scholarly journals On a Computing Method for Nonlinear Free Surface Flow Causing Spray Ejection

2008 ◽  
Vol 8 (0) ◽  
pp. 89-106
Author(s):  
Hajime Kihara
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Nonlinear Free Surface ◽  
Computing Method

Surface Ship Total Resistance Prediction Based on a Nonlinear Free Surface Potential Flow Solver and a Reynolds-Averaged Navier-Stokes Viscous Correction

2007 ◽  
Vol 51 (01) ◽  
pp. 47-64
Author(s):  
James C. Huan ◽  
Thomas T. Huang
Keyword(s):  
Free Surface ◽  
Surface Potential ◽  
Potential Flow ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Navier Stokes ◽  
Total Resistance ◽  
Flow Solver ◽  
Resistance Prediction ◽  
Nonlinear Free Surface

A fast turnaround and an accurate computational fluid dynamics (CFD) approach for ship total resistance prediction is developed. The approach consists of a nonlinear free surface potential flow solver (PShip code) with a wet-or-dry transom stern model, and a Reynolds-averaged Navier-Stokes (RANS) equation solver that solves viscous free surface flow with a prescribed free surface given from the PShip. The prescribed free surface RANS predicts a viscous correction to the pressure resistance (viscous form) and viscous flow field around the hull. The viscous free surface flow solved this way avoids the time-consuming RANS iterations to resolve the free surface profile. The method, however, requires employing a flow characteristic-based nonreflecting boundary condition at the free surface. The approach can predict the components of ship resistance, the associated wave profile around the hull, and the sinkage and trim of the ship. Validation of the approach is presented with Wigley, Series 60 (CB = 0.6), and NSWCCD Model 5415 hulls. An overall accuracy of ±2% for ship total resistance prediction is achieved. The approach is applied to evaluating the effects of a stern flap on a DD 968 model on ship performance. An empirical viscous form resistance formula is also devised for a quick ship total resistance estimate.

Nonlinear free-surface flow due to an impulsively started submerged point sink

1998 ◽  
Vol 364 ◽  
pp. 325-347 ◽  
Author(s):  
MING XUE ◽  
DICK K. P. YUE
Keyword(s):  
Free Surface ◽  
Steady State ◽  
Numerical Study ◽  
Free Surface Flow ◽  
Small Time ◽  
Surface Flow ◽  
Boundary Integral ◽  
Critical Regime ◽  
Gravitational Acceleration ◽  
Nonlinear Free Surface

The unsteady fully nonlinear free-surface flow due to an impulsively started submerged point sink is studied in the context of incompressible potential flow. For a fixed (initial) submergence h of the point sink in otherwise unbounded fluid, the problem is governed by a single non-dimensional physical parameter, the Froude number, [Fscr ]≡Q/4π(gh5)1/2, where Q is the (constant) volume flux rate and g the gravitational acceleration. We assume axisymmetry and perform a numerical study using a mixed-Eulerian–Lagrangian boundary-integral-equation scheme. We conduct systematic simulations varying the parameter [Fscr ] to obtain a complete quantification of the solution of the problem. Depending on [Fscr ], there are three distinct flow regimes: (i) [Fscr ]<[Fscr ]1≈0.1924 – a ‘sub-critical’ regime marked by a damped wave-like behaviour of the free surface which reaches an asymptotic steady state; (ii) [Fscr ]1<[Fscr ]<[Fscr ]2≈0.1930 – the ‘trans-critical’ regime characterized by a reversal of the downward motion of the free surface above the sink, eventually developing into a sharp upward jet; (iii) [Fscr ]>[Fscr ]2 – a ‘super-critical’ regime marked by the cusp-like collapse of the free surface towards the sink. Mechanisms behind such flow behaviour are discussed and hydrodynamic quantities such as pressure, power and force are obtained in each case. This investigation resolves the question of validity of a steady-state assumption for this problem and also shows that a small-time expansion may be inadequate for predicting the eventual behaviour of the flow.

Divergent low-Froude-number series expansion of nonlinear free-surface flow problems

1978 ◽  
Vol 361 (1705) ◽  
pp. 207-224 ◽  
Keyword(s):  
Free Surface ◽  
Froude Number ◽  
Continuous Wave ◽  
Free Surface Flow ◽  
Formal Series ◽  
Surface Flow ◽  
Exponential Integral ◽  
Flow Problems ◽  
Low Froude Number ◽  
Nonlinear Free Surface

The low-Froude-number approximation in free-surface hydrodynamics is singular, and leads to formal series in powers of the Froude number with zero radius of convergence. The properties of these divergent series are discussed for several types of two-dimensional flows. It is shown that the divergence is of ‘n!' or exponential-integral character. A potential or actual lack of uniqueness is discovered and discussed. The series are summed by use of suitable nonlinear iterative transformations, giving good accuracy even for moderately large Froude number. Converged ' solutions ’ are obtained in this way, which possess jump discontinuities on the free surface. These jumps can be explained and, in principle, removed, by consideration of appropriate choices for the branch cut of the limiting exponential-integral solution. For example, we provide here a solution for a continuous wave-like flow, behind a semi-infinite moving body.

