http://orcid.org/0000-0002-5316-4434
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ABSTRACT
This work presents a coupled lattice Boltzmann finite volume method for dealing with conjugate heat transfer problems. Lattice Boltzmann scheme is used for fluid-dynamics, while high-order finite volume method is implemented for temperature reconstruction. After a first validation with literature test cases, the method is applied to a heat exchanger with an insert made of porous medium, representative of an open-cell metal foam, innovative material largely used for its thermomechanical properties. This allows maximizing heat exchange processes with advantages in terms of efficiencies. Thus, the coupled method allows dealing with complex boundaries in multiphysics problems.
Nomenclature
| C | = | specific heat |
| dt | = | energy equation time-step |
| e | = | lattice Boltzmann local velocity |
| f | = | lattice Boltzmann population |
| F | = | force vector |
| F | = | force component in lattice Boltzmann stencil |
| g | = | gravitational acceleration |
| h | = | channel height |
| L | = | characteristic length |
| n | = | direction normal to surface |
| Npop | = | number of stencil directions |
| Nu | = | Nusselt number |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| Re | = | Reynolds number |
| Q | = | heat exchanged |
| = | heat flux | |
| t | = | time |
| T | = | temperature |
| = | non-dimensional temperature | |
| = | mean temperature | |
| u | = | fluid velocity vector |
| = | mean horizontal velocity | |
| u, v | = | velocity components |
| UC | = | characteristic velocity |
| X | = | position vector |
| x, y | = | spatial coordinates |
| = | non-dimensional coordinate | |
| w | = | lattice Boltzmann weight |
| Greek symbols | = | |
| α | = | lattice Boltzmann direction |
| β | = | thermal expansion coefficient |
| δ | = | metal layer height |
| Δx | = | grid spacing |
| ΔT | = | hot/Cold temperature difference |
| ϵ | = | metal foam porosity |
| κ | = | thermal conductivity |
| ν | = | lattice Boltzmann kinematic viscosity |
| ρ | = | density |
| τ | = | lattice Boltzmann relaxation time |
| χ | = | thermal diffusivity |
| Subscripts | = | |
| 0 | = | reference property |
| 1, 2, 3, 4 | = | heat exchanger sections |
| ave | = | average value |
| C | = | cold temperature |
| flu | = | fluid property |
| H | = | hot temperature |
| i, j | = | cartesian directions |
| max | = | maximum value |
| sol | = | solid property; |
| wall | = | wall property |
| Superscripts | = | |
| BW | = | backward differencing |
| eq | = | equilibrium distribution function |
| FW | = | forward differencing |
| t | = | time-step |
Nomenclature
| C | = | specific heat |
| dt | = | energy equation time-step |
| e | = | lattice Boltzmann local velocity |
| f | = | lattice Boltzmann population |
| F | = | force vector |
| F | = | force component in lattice Boltzmann stencil |
| g | = | gravitational acceleration |
| h | = | channel height |
| L | = | characteristic length |
| n | = | direction normal to surface |
| Npop | = | number of stencil directions |
| Nu | = | Nusselt number |
| Pr | = | Prandtl number |
| Ra | = | Rayleigh number |
| Re | = | Reynolds number |
| Q | = | heat exchanged |
| = | heat flux | |
| t | = | time |
| T | = | temperature |
| = | non-dimensional temperature | |
| = | mean temperature | |
| u | = | fluid velocity vector |
| = | mean horizontal velocity | |
| u, v | = | velocity components |
| UC | = | characteristic velocity |
| X | = | position vector |
| x, y | = | spatial coordinates |
| = | non-dimensional coordinate | |
| w | = | lattice Boltzmann weight |
| Greek symbols | = | |
| α | = | lattice Boltzmann direction |
| β | = | thermal expansion coefficient |
| δ | = | metal layer height |
| Δx | = | grid spacing |
| ΔT | = | hot/Cold temperature difference |
| ϵ | = | metal foam porosity |
| κ | = | thermal conductivity |
| ν | = | lattice Boltzmann kinematic viscosity |
| ρ | = | density |
| τ | = | lattice Boltzmann relaxation time |
| χ | = | thermal diffusivity |
| Subscripts | = | |
| 0 | = | reference property |
| 1, 2, 3, 4 | = | heat exchanger sections |
| ave | = | average value |
| C | = | cold temperature |
| flu | = | fluid property |
| H | = | hot temperature |
| i, j | = | cartesian directions |
| max | = | maximum value |
| sol | = | solid property; |
| wall | = | wall property |
| Superscripts | = | |
| BW | = | backward differencing |
| eq | = | equilibrium distribution function |
| FW | = | forward differencing |
| t | = | time-step |