Numerical simulations are used to investigate the hydrodynamic benefits of body–fin and fin–fin interactions in a fish model in carangiform swimming. The geometry and kinematics of the model are ...reconstructed in three-dimensions from high-speed videos of a live fish, Crevalle Jack (Caranx hippos), during steady swimming. The simulations employ an immersed-boundary-method-based incompressible Navier–Stokes flow solver that allows us to quantitatively characterize the propulsive performance of the fish median fins (the dorsal and the anal fins) and the caudal fin using three-dimensional full body simulations. This includes a detailed analysis of associated performance enhancement mechanisms and their connection to the vortex dynamics. Comparisons are made using three different models containing different combinations of the fish body and fins to provide insights into the force production. The results indicate that the fish produces high performance propulsion by utilizing complex interactions among the fins and the body. By connecting the vortex dynamics and surface force distribution, it is found that the leading-edge vortices produced by the caudal fin are associated with most of the thrust production in this fish model. These vortices could be strengthened by the vorticity capture from the vortices generated by the posterior body during undulatory motion. Meanwhile, the pressure difference between the two sides of posterior body resulting from the posterior body vortices (PBVs) helps with the alleviation of the body drag. The appearance of the median fins in the posterior region further strengthens the PBVs and caudal-fin wake capture mechanism. This work provides new physical insights into how body–fin and fin–fin interactions enhance thrust production in swimming fishes, and emphasizes that movements of both the body and fins contribute to overall swimming performance in fish locomotion.
In this paper, we present a new multiscale model reduction technique for the Stokes flows in heterogeneous perforated domains. The challenge in the numerical simulations of this problem lies in the ...fact that the solution contains many multiscale features and requires a very fine mesh to resolve all details. In order to efficiently compute the solutions, some model reductions are necessary. To obtain a reduced model, we apply the generalized multiscale finite element approach, which is a framework allowing systematic construction of reduced models. Based on this general framework, we will first construct a local snapshot space, which contains many possible multiscale features of the solution. Using the snapshot space and a local spectral problem, we identify dominant modes in the snapshot space and use them as the multiscale basis functions. Our basis functions are constructed locally with non-overlapping supports, which enhances the sparsity of the resulting linear system. In order to enforce the mass conservation, we propose a hybridized technique, and uses a Lagrange multiplier to achieve mass conservation. We will mathematically analyze the stability and the convergence of the proposed method. In addition, we will present some numerical examples to show the performance of the scheme. We show that, with a few basis functions per coarse region, one can obtain a solution with excellent accuracy.
The smoothness of topological interfaces often largely affects the fluid optimization and sometimes makes the density-based approaches, though well established in structural designs, inadequate. This ...paper presents a level-set method for topology optimization of steady-state Navier–Stokes flow subject to a specific fluid volume constraint. The solid-fluid interface is implicitly characterized by a zero-level contour of a higher-order scalar level set function and can be naturally transformed to other configurations as its host moves. A variational form of the cost function is constructed based upon the adjoint variable and Lagrangian multiplier techniques. To satisfy the volume constraint effectively, the Lagrangian multiplier derived from the first-order approximation of the cost function is amended by the bisection algorithm. The procedure allows evolving initial design to an optimal shape and/or topology by solving the Hamilton–Jacobi equation. Two classes of benchmarking examples are presented in this paper: (1) periodic microstructural material design for the maximum permeability; and (2) topology optimization of flow channels for minimizing energy dissipation. A number of 2D and 3D examples well demonstrated the feasibility and advantage of the level-set method in solving fluid–solid shape and topology optimization problems.
This article addresses the Cattaneo–Christov heat flux, radiation and joule heating model as applied to a Blasius–Rayleigh–Stokes flow through a transitive magnetic field. The mathematical models are ...converted into a pair of self-similarity equations by applying appropriate transformations. The reduced similarity equivalences are then solved numerically by the Runge–Kutta–Fehlberg 45th-order method. To better perceive the problem, the flow and energy transfer characteristics are explored for distinct values of different factors. From this analysis we found that Higher values of Q increase the f′η field and its interrelated thickness of the boundary layer. The temperature of the fluid and its interrelated layer thickness enhances for boost up values ofγ . Also found that the streamline graphs are dominant for Q=2 when compared with Q=0.5. The presence of Q has more impact on the results when compared to the case where Q is absent. The local RexCfx and NuxRex−12 scale back for increasing values of ω.
•The streamline graphs are dominant for Q=2 when compared with Q=0.5.•θ(η) field rises of enhanced values of R.•An intensification in the f′(η) field is seen with the increment of ω and Q.•Interrelated thickness of the thermal boundary layer decays for higher values of Pr.•The heat transfer rate is greater in the presence of R than in the absence of R.•The presence of Q has more impact on the results when compared to the case where Q is absent.
