A comparative study of immersed-boundary interpolation methods for a flow around a stationary cylinder at low Reynolds number

The accuracy and computational efficiency of various interpolation methods for the implementation of non grid-confirming boundaries is assessed. The aim of the research is to select an interpolation method that is both efficient and sufficiently accurate to be used in the simulation of vortex induced vibration of the flow around a deformable cylinder. Results are presented of an immersed boundary implementation in which the velocities near nonconfirming boundaries were interpolated in the normal direction to the walls. The flow field is solved on a Cartesian grid using a finite volume method with a staggered variable arrangement. The Strouhal number and Drag coefficient for various cases are reported. The results show a good agreement with the literature. Also, the drag coefficient and Strouhal number results for five different interpolation methods were compared it was shown that for a stationary cylinder at low Reynolds number, the interpolation method could affect the drag coefficient by a maximum 2% and the Strouhal number by maximum of 3%. In addition, the bi-liner interpolation method took about 2% more computational time per vortex shedding cycle in companion to the other methods

A parallel interaction potential approach coupled with the immersed boundary method for fully resolved simulations of deformable interfaces and membranes

In this paper we show and discuss the use of a versatile interaction potential approach coupled with an immersed boundary method to simulate a variety of flows involving deformable bodies. In particular, we focus on two kinds of problems, namely (i) deformation of liquid-liquid interfaces and (ii) flow in the left ventricle of the heart with either a mechanical or a natural valve. Both examples have in common the two-way interaction of the flow with a deformable interface or a membrane. The interaction potential approach (de Tullio & Pascazio, Jou. Comp. Phys., 2016; Tanaka, Wada and Nakamura, Computational Biomechanics, 2016) with minor modifications can be used to capture the deformation dynamics in both classes of problems. We show that the approach can be used to replicate the deformation dynamics of liquid-liquid interfaces through the use of ad-hoc elastic constants. The results from our simulations agree very well with previous studies on the deformation of drops in standard flow configurations such as deforming drop in a shear flow or a cross flow. We show that the same potential approach can also be used to study the flow in the left ventricle of the heart. The flow imposed into the ventricle interacts dynamically with the mitral valve (mechanical or natural) and the ventricle which are simulated using the same model. Results from these simulations are compared with ad- hoc in-house experimental measurements. Finally, a parallelisation scheme is presented, as parallelisation is unavoidable when studying large scale problems involving several thousands of simultaneously deforming bodies on hundreds of distributed memory computing processors

Fluid-solid thermal coupling in pipe and channel turbulent flows via a dual immersed boundary method

This study deals numerically with Fluid-Solid Thermal Interaction. Accurate representation of fluid-solid heat transfer is the key for designing heating and cooling systems. However, for industrial applications, the understanding of the conjugate heat transfer remains in deficit, especially near the fluid-solid interface. This research aims to develop an original, straightforward, geometrically flexible and accurate numerical tool to improve the understanding of turbulent heat transfer and problems involving scalar transport, via Direct Numerical Simulation or Implicit Large Eddy Simulation. The fluid dynamic and heat transfer governing equations are solved numerically by the Incompact3d code based on 6th-order compact schemes of finite differences, for spatial di erentiation in a Cartesian mesh. The time advancement is carried on by a 3th-order Adams-Bashforth together with a fractional time step. The solid geometry is represented by an Immersed Boundary Method based on momentum direct forcing. The thermal interaction is studied in pipe and plane channel turbulent flow. Periodic channel flow was evaluated for three thermal boundary conditions: imposed heat flux (Neumann-type), imposed temperature (Dirichlet-type) and fluid-solid thermal interaction (Dirichlet and Neumann type) at the wall/interface. Periodic pipe flow was evaluated for an imposed temperature at the wall. The convergence analysis shows a second order accuracy at the fluid-solid interface. The velocity and temperature statistics had an excellent agreement with the reference results, and the turbulent heat transfer phenomenon was consistently represented, even using lower spatial resolution than the thickness of the viscous sublayer.Este trabalho aborda numericamente o problema da Interação Térmica Fluido-Sólido. Uma representação precisa da transferência de calor é essencial no projeto de sistemas de aquecimento ou arrefecimento/resfriamento. Porém, para aplicações industriais, o entendimento da transferência de calor turbulenta se mantem limitado, especialmente na vizinhança da interface fluido-sólido. Esta pesquisa visa desenvolver uma ferramenta numérica original, simples de implementar e geometricamente flexível no intuito de aportar no entendimento da transferência de calor turbulenta e problemas envolvendo transporte escalar, via Simulação Numérica Direta ou Simulação Numérica Implícita de Grandes Escalas. As equações governantes são resolvidas numericamente aplicando o código Incompact3d, que se baseia no método de diferenças finitas compactas de sexta-ordem, para diferenciação espacial, e um esquema de Adams-Bashforth de terceira-ordem em conjunto com o método do passo fracionado. A geometria do sólido representada por meio de um Método de Fronteiras Imersas baseado na forçagem direta de quantidade de movimento, aplicada ao escoamento turbulento periódico em canal plano fechado e conduto circular. O escoamento em canal plano é avaliado para três condições de contorno térmicas: fluxo de calor imposto (tipo Neumann), temperatura imposta (tipo Dirichlet) e interação térmica fluido-sólido (tipo Dirichlet e Neumann) na parede/interface. O escoamento no conduto circular é avaliado para condição de temperatura imposta na parede. A análise de convergência, para escoamento laminar, mostra até sexta-ordem de precisão para canal plano submetido a temperatura constante e até segunda-ordem para as outras condições térmicas na parede e para escoamento em conduto circular. Nos casos turbulentos, as estatísticas básicas da velocidade e da temperatura tiveram um excelente ajuste a dados de referência, e o fenómeno de transferência de calor foi representado consistentemente, ainda para resoluções menores do que a espessura da camada limite viscosa

