Torsional Oscillations of a Shape-Morphing Plate in Viscous Fluids

2019 ◽  
Author(s):  
Syed N. Ahsan ◽  
Matteo Aureli
Keyword(s):  
Power Dissipation ◽  
Stokes Equations ◽  
Oscillation Amplitude ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Torsional Oscillations ◽  
Shape Morphing ◽  
Moment Control ◽  
Interaction Problem

Abstract In this paper, we investigate finite amplitude torsional oscillations of a shape-morphing plate submerged in a quiescent, Newtonian, incompressible fluid. To address this problem, we focus on a two-dimensional cross section of the plate and para-metrically study hydrodynamic moments and power dissipation during the plate oscillation as a function of the shape-morphing deformation intensity and the oscillation amplitude. This fluid-structure interaction problem is tackled within the framework of a computational fluid dynamics model where the fluid flow is described via the Navier-Stokes equations and the deformations of the structure are prescribed. The results demonstrate a gradual reduction of hydrodynamic moment and nonmonotonic power dissipation behavior as the imposed shape-morphing becomes more aggressive. In addition, power dissipation can be minimized for an optimum value of the shape-morphing intensity. Results from this study are relevant in underwater systems subjected to torsional oscillations and demonstrate an avenue for hydrodynamic moment control and reduction of energy losses.

scholarly journals Stokes’s Fundamental Contributions to Fluid Dynamics

2019 ◽  
pp. 115-128
Author(s):  
Peter Lynch
Keyword(s):  
Fluid Dynamics ◽  
Water Waves ◽  
Stokes Equations ◽  
Weather Prediction ◽  
Finite Amplitude ◽  
The Body ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Basic Equations ◽  
Primary Focus

George Gabriel Stokes made fundamental mathematical contributions to fluid dynamics that had profound practical consequences. The basic equations formulated by him play a central role in numerical weather prediction, in the simulation of blood flow in the body and in countless other important applications. In this chapter the primary focus is on the two most important areas of Stokes’s work on fluid dynamics, the derivation of the Navier–Stokes equations and the theory of finite amplitude oscillatory water waves.

scholarly journals SHOALING OF FINITE-AMPLITUDE WAVES ON PLANE BEACHES

1970 ◽  
Vol 1 (12) ◽  
pp. 21
Author(s):  
Robert K-C Chan ◽  
Robert L. Street
Keyword(s):  
Water Waves ◽  
Stokes Equations ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Finite Difference Equations ◽  
Rectangular Mesh ◽  
Finite Amplitude Waves ◽  
Large Water ◽  
Marker And Cell Method

This work focuses on the shoaling of large water waves with particular application to storm-generated waves and tsunamis The specific objective is the exact simulation on a digital computer of finite-amplitude waves advancing on a beach of constant slope The study is based on the simulation technique called SUMMAC (the Stanford-University-Modified Marker-And-Cell Method) The flow field is represented by a rectangular mesh of cells and by a line of hypothetical particles which defines the free surface Based on the Navier-Stokes equations, finite-difference equations were derived so that the entire flow configuration could be advanced through a finite increment of time The pressure and velocity components are used directly as the dependent variables Through extensive analyses and numerical experiments, this scheme was found to be computationally stable if the cell size and the time increment are properly selected As a specific example, the dynamics of a solitary wave passing from a zone of constant depth onto a sloping beach were simulated Primary attention was focused on the details of the water particle motions and the changes in the amplitude and shape of the wave as it climbed the slope The computed results are compared with the experiments with good agreement.

Numerical Simulation of Vortex Induced Vibration on an Elastically Mounted Cylinder

2004 ◽  
Author(s):  
Juan B. V. Wanderley ◽  
Carlos A. Levi
Keyword(s):  
Stokes Equations ◽  
Oscillation Amplitude ◽  
High Sensitivity ◽  
Flow Speed ◽  
Navier Stokes ◽  
Experimental Measurements ◽  
Navier Stokes Equations ◽  
Vortex Induced Vibration ◽  
Set Up ◽  
Lock In

The Vortex-induced vibration on a circular cylinder is investigated by the numerical solution of the unsteady Reynolds Average Navier-Stokes equations and results are compared with experimental measurements obtained by different authors. The Beam and Warming implicit factored scheme is used to solve the governing equations and the Baldwin and Lomax model is used to simulate the turbulent flow in the wake of the cylinder. The cylinder is laterally supported by a spring and a damper and is free to oscillate in the transversal direction in an initially uniform flow for the first flow speed investigated. For the subsequent speeds, the final condition obtained for the previous speed is used as initial condition to reproduce the actual experimental set up. In that case, the measurements are done by progressive increments of the flow speed retaining the fluid memory effect. The complexity and high sensitivity of the flow phenomenon at this configuration requires a very accurate and robust numerical model. Most of the known algorithms failed to duplicate the available experimental measurements. The numerical results for the transversal oscillation amplitude are compared to experimental data showing a fairly precise agreement at the difficult to simulate regime of the lock-in phenomenon.

