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ABSTRACT
In this article, the previously developed single block fully coupled algorithm [Citation1,Citation2] for solving three-dimensional incompressible turbulent flows is extended to resolve transient flows in multiple rotating reference frames using the arbitrary Lagrange–Euler (ALE) formulation. Details on the discretization of ALE terms along with a recently developed extension to the conservative and fully implicit treatment of multi-block interfaces into three-dimensional space are presented. To account for turbulence, the kω − SST turbulence model in ALE formulation is solved using Navier–Stokes equations. This multi-block transient coupled algorithm is embedded within the OpenFOAM® Computational Fluid Dynamics (CFD) library, and its performance evaluated in a real case involving a turbulent flow field in a swirl generator by comparing numerical predictions with experimental measurements.
Nomenclature
| A, a | = | coefficient matrix, coefficient matrix coefficient |
| ALE | = | arbitrary Lagrange–Euler |
| AMI | = | arbitrary mesh interface |
| b, b | = | source vector, source vector coefficient |
| D | = | Rhie–Chow numerical dissipation tensor |
| FFT | = | fast Fourier transform |
| g | = | geometric interpolation weighting factor |
| k | = | turbulence kinetic energy |
| MG | = | measurement gauge |
| MRF | = | multiple reference frame |
| p | = | pressure |
| S, S | = | surface normal vector, surface scalar |
| u, v, w | = | velocity components |
| u | = | velocity vector |
| = | volume, volume flux | |
| υ | = | kinematic viscosity |
| ρ | = | density |
| ω | = | turbulence frequency |
| = | Subscript | |
| C | = | cell under consideration |
| eff | = | refers to effective turbulent viscosity |
| f | = | refers to face |
| g | = | refers to grid |
| NB | = | refers to neighbors of cell C |
| rel | = | refers to relative velocity and/or flux |
| = | Superscript | |
| u, v, w | = | refers to velocity components |
| ‾ | = | linear interpolation to the face |
Nomenclature
| A, a | = | coefficient matrix, coefficient matrix coefficient |
| ALE | = | arbitrary Lagrange–Euler |
| AMI | = | arbitrary mesh interface |
| b, b | = | source vector, source vector coefficient |
| D | = | Rhie–Chow numerical dissipation tensor |
| FFT | = | fast Fourier transform |
| g | = | geometric interpolation weighting factor |
| k | = | turbulence kinetic energy |
| MG | = | measurement gauge |
| MRF | = | multiple reference frame |
| p | = | pressure |
| S, S | = | surface normal vector, surface scalar |
| u, v, w | = | velocity components |
| u | = | velocity vector |
| = | volume, volume flux | |
| υ | = | kinematic viscosity |
| ρ | = | density |
| ω | = | turbulence frequency |
| = | Subscript | |
| C | = | cell under consideration |
| eff | = | refers to effective turbulent viscosity |
| f | = | refers to face |
| g | = | refers to grid |
| NB | = | refers to neighbors of cell C |
| rel | = | refers to relative velocity and/or flux |
| = | Superscript | |
| u, v, w | = | refers to velocity components |
| ‾ | = | linear interpolation to the face |
Acknowledgments
The help of Sebastian Muntean (Polytechnic University of Timisoara) by providing the experimental data for the test case is gratefully acknowledged. The effort of the OpenFOAM Turbomachinery SIG (Olivier Petit) by providing the numerical setup for the test case is gratefully acknowledged.