Direct Numerical Simulation of Fully Resolved Liquid Droplets in a Turbulent Flow Michele Rosso & Said Elghobashi Department of Mechanical and Aerospace Engineering University of California, Irvine NCSA Blue Waters Symposium for Petascale Science and Beyond May 11, 2015 Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 1 / 15
Objective & motivation Objective Investigation of the two-way coupling effects of finite-size deformable liquid droplets on decaying isotropic turbulence using direct numerical simulation (DNS). Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 2 / 15
Objective & motivation Objective Investigation of the two-way coupling effects of finite-size deformable liquid droplets on decaying isotropic turbulence using direct numerical simulation (DNS). Motivation Dispersed liquid/gas multiphase flows occur in a wide range of natural phenomena and engineering devices, e.g. combustion of liquid fuel sprays. Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 2 / 15
Example of application I Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 3 / 15
Example of application II Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 4 / 15
Effect of dispersed solid spherical particles on the dissipation rate of TKE ( Lucci, Ferrante & Elghobashi, JFM 2010 ) Re λ N N p Φ v d /η 75 256 6400 0.1 16 Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 5 / 15
Computational requirements ◮ Simulation of single-phase isotropic turbulence with Re λ = 300 requires 2048 3 grid points in order to capture the smallest scales Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 6 / 15
Computational requirements ◮ Simulation of single-phase isotropic turbulence with Re λ = 300 requires 2048 3 grid points in order to capture the smallest scales ◮ On Blue Waters the simulation required 12 hrs and 65536 processors to advance the solution for about 3 large-eddy turnover times Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 6 / 15
Computational requirements ◮ Simulation of single-phase isotropic turbulence with Re λ = 300 requires 2048 3 grid points in order to capture the smallest scales ◮ On Blue Waters the simulation required 12 hrs and 65536 processors to advance the solution for about 3 large-eddy turnover times ◮ The simulation of dispersed two-phase turbulence requires about double the time of single-phase turbulence Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 6 / 15
Governing equations for incompressible two-phase flows ◮ Continuity equation: ∇ · u = 0 Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 7 / 15
Governing equations for incompressible two-phase flows ◮ Continuity equation: ∇ · u = 0 ◮ Momentum equations: � � ∂ t + ∇ · ( uu ) = − 1 ∂ u ∇ p + ∇ · T − ρ Fr k + f σ ρ Re We Dimensionless parameters: ρ gas � U � � ρ gas � U 2 � U 2 Re = � L We = � L Fr = µ gas � g � � σ � L Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 7 / 15
Interface definition & transport The gas/liquid interface Γ( t ) is described as the zero level set of a signed distance function φ ( x , t ) that is transported by the fluid velocity u via: ∂φ ∂ t + u · ∇ φ = 0 Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 8 / 15
Interface definition & transport The gas/liquid interface Γ( t ) is described as the zero level set of a signed distance function φ ( x , t ) that is transported by the fluid velocity u via: ∂φ ∂ t + u · ∇ φ = 0 In order to keep φ a signed distance function, a reinitialization equation is solved until convergence: ∂φ ∂τ = sign ( φ 0 )(1 − |∇ φ | ) where τ is a fictitious time and φ 0 is the level set function after the advection step. Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 8 / 15
Variable-Density Projection Method 1. A provisional velocity u ∗ is computed from u n , the velocity field at time n : u ∗ − u n = R n δ t where R n includes the convective, viscous, surface tension and gravity terms. Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 9 / 15
Variable-Density Projection Method 1. A provisional velocity u ∗ is computed from u n , the velocity field at time n : u ∗ − u n = R n δ t where R n includes the convective, viscous, surface tension and gravity terms. 2. A variable-coefficient Poisson’s equation is solved: � ∇ p n +1 � = ∇ · u ∗ ∇ · ρ n +1 δ t Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 9 / 15
Variable-Density Projection Method 1. A provisional velocity u ∗ is computed from u n , the velocity field at time n : u ∗ − u n = R n δ t where R n includes the convective, viscous, surface tension and gravity terms. 2. A variable-coefficient Poisson’s equation is solved: � ∇ p n +1 � = ∇ · u ∗ ∇ · ρ n +1 δ t 3. u ∗ is corrected to obtain u n +1 , the velocity field at time n + 1: u n +1 = u ∗ − δ t ∇ p n +1 ρ n +1 Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 9 / 15
Solution of the Variable-Coefficients Poisson’s equation � ∇ p n +1 � = ∇ · u ∗ ∇ · ρ n +1 δ t ◮ Equation is non-separable because ρ n +1 is variable Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 10 / 15
Solution of the Variable-Coefficients Poisson’s equation � ∇ p n +1 � = ∇ · u ∗ ∇ · ρ n +1 δ t ◮ Equation is non-separable because ρ n +1 is variable ◮ Direct application of FFT is not possible Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 10 / 15
Solution of the Variable-Coefficients Poisson’s equation � ∇ p n +1 � = ∇ · u ∗ ∇ · ρ n +1 δ t ◮ Equation is non-separable because ρ n +1 is variable ◮ Direct application of FFT is not possible ◮ It is mission critical since it accounts for about 70-80 % of the solution time Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 10 / 15
Solution of the Variable-Coefficients Poisson’s equation � ∇ p n +1 � = ∇ · u ∗ ∇ · ρ n +1 δ t ◮ Equation is non-separable because ρ n +1 is variable ◮ Direct application of FFT is not possible ◮ It is mission critical since it accounts for about 70-80 % of the solution time ◮ Solution is performed via the Conjugate Gradient method Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 10 / 15
Solution of the Variable-Coefficients Poisson’s equation � ∇ p n +1 � = ∇ · u ∗ ∇ · ρ n +1 δ t ◮ Equation is non-separable because ρ n +1 is variable ◮ Direct application of FFT is not possible ◮ It is mission critical since it accounts for about 70-80 % of the solution time ◮ Solution is performed via the Conjugate Gradient method ◮ A Geometric Algebraic Multigrid preconditioner is used Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 10 / 15
Solution of the Variable-Coefficients Poisson’s equation � ∇ p n +1 � = ∇ · u ∗ ∇ · ρ n +1 δ t ◮ Equation is non-separable because ρ n +1 is variable ◮ Direct application of FFT is not possible ◮ It is mission critical since it accounts for about 70-80 % of the solution time ◮ Solution is performed via the Conjugate Gradient method ◮ A Geometric Algebraic Multigrid preconditioner is used ◮ We rely on the PETSc library for the solution of the linear system Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 10 / 15
Current limitations ◮ A 3D domain decomposition is used to partition the computational domain Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 11 / 15
Current limitations ◮ A 3D domain decomposition is used to partition the computational domain ◮ Each subdomain is local to a processor Michele Rosso & Said Elghobashi (UCI) DNS of liquid droplets in turbulence Blue Waters Symposium-May 11, 2015 11 / 15
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