A Lumped-Parameter Model for Stagnant Thermal Conductivity of Spatially Periodic Porous Media

Based on a lumped-parameter method, algebraic expressions for the stagnant thermal conductivity of some two-dimensional and three-dimensional spatially periodic media are obtained. The geometries under consideration include arrays of touching and non-touching in-line square and circular cylinders (two-dimensional), as well as touching and nontouching in-line cubes (three-dimensional). A comparison of results based on these algebraic expressions with existing numerical solutions and experimental data shows that they are in excellent agreement.

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Review of Three Dimensional Dynamic Analyses of Circular Cylinders and Cylindrical Shells

Applied Mechanics Reviews ◽

10.1115/1.3111064 ◽

1994 ◽

Vol 47 (10) ◽

pp. 501-516 ◽

Cited By ~ 74

Author(s):

Kostas P. Soldatos

Keyword(s):

Cylindrical Shells ◽

Three Dimensional ◽

Circular Cylinders ◽

Accurate Information ◽

Two Dimensional ◽

Governing Equations ◽

Complicated Form ◽

Dynamic Analyses ◽

Cylindrical Panels ◽

Elastic Cylinders

There is an increasing usefulness of exact three-dimensional analyses of elastic cylinders and cylindrical shells in composite materials applications. Such analyses are considered as benchmarks for the range of applicability of corresponding studies based on two-dimensional and/or finite element modeling. Moreover, they provide valuable, accurate information in cases that corresponding predictions based on that later kind of approximate modeling is not satisfactory. Due to the complicated form of the governing equations of elasticity, such three-dimensional analyses are comparatively rare in the literature. There is therefore a need for further developments in that area. A survey of the literature dealing with three-dimensional dynamic analyses of cylinders and open cylindrical panels will serve towards such developments. This paper presents such a survey within the framework of linear elasticity.

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Metric for attractor overlap

Journal of Fluid Mechanics ◽

10.1017/jfm.2019.447 ◽

2019 ◽

Vol 874 ◽

pp. 720-755 ◽

Cited By ~ 6

Author(s):

Rishabh Ishar ◽

Eurika Kaiser ◽

Marek Morzyński ◽

Daniel Fernex ◽

Richard Semaan ◽

...

Keyword(s):

Boundary Layer ◽

Turbulent Boundary Layer ◽

Three Dimensional ◽

Particle Image Velocimetry Data ◽

Open Loop ◽

Operating Conditions ◽

Wall Turbulence ◽

Circular Cylinders ◽

Two Dimensional ◽

Starting Point

We present the first general metric for attractor overlap (MAO) facilitating an unsupervised comparison of flow data sets. The starting point is two or more attractors, i.e. ensembles of states representing different operating conditions. The proposed metric generalizes the standard Hilbert-space distance between two snapshot-to-snapshot ensembles of two attractors. A reduced-order analysis for big data and many attractors is enabled by coarse graining the snapshots into representative clusters with corresponding centroids and population probabilities. For a large number of attractors, MAO is augmented by proximity maps for the snapshots, the centroids and the attractors, giving scientifically interpretable visual access to the closeness of the states. The coherent structures belonging to the overlap and disjoint states between these attractors are distilled by a few representative centroids. We employ MAO for two quite different actuated flow configurations: a two-dimensional wake with vortices in a narrow frequency range and three-dimensional wall turbulence with a broadband spectrum. In the first application, seven control laws are applied to the fluidic pinball, i.e. the two-dimensional flow around three circular cylinders whose centres form an equilateral triangle pointing in the upstream direction. These seven operating conditions comprise unforced shedding, boat tailing, base bleed, high- and low-frequency forcing as well as two opposing Magnus effects. In the second example, MAO is applied to three-dimensional simulation data from an open-loop drag reduction study of a turbulent boundary layer. The actuation mechanisms of 38 spanwise travelling transversal surface waves are investigated. MAO compares and classifies these actuated flows in agreement with physical intuition. For instance, the first feature coordinate of the attractor proximity map correlates with drag for the fluidic pinball and for the turbulent boundary layer. MAO has a large spectrum of potential applications ranging from a quantitative comparison between numerical simulations and experimental particle-image velocimetry data to the analysis of simulations representing a myriad of different operating conditions.