Isogeometric analysis (IGA) is emerging as a technology bridging computer aided geometric design (CAGD), most commonly based on Non-Uniform Rational B-Splines (NURBS) surfaces, and engineering ...analysis. In finite element and boundary element isogeometric methods (FE-IGA and IGA-BEM), the NURBS basis functions that describe the geometry define also the approximation spaces. In the FE-IGA approach, the surfaces generated by the CAGD tools need to be extended to volumetric descriptions, a major open problem in 3D. This additional passage can be avoided in principle when the partial differential equations to be solved admit a formulation in terms of boundary integral equations, leading to boundary element isogeometric analysis (IGA-BEM). The main advantages of such an approach are given by the dimensionality reduction of the problem (from volumetric-based to surface-based), by the fact that the interface with CAGD tools is direct, and by the possibility to treat exterior problems, where the computational domain is infinite. By contrast, these methods produce system matrices which are full, and require the integration of singular kernels. In this paper we address the second point and propose a nonsingular formulation of IGA-BEM for 3D Stokes flows, whose convergence is carefully tested numerically. Standard Gaussian quadrature rules suffice to integrate the boundary integral equations, and carefully chosen known exact solutions of the interior Stokes problem are used to correct the resulting matrices, extending the work by Klaseboer et al. (2012) 27 to IGA-BEM.
We present a semi-numerical method for solving the dynamics of microplates in viscous fluids. The method is based on the Kirchhoff plate equation with a hydrodynamic force deduced from the Stokes ...equations. The equation of motion is solved with the Galerkin mode decomposition (GMD) using the vacuum vibrational modes of cantilevered microplates as the basis functions. We investigate the Q-factor of the vibrational modes of microplate-resonators in gases and liquids. In gases, the Euler–Bernoulli (EB) modes (modes with nodal lines only along the plate’s width) exhibit the lowest Q-factors, while non-EB modes exhibit the highest Q-factors. In liquids, the opposite is found. EB modes exhibit the highest Q-factors, and non-EB modes lower Q-factors. We name this opposite Q-factor pattern in gases and liquids the gas-liquid-Q-inversion (GL-Q-inversion). Experiments in water and air showed a Q-factor agreement with the GL-Q-inversion, and differences in Q-factor between simulation and experiments were below 25%. Further numerical analysis reveals the physical mechanism underlying the GL-Q-inversion in terms of the system’s stored and dissipated energy. The results and methods shown here will pave the way to efficiently exploit the two-dimensional vibrational modes of microplate-resonators to improve their performance in gaseous and liquid environments.
•We propose a method for computing the dynamics of MEMS plate resonators in fluids.•Resonance frequency and Q-factor of different modes in distinct fluids are calculated.•The method reveals an unexpected modal Q-factor inversion between gases and liquids.•Experiments showed the gas-liquid-Q-factor inversion and the method’s accuracy.•Analyzing dissipated and stored energy reveals the origin of the Q-factor inversion.
In order to explicitly and smoothly implement fluid-based topology optimization for improving the performance and manufacturing efficiency of flow systems, the moving morphable void (MMV) method is ...employed to optimize the steady-state navier-stokes (NS) flow for minimizing the dissipation energy under a volume constraint. To this end, a MMV-based Brinkman term is proposed to penalize the velocity in solid area, which can expand the region controlled by the NS flow equilibrium equation from fluid to whole design domain, and can also establish the relationship between design variables and governing equations. Then, a MMV-based optimization model of NS flow is proposed and the design variables are updated by the method of moving asymptotes according to the sensitivity analysis. In benchmark examples, we can precisely track the topology boundary with detailed geometric information without the intuitive geometric judgement error. Also, by means of contrasting the results of proposed method with previous work, the effectiveness and advantages of the MMV method can be confirmed.
We derived the Stokes equations and velocity potential around a hyperspherical obstacle in n-dimensional space. The objectives of this study were to understand the hyperspace through the physics in ...the space and to bring the analytical solution of fluid flow in hyperspace for numerical simulation. The equations were obtained from the n-dimensional Navier-Stokes equation assuming the low Reynolds number flow. These were generalized formulae from a 3-dimensional system to an n-dimensional one. Our results show that the effect of the hyperspherical obstacle on the uniform flow is localized in higher dimensional spaces. We visualized the flow using the collections of hypersections.
The efficient simulation of fluid-structure interactions at zero Reynolds number requires the use of fast summation techniques in order to rapidly compute the long-ranged hydrodynamic interactions ...between the structures. One approach for periodic domains involves utilising a compact or exponentially decaying kernel function to spread the force on the structure to a regular grid where the resulting flow and interactions can be computed efficiently using an FFT-based solver. A limitation to this approach is that the grid spacing must be chosen to resolve the kernel and thus, these methods can become inefficient when the separation between the structures is large compared to the kernel width. In this paper, we address this issue for the force-coupling method (FCM) by introducing a modified kernel that can be resolved on a much coarser grid, and subsequently correcting the resulting interactions in a pairwise fashion. The modified kernel is constructed to ensure rapid convergence to the exact hydrodynamic interactions and a positive-splitting of the associated mobility matrix. We provide a detailed computational study of the methodology and establish the optimal choice of the modified kernel width, which we show plays a similar role to the splitting parameter in Ewald summation. Finally, we perform example simulations of rod sedimentation and active filament coordination to demonstrate the performance of fast FCM in application.
•A modified kernel and velocity correction scheme are developed to accelerate the force-coupling method (FCM).•In several cases, fast FCM is an order of magnitude faster than the standard FCM algorithm.•Fast FCM is extended to include point torques on the particles.•Fast FCM is shown to yield positive splitting, which is important for simulations involving thermal fluctuations.•The effectiveness of fast FCM is demonstrated through simulations of rod suspensions and arrays of flexible filaments.
PDF
