A numerical investigation of fluid flows induced by the oscillations of thin plates and evaluation of the associated hydrodynamic forces

2019 ◽  
Vol 874 ◽  
pp. 1057-1095 ◽  
Author(s):  
Artem N. Nuriev ◽  
Airat M. Kamalutdinov ◽  
Andrey G. Egorov
Keyword(s):  
Stokes Equations ◽  
Experimental Studies ◽  
Flow Regimes ◽  
Hydrodynamic Forces ◽  
Thin Plates ◽  
Oscillatory Process ◽  
Dimensionless Frequency ◽  
Two Dimensional ◽  
Wide Range ◽  
Hydrodynamic Influence

The paper is devoted to the problem of harmonic oscillations of thin plates in a viscous incompressible fluid. The two-dimensional flows caused by the plate oscillations and their hydrodynamic influence on the plates are studied. The fluid motion is described by the non-stationary Navier–Stokes equations, which are solved numerically on the basis of the finite volume method. The simulation is carried out for plates with different thicknesses and shapes of edges in a wide range of control parameters of the oscillatory process: dimensionless frequency and amplitude of oscillations. For the first time in the framework of one model all two-dimensional flow regimes, which were found earlier in experimental studies, are described. Two new flow regimes emerging along the stability boundaries of symmetric flow regimes are localized. The map of flow regimes in the frequency–amplitude plane is constructed. The analysis of the hydrodynamic influence of flows on the plates allow us to establish new effects associated with the influence of the shape of the plates on the drag and inertia forces. Due to these effects, the values of hydrodynamic forces can differ by 90 % at the same parameters of the oscillation. The lower and upper estimates of hydrodynamic forces obtained in the work have a good agreement with the experimental data presented in the literature.

Transverse Oscillations of a Jet in a Jet-Splitter System

1972 ◽  
Vol 94 (3) ◽  
pp. 675-681 ◽  
Author(s):  
D. O. Rockwell
Keyword(s):  
Reynolds Number ◽  
Strouhal Number ◽  
Nozzle Exit ◽  
Reynolds Numbers ◽  
Dimensionless Frequency ◽  
Two Dimensional ◽  
Vena Contracta ◽  
Wide Range ◽  
Jet Behavior ◽  
Transverse Oscillations

The fundamental transverse oscillations of a liquid jet which impinged upon a flow splitter were examined for a wide range of dimensionless splitter distance, nozzle exit Reynolds number, and dimensionless frequency. The results are presented in the form of a design map. The data, taken at low nozzle aspect ratio, reveal that fundamental (stage 1) oscillations can exist for Reynolds numbers up to at least 7000. Up to Reynolds numbers of about 3000, the jet behavior is Reynolds number dependent for all values of splitter distance. Beyond Reynolds number of 3000 the jet behavior is independent of Reynolds number. In general, the Strouhal number, based on nozzle exit-splitter distance, decreases with increasing values of splitter distance. Jets issuing from nozzles with no parallel development sections were considered. Jet nozzle shape influences the dimensionless frequency of oscillation in that the effect of a vena contracta formation outside the nozzle exit is to yield a higher value of dimensionless frequency relative to nozzles which produce parallel flow with small boundary layer thickness at the exit. Similar decreases have been found for two-dimensional jets. Of the above findings, the only comparable results for two-dimensional jets are variations in Strouhal number with nozzle exit-splitter distance.

Prediction of Wall-Jet and Wall-Wake Flows

1970 ◽  
Vol 12 (6) ◽  
pp. 404-420 ◽  
Author(s):  
S. C. Kacker ◽  
J. H. Whitelaw
Keyword(s):  
Film Cooling ◽  
Stokes Equations ◽  
Numerical Procedure ◽  
Navier Stokes ◽  
Wall Jet ◽  
Two Dimensional ◽  
Constant Property ◽  
Navier Stokes Equations ◽  
Wake Flows ◽  
Wide Range

An existing numerical procedure for solving the steady, two-dimensional, constant property form of the Navier–Stokes equations, has been used to obtain predictions of mean and fluctuating properties downstream of a two-dimensional wall jet. The Prandtl–Kolmogorov model of turbulence, with a simple empirical expression for the length scale, is shown to permit satisfactory predictions over a wide range of flow situations. These flow situations are relevant to the design of film-cooling slots.

