High order schemes on three-dimensional general polyhedral meshes - Application to the level set method

In this article, we detail the methodology developed to construct arbitrarily high order schemes - linear and WENO - on 3D mixed-element unstructured meshes made up of general convex polyhedral elements. The approach is tailored specifically for the solution of scalar level set equations for application to incompressible two-phase flow problems. The construction of WENO schemes on 3D unstructured meshes is notoriously difficult, as it involves a much higher level of complexity than 2D approaches. This due to the multiplicity of geometrical considerations introduced by the extra dimension, especially on mixed-element meshes. Therefore, we have specifically developed a number of algorithms to handle mixed-element meshes composed of convex polyhedra with convex polygonal faces. The contribution of this work concerns several areas of interest: the formulation of an improved methodology in 3D, the minimisation of computational runtime in the implementation through the maximum use of pre-processing operations, the generation of novel methods to handle complex 3D mixed-element meshes and finally the application of the method to the transport of a scalar level set. © 2012 Global-Science Press.

Low-order modelling of ducted flames with temporally varying equivalence ratio in realistic geometries

The interaction between unsteady heat release and acoustic pressure oscillations in gas turbines results in self-excited combustion oscillations which can potentially be strong enough to cause significant structural damage to the combustor. Correctly predicting the interaction of these processes, and anticipating the onset of these oscillations can be difficult. In recent years much research effort has focused on the response of premixed flames to velocity and equivalence ratio perturbations. In this paper, we develop a flame model based on the socalled G-Equation, which captures the kinematic evolution of the flame surfaces, under the assumptions of axisymmetry, and ignoring vorticity and compressibility. This builds on previous work by Dowling [1], Schuller et al. [2], Cho & Lieuwen [3], among many others, and extends the model to a realistic geometry, with two intersecting flame surfaces within a non-uniform velocity field. The inputs to the model are the free-stream velocity perturbations, and the associated equivalence ratio perturbations. The model also proposes a time-delay calculation wherein the time delay for the fuel convection varies both spatially and temporally. The flame response from this model was compared with experiments conducted by Balachandran [4, 5], and found to show promising agreement with experimental forced case. To address the primary industrial interest of predicting self-excited limit cycles, the model has then been linked with an acoustic network model to simulate the closed-loop interaction between the combustion and acoustic processes. This has been done both linearly and nonlinearly. The nonlinear analysis is achieved by applying a describing function analysis in the frequency domain to predict the limit cycle, and also through a time domain simulation. In the latter case, the acoustic field is assumed to remain linear, with the nonlinearity in the response of the combustion to flow and equivalence ratio perturbations. A transfer function from unsteady heat release to unsteady pressure is obtained from a linear acoustic network model, and the corresponding Green function is used to provide the input to the flame model as it evolves in the time domain. The predicted unstable frequency and limit cycle are in good agreement with experiment, demonstrating the potential of this approach to predict instabilities, and as a test bench for developing control strategies. Copyright © 2011 by ASME.

Combustion rumble prediction with integrated computational-fluid-dynamics/ low-order-model methods

The pressure oscillation within combustion chambers of aeroengines and industrial gas turbines is a major technical challenge to the development of high-performance and low-emission propulsion systems. In this paper, an approach integrating computational fluid dynamics and one-dimensional linear stability analysis is developed to predict the modes of oscillation in a combustor and their frequencies and growth rates. Linear acoustic theory was used to describe the acoustic waves propagating upstream and downstream of the combustion zone, which enables the computational fluid dynamics calculation to be efficiently concentrated on the combustion zone. A combustion oscillation was found to occur with its predicted frequency in agreement with experimental measurements. Furthermore, results from the computational fluid dynamics calculation provide the flame transfer function to describe unsteady heat release rate. Departures from ideal one-dimensional flows are described by shape factors. Combined with this information, low-order models can work out the possible oscillation modes and their initial growth rates. The approach developed here can be used in more general situations for the analysis of combustion oscillations. Copyright © 2012 by the American Institute of Aeronautics and Astronautics, Inc. All rights reserved.

Semi-implicit second order finite volume jet stream computations

Semi-implicit, second order temporal and spatial finite volume computations of the flow in a differentially heated rotating annulus are presented. For the regime considered, three cyclones and anticyclones separated by a relatively fast moving jet of fluid or "jet stream" are predicted. Two second order methods are compared with, first order spatial predictions, and experimental measurements. Velocity vector plots are used to illustrate the predicted flow structure. Computations made using second order central differences are shown to agree best with experimental measurements, and to be stable for integrations over long time periods (> 1000s). No periodic smoothing is required to prevent divergence.

High-order DES and zonal LES of a labyrinth seal

Hybrid numerical large eddy simulation (NLES) and detached eddy simulation (DES) methods are assessed on a labyrinth seal geometry. A high sixth order discretization scheme is used and is validated using a test case of a two dimensional vortex. The hybrid approach adopts a new blending function and along with DES is initially validated using a simple cavity flow. The NLES method is also validated outside of RANS zones. It is found that there is very little resolved turbulence in the cavity for the DES simulation. For the labyrinth seal calculations the DES approach is problematic giving virtually no resolved turbulence content. It is seen that over the tooth tips the extent of the LES region is small and is likely to be a strong contributor to excessive flow damping in these regions. On the other hand the zonal Hamilton-Jacobi approach did not suffer from this trait. In both cases the meshes used are considered to be hybrid RANS-LES adequate. Fortunately (or perhaps unfortunately) the DES profiles are in agreement with the time mean experimental measurements. It is concluded that for an inexperienced CFD practitioner this could have wider implications particularly if transient results such as unsteady loading are desired. Copyright © 2012 by the American Institute of Aeronautics and Astronautics, Inc.