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Fig. 10. Comparison of measured and predicted vertical displacement of the floating solid experiment.

Figure 10 Comparison of measured and predicted vertical displacement of the floating solid experiment.

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Fig. 2. Schematical diagram to depict the conceptural steps of the moving solid algorithm. (a) A numerical cell is partially occupied by a solid material (in gray) with a moving speed (blue arrow). (b) The effective volume of the fluid cell is @V. (c) The partial-cell method expands the cell back to the original size with the same effective cell volume 0V. The speed of the moving solid therefore can be applied on the cell face. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) In this study, a two-way coupled Moving Solid Algorithm (MSA) was proposed to calculate the motion of the solids in water flows with free surface. The water flow was solved by a Large Eddy Sim- ulation model, and the water surface was tracked by the Volume of Fluid (VOF) method using a fixed grid. The motion of the solids was
Fig. 2. Schematical diagram to depict the conceptural steps of the moving solid algorithm. (a) A numerical cell is partially occupied by a solid material (in gray) with a moving speed (blue arrow). (b) The effective volume of the fluid cell is @V. (c) The partial-cell method expands the cell back to the original size with the same effective cell volume 0V. The speed of the moving solid therefore can be applied on the cell face. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) In this study, a two-way coupled Moving Solid Algorithm (MSA) was proposed to calculate the motion of the solids in water flows with free surface. The water flow was solved by a Large Eddy Sim- ulation model, and the water surface was tracked by the Volume of Fluid (VOF) method using a fixed grid. The motion of the solids was
Fig. 1. Schematic diagram to illustrate no-slip boundary condition on a moving solid. The grid is the fluid grid. The gray area represents a solid block. The red dot is the centroid of the block. The black and blue arrows are the moving vector of the block. (a) A moving block in the fluid domain. (b) The velocity vectors on the surfaces of the block. (c) A typical fluid cell (boundary in red) locates on the interface of the solid block and fluid. (For interpretation of the references to color in this figure legend, the reade1 is referred to the web version of this article.)
Fig. 1. Schematic diagram to illustrate no-slip boundary condition on a moving solid. The grid is the fluid grid. The gray area represents a solid block. The red dot is the centroid of the block. The black and blue arrows are the moving vector of the block. (a) A moving block in the fluid domain. (b) The velocity vectors on the surfaces of the block. (c) A typical fluid cell (boundary in red) locates on the interface of the solid block and fluid. (For interpretation of the references to color in this figure legend, the reade1 is referred to the web version of this article.)
Fig. 5. The array of virtual pressure sensors (VPS) distributed on the surfaces of the solid. The red dots are the location of the VPS. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Fig. 4. Schematic diagram of the rotation of the soild, x, y, z are the global coordinate axes, x’ y’ z’ are the principal axes of the moment.
Fig. 5. The array of virtual pressure sensors (VPS) distributed on the surfaces of the solid. The red dots are the location of the VPS. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.) Fig. 4. Schematic diagram of the rotation of the soild, x, y, z are the global coordinate axes, x’ y’ z’ are the principal axes of the moment.
Fig. 3. Schematic diagram of moving solids in fluid. The arrows are the fluid pressure acting on the surfaces of the solid.
Fig. 3. Schematic diagram of moving solids in fluid. The arrows are the fluid pressure acting on the surfaces of the solid.
Fig. 6. Schematic diagram of the pressure interpolation. The solid black line represents the location of the solid, the grey dotted lines represent the computa- tional grid for fluid flow, the grey diamonds represent the grid center, the red circles are VPS. The black diamonds represent the cell center that used for the pressure interpolation of the VPS (red circles). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
Fig. 6. Schematic diagram of the pressure interpolation. The solid black line represents the location of the solid, the grey dotted lines represent the computa- tional grid for fluid flow, the grey diamonds represent the grid center, the red circles are VPS. The black diamonds represent the cell center that used for the pressure interpolation of the VPS (red circles). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
where the subscripts i, j = 1, 2, 3 are the global coordinate axes, F; is the force acting on the element, and a; is the i-th component of the Fig. 7. Photograph of the experimental setup of the falling cube.
where the subscripts i, j = 1, 2, 3 are the global coordinate axes, F; is the force acting on the element, and a; is the i-th component of the Fig. 7. Photograph of the experimental setup of the falling cube.