Numerical study of ribbon-induced transition in Blasius flow

1987 ◽  
Vol 178 ◽  
pp. 345-365 ◽  
Author(s):  
Philippe R. Spalart ◽  
Kyung-Soo Yang
Keyword(s):  
Stokes Equations ◽  
Numerical Study ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equations ◽  
Random Disturbances ◽  
Rapid Amplification ◽  
Dimensional Wave

The early three-dimensional stages of transition in the Blasius boundary layer are studied by numerical solution of the Navier-Stokes equations. A finite-amplitude two-dimensional wave and low-amplitude three-dimensional random disturbances are introduced. Rapid amplification of the three-dimensional components is observed and leads to transition. For intermediate amplitudes of the two-dimensional wave the breakdown is of subharmonic type, and the dominant spanwise wavenumber increases with the amplitude. For high amplitudes the energy of the fundamental mode is comparable to the energy of the subharmonic mode, but never dominates it; the breakdown is of mixed type. Visualizations, energy histories, and spectra are presented. The sensitivity of the results to various physical and numerical parameters is studied. The agreement with experimental and theoretical results is discussed.

Interaction of a deformable free surface with statistically steady homogeneous turbulence

2010 ◽  
Vol 658 ◽  
pp. 33-62 ◽  
Author(s):  
XIN GUO ◽  
LIAN SHEN
Keyword(s):  
Free Surface ◽  
Surface Deformation ◽  
Stokes Equations ◽  
Pseudospectral Method ◽  
Vertical Direction ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Surface Boundary ◽  
Navier Stokes Equations ◽  
Surface Boundary Conditions

Direct numerical simulation is performed for the interaction between a deformable free surface and the homogeneous isotropic turbulent flow underneath. The Navier–Stokes equations subject to fully nonlinear free-surface boundary conditions are simulated by using a pseudospectral method in the horizontal directions and a finite-difference method in the vertical direction. Statistically, steady turbulence is generated by using a linear forcing method in the bulk flow below. Through investigation of cases of different Froude and Weber numbers, the present study focuses on the effect of surface deformation of finite amplitude. It is found that the motion of the free surface is characterized by propagating waves and turbulence-generated surface roughness. Statistics of the turbulence field near the free surface are analysed in detail in terms of fluctuations of velocity, fluctuations of velocity gradients and strain rates and the energy budget for horizontal and vertical turbulent motions. Our results illustrate the effects of surface blockage and vanishing shear stress on the anisotropy of the flow field. Using conditional averaging analysis, it is shown that splats and antisplats play an essential role in energy inter-component exchange and vertical transport.

scholarly journals Vorticity evolution in perturbed Poiseuille flow

2013 ◽  
Vol 40 (1) ◽  
pp. 71-86
Author(s):  
Milos Jovanovic
Keyword(s):  
Poiseuille Flow ◽  
Chebyshev Polynomials ◽  
Stokes Equations ◽  
Hydrodynamic Instability ◽  
Finite Amplitude ◽  
Trigonometric Polynomials ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Vorticity Evolution ◽  
Sommerfeld Equation

We consider numerical simulation of temporal hydrodynamic instability with finite amplitude perturbations in plane incompressible Poiseuille flow. Two dimensional Navier Stokes equations have been used and reduced to vorticity-stream function form. Trigonometric polynomials have been used in homogeneous direction and Chebyshev polynomials in inhomogeneous direction. The problem of boundary conditions for vorticity has been solved by using the method of influence matrices. The Orr-Sommerfeld equation has been solved by Chebyshev polynomials, and linear combination of the obtained eigenfunctions has been optimized with regard to the corresponding eigenvalue. We present here the results of simulation for the perturbations optimized in regard to the least stable eigenvalue for the Reynolds number Re=1000.

scholarly journals Nonlinear control of unsteady finite-amplitude perturbations in the Blasius boundary-layer flow

2013 ◽  
Vol 737 ◽  
pp. 440-465 ◽  
Author(s):  
S. Cherubini ◽  
J.-C. Robinet ◽  
P. De Palma
Keyword(s):  
Stokes Equations ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Control Procedure ◽  
Normal Velocity ◽  
Optimal Control Strategy ◽  
Navier Stokes Equations ◽  
Target Time ◽  
Layer Flow ◽  
Laminar State

