Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our User Agreement and Privacy Policy.

Slideshare uses cookies to improve functionality and performance, and to provide you with relevant advertising. If you continue browsing the site, you agree to the use of cookies on this website. See our Privacy Policy and User Agreement for details.

Like this presentation? Why not share!

- Particle-based fluid simulations u... by Altair 282 views
- AA, Combined Paper on Sustainable C... by Farah Naz 399 views
- Design Competition - Riyadh Station... by Farah Naz 645 views
- Energy Efficient Factory by Farah Naz 316 views
- Anirudh Krishnakumar Resume by Anirudh Krishnakumar 41 views
- Landscaping Project, Bostob, MA, US... by Farah Naz 146 views

789 views

682 views

682 views

Published on

No Downloads

Total views

789

On SlideShare

0

From Embeds

0

Number of Embeds

4

Shares

0

Downloads

25

Comments

0

Likes

1

No embeds

No notes for slide

- 1. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University MSc. THESIS DEFENSE on NUMERICAL SIMULATION FOR THERMAL FLOW CASES USING SMOOTHED PARTICLE HYDRODYNAMICS METHOD Under supervision of Prof. Essam E. Khalil Dr. Essam Abo-Serie Dr. Hatem Haridy Presented by Eng. Tarek M. ElGammal
- 2. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 2
- 3. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University Objective Introduction SPH General View Literature Survey Numerical Model Results Conclusion Future Work 3
- 4. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 4
- 5. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University • Introducing the mesh-less method (Smoothed Particle Hydrodynamics: SPH) as a promising alternative for computing engineering problems. • Comparison with the meshed approach based on the accuracy and time consumption. • Optimizing the solution parameters to maintain stability and reduce error. • Trying to make a good start to develop a software package for solving engineering cases. 5
- 6. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 6
- 7. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University • Numerical solution merits: 1. Fast Performance 2. Cheapness 3. Compromising results • Famous Numerical Method Prediction & Validation Mesh Based Methods CSM, CFD & CHT 7
- 8. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University Mesh deformation Results inaccuracy Huge memories & processors High computational time Meshed Methods Simulation Problems BREAKDOWN 8
- 9. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 9
- 10. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 10
- 11. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University • SPH - Smoothed particle hydrodynamics • Mesh-less Lagrangian numerical method • Firstly used in 1977 • Developed for Solid mechanics, fluid dynamics • Competitive to traditional numerical method 11
- 12. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University Mesh MethodMeshless Method 12
- 13. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University Fluid is continuum and not discrete Properties of particles V, P, T, etc. have to take into account the properties of neighbor particles 13
- 14. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University Math 14
- 15. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University Momentum equation Energy equation Continuity equation Density summation 22
- 16. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University Heat Conduction equation Equation of state Adiabatic sound speed equation 23
- 17. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University • Important Additions 1- Boundary deficiency treatments: Truncation of the particle kernel zone by the solid boundary (or the free surface) Inaccurate results for particles near the boundary and unphysical penetrations. SOLUTION a) Boundary Particles b) Virtual Particles 24
- 18. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 1a) Boundary Particles Particles are located at the boundaries to produce a repulsive force for every fluid particle within its kernel. 1b) Virtual (Ghost) Particles These particles have the same values depending on the interior real particles nearby the boundaries which act as mirrors. 25
- 19. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 26
- 20. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 2- Particles interpenetration treatment Sharp variations in the flow & wave discontinuities Particles interpenetration and system collapse SOLUTION a) Artificial Viscosity b) Average Velocity 27
