CFD Simulations of a Semi-Submersible With Absorbing Boundary Conditions

2009 ◽  
Author(s):  
Peter R. Wellens ◽  
Roel Luppes ◽  
Arthur E. P. Veldman ◽  
Mart J. A. Borsboom
Keyword(s):  
Boundary Conditions ◽  
Stokes Equations ◽  
Computing Time ◽  
Height Function ◽  
Absorbing Boundary Conditions ◽  
Navier Stokes ◽  
Two Phase ◽  
Absorbing Boundary ◽  
Wide Range ◽  
Grid Points

The CFD tool ComFLOW is suitable for simulations of two-phase flows in offshore applications. ComFLOW solves the Navier-Stokes equations in both water and (compressible) air. The water surface is advected through a Volume-of-Fluid method, with a height-function approach for improved accuracy. By employing Absorbing Boundary Conditions (ABC), boundaries can be located relatively close to an object, without influencing outgoing waves or generating numerical reflections that affect the waves inside the flow domain. Traditionally, boundaries are located far from the obstacle to avoid reflections; even when numerical damping zones are used. Hence, with the ABC approach less grid points are required for the same accuracy, which reduces the computing time considerably. Simulations of a semi-submersible model are compared to measurements. The overall agreement is reasonably good, for a wide range of wave conditions. The ABC performs well; numerical reflections are almost absent. Moreover, computing times reduce with a factor four compared to damping zone techniques.

scholarly journals Development of Hybrid Airlift-Jet Pump with Its Performance Analysis

2018 ◽  
Vol 8 (9) ◽  
pp. 1413 ◽  
Author(s):  
Dan Yao ◽  
Kwongi Lee ◽  
Minho Ha ◽  
Cheolung Cheong ◽  
Inhiug Lee
Keyword(s):  
Boundary Conditions ◽  
Mass Flow Rate ◽  
Mass Flow ◽  
Flow Rate ◽  
Stokes Equations ◽  
Flow Characteristics ◽  
Operating Conditions ◽  
Navier Stokes ◽  
Jet Pump ◽  
Two Phase

A new pump, called the hybrid airlift-jet pump, is developed by reinforcing the advantages and minimizing the demerits of airlift and jet pumps. First, a basic design of the hybrid airlift-jet pump is schematically presented. Subsequently, its performance characteristics are numerically investigated by varying the operating conditions of the airlift and jet parts in the hybrid pump. The compressible unsteady Reynolds-averaged Navier-Stokes equations, combined with the homogeneous mixture model for multiphase flow, are used as the governing equations for the two-phase flow in the hybrid pump. The pressure-based methods combined with the Pressure-Implicit with Splitting of Operators (PISO) algorithm are used as the computational fluid dynamics techniques. The validity of the present numerical methods is confirmed by comparing the predicted mass flow rate with the measured ones. In total, 18 simulation cases that are designed to represent the various operating conditions of the hybrid pump are investigated: eight of these cases belong to the operating conditions of only the jet part with different air and water inlet boundary conditions, and the remaining ten cases belong to the operating conditions of both the airlift and jet parts with different air and water inlet boundary conditions. The mass flow rate and the efficiency are compared for each case. For further investigation into the detailed flow characteristics, the pressure and velocity distributions of the mixture in a primary pipe are compared. Furthermore, a periodic fluctuation of the water flow in the mass flow rate is found and analyzed. Our results show that the performance of the jet or airlift pump can be enhanced by combining the operating principles of two pumps into the hybrid airlift-jet pump, newly proposed in the present study.

scholarly journals On periodic solutions for one-phase and two-phase problems of the Navier–Stokes equations

2020 ◽  
Author(s):  
Thomas Eiter ◽  
Mads Kyed ◽  
Yoshihiro Shibata
Keyword(s):  
Free Boundary ◽  
Boundary Conditions ◽  
Periodic Solutions ◽  
Parabolic Equations ◽  
Stokes Equations ◽  
Transmission Conditions ◽  
Navier Stokes ◽  
Two Phase ◽  
Navier Stokes Equations ◽  
Linearized Equations

