An Assessment of Prediction Methods for Waves Inside the Moonpool of a Vessel (Comparisons of Numerical Solutions With Experiments)

2015 ◽  
Author(s):  
Yusong Cao ◽  
Fuwei Zhang ◽  
Tae-Hwan Joung ◽  
Anders Ostman ◽  
Trygve Kristiansen
Keyword(s):  
Cfd Simulation ◽  
Numerical Solutions ◽  
Prediction Methods ◽  
Diffraction Radiation ◽  
Linear Wave ◽  
Water Tank ◽  
Linear Solution ◽  
Physical Test ◽  
Flow Solver ◽  
Radiation Theory

This paper presents a preliminary assessment of the computational accuracy and efficiency of three different prediction methods for the water motion inside the moonpool of a rectangular box with forced vertical motion in a water tank. The first method is a linear solution method based on the linear wave diffraction/radiation theory (WAMIT). The second one is a method based on a CFD simulation (STAR-CCM+), the third method is a hybrid method combining a potential flow solver and a viscous flow solver (PVC3D). The accuracy of each method is assessed by comparing the prediction with the physical test data. The computational efficiency (complexity of setting up the computation and the computation speed) of the methods is discussed.

Non-linear wave propagation in a relaxing gas

1969 ◽  
Vol 39 (2) ◽  
pp. 329-345 ◽  
Author(s):  
H. Ockendon ◽  
D. A. Spence
Keyword(s):  
Numerical Solutions ◽  
Perturbation Technique ◽  
Finite Amplitude ◽  
Linear Wave ◽  
Singular Perturbation Technique ◽  
Linear Solution ◽  
Non Linear ◽  
Linear Wave Propagation ◽  
Two Temperatures ◽  
Propagation Of Waves

We consider the propagation of waves of small finite amplitude ε in a gas whose internal energy is characterized by two temperatures T (translational) and Ti (internal) in the form e = CvfT + CvfTi, and Ti is governed by a rate equation dTi/dt = (T − Ti)/τ. By means of approximations appropriate for a wave advancing into an undisturbed region x > 0, we show that to order εδ, the equation satisfied by velocity takes the non-linear form \[ \bigg(\tau\frac{\partial}{\partial t}+1\bigg)\bigg\{\frac{\partial u}{\partial t}+\bigg(a_1+\frac{\gamma + 1}{2}u\bigg)\frac{\partial u}{\partial x}-{\textstyle\frac{1}{2}}\lambda\frac{\partial^2u}{\partial x^2}\bigg\}=(a_1-a_0)\frac{\partial u}{\partial x}, \] where a1, a0 are the frozen and equilibrium speeds of sound in the undisturbed region, δ = ½(1 − (a20/a21)), and λ is the diffusivity of sound due to viscosity and heat conduction (λ may be neglected except when discussing the fine structure of a discontinuity). Some numerical solutions of this model equation are given.When ε is small compared with δ, it is also possible to construct a solution for the flow produced by a piston moving with a constant velocity by means of a sequence of matched asymptotic expansions. The limit reached for large times for either compressive or expansive pistons is the expected non-linear solution of the exact equations. For a certain range of advancing piston speeds, this is a fully dispersed wave with velocity U in the range a0 < U < a1. If U > a1 the solution is discontinuous, and indeterminate in the absence of viscosity; a singular perturbation technique based on λ is then used to determine the structure of the wave head.

Generation of Regular and Irregular Waves in Navier-Stokes CFD Solvers by Matching With the Nonlinear Potential Wave Solution at the Boundaries

2018 ◽  
Author(s):  
Youngmyung Choi ◽  
Benjamin Bouscasse ◽  
Sopheak Seng ◽  
Guillaume Ducrozet ◽  
Lionel Gentaz ◽  
...  
Keyword(s):  
Viscous Flow ◽  
Open Source ◽  
Cfd Simulation ◽  
Irregular Waves ◽  
Navier Stokes ◽  
Wave Fields ◽  
Flow Solver ◽  
Nonlinear Potential ◽  
Simulation Parameters ◽  
2D And 3D

