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 |