Turbulent plane channel flow with smooth walls

Overview

Replicates Poletto et al.'s 58 setup and settings for Direct numerical simulation of turbulent channel flow up to Ret=590 51
References: Van Driest (1956) 84, Smagorinsky (1963) 64, Kim et al. (1987) 28, Moser et al. (1999) 51, and Poletto et al. (2013) 58 (Synthetic turbulence inflow generator)
See the resources section for additional data files

Flow physics:

Solver:

Tutorial case:

Physical domain:

The case is a statistically-developing internal flow through parallel smooth walls which are two characteristic-length apart.
- $x$ : Longitudinal direction (Mean-flow direction)
- $y$ : Vertical direction (Wall-normal direction)
- $z$ : Spanwise direction (Statistically homogeneous direction)
- $O$ : Origin at the left-bottom corner of the numerical domain

Physical modelling:

Reynolds number based on friction velocity: $\text{Re}_{u_\tau} = \vert \mathbf{U}_\tau \vert \delta / \nu_\text{fluid} = 395$ $Re_{u_{τ}} = ∣ U_{τ} ∣ δ / ν_{fluid} = 395$ [-]
- (Estimated) Friction velocity: $\mathbf{U}_\tau = (1.0, 0.0, 0.0)$ , and $\vert \mathbf{U}_\tau \vert = u_\tau = 1.0$ [m⋅s-1]
- Characteristic length (Channel half-height): $\delta = 1.0$ [m]
- Kinematic viscosity of fluid: $\nu_{\text{fluid}} \approx 0.002532$

\[m<sup>2</sup>⋅s<sup>-1</sup>\]

\[m⋅s<sup>-1</sup>\]

Turbulence model: Large eddy simulation with the Smagorinsky sub-filter scale model utilising the van Driest wall-damping function. The sub-filter scale model constants:
- $$ C_k \approx 0.02655 $$
- $$ C_e = 1.048 $$
- $$ C_s \approx 0.065 $$

- \$$ C_s = (C_k {C_k/C_e}^{0.5} )^{0.5} $$

Numerical domain modelling:

Numerical domain (not in scale)

Spatial domain discretisation:

Mesh type: Rectangular cuboid mesh
Mesher: blockMesh
Number of nodes, $N$ : $(N_x, N_y, N_z) = (500, 46, 82)$ [nodes]
Spatial resolution $(\Delta)$ $(Δ)$ distribution:
- Uniform in $(x, z)$ -directions
- Stretched in $(y)$ -direction; clustered nearby walls
Uniform mesh particulars:
- $\Delta_x^+ = (\Delta_x u_\tau )/\nu_{\text{fluid}} \approx 49.6$ [-]
- $\Delta_z^+ \approx 15.1$ [-]
Wall-normal mesh particulars:
- Simple grading expansion ratio: 25.0 [-] (From top to bottom wall, the ratio is 0.04)
- First wall-normal node height: $\Delta_y^+ \approx 1.1$
- Mesh details:

Temporal domain discretisation:

Time-step size: $\Delta_t = 0.004$ [s]
Estimated Courant-Friedrichs-Lewy (CFL) number based on ${ \overline{u_x} }_{y^+ = 392} = 20.133$ [m⋅s-1]: CFL $\approx 0.64$

Equation discretisation:

Spatial derivatives and variables:

Temporal derivatives and variables:

Numerical boundary conditions:

Solution algorithms and solvers:

Field	Linear Solver	Smoother
`U`	smooth	GaussSeidel
`p`	GAMG	GaussSeidel
`nuTilda`	smooth	GaussSeidel

Initialisation and sampling:

Computation time for a single domain pass-through based on ${ \overline{U_x} }_{y^+ = 392} = 20.133$ ) [m2⋅s-1] $\approx 3.121$ [s]
Initialisation pass-throughs = $\approx 2.7$ 58
Sampling pass-throughs = $\approx 24.5$ 58

List of metrics:

Prescribed vs. reproduced Reynolds stress tensor components at inlet patch
$\overline{u^\prime u^\prime}$ downstream development vs. $x/ \delta$
$\overline{v^\prime v^\prime}$ downstream development vs. $x/ \delta$
$\overline{u^\prime v^\prime}$ downstream development vs. $x/ \delta$
Surface skin friction coefficient $\mathrm{C}_f$ vs. $x/ \delta$
Streamwise mean flow speed and Reynolds stress tensor components at uniform-interval downstream profiles
Streamwise vorticity $\omega_x$ at $x/ \delta = 0.1$
Streamwise vorticity $\omega_x$ at $x/ \delta = 1.0$
Metrics are time and spanwise averaged
$< \cdot >$ is the time-averaging operator