Kostas Karagiozis

A low numerical dissipation immersed interface method for the compressible Navier-Stokes equations

A numerical method to solve the compressible Navier-Stokes equations around objects of arbitrary shape using Cartesian grids is described. The approach considered here uses an embedded geometry representation of the objects and approximate the governing equations with a low numerical dissipation centered finite-difference discretization. The method is suitable for compressible flows without shocks and can be classified as an immersed interface method. The objects are sharply captured by the Cartesian mesh by appropriately adapting the discretization stencils around the irregular grid nodes, located around the boundary. In contrast with available methods, no jump conditions are used or explicitly derived from the boundary conditions, although a number of elements are adopted from previous immersed interface approaches. A new element in the present approach is the use of the summation-by-parts formalism to develop stable non-stiff first-order derivative approximations at the irregular grid points. Second-order derivative approximations, as those appearing in the transport terms, can be stiff when irregular grid points are located too close to the boundary. This is addressed using a semi-implicit time integration method. Moreover, it is shown that the resulting implicit equations can be solved explicitly in the case of constant transport properties. Convergence studies are performed for a rotating cylinder and vortex shedding behind objects of varying shapes at different Mach and Reynolds numbers.

Computational fluid-structure interaction methods for simulation of inflatable aerodynamic decelerators

Inflatable aerodynamic decelerators have potential advantages for planetary re-entry in robotic and human exploration missions. It is theorized that volume-mass characteristics of these decelerators are superior to those of common supersonic/subsonic parachutes and after deployment they may suffer no instabilities at high Mach numbers. A high fidelity computational fluid-structure interaction model is employed to investigate the behavior of tension cone inflatable aeroshells at supersonic speeds up to Mach 2.0. The computational framework targets the large displacements regime encountered during the inflation of the decelerator using fast level set techniques to incorporate boundary conditions of the moving structure. The preliminary results indicate large but steady aeroshell displacement with rich dynamics, including buckling of the inflatable torus that maintains the decelerator open under normal operational conditions, owing to interactions with the turbulent wake. Copyright

Stability and Non-Linear Dynamics of Clamped Circular Cylindrical Shells in Contact with Flowing Fluid

This study presents experimental results on the non-linear dynamics and stability characteristics of a thin-walled clamped-clamped circular cylindrical shell in contact with fluid. It also discusses theoretical results for simply-supported shells conveying inviscid and incompressible fluid. The non-linear Donnell shallow shell theory, with structural damping, is used to describe the large-amplitude shell vibrations. The interaction between the flowing fluid and the shell structure is formulated with linear potential flow theory. The aim of the experimental study was to gather for the first time important data points of the critical flow velocity for instability and maximum flexural displacement, and to analyze the experimental results to validate the theoretical model. The experimental study involved two set-ups: one containing a clamped-clamped silicone rubber shell and flowing air in internal and external flow configurations, and the second an aluminum shell and water as the flowing fluid. The interaction between the shell and the fully developed flow, in both cases, gives instabilities in the form of divergence at sufficiently high flow velocities. The experimental results show a softening type nonlinear behaviour with a large hysteresis in the velocity for the onset and cessation of divergence.

Nonlinear Vibration of Plates and Higher Order Theory for Different Boundary Conditions

There are numerous applications of plate structures found in structural, aerospace and marine engineering. The present study extends the previous work by Amabili and Sirwan [1] investigating the performance of isotropic and laminate composite rectangular plates with different boundary conditions subjected to an external point force with an excitation frequency that lies in the neighbourhood of the fundamental mode of the plate. The analysis is performed using three different nonlinear plate theories, namely: i) the classical Von Karman theory, ii) first-order shear deformation theory, and iii) third-order shear deformation theory. Three different boundary conditions are considered in the investigation: a) classical clamped boundary conditions, b) simply-supported ends with immovable edges, and c) simply-supported ends with movable boundaries. In addition, the effect of thickness was also considered in the analysis and different values for the plate thickness were assumed. The results investigate the accuracy of lower order theories versus higher order shear deformation theories, the effect of boundary conditions and highlight the differences in the responses obtained from isotropic and laminate composite rectangular plates.Copyright

Computational fluid-structure interaction of DGB parachutes in compressible fluid flow

