A Simple Physical Model for Control of an Propellerless Aquatic Robot

2021 ◽  
pp. 1-13
Author(s):  
Yury Karavaev ◽  
Anton Klekovkin ◽  
Ivan Mamaev ◽  
Valentin Tenenev ◽  
Evgeny Vetchanin
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Viscous Friction ◽  
Body Motion ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Straight Line ◽  
Simple Physical Model ◽  
Added Masses ◽  
Internal Rotor

Abstract This paper is concerned with the motion of an aquatic robot whose body has the form of a sharp-edged foil. The robot is propelled by rotating the internal rotor without shell deformation. The motion of the robot is described by a finitedimensional mathematical model derived from physical considerations. This model takes into account the effect of added masses and viscous friction. The parameters of the model are calculated from comparison of experimental data and numerical solution to the equations of rigid body motion and the Navier – Stokes equations. The proposed mathematical model is used to define controls implementing straight-line motion, motion in a circle and motion along a complex trajectory. Experiments for estimation of the efficiency of the model have been conducted.

Mathematical study of a single leukocyte in microchannel flow

2018 ◽  
Vol 13 (5) ◽  
pp. 43 ◽  
Author(s):  
S. Boujena ◽  
O. Kafi ◽  
A. Sequeira
Keyword(s):  
Mathematical Model ◽  
Numerical Approximation ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Microchannel Flow ◽  
Navier Stokes Equations ◽  
Coupled Problem ◽  
Inflammatory Drugs ◽  
The Mathematical Model ◽  
Rate Type

The recruitment of leukocytes and subsequent rolling, activation, adhesion and transmigration are essential stages of an inflammatory response. Chronic inflammation may entail atherosclerosis, one of the most devastating cardiovascular diseases. Understanding this mechanism is of crucial importance in immunology and in the development of anti-inflammatory drugs. Micropipette aspiration experiments show that leukocytes behave as viscoelastic drops during suction. The flow of non-Newtonian viscoelastic fluids can be described by differential, integral and rate-type constitutive equations. In this study, the rate-type Oldroyd-B model is used to capture the viscoelasticity of the leukocyte which is considered as a drop. Our main goal is to analyze a mathematical model describing the deformation and flow of an individual leukocyte in a microchannel flow. In this model we consider a coupled problem between a simplified Oldroyd-B system and a transport equation which describes the density considered as non constant in the Navier–Stokes equations. First we present the mathematical model and we prove the existence of solution, then we describe its numerical approximation using the level set method. Through the numerical simulations we analyze the hemodynamic effects of three inlet velocity values. We note that the hydrodynamic forces pushing the cell become higher with increasing inlet velocities.

Viscosity Effects on the Radiation Hydrodynamics of Horizontal Cylinders

1991 ◽  
Vol 113 (4) ◽  
pp. 334-343 ◽  
Author(s):  
R. W. Yeung ◽  
C.-F. Wu
Keyword(s):  
Numerical Solutions ◽  
Stokes Equations ◽  
Small Body ◽  
Low Frequency ◽  
Body Motion ◽  
Navier Stokes ◽  
Inviscid Fluid ◽  
Viscous Effects ◽  
Navier Stokes Equations ◽  
Horizontal Cylinders

The problem of a body oscillating in a viscous fluid with a free surface is examined. The Navier-Stokes equations and boundary conditions are linearized using the assumption of small body-motion to wavelength ratio. Generation and diffusion of vorticity, but not its convection, are accounted for. Rotational and irrotational Green functions for a divergent and a vorticity source are presented, with the effects of viscosity represented by a frequency Reynolds number Rσ = g2/νσ3. Numerical solutions for a pair of coupled integral equations are obtained for flows about a submerged cylinder, circular or square. Viscosity-modified added-mass and damping coefficients are developed as functions of frequency. It is found that as Rσ approaches infinity, inviscid-fluid results can be recovered. However, viscous effects are important in the low-frequency range, particularly when Rσ is smaller than O(104).

Mathematical and Physical Modeling of Three-Phase Gas-Stirred Ladles

2016 ◽  
Vol 1812 ◽  
pp. 29-34
Author(s):  
Juan A. López ◽  
Marco A. Ramírez-Argáez ◽  
Adrián M. Amaro-Villeda ◽  
Carlos González
Keyword(s):  
Mathematical Model ◽  
Physical Model ◽  
Stokes Equations ◽  
Steel Slag ◽  
Flow Patterns ◽  
Navier Stokes ◽  
Steel Ladle ◽  
Phase System ◽  
Navier Stokes Equations ◽  
Three Phase

ABSTRACTA very realistic 1:17 scale physical model of a 140-ton gas-stirred industrial steel ladle was used to evaluate flow patterns measured by Particle Image Velocimetry (PIV), considering a three-phase system (air-water-oil) to simulate the argon-steel-slag system and to quantify the effect of the slag layer on the flow patterns. The flow patterns were evaluated for a single injector located at the center of the ladle bottom with a gas flow rate of 2.85 l/min, with the presence of a slag phase with a thickness of 0.0066 m. The experimental results obtained in this work are in excellent agreement with the trends reported in the literature for these gas-stirred ladles. Additionally, a mathematical model was developed in a 2D gas-stirred ladle considering the three-phase system built in the physical model. The model was based on the Eulerian approach in which the continuity and the Navier Stokes equations are solved for each phase. Therefore, there were three continuity and six Navier-Stokes equations in the system. Additionally, turbulence in the ladle was computed by using the standard k-epsilon turbulent model. The agreement between numerical simulations and experiments was excellent with respect to velocity fields and turbulent structure, which sets the basis for future works on process analysis with the developed mathematical model, since there are only a few three-phase models reported so far in the literature to predict fluid dynamics in gas-stirred steel ladles.

