Thesis Defense 2013 lty of Engineering Cairo University MSc. THESIS DEFENSE on NUMERICAL SIMULATION FOR THERMAL FLOW CASES USING SMOOTHED PARTICLE HYDRODYNAMICS METHOD دام خ ت س ا ب ة ارير ح ان بر سلاتاخ ل ةي دد ع ة جد م ن ةري ا ق ت م ل ا ة ي ك ي م ا ي ي رود دي ه ل ا ات/ ي ي ر ج ل ا ة ق ير طUnder supervision of Prof. Essam E. Khalil Dr. Essam Abo-Serie Dr. Hatem Haridy Presented by Eng. Tarek M. ElGammal
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MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
MSc. THESIS DEFENSE on
NUMERICAL SIMULATION FOR THERMAL FLOW CASES USING SMOOTHED PARTICLE
• 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.
Objective
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MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
INTRODUCTION
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MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
Introduction
• Numerical solution merits:1. Fast Performance2. Cheapness 3. Compromising results• Famous Numerical Method
Prediction &
Validation
Mesh Based Methods
CSM, CFD & CHT7
MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
Introduction
Mesh deformation Results inaccuracy
Huge memories & processors
High computational time
Meshed Methods Simulation Problems
BREAKDOWN
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MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
Introduction
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MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
SPH GENERAL VIEW
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MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
SPH General view
• SPH - Smoothed particle hydrodynamics
• Mesh-less Lagrangian numerical method
• Firstly used in 1977
• Developed for Solid mechanics, fluid dynamics
• Competitive to traditional numerical method
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MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
Mesh Method
SPH General view
Meshless Method
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MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
Fluid is continuum and not discrete
Properties of particlesV, P, T, etc. haveto take into accountthe properties ofneighbor particles
SPH General view
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MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
Math
SPH General view
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Math
Math
Math
Math
MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
SPH General view
Momentum equation
Energy equation
Continuity equation Density summation
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MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
SPH General viewHeat Conduction equation
Equation of state
Adiabatic sound speed equation
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MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
• Important Additions1- Boundary deficiency treatments:
Truncation of the particle kernel zone by the solid boundary (or the free surface)
SPH General view
Inaccurate results for particles near the boundary and unphysical penetrations.
SOLUTIONa) Boundary Particles b) Virtual Particles
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MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
1a) Boundary ParticlesParticles are located at the boundaries to produce a
repulsive force for every fluid particle within its kernel.
SPH General view
1b) Virtual (Ghost) ParticlesThese particles have the same values depending on the interior real particles nearby the boundaries which act as mirrors.
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MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
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MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
2- Particles interpenetration treatment
SPH General view
Sharp variations in the flow & wave discontinuities
Particles interpenetration and system collapse
SOLUTIONa) Artificial Viscosity b) Average Velocity
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MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
2a) Artificial viscosityComposed 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.
SPH General view
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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.
SPH General view
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MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
LITERATURE SURVEY
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MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
• Shock tubeLiu 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 conductionFinite 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.
Literature Survey
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MSc. Thesis Defense 2013
Faculty of Engineering Cairo University
• 2-D Heat conductionR. 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 StrokeFazio 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.