Abstract This paper is devoted to proving the existence of time-periodic solutions of one-phase or two-phase problems for the Navier–Stokes equations with small periodic external forces when the reference domain is close to a ball. Since our problems are formulated in time-dependent unknown domains, the problems are reduced to quasilinear systems of parabolic equations with non-homogeneous boundary conditions or transmission conditions in fixed domains by using the so-called Hanzawa transform. We separate solutions into the stationary part and the oscillatory part. The linearized equations for the stationary part have eigen-value 0, which is avoided by changing the equations with the help of the necessary conditions for the existence of solutions to the original problems. To treat the oscillatory part, we establish the maximal $$L_p$$ L p –$$L_q$$ L q regularity theorem of the periodic solutions for the system of parabolic equations with non-homogeneous boundary conditions or transmission conditions, which is obtained by the systematic use of $${\mathcal R}$$ R -solvers developed in Shibata (Diff Int Eqns 27(3–4):313–368, 2014; On the $${{\mathcal {R}}}$$ R -bounded solution operators in the study of free boundary problem for the Navier–Stokes equations. In: Shibata Y, Suzuki Y (eds) Springer proceedings in mathematics & statistics, vol. 183, Mathematical Fluid Dynamics, Present and Future, Tokyo, Japan, November 2014, pp 203–285, 2016; Comm Pure Appl Anal 17(4): 1681–1721. 10.3934/cpaa.2018081, 2018; $${{\mathcal {R}}}$$ R boundedness, maximal regularity and free boundary problems for the Navier Stokes equations, Preprint 1905.12900v1 [math.AP] 30 May 2019) to the resolvent problem for the linearized equations and the transference theorem obtained in Eiter et al. ($${{\mathcal {R}}}$$ R -solvers and their application to periodic $$L_p$$ L p estimates, Preprint in 2019) for the $$L_p$$ L p boundedness of operator-valued Fourier multipliers. These approaches are the novelty of this paper.

Stability of wide‐angle absorbing boundary conditions for the wave equation

Geophysics ◽  
1989 ◽  
Vol 54 (9) ◽  
pp. 1153-1163 ◽  
Author(s):  
R. A. Renaut ◽  
J. Petersen
Keyword(s):  
Wave Equation ◽  
Boundary Conditions ◽  
Least Squares ◽  
Absorbing Boundary Conditions ◽  
Computational Domain ◽  
Wide Angle ◽  
Courant Number ◽  
Absorbing Boundary ◽  
Wide Range ◽  
Artificial Boundaries

Numerical solution of the two‐dimensional wave equation requires mapping from a physical domain without boundaries to a computational domain with artificial boundaries. For realistic solutions, the artificial boundaries should cause waves to pass directly through and thus mimic total absorption of energy. An artificial boundary which propagates waves in one direction only is derived from approximations to the one‐way wave equation and is commonly called an absorbing boundary. Here we investigate order 2 absorbing boundary conditions which include the standard paraxial approximation. Absorption properties are compared analytically and numerically. Our numerical results confirm that the [Formula: see text] or Chebychev‐Padé approximations are best for wide‐angle absorption and that the Chebychev or least‐squares approximations are best for uniform absorption over a wide range of incident angles. Our results also demonstrate, however, that the boundary conditions are stable for varying ranges of Courant number (ratio of time step to grid size). We prove that there is a stability barrier on the Courant number specified by the coefficients of the boundary conditions. Thus, proving stability of the interior scheme is not sufficient. Furthermore, waves may radiate spontaneously from the boundary, causing instability, even if the stability bound on the Courant number is satisfied. Consequently, the Chebychev and least‐squares conditions may be preferred for wide‐angle absorption also.

scholarly journals Absorbing boundary conditions for acoustic and elastic wave equations

1977 ◽  
Vol 67 (6) ◽  
pp. 1529-1540 ◽  
Author(s):  
Robert Clayton ◽  
Björn Engquist
Keyword(s):  
Boundary Conditions ◽  
Elastic Wave ◽  
Wave Equations ◽  
Absorbing Boundary Conditions ◽  
Limited Area ◽  
Absorbing Boundary ◽  
Physical Behavior ◽  
Wide Range ◽  
Elastic Wave Equations ◽  
Numerical Wave

abstract Boundary conditions are derived for numerical wave simulation that minimize artificial reflections from the edges of the domain of computation. In this way acoustic and elastic wave propagation in a limited area can be efficiently used to describe physical behavior in an unbounded domain. The boundary conditions are based on paraxial approximations of the scalar and elastic wave equations. They are computationally inexpensive and simple to apply, and they reduce reflections over a wide range of incident angles.