“ The fluid pressures, on the surfaces of the solid, were calculated by the Navier Stokes equations and integrated to get the total force experienced by the solid. Virtual pressure sensors (VPS) were employed to obtain the fluid pressure on the solid surface (see Fig. 5). The density of the VPS is defined according to the complex- ity of the pressure field. In addition, the locations of the VPS are usually not intersected with the cell-centered pressure in the fluid mesh. An interpolation scheme is needed to calculate the pressure of the VPS. In this study, Inverse Distance Weighting (IDW) is uti- lized in the interpolation. The weighting function of the fluid cells is computed as:
“ The fluid pressures, on the surfaces of the solid, were calculated by the Navier Stokes equations and integrated to get the total force experienced by the solid. Virtual pressure sensors (VPS) were employed to obtain the fluid pressure on the solid surface (see Fig. 5). The density of the VPS is defined according to the complex- ity of the pressure field. In addition, the locations of the VPS are usually not intersected with the cell-centered pressure in the fluid mesh. An interpolation scheme is needed to calculate the pressure of the VPS. In this study, Inverse Distance Weighting (IDW) is uti- lized in the interpolation. The weighting function of the fluid cells is computed as:
Fig. 9. Sanpshots of numerical (left) and experimental (right) results of the floating block in the water tank For the unsteady flow calculation, the time derivative term uses the forward difference scheme. The initial time step for the LES model was set as At=1 x 10-*s, and the Courant number was Cr = 0.85, which led to the minimum time step of 1 x 10-*s. The convergence criterion for the momentum equations was set as 1x10-° The time step to compute the solid movement was At=1 x 10~°s, which is much smaller than the time step for fluid. In order to demonstrate the accuracy of the numerical model the simulation results of the present model were compared with two laboratory experiments. The first experiment was a cube (hea- vier than water) falling into a tank of water. The second experi- ment was a wooden block (lighter than water) rising from the bottom of a water tank. The results are discussed in the following sections.
Fig. 9. Sanpshots of numerical (left) and experimental (right) results of the floating block in the water tank For the unsteady flow calculation, the time derivative term uses the forward difference scheme. The initial time step for the LES model was set as At=1 x 10-*s, and the Courant number was Cr = 0.85, which led to the minimum time step of 1 x 10-*s. The convergence criterion for the momentum equations was set as 1x10-° The time step to compute the solid movement was At=1 x 10~°s, which is much smaller than the time step for fluid. In order to demonstrate the accuracy of the numerical model the simulation results of the present model were compared with two laboratory experiments. The first experiment was a cube (hea- vier than water) falling into a tank of water. The second experi- ment was a wooden block (lighter than water) rising from the bottom of a water tank. The results are discussed in the following sections.
Fig. 11. Side view of the instantaneous velocity vectors around the block. (a) t= 0.11 s; (b) t=0.25 s; (c) t=0.61s
Fig. 11. Side view of the instantaneous velocity vectors around the block. (a) t= 0.11 s; (b) t=0.25 s; (c) t=0.61s
Fig. 12. Side view of the pressure distribution around the block, pressure in [Pa]. (a) t= 0.11 s; (b) t=0.25 s; (c) t=0.61s The size of the water tank was 150 mm x 140 mm x 140 mm, and the water depth in the tank was 52 mm. A rectangular wooden block (width W = 48 mm, length L = 49 mm, height H = 24 mm, and density 800.52 kg/m*) was released from the bottom of the water Notice in Fig. 8(b), the simulated vertical displacement of the cube near the bottom of the tank deviated from the experimental points. The simulated displacement exhibited a re-bound behavior, while the measured displacement just gradually decreased to zero. The maximum difference between the simulated and measured
Fig. 12. Side view of the pressure distribution around the block, pressure in [Pa]. (a) t= 0.11 s; (b) t=0.25 s; (c) t=0.61s The size of the water tank was 150 mm x 140 mm x 140 mm, and the water depth in the tank was 52 mm. A rectangular wooden block (width W = 48 mm, length L = 49 mm, height H = 24 mm, and density 800.52 kg/m*) was released from the bottom of the water Notice in Fig. 8(b), the simulated vertical displacement of the cube near the bottom of the tank deviated from the experimental points. The simulated displacement exhibited a re-bound behavior, while the measured displacement just gradually decreased to zero. The maximum difference between the simulated and measured
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Computational Fluid MechanicsComputational Fluid Dynamics (CFD) modelling and simulationFluid and Solid interactionComputational Fluid-Structure InteractionSolid Fluid InteractionCFD simulationComputational Fluids Dynamics (CFD)
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