Numerical Investigation of Water-entry of a ... - Semantic Scholar
Numerical Investigation of Water-entry of a Hemisphere Cylinder used for Micro-communication Sonobuoy Casing JianKang Li 1, Amir Anvar 2 School of Mechanical Engineering The University of Adelaide Adelaide, Australia 5005 1 [email protected] 2 [email protected] Abstract—The purpose of this paper is to present the investigation of impact pressure acting on the hemisphere cylinder when it hits the water. In this paper, a two-dimensional hemisphere cylinder is built to simulate the water-entry problem. The model enters into the calm water verticals with initial velocity in y-direction at 10m/s. The transient flow simulation is carried out using Fluent k-ε turbulent model, dynamic mesh method and 6DOF solver. The volume of fluid (VOF) and user defined function are utilized to track the free-surface and the trajectory of the impacting hemisphere cylinder. The pressure and velocity distribution is investigated. The results show the Fluent k-ε turbulent model can predict the pressure distribution on the hemisphere cylinder accurately. Keywords- Impact Pressure, Hemisphere Cylinder, VOF, UDF, Dynamic Mesh
I.
INTRODUCTION
The hemisphere cylinder model used for the simulation is the physical casing of the micro-communication sonobuoy. The micro-communication sonobuoy will be deployed by UAVs and fall into the water before being activated (see figure 1). The moment when the micro-communication sonobuoy impacts the water the impact pressure can be up to an extreme high value. The impacting pressure will damage the physical casing of the micro-communication sonobuoy. As the physical casing works as the protector of inner electronics, the damage of physical casing can lead to catastrophic consequence to the electronics and terminate the underwater communication.
Water-entry of an object is a difficult topic for aerial and naval hydrodynamic [1]. The impact pressure induced at the moment when the object hits the water can reach to a very high value [2]. This may lead to damage to the object. In order to avoid any damage on impacting objects, the study on impact pressure on impacting objects is essential. The first water-entry problem was studied by Von Karmen et.al [5]. They mainly focused on the analytical approaches to the problem. However, the pressure distribution on impacting objects is quite complicated. Many phenomenons cannot be well explained by the analytical methods. With the development of computational fluid dynamic theory and software in calculation and analysis of fluid mechanics in industry, the simulation of the water-entry is easier and easier. Currently, many numerical methods are applied in simulating the water-entry problem. Zhao et.al (1993) [6] presented a numerical method to study the water-entry of a two dimensional body of arbitrary cross-section. Shao et al (2009) simulated the water-entry of a wedge using smoothed particle hydrodynamics method (SPH) [3]. This paper presents a VOF method and turbulent model to simulate the process of hemisphere cylinder. In this paper, a two dimensional hemisphere cylinder with calm water is used to study the impact pressure distribution and the velocity field. The study of the pressure distribution and velocity field can instruct the casing design of micro-communication sonobuoy. The influence on pressure distribution caused by air cavity and the formation of air cavity are neglected. II.
TWO DIMENSIONAL HEMISPHERE CYLINDE MODEL
A. Problem description The simplified schematic problem of the microcommunication sonobuoy entering water is shown in figure 2. The hemisphere cylinder falls into water with an initial velocity 10 m/s in y-direction. The water is assumed to be calm water and the dimension of the water tank used for the simulation is 1x3 m. The fluid domain is divided into two parts: water and air. Figure 1. Deployment Scenario [7]
Specifically, the interest is the impact pressure acting on the bottom dome-shape wall. Therefore, the meshing density around the hemisphere cylinder wall is much higher than other fluid domains. This can reduce the time for computing the simulation and avoid unnecessary workloads. The validation of the mesh is carried out by using four types of mesh. Each type of mesh is used to simulate the steady turbulent flow under the same boundary conditions and solution methods. After simulation the results are compared using maximum static pressure as referencing index. The comparison is shown in table 1.
Figure 2. Problem Description Schematic B. Governing equations The governing equations for the incompressible flow are the continuity equation and the Navier-Stokes momentum conservation equations shown as below:
( u ) ( v) 0 x y
(1)
Where u and v are the velocity vectors in x and y direction in Cartesian coordinate system.， is the density of fluid.
