Physics of Bubble-Propelled Microrockets

A popular method to induce synthetic propulsion at the microscale is to use the forces created by surface-produced gas bubbles inside the asymmetric body of a catalytic swimmer (referred to in the literature as microrocket). Gas bubbles nucleate and grow within the swimmer and migrate toward one of its openings due to asymmetric geometric conﬁnement, generating a net hydrodynamic force which propels the device. Here, numerical simulations are used to develop a joint chemical (diffusive) and hydrodynamic (Stokes) analysis of the bubble growth within a conical catalytic microrocket and of the associated bubble and microrocket motion. With this computational model, the bubble dynamics are solved for over one bubble cycle ranging from its nucleation to its exiting the conical rocket, and the propulsion characteristics are identiﬁed as a function of all design parameters (geometry and chemical activity of the motor, surface tension, physicochemical constants). The results suggest that hydrodynamics and chemistry partially decouple in the motion of the bubbles, with hydrodynamics determining the distance travelled by the microrocket over each cycle while chemistry sets the bubble ejection frequency. This numerical model allows for the identiﬁcation of an optimal microrocket shape and size for which the distance travelled per cycle duration is maximized.

Computational fluid dynamics for naval engineering problems

Nicola Parolini

The subject of this thesis is the numerical simulation of viscous free-surface flows in naval engineering applications. State-of-the-art numerical methods based on the solution of the Navier-Stokes equations are used to predict the flow around different classes of boats. We investigate the role of the Computational Fluid Dynamics in the design of racing boats, such as America's Cup yachts and Olympic class rowing hull. The mathematical models describing the different aspects of the physical problem, as well as the numerical methods adopted for their solution, are introduced and critically discussed. The different phases of the overall numerical simulation procedure, from grid generation through the solution of the flow equations to the post-processing of the results, are described. We present the numerical simulations that have been performed to investigate the role of different design parameters in the conception of America's Cup yachts and we describe how the results obtained from the simulations are integrated into the overall design process. The free-surface flow around an Olympic rowing boat is also considered. We propose a simplified approach to take into account the effect of the boat dynamics in the prediction of the hydrodynamic forces acting on the boat. Based on the results of the simulations, we propose a new design concept and we investigate its potential benefits on the boat performances. One of the aspects that is found to be not completely satisfactory, within the standard numerical methods adopted, is the modelling of complex free-surface flows. The second part of this thesis is devoted to a more theoretical and methodological investigation of this aspect. In particular, we present and analyse a new numerical method based on the level set approach for the solution of two-fluid flows. The numerical scheme based on a finite element discretization is introduced and different critical aspects of its implementation are discussed. In particular, we present and analyse a new technique for the stabilization of the advection equation associated to the level set problem. Moreover, we propose a new reinitialization procedure for the level set function which plays a crucial role in the accuracy of the algorithm. The convergence properties of this procedure are analysed and comparisons with more standard approaches are presented. Finally, the proposed method has been used to solve a variety of test cases concerning time dependent two-fluid viscous flows. The results of the simulation are presented and discussed.

EPFL2004

A semi-implicit approach for fluid-structure interaction based on an algebraic fractional step method

Annalisa Quaini, Alfio Quarteroni

We address the numerical simulation of fluid-structure interaction problems characterized by a strong added-mass effect. We propose a semi-implicit coupling scheme based on an algebraic fractional-step method. The basic idea of a semi-implicit scheme consists in coupling implicitly the added-mass effect, while the other terms (dissipation, convection and geometrical nonlinearities) are treated explicitly. Thanks to this kind of explicit–implicit splitting, computational costs can be reduced (in comparison to fully implicit coupling algorithms) and the scheme remains stable for a wide range of discretization parameters. In this paper we derive this kind of splitting from the algebraic formulation of the coupled fluid-structure problem (after finite-element space discretization). From our knowledge, it is the first time that algebraic fractional step methods, used thus far only for fluid problems in computational domains with rigid boundaries, are applied to fluid-structure problems. In particular, for the specific semi-implicit method presented in this work, we adapt the Yosida scheme to the case of a coupled fluid-structure problem. This scheme relies on an approximate LU block factorization of the matrix obtained after the discretization in time and space of the fluid-structure system. We analyze the numerical performances of this scheme on 2D fluid-structure simulations performed with a simple 1D structure model.

2007

Time-dependent algorithms for the simulation of viscoelastic flows with spectral element methods: applications and stability

Michel Deville, Nicolas Fietier

This paper presents the development of spectral element methods to simulate unsteady flows of viscoelastic fluids using a closed-form differential constitutive equation. The generation and decay Poiseuille planar flows are considered as benchmark problems to test the abilities of our computational method to deal with truly time-dependent flows. Satisfactory results converging toward steady-state regimes have been obtained for the flow through a four-to-one planar abrupt contraction with unsteady algorithms. Time-dependent simulations of viscoelastic flows are prone to numerical instabilities even for simple geometrical configurations. Possible methods to improve the numerical stability of the computational algorithms are discussed in view of the results carried out with numerical simulations for the flows through a straight channel and the four-to-one contraction.

2003

Computational fluid dynamics for naval engineering problems

Nicola Parolini

EPFL2004