B. C. Khoo

Experimental and numerical investigation of the dynamics of an underwater explosion bubble near a resilient/rigid structure

This paper deals with an experimental and numerical study of the dynamics of an underwater explosion and its associated fluid–structure interaction. Experimental studies of the complex fluid–structure interaction phenomena were carried out in a specially designed test pond. The pond is equipped with a high-speed camera and pressure and displacement sensors. The high-speed camera was used to capture the expansion and collapse of the gas bubble created by the explosion. Several different structures were used in the experiments, including both rigid and resilient plates of circular shape. The deformation of the plate was measured with a non-contact laser telemetry device. The numerical simulations of the explosion bubble interacting with a submerged resilient structure were performed using a three-dimensional bubble dynamics code in conjunction with a structural code. The bubble code is based on the boundary-element method (BEM) and has been coupled to a structural finite-element code (PAM-CRASH

Strong Interaction Between a Buoyancy Bubble and a Free Surface

^{\rm TM})

An implicit immersed boundary method for three-dimensional fluid-membrane interactions

. The experimental results were compared against the numerical results for different bubble–structure configurations and orientations. Several physical phenomena that have been observed, such as bubble jetting and bubble migration towards the structure are discussed.

On the boundary integral method for the rebounding bubble

The growth and collapse of buoyant vapor bubbles close to a free surface in an inviscid incompressible fluid is investigated in this paper. The strong interaction between the deforming bubble and the free surface is simulated numerically by a boundary-integral method (Taib 1985; Blake et al., 1987). Improvements are made in the calculation of the singular integrals, the use of nonuniform boundary elements, and the choice of time-step size. The present numerical results agree better with the experimental observations of Blake and Gibson (1981) than previous numerical predictions for bubbles initiated at one maximum radius from the free surface. There is also concurrence of flow features with the experiments for a bubble initiated as close as half maximum radius from the free surface, where other numerical efforts have failed. The effects of buoyancy on bubbles initiated close to a free surface are also investigated. Vastly different features, depending on the distance of the bubble to the free surface and the buoyancy-force parameter, have been observed.

Numerical simulation of nanosecond pulsed dielectric barrier discharge actuator in a quiescent flow

We present an implicit immersed boundary method for the incompressible Navier-Stokes equations capable of handling three-dimensional membrane-fluid flow interactions. The goal of our approach is to greatly improve the time step by using the Jacobian-free Newton-Krylov method (JFNK) to advance the location of the elastic membrane implicitly. The most attractive feature of this Jacobian-free approach is Newton-like nonlinear convergence without the cost of forming and storing the true Jacobian. The Generalized Minimal Residual method (GMRES), which is a widely used Krylov-subspace iterative method, is used to update the search direction required for each Newton iteration. Each GMRES iteration only requires the action of the Jacobian in the form of matrix-vector products and therefore avoids the need of forming and storing the Jacobian matrix explicitly. Once the location of the boundary is obtained, the elastic forces acting at the discrete nodes of the membrane are computed using a finite element model. We then use the immersed boundary method to calculate the hydrodynamic effects and fluid-structure interaction effects such as membrane deformation. The present scheme has been validated by several examples including an oscillatory membrane initially placed in a still fluid, capsule membranes in shear flows and large deformation of red blood cells subjected to stretching force.

Turbulent boundary layer over a compliant surface: absolute and convective instabilities

The formation of a toroidal bubble towards the end of the bubble collapse stage in the neighbourhood of a solid boundary has been successfully studied using the boundary integral method. The further evolution (rebound) of the toroidal bubble is considered with the loss of system energy taken into account. The energy loss is incorporated into a mathematical model by a discontinuous jump in the potential energy at the minimum volume during the short collapse–rebound period accompanying wave emission. This implementation is first tested with the spherically oscillating bubble system using the theoretical Rayleigh–Plesset equation. Excellent agreement with experimental data for the bubble radius evolution up to three oscillation periods is obtained. Secondly, the incorporation of energy loss is tested with the motion of an oscillating bubble system in the neighbourhood of a rigid boundary, in an axisymmetric geometry, using a boundary integral method. Example calculations are presented to demonstrate the possibility of capturing the peculiar entity of a counterjet, which has been reported only in recent experimental studies.

