scholarly journals CFD Simulation and Experimental Study on Coupled Motion Response of Ship with Tank in Beam Waves

2022 ◽  
Vol 10 (1) ◽  
pp. 113
Author(s):  
Tao He ◽  
Dakui Feng ◽  
Liwei Liu ◽  
Xianzhou Wang ◽  
Hua Jiang
Keyword(s):  
Working Conditions ◽  
Large Scale ◽  
Cfd Simulation ◽  
Stokes Equations ◽  
Body Motion ◽  
Time Step ◽  
Coupled Motion ◽  
Motion Response ◽  
Time Step Size ◽  
Tank Sloshing

Tank sloshing is widely present in many engineering fields, especially in the field of marine. Due to the trend of large-scale liquid cargo ships, it is of great significance to study the coupled motion response of ships with tanks in beam waves. In this study, the CFD (Computational Fluid Dynamics) method and experiments are used to study the response of a ship with/without a tank in beam waves. All the computations are performed by an in-house CFD solver, which is used to solve RANS (Reynold Average Navier-Stokes) equations coupled with six degrees-of-freedom solid-body motion equations. The Level Set Method is used to solve the free surface. Verification work on the grid number and time step size has been conducted. The simulation results agree with the experimental results well, which shows that the numerical method is accurate enough. In this paper, several different working conditions are set up, and the effects of the liquid height in the tank, the size of the tank and the wavelength ratio of the incident wave on the ship’s motion are studied. The results show the effect of tank sloshing on the ship’s motion in different working conditions.

scholarly journals Analysis of a Decoupled Time-Stepping Scheme for Evolutionary Micropolar Fluid Flows

2016 ◽  
Vol 2016 ◽  
pp. 1-13 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Micropolar Fluid ◽  
Stokes Equations ◽  
Fluid Model ◽  
Navier Stokes ◽  
Optimal Order ◽  
Step Size ◽  
Time Step ◽  
Order Error ◽  
Time Step Size ◽  
Time Stepping

Micropolar fluid model consists of Navier-Stokes equations and microrotational velocity equations describing the dynamics of flows in which microstructure of fluid is important. In this paper, we propose and analyze a decoupled time-stepping algorithm for the evolutionary micropolar flow. The proposed method requires solving only one uncoupled Navier-Stokes and one microrotation subphysics problem per time step. We derive optimal order error estimates in suitable norms without assuming any stability condition or time step size restriction.

scholarly journals Studying Inertia Effects in Open Channel Flow Using Saint-Venant Equations

Water ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 1652
Author(s):  
Dong-Sin Shih ◽  
Gour-Tsyh Yeh
Keyword(s):  
Stokes Equations ◽  
Field Application ◽  
Benchmark Problems ◽  
Algebraic Equations ◽  
Step Size ◽  
Time Step ◽  
Cross Sectional ◽  
Inertia Effects ◽  
Time Step Size ◽  
Saint Venant Equations

One-dimensional (1D) Saint-Venant equations, which originated from the Navier–Stokes equations, are usually applied to express the transient stream flow. The governing equation is based on the mass continuity and momentum equivalence. Its momentum equation, partially comprising the inertia, pressure, gravity, and friction-induced momentum loss terms, can be expressed as kinematic wave (KIW), diffusion wave (DIW), and fully dynamic wave (DYW) flow. In this study, the method of characteristics (MOCs) is used for solving the diagonalized Saint-Venant equations. A computer model, CAMP1DF, including KIW, DIW, and DYW approximations, is developed. Benchmark problems from MacDonald et al. (1997) are examined to study the accuracy of the CAMP1DF model. The simulations revealed that CAMP1DF can simulate almost identical results that are valid for various fluvial conditions. The proposed scheme that not only allows a large time step size but also solves half of the simultaneous algebraic equations. Simulations of accuracy and efficiency are both improved. Based on the physical relevance, the simulations clearly showed that the DYW approximation has the best performance, whereas the KIW approximation results in the largest errors. Moreover, the field non-prismatic case of the Zhuoshui River in central Taiwan is studied. The simulations indicate that the DYW approach does not ensure achievement of a better simulation result than the other two approximations. The investigated cross-sectional geometries play an important role in stream routing. Because of the consideration of the acceleration terms, the simulated hydrograph of a DYW reveals more physical characteristics, particularly regarding the raising and recession of limbs. Note that the KIW does not require assignment of a downstream boundary condition, making it more convenient for field application.