Nonlinear Free-Surface Flow Around an Impulsively Moving Cylinder

1989 ◽  
Vol 33 (03) ◽  
pp. 194-202
Author(s):  
Keh-Han Wang ◽  
Allen T. Chwang
Keyword(s):  
Free Surface ◽  
Free Surface Flow ◽  
Small Time ◽  
Surface Flow ◽  
Surface Elevation ◽  
Cylinder Surface ◽  
Cylinder Wall ◽  
Free Surface Elevation ◽  
Moving Cylinder ◽  
Nonlinear Free Surface

Nonlinear free-surface flow around an impulsively accelerating, vertical surface-piercing cylinder is investigated analytically. The exact solutions for the velocity potential and free-surface elevation are derived up to the third order by the small-time-expansion method. The hydrodynamic pressure acting on the cylinder wall is also obtained. A constant horizontal acceleration is considered to illustrate our theoretical results. It is found that, during the initial stage of this impulsive motion, no travelling free-surface waves are present. A surge of water appears on the upwind face and a depression forms on the down-wind face. The second-order free-surface elevation is singular along the contact line between the fluid surface and the cylinder surface. The nonlinear pressure distribution on the cylinder surface has been determined.

Comparative Study on the Wave Impact Load in a Sloshing Tank

2004 ◽  
Author(s):  
J. H. Kyoung ◽  
J. W. Kim ◽  
K. J. Bai
Keyword(s):  
Free Surface ◽  
Impact Load ◽  
Three Dimensional ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Wave Impact ◽  
Time Step ◽  
Surface Conditions ◽  
Nonlinear Free Surface ◽  
The Impact

Wave impact load occurring in a liquid storage tank during a sloshing motion is numerically simulated. Due to a violent sloshing, an excessive impact load can cause a critical damage to the tank structure. Recently this type of the accidents are reported and the problem becomes an important research topic in LNG (Liquefied Natural Gas) Tanker and FPSO (Floating Production Storage Offloading) design. To predict the sloshing impact load, Morison’s formula could be used for a practical reason. But using the Morison formula may provide directly an inaccurate estimation for the impact load because this formula is based on the linear model in the present nonlinear dominating phenomena. In this study, the wave impact load on the structure is obtained by imposing the exact nonlinear free surface conditions numerically and compared with that predicted by Morison’s formula. As a numerical method, a three-dimensional free surface flow in a tank is formulated in the scope of potential flow theory with the nonlinear free-surface conditions. A finite-element method based on Hamilton’s principle is employed as a numerical scheme. The problem is treated as an initial-value problem. The nonlinear problem is numerically solved through an iterative method at each time step.

Numerical Computations for a Nonlinear Free Surface Problem in Shallow Water

2002 ◽  
Author(s):  
K. J. Bai ◽  
J. H. Kyoung ◽  
J. W. Kim
Keyword(s):  
Free Surface ◽  
Shallow Water ◽  
Flow Problem ◽  
Free Surface Flow ◽  
Surface Flow ◽  
Nonlinear Phenomena ◽  
Local Flow ◽  
Highly Nonlinear ◽  
Nonlinear Free Surface ◽  
Good Agreement

This paper describes a finite element method applied to a nonlinear free surface flow problem for a ship moving in three dimensions. The physical model is taken to simulate the towing tank experimental conditions. The exact nonlinear free-surface flow problem formulated by an initial/boundary value problem is replaced by an equivalent weak formulation. The same problem was considered earlier by Bai, et. al. [1] where some irregularities were observed in the downstream waves and a transom stern ship geometry could not be treated. In the present paper, specifically, three improvements are made from the earlier work. The first improvement is the introduction of the 5-point Chebyshev filtering scheme which eliminates the irregular and saw-toothed waves in the downstream. The second improvement is that now we can treat a transom stern ship geometry. The third improvement is the introduction of a new boundary condition to simulate a dry bottom behind a transom stern ship which is stretched from the free surface to the bottom at a high Froude number. Computations are made for two models. The first model is tested for the generation of the solitons in the upstream and smooth waves in the downstream. The second model is used to compute the generation of a dry bottom behind a transom stern which is one of highly nonlinear phenomena. The results of the first model show a good agreement with previous results for the generation of the solitons. The results of the second model also show a good agreement with the preliminary experimental observation for a dry-bottom, which will be reported in near future. The numerical simulation of the second model can be applied to the local flow behind a sail of a submarine in cruise, a sloshing problem in LNG tankers, and a dam breaking problem. Both computed models are assumed to be in shallow water for simplicity. However, the present numerical method can treat arbitrary water-depth and practical ship geometries.

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