Fluid dynamic turbulence is one of the most challenging computational physics problems because of the extremely wide range of time and space scales involved, the strong nonlinearity of the governing equations, and the many practical and important applications. While most linear fluid instabilities are well understood, the nonlinear interactions among them makes even the relatively simple limit of homogeneous isotropic turbulence difficult to treat physically, mathematically, and computationally. Turbulence is modeled computationally by a two-stage bootstrap process. The first stage, direct numerical simulation, attempts to resolve the relevant physical time and space scales but its application is limited to diffusive flows with a relatively small Reynolds number (Re). Using direct numerical simulation to provide a database, in turn, allows calibration of phenomenological turbulence models for engineering applications. Large eddy simulation incorporates a form of turbulence modeling applicable when the large-scale flows of interest are intrinsically time dependent, thus throwing common statistical models into question. A promising approach to large eddy simulation involves the use of high-resolution monotone computational fluid dynamics algorithms such as flux-corrected transport or the piecewise parabolic method which have intrinsic subgrid turbulence models coupled naturally to the resolved scales in the computed flow. The physical considerations underlying and evidence supporting this monotone integrated large eddy simulation approach are discussed.

New insights into large eddy simulation

https://backend.orbit.dtu.dk/ws/files/256022566/1_s2.0_S0376042121000427_main.pdf

Turbulent boundary layer trailing-edge noise: Theory, computation, experiment, and application

A high-order adaptive Cartesian cut-cell method for simulation of compressible viscous flow over immersed bodies

Combined near and far field aeroacoustic measurements have been carried out during an original laboratory scale low Mach number (0–0.3) experiment about the tip leakage flow past a single non-rotating airfoil. Such measurements were made possible by the use of a single airfoil located in the potential core of an open jet flow in the anechoic wind tunnel of the Ecole Centrale de Lyon. The airfoil was mounted between two flat plates. A strong tip clearance flow was achieved without rotation by paying a special attention to the choice of the airfoil which was a 5% camber, 10% thickness NACA5510 airfoil that provided a high lift at a 15° angle of attack. The experiment gave rise to an extensive data set obtained with several flow velocity measurement techniques (HWA, LDA, PIV), steady and unsteady pressure measurements on the airfoil and the casing plate as well as far field pressure measurements. Further, cross-analyses of various velocity and pressure signals allowed to locating sources and identifying their mechanisms. Results showed evidence of two components of tip leakage broadband self noise.

Aeroacoustic investigation of a single airfoil tip leakage flow

Effects of tip-gap width on the flow field in an axial fan

The turbulent low Mach number flow through an axial fan at a Reynolds number of 9.36 × 105 based on the outer casing diameter is investigated by large-eddy simulation. A finite-volume flow solver in an unstructured hierarchical Cartesian setup for the compressible Navier-Stokes equations is used. To account for sharp edges, a fully conservative cut-cell approach is applied. A newly developed rotational periodic boundary condition for Cartesian meshes is introduced such that the simulations are performed just for a 72° segment, i.e., the flow field over one out of five axial blades is resolved. The focus of this numerical analysis is on the development of the vortical flow structures in the tip-gap region. A detailed grid convergence study is performed on four computational grids with 50 × 106, 250 × 106, 1 × 109, and 1.6 × 109 cells. Results of the instantaneous and the mean fan flow field are thoroughly analyzed based on the solution with 1 × 109 cells. High levels of turbulent kinetic energy and pressure fluctuations are generated by a tip-gap vortex upstream of the blade, the separating vortices inside the tip gap, and a counter-rotating vortex on the outer casing wall. An intermittent interaction of the turbulent wake, generated by the tip-gap vortex, with the downstream blade, leads to a cyclic transition with high pressure fluctuations on the suction side of the blade and a decay of the tip-gap vortex. The disturbance of the tip-gap vortex results in an unsteady behavior of the turbulent wake causing the intermittent interaction. For this interaction and the cyclic transition, two dominant frequencies are identified which perfectly match with the characteristic frequencies in the experimental sound power level and therefore explain their physical origin.

