12th Workshop on Two-Phase Flow Predictions, 21-25 March 2010, Halle (Germany)

| TEST CASE: LES of particle-laden turbulent channel flow

GROUP UUD-UPI: C. Marchioli, A. Soldati, Dept. Energy Technologies, University of Udine & M.V. Salvetti, Dept. Aerospace Engineering, University of Pisa (Italy) GROUP TUE: J.G.M. Kuerten, Dept. Mechanical Engineering, Technische Universiteit Eindhoven (Netherlands) GROUP IMFT-ASU: A. Ndri Konan, P. Fede, O. Simonin, Université de Toulouse; INPT, UPS; Institut de Mécanique des Fluides de Toulouse; CNRS (France) & K.D. Squires, Mechanical and Aerospace Engineering Dept., Arizona State University (USA) GROUP TUM: C. Gobert, M. Manhart, Dept. Civil Engineering, Munich University of Technology (Germany)

Equation of particle motion (with drag and inertia)

\frac{dx_{i}}{dt} = v_{i} , \frac{dv_{i}}{dt} = \frac{û(x_{i},t)−v_{i}}{τ_{p}} (1 + 0.15Re_{p}^{0.687}),

x_{i}, v_{i} and τ_{p}: particle position, velocity and relaxation time. û(x, t): filtered fluid velocity (issued by LES).

Method (LES of particle-laden flow)

• COMMON BASE-SIMULATION PARAMETERS

– Shear Reynolds number (based on half channel height) : Re_{τ} = 150

– Particle Stokes number: St = 1, 5 and 25

– Size of the computational domain (streamwise, wallnormal, spanwise): L_{x} × L_{z} × L_{y} = 4πh × 2h × 2πh

– Grid resolution: N_{x} × N_{z} × N_{y} = 64 × 65 × 64

– Tracked particles: N_{p} = 10^{5} particles for each St

• GROUP UUD-UPI (Marchioli, Soldati, Salvetti)

– Flow solver: Fourier-Galerkin (streamwise-spanwise) and Chebyshev collocation method (wall-normal)

– SGS model: dynamic eddy-viscosity model

– Time integration of fluid: 2^{nd}-order Adams-Bashforth (nonlinear terms), implicit Crank-Nicolson (linear terms)

– Time integration of particles: 4^{th}-order Runge-Kutta – Fluid velocity interpolation: 6^{th}-order Lagrange polyn.

• GROUP TUE (Kuerten)

– Flow solver: Fourier-Galerkin (streamwise-spanwise) and Chebyshev collocation method (wall-normal)

– SGS model: dynamic eddy-viscosity model

– Time integration of fluid: 3^{rd}-order Runge-Kutta (nonlinear terms) and implicit Crank-Nicolson (linear terms)

– Time integration of particles: 2^{nd}-order Heun method – Fluid velocity interpolation: 4^{th}-order Lagrange-Hermite

• GROUP IMFT-ASU (Konan, Fede, Simonin, Squires)

– Flow solver: fractional-step method for the NS equations. Spatial derivatives evaluated using 2^{nd}-order centered differences

– SGS model: eddy-viscosity model with wall damping – Time integration of fluid: 2^{nd}-order Adams-Bashforth

(nonlinear terms) and Crank-Nicolson (linear terms)

– Time integration of particles: 2^{nd}-order Adams-Bashforth

– Fluid velocity interpolation: 4^{th}-order Lagrange polyn.

• GROUP TUM (Gobert, Manhart)

– Flow solver: finite-volume method for the NS equations. Spatial derivatives evaluated using 2^{nd}-order centered differences

– SGS model: dynamic Lagrange Smagorinsky eddyviscosity model

– Time integration of fluid: 3^{rd}-order Runge-Kutta

– Time integration of particles: 4^{th}-order adaptive linearimplicit Runge-Kutta (Rosenbrock-Wanner scheme)

– Fluid velocity interpolation: 4^{th}-order Lagrange polyn.

Results

Mean and RMS Fluid Velocities:

Mean and RMS Particle Velocities:

Particle Concentrations: