Stuart Connell

Three-dimensional unstructured adaptive multigrid scheme for the Navier-Stokes equations

A solution adaptive multigrid scheme for solving the three-dimensional Navier-Stokes equations on unstructured meshes is presented. The algorithm solves the equations on a fully unstructured mesh of tetrahedral elements, using a multigrid time-marching scheme. The initial unstructured mesh is successively refined based on gradients in the flow solution, with the multigrid levels being determined by the refinement procedure. Important issues related to solving viscous flows on unstructured meshes are discussed. These include calculation of the viscous stress terms in a manner that prevents wiggles, calculation of the time steps to include both inviscid and viscous effects, numerical smoothing considerations, minimization of computer storage requirements, and implementation of the k-e turbulence model. Solutions are presented for several examples of industrial importance that illustrate the potential of the method, including transonic flow about an aircraft engine nacelle, and in both rotating and nonrotating turbomachinery passages.

Semi-structured mesh generation for 3D Navier-Stokes calculations

In the current work a method which builds layers of highly stretched prismatic cells on an existing unstructured surface triangulation is described. The outer surface of this inflated triangulation provides a natural starting point for the advancing front algorithm used to fill the interior with tetrahedra. Care is taken to limit the possibility of a crossed-over mesh in concave geometrical regions. If the mesh does cross over then the offending cells are removed.

A Comparison of Advanced Numerical Techniques to Model Transient Flow in Turbomachinery Blade Rows

Computational predictions of the transient flow in multiple blade row turbomachinery configurations are considered. For cases with unequal numbers of blades/vanes in adjacent rows (“unequal pitch”) a computation over multiple passages is required to ensure that simple periodic boundary conditions can be applied. For typical geometries, a time accurate solution requires computation over a significant portion of the wheel. A number of methods are now available that address the issue of unequal pitch while significantly reducing the required computation time. Considered here are a family of related methods (“Transformation Methods”) which transform the equations, the solution or the boundary conditions in a manner that appropriately recognizes the periodicity of the flow, yet do not require solution of all or a large number of the blades in a given row. This paper will concentrate on comparing and contrasting these numerical treatments. The first method, known as “Profile Transformation”, overcomes the unequal pitch problem by simply scaling the flow profile that is communicated between neighboring blade rows, yet maintains the correct blade geometry and pitch ratio. The next method, known as the “Fourier Transformation” method applies phase shifted boundary conditions. To avoid storing the time history on the periodic boundary, a Fourier series method is used to store information at the blade passing frequency (BPF) and its harmonics. In the final method, a pitch-wise time transformation is performed that ensures that the boundary is truly periodic in the transformed space. This method is referred to as “Time Transformation”. The three methods have recently been added to a commercially-available CFD solver which is pressure based and implicit in formulation. The results are compared and contrasted on two turbine cases of engineering significance: a high pressure power turbine stage and a low pressure aircraft engine turbine stage. The relative convergence rates and solution times are examined together with the effect of non blade passing frequencies in the flow field. Transient solution times are compared with more conventional steady stage analyses, and in addition detailed flow physics such as boundary layer transition location are examined and reported.Copyright

Adaptive Unstructured 2D Navier-Stokes Solutions on Mixed Quadrilateral/Triangular Meshes

This paper presents a solution adaptive scheme for solving the Navier-Stokes equations on an unstructured mixed grid of triangles and quadrilaterals. The solution procedure uses an explicit Runge-Kutta finite volume time marching scheme with an adaptive blend of second and fourth order smoothing. The governing equations are solved in a 2D, axisymmetric or quasi-3D form.In viscous regions quadrilateral elements are used to facilitate the one dimensional refinement required for the efficient resolution of boundary layers and wakes. The effect of turbulence is incorporated through using either a Baldwin-Lomax or k-e turbulence model.Solutions are presented for several examples that illustrate the capability of the algorithm to predict viscous phenomena accurately. The examples are a transonic turbine, a nozzle and a combustor diffuser.© 1993 ASME

The Efficient Computation of Transient Flow in Turbine Blade Rows Using Transformation Methods

Computational predictions of the transient flow in turbine blade rows are considered. Adjacent blade rows typically contain unequal numbers of blades and vanes, requiring a computation over multiple passages per row to permit application of simple periodic boundary conditions. For typical geometries, use of conventional solution methods requires computation over all or a significant portion of the wheel to ensure a time accurate solution.The computational load is significantly reduced by methods which enable a one or two-passage solution to accurately model the full wheel (or part wheel, if applicable) solution. In this work, three methods are used: Profile Transformation, Fourier Transformation and Time Transformation.This paper will concentrate on the evaluation of these methods on two turbine geometries. The first test case is a frozen gust analysis for a high pressure transonic turbine; the geometry includes hub and casing cavities together with a complex tip. The second test case is a low pressure turbine stage run over a range of operating points. Comparisons between the various methods and the equivalent part wheel periodic solution are made to demonstrate the accuracy and computational efficiency of the transformation methods.Copyright

Efficient Computation of Large Pitch Ratio Transonic Flow in a Fan With Inlet Distortion

Modeling the unsteady flow of a fan subject to an inlet distortion is computationally expensive due to the need to model the full-annulus. Using the Fourier Transformation (FT) method in ANSYS CFX, which recognizes phase-shifted periodic boundary conditions, the fan inlet distortion simulation can be achieved efficiently by solving just two passages. The FT method can handle very large inlet distortion to blade passage pitch ratios such as the case of the problem simulated in this work. The analysis considers transonic flow through a fan with high bypass ratio subjected to an inlet total pressure distortion. The inlet disturbance traverses the inlet once per revolution and is intended to simulate the inlet flow distortion seen by an aircraft engine fan during take-off conditions. The pressure ratio across the fan is chosen so that the fan moves from a started to un-started condition as the disturbance moves past the inlet. This condition will provide a rigorous test of the FT method. The FT method is validated by comparing to the equivalent full-annulus unsteady solution. The FT unsteady solution compares remarkably well with the reference solution and is able to reproduce the detailed dynamics of the shock movement. Moreover, the solution from the FT method is also able to reproduce the efficiency, viscous effects and blade loading from the full-annulus case. The FT solution is obtained with a 5X reduction in CPU time and a 10X reduction in memory requirement.

Quasi-3D Solutions for Transonic, Inviscid Flows by Adapative Triangulation

This paper describes an algorithm for computing two-dimensional transonic, inviscid flows. The solution procedure uses an explicit Runge-Kutta time marching, finite volume scheme. The computational grid is an irregular triangulation. The algorithm can be applied to arbitrary two-dimensional geometries. When used for analyzing flows in blade rows, terms representing the effects of changes in streamsheet thickness and radius, and the effects of rotation, are included. The solution is begun on a coarse grid, and grid points are added adaptively during the solution process, using criteria such as pressure and velocity gradients.Advantages claimed for this approach are (a) the capability of handling arbitrary geometries (e.g., multiple, dissimilar blades), (b) the ability to resolve small-scale features (e.g., flows around leading edges, shocks) with arbitrary precision, and (c) freedom from the necessity of generating “good” grids (the algorithm generates its own grid, given an initial coarse grid).Solutions are presented for several examples that illustrate the usefulness of the algorithm.Copyright