An Immersed Interface Method for the Incompressible Navier-Stokes Equations with Discontinuous Viscosity Across the Interface

We present a numerical study of nanosecond pulsed dielectric barrier discharge (DBD) actuator operating in quiescent air at atmospheric condition. Our study concentrates on plasma discharge induced fluid dynamics and on exploration of parametric space of interest for voltage pulse in an attempt to shed some light into elucidation of the mechanisms whereby the generated shock wave propagates through and affects the external flow. Specifically, a one-dimensional, self-similar, local ionization kinetic model recently developed to predict key parameters of nanosecond pulsed plasma discharge is coupled with the compressible Navier-Stokes equations possibly for the first time. Within the considered range of parameters of the plasma model which is justified for the modeling of surface nanosecond pulsed discharge at atmospheric pressure, our coupled method is able to provide satisfactory prediction of the shock structure generated by the actuator for comparison with experiment, not only in the qualitative shock wave shape but also in quantitative shock front displacement. We provide a comprehensive analysis of the gas heating, shock wave initiation and evolution processes. For example, the characteristic time of the rapid localized heating responsible for shock wave generation, which is yet to be quantified experimentally, is found to be ∼350 ns. We conduct a parametric investigation by varying the peak voltage from 10 kV to 50 kV and rise time from 5 ns to 150 ns. The pressure wave whose behavior is found to be dominated by input voltage amplitude, introduces highly transient, localized disturbance to the quiescent air. In addition, the vortex induced by the shock passage is relatively weak. The interplay of the induced flows by a few successive plasma discharges operating at continuous mode does not appear to be significant, especially at low voltage amplitude.

An immersed interface method for Stokes flows with fixed/moving interfaces and rigid boundaries

A theoretical model for the instability of two-dimensional turbulent boundary layer over compliant surfaces is described. The principal Reynolds stress is modelled by a well-established mixing-length eddy-viscosity formulation of van Driest. The perturbations of the mean velocity and Reynolds stress fields are coupled via the turbulence model. The investigation of instability is carried out from a time-asymptotic spatio-temporal perspective that classifies instabilities as being either convective or absolute. The occurrence of convective and absolute instabilities over viscoelastic compliant layers is elucidated. Compliant surfaces with low damping are susceptible to convective instability, which gives way to an absolute instability when the surfaces become highly damped. The theoretical results are compared against experimental observations of surface waves on elastic and viscoelastic compliant layers.

Application of GDQ scheme to simulate natural convection in a square cavity

Abstract SWe present an immersed interface algorithm forthe incompressible Navier Stokes equations. The interface isrepresented by cubic splines which are interpolated through aset of Lagrangian control points. The position of the controlpoints is implicitly updated using the uid velocity. The forcesthat the interface exerts on the uid are computed from theconstitutive relation of the interface and are applied to the uidthrough jumps in the pressure and jumps in the derivativesof pressure and velocity. A projection method is used to timeadvance the Navier-Stokes equations on a uniform cartesianmesh. The Poisson-like equations required for the implicit so-lution of the diffusive and pressure terms are solved using afast Fourier transform algorithm. The position of the interface isupdated implicitly using a quasi-Newton method (BFGS) withineach timestep. Several examples are presented to illustrate theexibility of the presented approach. I. I NTRODUCTION We consider an incompressible uid in a 2-dimensionaldomainthat contains a material interface (t). The Navier-Stokes equations are written as,

The flow between a rotating and a stationary disc : application to near-wall hot-wire calibration

We present an immersed interface method for solving the incompressible steady Stokes equations involving fixed/moving interfaces and rigid boundaries (irregular domains). The fixed/moving interfaces and rigid boundaries are represented by a number of Lagrangian control points. In order to enforce the prescribed velocity at the rigid boundaries, singular forces are applied on the fluid at these boundaries. The strength of singular forces at the rigid boundary is determined by solving a small system of equations. For the deformable interfaces, the forces that the interface exerts on the fluid are calculated from the configuration (position) of the deformed interface. The jumps in the pressure and the jumps in the derivatives of both pressure and velocity are related to the forces at the fixed/moving interfaces and rigid boundaries. These forces are interpolated using cubic splines and applied to the fluid through the jump conditions. The positions of the deformable interfaces are updated implicitly using a quasi-Newton method (BFGS) within each time step. In the proposed method, the Stokes equations are discretized via the finite difference method on a staggered Cartesian grid with the incorporation of jump contributions and solved by the conjugate gradient Uzawa-type method. Numerical results demonstrate the accuracy and ability of the proposed method to simulate incompressible Stokes flows with fixed/moving interfaces on irregular domains.