Adapting a Linear Potential Theory Solver for the Outer Hull to Account for Fluid Dynamics in Tanks

2013 ◽  
Author(s):  
Arild Ludvigsen ◽  
Zhi Yuan Pan ◽  
Peng Gou ◽  
Torgeir Vada
Keyword(s):  
Fluid Dynamics ◽  
Boundary Value ◽  
Fem Analysis ◽  
Computer Code ◽  
Added Mass ◽  
Geometrical Shape ◽  
Linear Potential ◽  
Local Pressure ◽  
Local Loads ◽  
Outer Solution

The linear boundary value problem for the wave dynamics inside a tank is very similar to the solution for the outer hull. Because of this, the boundary value solver for the outer hull can be re-used for the tank. The oscillating hydrostatic pressure in the tank may also be calculated in the same way as for the outer hull. Thereby, the hydrostatic coefficients from the tank can also be obtained from the outer solution. This makes it, in principle, easy to adapt outer solution computer code to also account for the inner solutions for all the tanks. The procedure is discussed by Newman (2005). We have used it in a different way, isolating the tank solution into more flexible independent sub-runs. This approach provides part-results for the tanks, like added mass and restoring from the tanks. It also has numerical benefits, with the possibility to reuse the calculations for tanks of equal geometrical shape. We have also extended the procedure to account for full tanks without waves and restoring effects. The linear tank fluid dynamics is programmed into a quite general hydrodynamic frequency domain solver, with the possibility of automatic transferring of local loads to structural (FEM) analysis. Results for local loads are presented. A simpler method of quasi-static loading in tanks is discussed, with comparison to the present method. Effects on global motions and local pressure coming from the tank dynamics contributions are pointed out, such as the shifted resonance of the vessel and the added mass which differs from rigid masses of the tanks.

Strong solution of a hydrodinamics problem with memory

2021 ◽  
Vol 34 ◽  
pp. 62-74
Author(s):  
Mykola Krasnoshchok
Keyword(s):  
Fluid Dynamics ◽  
Fractional Derivative ◽  
Strong Solution ◽  
Applied Mathematics ◽  
Boundary Value ◽  
Initial Boundary ◽  
Evolutionary Equation ◽  
Liouville Derivative ◽  
Initial Boundary Value ◽  
Bio Engineering

In the last few years, the concepts of fractional calculus were frequently applied to other disciplines. Recently, this subject has been extended in various directions such as signal processing, applied mathematics, bio-engineering, viscoelasticity, fluid mechanics, and fluid dynamics. In fluid dynamics, the fractional derivative models were used widely in the past for the study of viscoelastic materials such as polymers in the glass transition and in the glassy state. Recently, it has increasingly been seen as an efficient tool through which a useful generalization of physical concepts can be obtained. The fractional derivatives used most are the Riemann--Liouville fractional derivative and the Caputo fractional derivative. It is well known that these operators exhibit difficulties in applications. For example, the Riemann--Liouville derivative of a constant is not zero. We deal with so called temporal fractional derivative as a prototype of general fractional derivative. We prove the global strong solvability of a linear and quasilinear initial-boundary value problems with a singular complete monotone kernels. Our main tool is a theory of evolutionary integral equations. An abstract fractional order differential equation is studied, which contains as particular case the Rayleigh–Stokes problem for a generalized second-grade fluid with a fractional derivative model. This paper concerns with an initial-boundary value problem for the Navier--Stokes--Voigt equations describing unsteady flows of an incompressible viscoelastic fluid. We give the strong formulation of this problem as a nonlinear evolutionary equation in Sobolev spaces. Using the Galerkin method with a special basis of eigenfunctions of the Stokes operator, we construct a global-in-time strong solution in two-dimensional domain. We also establish an $L_2$ decay estimate for the velocity field under the assumption that the external forces field is conservative.

scholarly journals Reflection Method for Mathematical Modeling of Potential Fields in Multi-Layer Media

2019 ◽  
Vol 224 ◽  
pp. 01004
Author(s):  
Oleg Yaremko ◽  
Natalia Yaremko
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Field Potential ◽  
Computer Code ◽  
Potential Fields ◽  
Reflection Method ◽  
Dirichlet Problems ◽  
Thermal Fields ◽  
Dirichlet Model ◽  
Fourth Kind

In this paper, potential fields in areas with plane and circular symmetry have been studied. In this case, the field potential is defined as the sum of solutions of Dirichlet model boundary value problems. The reflection method is used for the modeling of stationary thermal fields in multilayer media. By applying the reflection method, we found analytical solutions of boundary value problems with boundary conditions of the fourth kind for the Laplace equations and developed new computational algorithms. The developed algorithms can be easily implemented and transformed into a computer code. First of all, these algorithms implement consistent solutions of the Dirichlet problems for the model domains that allows using libraries of subroutines. Secondly, they have high algorithmic efficiency. It has been shown that reflection method is identical to the method of transformation operators and proved that transformation operator can be decomposed into a series of successive reflections from the external and internal boundaries. Finally, a physical interpretation of the reflection method has been discussed in detail.