scholarly journals Turbulent 2.5-dimensional dynamos

2016 ◽  
Vol 799 ◽  
pp. 246-264 ◽  
Author(s):  
K. Seshasayanan ◽  
A. Alexakis
Keyword(s):  
Turbulent Flows ◽  
Large Scale ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Wide Range ◽  
Two Dimensional Flow

We study the linear stage of the dynamo instability of a turbulent two-dimensional flow with three components $(u(x,y,t),v(x,y,t),w(x,y,t))$ that is sometimes referred to as a 2.5-dimensional (2.5-D) flow. The flow evolves based on the two-dimensional Navier–Stokes equations in the presence of a large-scale drag force that leads to the steady state of a turbulent inverse cascade. These flows provide an approximation to very fast rotating flows often observed in nature. The low dimensionality of the system allows for the realization of a large number of numerical simulations and thus the investigation of a wide range of fluid Reynolds numbers $Re$, magnetic Reynolds numbers $Rm$ and forcing length scales. This allows for the examination of dynamo properties at different limits that cannot be achieved with three-dimensional simulations. We examine dynamos for both large and small magnetic Prandtl-number turbulent flows $Pm=Rm/Re$, close to and away from the dynamo onset, as well as dynamos in the presence of scale separation. In particular, we determine the properties of the dynamo onset as a function of $Re$ and the asymptotic behaviour in the large $Rm$ limit. We are thus able to give a complete description of the dynamo properties of these turbulent 2.5-D flows.

scholarly journals Nonlinear dynamics of surfactant-laden two-fluid Couette flows in the presence of inertia

2016 ◽  
Vol 802 ◽  
pp. 5-36 ◽  
Author(s):  
A. Kalogirou ◽  
D. T. Papageorgiou
Keyword(s):  
Stokes Equations ◽  
Travelling Waves ◽  
Type Theorem ◽  
Three Dimensional ◽  
Two Dimensional ◽  
One Dimensional ◽  
Wide Range ◽  
Time Periodic ◽  
Two Fluid ◽  
Permanent Form

The nonlinear stability of immiscible two-fluid Couette flows in the presence of inertia is considered. The interface between the two viscous fluids can support insoluble surfactants and the interplay between the underlying hydrodynamic instabilities and Marangoni effects is explored analytically and computationally in both two and three dimensions. Asymptotic analysis when one of the layers is thin relative to the other yields a coupled system of nonlinear equations describing the spatio-temporal evolution of the interface and its local surfactant concentration. The system is non-local and arises by appropriately matching solutions of the linearised Navier–Stokes equations in the thicker layer to the solution in the thin layer. The scaled models are used to study different physical mechanisms by varying the Reynolds number, the viscosity ratio between the two layers, the total amount of surfactant present initially and a scaled Péclet number measuring diffusion of surfactant along the interface. The linear stability of the underlying flow to two- and three-dimensional disturbances is investigated and a Squire’s type theorem is found to hold when inertia is absent. When inertia is present, three-dimensional disturbances can be more unstable than two-dimensional ones and so Squire’s theorem does not hold. The linear instabilities are followed into the nonlinear regime by solving the evolution equations numerically; this is achieved by implementing highly accurate linearly implicit schemes in time with spectral discretisations in space. Numerical experiments for finite Reynolds numbers indicate that for two-dimensional flows the solutions are mostly nonlinear travelling waves of permanent form, even though these can lose stability via Hopf bifurcations to time-periodic travelling waves. As the length of the system (that is the wavelength of periodic waves) increases, the dynamics becomes more complex and includes time-periodic, quasi-periodic as well as chaotic fluctuations. It is also found that one-dimensional interfacial travelling waves of permanent form can become unstable to spanwise perturbations for a wide range of parameters, producing three-dimensional flows with interfacial profiles that are two-dimensional and travel in the direction of the underlying shear. Nonlinear flows are also computed for parameters which predict linear instability to three-dimensional disturbances but not two-dimensional ones. These are found to have a one-dimensional interface in a rotated frame with respect to the direction of the underlying shear and travel obliquely without changing form.