A Comparison of Strong and Weak Coupling Schemes for Computational Aeroelasticity in OpenFOAM

2018 ◽  
Author(s):  
Sabet Seraj ◽  
Amin Fereidooni ◽  
Anant Grewal
Keyword(s):  
Rigid Body ◽  
Strong Coupling ◽  
Weak Coupling ◽  
Body Motion ◽  
Coupling Scheme ◽  
Lower Sensitivity ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Structure Interaction

Two coupling schemes for fluid-structure interaction using the OpenFOAM structural solver sixDoF Rigid Body Motion are developed. The first scheme is developed by modifying the baseline leapfrog weak coupling scheme to minimize the lag between the fluid and structural solvers. The second is a strong coupling scheme based on the Crank-Nicolson method. The two newly implemented schemes and the baseline are compared through the aeroelastic simulation of a NACA 64A010 airfoil and the Benchmark Supercritical Wing. The aeroelastic solutions obtained using the newly implemented schemes exhibit significantly lower sensitivity to changes in time step size compared to the baseline weak coupling scheme. The modified weak coupling and strong coupling schemes perform comparably for the cases studied.

Comparative Study of the Inline Configuration Wind Farm

2019 ◽  
Vol 142 (6) ◽  
Author(s):  
Alaa S. Hasan ◽  
Tarek Elgammal ◽  
Randall S. Jackson ◽  
Ryoichi S. Amano
Keyword(s):  
Wind Turbine ◽  
Large Scale ◽  
Wind Farm ◽  
Stokes Equations ◽  
Experimental Testing ◽  
Wind Tunnel Test ◽  
Body Motion ◽  
Computational Domain ◽  
Horizontal Axis Wind Turbine ◽  
Depth Analysis

Abstract This research provides an in-depth analysis of the flow around the rotor and in the wake of a single horizontal axis wind turbine (HAWT) model at different free stream velocities and tip speed ratios (TSRs). Moreover, it extracts some recommendations that might be beneficial for large-scale projects such as wind farm layout design and power output prediction. For this purpose, modeling and experimental testing of a wind tunnel test section, including a single wind turbine model inside were created and validated against present experimental data of the same model. The large Eddy simulation (LES) was used as a numerical approach to model the Navier–Stokes equations. The computational domain was divided into two areas: rotational and stationary. The unsteady rigid body motion (RBM) model was adopted to represent the rotor rotation accurately.

scholarly journals Stability of Finite Difference Discretizations of Multi-Physics Interface Conditions

2013 ◽  
Vol 13 (2) ◽  
pp. 386-410 ◽  
Author(s):  
Björn Sjögreen ◽  
Jeffrey W. Banks
Keyword(s):  
Stokes Equations ◽  
Normal Mode Analysis ◽  
Linear Equations ◽  
Mode Analysis ◽  
Navier Stokes ◽  
Computational Domain ◽  
Interface Conditions ◽  
Step Size ◽  
Time Step ◽  
Time Step Size

AbstractWe consider multi-physics computations where the Navier-Stokes equations of compressible fluid flow on some parts of the computational domain are coupled to the equations of elasticity on other parts of the computational domain. The different subdomains are separated by well-defined interfaces. We consider time accurate computations resolving all time scales. For such computations, explicit time stepping is very efficient. We address the issue of discrete interface conditions between the two domains of different physics that do not lead to instability, or to a significant reduction of the stable time step size. Finding such interface conditions is non-trivial.We discretize the problem with high order centered difference approximations with summation by parts boundary closure. We derive L2 stable interface conditions for the linearized one dimensional discretized problem. Furthermore, we generalize the interface conditions to the full non-linear equations and numerically demonstrate their stable and accurate performance on a simple model problem. The energy stable interface conditions derived here through symmetrization of the equations contain the interface conditions derived through normal mode analysis by Banks and Sjögreen in [8] as a special case.

