Nonlinear Potential Flow Solver Development in OpenFOAM

Transcription

1 Nonlinear Potential Flow Solver Development in OpenFOAM A. Mehmood Plymouth University, UK April 19,2016 A. Mehmood

2 Table of Contents 1 Motivation 2 Solution Methodology Mathematical Formulation Sequence of the Solution Procedure 3 Results and Discussion Standing Waves Progressive Waves 4 Conclusions and Future Directions A. Mehmood

3 Motivation Wave Structure Interaction Simulation Environment A. Mehmood

4 Solution Methodology Wave Tank y axis Free surface x axis A. Mehmood

5 Solution Methodology Mathematical Formulation Mathematical Formulation φ x 1 φ = F (y, t) 2 y axis φ t = gη 1 2 φ. φ η t = φ y φ x η x 2 φ = 0 φ y = 0 η t = u.n n y x axis t + c φ n = 0 1 Mayer, S, Garapon, A and Sorensen, LS (1998). A fractional step method for unsteady free surface flow with applications to non-linear wave dynamics, Intl J Numerical Methods in Fluids, 28(2), A. Mehmood

6 Solution Methodology Sequence of the Solution Procedure Generate the grid Generate the grid A. Mehmood

7 Solution Methodology Sequence of the Solution Procedure Apply the boundary conditions Apply the boundary conditions at the face center A. Mehmood

8 Solution Methodology Sequence of the Solution Procedure Solve Laplace s equation Solve Laplace s equation for the velocity potential. Compute the required variables (i.e., velocities u = φ, fluxes). A. Mehmood

9 Solution Methodology Sequence of the Solution Procedure Solve Laplace s equation Solve Laplace s equation for the velocity potential. Compute the required variables (i.e., velocities u = φ, fluxes). A. Mehmood

10 Solution Methodology Sequence of the Solution Procedure Complications of implementation of the Solver in OpenFOAM Simplest idea for automatic mesh motion in the FV framework would be to solve an equation to provide point motion However, as the FVM provides the solution in cell centres and motion is required on the points(vertices), this necessarily leads to interpolation

11 Solution Methodology Sequence of the Solution Procedure Complications of implementation of the Solver in OpenFOAM Simplest idea for automatic mesh motion in the FV framework would be to solve an equation to provide point motion However, as the FVM provides the solution in cell centres and motion is required on the points(vertices), this necessarily leads to interpolation

12 Solution Methodology Sequence of the Solution Procedure Complications of implementation of the Solver in OpenFOAM Simplest idea for automatic mesh motion in the FV framework would be to solve an equation to provide point motion However, as the FVM provides the solution in cell centres and motion is required on the points(vertices), this necessarily leads to interpolation η t = u.n n y A. Mehmood

13 Solution Methodology Sequence of the Solution Procedure Automatic Mesh Motion in OpenFOAM Motion will be obtained by solving a mesh motion equation, where free surface motion acts as a boundary condition A. Mehmood

14 Solution Methodology Sequence of the Solution Procedure Automatic Mesh Motion in OpenFOAM Motion will be obtained by solving a mesh motion equation, where free surface motion acts as a boundary condition Automatic mesh motion determines the position of internal points based on the free surface motion A. Mehmood

15 Solution Methodology Sequence of the Solution Procedure Automatic Mesh Motion in OpenFOAM Motion will be obtained by solving a mesh motion equation, where free surface motion acts as a boundary condition Automatic mesh motion determines the position of internal points based on the free surface motion The role of internal point motion is to accommodate changes in the domain shape (boundary motion) and preserve the validity and quality of the mesh A. Mehmood

16 Solution Methodology Sequence of the Solution Procedure Automatic Mesh Motion in OpenFOAM Motion will be obtained by solving a mesh motion equation, where free surface motion acts as a boundary condition Automatic mesh motion determines the position of internal points based on the free surface motion The role of internal point motion is to accommodate changes in the domain shape (boundary motion) and preserve the validity and quality of the mesh Internal point motion can be specified in a number of ways, without user interaction A. Mehmood

17 Solution Methodology Sequence of the Solution Procedure Automatic Mesh Motion in OpenFOAM Motion will be obtained by solving a mesh motion equation, where free surface motion acts as a boundary condition Automatic mesh motion determines the position of internal points based on the free surface motion The role of internal point motion is to accommodate changes in the domain shape (boundary motion) and preserve the validity and quality of the mesh Internal point motion can be specified in a number of ways, without user interaction Choices for a simplified mesh motion equation: Laplace equation with constant and variable diffusivity diffusivity > quadratic inversedistance A. Mehmood

18 Results and Discussion Standing Waves Standing Waves set up η(x, t) = a cos(kx) cos(ωt)+ πa 2 [ cos 2 1 (ωt) λ 4 cosh 2 (kh) + 3 cos(2ωt) ] 4 sinh 2 cos(2kx) (1) (kh) y axis x axis φ t = gη 1 2 φ. φ η t = u.n n y φ x = 0 φ y = 0 2 φ = 0 φ x = 0 A. Mehmood