Small-scale two-dimensional turbulence shaped by bulk viscosity

2019 ◽  
Vol 875 ◽  
pp. 974-1003
Author(s):  
Emile Touber
Keyword(s):  
Kinetic Energy ◽  
Bulk Viscosity ◽  
Shear Viscosity ◽  
Stokes Equations ◽  
Experimental Studies ◽  
Turbulence Kinetic Energy ◽  
Small Scale ◽  
Two Dimensional ◽  
Large Bulk ◽  
High Bulk

Bulk-to-shear viscosity ratios of three orders of magnitude are often reported in carbon dioxide but are always neglected when predicting aerothermal loads in external (Mars exploration) or internal (turbomachinery, heat exchanger) turbulent flows. The recent (and first) numerical investigations of that matter suggest that the solenoidal turbulence kinetic energy is in fact well predicted despite this seemingly arbitrary simplification. The present work argues that such a conclusion may reflect limitations from the choice of configuration rather than provide a definite statement on the robustness of kinetic-energy transfers to the use of Stokes’ hypothesis. Two distinct asymptotic regimes (Euler–Landau and Stokes–Newton) in the eigenmodes of the Navier–Stokes equations are identified. In the Euler–Landau regime, the one captured by earlier studies, acoustic and entropy waves are damped by transport coefficients and the dilatational kinetic energy is dissipated, even more rapidly for high bulk-viscosity fluids and/or forcing frequencies. If the kinetic energy is initially or constantly injected through solenoidal motions, effects on the turbulence kinetic energy remain minor. However, in the Stokes–Newton regime, diffused bulk compressions and advected isothermal compressions are found to prevail and promote small-scale enstrophy via vorticity–dilatation correlations. In the absence of bulk viscosity, the transition to the Stokes–Newton regime occurs within the dissipative scales and is not observed in practice. In contrast, at high bulk viscosities, the Stokes–Newton regime can be made to overlap with the inertial range and disrupt the enstrophy at small scales, which is then dissipated by friction. Thus, flows with substantial inertial ranges and large bulk-to-shear viscosity ratios should experience enhanced transfers to small-scale solenoidal kinetic energy, and therefore faster dissipation rates leading to modifications of the heat-transfer properties. Observing numerically such transfers is still prohibitively expensive, and the present simulations are restricted to two-dimensional turbulence. However, the theory laid here offers useful guidelines to design experimental studies to track the Stokes–Newton regime and associated modifications of the turbulence kinetic energy, which are expected to persist in three-dimensional turbulence.

Topology of three-dimensional steady cellular flow in a two-sided anti-parallel lid-driven cavity

2017 ◽  
Vol 826 ◽  
pp. 302-334 ◽  
Author(s):  
Francesco Romanò ◽  
Stefan Albensoeder ◽  
Hendrik C. Kuhlmann
Keyword(s):  
Reynolds Number ◽  
Limit Cycle ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Convection Cell ◽  
Two Dimensional ◽  
Three Dimensional Flow ◽  
Driven Cavity ◽  
Dimensional Flow ◽  
Wide Range

The structure of the incompressible steady three-dimensional flow in a two-sided anti-symmetrically lid-driven cavity is investigated for an aspect ratio $\unicode[STIX]{x1D6E4}=1.7$ and spanwise-periodic boundary conditions. Flow fields are computed by solving the Navier–Stokes equations with a fully spectral method on $128^{3}$ grid points utilizing second-order asymptotic solutions near the singular corners. The supercritical flow arises in the form of steady rectangular convection cells within which the flow is point symmetric with respect to the cell centre. Global streamline chaos occupying the whole domain is found immediately above the threshold to three-dimensional flow. Beyond a certain Reynolds number the chaotic sea recedes from the interior, giving way to regular islands. The regular Kolmogorov–Arnold–Moser tori grow with increasing Reynolds number before they shrink again to eventually vanish completely. The global chaos at onset is traced back to the existence of one hyperbolic and two elliptic periodic lines in the basic flow. The singular points of the three-dimensional flow which emerge from the periodic lines quickly change such that, for a wide range of supercritical Reynolds number, each periodic convection cell houses a double spiralling-in saddle focus in its centre, a spiralling-out saddle focus on each of the two cell boundaries and two types of saddle limit cycle on the walls. A representative analysis for $\mathit{Re}=500$ shows chaotic streamlines to be due to chaotic tangling of the two-dimensional stable manifold of the central spiralling-in saddle focus and the two-dimensional unstable manifold of the central wall limit cycle. Embedded Kolmogorov–Arnold–Moser tori and the associated closed streamlines are computed for several supercritical Reynolds numbers owing to their importance for particle transport.