(ui ) (ui u j ) 1 p 1 ij fi xi x j t x j
(2)
Table 1. Comparison of maximum static types of mesh. Mesh Types 1 2 Number of nodes 26475 1544 5 Number of elements 25855 3028 6 Maximum 5.22e+ 5.23e Pressure(Pa) 04 +04
pressure of four 3 4283 1 4224 1 5.14e +04
4 55387 54714 5.18e +04
According to the comparison, the mesh type 2 is selected and the elements shape is triangle. The mesh density around the hemisphere cylinder is much higher than other areas. This can ensure the results are more accurate.
f i represents the other momentum forcing components. u j , ui are the velocity Where p is the static pressure,
Triangular Mesh of the Computational Domai
vectors. ij , the viscous term, is shown as below:
ij (
(u i ) (u j ) ) t x j
(3)
C. Turbulent model In this paper, the hemisphere cylinder model has an initial velocity of 10 m/s impacting the water. The bottom part of the model is a semi-sphere with a 58mm diameter. The Reynolds number is calculated using the equation shown as below:
Re
VD
(4)
Where is the density of the fluid, and V is the velocity of the falling hemisphere cylinder. D is the diameter of the sphere, and is the dynamic viscosity of the fluid.
Figure 3. Triangular Mesh of Computational Domain E. Boundary Conditions For transient flow model, the boundary conditions are shown in figure 4. The top edge of the tank is the pressure outlet, the bottom, left and right edges of the tank are the walls with zero shear force. The hemisphere cylinder is the moving wall.
The Reynolds number for simulation in this paper is Re 5.79 105 . Therefore, the flow is fully turbulent and the k-ε turbulent model is used in the simulation. The standard k-ε turbulent model can accurately calculate the pressure and velocity field. D. Meshing Meshing is critical to the desired accurate results. A good mesh can increase the accuracy of results and reduce the computational cost as well. In this paper, the main concern is the pressure distribution on the hemisphere cylinder wall.
Figure 4. Boundary Conditions of Transient Flow Model
III.
RESULTS AND DISCUSSION
VOF model is used for the multiphase flow and six degree of freedom solver is used to calculate the buoyancy force and the drag force when the hemisphere travels through the water. This simulation uses user defined function to initialize the calculation and specify the boundary conditions of the moving wall. From figures 5, 6, 7 and 8, when the hemisphere cylinder enters into the water, the air cavity is generated at the back of the hemisphere. The generation of the air cavity can influence the impacting pressure acting on the dome-shape bottom. However, in this paper, the effect of the air cavity is neglected. In figures 9 and 10, the maximum pressure acts on the dome-shape bottom and the value is 60000 Pa. The pressure acting on the dome-shape bottom decreases when the hemisphere cylinder enters into deep water. Therefore, the moment when the micro-communication sonobuoy hits the water surface is vital to casing design and the protection of the underwater communication electronic system.
Figure 6. Water-entry of Hemisphere cylinder at t=0.012s
The velocity in y direction shows reasonable values in figures 11 and 12. The maximum velocity is distributed around the both sides of the dome-shape bottom. The minimum velocity is at the back of the hemisphere cylinder. The vortices are generated around the back of the hemisphere cylinder.
Figure 7. Water-entry of Hemisphere cylinder at t=0.029s
Figure 5. Water-entry of Hemisphere cylinder at t=0.006s
Figure 8. Water-entry of Hemisphere cylinder at t=0.062s
Figure 9. Pressure distribution of water entry of Hemisphere cylinder at t=0.006s Figure 12. Y-direction velocity distribution of water entry of Hemisphere cylinder at T=0.048s
IV.
CONCLUSION
The Fluent k-ε turbulent model, dynamic mesh method and 6DOF solver are capable to simulate the water-entry of hemisphere cylinder. The results show the impact pressure is much higher than that in a steady flow condition. The results obtained from the simulation can be used to guide the selection of material and design of physical casing of microcommunication sonobuoy. By doing so, the underwater communication electronic equipment can be well protected by the physical casing (see figure 13). Figure 10. Pressure distribution of water entry of Hemisphere cylinder at t=0.012s
Figure 13. The real-time Oceanic Trial of Micro-sonobuoy The use of dynamic mesh in fluent is difficult as many parameters can influence the simulation. Setting proper parameters for dynamic mesh is crucial to the success of simulation and the accuracy of the results. Figure 11. Y-direction velocity distribution of water entry of Hemisphere cylinder at T=0.023s
The time-step should be set according to the boundary conditions of the simulation. If the time-step is set to a big value, the simulation may be stopped due to a high courant number or negative volume of cell.
ACKNOWLEDGMENT The author appreciates the support and guidance from associate professor Amir and the Defence Science and Technology Organisation (DSTO) for sponsoring this research project. REFERENCES [1] Ferziger J.H. and Peric M., 2002. Computational Methods for Fluid Dynamics (3rd edn). Springer: New York. [2] GreenhowM. andMoyo S., 1997.Water entry and exit of horizontal circular cylinders. Philosophical Transactions of Royal Society A 355(1724), 551-63. [3] Shao S. D., 2009. Incompressible SPH simulation of water entry of a free-falling object. International [4] Sussman M., Smereka P., Osher S., 1994. A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow. Journal of Computational Physics 114, 146-159. [5] Von Karman T., 1929. the impact of seaplane floats during landing. NACA Technical Note,vol. 321.Wahsington, DC:NACA. [6] Zhao R., Faltinsen O., Aarsnes J., 1997. Water entry of arbitrary two-dimensional sections with and without flow separation, in: 21st Symposium on Naval Hydrodynamics. [7] Nicholas Schulze and Frederik Visser, 2010 “Designed and built a deployable micro-communication sonobuoy prototype”, Final Report, the University of Adelaide.