The capability of wave generation and absorption in a viscous flow solver becomes important for achieving realistic simulations in naval and offshore fields. This study presents an efficient generation of nonlinear wave fields in the viscous flow solver by using a nonlinear potential solver called higher-order spectral method (HOS). The advantages of using a fully nonlinear potential solver for the generation of irregular waves are discussed. In particular, it is shown that the proposed method allows the CFD simulation to start at the time and over the space of interest, retrieved from the potential flow solution. The viscous flow solver is based on the open source library OpenFOAM. The potential solvers used to generate waves are the open source solvers HOS-Ocean and HOS-NWT (Numerical Wave Tank). Several simulation parameters in the CFD solver are investigated in the present study. A HOS wrapper program is newly developed to regenerate wave fields in the viscous flow solver. The wrapper program is validated with OpenFOAM for 2D and 3D regular and irregular waves using relaxation zones. Finally, the extreme waves corresponding to the 1000 year return period condition in the Gulf of Mexico are simulated with the viscous flow solver and the wave elevation is compared with the experiments.

The Ocean Mesoscale Regime of the Reduced-Gravity Quasigeostrophic Model

2019 ◽  
Vol 49 (10) ◽  
pp. 2469-2498 ◽  
Author(s):  
R. M. Samelson ◽  
D. B. Chelton ◽  
M. G. Schlax
Keyword(s):  
Numerical Solutions ◽  
Signal Propagation ◽  
Model Parameters ◽  
Linear Wave ◽  
Mesoscale Variability ◽  
Reduced Gravity ◽  
Stochastic Field ◽  
Stochastic Forcing ◽  
Frequency Spectra ◽  
Quasigeostrophic Model

AbstractA statistical-equilibrium, geostrophic-turbulence regime of the stochastically forced, one-layer, reduced-gravity, quasigeostrophic model is identified in which the numerical solutions are representative of global mean, midlatitude, open-ocean mesoscale variability. Solutions are forced near the internal deformation wavenumber and damped linearly and by high-wavenumber enstrophy dissipation. The results partially rationalize a recent semiempirical stochastic field model of mesoscale variability motivated by a global eddy identification and tracking analysis of two decades of satellite altimeter sea surface height (SSH) observations. Comparisons of model results with observed SSH variance, autocorrelation, eddy, and spectral statistics place constraints on the model parameters. A nominal best fit is obtained for a dimensional SSH stochastic-forcing variance production rate of 1/4 cm2 day−1, an SSH damping rate of 1/62 week−1, and a stochastic forcing autocorrelation time scale near or greater than 1 week. This ocean mesoscale regime is nonlinear and appears to fall near the stochastic limit, at which wave-mean interaction is just strong enough to begin to reduce the local mesoscale variance production, but is still weak relative to the overall nonlinearity. Comparison of linearly inverted wavenumber–frequency spectra shows that a strong effect of nonlinearity, the removal of energy from the resonant linear wave field, is resolved by the gridded altimeter SSH data. These inversions further suggest a possible signature in the merged altimeter SSH dataset of signal propagation characteristics from the objective analysis procedure.

Uncertainty Estimation for Numerical Solutions of Wall Bounded Turbulent Flows

2006 ◽  
Author(s):  
Francisco Elizalde-Blancas ◽  
Ismail Celik ◽  
Suryanarayana Pakalapati
Keyword(s):  
Laminar Flow ◽  
Turbulent Flows ◽  
Numerical Solutions ◽  
Turbulence Models ◽  
Grid Size ◽  
Gradient Term ◽  
True Error ◽  
Flow Solver ◽  
Solution Convergence ◽  
Manufactured Solution

In this study numerical solutions are presented for a steady state, incompressible, 2-D turbulent flow near a wall. For this specific problem a manufactured (exact) solution was provided by the organizers of the 2006 Lisbon Workshop [6]. With the help of manufactured solution, assessment of the true error and other relevant uncertainty measures are possible. The calculations were performed using the commercial flow solver FLUENT along with some user defined functions to define source terms and velocity profiles at boundaries. Though the flow regime is turbulent; the numerical solution is carried out for pseudo-laminar flow. This was done in order to avoid the errors implicit in turbulence models. The transformation from turbulent to laminar flow was done by defining a momentum source term which precludes the pressure gradient term. A detailed grid convergence analysis was performed. Using three-grid triplets the limiting values of the variables solved as the grid size tends to zero were calculated using different extrapolations. The L2 norms of the true error obtained from various extrapolations are assessed. These results exhibit solution convergence as the grid size decreases. It was also shown that cubic spline extrapolation perform the best among the methods considered.