Numerical Simulation of Vortex Induced Vibration Using the K-ε Model

2006 ◽  
Author(s):  
Juan B. V. Wanderley ◽  
Gisele H. B. Souza ◽  
Carlos Levi
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Body Motion ◽  
Navier Stokes ◽  
Experimental Investigations ◽  
Real Problem ◽  
Navier Stokes Equations ◽  
Vortex Induced Vibration ◽  
Selection Of

Numerical simulations of Vortex Induced Vibration have been failing to duplicate accurately experimental data mostly due to the complexity of the physics involved in the real problem. Therefore, a careful and comprehensive investigation on CFD algorithms is still required to indicate the most suitable numerical scheme to handle such a complicate problem. Grid generation, boundary condition implementation, and coupling between the fluid flow governing equations and body motion equation are known to have strong influence on the qualities of the numerical results. This work presents results obtained from a long-term investigation featuring different CFD methods. The investigations enabled the selection of a very effective algorithm that showed an outstanding agreement between experiment and numerical simulation of the VIV phenomenon. Good agreement is obtained in the entire range of reduced velocity covered by the experimental investigations. The successful algorithm discussed here applies the Beam and Warming implicit scheme to solve the two-dimensional slightly compressible Navier–Stokes equations with the K-ε turbulence model to simulate the turbulent flow at the wake of the cylinder.

scholarly journals NUMERICAL SIMULATIONS OF LOW REYNOLDS NUMBER FLOWS PAST ELASTICALLY MOUNTED CYLINDER

2012 ◽  
Vol 11 (1-2) ◽  
pp. 61
Author(s):  
R. A. Gonçalves ◽  
P. R. F. Teixeira ◽  
E. Didier
Keyword(s):  
Vortex Shedding ◽  
Stokes Equations ◽  
Reynolds Numbers ◽  
Body Motion ◽  
Petroleum Exploration ◽  
Navier Stokes ◽  
Generation Process ◽  
Navier Stokes Equations ◽  
Eulerian Formulation ◽  
Low Reynolds

The vortex-induced vibration (VIV) phenomenon has drawn the attention of researchers in Engineering for several decades. An example is the riser used for petroleum exploration, in which it is subjected to marine flows that may cause oscillations due to vortex shedding. In this paper, numerical analyses of the phenomena that occur in the interaction among flows at low Reynolds numbers and elastically mounted cylinders are presented. The simulation is carried out by using the numerical model Ifeinco that uses a semi-implicit two-step Taylor-Galerkin method to discretize the Navier-Stokes equations and the arbitrary Lagrangean-Eulerian formulation to follow the cylinder motion. The rigid body motion description is calculated by using the Newmark method. Firstly, the characteristics of the vortex generation process for the fixed cylinder are analyzed. In this case, the Strouhal number, the mean drag and the RMS lift coefficients for Reynolds numbers ranging from 90 to 140 are shown. Afterwards, an analysis of a flexible supported cylinder (with a spring and a damper) in transverse direction subject to flows with Reynolds numbers ranging from 90 to 140 is carried out. The cylinder displacement and the vibration frequencies are studied; the synchronization between the vortex shedding and the vibration frequency (lock-in) is analyzed. Similar results to the experimental ones developed by Anagnostopoulos and Bearman (1992) were obtained in this study.

scholarly journals Investigation on Resistance, Squat and Ship-Generated Waves of Inland Convoy Passing Bridge Piers in a Confined Waterway

2021 ◽  
Vol 9 (10) ◽  
pp. 1125
Author(s):  
Peng Du ◽  
Abdellatif Ouahsine ◽  
Philippe Sergent ◽  
Yannick Hoarau ◽  
Haibao Hu
Keyword(s):  
Stokes Equations ◽  
Lateral Position ◽  
Wave Pattern ◽  
Body Motion ◽  
Bridge Piers ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Sliding Mesh ◽  
Experimental Approaches ◽  
Mesh Technique

The average and unsteady hydrodynamics of an inland convoy passing bridge piers in a confined waterway were investigated using both numerical and experimental approaches. The numerical simulations are realized by solving the RANS (Reynolds-averaged Navier–Stokes) equations accounting for the solid body motion using the sliding mesh technique, while the experiments were carried out in the towing tank. The advancing resistance, trim, sinkage and ship-generated waves were analyzed as functions of the water depth, distance between bridge piers, draught and velocity. The existence of the piers is found to only influence the transient hydrodynamics of the convoy, but not the averaged properties. The ship-generated waves, especially the wave profiles at a specific lateral position, were characterized. Two wave crests exist at the pier position because of the additional reflections, creating a very complex wave pattern in the confined waterway.