A Discrete-Forcing Immersed Boundary Method for the Fluid-Structure Interaction of an Elastic Slender Body

2011 ◽  
Author(s):  
Injae Lee ◽  
Haecheon Choi
Keyword(s):  
Immersed Boundary Method ◽  
Present Method ◽  
Stokes Equations ◽  
Slender Body ◽  
Body Motion ◽  
Computational Time ◽  
Immersed Boundary ◽  
Flexible Beam ◽  
Time Step ◽  
Boundary Method

In the present study, a new immersed boundary method for the simulation of flow around an elastic slender body is suggested. The present method is based on the discrete-forcing immersed boundary method by Kim et al. (J. Comput. Phys., 2001) and is fully coupled with the elastic slender body motion. The incompressible Navier-Stokes equations are solved in an Eulerian coordinate and the elastic slender body motion is described in a Lagrangian coordinate, respectively. The elastic slender body is modeled as a thin flexible beam and is segmented by finite number of blocks. Each block is then moved by the external and internal forces such as the hydrodynamic, tension, bending, and buoyancy forces. With the proposed method, we simulate several flow problems including flows over a flexible filament, an oscillating insect wing, and a flapping flag. We show that the present method does not impose any severe limitation on the size of computational time step. The results obtained agree very well with those from previous studies.

Numerical Study on the Effect of a Volute on Surge Phenomena in a Centrifugal Compressor

2016 ◽  
Author(s):  
S. H. Jeon ◽  
D. H. Hwang ◽  
J. H. Park ◽  
C. H. Kim ◽  
J. H. Baek ◽  
...  
Keyword(s):  
Centrifugal Compressor ◽  
Stokes Equations ◽  
Flow Instability ◽  
Numerical Study ◽  
Pressure Ratio ◽  
Unstable Flow ◽  
Step Size ◽  
Time Step ◽  
Time Step Size ◽  
Blade Passing Frequency

Numerical investigation of the effect of the volute on stall flow phenomenon is presented by solving three-dimensional Reynolds-averaged compressible Navier-Stokes equations. Two different configurations of a centrifugal compressor were used to compare their performance: One is an original centrifugal compressor which is composed of impeller, splitter, vaned diffuser and a volute and the other is the one without a volute. Steady calculations were performed to predict aerodynamic performance in terms of the pressure ratio, efficiency and mass flow rate. The results show that the operating range of the compressor with a volute is narrower than that of the compressor without a volute. This can be interpreted that flow instability is strongly influenced by the tongue of a volute which is highly asymmetric. Unsteady calculations were also performed with a time-step size of 38μs corresponding to a pitch angle of 5 degrees at the given rotational speed. The flow characteristics for two configurations are analyzed and compared at various instantaneous times showing unsteady dynamic features. Based on the unsteady flow simulation, fast Fourier transform at several discrete points in semi-vaneless space was performed at peak efficiency and near surge point in order to illustrate the unstable flow physics in both configurations. It is found that the blade passing frequency is dominant, indicating that diffuser passages have a periodicity of 40 degrees due to the rotational blades. Besides blade passing frequency, there were several noticeable frequencies which affect the instability of the whole system. Those frequencies in both configurations are compared and analyzed in various aspects.