A numerical simulation method for bionic fish self-propelled swimming under control based on deep reinforcement learning

2020 ◽  
Vol 234 (17) ◽  
pp. 3397-3415
Author(s):  
Lang Yan ◽  
Xinghua Chang ◽  
Runyu Tian ◽  
Nianhua Wang ◽  
Laiping Zhang ◽  
...  
Keyword(s):  
Reinforcement Learning ◽  
Motion Control ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Coupling Method ◽  
Computational Domain ◽  
Two Dimensional ◽  
Fish Swimming ◽  
Fish Model ◽  
Wide Range

In order to simulate the under control self-propelled swimming of bionic fishes, a coupling method of hydrodynamics/kinematics/motion-control is presented in this paper. The Navier-Stokes equations in the arbitrary Lagrangian-Eulerian framework are solved in parallel based on the computational domain decomposition to simulate the unsteady flow field efficiently. The flow dynamics is coupled with the fish dynamics in an implicit way by a dual-time stepping approach. In order to discretize the computational domain during a wide range maneuver, an overset grid approach with a parallel implicit hole-cutting technique is adopted and coupled with morphing hybrid grids around the undulation body. The motion control of the fish swimming is realized by a deep reinforcement learning algorithm, which makes the fish model choose proper undulation manner according to a specific purpose. By adding random disturbances in the training process of fish swimming along a straight line, a simplified two-dimensional fish model obtains the ability to swim along a specific trajectory. Then in subsequent tests, the two-dimensional fish model is able to swim along more complex curves with obstacles. Finally, the starting process of a three-dimensional tuna-like model is simulated preliminarily to validate the ability of the coupling method for three-dimensional complex configurations. The numerical results demonstrate that this study could be used to explore the swimming mechanism of fishes in complex environments and to guide how robotic fishes can be controlled to accomplish their tasks.

scholarly journals Intermittency effects in single- and multi-phase flow and anomalous transport in heterogeneous porous media

2021 ◽  
Vol 1 (1) ◽  
Author(s):  
Zoë Penko ◽  
Yaofa Li ◽  
Diogo Bolster ◽  
Kenneth T. Christensen
Keyword(s):  
Porous Media ◽  
Prediction Models ◽  
Experimental Studies ◽  
Flow Regimes ◽  
Heterogeneous Porous Media ◽  
Phase Flow ◽  
Pore Scale ◽  
Wide Range ◽  
Multi Phase Flow ◽  
Multi Phase

Multi-phase flow and transport in porous media is prevalent in a wide range of challenging fluid mechanics problems related to sustainability, energy, and the environment. Accurate prediction of the displacement and interaction of such flows is vital in addressing these problems. In particular it is critical to understand the small- or pore-scale flow and its spatial and temporal evolution, which can impact behaviors at system scales in a nontrivial manner. Intermittency is a phenomenon currently observed in numerical and experimental studies of single-phase flow (Anna et al., n.d.; Morales et al., n.d.), but the case of multi-phase flow has yet to receive much study due to challenges faced in both simulations and experiments. The underlying physics of spreading, mixing, and interfacial processes must be understood for accurate predictions of transport in multi-phase flow systems. Therefore, a comprehensive understanding of multi-phase flow at these very small scales is necessary in the development of accurate system-scale prediction models. We present results from a coordinated numerical and experimental study of intermittency effects over a range of viscous and inertial flow regimes in single- and multi-phase flows in 2D heterogeneous micromodels to quantify Lagrangian flow statistics to better inform pore-scale models. The applicability of different modeling frameworks such as the correlated-continuous time random walk is tested by studying statistics of particle trajectories obtained by particle tracking velocimetry (PTV) measurements and Lattice Boltzmann simulations from single- and multi-phase flows. The results make particular note of the influence of the pore Reynolds number (Re) and inertial effects on intermittency, and compare these effects in the two flow regimes.