Numerical Simulation on Undulatory Flow of Swimming Fish

2013 ◽  
Vol 353-356 ◽  
pp. 2545-2549
Author(s):  
Xu Zhang ◽  
Xiu Bin He
Keyword(s):  
Numerical Simulation ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Time Stepping ◽  
Dual Time Stepping ◽  
Straight Line ◽  
Volume Method ◽  
Undulatory Swimming

A numerical simulation is carried out to investigate the unsteady flows over a swimming fish. The three-dimensional incompressible Navier-Stokes equations are solved using the finite volume method with artificial compressibility and dual time stepping approaches on unstructured moving grid. A realistic fish-like body is modeled, which undergoes undulatory swimming in a straight line. Both inviscid and viscous flows have been simulated to study the flow structures.

INTRODUCING OF INTERNAL VISCOUS FRICTION IN EQUATIONS OF BEAM OSCILLATION AS LONG RECTANGULAR STRIP

2021 ◽  
pp. 54-58
Author(s):  
E.M. Zveriaev ◽  
Keyword(s):  
Stokes Equations ◽  
Asymptotic Series ◽  
Viscous Friction ◽  
Theory Of Elasticity ◽  
Navier Stokes ◽  
Dimensional Theory ◽  
Navier Stokes Equations ◽  
One Dimensional ◽  
The One ◽  
Beam Oscillation

Abstract. On the base of the method of simple iterations generalising methods of semi-inverse one of Saint-Venant, Reissner and Timoshenko the one-dimensional theory is constructed using the example of dynamic equations of a plane problem of elasticity theory for a long elastic strip. The resolving equation of that one-dimensional theory coincides with the equation of beam vibrations. The other problems with unknowns are determined without integration by direct calculations. In the initial equations of the theory of elasticity the terms corresponding to the viscous friction in the Navier-Stokes equations are introduced. The asymptotic characteristics of the unknowns obtained by the method of simple iterations allow to search for a solution in the form of expansions of the unknowns into asymptotic series. The resolving equation contains a term that depends on the coefficient of viscous friction.

Study of Maneuverability of Container Ship With Nonlinear and Roll-Coupled Effects by Numerical Simulations Using RANSE-Based Solver

2016 ◽  
Vol 138 (4) ◽  
Author(s):  
R. Rajita Shenoi ◽  
P. Krishnankutty ◽  
R. Panneer Selvam
Keyword(s):  
Mathematical Model ◽  
High Speed ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Container Ship ◽  
Navier Stokes Equations ◽  
Hydrodynamic Derivatives ◽  
Computational Fluid Dynamics Cfd ◽  
Experimental Values ◽  
The Mathematical Model

The examination of maneuvering qualities of a ship is necessary to ensure its navigational safety and prediction of trajectory. The study of maneuverability of a ship is a three-step process, which involves selection of a suitable mathematical model, estimation of the hydrodynamic derivatives occurring in the equation of motion, and simulation of the standard maneuvering tests to determine its maneuvering qualities. This paper reports the maneuvering studies made on a container ship model (S175). The mathematical model proposed by Son and Nomoto (1981, “On Coupled Motion of Steering and Rolling of a High Speed Container Ship,” J. Soc. Nav. Arch. Jpn., 150, pp. 73–83) suitable for the nonlinear roll-coupled steering model for high-speed container ships is considered here. The hydrodynamic derivatives are determined by numerically simulating the planar motion mechanism (PMM) tests in pure yaw and combined sway–yaw mode using an Reynolds-Averaged Navier–Stokes Equations (RANSE)-based computational fluid dynamics (CFD) solver. The tests are repeated with the model inclined at different heel angles to obtain the roll-coupled derivatives. Standard definitive maneuvers like turning tests at rudder angle, 35 deg and 20 deg/20 deg zig-zag maneuvers are simulated using the numerically obtained derivatives and are compared with those obtained using experimental values.

Vibrations of Circular Cylindrical Shells With Nonuniform Constraints, Elastic Bed and Added Mass Coupled to Internal, External and Annular Flow

2002 ◽  
Author(s):  
M. Amabili ◽  
R. Garziera
Keyword(s):  
Annular Flow ◽  
Stokes Equations ◽  
Computer Code ◽  
Inviscid Flow ◽  
Navier Stokes ◽  
Navier Stokes Equations ◽  
Viscous Forces ◽  
Added Masses ◽  
Circular Cylindrical Shells ◽  
Lumped Masses

The effect of steady viscous forces on vibrations of shell with internal and annular flow has been considered by using the time-mean Navier-Stokes equations. The model developed by Amabili & Garziera (2000), capable of simulating shells with non-uniform boundary conditions, added masses and partial elastic bed, has been extended to include non-uniform prestress. The effect of steady viscous forces has been added to the inviscid flow formulation considered by Amabili & Garziera (2002). The computer code DIVA has been developed by using the model developed in the present study. It has been validated by comparison with available results for shells with uniform constraints and has been used to study shells with non-uniform constraints and added lumped masses.

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