Smoothed Profile Method for Particulate Two-Phase Flow

2008 ◽  
Author(s):  
Xian Luo ◽  
Martin R. Maxey ◽  
George E. Karniadakis
Keyword(s):  
Numerical Simulations ◽  
Stokes Equations ◽  
Integration Scheme ◽  
Force Density ◽  
Step Size ◽  
Time Step ◽  
Element Discretization ◽  
Profile Method ◽  
Time Step Size ◽  
Smoothed Profile Method

We re-formulate and demonstrate a new method for particulate flows, the so-called “Smoothed Profile” method (SPM) first proposed in [1]. The method uses a fixed computational mesh, which does not conform to the geometry of the particles. The particles are represented by certain smoothed indicator profiles to construct a smooth body force density term added into the Navier-Stokes equations. The SPM imposes accurately and efficiently the rigid-body constraint inside the particles. In particular, while the original method employs a fully-explicit time-integration scheme, we develop a high-order semi-implicit splitting scheme, which we implement in the context of spectral/hp element discretization. We show that the modeling error of SPM has a non-monotonic dependence on the time step size Δt. The optimum time step size balances the thickness of the Stokes layer and that of the profile interface. Subsequently, we present several numerical simulations, including flow past three-dimensional complex-shaped particles and two interacting microspheres, which are compared against full direct numerical simulations and the force coupling method (FCM).

scholarly journals Multi-Degree of Freedom Propeller Force Models Based on a Neural Network and Regression

2020 ◽  
Vol 8 (2) ◽  
pp. 89 ◽  
Author(s):  
Bradford Knight ◽  
Kevin Maki
Keyword(s):  
Neural Network ◽  
Stokes Equations ◽  
Equations Of Motion ◽  
Open Water ◽  
Small Time ◽  
Training Data ◽  
Step Size ◽  
Time Step ◽  
Neural Network Approach ◽  
Time Step Size

Accurate and efficient prediction of the forces on a propeller is critical for analyzing a maneuvering vessel with numerical methods. CFD methods like RANS, LES, or DES can accurately predict the propeller forces, but are computationally expensive due to the need for added mesh discretization around the propeller as well as the requisite small time-step size. One way of mitigating the expense of modeling a maneuvering vessel with CFD is to apply the propeller force as a body force term in the Navier–Stokes equations and to apply the force to the equations of motion. The applied propeller force should be determined with minimal expense and good accuracy. This paper examines and compares nonlinear regression and neural network predictions of the thrust, torque, and side force of a propeller both in open water and in the behind condition. The methods are trained and tested with RANS CFD simulations. The neural network approach is shown to be more accurate and requires less training data than the regression technique.

INFLUENCE OF PENALIZATION AND BOUNDARY TREATMENT ON THE STABILITY AND ACCURACY OF HIGH-ORDER DISCONTINUOUS GALERKIN SCHEMES FOR THE COMPRESSIBLE NAVIER-STOKES EQUATIONS

2013 ◽  
Vol 21 (01) ◽  
pp. 1250019
Author(s):  
ANDREAS RICHTER ◽  
EVA BRUSSIES ◽  
JÖRG STILLER
Keyword(s):  
Discontinuous Galerkin ◽  
Stokes Equations ◽  
Critical Time ◽  
High Order ◽  
Condition Numbers ◽  
Navier Stokes ◽  
Time Step ◽  
Navier Stokes Equations ◽  
Time Step Size ◽  
Boundary Treatment

A high-order interior penalty discontinuous Galerkin method for the compressible Navier–Stokes equations is introduced, which is a modification of the scheme given by Hartmann and Houston. In this paper we investigate the influence of penalization and boundary treatment on accuracy. By observing eigenvalues and condition numbers, a lower bound for the penalization term μ was found, whereas convergence studies depict reasonable upper bounds and a linear dependence on the critical time step size. By investigating conservation properties we demonstrate that different boundary treatments influence the accuracy by several orders of magnitude, and propose reasonable strategies to improve conservation properties.

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