5 An LES study and ... in-line tube-banks where τ$_{ij}$ denotes the subgrid scale (SGS herefrom) stress tensor defined by The filtered equations are unclosed since the SGS stress tensor τ$_{ij}$ is unknown. The SGS stress tensor can be modelled based on an isotropic eddy-viscosity model as: where ν$_{t}$ denotes the SGS eddy viscosity, and S$_{ij}$ is the resolved rate of strain tensor given by where ν$_{t}$ is computed in terms of the Smagorinsky [31] type eddy-viscosity model using where C$_{ν}$ denotes the Smagorinsky coefficient, | S | the modulus of rate of strain tensor for the resolved scales, and Δ denotes the grid filter length obtained from Consequently, the SGS stress tensor is computated as following This model claims to be simple and efficient. It needs merely a constant in priori value for C$_{ν}$ . Nevertheless, work from [32, 33, 34] has shown different values of C$_{ν}$ for distinct flows. Hence, the τ$_{ij}$ − 1 3 δ$_{ij}$ τ$_{ij}$ = − 2 C$_{ν}$ Δ $^{2}$| S | S$_{ij}$ (12) Δ = V 1 / 3 (11) | S | = $^{√}$2 S$_{ij}$ S$_{ij}$ (10) ν$_{t}$ = C$_{ν}$ Δ $^{2}$| S | (9) S$_{ij}$ = 1 2 $^{(}$∂u$_{i}$ ∂x$_{j}$ + ∂u$_{j}$ ∂x$_{i}$$^{)}$ (8) τ$_{ij}$ − 1 3 τ$_{kk}$δ$_{ij}$ = − 2 ν$_{t}$S$_{ij}$ (7) τ$_{ij}$ = u$_{i}$u$_{j}$ − u$_{i}$u$_{j}$ (6) ∂u$_{i}$ ∂t + ∂u$_{i}$u$_{j}$ ∂x$_{j}$ = − 1 ρ ∂p ∂x$_{i}$ + ∂ ∂x$_{j}$ ( ν ∂u$_{i}$ ∂x$_{j}$$^{)}$ − ∂τ$_{ij}$ ∂x$_{j}$ (5)