G. Pascazio

An immersed boundary method for compressible flows using local grid refinement

This paper combines a state-of-the-art method for solving the three-dimensional preconditioned Navier-Stokes equations for compressible flows with an immersed boundary approach, to provide a Cartesian-grid method for computing complex flows over a wide range of the Mach number. Moreover, a flexible local grid refinement technique is employed to achieve high resolution near the immersed body and in other high-flow-gradient regions at a fraction of the cost required by a uniformly fine grid. The method is validated versus well documented steady and unsteady test problems, for a wide range of both Reynolds and Mach numbers. Finally, and most importantly, for the case of the laminar compressible steady flow past an NACA-0012 airfoil, a thorough mesh-refinement study shows that the method is second-order accurate.

The preferential targeting of the diseased microvasculature by disk-like particles

Different classes of nanoparticles (NPs) have been developed for controlling and improving the systemic administration of therapeutic and contrast agents. Particle shape has been shown to be crucial in the vascular transport and adhesion of NPs. Here, we use mesoporous silicon non-spherical particles, of disk and rod shapes, ranging in size from 200nm to 1800nm. The fabrication process of the mesoporous particles is described in detail, and their transport and adhesion properties under flow are studied using a parallel plate flow chamber. Numerical simulations predict the hydrodynamic forces on the particles and help in interpreting their distinctive behaviors. Under microvascular flow conditions, for disk-like shape, 1000×400nm particles show maximum adhesion, whereas smaller (600×200nm) and larger (1800×600nm) particles adhere less by a factor of about two. Larger rods (1800×400nm) are observed to adhere at least 3 times more than smaller ones (1500×200nm). For particles of equal volumes, disks adhere about 2 times more than rods. Maximum adhesion for intermediate sized disks reflects the balance between adhesive interfacial interactions and hydrodynamic dislodging forces. In view of the growing evidence on vascular molecular heterogeneity, the present data suggests that thin disk-like particles could more effectively target the diseased microvasculature as compared to spheres and slender rods.

A review of vorticity conditions in the numerical solution of the ζ-ψ equations

Abstract In this review the conditions to be imposed on the vorticity in the calculation of two-dimensional incompressible viscous flows are discussed. Existing boundary vorticity formulas, commonly regarded as a surrogate Dirichlet boundary condition for the vorticity, are more properly interpreted as the discrete counterpart of the Neumann boundary condition for the stream function. This viewpoint helps to elucidate the algebraic equivalence of coupled numerical methods with uncoupled methods based on conditions of integral type for the vorticity. A unified understanding of several available treatments for determining correct vorticity boundary values is achieved by including in the present analysis spatial discretizations by finite differences and finite elements, coupled and uncoupled formulations of the problem as well as steady and unsteady equations. Results of some test calculations are presented to illustrate the numerical consequences of the analysis.

Turbulent thermal convection over grooved plates

Direct numerical simulations of thermal convection over grooved plates are presented and discussed, in comparison with the standard flat-plate case, in order to gain a better understanding of the altered near-wall dynamics and of the enhancement of the heat transfer. The simulations are performed in a cylindrical cell of aspect-ratio (diameter over cell height) r = 1/2 at fixed Prandtl number Pr = 0.7 with the Rayleigh number Ra ranging from 2 × 10 6 to 2 × 10 11 . The results show an increase of heat transfer, or in non-dimensional form the Nusselt number Nu, when the mean thermal boundary-layer thickness becomes smaller than the groove height, in agreement with earlier experimental investigations available from the literature. The present increase, however, results in a steeper power law of the Nu vs. Ra law rather than a simple upward shift of the Nu law of the flat plate. This finding agrees with some studies, but it is at variance with others. Possible causes for this difference are discussed with the help of an electrical analogy.

A numerical method for turbomachinery aeroelasticity

This work provides an accurate and efficient numerical method for turbomachinery flutter. The unsteady Euler or Reynolds-averaged Navier-Stokes equations are solved in integral form, the blade passages being discretised using a background fixed C-grid and a body-fitted C-grid moving with the blade. In the overlapping region data are exchanged between the two grids at every time step, using bilinear interpolation. The method employs Roes second-order-accurate flux difference splitting scheme for the inviscid fluxes, a standard second-order discretisation of the viscous terms, and a three-level backward difference formula for the time derivatives. The dual-time-stepping technique is used to evaluate the nonlinear residual at each time step. The state-of-the-art second-order accuracy of unsteady transonic flow solvers is thus carried over to flutter computations. The code is proven to be accurate and efficient by computing the 4th Aeroelastic Standard Configuration, namely, the subsonic flow through a turbine cascade with flutter instability in the first bending mode, where viscous effect are found practically negligible. Then, for the very severe 11th Aeroelastic Standard Configuration, namely, transonic flow through a turbine cascade at off-design conditions, benchmark solutions are provided for various values of the inter-blade phase angle.

Third-order-accurate fluctuation splitting schemes for unsteady hyperbolic problems

This paper provides a two-dimensional fluctuation splitting scheme for unsteady hyperbolic problems which achieves third-order accuracy in both space and time. For a scalar conservation law, the sufficient conditions for a stable fluctuation splitting scheme to achieve a prescribed order of accuracy in both space and time are derived. Then, using a quadratic space approximation of the solution over each triangular element, based on the reconstruction of the gradient at the three vertices, and a four-level backward discretization of the time derivative, an implicit third-order-accurate scheme is designed. Such a scheme is extended to the Euler system and is validated versus well-known scalar-advection problems and inviscid discontinuous flows.