- 21. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 2a) Artificial viscosity Composed of shear and bulk viscosities to transform the sharp kinetic energy into heat. It’s represented in a form of viscous dissipation term in the momentum & energy equations. 28
- 22. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 2b) Average velocity (XSPH ): It makes velocity closer to the average velocity of the neighboring particles. In incompressible flows, it can keep the particles more orderly. In compressible flows, it can effectively reduce unphysical interpenetration. 29
- 23. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 30
- 24. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University • Shock tube Liu G. R. and M. B. Liu (2003): Introduction of SPH solution for shock wave propagation inside 1-D shock tube and comparison to G. A. Sod finite difference solution (1978). Limitation: Incomplete solution due to boundary deficiency • 1-D Heat conduction Finite Difference solution based on (Crank Nicholson) solution for time developed function in 1-D space. Limitation: Solution in SPH for transient period doesn’t exist. 31
- 25. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University • 2-D Heat conduction R. Rook et al. (2007): Formula for Laplacian derivative. 2-D heat conduction within a square plate of isothermal walls compared to the analytical solution. Limitation: Simple value of (h) besides boundary deficiency • Compression Stroke Fazio R. & G. Russo (2010) Second order boundary conditions for 1-D piston problems solved by central lagrangian scheme Limitation: Solution in SPH for transient period of compression stroke doesn’t exist. 32
- 26. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 33
- 27. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University A) Shock tube P= 1 N/m2 P= 0.1795 N/m2 ρ= 1 kg/m3 ρ= 0.25 kg/m3 e= 2.5 kJ/kg e= 1.795 kJ/kg u= 0 m/s u= 0 m/s Nx=320 Nx=80 m= 0.00187 kg, Cv= 0.715 kJ/kg.K, γ= 1.4, dτ=0.005 s 34
- 28. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University • Smoothing length (h) • Smoothing Kernel function • Virtual Particles & boundary conditions • Boundary force • Artificial Viscosity B-spline kernel function Fixed no./ symmetry conditions (except the velocity) D=0.01, r0= 1.25x10-5 m, n1=12 & n2=4 απ=βπ= 1 & φ=0. 1h 35
- 29. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University I. Shock tube 1- Validation Pressure and internal energy distribution inside shock tube after 0.2s (2 solution) 36
- 30. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University I. Shock tube 1- Validation Density and velocity distribution inside shock tube after 0.2s (2 solution) 37
- 31. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University I. Shock tube 2- Progressive time Properties distribution inside shock tube after wave reflection 38
- 32. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University B) 1-D Heat Conduction ti=0 C tb1=100 Ctb2=0 C L =1 cm ρ=2700 kg/m3 α = 0.84 cm2/sec F.D. (C.N.) SPH dx=0.1 cm, dτ=0.01 sec Analytical solution 39
- 33. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University • Smoothing length (h) • Smoothing Kernel function B-spline kernel function 40
- 34. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University II. 1-D heat conduction 1- Optimum Smoothing length percentage error ( ) 41 Comparison of maximum percentage error for different smoothing length
- 35. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University II. 1-D heat conduction 2- Error Analysis 42
- 36. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 43
- 37. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University C) 2-D transient conduction with isothermal boundaries ti=100 oC a=10 cm aAnalytical solution 44
- 38. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 1521 particles Boundary Particles 160 dx Smoothing length (h): h= C . dx (parametric study) Kernel Function: Cubic B-Spline, dt=0.001 s Virtual Particles 45
- 39. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University III. 2-D Heat Conduction Minimum error at the centre region Error = Tref – Tc Tref is the analytical solution temperature Tc is computed SPH temperature 46 1- Smoothing Length effect
- 40. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University III. 2-D Heat Conduction Temperature Contours after 8s (3 solutions) 47 1- Smoothing Length and Virtual Particles effect
- 41. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University III. 2-D Heat Conduction 2- Virtual Particles effect Temperature Contours after 8s (3 solutions) 48
- 42. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University III. 2-D Heat Conduction 2- Virtual Particles effect Temperature Contours after 8s (3 solutions) 49