I.
INTRODUCTION
The hemisphere cylinder model used for the simulation is the physical casing of the micro-communication sonobuoy. The micro-communication sonobuoy will be deployed by UAVs and fall into the water before being activated (see figure 1). The moment when the micro-communication sonobuoy impacts the water the impact pressure can be up to an extreme high value. The impacting pressure will damage the physical casing of the micro-communication sonobuoy. As the physical casing works as the protector of inner electronics, the damage of physical casing can lead to catastrophic consequence to the electronics and terminate the underwater communication.
Water-entry of an object is a difficult topic for aerial and naval hydrodynamic [1]. The impact pressure induced at the moment when the object hits the water can reach to a very high value [2]. This may lead to damage to the object. In order to avoid any damage on impacting objects, the study on impact pressure on impacting objects is essential. The first water-entry problem was studied by Von Karmen et.al [5]. They mainly focused on the analytical approaches to the problem. However, the pressure distribution on impacting objects is quite complicated. Many phenomenons cannot be well explained by the analytical methods. With the development of computational fluid dynamic theory and software in calculation and analysis of fluid mechanics in industry, the simulation of the water-entry is easier and easier. Currently, many numerical methods are applied in simulating the water-entry problem. Zhao et.al (1993) [6] presented a numerical method to study the water-entry of a two dimensional body of arbitrary cross-section. Shao et al (2009) simulated the water-entry of a wedge using smoothed particle hydrodynamics method (SPH) [3]. This paper presents a VOF method and turbulent model to simulate the process of hemisphere cylinder. In this paper, a two dimensional hemisphere cylinder with calm water is used to study the impact pressure distribution and the velocity field. The study of the pressure distribution and velocity field can instruct the casing design of micro-communication sonobuoy. The influence on pressure distribution caused by air cavity and the formation of air cavity are neglected. II.
TWO DIMENSIONAL HEMISPHERE CYLINDE MODEL
A. Problem description The simplified schematic problem of the microcommunication sonobuoy entering water is shown in figure 2. The hemisphere cylinder falls into water with an initial velocity 10 m/s in y-direction. The water is assumed to be calm water and the dimension of the water tank used for the simulation is 1x3 m. The fluid domain is divided into two parts: water and air. Figure 1. Deployment Scenario [7]
Specifically, the interest is the impact pressure acting on the bottom dome-shape wall. Therefore, the meshing density around the hemisphere cylinder wall is much higher than other fluid domains. This can reduce the time for computing the simulation and avoid unnecessary workloads. The validation of the mesh is carried out by using four types of mesh. Each type of mesh is used to simulate the steady turbulent flow under the same boundary conditions and solution methods. After simulation the results are compared using maximum static pressure as referencing index. The comparison is shown in table 1.
Figure 2. Problem Description Schematic B. Governing equations The governing equations for the incompressible flow are the continuity equation and the Navier-Stokes momentum conservation equations shown as below:
( u ) ( v) 0 x y
(1)
Where u and v are the velocity vectors in x and y direction in Cartesian coordinate system.， is the density of fluid.
(ui ) (ui u j ) 1 p 1 ij fi xi x j t x j
(2)
Table 1. Comparison of maximum static types of mesh. Mesh Types 1 2 Number of nodes 26475 1544 5 Number of elements 25855 3028 6 Maximum 5.22e+ 5.23e Pressure(Pa) 04 +04
pressure of four 3 4283 1 4224 1 5.14e +04
4 55387 54714 5.18e +04
According to the comparison, the mesh type 2 is selected and the elements shape is triangle. The mesh density around the hemisphere cylinder is much higher than other areas. This can ensure the results are more accurate.
f i represents the other momentum forcing components. u j , ui are the velocity Where p is the static pressure,
Triangular Mesh of the Computational Domai
vectors. ij , the viscous term, is shown as below:
ij (
(u i ) (u j ) ) t x j
(3)
C. Turbulent model In this paper, the hemisphere cylinder model has an initial velocity of 10 m/s impacting the water. The bottom part of the model is a semi-sphere with a 58mm diameter. The Reynolds number is calculated using the equation shown as below:
Re
VD
(4)
Where is the density of the fluid, and V is the velocity of the falling hemisphere cylinder. D is the diameter of the sphere, and is the dynamic viscosity of the fluid.
