Leo M. González

On the consistency of MPS

Abstract The consistency of the Moving Particle Semi-implicit (MPS) method in reproducing the gradient, divergence and Laplacian differential operators is discussed in the present paper. Its relation to the Smoothed Particle Hydrodynamics (SPH) method is rigorously established. The application of the MPS method to solve the Navier–Stokes equations using a fractional step approach is treated, unveiling inconsistency problems when solving the Poisson equation for the pressure. A new corrected MPS method incorporating boundary terms is proposed. Applications to one dimensional boundary value Dirichlet and mixed Neumann–Dirichlet problems and to two-dimensional free-surface flows are presented.

A Boundary Integral SPH Formulation Consistency and Applications to ISPH and WCSPH

One of the historical problems appearing in SPH formulations is the inconsistencies coming from the inappropriate implementation of boundary conditions. In this work, this problem has been investigated; instead of using typical methodologies such as extended domains with ghost or dummy particles where severe inconsistencies are found, we included the boundary terms that naturally appear in the formulation. First, we proved that in the 1D smoothed continuum formulation, the inclusion of boundary integrals allows for a consistent O (h) formulation close to the boundaries. Second, we showed that the corresponding discrete version converges to a certain solution when the discretization SPH parameters tend to zero. Typical tests with the first and second derivative operators confirm that this boundary condition implementation works consistently. The 2D Poisson problem, typically used in ISPH, was also studied, obtaining consistent results. For the sake of completeness, two practical applications, namely, the duct flow and a sloshing tank, were studied with the results showing a rather good agreement with former experiments and previous results. Subject Index: 024

Finite Element Methods for Viscous Incompressible BiGlobal Instability Analysis on Unstructured Meshes

Viscous linear 3-D BiGlobal instability analyses of incompressible flows have been performed using finite element numerical methods, with a view to extend the scope of application of this analysis methodology to flows over complex geometries. The initial value problem (IVP), based on the linearized Navier-Stokes equations (LNSE), as well as the real and the complex partial-differential-equation-based generalized eigenvalue problems (EVP), have been solved. A mixed P 2 P 1 finite element spatial discretization on unstructured meshes for both the LNSE and the EVP approaches has been used. For the time-discretization of the LNSE a characteristics method has been used for the first time in the context of flow stability analysis; the complex BiGlobal EVP has also been solved for the first time in the context of a finite element numerical discretization. In either its real or its complex form, the EVP has been solved without the need to introduce pseudocompressibility into the incompressible equations, which has simplified the systems to be solved without sacrificing accuracy. An Arnoldi approach has been used to recover the most significant eigenvalues. In this context, the associated solutions to the resulting linear systems were obtained by iterative methods: generalized minimal residual with incomplete lower-upper preconditioning or conjugate gradient with I-Cholesky preconditioning, depending on whether the coefficient matrix was symmetric or not. The 3-D instability of the classic 2-D lid-driven cavity flow and that of the rectangular duct flow were used as validation cases for the real and complex EVP, respectively. New results have been obtained for the 3-D BiGlobal instability of two closed and one open flow, namely, the regularized lid-driven cavity of rectangular and triangular shape and flow in the wake of a model bluff body.

An extended validation of the last generation of particle finite element method for free surface flows

In this paper, a new generation of the particle method known as Particle Finite Element Method (PFEM), which combines convective particle movement and a fixed mesh resolution, is applied to free surface flows. This interesting variant, previously described in the literature as PFEM-2, is able to use larger time steps when compared to other similar numerical tools which implies shorter computational times while maintaining the accuracy of the computation. PFEM-2 has already been extended to free surface problems, being the main topic of this paper a deep validation of this methodology for a wider range of flows. To accomplish this task, different improved versions of discontinuous and continuous enriched basis functions for the pressure field have been developed to capture the free surface dynamics without artificial diffusion or undesired numerical effects when different density ratios are involved. A collection of problems has been carefully selected such that a wide variety of Froude numbers, density ratios and dominant dissipative cases are reported with the intention of presenting a general methodology, not restricted to a particular range of parameters, and capable of using large time-steps. The results of the different free-surface problems solved, which include: Rayleigh-Taylor instability, sloshing problems, viscous standing waves and the dam break problem, are compared to well validated numerical alternatives or experimental measurements obtaining accurate approximations for such complex flows.

