Multigrid Finite Volume Method Research Articles

Vorticity dynamics and control of the turning locomotion of 3D bionic fish

Numerical simulations of the turning manoeuvre of a 3D bionic fish in a viscous flow are conducted in the present study using a 3D computational fluid dynamics package, which includes the adaptive multi-grid finite volume method, the immersed boundary method, the volume of fluid method, and the control strategy of fish swimming. The 3D bionic fish can turn quickly primarily using the directional control strategy of the swing of the head, in which the impacts of the swing of the fish body and the caudal fin on the directional control are also taken into account. This result demonstrates that the directional control strategy of the swing of the head is effective. An in-depth analysis of the fluid mechanism of the swimming manoeuvre of the 3D bionic fish reveals that the rotation moment in favour of turning motion is obtained by the pressure around the body of the fish, which is induced by the wake vortex, and the swing of the fish can manipulate the location and the strength of vortices shed from the fish body.

A study of a three-dimensional self-propelled flying bird with flapping wings

In this paper, a study of a three-dimensional (3D) self-propelled bionic flying bird in a viscous flow is carried out. This bionic bird is propelled and lifted through flapping and rotating wings, and better flying can be achieved by adjusting the flapping and rotation motion of wings. In this study, we found that the bird can fly faster forward and upward with appropriate center of rotation and oscillation without more energy consumption and have perfect flight performance at a certain angle of attack by adjusting the center of oscillation. The study utilizes a 3D computational fluid dynamics package which constitutes combined immersed boundary method and the volume of fluid method. In addition, it includes adaptive multigrid finite volume method and control strategy of swimming and flying.

Vorticity Dynamics and Control of the Three Dimensional Self-propelled Travelling Wave Wall in Ground Effect

Undulatory rays, propelled by the enlarged pectoral fin on both sides of body, swim close to the substrate. The pectoral fins undulate in the form of a three-dimensional traveling wave. However, the physical mechanisms of the 3D traveling wave in ground effect are especially unknown. The self-propelled locomotion of the 3D traveling wave wall in ground effect is investigated in this study, with a 3D computational fluid dynamics package that combines the immersed boundary method, the volume of fluid method, the adaptive multi-grid finite volume method, and the control strategy of swimming. The influences of ground effect on the locomotion of the 3D traveling wave wall are analyzed. The fluid mechanisms of swimming of the 3D traveling wave wall in ground effect are revealed using vorticity dynamics. From numerical simulations and vorticity dynamics, it is found that the 3D traveling wave wall can achieve high swimming performance on the bottom of water through flow control.

Shape optimization of the caudal fin of the three-dimensional self-propelled swimming fish

Shape optimization of the caudal fin of the three-dimensional self-propelled swimming fish, to increase the swimming efficiency and the swimming speed and control the motion direction more easily, is investigated by combining optimization algorithms, unsteady computational fluid dynamics and dynamic control in this study. The 3D computational fluid dynamics package contains the immersed boundary method, volume of fluid method, the adaptive multi-grid finite volume method and the control strategy of fish swimming. Through shape optimizations of various swimming speeds, the results show that the optimal caudal fins of different swimming modes are not exactly the same shape. However, the optimal fish of high swimming speed, whose caudal fin shape is similar to the crescent, also have higher efficiency and better maneuverability than the other optimal bionic fish at low and moderate swimming speeds. Finally, the mechanisms of vorticity creation of different optimal bionic fish are studied by using boundary vorticity-flux theory, and three-dimensional wake structures of self-propelled swimming of these fish are comparatively analyzed. The study of vortex dynamics reveals the nature of efficient swimming of the 3D bionic fish with the lunate caudal fin.

Numerical simulations and vorticity dynamics of self-propelled swimming of 3D bionic fish

Numerical simulations and the control of self-propelled swimming of three-dimensional bionic fish in a viscous flow and the mechanism of fish swimming are carried out in this study, with a 3D computational fluid dynamics package, which includes the immersed boundary method and the volume of fluid method, the adaptive multi-grid finite volume method, and the control strategy of fish swimming. Firstly, the mechanism of 3D fish swimming was studied and the vorticity dynamics root was traced to the moving body surface by using the boundary vorticity-flux theory. With the change of swimming speed, the contributions of the fish body and caudal fin to thrust are analyzed quantitatively. The relationship between vortex structures of fish swimming and the forces exerted on the fish body are also given in this paper. Finally, the 3D wake structure of self-propelled swimming of 3D bionic fish is presented. The in-depth analysis of the 3D vortex structure in the role of 3D biomimetic fish swimming is also performed.

Where is the rudder of a fish?: the mechanism of swimming and control of self-propelled fish school

Numerical simulation and control of self-propelled swimming of two- and three-dimensional biomimetic fish school in a viscous flow are investigated. With a parallel computational fluid dynamics package for the two- and three-dimensional moving boundary problem, which combines the adaptive multi-grid finite volume method and the methods of immersed boundary and volume of fluid, it is found that due to the interactions of vortices in the wakes, without proper control, a fish school swim with a given flapping rule can not keep the fixed shape of a queue. In order to understand the secret of fish swimming, a new feedback control strategy of fish motion is proposed for the first time, i.e., the locomotion speed is adjusted by the flapping frequency of the caudal, and the direction of swimming is controlled by the swinging of the head of a fish. Results show that with this feedback control strategy, a fish school can keep the good order of a queue in cruising, turning or swimming around circles. This new control strategy, which separates the speed control and direction control, is important in the construction of biomimetic robot fish, with which it greatly simplifies the control devices of a biomimetic robot fish.