Estimation of BOP Stack Drag and Added Mass Using Computational Fluid Dynamics

2017 ◽  
Author(s):  
Carlos F. Lopez ◽  
Harbinder Pordal ◽  
Kenneth Bhalla ◽  
Matthew J. Stahl
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Added Mass

Some Boundary Value Problems of Elastic Media Containing Rigid Inclusions Under Compressive Mechanical Loads

2009 ◽  
Author(s):  
Vahagn Makaryan ◽  
Michael Sutton ◽  
Gurgen Chlingaryan ◽  
Davresh Hasanyan ◽  
Xiaomin Deng
Keyword(s):  
Boundary Value Problems ◽  
Elastic Medium ◽  
Integral Transformation ◽  
Logarithmic Singularity ◽  
Boundary Value ◽  
Compressive Loading ◽  
Geometrical Shape ◽  
Square Root ◽  
End Points ◽  
Square Root Singularity

In this work we discuss some 2D boundary-value problems related to an elastic medium containing a thin rigid inclusion with general geometrical shape located in the interface between two separate elastic half-planes and subjected to compressive loading. Assuming perfect bonding between the inclusion and elastic medium, Fourier and Henkel integral transformation techniques are used to obtain the exact solution for the problem. Explicit forms are presented for arbitrary forms of thin inclusions, demonstrating that the tangent shear stress at the end-points of the inclusion has a square-root singularity. It is also shown that the normal stress has a logarithmic singularity when the end-points of the inclusion are approached from the inside of the inclusion and a square-root singularity when the end-points of the inclusion are approached from the outside of the inclusion. For special, extreme cases the solutions for anti-cracks are also presented.

Computational Fluid Dynamics Simulation of Airflow Alteration in the Trachea Before and After Vascular Ring Surgery

2013 ◽  
Author(s):  
Tzu-Ching Shih ◽  
Tzyy-Leng Horng ◽  
Fong-Lin Chen
Keyword(s):  
Fluid Dynamics ◽  
Computational Fluid Dynamics ◽  
Vascular Ring ◽  
Dynamics Simulation ◽  
Positive Pressure ◽  
Local Pressure ◽  
Pressure Drops ◽  
Vascular Rings ◽  
Before And After ◽  
Key Factor

Vascular rings, congenital intracardic anomalies of the aortic arch and the vessels emerging from the heart, completely encircle the trachea and esophagus [1]. The vascular ring results in narrowing and obstruction of the trachea and the esophagus. Due to the existence of a complete or partial vascular ring compressing either the trachea or esophagus, symptoms of a vascular ring in children include cough, stridor, chronic cough, dysphagia, persistent wheeze, and noisy breathing [2]. Some studies reported that the vascular ring surgery provides an excellent chance to improve the patient respiration conditions, especially for relief of symptoms [1–3]. Al-Bassam et al. reported that the thoracoscopic division of vascular rings in infants and children is a safe and effective surgery rather than an open thoracotomy[4]. Even after the treatment of a surgical division of the vascular ring, however, the fixed obstruction is relieved but the patient continues to have dynamic collapse because the compressed trachea segment is always malacic. Airway resistance to flow in the airway, thus, is a key factor for not only clinical diagnosis severity assessment but also therapeutic decision in tracheal stenosis. Furthermore, Malvè et al. (2011) utilized the finite element-based commercial software code (ADINA R&D Inc.) to model the fluid structure interaction of a human trachea under different ventilation conditions [5]. They also found that the positive pressure in the trachea does not result in the airway collapse during the time period of mechanical breathing. Therefore, the purpose of this study is to use the computational fluid dynamics (CFD) technique to calculate the local pressure drops in the tracheal segment for different inspiratory and expiratory flow rates due to preoperative and preoperative vascular ring surgery.

scholarly journals Some remarks on a Neumann boundary value problem arising in fluid dynamics

2004 ◽  
Vol 45 (3) ◽  
pp. 327-332 ◽  
Author(s):  
Pedro J. Torres
Keyword(s):  
Fluid Dynamics ◽  
Banach Space ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Boundary Value Problem ◽  
Positive Solution ◽  
Boundary Value ◽  
Neumann Boundary ◽  
Uniform Bounds ◽  
Neumann Boundary Value Problem

AbstractIt is proved that the Neumann boundary value problem, which Mays and Norbury have recently connected with a certain fluid dynamics equation, has a positive solution for any positive value of a particular parameter. Uniform bounds for the solutions and symmetry on a given range of the parameter are also introduced. The proofs include Krasnoselskii's classical fixed-point theorem on cones of a Banach space and basic comparison techniques.

Ultimate Strength of a Capesize Bulk Carrier in Hogging and Alternate Hold Loading Condition

2010 ◽  
Author(s):  
Zhi Shu ◽  
Torgeir Moan
Keyword(s):  
Ultimate Strength ◽  
Loading Condition ◽  
Fe Analysis ◽  
Fe Model ◽  
Bulk Carrier ◽  
Local Pressure ◽  
Local Loads ◽  
Hull Girder ◽  
Bulk Carriers ◽  
Global And Local

The ultimate hull girder strength of a Capesize bulk carrier under combined global and local loads in hogging and alternate loading condition (AHL) is evaluated using nonlinear finite element (FE) analysis with ABAQUS software. A three-cargo-hold FE model with fine mesh in the middle cargo hold is developed for the nonlinear FE analysis. The initial geometrical imperfections are introduced in the double bottom of the middle cargo hold. Both material and geometrical nonlinearities are taken into account in the FE model. The most critical situation for the longitudinal strength assessment of bulk carriers in hogging is the AHL condition with middle cargo hold empty under combined global and local loads. The local loads, i.e. the external sea pressure and internal cargo pressure are adopted according to Common Structural Rules for bulk carriers (CSR-BC). The ultimate hull girder strength with various local pressure load levels is investigated for the heavy cargo AHL in hogging condition. It is found that the ultimate strength of the hull girder can be significantly reduced due to the action of the local pressure loads compared with that obtained under pure hogging bending.

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