Bouncing dynamics of resistive microswitches with an adhesive tip

This paper provides a detailed analysis of the dynamic response of a resistive microswitch. The analysis has been carried out by modeling the microswitch as a cantilever beam, according to the Euler-Bernoulli theory, and considering the damping interaction of the moving beam with the surrounding fluid. Attention has been given to the bouncing of the beam tip on the substrate upon actuation. A general adhesive-repulsive force has been applied at the tip of the beam to model its interaction with the substrate, where the attractive contribution is described by a van der Waals-like term and the repulsive contribution by a classical linear elastic springlike term. The resulting problem has been solved using a second-order-accurate finite difference scheme. It is shown that by tuning the adhesive interaction at the tip/substrate interface the number and amplitude of the bounces can be significantly reduced in favor of the system reliability and performance. Also design maps have been proposed to estimate the ac...

A Numerical Method for Turbomachinery Aeroelasticity

This work provides an accurate and efficient numerical method for turbomachinery flutter. The unsteady Euler or Reynolds-averaged Navier–Stokes (RANS) equations are solved in integral form, the blade passages being discretised using a background fixed C-grid and a body-fitted C-grid moving with the blade. In the overlapping region data are exchanged between the two grids at every time step, using bilinear interpolation. The method employs Roe’s second-order-accurate flux difference splitting scheme for the inviscid fluxes, a standard second-order discretisation of the viscous terms, and a three-level backward difference formula for the time derivatives. The state-of-the-art second-order accuracy of numerical methods for unsteady compressible flows with shocks is thus carried over, for the first time to the authors knowledge, to flutter computations. The dual time stepping technique is used to evaluate the nonlinear residual at each time step, thus extending to turbomachinery aeroelasticity the state-of-the-art efficiency of unsteady RANS solvers. The code is proven to be accurate and efficient by computing the 4th Aeroelastic Standard Configuration, namely, the subsonic flow through a turbine cascade with flutter instability in the first bending mode, where viscous effect are found practically negligible. Then, the very severe 11th Aeroelastic Standard Configuration is computed, namely, the transonic flow through a turbine cascade at off-design conditions, where the turbulence model is found to be the critical feature of the method.Copyright

Residual distribution schemes for advection and advection-diffusion problems on quadrilateral cells

This paper provides a study of some difficulties arising when extending residual distribution schemes for scalar advection and advection-diffusion problems from triangular grids to quadrilateral ones. The Fourier and truncation error analyses on a structured mesh are employed and a generalized modified wavenumber is defined, which provides a general framework for the multidimensional analysis and comparison of different schemes. It is shown that, for the advection equation, linearity preserving schemes for quadrilaterals provide lower dissipation with respect to their triangle-based counterparts and very low or no damping for high frequency Fourier modes on structured grids; therefore, they require an additional artificial dissipation term for damping marginally stable modes in order to be employed with success for pure advection problems. In the case of advection-diffusion problems, a hybrid approach using an upwind residual distribution scheme for the convective fluctuation and any other scheme for the diffusion term is only first-order accurate. On the other hand, distributing the entire residual by an upwind scheme provides second-order accuracy; however, such an approach is unstable for diffusion dominated problems, since residual distribution schemes are characterized by undamped modes associated with the discretization of the diffusive fluctuation. The present analysis allows one to determine the conditions for a stable hybrid approach to be second-order accurate and to design an optimal scheme having minimum dispersion error on a nine-point stencil. Well-documented testcases for advection and advection-diffusion problems are used to compare the accuracy properties of several schemes.

A moving-least-squares immersed boundary method for simulating the fluid-structure interaction of elastic bodies with arbitrary thickness

A versatile numerical method is presented to predict the fluid-structure interaction of bodies with arbitrary thickness immersed in an incompressible fluid, with the aim of simulating different biological engineering applications. A direct-forcing immersed boundary method is adopted, based on a moving-least-squares approach to reconstruct the solution in the vicinity of the immersed surface. A simple spring-network model is considered for describing the dynamics of deformable structures, so as to easily model and simulate different biological systems that not always may be described by simple continuum models, without affecting the computational time and simplicity of the overall method. The fluid and structures are coupled in a strong way, in order to avoid instabilities related to large accelerations of the bodies. The effectiveness of the method is validated by means of several test cases involving: rigid bodies, either falling in a quiescent fluid, fluttering or tumbling, or transported by a shear flow; infinitely thin elastic structures with mass, such as a two-dimensional flexible filament and, concerning three-dimensional cases, a flapping flag and an inverted flag in a free stream; finally, a three-dimensional model of a bio-prosthetic aortic valve opening and closing under a pulsatile flowrate. A very good agreement is obtained in all the cases, comparing with available experimental data and numerical results obtained by different methods. In particular, the method is shown to be second-order accurate by means of a mesh-refinement study. Moreover, it is able to provide results comparable with those of sharp direct-forcing approaches, and can manage high pressure differences across the surface, still obtaining very smooth hydrodynamic forces.