Onset of three-dimensional flow instabilities in lid-driven circular cavities

Three-dimensional instabilities for two circular lid-driven cavities are investigated by a linear stability analysis and direct numerical simulations using high order spectral techniques. Two circular geometries have been analysed and compared: a circular cavity with a horizontal top boundary and a circular cavity with a circular lid. Compared to more classic results for squared and rectangular lid driven cavities, the corners of these rounded geometries have been partially or totally removed. Critical Reynolds numbers, neutral curves, and three dimensional structures associated with the least stable modes have been identified by the linear stability analysis and then confirmed by spectral direct numerical simulations. We show that the geometries that present fewer sharp corners have enhanced stability: the circular cavity with a flat lid presents the first bifurcation at (Rec,kc)≈(1362,25) whilst the circular lid bifurcates at (Rec,kc)≈(1438,18), where Rec is the critical Reynolds number based on the cavity diameter and lid tangential velocity, and kc is the spanwise wavenumber. Neutral curves and properties of the leading three-dimensional flow structures are documented, and analogies to instabilities in other lid-driven cavities are discussed. Additionally, we include results for the adjoint problem and the structural sensitivity 3D iso-maps (i.e., wavemaker regions), to show that the cavity corners play a relevant role in the generation of 3D instabilities.

The scenario of two-dimensional instabilities of the cylinder wake under electrohydrodynamic forcing: a linear stability analysis

We propose to study the stability properties of an air flow wake forced by a dielectric barrier discharge (DBD) actuator, which is a type of electrohydrodynamic (EHD) actuator. These actuators add momentum to the flow around a cylinder in regions close to the wall and, in our case, are symmetrically disposed near the boundary layer separation point.Since the forcing frequencies, typical of DBD, are much higher than the natural shedding frequency of the flow, we will be considering the forcing actuation as stationary.In the first part, the flow around a circular cylinder modified by EHD actuators will be experimentally studied by means of particle image velocimetry (PIV). In the second part, the EHD actuators have been numerically implemented as a boundary condition on the cylinder surface. Using this boundary condition, the computationally obtained base flow is then compared with the experimental one in order to relate the control parameters from both methodologies.After validating the obtained agreement, we study the Hopf bifurcation that appears once the flow starts the vortex shedding through experimental and computational approaches. For the base flow derived from experimentally obtained snapshots, we monitor the evolution of the velocity amplitude oscillations. As to the computationally obtained base flow, its stability is analyzed by solving a global eigenvalue problem obtained from the linearized Navier–Stokes equations. Finally, the critical parameters obtained from both approaches are compared.

Global Stability Analysis of a Compressible Turbulent Flow Around a High-Lift Configuration

The stability of flow over a complex high-lift configuration with significant regions of separated flow is analyzed. Current state-of-the-art flow solvers encounter difficulties in predicting both the onset of flow separation over similar configurations and the progression of the separated region when the angle of attack is increased. The present analysis provides useful insights into the mechanisms responsible for limiting the maximum lift on multielement wing configurations by relating flow separation with the onset of flow instability. A steady solution based on a finite volume discretization is used as the basic state for the linear stability analysis. The resulting generalized eigenvalue problem has been solved using a Krylov subspace projection technique in the form of the Arnoldi iterative method. This methodology is first applied to a NACA0012 test case at subsonic and transonic conditions. Then, for the first time, the stability of flow over an industrial multicomponent geometry involving the A31...

