Development of immersed boundary phase field lattice boltzmann method for solid multiphase flow interactions

... Remarks 142 vi Chapter Application of Immersed Boundary- Phase Field- Lattice Boltzmann Method for Solid- Multiphase Flow Interactions 161 6.1 Solid- Multiphase Flow Interactions 162 6.2 Simulation ... layer formed on solid surface Chapter presents application of immersed boundary phase- field lattice Boltzmann method to study solid- multiphase flow interactions An introduction of solid- multiphase ... Modeling of Multiphase Flow 1.2.1 Navier-Stokes solvers for multiphase flow simulation 1.2.2 Lattice Boltzmann methods for multiphase flow simulation 1.2.3 Challenges faced by phase- field LBM...

Development of immersed boundary methods for isothermal and thermal flows 1

... “so-called immersed boundary methods are not real immersed boundary methods and therefore fall out of the scope of the present 13 Chapter Introduction thesis 1. 3 Brief review of Immersed boundary ... function-vorticity formulation-based immersed boundary method; The reported immersed boundary methods for thermal flows are not capable of exactly satisfying the Dirichlet thermal condition on the immersed boundary ... incompressible viscous flows is desired 1. 3.3 Applications of immersed boundary method The popularity of immersed boundary method has seen increased for flow problems with complex or /and moving boundaries...

Development of immersed boundary methods for isothermal and thermal flows 2

... Δs1 ⎟⎜ 21 Dh N ⎟ ⎜ Dh Δs1 ⎟⎜ ⎟⎜ MN ⎟ ⎜ Dh ⎠ ⎝ DhN 1Δs1 12 Dh 22 Dh DhM 12 Dh Δs2 22 Dh Δs2 DhN Δs2 DhM ΔsM ⎞ ⎟ Dh M ΔsM ⎟ ⎟ ⎟ NM Dh ΔsM ⎟ ⎠ (2. 25) ⎛ U n +1 B ,1 ⎜ n +1 U [B F ] = ⎜ B ,2 ⎜ ⎜ n ... (2. 28) ρU ∞ D 43 Chapter Governing Equations and Boundary Condition-Enforced IBM CL = FL (2. 29) ρU ∞ D where FD and FL are the drag and lift forces on the cylinder surface For unsteady flows, ... (20 09) and Zhou & Shu (20 11) The variation of time-mean drag and r.m.s value of lift and drag versus fc / f s also match well with the results from Guilmineau et al (20 02) , Lee et al (20 09) and...

Development of immersed boundary methods for isothermal and thermal flows 3

... ∂x (3. 3) and the stream function is related to the velocity by u= ∂ϕ ∂y v=− (3. 4) ∂ϕ ∂x (3. 5) Note that ω + Θ in Eq (3. 3) is the physical vorticity Eqs (3. 1) to (3. 5) together with Eqs (2 .3) and ... (3. 8) and (3. 9) and obtain predicted vorticity ω * and stream function ϕ * ; 2) Substitute ϕ * to Eqs (3. 4) and (3. 5) to calculate the predicted velocity * field u ; 3) Compute the elements of ... Substituting Eqs (3. 10) and (3. 11) into Eq (3. 3) and using Eq (3. 9) gives Θ= ∂ ( Δu ) ∂ ( Δ v ) − ∂y ∂x (3. 12) It should be noted that the key step in the proposed stream function-vorticity formulation-based...

Development of immersed boundary methods for isothermal and thermal flows 4

... = TB (X(s, t ), t ) (4. 4) Here Eqs (4. 1a), (4. 2), (4. 3) describe forced convection problems while Eqs (4. 1b), (4. 2), (4. 3) describe natural convection problems In Eq (4. 1b), the Boussinesq approximation ... ∫ − T Γ total Γ Lref (4. 22) where Ltotal is the total length of the immersed boundary Ltotal = ∫ Γ (4. 23) ds As shown in Eqs (4. 21) and (4. 22), the evaluation of local and average Nusselt numbers ... gap space 4. 4 Conclusions In this chapter, a boundary condition-enforced immersed boundary method is developed for heat transfer problems The effect of thermal boundaries on the flow and temperature...

Development of immersed boundary methods for isothermal and thermal flows 5

... releases constant and uniform heat flux is simulated for several low and moderate Reynolds numbers of 1 35 Chapter An Efficient IBM for Thermal Flow Problems with Heat Flux Boundary Condition ... investigations are carried out for three Rayleigh numbers of Ra = 1000, 57 00 and 5 10 while Prandtl number is kept at Pr = 0.7 The initial conditions are set as zero for u and T∞ for T in the whole computational ... Ra = 57 00 Ra = 5 10 Fig 5. 6 Streamlines (left) and isotherms (right) for different Ra 148 Chapter An Efficient IBM for Thermal Flow Problems with Heat Flux Boundary Condition θ Fig 5. 7 Effect...

Development of immersed boundary methods for isothermal and thermal flows 6

... in Fig 6. 10 To get a clear view of the ground effect on the aerodynamic forces, C H 161 Chapter Applications of Developed IBM Solvers to Simulate 2D Fluid and Thermal Flows and CV for the ... (see Fig 6. 25(a) and Fig .6. 25(c) for comparison), but higher vibration frequencies play a role of progressively reducing the longitudinal vortex spacing (see Fig 6. 26( b) and Fig 6. 25(c) for comparison) ... Fig 6. 13 The development of vortex structure in the forth stroke at Gc = 199 Chapter Applications of Developed IBM Solvers to Simulate 2D Fluid and Thermal Flows Fig 6. 14 Comparison of time-dependent...