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Nonlinear evolution of interacting oblique waves on two-dimensional shear layers

Journal of Fluid Mechanics ◽

10.1017/s002211208900251x ◽

1989 ◽

Vol 207 ◽

pp. 97-120 ◽

Cited By ~ 66

Author(s):

M. E. Goldstein ◽

S.-W. Choi

Keyword(s):

Wave Amplitude ◽

Numerical Solutions ◽

Nonlinear Evolution ◽

Three Dimensional ◽

Shear Layers ◽

Instability Wave ◽

Two Dimensional ◽

Instability Waves ◽

Downstream Distance ◽

Parallel Streams

We consider the effects of critical-layer nonlinearity on spatially growing oblique instability waves on nominally two-dimensional shear layers between parallel streams. The analysis shows that three-dimensional effects cause nonlinearity to occur at much smaller amplitudes than it does in two-dimensional flows. The nonlinear instability wave amplitude is determined by an integro-differential equation with cubic-type nonlinearity. The numerical solutions to this equation are worked out and discussed in some detail. We show that they always end in a singularity at a finite downstream distance.

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Analysis of Fly Fishing Rod Casting Dynamics

Shock and Vibration ◽

10.1155/2011/859054 ◽

2011 ◽

Vol 18 (6) ◽

pp. 839-855

Author(s):

Gang Wang ◽

Norman Wereley

Keyword(s):

Finite Element ◽

Initial Boundary ◽

Element Model ◽

Nonlinear Finite Element ◽

Lumped Parameter Model ◽

Parameter Method ◽

Line System ◽

Fly Fishing ◽

Lumped Parameter ◽

Rigid Rod

An analysis of fly fishing rod casting dynamics was developed comprising of a nonlinear finite element representation of the composite fly rod and a lumped parameter model for the fly line. A nonlinear finite element model was used to analyze the transient response of the fly rod, in which fly rod responses were simulated for a forward casting stroke. The lumped parameter method was used to discretize the fly line system. Fly line motions were simulated during a cast based on fly rod tip response, which was used as the initial boundary condition for the fly line. Fly line loop generation, propagation, and line turn-over were simulated numerically. Flexible rod results were compared to the rigid rod case, in which the fly tip path was prescribed by a given fly rod butt input. Our numerical results strongly suggest that nonlinear flexibility effects on the fly rod must be included in order to accurately simulate casting dynamics and associated fly line motion.

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Singularities in solutions of the three-dimensional laminar-boundary-layer equations

Journal of Fluid Mechanics ◽

10.1017/s0022112085003470 ◽

1985 ◽

Vol 160 ◽

pp. 257-279 ◽

Cited By ~ 6

Author(s):

James C. Williams

Keyword(s):

Boundary Layer ◽

Laminar Boundary Layer ◽

Numerical Solutions ◽

Three Dimensional ◽

Two Dimensional ◽

Unsteady Boundary Layer ◽

Boundary Layer Flows ◽

Boundary Layer Equations ◽

New Type ◽

Steady Laminar

The three-dimensional steady laminar-boundary-layer equations have been cast in the appropriate form for semisimilar solutions, and it is shown that in this form they have the same structure as the semisimilar form of the two-dimensional unsteady laminar-boundary-layer equations. This similarity suggests that there may be a new type of singularity in solutions to the three-dimensional equations: a singularity that is the counterpart of the Stewartson singularity in certain solutions to the unsteady boundary-layer equations.A family of simple three-dimensional laminar boundary-layer flows has been devised and numerical solutions for the development of these flows have been obtained in an effort to discover and investigate the new singularity. The numerical results do indeed indicate the existence of such a singularity. A study of the flow approaching the singularity indicates that the singularity is associated with the domain of influence of the flow for given initial (upstream) conditions as is prescribed by the Raetz influence principle.