- 43. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 50
- 44. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University D) 1-D/ 2-D adiapatic compression stroke Specification: D=0.1285 m, Ls=1.2D = 0.15842 m, N= 1000 rpm, rc = 6 Medium (Air): Pi= 1*105 Pa, Ti= 300 K, ρi = 0.973 kg/m3, ui=0 m/s Cv= 717.5 J/kg, γ= 1.4 Time step: dτ=0.00001 sec Virtual particles 51
- 45. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 1-D 2-D Discretization Total: Nx Boundary: (2) Interior: (Nx-2) Total: Na= (Nx) x (Ny) Boundary: 2Ny + 2(Nx-2) Interior: (Nx-2) x (Ny-2) Smoothing length (h) Smoothing Kernel function B-spline kernel function B-spline kernel function Boundary repulsive force D=0.01 m2/sec2, r0= 1.25x10-5 m, n1=12 & n2=4 D = 2.75x10-3 m2/sec2, r0= 0.15 dx, n1 = 12, n2 = 4 Artificial Viscosity απ=0.1, βπ= 0 & φ=0. 1h απ= 0.005, βπ= 0.005 & φ=0. 1h Average Velocity ϵ = 0.9 Reference Isentropic relation Isentropic relation 52
- 46. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University • Virtual Particles & boundary conditions - Variable no. - Symmetry conditions at cylinder wall - Moving piston boundary conditions: 53
- 47. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University IV. 1-D Compression stroke 1- Optimum Smoothing Length Optimum smoothing length of different particle number based on minimum error of pressure y = 0.04x - 0.24 0 0.5 1 1.5 2 2.5 3 31 41 51 61 71 81 optimumsmoothinglengthfactor (h_opt/dx) Number of Particles Nx optimized factor of smoothing length at different particles numbers hopt/dx Poly. (hopt/dx) 54
- 48. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University IV. 1-D Compression stroke 1- Optimum Smoothing Length Percentage error and time consumption of different particles number 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 41 51 61 71 Absolutemaximumpercentageerror(%) Number of Particles Nx Percentage error for different particles numbers 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 41 51 61 71 computationaltime(sec) Number of Particles Nx calculation time for different particles numbers 55
- 49. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University IV. 1-D Compression stroke 2- Transient Period Properties variation inside the cylinder at different times (compared to the reference value) 56 Pistonlocation Cylinderhead Pistonlocation Cylinderhead Pistonlocation Cylinderhead Pistonlocation Cylinderhead
- 50. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 57 IV. 2-D Compression stroke
- 51. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University V. 2-D Compression stroke 1- Transient Period 58 Cylinder properties variation inside the cylinder with crank angle
- 52. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 59
- 53. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University • SPH is (Real Flow) solution. • Adaptive nature is a merit for solving complex problems. • SPH converges better than F.D. In some case. • Every solution has an optimum smoothing length (hopt ) . • hopt changes at different number of discretizing particles (N). May other parameters affect it like the initial gradients and material properties. • Virtual Particles are capable of solving boundary inconsistency and improper penetrations. 60
- 54. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University • Boundary conditions should be carefully treated at the virtual particle to obtain the adequate results. • Two Techniques of virtual particles are: fixed or variable number. • Suitable small value coefficients in SPH solution controlling terms. • For well simulating the discontinuity waves, reviewed artificial viscosity and DSPH are recommended in such cases. 61
- 55. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 62
- 56. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University • Working on more complex cases (industry). • Introducing Laminar shear term/turbulence models. • Relating between (hopt) and initial physical quantities (e.g. temperature gradient and particles spacing). • Using variable smoothing length based on the problem gradients is an important issue. • Coding using more efficient software products: e.g. Python, Octave 63
- 57. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 64
- 58. MSc. Thesis Defense 2013 Faculty of Engineering Cairo University 65

No public clipboards found for this slide

×
### Save the most important slides with Clipping

Clipping is a handy way to collect and organize the most important slides from a presentation. You can keep your great finds in clipboards organized around topics.

Be the first to comment