Effect of turbulent fluctuations on the drag and lift forces on a towed sphere and its boundary layer

The impact of turbulent fluctuations on the forces exerted by a fluid on a towed spherical particle is investigated by means of high-resolution direct numerical simulations. The measurements are carried out using a novel scheme to integrate the two-way coupling between the particle and the incompressible surrounding fluid flow maintained in a high-Reynolds-number turbulent regime. The main idea consists in combining a Fourier pseudo-spectral method for the fluid with an immersed-boundary technique to impose the no-slip boundary condition on the surface of the particle. Benchmarking of the code shows a good agreement with experimental and numerical measurements from other groups. A study of the turbulent wake downstream the sphere is also reported. The mean velocity deficit is shown to behave as the inverse of the distance from the particle, as predicted from classical similarity analysis. This law is reinterpreted in terms of the principle of "permanence of large eddies" that relates infrared asymptotic self-similarity to the law of decay of energy in homogeneous turbulence. The developed method is then used to attack the problem of an upstream flow that is in a developed turbulent regime. It is shown that the average drag force increases as a function of the turbulent intensity and the particle Reynolds number. This increase is significantly larger than predicted by standard drag correlations based on laminar upstream flows. It is found that the relevant parameter is the ratio of the viscous boundary layer thickness to the dissipation scale of the ambient turbulent flow. The drag enhancement can be motivated by the modification of the mean velocity and pressure profile around the sphere by small scale turbulent fluctuations.Comment: 24 pages, 22 figure

Resolved simulations of submarine avalanches with a simple soft-sphere / immersed boundary method

Physical mechanisms at the origin of the transport of solid particles in a fluid are still a matter of debate in the physics community. Yet, it is well known that these processes play a fundamental role in many natural configurations, such submarines landslides and avalanches, which may have a significant environmental and economic impact. The goal here is to reproduce the local dynamics of such systems from the grain scale to that of thousands of grains approximately. To this end a simple soft-sphere collision / immersed-boundary method has been developed in order to accurately reproduce the dynamics of a dense granular media collapsing in a viscous fluid. The fluid solver is a finite-volume method solving the three-dimensional, time-dependent Navier-Stokes equations for a incompressible flow on a staggered. Here we use a simple immersed-boundary method consisting of a direct forcing without using any Lagrangian marking of the boundary, the immersed boundary being defined by the variation of a solid volume fraction from zero to one. The granular media is modeled with a discrete element method (DEM) based on a multi-contact soft-sphere approach. In this method, an overlap is allowed between spheres which mimics the elasto-plastic deformation of real grain, and is used to calculate the contact forces based on a linear spring model and a Coulomb criterion. Binary wall-particle collisions in a fluid are simulated for a wide range of Stokes number ranging from 10-¹ to 10⁴. It is shown that good agreement is observed with available experimental results for the whole range of investigated parameters, provided that a local lubrication model is used when the distance of the gap between the particles is below a fraction of the particle radius. A new model predicting the coefficient of restitution as a function of the Stokes number and the relative surface roughness of the particles is proposed. This model, which makes use of no adjustable constant, is shown to be in good agreement with available experimental data. Finally, simulations of dense granular flows in a viscous fluid are performed. The present results are encouraging and open the way for a parametric study in the parameter space initial aspect ratio - initial packing