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ABSTRACT
In this paper, a ghost fluid thermal lattice Boltzmann method is developed to simulate Dirichlet and Neumann thermal boundary conditions at curved boundaries. As such, a new formulation for both thermal boundary conditions is developed using a bilinear interpolation method. The presented method is also formulated to address the special cases that arise when the values of the macroscopic variables are interpolated at the image points surrounded by many solid nodes as well as the fluid nodes. The results of the presented method are compared to those available in the literature from conventional numerical methods, and excellent agreement is observed.
Nomenclature
| a, b, c, d | = | coefficients of equation |
| c | = | lattice streaming speed |
| Cd | = | drag coefficient |
| Cl | = | lift coefficient |
| cs | = | speed of sound |
| d | = | cylinder diameter (m) |
| d1, d2 | = | gap between the channel wall and the cylinder (defined in Eq. 32) |
| ei | = | discrete velocity |
| FD | = | drag force per unite length of cylinder (kg m/s2) |
| FL | = | lift force per unite length of cylinder (kg m/s2) |
| fi | = | density distribution functions |
| = | equilibrium distribution functions | |
| = | postcollision distribution functions | |
| gi | = | internal energy distribution functions |
| = | internal energy equilibrium distribution functions | |
| H | = | half channel height (m) |
| k | = | thermal conductivity (W/mK) |
| L | = | dimensionless length of the computational domain |
| Lu | = | dimensionless upstream distance |
| Ld | = | dimensionless downstream distance |
| n | = | normal coordinate |
| NuL | = | local Nusselt number |
| Nu | = | average Nusselt number |
| P | = | pressure |
| Pr | = | Prandtl number |
| q | = | heat flux vector (W/m2) |
| r | = | ratios (m) |
| Re | = | Reynolds number |
| T | = | temperature (K) |
| Tw | = | solid obstacle temperature (k) |
| u | = | macroscopic velocity vector (m/s) |
| = | average velocity (m/s) | |
| Umax | = | maximum velocity at the center of the channel (m/s) |
| wi | = | equilibrium distribution weight |
| x, y | = | x- and y-coordinate directions (m) |
| α | = | thermal diffusivity (m2/s) |
| β | = | blockage ratio (β = d/2H) |
| γ | = | gap ratio |
| δ | = | gap between the channel wall and the cylinder (m) |
| Δℓ | = | distance between the GP and the related IP (m) |
| δt | = | time step |
| δx | = | lattice step |
| υ | = | kinematic viscosity (m2/s) |
| ρ | = | density (kg/m3) |
| τg | = | dimensionless internal energy relaxation times |
| τυ | = | dimensionless momentum relaxation times |
| ϕ | = | general macroscopic variables |
| ωi | = | angular velocity (rad/s) |
| Subscripts | = | |
| BI | = | boundary intersection point |
| GP | = | ghost point |
| IP | = | image point |
| Superscripts | = | |
| eq | = | equilibrium |
| neq | = | nonequilibrium |
Nomenclature
| a, b, c, d | = | coefficients of equation |
| c | = | lattice streaming speed |
| Cd | = | drag coefficient |
| Cl | = | lift coefficient |
| cs | = | speed of sound |
| d | = | cylinder diameter (m) |
| d1, d2 | = | gap between the channel wall and the cylinder (defined in Eq. 32) |
| ei | = | discrete velocity |
| FD | = | drag force per unite length of cylinder (kg m/s2) |
| FL | = | lift force per unite length of cylinder (kg m/s2) |
| fi | = | density distribution functions |
| = | equilibrium distribution functions | |
| = | postcollision distribution functions | |
| gi | = | internal energy distribution functions |
| = | internal energy equilibrium distribution functions | |
| H | = | half channel height (m) |
| k | = | thermal conductivity (W/mK) |
| L | = | dimensionless length of the computational domain |
| Lu | = | dimensionless upstream distance |
| Ld | = | dimensionless downstream distance |
| n | = | normal coordinate |
| NuL | = | local Nusselt number |
| Nu | = | average Nusselt number |
| P | = | pressure |
| Pr | = | Prandtl number |
| q | = | heat flux vector (W/m2) |
| r | = | ratios (m) |
| Re | = | Reynolds number |
| T | = | temperature (K) |
| Tw | = | solid obstacle temperature (k) |
| u | = | macroscopic velocity vector (m/s) |
| = | average velocity (m/s) | |
| Umax | = | maximum velocity at the center of the channel (m/s) |
| wi | = | equilibrium distribution weight |
| x, y | = | x- and y-coordinate directions (m) |
| α | = | thermal diffusivity (m2/s) |
| β | = | blockage ratio (β = d/2H) |
| γ | = | gap ratio |
| δ | = | gap between the channel wall and the cylinder (m) |
| Δℓ | = | distance between the GP and the related IP (m) |
| δt | = | time step |
| δx | = | lattice step |
| υ | = | kinematic viscosity (m2/s) |
| ρ | = | density (kg/m3) |
| τg | = | dimensionless internal energy relaxation times |
| τυ | = | dimensionless momentum relaxation times |
| ϕ | = | general macroscopic variables |
| ωi | = | angular velocity (rad/s) |
| Subscripts | = | |
| BI | = | boundary intersection point |
| GP | = | ghost point |
| IP | = | image point |
| Superscripts | = | |
| eq | = | equilibrium |
| neq | = | nonequilibrium |