Figure 3. Triangular Mesh of Computational Domain E. Boundary Conditions For transient flow model, the boundary conditions are shown in figure 4. The top edge of the tank is the pressure outlet, the bottom, left and right edges of the tank are the walls with zero shear force. The hemisphere cylinder is the moving wall.
The Reynolds number for simulation in this paper is Re 5.79 105 . Therefore, the flow is fully turbulent and the k-ε turbulent model is used in the simulation. The standard k-ε turbulent model can accurately calculate the pressure and velocity field. D. Meshing Meshing is critical to the desired accurate results. A good mesh can increase the accuracy of results and reduce the computational cost as well. In this paper, the main concern is the pressure distribution on the hemisphere cylinder wall.
Figure 4. Boundary Conditions of Transient Flow Model
III.
RESULTS AND DISCUSSION
VOF model is used for the multiphase flow and six degree of freedom solver is used to calculate the buoyancy force and the drag force when the hemisphere travels through the water. This simulation uses user defined function to initialize the calculation and specify the boundary conditions of the moving wall. From figures 5, 6, 7 and 8, when the hemisphere cylinder enters into the water, the air cavity is generated at the back of the hemisphere. The generation of the air cavity can influence the impacting pressure acting on the dome-shape bottom. However, in this paper, the effect of the air cavity is neglected. In figures 9 and 10, the maximum pressure acts on the dome-shape bottom and the value is 60000 Pa. The pressure acting on the dome-shape bottom decreases when the hemisphere cylinder enters into deep water. Therefore, the moment when the micro-communication sonobuoy hits the water surface is vital to casing design and the protection of the underwater communication electronic system.
Figure 6. Water-entry of Hemisphere cylinder at t=0.012s
The velocity in y direction shows reasonable values in figures 11 and 12. The maximum velocity is distributed around the both sides of the dome-shape bottom. The minimum velocity is at the back of the hemisphere cylinder. The vortices are generated around the back of the hemisphere cylinder.
Figure 7. Water-entry of Hemisphere cylinder at t=0.029s
Figure 5. Water-entry of Hemisphere cylinder at t=0.006s
Figure 8. Water-entry of Hemisphere cylinder at t=0.062s
Figure 9. Pressure distribution of water entry of Hemisphere cylinder at t=0.006s Figure 12. Y-direction velocity distribution of water entry of Hemisphere cylinder at T=0.048s
IV.
CONCLUSION
The Fluent k-ε turbulent model, dynamic mesh method and 6DOF solver are capable to simulate the water-entry of hemisphere cylinder. The results show the impact pressure is much higher than that in a steady flow condition. The results obtained from the simulation can be used to guide the selection of material and design of physical casing of microcommunication sonobuoy. By doing so, the underwater communication electronic equipment can be well protected by the physical casing (see figure 13). Figure 10. Pressure distribution of water entry of Hemisphere cylinder at t=0.012s
Figure 13. The real-time Oceanic Trial of Micro-sonobuoy The use of dynamic mesh in fluent is difficult as many parameters can influence the simulation. Setting proper parameters for dynamic mesh is crucial to the success of simulation and the accuracy of the results. Figure 11. Y-direction velocity distribution of water entry of Hemisphere cylinder at T=0.023s
The time-step should be set according to the boundary conditions of the simulation. If the time-step is set to a big value, the simulation may be stopped due to a high courant number or negative volume of cell.
ACKNOWLEDGMENT The author appreciates the support and guidance from associate professor Amir and the Defence Science and Technology Organisation (DSTO) for sponsoring this research project. REFERENCES [1] Ferziger J.H. and Peric M., 2002. Computational Methods for Fluid Dynamics (3rd edn). Springer: New York. [2] GreenhowM. andMoyo S., 1997.Water entry and exit of horizontal circular cylinders. Philosophical Transactions of Royal Society A 355(1724), 551-63. [3] Shao S. D., 2009. Incompressible SPH simulation of water entry of a free-falling object. International [4] Sussman M., Smereka P., Osher S., 1994. A Level Set Approach for Computing Solutions to Incompressible Two-Phase Flow. Journal of Computational Physics 114, 146-159. [5] Von Karman T., 1929. the impact of seaplane floats during landing. NACA Technical Note,vol. 321.Wahsington, DC:NACA. [6] Zhao R., Faltinsen O., Aarsnes J., 1997. Water entry of arbitrary two-dimensional sections with and without flow separation, in: 21st Symposium on Naval Hydrodynamics. [7] Nicholas Schulze and Frederik Visser, 2010 “Designed and built a deployable micro-communication sonobuoy prototype”, Final Report, the University of Adelaide.
