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ABSTRACT
This paper presents large eddy simulation (LES) results of convective heat transfer and incompressible-fluid flow around a square cylinder (SC) at Reynolds numbers in the range from 103 to 3.5 × 105. The LES uses the swirling-strength based sub-grid scale (SbSGS) model. Several flow properties at turbulent regime are explored, including lift and drag coefficients, time-spanwise averaged sub-grid viscosity, and Kolmogorov micro-scale. Local and mean Nusselt numbers of convective heat transfer from the SC under isothermal wall temperature are predicted and compared with empirical results.
Nomenclature
| A | = | matrix expression of velocity gradient ∇u |
| aij | = | element of matrix A |
| B | = | spanwise length of square cylinder (m) |
| Cμ | = | artificially defined constant in Eq. (1) |
| d | = | cross-sectional side length of SC (m) |
| fI | = | FSI, factor of swirling-strength intermittency, given by Eq. (2) |
| = | turbulence kinetic energy | |
| Num | = | mean Nusselt number |
| p | = | normalized pressure |
| Re = duin/ν | = | Reynolds number |
| Smax | = | assumed allowable total error |
| T | = | temperature (K) |
| Tw | = | temperature on SC wall surface (K) |
| T∞ | = | temperature of incoming flow fluid |
| u | = | velocity vector |
| uin | = | incoming flow speed (m/s) |
| u, v, w | = | normalized velocity components (m/s) |
| x, y, z | = | Cartesian coordinates |
| ε | = | dissipation rate of k |
| λci | = | swirling-strength (1/s) |
| λ = λcr + iλci | = | eigenvalue of ∇u |
| ρ | = | fluid density (kg/m3) |
| ν | = | fluid kinematic viscosity (m2/s) |
| νs | = | sub-grid viscosity (m2/s) |
| νsr =νs/ν | = | viscosity ratio |
| (νsr)pm | = | time-averaged (νsr)peak |
| = | root mean square of (νsr)peak | |
| (νsr)peak | = | peak value of νsr |
| Θ | = | normalized temperature |
| θ | = | normalized temperature fluctuation |
Nomenclature
| A | = | matrix expression of velocity gradient ∇u |
| aij | = | element of matrix A |
| B | = | spanwise length of square cylinder (m) |
| Cμ | = | artificially defined constant in Eq. (1) |
| d | = | cross-sectional side length of SC (m) |
| fI | = | FSI, factor of swirling-strength intermittency, given by Eq. (2) |
| = | turbulence kinetic energy | |
| Num | = | mean Nusselt number |
| p | = | normalized pressure |
| Re = duin/ν | = | Reynolds number |
| Smax | = | assumed allowable total error |
| T | = | temperature (K) |
| Tw | = | temperature on SC wall surface (K) |
| T∞ | = | temperature of incoming flow fluid |
| u | = | velocity vector |
| uin | = | incoming flow speed (m/s) |
| u, v, w | = | normalized velocity components (m/s) |
| x, y, z | = | Cartesian coordinates |
| ε | = | dissipation rate of k |
| λci | = | swirling-strength (1/s) |
| λ = λcr + iλci | = | eigenvalue of ∇u |
| ρ | = | fluid density (kg/m3) |
| ν | = | fluid kinematic viscosity (m2/s) |
| νs | = | sub-grid viscosity (m2/s) |
| νsr =νs/ν | = | viscosity ratio |
| (νsr)pm | = | time-averaged (νsr)peak |
| = | root mean square of (νsr)peak | |
| (νsr)peak | = | peak value of νsr |
| Θ | = | normalized temperature |
| θ | = | normalized temperature fluctuation |