Nonlinear Superposition Methods Applied to Continuous Ocean Wave Spectra

2011 ◽  
Vol 134 (1) ◽  
Author(s):  
Thomas B. Johannessen
Keyword(s):  
Model Comparison ◽  
Harmonic Wave ◽  
Vertical Cylinder ◽  
Wave Profile ◽  
Ocean Wave ◽  
Irregular Waves ◽  
Linear Wave ◽  
Beam Model ◽  
Wave Spectra ◽  
Linear Solution

The present paper addresses the challenges associated with applying weakly nonlinear mode-coupled solutions for wave interaction problems to irregular waves with continuous spectra. Unlike the linear solution, the nonlinear solutions will be strongly dependent on cut-off frequency for problems such as the wave elevation itself or loads on a slender cylinder used together with typical ocean wave spectra. It is found that the divergence of the solutions with respect to the cut-off frequency is related to the nonlinear interaction between waves with very different frequencies. This is, in turn, linked to a long standing discussion about the ability of mode-coupled methods to describe the modulation of a short wave due to the presence of a long wave. In cases where nonlinear properties associated with a measured or assumed history of the surface elevation is sought, it is not necessary to calculate accurately the nonlinear evolution of the wave field in space and time. For such cases it is shown that results which are independent of frequency cut-off may be obtained by introducing a maximum bandwidth in frequency between waves which are allowed to interact. It is shown that a suitable bandwidth can be found by applying this method to the problem of back-calculating a linear wave profile from a measured wave profile. In order to verify that this choice of bandwidth is suitable for second and third order terms, nonlinear loads on a slender vertical cylinder are calculated using the FNV method of Faltinsen, Newman, and Vinje (1995, “Nonlinear Wave Loads on a Slender, Vertical Cylinder,” J. Fluid Mech., 289, pp. 179–198). The method is used to compare loads calculated based on measured surface elevations with measurements of loads on two cylinders with different diameters. This comparison indicates that the bandwidth formulation is suitable and that the FNV solution gives a reasonable estimate of loading on slender cylinders. There are, however, loading mechanisms that the FNV solution does not describe, notably the secondary loading cycle first observed by Grue et al. (1993, Higher Harmonic Wave Exciting Forces on a Vertical Cylinder, Institute of Mathematics, University of Oslo, Preprint No. 2). Finally, the method is employed to calculate the ringing response on a large concrete gravity base platform. The base moment response is calculated using the FNV loading on the shafts and linear loads from a standard diffraction code, together with a structural finite element beam model. Comparison with results from a recent model testing campaign shows a remarkable agreement between the present method and the measured response.

Hydroelastic Modeling of a Compliant Offshore Tower: Formulation

2003 ◽  
Author(s):  
Jinzhu Xia ◽  
Quanming Miao ◽  
Nicholas Haritos ◽  
Beverley Ronalds
Keyword(s):  
Oil And Gas ◽  
Equations Of Motion ◽  
Fluid Structure Interaction ◽  
Coupled System ◽  
Dynamic Responses ◽  
Variation Principle ◽  
Diffraction Radiation ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Radiation Theory

Offshore oil and gas can be produced using a variety of platform types. One option, the compliant offshore tower, has proven to be an economic solution in moderately deep water (300–600m). In this paper, the wave-induced global dynamic responses of a compliant tower in wind, current and waves are studied in the context of fluid-structure interaction. A beam undergoing transverse and axial motion models the vertical member of the tower. The beam is supported by a linear-elastic torsional spring at the bottom end and a point mass and a buoyant chamber is located at the top free end. The fluid forces on the beam are modeled using the Morison equation while the hydrodynamic forces on the chamber are obtained based on the three-dimensional diffraction-radiation theory. By applying Hamilton’s variation principle, the equations of motion are derived for the coupled fluid-structure interaction system. The non-linear coupled system equations that emanate from this new approach can then be solved numerically in the time domain.

