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A two-phase flow model is developed to study violent impact flow problem. The model governed by the Navier-Stokes equations with free surface boundary conditions is solved by a Constrained Interpolation Profile (CIP)-based high-order finite difference method on a fixed Cartesian grid system. The free surface is immersed in the computation domain and expressed by a one-fluid density function. An accurate Volume of Fluid (VOF)-type scheme, the Tangent of Hyperbola for Interface Capturing (THINC), is combined for the free surface treatment. Results of another two free surface capturing methods, the original VOF and CIP, are also presented for comparison. The validity and utility of the numerical model are demonstrated by applying it to two dam-break problems: a small-scale two-dimensional (2D) and three-dimensional (3D) full scale simulations and a large-scale 2D simulation. Main attention is paid to the water elevations and impact pressure, and the numerical results show relatively good agreement with available experimental measurements. It is shown that the present numerical model can give a satisfactory prediction for violent impact flow.

Violent water impact may occur in many hydrodynamics problems associated with important coastal and offshore engineering applications. Wave breaking in harbors, coastal areas, and offshore platforms, liquid sloshing in tank, and green water on decks are the most common examples of this class of problems. Accurate evaluation of such impact forces and possible structure responses is important for structure safety and disaster prevention. Water impacts are usually characterized by nonlinear phenomena, distorted free surfaces, and large amplitude structure responses for freely floating bodies, and their analysis is very complex. Analytical methods are only available for simple cases such as linear problems while laboratory tests are limited by high cost and technical limitations of the experimental facilities. As a result, there is an increasing interest in numerically simulating distorted free surfaces and their violent impacts on engineering structures.

Due to the possible similarity between green water impact and dam-break flow, dam-break flow theory has been widely used to study violent impact problems due to green water incidents [

For numerical study of violent impact flow problems, the nonlinear distorted free surface is one of its main difficulties. Among the available strategies to numerically construct an interface, the VOF method is one of the most popular methods in water-surface capturing, first introduced by Hirt and Nichols [

To solve the above-mentioned difficulties, a constrained interpolation profile (CIP) method combined with a surface capturing scheme, THINC, is applied to the study. The Constrained Interpolation Profile (CIP) method was developed by Yabe et al. [

The dam-break flow is widely used to examine the performance of various numerical techniques designed for simulating the surface interfacial and impact problems. The development of water flow along the floor after the sudden break of the dam has been a conventional target for numerical studies, but our research interest is in the second stage of the flow development, that is, the flow after impact on the vertical wall. In the second stage, overturning and breaking of the free surface as well as air entrapment are observed, and the computation of these complicated phenomena is a more challenging subject. Many models [

The objective of the study is to examine the performance of the model based on the CIP method and THINC scheme for simulating the violent impact and the dam-break flow problems. We use two dam-break experiments: a small-scale experiment and a relatively large-scale experiment to validate the numerical model. In the small-scale case, both a 2D- and a 3D-CIP-based models are used for analyzing the water collapse flow and the pressure on the opposite wall to examine the difference in simulations in different dimensions. In the relative large-scale case, we analyze the effect of air cushion caused by the backward plunging water reentering the main forward flow, which plays an important role in the calculation of impact pressure and water height on the second stage of the flow.

This paper is organized as follows. In Section

We consider an unsteady, viscous (laminar), and incompressible flow. The governing equations are as follows:

The time evolution of (

The advection phase computation of (

This is a Poisson type equation for the pressure calculation. Equation (

In the dam-break simulation, two density functions

After all of the density functions have been determined, any physical property

The drawback of the averaging process of (

The THINC scheme proposed by Xiao et al. [

Concept of the THINC scheme.

The dam-break flow is widely used as a benchmark test of violent impact flow on the deck to check the computation accuracy for a largely distorted free surface. Its simple initial and boundary conditions make the validation of computation and experiment quite straightforward. In this study, we reproduce two dam-break experiments numerically: one is in a small-scale tank performed by Hu and Kashiwagi [

This test case was originally performed for validation of a 2D-CIP-based model by Hu and Kashiwagi [

Schematic sketch of the dam-break simulation corresponding to reference.

