and machine learning technologies to develop a smart proxy model of the Scurry Area Canyon Reef Operators Committee (SACROC) oilfield, located in the Permian Basin, TX, USA. Smart proxy models can be used to facilitate injection-production optimization for CO2-EOR projects. The use of a coupled grid-based, and well-based surrogate reservoir model (SRM) (also known as smart proxy modeling) was investigated as the base of the optimization. A fit-for-purpose coupled SRM, which executes in seconds, was built based on high-resolution numerical reservoir simulation models of the northern platform of the SACROC oilfield. This study is unique as it is the first application of coupled SRM at a large oilfield. The developed SRM was able to identify the dynamic reservoir properties (pressure, saturations, and component mole-fraction) at every grid-block, along with the production characteristics (pressure and rate) at each well. Recent attempts to use machine learning and pattern recognition to build proxy models have been simplistic, with limited predictive capabilities. The geological model used in this study is comprised of more than nine million grid blocks. The high correlation between the actual component and SRM, which can be visualized by mapping the properties, along with the fast footprint of the developed model demonstrate the successful application of this methodology. Full article
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Open AccessArticle
On the Asymmetric Spectral Broadening of a Hydrodynamic Modulated Wave Train in the Optical Regime
Received: 8 February 2019 / Revised: 1 April 2019 / Accepted: 16 April 2019 / Published: 2 May 2019
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Abstract
Amplitude modulation of a propagating wave train has been observed in various media including hydrodynamics and optical fibers. The notable difference of the propagating wave trains in these media is the magnitude of the nonlinearity and the associated spectral bandwidth. The nonlinearity and [...] Read more.
Amplitude modulation of a propagating wave train has been observed in various media including hydrodynamics and optical fibers. The notable difference of the propagating wave trains in these media is the magnitude of the nonlinearity and the associated spectral bandwidth. The nonlinearity and dispersion parameters of optical fibers are two orders of magnitude smaller than the hydrodynamic counterparts, and therefore, considered to better assure the slowly varying envelope approximation (SVEA) of the nonlinear Schrödinger equations (NLSE). While most optics experiment demonstrate an NLSE-like symmetric solutions, experimental studies by Dudley et al. (Optics Express, 2009, 17, 21497–21508) show an asymmetric spectral evolution in the dynamics of unstable electromagnetic waves with high intensities. Motivated by this result, the hydrodynamic Euler equation is numerically solved to study the long-term evolution of a water-wave modulated wave train in the optical regime, i.e., at small steepness and spectral bandwidth. As the initial steepness is increased, retaining the initial spectral bandwidth thereby increasing the Benjamin–Feir Index, the modulation localizes, and the asymmetric and broad spectrum appears. While the deviation of the evolution from the NLSE solution is a result of broadband dynamics of free wave interaction, the resulting asymmetry of the spectrum is a consequence of the violation of the SVEA. Full article
(This article belongs to the Special Issue Nonlinear Wave Hydrodynamics)
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