Cut-cell method based large-eddy simulation of tip-leakage flow

The flow field in a complete one-stage axial-flow turbine with 30 stator and 62 rotor blades is investigated by large-eddy simulation (LES). To solve the compressible Navier-Stokes equations, a massively parallelized finite-volume flow solver based on an efficient Cartesian cut-cell/level-set approach, which ensures a strict conservation of mass, momentum and energy, is used. This numerical method contains two adaptive Cartesian meshes, one mesh to track the embedded surface boundaries and a second mesh to resolve the fluid domain and to solve the conservation equations. The overall approach allows large scale simulations of turbomachinery applications with multiple relatively moving boundaries in a single frame of reference. The relative motion of the geometries is described by a kinematic motion level-set interface method. The focus of the numerical analysis is on the flow inside the rim seal between the stator and the rotor disks. Full $360^{\circ }$
 computations of the turbine stage are performed for two rim seal configurations. First, the impact of the mesh resolution on the LES results is analyzed for the single lip rim seal configuration. Second, the LES results are compared to experimental data, followed by a detailed analysis of the unsteady flow field. For the single lip rim seal configuration, two modes unrelated to the rotor frequency and its harmonics are identified inside the rotor-stator wheel space, where the first more dominant mode shows a major impact on the ingress of the hot gas into the rotor-stator wheel space. The second mode is a counter-rotating mode which results from the interaction of the first mode with the flow field downstream of the stator blades. Third, at the same operating condition a modified configuration with a double lip rim seal is investigated and compared to the reference configuration to demonstrate the impact of the rim seal geometry on the overall flow field. The additional lip on the rotor disk damps the aforementioned modes and reduces the ingress of the hot gas resulting in an increase of the cooling effectiveness inside the rotor-stator wheel space, which is in a good agreement with the experimental results.

Large-Eddy Simulation of the Unsteady Full 3D Rim Seal Flow in a One-Stage Axial-Flow Turbine

An efficient Cartesian cut-cell/level-set method based on a multiple grid approach to simulate turbulent turbomachinery flows is presented. The finite-volume approach in an unstructured hierarchical Cartesian setup with a sharp representation of the complex moving boundaries embedded into the computational domain, which are described by multiple level-sets, ensures a strict conservation of mass, momentum, and energy. Furthermore, an efficient kinematic motion level-set interface method for the rotation of embedded boundaries described by multiple level-set fields on a computational domain distributed over several processors is introduced. This method allows the simulation of multiple boundaries rotating relatively to each other in a fixed frame of reference. To demonstrate the efficiency of the numerical method and the quality of the computed findings the generic test problem of a rotating cylinder surrounded by a stationary hull and the flow over a ducted rotating axial fan with a stationary turbulence generating grid at the inflow are simulated. The computational results of the axial fan show a good agreement with the experimental data.

An Adaptive Cartesian Mesh Based Method to Simulate Turbulent Flows of Multiple Rotating Surfaces

The viscous flow around a rotating axial fan at a Reynolds number of 9.36 × 10 based on the outer casing diameter is investigated by large-eddy simulation (LES) with special focus on the tip-leakage flow region. A massively parallelized finite-volume flow solver for compressible flows based on hierarchical Cartesian grids is used. The immersed boundaries of the fan geometry are handled by a fully conservative cut-cell method. A 72◦ segment, which includes one of the five fan blades, is resolved with approx. 250 million cells, for which a rotational periodic boundary condition for Cartesian meshes has been developed. Results of the instantaneous and the mean fan flow field are discussed and compared to Reynolds-averaged Navier-Stokes (RANS) results of a 360◦ simulation. The main differences are observed for the turbulent kinetic energy in the wake region generated by the tip-gap vortex. Furthermore, the influence of the tip-gap size on the vortical structures is investigated. It is shown that a reduction of the tip-gap size leads to a change of the shape and size of the tip-gap vortex. Additionally, more separation and counter-rotating vortices are generated inside the tip-gap, which, however, result in a lower turbulent kinetic energy.

Alexej Pogorelov

Papers

Cut-cell method based large-eddy simulation of tip-leakage flow

Effects of tip-gap width on the flow field in an axial fan

Large-Eddy Simulation of the Unsteady Full 3D Rim Seal Flow in a One-Stage Axial-Flow Turbine

An Adaptive Cartesian Mesh Based Method to Simulate Turbulent Flows of Multiple Rotating Surfaces

Cut-Cell Method Based Large-Eddy Simulation of a Tip-Leakage Vortex of an Axial Fan