Bodies In Viscous Flow Research Articles

A numerical method for suspensions of articulated bodies in viscous flows

An articulated body is defined as a finite number of rigid bodies connected by a set of arbitrary constraints that limit the relative motion between pairs of bodies. Such a general definition encompasses a wide variety of situations in the microscopic world, from bacteria to synthetic micro-swimmers, but it is also encountered when discretizing inextensible bodies, such as filaments or membranes. In this work we consider hybrid articulated bodies, i.e. constituted of both linear chains, such as filaments, and closed-loop chains, such as membranes. Simulating suspensions of such articulated bodies requires to solve the hydrodynamic interactions between large collections of objects of arbitrary shape while satisfying the multiple constraints that connect them. Two main challenges arise in this task: limiting the cost of the hydrodynamic solves, and enforcing the constraints within machine precision at each time-step. To address these challenges we propose a formalism that combines the body mobility problem in Stokes flow with a velocity formulation of the constraints, resulting in a mixed mobility-resistance problem. While resistance problems are known to scale poorly with the particle number, our preconditioned iterative solver is not sensitive to the system size, therefore allowing to study large suspensions with quasilinear computational cost. Additionally, constraint violations, e.g. due to discrete time-integration errors, are prevented by correcting the particles' positions and orientations at the end of each time-step. Our correction procedure, based on a nonlinear minimisation algorithm, has negligible computational cost and preserves the accuracy of the time-integration scheme. The versatility of our method allows to study a plethora of articulated systems within a unified framework. We showcase its robustness and scalability by exploring the locomotion modes of a model microswimmer inspired by the diatom colony Bacillaria Paxillifer, and by simulating large suspensions of bacteria interacting near a no-slip boundary. Finally, we provide a Python implementation of our framework in a collaborative publicly available code, where the user can prescribe a set of constraints through a single input file to study a wide spectrum of applications involving suspensions of articulated bodies.

Tubular-body theory for viscous flows

Cable-like bodies play a key role in many interdisciplinary systems but are hard to simulate. Asymptotic theories, called slender-body theories, are effective but apply in specific regimes and can be hard to extend beyond leading order. In this letter we develop an exact slender-body-like theory for the surface traction of cable-like bodies in viscous flow. This theory expresses the traction as a series of solutions to a well-behaved one-dimensional Fredholm integral equation of the second kind. This process can be simply generalised to other systems.

Regularized Stokeslets Lines Suitable for Slender Bodies in Viscous Flow

Slender-body approximations have been successfully used to explain many phenomena in low-Reynolds number fluid mechanics. These approximations typically use a line of singularity solutions to represent flow. These singularities can be difficult to implement numerically because they diverge at their origin. Hence, people have regularized these singularities to overcome this issue. This regularization blurs the force over a small blob and thereby removing divergent behaviour. However, it is unclear how best to regularize the singularities to minimize errors. In this paper, we investigate if a line of regularized Stokeslets can describe the flow around a slender body. This is achieved by comparing the asymptotic behaviour of the flow from the line of regularized Stokeslets with the results from slender-body theory. We find that the flow far from the body can be captured if the regularization parameter is proportional to the radius of the slender body. This is consistent with what is assumed in numerical simulations and provides a choice for the proportionality constant. However, more stringent requirements must be placed on the regularization blob to capture the near field flow outside a slender body. This inability to replicate the local behaviour indicates that many regularizations cannot satisfy the no-slip boundary conditions on the body’s surface to leading order, with one of the most commonly used blobs showing an angular dependency of velocity along any cross section. This problem can be overcome with compactly supported blobs, and we construct one such example blob, which can be effectively used to simulate the flow around a slender body.

Hydrodynamic impulse generated by slender bodies in viscous flow

The forces and moments on slender axisymetric bodies are studied using a hydrodynamic impulse formulation for viscous flow in non-inertial body frames of reference. The problems of steady translation and steady turning are specifically addressed. A computational fluid dynamics data base is used to evaluate the hydrodynamic impulse for 3 submarine shaped bodies with slenderness ratios of 7.35, 8.38, and 8.75. It was found that the forces and moments calculated using the hydrodynamic impulse formulation give equivalent forces and moment to the traditional method of integrating pressure and shear stress on the body. In addition, it is shown that the lateral force distribution can be calculated directly from the Lamb vector distribution over cross sectional planes. Linearized forms of the hydrodynamic impulse equations are derived for both translation and steady rotation.

Span Efficiencies of Wings at Low Reynolds Numbers

Elegant and inviscid analytical theory can predict the induced drag on lifting wings of finite span. The theoretical prediction is then often modified by multiplication with a dimensionless coefficient for which the departure from a value of 1 is used as a way to incorporate realistic and necessary departures from the idealized model. Unfortunately, there are conflicting definitions of these dimensionless coefficients, often known as span efficiencies, so that even if numerical values are assigned in a clear and transparent fashion, their application and validity remain unclear. Here, the differences between two commonly used definitions of span efficiency are identified and it is shown that for the case of airfoil sections and finite wings at chordwise Reynolds numbers less than 10 5 , neither one has values close to those commonly assumed in the aeronautics literature. The cause of these significant viscous modifications to inviscid theory is traced to the movement of separation points from the trailing edge of real airfoils. A modified nomenclature is suggested to reduce the likelihood of confusion, and appropriate formulations for the drag of streamlined bodies in viscous flows at moderate Reynolds number are considered, with application to small-scale flying devices, both natural and engineered.

Simulation and experimental validation of the motion of immersed rigid bodies in viscous flows

In this work we present the numerical analysis of the motion of a rigid body immersed in a viscous fluid. The fluid flow induced by the gravity-driven motion of a rigid body is particularly analysed using cylinders and spheres. The Navier–Stokes equations coupled with the interface motion are solved in the framework of a finite element formulation. The interface of the rigid body is represented using a moving Lagrangian interface technique (MLIT). The proposed formulation is applied to describe the two-dimensional motion of a cylinder between parallel walls as well as the axisymmetric representation of a sphere assessing in both cases the effects of the walls distance on the velocity developed by such bodies. The numerical predictions are verified using different models for the analysis of the problem, and are validated by comparison with theoretical–empirical correlations. Moreover, the computed body velocities are compared with experimental data reported in the literature as well as measurements obtained from experiments carried out in the framework of the present work.