Session HM: Turbulence Simulations III

LES of the flow around a marine propeller

LES of the flow around a marine propeller, in the crashback mode of operation is performed. Crashback refers to the mode where the propeller rotates in the reverse direction while the vessel moves in the forward direction. It is characterized by massive flow separation and unsteady propeller loads, which affect both blade life, and maneuverability. The simulations are performed in a rotating frame of reference on unstructured grids using the algorithm developed by Mahesh at al. (2004, J. Comput. Phys. 197). The flow is computed for as long as 300 propeller revolutions at experimental Reynolds number, in order to resolve low frequency fluctuations of thrust, torque and side-forces on the propeller. Their average and rms values, and power spectral density show good agreement with experiment. The circumferentially averaged flow is also in good agreement with experiment for mean and turbulence quantities. A prominent feature of the flow is a ring vortex that is highly unsteady. The ring vortex will be used to explain the fluctuating loads on the propeller. Also, a simplified model will be discussed, where the propeller is replaced by an actuator disk.   

Large Eddy Simulation (LES) of turbulent flows within rotating cavities using a spectral vanishing viscosity (SVV) model

The highly accurate computation of turbulent rotating flows within cavity is of interest for both engineering applications (turbomachinaries), and fundamental research (one of the simplest cases with 3D turbulent boundary layers). LES results based on a SVV model will be presented in a shrouded rotor-stator cavity ($\Delta $R/H=5, (R$_{in}$+R$_{out})$/$\Delta $R=3.37) for Reynolds numbers up to Re=10$^{6}$. The second-order SVV operator is implemented in a Chebyshev-collocation Fourier-Galerkin pseudo-spectral code for solving cylindrical Navier-Stokes equations. The SVV model is shown to lead to stable discretizations without sacrificing the formal accuracy, i.e., exponential convergence, in the proposed discretization. As far as the authors are aware, efficient LES of fully turbulent flow in an actual shrouded rotor-stator cavity has not been performed before. Turbulent quantities are shown to compare very favourably with results of Direct Numerical Simulation (DNS) and experimental measurements. The results show a highly complex structure of the flow, involving laminar, transitional, and turbulent flow regions.   

Hybrid RANS/LES of 3D boundary layers

We describe hybrid LES/RANS calculations of 3D boundary layers, in which RANS is used in the equilibrium region of the flow, and LES is performed in the region where the flow is turning. The 3D boundary layer is obtained by applying a spanwise pressure gradient to a flat-plate boundary layer. At the RANS/LES interface, a synthetic turbulence generation and a controlled forcing loop are used to generate realistic turbulent eddies rapidly and match the RANS statistics. When the RANS/LES interface is placed in a region where the turning of the flow is relatively mild, a control based on the Reynolds shear stresses $\langle$ u' v' $\rangle$ gives good agreement with the reference LES.   

Numerical Simulations of the flow past a two-dimensional bump

The flow past a two-dimensional bump at momentum Reynolds number 12170 has been computed using Wall-modeled Large-Eddy Simulation (WMLES). The bump geometry consists of long convex region joined by two short concave region at its two ends. The flow experiences both concave and convex curvature effects and also favorable and adverse pressure gradient effects. The wall-layer model employed is based on the Detached Eddy Simulation (DES) technique, in which the Spalart-Allmaras model is modified to represent all the scales of motion in the RANS region near the wall, but only the subgrid eddies in the LES zone in the outer region. First, DES alone was used as a wall-layer model; in a second simulation stochastic forcing was applied in the RANS/LES interface region to aid the generation of eddies. The mean velocity is predicted reasonably well by both the simulations, but the simulation with the stochastic forcing predicts the Reynolds stresses better. The use of a DES based wall-model has enabled to perform simulations at a fraction of the cost of the wall-resolved calculation.   

Towards wall filtering for LES of wall bounded flows

Large filter widths are necessary for LES to efficiently compute large scales of high Reynolds number flows. If large filter widths are used near wall, the no-slip boundary condition does not apply anymore. Vanishing filter width near the interface will introduce commutation error. Recently, Templeton \& Shoeybi (\emph{Multiscale Mod. Sim.}, 2006) proposed an approach based on filtering the solution over an infinite domain for one-dimensional problems. This allows the LES equations, including boundary conditions, to be precisely defined without any commutation error. In this work, the method is extended to higher dimensional spaces and is applied to incompressible Navier-Stokes equations. A particular challenge with these equations is the treatment of the pressure which plays the role of both an applied force and a Lagrange multiplier to enforce the divergence-free constraint. Results for several systems, including the heat equation, Burgers' equation, and higher dimensional Navier-Stokes equations will be presented.   

Smagorinsky constant in LES modeling of anisotropic MHD turbulence

Turbulent fluctuations in MHD flows can become strongly anisotropic or even quasi-two-dimensional under the action of an applied magnetic field. We investigate this phenomenon in the case of low magnetic Reynolds numbers. It has been found in earlier DNS and LES of homogeneous turbulence that the degree of anisotropy is predominantly determined by the value of the magnetic interaction parameter and only slightly depends on the Reynolds number, type of large-scale dynamics, and the length scale. Furthermore, it has been demonstrated that the dynamic Smagorinsky model is capable of self-adjustment to the effects of anisotropy. In this presentation, we capitalize on these results and employ dynamic model simulations to derive a simple and effective generalization of the traditional non-dynamic Smagorinsky model to the case of anisotropic MHD turbulence.