CFD Simulations on the Vortex-Induced Vibrations of a Flexible Cylinder With Wake Interference

In this work, CFD computations showing the dynamic response of a long flexible cylinder subject to a stepped current immersed in the wake of another cylinder are presented. These two cylinders are placed upstream in tandem configuration, where the flexible cylinder is excited by vortex shedding mechanisms. This work completes from the computational point of view, the research started 2 years ago with experiments conducted at the E.T.S.I. Navales towing tank of the Technical University of Madrid. The flexible cylinder studied is 3 m long having an external diameter of 16 mm. A combination of two codes that simulate the fluid-structure interaction phenomenon was used to obtain the velocity and pressure fields and also to measure the deformation of the cylinder at the same points where the strain gauges where placed during the experiment. This code communicates a finite volume (FV) software that solves the Navier-Stokes equations and reports the shear and pressure fields on the flexible cylinder to a second finite element (FEM) code that is able to compute stresses and deformations. Deformations are reported back to the first fluid solver in order to compute the next time step. In the experiments, only the 65% length of the cylinders were under the water surface, consequently a VOF technique was used to simulate the free surface separation between air and water. The numerical stability of these two combined codes is one of the most delicate aspects of the simulation. Taking into account that the upstream cylinder was orders of magnitude more rigid than the downstream one, we considered the upstream cylinder as stationary and consequently having no role during the FEM calculation. Boundary conditions for the flexible cylinder where such that they should imitate the universal joints used in the experiments. The fundamental natural frequencies of oscillation were monitored and compared to the towing tank experiments.Copyright

Towing Tank Experiments on the Vortex-Induced Vibrations of a Flexible Cylinder With Wake Interference

We describe recent results showing the dynamic response, excited by vortex shedding, of a long flexible cylinder subject to a stepped current immersed in the wake of another cylinder, placed upstream in tandem configuration. Experiments were conducted at the E.T.S.I. Navales towing tank of the Technical University of Madrid during March 2012. The tank is 80 m long with a cross-section of 4 × 2.5 m. A supporting structure was designed in order to provide support for a 3 m long cylinder with an external diameter of 16 mm. The cylinder was instrumented with strain gauges providing curvature measurements in the in-line and the cross-flow directions at 11 locations along its length. Tension and drag forces were also measured at both ends of the model. For these experiments, the upstream rigid cylinder was made stationary by fixing it at both ends, and it was located at different centre to centre distances.More than 200 runs were conducted, with its lower 65% length under the water free surface, connected to the structure by means of universal joints. The supporting structure allowed to configure different top end conditions and to apply different top tensions. Tests were conducted with speeds up to 1.4 m/s. The cylinder had a low flexural stiffness of 6.04 Nm2 and low mass ratio of 2.7. Fundamental natural frequencies were in the range from about 2.3 to 6.2 Hz, and the cylinder responded in modes up to the third cross-flow.Copyright

Towing Tank Experiments on the Vortex-Induced Vibrations of a Long Flexible Cylinder in a Stepped Current

We describe recent results showing the dynamic response, excited by vortex shedding, of a long flexible cylinder subject to a stepped current. The experiments were conducted at the Naval Architecture Department towing tank of the Technical University of Madrid (UPM) during March 2012. The tank is 100 m long with a cross-section of 3.8 × 2.5 m, and it is able to deliver speeds over 4 m/s. A supporting structure was designed in order to provide support for a 3 m long cylinder with an external diameter of 19 mm. The cylinder was instrumented with strain gauges providing curvature measurements in the in-line and the cross-flow directions at 11 locations along its length. Tension and drag forces were also measured at both ends of the model. More than 50 runs were conducted with the cylinder being placed vertically having its lower 65% length under the water free surface, connected to the structure by means of universal joints. The supporting structure allowed to configure different top end conditions and to apply different top tensions. Tests were conducted for Reynolds numbers as high as 34000. The cylinder had a low flexural stiffness and very low mass ratio m* of 0.67. Fundamental natural frequencies were in the range from about 4 to 7.9 Hz, and the cylinder responded in modes up to the third cross-flow. In this article we will describe the experiments and the instrumentation used, the modal tests conducted and the results obtained during the experiments.Copyright