This paper describes large-scale simulations of compressible flows over a supersonic disk-gap-band parachute system. An adaptive mesh refinement method is used to resolve the coupled fluid-structure model. The fluid model employs large-eddy simulation to describe the turbulent wakes appearing upstream and downstream of the parachute canopy and the structural model employed a thin-shell finite element solver that allows large canopy deformations by using subdivision finite elements. The fluid-structure interaction is described by a variant of the Ghost-Fluid method. The simulation was carried out at Mach number 1.96 where strong nonlinear coupling between the system of bow shocks, turbulent wake and canopy is observed. It was found that the canopy oscillations were characterized by a breathing type motion due to the strong interaction of the turbulent wake and bow shock upstream of the flexible canopy.Copyright

Hyperchaotic Behaviour of Shells Subjected to Flow and External Force

This study treats the nonlinear behaviour of cylindrical shells subjected to internal fluid flow and to an external periodic transverse point force. The shell is supported at both ends by axial and rotational springs capable of simulating boundary conditions ranging from clamped to simple supports. This complex boundary condition configuration is preferred in our analysis in order to be able to compare theoretical findings with water-tunnel experiments available in the literature. The external concentrated point force is applied at mid-length of the immersed shell structure acting in the radial direction and the excitation frequency values lie within the spectral neighbourhood of one of the shell’s lowest frequencies for different flow velocities. The structural model is based on the full nonlinear Donnell shell equations of motion including the effect of the in-plane inertia and accounting for geometric imperfections. The fluid is assumed to be incompressible and inviscid and the flow isentropic and irrotational; it is modelled using potential flow theory with the addition of unsteady viscous terms obtained from the time-averaged Navier-Stokes equations. The coupled system is discretized using a solution expansion based on trigonometric functions satisfying the shell boundary conditions exactly. Numerical results show the nonlinear response at different flow velocities for (i) a fixed excitation amplitude and variable excitation frequency, and (ii) fixed excitation frequency varying the excitation amplitude. Bifurcation diagrams of Poincare maps obtained from direct time integration are presented, as well as the maximum Lyapunov exponent, in order to classify the system dynamics. In particular, periodic, quasi-periodic, sub-harmonic and chaotic responses have been detected. The full spectrum of the Lyapunov exponents and the Lyapunov dimension have been calculated for the chaotic response; they reveal the occurrence of large-dimension hyperchaos.Copyright

Chaotic Vibrations of Circular Shells Conveying Flowing Fluid

Shells containing flowing fluids are widely used in engineering applications, and they are subject to manifold excitations of different kinds, including flow excitations. Usually these shells are made as thin as possible for weight and cost economy; therefore, they are quite fragile, and their response to such excitations is of great interest. The response of a shell conveying fluid to harmonic excitation, in the spectral neighbourhood of one of the lowest natural frequencies, is investigated for different flow velocities. The theoretical model has been developed using the Donnell theory retaining in-plane inertia. Linear potential flow theory is applied to describe the fluid-structure interaction, and the steady viscous effects are added to take into account flow viscosity. For different amplitudes and frequencies of the excitation and for different flow velocities, the following are investigated numerically: (i) periodic response of the system; (ii) unsteady and stochastic motion; (iii) loss of stability by jumps to bifurcated branches. The effect of the flow velocity on the nonlinear periodic response of the system has also been investigated. Poincare maps, bifurcation diagrams and Lyapunov exponents have been used to study the unsteady and stochastic dynamics of the system.Copyright

Nonlinear Vibrations and Stability of Shells Conveying Water Flow

Shells containing flowing fluids are widely used in engineering applications, and they are subject to manifold excitations of different kinds, including flow excitations. The response of a shell conveying fluid to harmonic excitation, in the spectral neighbourhood of one of the lowest natural frequencies, is investigated for different flow velocities. The theoretical model has been developed using the Donnell theory retaining in-plane inertia. Linear potential flow theory is applied to describe the fluid-structure interaction, and the steady viscous effects are added to take into account flow viscosity. For different amplitudes and frequencies of the excitation and for different flow velocities, the following are investigated numerically: (i) periodic response of the system; (ii) unsteady and stochastic motion; (iii) loss of stability by jumps to bifurcated branches. The effect of the flow velocity on the nonlinear periodic response of the system has also been investigated. Bifurcation diagrams and Lyapunov exponents have been used to study the unsteady and stochastic dynamics of the system.© 2009 ASME