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Applying Ensemble Kalman Filter to Transonic Flows Through a Two-Dimensional Turbine Cascade

Journal of Fluids Engineering ◽

10.1115/1.4052472 ◽

2021 ◽

Vol 143 (12) ◽

Author(s):

Sasuga Ito ◽

Masato Furukawa ◽

Kazutoyo Yamada ◽

Kaito Manabe

Keyword(s):

Kalman Filter ◽

Ensemble Kalman Filter ◽

Numerical Solutions ◽

Stokes Equations ◽

Three Dimensional ◽

Navier Stokes ◽

Optimization Approach ◽

Two Dimensional ◽

Turbine Cascade ◽

Eddy Simulation

Abstract Turbulence is one of the most important phenomena in fluid dynamics. Large eddy simulation (LES) generally allows us to analyze smaller eddies than when using simulations based on unsteady Reynolds-averaged Navier–Stokes equations (URANS). In addition, the numerical solutions of LES show good agreements with experiments and numerical solutions based on direct numerical simulation. URANS simulations are, however, frequently used in academia and industry because LES computations are much more expensive compared with URANS simulations. In this investigation, an optimization of unsolved coefficients of the k–ω two equations model is performed on the transonic flow around T106A low-pressure turbine cascade to improve the accuracy of turbulence prediction with URANS. For the optimization approach, two-dimensional URANS is combined with ensemble Kalman filter which is one of the data assimilation techniques. In the assimilation process, a time- and spanwise-averaged LES result is used as pseudo-experimental data. Three-dimensional URANS simulations are performed for the evaluation of the optimization effect. URANS simulations are also applied to a different turbine cascade flow for the evaluation of the robustness of the optimized coefficients. These URANS results confirmed that the optimized coefficients improve the accuracy of turbulence prediction.

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The total cavopulmonary connection resistance: a significant impact on single ventricle hemodynamics at rest and exercise

AJP Heart and Circulatory Physiology ◽

10.1152/ajpheart.00628.2008 ◽

2008 ◽

Vol 295 (6) ◽

pp. H2427-H2435 ◽

Cited By ~ 82

Author(s):

Kartik S. Sundareswaran ◽

Kerem Pekkan ◽

Lakshmi P. Dasi ◽

Kevin Whitehead ◽

Shiva Sharma ◽

...

Keyword(s):

Heart Rate ◽

Single Ventricle ◽

Fluid Dynamic ◽

Three Dimensional ◽

Lumped Parameter Model ◽

Total Cavopulmonary Connection ◽

Dynamic Simulations ◽

Lumped Parameter ◽

The Impact ◽

Cavopulmonary Connection

Little is known about the impact of the total cavopulmonary connection (TCPC) on resting and exercise hemodynamics in a single ventricle (SV) circulation. The aim of this study was to elucidate this mechanism using a lumped parameter model of the SV circulation. Pulmonary vascular resistance (1.96 ± 0.80 WU) and systemic vascular resistances (18.4 ± 7.2 WU) were obtained from catheterization data on 40 patients with a TCPC. TCPC resistances (0.39 ± 0.26 WU) were established using computational fluid dynamic simulations conducted on anatomically accurate three-dimensional models reconstructed from MRI ( n = 16). These parameters were used in a lumped parameter model of the SV circulation to investigate the impact of TCPC resistance on SV hemodynamics under resting and exercise conditions. A biventricular model was used for comparison. For a biventricular circulation, the cardiac output (CO) dependence on TCPC resistance was negligible (sensitivity = −0.064 l·min−1·WU−1) but not for the SV circulation (sensitivity = −0.88 l·min−1·WU−1). The capacity to increase CO with heart rate was also severely reduced for the SV. At a simulated heart rate of 150 beats/min, the SV patient with the highest resistance (1.08 WU) had a significantly lower increase in CO (20.5%) compared with the SV patient with the lowest resistance (50%) and normal circulation (119%). This was due to the increased afterload (+35%) and decreased preload (−12%) associated with the SV circulation. In conclusion, TCPC resistance has a significant impact on resting hemodynamics and the exercise capacity of patients with a SV physiology.