OPTIMAL CONVERGENCE OF NON-OVERLAPPING SCHWARZ METHODS FOR THE HELMHOLTZ EQUATION

2005 ◽  
Vol 13 (03) ◽  
pp. 525-545 ◽  
Author(s):  
FRÉDÉRIC MAGOULÈS ◽  
ROMAN PUTANOWICZ
Keyword(s):  
Boundary Conditions ◽  
Helmholtz Equation ◽  
Absorbing Boundary Conditions ◽  
Dirichlet Boundary Conditions ◽  
Absorbing Boundary ◽  
Comparative Performance ◽  
Schwarz Method ◽  
Wide Range ◽  
Schwarz Algorithm ◽  
Overlapping Schwarz

The non-overlapping Schwarz method with absorbing boundary conditions instead of the Dirichlet boundary conditions is an efficient variant of the overlapping Schwarz method for the Helmholtz equation. These absorbing boundary conditions defined on the interface between the subdomains are the key ingredients to obtain a fast convergence of the iterative Schwarz algorithm. In a one-way subdomains splitting, non-local optimal absorbing boundary conditions can be obtained and leads to the convergence of the Schwarz algorithm in a number of iterations equal to the number of subdomains minus one. This paper investigates different local approximations of these optimal absorbing boundary conditions for finite element computations in acoustics. Different approaches are presented both in the continuous and in the discrete analysis, including high-order optimized continuous absorbing boundary conditions, and discrete absorbing boundary conditions based on algebraic approximation. A wide range of new numerical experiments performed on unbounded acoustics problems demonstrate the comparative performance and the robustness of the proposed methods on general unstructured mesh partitioning.

scholarly journals Two-level, two-phase model for intense, turbulent sediment transport

2018 ◽  
Vol 839 ◽  
pp. 198-238 ◽  
Author(s):  
Jose M. Gonzalez-Ondina ◽  
Luigi Fraccarollo ◽  
Philip L.-F. Liu
Keyword(s):  
Sediment Transport ◽  
Stokes Equations ◽  
Navier Stokes ◽  
Small Scale ◽  
High Concentration ◽  
Two Phase ◽  
Theoretical Derivation ◽  
Length Scales ◽  
Fluid Turbulence ◽  
Wide Range

The study of sediment transport requires in-depth investigation of the complex effects of sediment particles in fluid turbulence. In this paper we focus on intense sediment transport flows. None of the existing two-phase models in the literature properly replicates the liquid and solid stresses in the near bed region of high concentration of sediment. The reason for this shortcoming is that the physical processes occurring at the length scale of the particle collisions are different from those occurring at larger length scales and therefore, they must be modelled independently. We present here a two-level theoretical derivation of two-phase, Favre averaged Navier–Stokes equations (FANS). This approach treats two levels of energy fluctuations independently, those associated with a granular spatial scale (granular temperature and small-scale fluid turbulence) and those associated with the ensemble average (turbulent kinetic energy for the two phases). Although similar attempts have been made by other researchers, the two level approach ensures that the two relevant length scales are included independently in a more consistent manner. The model is endowed with a semi-empirical formulation for the granular scale fluid turbulence, which is important even in the dense collisional shear layer, as has been recently recognized. As a result of the large and small scale modelling of the liquid and solid fluctuations, predictions are promising to be reliable in a wide range of flow conditions, from collisional to turbulent suspensions. This model has been validated for steady state flows with intense, collisional or mixed collisional–turbulent sediment transport, using various sources of detailed experimental data. It compares well with the experimental results in the whole experimental range of Shields parameters, better than previous models, although at the cost of increased complexity in the equations. Further experiments on turbulent suspensions would be necessary to definitely assess the model capabilities.

Adaptive Grid Refinement for Two-Phase Offshore Applications

2018 ◽  
Author(s):  
Peter van der Plas ◽  
Arthur E. P. Veldman ◽  
Henk Seubers ◽  
Joop Helder ◽  
Ka-Wing Lam
Keyword(s):  
Cfd Simulation ◽  
Simulation Method ◽  
Breaking Waves ◽  
Absorbing Boundary Conditions ◽  
Grid Refinement ◽  
Two Phase ◽  
Absorbing Boundary ◽  
Irregular Wave ◽  
Area Of Interest ◽  
Wide Range

In the past, the CFD simulation method ComFLOW has been successfully applied in a wide range of offshore applications, involving wave simulations and impact calculations. In many of these calculations the area of interest comprises a small part of the domain and remains fixed in time, which allows for efficient grid refinement by means of grid stretching or static local refinement. However, when trying to accurately resolve the surface dynamics and kinematics of irregular and breaking waves, the resolution requirements are strongly time-dependent and difficult to predict in advance. Efficient grids can only be obtained by means of time-adaptive refinement. A Cartesian block-based refinement approach is followed which allows for efficient grid adaptation, with moderate overhead. An array-based data structure is employed which exploits the semi-structured nature of the Cartesian block grid. Currently we are testing the method with the simulation of lifeboat drops in regular and irregular wave conditions. This poses several challenges such as accurately imposing the incoming waves and modifying the absorbing boundary conditions to support two-phase flow. To reduce the wall-clock time, the simulation method has been parallelized.

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