Numerical investigation of the oscillatory flow around a circular cylinder close to a wall at moderate Keulegan–Carpenter and low Reynolds numbers

2009 ◽  
Vol 627 ◽  
pp. 259-290 ◽  
Author(s):  
PIETRO SCANDURA ◽  
VINCENZO ARMENIO ◽  
ENRICO FOTI
Keyword(s):  
Circular Cylinder ◽  
Oscillatory Flow ◽  
Three Dimensional ◽  
Hydrodynamic Forces ◽  
Transverse Force ◽  
Vortex Structures ◽  
Time Development ◽  
Two Dimensional ◽  
Wide Range ◽  
Three Dimensional Simulations

The oscillatory flow around a circular cylinder close to a plane wall is investigated numerically, by direct numerical simulation of the Navier–Stokes equations. The main aim of the research is to gain insight into the effect of the wall on the vorticity dynamics and the forces induced by the flow over the cylinder. First, two-dimensional simulations are performed for nine values of the gap-to-diameter ratio e. Successively, three-dimensional simulations are carried out for selected cases to analyse the influence of the gap on the three-dimensional organization of the flow. An attempt to explain the pressure distribution around the cylinder in terms of vorticity time development is presented. Generally, the time development of the hydrodynamic forces is aperiodic (i.e. changes from cycle to cycle). In one case (Re = 200), when the distance of the cylinder from the wall is reduced, the behaviour of the flow changes from aperiodic to periodic. When the cylinder approaches the wall the drag coefficient of the in-line force increases in a qualitative agreement with the results reported in literature. The transverse force is not monotonic with the reduction of the gap: it first decreases down to a minimum, and then increases with a further reduction of the gap. For intermediate values of the gap the decrease of the transverse force is due to the reduction of the angle of ejection of the shedding vortices caused by the closeness of the wall; for small gaps the increase of the transverse force is due to the strong interaction between the vortex system ejected from the cylinder and the shear layer generated on the wall.Three-dimensional simulations show that the flow is unstable with respect to spanwise perturbations which cause the development of three-dimensional vortices and the distortion of the two-dimensional ones generated by flow separation.In all the analysed cases, the three-dimensional effects on the hydrodynamic forces are clearly attenuated when the cylinder is placed close to the wall.The spanwise modulation of the vortex structures induces oscillations of the sectional forces along the axis of the cylinder which in general are larger for the transverse sectional force. In the high-Reynolds-number case (Re = 500), the reduction of the gap produces a large number of three-dimensional vortex structures developing over a wide range of spatial scales. This produces homogenization of the flow field along the spanwise direction and a consequent reduction of the amplitudes of oscillation of the sectional forces.

Numerical and Experimental Investigation on the Flow Induced Oscillations of a Single-Blade Pump Impeller

2005 ◽  
Vol 128 (4) ◽  
pp. 783-793 ◽  
Author(s):  
F.-K. Benra
Keyword(s):  
Stokes Equations ◽  
Sewage Water ◽  
Hydrodynamic Forces ◽  
Time Dependent ◽  
Outer Side ◽  
Water Pump ◽  
Pump Rotor ◽  
Wide Range ◽  
Dependent Flow ◽  
Blade Pump

This contribution is addressed to the periodically unsteady flow forces of a single-blade sewage water pump, which affect the impeller and produce radial deflections of the pump shaft. The hydrodynamic excitation forces were calculated from the time dependent flow field, which was computed by numerical simulation of the three-dimensional, viscous, time-dependent flow in the pump. A commercial computer code was used to determine the time accurate Reynolds averaged Navier-Stokes equations. The transient radial flow forces at all time steps for a complete impeller revolution affect the rotor of the single-blade pump and stimulate it to strong oscillations. To determine the influence of the vibration stimulation forces on the dynamic behavior of the pump rotor, an investigation of the rotor’s structural dynamics was accomplished. A dynamic time analysis for the pump rotor provided the dynamic answer from the structural model of the rotor under the influence of the flow forces. The hydrodynamic forces, which were calculated before, were defined as external forces and applied as the load on the rotor. The resulting impeller deflections were calculated by a transient analysis of the pump rotor system using the commercial finite element method software PROMECHANICA. To verify the results obtained by standard numerical methods, the radial deflections of the impeller of a commercial sewage water pump, which has been investigated numerical in advance, were measured for the horizontal and for the vertical coordinate direction by proximity sensors. The measured data were compared to the computed amounts for a wide range of pump operation. The results show a good agreement for a strong part of an impeller revolution for all investigated operating points. The simultaneous measurement of vibration accelerations at the outer side of the pump casing showed the effects of the time-dependent flow, which produce hydrodynamic forces acting at the impeller of the pump and stimulating it to strong oscillations.

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