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A two-dimensional depth-averaged -rheology for dense granular avalanches

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.684 ◽

2015 ◽

Vol 787 ◽

pp. 367-395 ◽

Cited By ~ 43

Author(s):

J. L. Baker ◽

T. Barker ◽

J. M. N. T. Gray

Keyword(s):

Velocity Profile ◽

Numerical Solutions ◽

Three Dimensional ◽

Theoretical Models ◽

Quantitative Agreement ◽

Surface Velocity ◽

Momentum Balance ◽

Test Case ◽

Two Dimensional ◽

Uniform Solution

Steady uniform granular chute flows are common in industry and provide an important test case for new theoretical models. This paper introduces depth-integrated viscous terms into the momentum-balance equations by extending the recent depth-averaged ${\it\mu}(I)$-rheology for dense granular flows to two spatial dimensions, using the principle of material frame indifference or objectivity. Scaling the cross-slope coordinate on the width of the channel and the velocity on the one-dimensional steady uniform solution, we show that the steady two-dimensional downslope velocity profile is independent of scale. The only controlling parameters are the channel aspect ratio, the slope inclination angle and the frictional properties of the chute and the sidewalls. Solutions are constructed for both no-slip conditions and for a constant Coulomb friction at the walls. For narrow chutes, a pronounced parabolic-like depth-averaged downstream velocity profile develops. However, for very wide channels, the flow is almost uniform with narrow boundary layers close to the sidewalls. Both of these cases are in direct contrast to conventional inviscid avalanche models, which do not develop a cross-slope profile. Steady-state numerical solutions to the full three-dimensional ${\it\mu}(I)$-rheology are computed using the finite element method. It is shown that these solutions are also independent of scale. For sufficiently shallow channels, the depth-averaged velocity profile computed from the full solution is in excellent agreement with the results of the depth-averaged theory. The full downstream velocity can be reconstructed from the depth-averaged theory by assuming a Bagnold-like velocity profile with depth. For wide chutes, this is very close to the results of the full three-dimensional calculation. For experimental validation, a laser profilometer and balance are used to determine the relationship between the total mass flux in the chute and the flow thickness for a range of slope angles and channel widths, and particle image velocimetry (PIV) is used to record the corresponding surface velocity profiles. The measured values are in good quantitative agreement with reconstructed solutions to the new depth-averaged theory.

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On the nature of unsteady three-dimensional laminar boundary-layer separation

Journal of Fluid Mechanics ◽

10.1017/s0022112078002086 ◽

1978 ◽

Vol 88 (2) ◽

pp. 241-258 ◽

Cited By ~ 2

Author(s):

James C. Williams

Keyword(s):

Boundary Layer ◽

Laminar Boundary Layer ◽

Numerical Solutions ◽

Three Dimensional ◽

Boundary Layer Separation ◽

The Body ◽

Two Dimensional ◽

Boundary Layer Equations ◽

Unsteady Separation ◽

Cavity Flow Predictions Based on the Euler Equations

Journal of Fluids Engineering ◽

10.1115/1.2910238 ◽

1994 ◽

Vol 116 (1) ◽

pp. 36-44 ◽

Cited By ~ 37

Author(s):

Manish Deshpande ◽

Jinzhang Feng ◽

Charles L. Merkle

Keyword(s):

Numerical Solutions ◽

Three Dimensional ◽

Leading Edge ◽

Cavity Flow ◽

Cavity Surface ◽

Computational Domain ◽

Two Dimensional ◽

Sheet Cavitation ◽

Inception Point ◽

Euler Solver

An Euler solver based on artificial-compressibility and pseudo-time stepping is developed for the analysis of partial sheet cavitation in two-dimensional cascades and on isolated airfoils. The computational domain is adapted to the evolution of the cavity surface and the boundary conditions are implemented on the cavity interface. This approach enables the cavitation pressure condition to be incorporated directly without requiring the specification of the cavity length or the location of the inception point. Numerical solutions are presented for a number of two-dimensional cavity flow problems, including both leading edge cavitation and the more difficult mid-chord cavitation condition. Validation is accomplished by comparing with experimental measurements and nonlinear panel solutions from potential flow theory. The demonstrated success of the Euler cavitation procedure implies that it can be incorporated in existing incompressible CFD codes to provide engineering predictions of cavitation. In addition, the flexibility of the Euler formulation may allow extension to more complex problems such as viscous flows, time-dependent flows and three-dimensional flows.

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