Numerical simulations and analysis of the turbulent flow field in a practical gas turbine engine combustor

The turbulent flow field in a practical gas turbine combustor is very complex because of the interactions between various flows resulting from components like multiple types of swirlers, dilution holes, and liner effusion cooling holes. Numerical simulations of flows in such complex combustor configurations are challenging. The challenges result from (a) the complexities of the interfaces between multiple three-dimensional shear layers, (b) the need for proper treatment of a large number of tiny effusion holes with multiple angles, and (c) the requirements for fast turnaround times in support of engineering design optimization. Both the Reynolds averaged Navier–Stokes simulation (RANS) and the large eddy simulation (LES) for the practical combustor geometry are considered. An autonomous meshing using the cut-cell Cartesian method and adaptive mesh refinement (AMR) is demonstrated for the first time to simulate the flow in a practical combustor geometry. The numerical studies include a set of computations of flows under a prescribed pressure drop across the passage of interest and another set of computations with all passages open with a specified total flow rate at the plenum inlet and the pressure at the exit. For both sets, the results of the RANS and the LES flow computations agree with each other and with the corresponding measurements. The results from the high-resolution LES simulations are utilized to gain fundamental insights into the complex turbulent flow field by examining the profiles of the velocity, the vorticity, and the turbulent kinetic energy. The dynamics of the turbulent structures are well captured in the results of the LES simulations.

A Cut-Cell Polyhedral Finite Element Model for Coupled Fluid Flow and Mechanics in Fractured Reservoirs

Mechanical deformation induced by injection and withdrawal of fluids from the subsurface can significantly alter the flow paths in naturally fractured reservoirs. Modeling coupled fluid-flow and mechanical deformation in fractured reservoirs relies on either sophisticated gridding techniques, or enhancing the variables (degrees-of-freedom) that represent the physics in order to describe the behavior of fractured formation accurately. The objective of this study is to develop a spatial discretization scheme that cuts the "matrix" grid with fracture planes and utilizes traditional formulations for fluid flow and geomechanics. The flow model uses the standard low-order finite-volume method with the Compartmental Embedded fracture Model (cEDFM). Due to the presence of non-standard polyhedra in the grid after cutting/splitting, we utilize numerical harmonic shape functions within a Polyhedral finite-element (PFE) formulation for mechanical deformation. In order to enforce fracture-contact constraints, we use a penalty approach. We provide a series of comparisons between the approach that uses conforming Unstructured grids and a Discrete Fracture Model (Unstructured DFM) with the new cut-cell PFE formulation. The manuscript analyzes the convergence of both methods for linear elastic, single-fracture slip, and Mandel’s problems with tetrahedral, Cartesian, and PEBI-grids. Finally, the paper presents a fully-coupled 3D simulation with multiple inclined intersecting faults activated in shear by fluid injection, which caused an increase in effective reservoir permeability. Our approach allows for great reduction in the complexity of the (gridded) model construction while retaining the solution accuracy together with great saving in the computational cost compared with UDFM. The flexibility of our model with respect to the types of grid polyhedra allows us to eliminate mesh artifacts in the solution of the transport equations typically observed when using tetrahedral grids and two-point flux approximation.

The Modified LS-STAG Method Application for Planar Viscoelastic Flow Computation in a 4:1 Contraction Channel

In this study we present the modification of the LS-STAG immersed boundary cut-cell method. This modification is designed for viscoelastic fluids. Linear and quasilinear viscoelastic fluid models of a rate type are considered. The obtained numerical method is implemented in the LS-STAG software package developed by the author. This software is created for viscous incompressible flows simulation both by the LS-STAG method and by it developed modifications. Besides of this, the software package is designed to compute extra-stresses for viscoelastic Maxwell, Jeffreys, upper-convected Maxwell, Maxwell-A, Oldroyd-B, Oldroyd-A, Johnson --- Segalman fluids on the LS-STAG mesh. The construction of convective derivatives discrete analogues is described for Oldroyd, Cotter --- Rivlin, Jaumann --- Zaremba --- Noll derivatives. The centers of base LS-STAG mesh cells are the locations for shear non-Newtonian stresses computation. The corners of these cells are the positions for normal non-Newtonian stresses computation. The first order predictor--corrector scheme is the basis for time-stepping numerical algorithm. Benchmark solutions for the planar flow of Oldroyd-B fluid in a 4:1 contraction channel are presented. A critical value of Weissenberg number is defined. Computational results are in good agreement with the data known in the literature

An Unfitted dG Scheme for Coupled Bulk-Surface PDEs on Complex Geometries

The unfitted discontinuous Galerkin (UDG) method allows for conservative dG discretizations of partial differential equations (PDEs) based on cut cell meshes. It is hence particularly suitable for solving continuity equations on complex-shaped bulk domains. In this paper based on and extending the PhD thesis of the second author, we show how the method can be transferred to PDEs on curved surfaces. Motivated by a class of biological model problems comprising continuity equations on a static bulk domain and its surface, we propose a new UDG scheme for bulk-surface models. The method combines ideas of extending surface PDEs to higher-dimensional bulk domains with concepts of trace finite element methods. A particular focus is given to the necessary steps to retain discrete analogues to conservation laws of the discretized PDEs. A high degree of geometric flexibility is achieved by using a level set representation of the geometry. We present theoretical results to prove stability of the method and to investigate its conservation properties. Convergence is shown in an energy norm and numerical results show optimal convergence order in bulk/surface H 1 {H^{1}} - and L 2 {L^{2}} -norms.