19 Results and Discussion Standing Waves Time Histories of Wave Elevation Analtic (linear) m Numerical m Analtic (linear) 0.01 m Numerical 0.01 m 0.01 Surface elevation Time Time trace plots numerical theoretical 1st-order theoretical 2nd-order η/a t/t Figure: Time history of free surface elevation at the centre of the domain A. Mehmood

20 Results and Discussion Standing Waves Variation of wave period Airy 2nd order ampl 005 ampl 01 Time [sec] H Figure: Variation of wave period against mean water depth normalized by wavelength A. Mehmood

21 Results and Discussion Standing Waves Standing Wave Animation wave amplitude Initial wave profile wave amplitude Initial wave profile H H A. Mehmood

22 Results and Discussion Progressive Waves Progressive Waves set up 1 φ x = u x(y, t) 2 y axis φ t = gη 1 2 φ. φ η t = u.n n y x axis φ = 0 φ t + c φ n = 0 3 φ y = 0 A. Mehmood

23 Results and Discussion Progressive Waves Progressive Waves 1.5 x=6.0 m η/a t/t (a) a = 0.01 m, H = 1.5 m, T=1.5 s 1.5 x=6.0 m η/a t/t (b) a = 0.06 m, H = 1.0 m, T=1.5 s. Figure: Time history of free surface elevation at location x = 6.0 m (from inlet boundary) A. Mehmood

24 Results and Discussion Progressive Waves Comparison with Experiment (F.Gao-2003) 8.85m φ x = u x(t) 0.28m zerograd 1 Gao, F, (2003). An efficient finite element technique for free surface flow, Ph.D. thesis, Brighton University, UK. 1 A. Mehmood

25 Results and Discussion Progressive Waves Comparison with Experiment (F.Gao-2003) 0.28m 0.55m 8.85m numerical simulations experiment by Gao-2003 x = 0.55 m Surface elevation (m) Time (s) Figure: Time history of wave elevation at location x = 0.55 m. A. Mehmood

26 Results and Discussion Progressive Waves Comparison with Experiment (F.Gao-2003) 0.28m 3.55m Surface elevation (m) numerical simulations-graded experiment by Gao-2003 x = 3.55 m Time (s) Figure: Time history of wave elevation at location x = 3.55 m. A. Mehmood

27 Results and Discussion Progressive Waves Comparison with Experiment (F.Gao-2003) 0.28m 8.85m 5.45m numerical simulations-graded experiment by Gao-2003 x = 5.45 m Surface elevation (m) Time (s) Figure: Time history of wave elevation at location x = 5.45 m. A. Mehmood

28 Results and Discussion Progressive Waves Comparison with experiment A. Mehmood

29 Conclusions and Future Directions Conclusions and Future Directions Developed a free surface tracking solver for numerical simulation of unsteady irrotational fully non-linear water waves A. Mehmood

30 Conclusions and Future Directions Conclusions and Future Directions Developed a free surface tracking solver for numerical simulation of unsteady irrotational fully non-linear water waves The solver has been validated by application to a number of test cases, ranging from shallow water standing waves to different wave amplitudes progressive waves A. Mehmood

31 Conclusions and Future Directions Conclusions and Future Directions Developed a free surface tracking solver for numerical simulation of unsteady irrotational fully non-linear water waves The solver has been validated by application to a number of test cases, ranging from shallow water standing waves to different wave amplitudes progressive waves Solution of Laplace s equation for the velocity potential, the non-linear free surface boundary conditions, the wave generation and the absorption boundary conditions are all not part of the standard OpenFOAM R distribution A. Mehmood

32 Conclusions and Future Directions Conclusions and Future Directions Developed a free surface tracking solver for numerical simulation of unsteady irrotational fully non-linear water waves The solver has been validated by application to a number of test cases, ranging from shallow water standing waves to different wave amplitudes progressive waves Solution of Laplace s equation for the velocity potential, the non-linear free surface boundary conditions, the wave generation and the absorption boundary conditions are all not part of the standard OpenFOAM R distribution Coupling to available Navier-Stokes solvers in OpenFOAM R A. Mehmood

33 Conclusions and Future Directions Conclusions and Future Directions Developed a free surface tracking solver for numerical simulation of unsteady irrotational fully non-linear water waves The solver has been validated by application to a number of test cases, ranging from shallow water standing waves to different wave amplitudes progressive waves Solution of Laplace s equation for the velocity potential, the non-linear free surface boundary conditions, the wave generation and the absorption boundary conditions are all not part of the standard OpenFOAM R distribution Coupling to available Navier-Stokes solvers in OpenFOAM R The developed solver and the associated boundary conditions will be released as an open-source for the marine and offshore community A. Mehmood

34 Conclusions and Future Directions Thank you A. Mehmood