Computational Investigation on Centrifugal Compressor Performance at Various Altitudes

2011 ◽  
Vol 230-232 ◽  
pp. 1123-1128
Author(s):  
Yu Wang ◽  
Zhen Luo
Keyword(s):  
Gas Turbine ◽  
Centrifugal Compressor ◽  
Cfd Simulation ◽  
Numerical Solutions ◽  
Weight Ratio ◽  
Critical Factor ◽  
Computational Method ◽  
Turbine Engines ◽  
Gas Turbine Engines ◽  
Ambient Temperatures

Small gas turbine engines have been considered as a potential and popular mean of propulsion for Unmanned Aerial Vehicles (UAV). With the advantage of high thrust/power-to-weight-ratio from these engines, small aircraft can have larger payload allowance and higher altitude capability. However, at present, these gas turbine engines are not mature enough to perform critical mission for UAV. To be used for such critical mission, these gas turbine engines need a better reliability, efficiency and endurance. The capability of the engine to work efficiently in conditions at different altitude with the variant of air density is a critical factor related to higher operational ceiling. Hence this work aims to present a Computational Fluid Dynamics (CFD) simulation approach focusing on centrifugal compressors which are applied to turbo machines. A computational method is developed for studying the performance of small gas turbine engines over a range of altitude and ambient temperatures under different engine rates, and a centrifugal compressor simulation model is generated by using CFD techniques. Through numerical solutions obtained for different mesh sets the finest mesh of the model was determined. The performance curves obtained by the CFD simulation has been compared with the results obtained from the analytical method.

Wave Kinematics and Seakeeping Calculation With Varying Bathymetry

2009 ◽  
Author(s):  
Guillaume de Hauteclocque ◽  
Fla´via Rezende ◽  
Yann Giorgiutti ◽  
Xiao-Bo Chen
Keyword(s):  
Boundary Element Method ◽  
Wave Field ◽  
Incident Wave ◽  
Added Mass ◽  
Radiation Damping ◽  
Floating Body ◽  
Diffraction Radiation ◽  
Constant Depth ◽  
Wave Kinematics ◽  
Radiation Theory

Diffraction/Radiation theory is used to calculate the wave kinematics and the motions of a floating body in area of varying bathymetry. The bathymetry is modeled as a second body, which, without special measures, leads to spurious reflection at the edge of the mesh. A modified formulation of the Boundary Element Method is introduced to model partially transparent panels. Those panels, when properly used to smoothly extend the actual (opaque) bathymetry, allow much more accurate computation. The efficiency of the method is tested with regards of several parameters concerning the bathymetry size and the way to smooth the truncation. Numerical results are satisfactorily compared with a 3D shallow water code based on Green-Naghdi theory. The sensitivity to the slope on the ship response is then investigated (motion, added mass, radiation damping and second order loads). The differences with the constant depth calculations are significant, due to the modified incident wave field, but also due to modified added mass and radiation damping terms. The method presented here could be useful in the context of LNG terminals where the depth is quite shallow and the bathymetric variations significant.

Combined Experimental - Numerical Approach for the Fuel Jet Study in a LPP Combustor

2011 ◽  
Author(s):  
Amedeo Amoresano ◽  
Maria Cristina Cameretti ◽  
Raffaele Tuccillo
Keyword(s):  
Cfd Simulation ◽  
Fluid Dynamic ◽  
Numerical Approach ◽  
Experimental Information ◽  
Liquid Fuels ◽  
Injection System ◽  
Spray Parameters ◽  
Flow Solver ◽  
Fuel Jet ◽  
Fuel Vapour

The purpose of the paper is the investigation of the phenomena that mainly affect the mixture preparation and the combustion development in lean-premixed chambers supplied with liquid fuels (LPP). In such a study, the experimental analysis, performed by PDA based measurements, is supported and addressed by a CFD tool that is able to simulate the injection conditions, by isolating and studying some specific phenomena. A 3-D fluid dynamic code (i.e., the FLUENT® flow solver) has been used to simulate the spray pattern in the chamber. Preliminarily, the numerical simulation refer to cold flow conditions, in order to validate the estimation of the fundamental spray parameters through the comparison with the experimental data; in a second step, the calculations employ boundary conditions close to those occurring in the actual combustor operation, in order to predict the fuel vapour distribution throughout the premixing chamber. In particular, the fuel is injected under the typical conditions that occur in the injection system of a gas turbine LPP combustor. In this phase, the experimental information are introduced in terms of air and fuel mass flow rates and of inlet characteristics of the air flow entering the prevaporizing chamber, in order to predict the fuel vapour formation and distribution. The paper also compares different approaches that have been experienced for the CFD simulation.

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