In the simulations, three interface capturing methods, VOF, CIP, and THINC, are used for the 2D computation, and the results for the free surface variations (

Comparison of density function contours at

The 2D impact pressure using different free surface capturing methods is shown in Figure

Impact pressure caused by 2D dam-break flow.

The full scale 3D computations are run using the same scale as the experiment [

Snapshots at

The simulation of 3D dam breaking has been run on three different grids to investigate the behavior under grid refinement. The number of grid points used is

Impact pressure (3D) using different grid sizes (a) and using different free surface capturing methods (b).

Figure

Evolution of the 3D water collapse and interaction with the opposite wall.

In this section, a relative large-scale experimental test performed at MARIN by Zhou et al. [

Problem definition and measurement points for water heights and pressure (in m).

The experimental water tank is 3.22 m in length, 1.0 m in width, and 2.0 m in height. The initial water column is placed behind the flap with the size of 1.2 m in length, 1.0 m in width, and 0.6 m in height. For comparison, we use the water heights measured by two standard capacitive wave gauges. The two probe points, H1 and H2, locate at 2.725 m and 2.228 m away from the left wall of the tank, respectively. The pressure history measured by a circular pressure transducer of 0.09 m diameter at a point P2, 0.16 m above the bottom on the right wall of the tank is presented for comparison.

The effects of both the grid spacing and the time step are carefully investigated, and the values shown in what follows are considered reasonable choices. In the computation, a variable grid is used, in which the grid points are concentrated near the floor and the right wall. The grid number is

Three interface capturing methods, VOF, CIP, and THINC, are also used in this simulation, and the results for the free-surface variation are compared in Figure

Comparisons of density function contours. The three lines indicate that

The conservation of water mass in the computations for different interface-capturing schemes is checked. Figure

Conservation of liquid mass for different interface-capturing schemes.

Figure

Time history of the water front toe

In Figure

Vertical water heights at two measurement points: (a) H1, (b) H2.

Effect of air on water height of H1.

The evolution of the pressure field and free surface for the dam-break flow is presented in Figure

Pressure field and free surface of dam-break flow at different time.

In Figure

Pressure time history at a measurement point P2 on the right wall: (a) CIP, (b) SPH [

In this paper, we present a numerical model adopting the CIP method as the base flow solver to deal with multiphase flow problems with complicated free surface deformation. The THINC scheme is adopted in the interface capturing calculation and compared with other two capturing methods, VOF and CIP, from many aspects. This model is used to simulate two violent impact flow problems due to 2D and 3D dam-break flows and validated with experimental results.

Comparisons among the three free surface capturing methods in the two experiments, VOF, CIP and THINC, show that the VOF method (SLIC) has a good performance of mass conservation but the surface profile is not good, and the CIP method causes mass loss and has thick free surface, while the THINC scheme works much better than the other two schemes in terms of mass conservation and the suppression of interface smearing.

In the small-scale experiment, we perform both 2D and 3D computations and get that the complex distorted free surface with 3D breaking wave pattern can be simulated well. In the large-scale experiment, water elevations at two points H1 and H2 in the wave tank are calculated numerically and compared with experimental measurements. Though there is discrepancy at H1 when the water is overturning from the vertical wall, which is mainly caused by the entrapped air, the overall tendency at H2 is pretty good.

The water impact pressure on the vertical wall is numerically computed in two experiments. Though there is some difference, especially in the larger-scale case, the tendency of the impact pressure can be predicted with acceptable accuracy by this model.

It is proved that the CIP-based model combining the THINC free surface capturing scheme is effective in resolving violent free surface flow problem and the 3D calculation can give more details of the violent flow problem. For more accurate computations, we need more numerical model investigation (like 3D simulation or compressible flow consideration) and supplementary experimental study.

This work is jointly supported by the National Natural Science Foundation of China (51209184 and 51279186), Fundamental Research Funds for the Central Universities (2012QNA4020), Educational Commission of Zhejiang Province of China (Y201225713), Key Laboratory of Water-Sediment Sciences and Water Disaster Prevention of Hunan Province (Grant no. 2013SS03), and Scientific Research Foundation of Shandong University of Science and Technology for Recruited Talents.