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Abstract
In previous work (Zhang et al. 2007) several Reynolds-averaged Navier–Stokes turbulent models were evaluated by the classic natural convection experiment. It was demonstrated that the V2f turbulent model shows the best overall performance compared to other models in terms of accuracy of temperature, velocity, and turbulent kinetic energy. However, all compared turbulent models cannot simulate the pseudo-laminar phenomenon in the center zone of the classic natural convection experiment. Moreover, the V2f model needs to solve four equations, and the transport equation for the wall normal stress () and the elliptic equation for the relaxation function (f) make the model numerically unstable. Based on the idea of the V2f model, an anisotropic model (BV2fAM) was developed. In the BV2fAM model,
as the turbulent kinetic intensity normal to streamlines was adopted and computed by local turbulent kinetic energy and local flow characteristic variable instead of the
transport equation. The validity of the developed BV2fAM model was confirmed by two benchmark cases (classic natural convection in a tall cavity and mixed convection in a square cavity). It can be seen that the developed BV2fAM model can yield better simulated results of temperature, velocity, and turbulent kinetic energy than other compared models. Moreover, it can simulate the pseudo-laminar phenomenon in the center zone of the classic natural convection experiment.
Nomenclature
| CP | = | |
| D | = | cavity depth (m) |
| g | = | gravitational acceleration (m/s2) |
| H | = | cavity height (m) |
| k | = | turbulent kinetic energy (m2/s2) |
| L | = | turbulent space scale (m) |
| T | = | temperature (K) |
| Ts | = | turbulent time scale (s) |
| ui | = | velocity component (m/s) |
| V | = | vertical velocity (m/s) |
| W | = | cavity width (m) |
| x | = | Cartesian axis direction (m) |
| y | = | Cartesian axis direction (m) |
| z | = | Cartesian axis direction (m) |
Special characters
| β | = | thermal expansion coefficient (1/K) |
| ϵ | = | turbulent kinetic energy dissipation rate (m2/s3) |
| θ | = | dimensionless temperature (—) |
| μ | = | molecular viscosity (Pa·s) |
| μt | = | turbulent viscosity (Pa·s) |
| νt | = | turbulent kinematic viscosity (m2/s) |
| ρ | = | density of air (kg/m3) |
Superscripts
| − | = | time-averaged quantities |
| ′ | = | fluctuating quantities |
Subscripts
| air | = | air |
| cell | = | calculation cell |
| cold | = | cold wall |
| fl | = | floor |
| Hot | = | hot wall |
| in | = | inlet |
| max | = | maximum |
| min | = | minimum |
| ref | = | reference conditions |
| rms | = | root mean square |
| w | = | wall |