Numerical simulations of self-propelled swimming of 3D bionic fish school

Numerical simulations of self-propelled swimming of a three dimensional bionic fish and fish school in a viscous fluid are carried out. This is done with the assistance of a parallel software package produced for 3D moving boundary problems. This computational fluid dynamics package combines the adaptive multi-grid finite volume method, the immersed boundary method and VOF (volume of fluid) method. By using the package results of the self-propelled swimming of a 3D bionic fish and fish school in a viscous fluid are obtained. With comparison to the existing experimental measurements of living fishes, the predicted structure of vortical wakes is in good agreement with the measurements.

Effect of the Intermolecular Forces on the Flying Attitude of Sub-5 NM Flying Height Air Bearing Sliders in Hard Disk Drives

When the spacing between the slider and the disk is smaller than 10 nm, the effect of the intermolecular forces between the two solid surfaces can no longer be ignored. This effect on the flying attitude of practical slider designs is investigated here numerically. The three-dimensional slider surface is discretized into non-overlapping unstructured triangles. The intermolecular forces between each triangular cell of the slider and the disk surface are formulated, and their contributions to the total vertical force, as well as the pitch and roll moments, are included in a previously developed steady state air bearing design code based on a multi-grid finite volume method with unstructured triangular grids [3–5]. It is found that the van der Waals force has significant influence on the flying height and has non-negligible effect on the pitch angle for both positive pressure sliders and negative pressure sliders, when the flying height is below 5 nm. When the flying height is below 0.5 nm, the repulsive portion of the intermolecular force becomes important and also has to be included.

Local block refinement with a multigrid flow solver

AbstractA local block refinement procedure for the efficient computation of transient incompressible flows with heat transfer is presented. The procedure uses patched structured grids for the blockwise refinement and a parallel multigrid finite volume method with colocated primitive variables to solve the Navier‐Stokes equations. No restriction is imposed on the value of the refinement rate and non‐integer rates may also be used. The procedure is analysed with respect to its sensitivity to the refinement rate and to the corresponding accuracy. Several applications exemplify the advantages of the method in comparison with a common block structured grid approach. The results show that it is possible to achieve an improvement in accuracy with simultaneous significant savings in computing time and memory requirements. Copyright © 2002 John Wiley & Sons, Ltd.

Numerical simulation of coupled fluid–solid problems

A multi-grid finite-volume method is presented for the prediction of coupled fluid–solid problems in complex geometries. Whereby a unified finite-volume approach, based on the concept of block-structured grids is employed for the handling of the complexity of the geometry and the fluid–solid coupling. A high numerical efficiency is obtained with a non-linear multi-grid method using a pressure-correction-based scheme as a smoother. A number of numerical experiments were used to verify the accuracy and numerical efficiency of the method. Additionally to illustrate the capabilities of the approach results for two practical applications are presented.

A visualization and computational study of horizontal Bridgman crystal growth

A transparent three-zone horizontal Bridgman furnace was used for the crystal growth of sodium nitrate. During crystal growth, the heating profiles and the growth front shape as well as flow patterns were recorded. To further understand the heat flow, a three-dimensional computer model based on an efficient multigrid finite volume method was also used to simulate the growth. Key process parameters, including the heating profiles, the growth rate, and the booster heating, were considered and their effects on the interface shape and the flow structures were discussed. It was observed that both buoyancy and Marangoni flows were dominant in the melt causing a highly concave interface. As a result, single-crystal growth was very difficult. Suitable insulation at the furnace bottom reduced interface deflection. Further, interface inversion was obtained by using a booster heating while keeping a cold spot at the top furnace wall near the interface by blowing cooling air. The obtained convex interface shape thus made the growth of a single crystal much easier.

Fluid flow and heat transfer test problems for non‐orthogonal grids: Bench‐mark solutions

AbstractFour problems of fluid flow and heat transfer were designed in which non‐orthogonal, boundary‐fitted grids were to be used. These are proposed to serve as test cases for testing new solution methods. This paper presents solutions of the test problems obtained by using a multigrid finite volume method with grids of up to 320 × 320 control volumes. Starting from zero fields, iterations were performed until the sum of the absolute residuals had fallen seven orders of magnitude, thus ensuring that the variable values did not change to six most significant digits. By comparing the solutions for successive grids at moderate Reynolds and Rayleigh numbers, the discretization errors were estimated to be lower than 0·1%. The results presented in this paper may thus serve for comparison purposes as bench‐mark solutions.

NUMERICAL SIMULATION OF BUOYANT AND THERMOCAPILLARY CONVECTION IN A SQUARE CAVITY

Numerical results are presented of the simulation of combined buoyant and thermocapillary convection in a square cavity, and comparison is made with experimental observations of Schwabe and Metzger [1]. The two-dimensional conservation equations for mass, momentum, and thermal energy (temperature) are solved using a multigrid finite-volume method and grids with up to 248 X 200 control volumes. Central differencing is used to discretize both convection and diffusion fluxes, and the coupling of pressure and velocity is achieved via the SIMPLE algorithm for colocated variable arrangement [2]. The discretization accuracy of the results is estimated to be of the order of 1% on the finest grid. The agreement with experimental results is fairly good; the reasons for observed discrepancies are also discussed.