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ABSTRACT
We performed a direct numerical simulation (DNS) of the turbulent natural convection between two parallel plates at a Rayleigh number of Ra = 8.0 × 106, focusing on the turbulent natural convection affected by radiation in an optically thick fluid . When the effects of the radiation were considered, the flow structure and temperature distribution in the channel changed as the optical thickness of the fluid increased. The effects of the radiation on the turbulent natural convection were clearly explained by the turbulence statistics from the DNS results.
Nomenclature
| cp | = | specific heat at constant pressure, |
| I | = | radiative intensity, W/m2sr |
| Ib | = | blackbody radiative intensity, W/m2sr |
| g | = | gravitational acceleration, m/s2 |
| G | = | incident radiation, W/m2 |
| = | production by buoyancy | |
| Gr | = | Grashof number |
| J | = | radiosity, W/m2 |
| k | = | thermal conductivity, W/mK |
| l | = | integral scale |
| L | = | computational domain size, m |
| P | = | pressure, N/m2 |
| Pl | = | Planck number |
| Pr | = | Prandtl number |
| Pvθ, Pθθ | = | production by the mean-temperature gradient |
| = | radiative heat flux, W/m2 | |
| Ra | = | Rayleigh number |
| Rvθ, Rθθ | = | production by radiation |
| = | frictional Reynolds number | |
| t | = | time, s |
| T | = | temperature, K |
| u, v, w | = | velocity fluctuation in x-, y-, and z-directions, m/s |
| ucom | = | horizontal velocity fluctuation |
| U, V, W | = | velocity, m/s |
| = | frictional velocity, m/s | |
| x, y, z | = | streamwise, wall-normal, and spanwise coordinate, m |
| Greek symbols | = | |
| α | = | thermal diffusivity, m2/s |
| β | = | volumetric thermal expansion coefficient, K−1 |
| Δ | = | channel half width, m |
| = | wall emissivity | |
| Φ | = | two-point correlation coefficient |
| κ | = | absorption coefficient, m−1 |
| ν | = | kinematic viscosity, m2/s |
| θ | = | temperature fluctuation, K |
| Θ | = | temperature, K |
| ρ | = | density, g/m3 |
| σ | = | Stephan–Boltzmann constant, W/m2K4 |
| τ | = | optical thickness |
| = | velocity time scale and temperature time scale | |
| ω | = | scattering albedo |
| Ω | = | solid angle, sr |
| Subscript and superscript | = | |
| c | = | cold |
| h | = | hot |
| rms | = | root mean square fluctuation intensity |
| ()* | = | nondimensional valuable |
| (¯) | = | average valuable |
Nomenclature
| cp | = | specific heat at constant pressure, |
| I | = | radiative intensity, W/m2sr |
| Ib | = | blackbody radiative intensity, W/m2sr |
| g | = | gravitational acceleration, m/s2 |
| G | = | incident radiation, W/m2 |
| = | production by buoyancy | |
| Gr | = | Grashof number |
| J | = | radiosity, W/m2 |
| k | = | thermal conductivity, W/mK |
| l | = | integral scale |
| L | = | computational domain size, m |
| P | = | pressure, N/m2 |
| Pl | = | Planck number |
| Pr | = | Prandtl number |
| Pvθ, Pθθ | = | production by the mean-temperature gradient |
| = | radiative heat flux, W/m2 | |
| Ra | = | Rayleigh number |
| Rvθ, Rθθ | = | production by radiation |
| = | frictional Reynolds number | |
| t | = | time, s |
| T | = | temperature, K |
| u, v, w | = | velocity fluctuation in x-, y-, and z-directions, m/s |
| ucom | = | horizontal velocity fluctuation |
| U, V, W | = | velocity, m/s |
| = | frictional velocity, m/s | |
| x, y, z | = | streamwise, wall-normal, and spanwise coordinate, m |
| Greek symbols | = | |
| α | = | thermal diffusivity, m2/s |
| β | = | volumetric thermal expansion coefficient, K−1 |
| Δ | = | channel half width, m |
| = | wall emissivity | |
| Φ | = | two-point correlation coefficient |
| κ | = | absorption coefficient, m−1 |
| ν | = | kinematic viscosity, m2/s |
| θ | = | temperature fluctuation, K |
| Θ | = | temperature, K |
| ρ | = | density, g/m3 |
| σ | = | Stephan–Boltzmann constant, W/m2K4 |
| τ | = | optical thickness |
| = | velocity time scale and temperature time scale | |
| ω | = | scattering albedo |
| Ω | = | solid angle, sr |
| Subscript and superscript | = | |
| c | = | cold |
| h | = | hot |
| rms | = | root mean square fluctuation intensity |
| ()* | = | nondimensional valuable |
| (¯) | = | average valuable |