Development of immersed boundary methods for isothermal and thermal flows 7

... (20 07) reported the variation of the drag and lift forces for Reynolds number of 50, 100 and 200 Yoon & Yang (20 07) , by performing a parametric study, estimated flow-induced forces on two 2 27 ... terms of temperature contours (isotherms) in Figs 7. 3 and 7. 4, for isothermal condition and isoflux condition, respectively As expected, the isotherms are symmetric about the centerline for both ... of Developed IBM Solvers to Simulate 3D Incompressible Thermal Flows Table 7. 6 Comparison of the time-mean drag and lift coefficients for tandem-sphere system at Re = 300 CD CL Upstream 0. 677 ...

Development of immersed boundary methods for isothermal and thermal flows 8

... overall width of the wake is larger The time-dependent hydrodynamic forces experienced by the fish for Re = 300 and 4000 are plotted in Figs 8. 18( a) and 8. 18( b), respectively, in forms of force coefficient ... cases of St = 0 .8 and 1.0 in Figs 8. 10(b) and 8. 10(c), a diamond-shaped region of high velocity exists immediately behind the flapping foil and there is no evidence of clear bifurcation for this ... other values of St = 0.35, 0 .8 and 1.0 are carried out for AR = The top views of the vortex structures for these cases are presented in Fig 8. 9 In combination with the plot in Fig 8. 4 for St = 0.6...

Development of immersed boundary methods for isothermal and thermal flows 9

... ( 199 7) 2807-28 19 Liu H., Wassersug R.J., Kawachi K., A computational fluid dynamics study of tadpole swimming, J Exp Biol., 199 ( 199 6) 1245-1260 Ljachowski D.N., J techn Phys., Leningrad, 99 9 ... Stability of flows past a pair of circular cylinders in a side-by-side arrangement, J Fluid Mech., 595 (2008) 491 -507 Mohd-Yusof J., Combined immersed boundaries/B-Splines methods for simulations of flows ... correction-based immersed boundary- lattice Boltzmann method and its applications, J Comp Phys., 228 (20 09) 196 3- 197 9 Wu J., Shu C., Particulate flow simulation via a boundary condition-enforced immersed boundary- lattice...

Development of immersed boundary methods for isothermal and thermal flows preface

... Pressure-velocity formulation-based 14 immersed boundary method 1.3.2 Stream 14 function-vorticity formulation-based immersed boundary method 18 1.3.3 Applications of immersed boundary method 20 ... Table 7.5 Comparison of the mean drag coefficients and Nusselt numbers for tandem-sphere system at Re = 40 251 Table 7.6 Comparison of the mean drag and lift coefficients for tandem-sphere system ... Time history of drag and lift coefficients for one transversely oscillating cylinder at Re = 185 67 XV Fig 2.13 Comparison of time-mean drag and r.m.s of drag and lift coefficients for one transversely...

Development of lattice boltzmann method for compressible flows

... 1.2 Lattice Boltzmann method 1.2.1 Basis of lattice Boltzmann method 1.2.2 Lattice Boltzmann models LB models for compressible ... kinetic method, direct simulation Monte Carlo, the lattice Boltzmann method, dissipative particle dynamics method, the molecular dynamics method, and so on 1.2 1.2.1 Lattice Boltzmann method Basis of ... because of the simple form of CF-VIIF This is a major advantage of our derivation method As shown in the next chapter, we will further extend this method to develop lattice Boltzmann models for compressible...

Development of organic inorganic composites by sol gel method for tooling materials

... reinforcement phase, or both in the composites Sol gel composites comprise inorganic- inorganic composites and organic- inorganic composites By doping ceramic reinforcement phase in inorganic sol gel ... DEVELOPMENT OF ORGANIC/ INORGANIC COMPOSITES BY SOL GEL METHOD FOR TOOLING MATERIALS LIU FENGMIN (B Eng., Beijing University of Aeronautics & Astronautics) A THESIS SUBMITTED FOR THE DEGREE OF ... volume of SiC-filled 61 organic/ inorganic composites Figure 4-14 Thermal conductivity of different volume of SiO2-filled 62 organic/ inorganic composites Figure 4-15 Organic/ inorganic composites...

Development of a flexible forcing immersed boundary lattice boltzmann method and its applications in thermal and particulate flows

... boundary – lattice Boltzmann method 15 1.6 Applications in thermal and moving boundary problems using immersed boundary – lattice Boltzmann method 17 1.6.1 Natural convection in a complex ... Immersed boundary – thermal lattice Boltzmann method IFEM Immersed finite element method IIM Immersed interface method ISLBM Interpolation-supplemented LBM LGCA lattice gas cellular automata LBE Lattice ... thermal flow problems such that both velocity and temperature boundary conditions are accurately satisfied 1.6 Applications boundary in thermal problems and using moving immersed boundary – lattice...

Development of a novel immersed boundary lattice boltzmann method and its applications

... Organization of The Thesis 23 Chapter Development of Efficient Lattice Boltzmann Method on Non-Uniform 25 Cartesian Mesh 2.1 Standard LBM 26 2.2 Taylor Series Expansion and Least Squares-base Lattice ... Non -Boundary Conforming Method 1.2.1 Sharp interface approach 1.2.2 Diffuse interface approach 1.2.2.1 Immersed boundary method 1.2.2.2 Force calculation in IBM 1.2.2.3 Advantages and disadvantages ... 1.2.2.3 Advantages and disadvantages of IBM The major advantage of IBM is its simplicity and easy implementation This is attributed to the decoupling of the solution of governing equation with the boundary...

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