AbstractThe present work provides an optimal control strategy, based on the nonlinear Navier–Stokes equations, aimed at hampering the rapid growth of unsteady finite-amplitude perturbations in a Blasius boundary-layer flow. A variational procedure is used to find the blowing and suction control law at the wall providing the maximum damping of the energy of a given perturbation at a given target time, with the final aim of leading the flow back to the laminar state. Two optimally growing finite-amplitude initial perturbations capable of leading very rapidly to transition have been used to initialize the flow. The nonlinear control procedure has been found able to drive such perturbations back to the laminar state, provided that the target time of the minimization and the region in which the blowing and suction is applied have been suitably chosen. On the other hand, an equivalent control procedure based on the linearized Navier–Stokes equations has been found much less effective, being not able to lead the flow to the laminar state when finite-amplitude disturbances are considered. Regions of strong sensitivity to blowing and suction have been also identified for the given initial perturbations: when the control is actuated in such regions, laminarization is also observed for a shorter extent of the actuation region. The nonlinear optimal blowing and suction law consists of alternating wall-normal velocity perturbations, which appear to modify the core flow structures by means of two distinct mechanisms: (i) a wall-normal velocity compensation at small times; (ii) a rotation-counterbalancing effect al larger times. Similar control laws have been observed for different target times, values of the cost parameter, and streamwise extents of the blowing and suction zone, meaning that these two mechanisms are robust features of the optimal control strategy, provided that the nonlinear effects are taken into account.

Nonlinear Theory of Tear Film Rupture

2000 ◽  
Vol 122 (5) ◽  
pp. 498-503 ◽  
Author(s):  
Madhu Sudan Reddy Gorla ◽  
Rama Subba Reddy Gorla
Keyword(s):  
Body Force ◽  
Stokes Equations ◽  
Tear Film ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Force Term ◽  
Initial Value ◽  
Film Rupture ◽  
Navier Stokes Equations ◽  
The Stability

Nonlinear thin film rupture has been analyzed by investigating the stability of tear films to finite amplitude disturbances. The dynamics of the liquid film is formulated using the Navier–Stokes equations, including a body force term due to van der Waals attractions. The governing equation was solved by the finite difference method as part of an initial value problem for spatial periodic boundary conditions. The rupture of the tear film covering the cornea and the formation of dry spots is an important phenomenon in various pathological states associated with a dry eye. [S0148-0731(00)00605-1]

Effect of Electrostatic Field on Film Rupture

1999 ◽  
Vol 121 (3) ◽  
pp. 651-655 ◽  
Author(s):  
Rama Subba Reddy Gorla ◽  
Larry W. Byrd
Keyword(s):  
Electric Field ◽  
Electrostatic Field ◽  
Body Force ◽  
Stokes Equations ◽  
Finite Amplitude ◽  
Navier Stokes ◽  
Film Rupture ◽  
Navier Stokes Equations ◽  
Long Wavelength ◽  
The Stability

Nonlinear thin film rupture has been analyzed by investigating the stability of films under the influence of a nonuniform electrostatic field to finite amplitude disturbances. The dynamics of the liquid film is formulated using the Navier-Stokes equations including a body force term due to van der Waals attractions. The effect of the electric field is included in the analysis only in the boundary condition at the liquid vapor interface. The governing equation was solved by finite difference method as part of an initial value problem for spatial periodic boundary conditions. The electric field stabilizes the film and increases the time to rupture when a long wavelength perturbation is introduced.

scholarly journals Passive separation control using a self-adaptive hairy coating

2009 ◽  
Vol 627 ◽  
pp. 451-483 ◽  
Author(s):  
JULIEN FAVIER ◽  
ANTOINE DAUPTAIN ◽  
DAVIDE BASSO ◽  
ALESSANDRO BOTTARO
Keyword(s):  
Circular Cylinder ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Separation Control ◽  
Test Case ◽  
Navier Stokes Equations ◽  
Partitioned Approach ◽  
Passive Separation ◽  
Two Dimensional Flow ◽  
Interaction Problem

A model of hairy medium is developed using a homogenized approach, and the fluid flow around a circular cylinder partially coated with hair is analysed by means of numerical simulations. The capability of this coating to adapt to the surrounding flow is investigated, and its benefits are discussed in the context of separation control. This fluid–structure interaction problem is solved with a partitioned approach, based on the direct resolution of the Navier–Stokes equations together with a nonlinear set of equations describing the dynamics of the coating. A volume force, arising from the presence of a cluster of hair, provides the link between the fluid and the structure problems. For the structure part, a subset of reference elements approximates the whole layer. The dynamics of these elements is governed by a set of equations based on the inertia, elasticity, interaction and losses effects of articulated rods. The configuration chosen is that of the two-dimensional flow past a circular cylinder at Re = 200, a simple and well-documented test case. Aerodynamics performances quantified by the Strouhal number, the drag and the maximum lift in the laminar unsteady regime are modified by the presence of the coating. A set of parameters corresponding to a realistic coating (length of elements, porosity, rigidity) is found, yielding an average drag reduction of 15% and a decrease of lift fluctuations by about 40%, associated to a stabilization of the wake.

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