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

Abstract

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.

Flutter and Resonant Vibration Characteristics of Engine Blades: An IGTI Scholar Paper

“…A systematic study to calculate forced response levels in a fan and a turbine and compare results with corresponding measured data was reported by Chiang and Kielb (1992). Row defects due to wake disturbances were modelled with a "semi-empirical rotor wake/vortex model" due to Maijigi and Gliebe (1984) and "measured data for inlet distortion and a quasi-3D Euler code" due to Holmes et al (1988) to represent pressure disturbances. Several references are cited in the paper and may be studied to examine how wake data, empirical models and CFD approaches have been used by several researchers to compute forcing functions.…”

Use of Advanced CFD Codes in the Turbomachinery Design Process

“…To improve the prediction of discontinuities such as shocks and slip lines, a Q3D Euler solver EULQ3D3 was developed using adaptive grids. The first version of EULQ3D3 solves the Euler equations on structured grids (Berger and Oliger, 1984;Bonomi, 1987;Fritts, 1988), the second version uses unstructured triangle grids (Holmes et al, 1983;Holmes, 1989).…”

“…To avoid the disadvantages noted above, a new version of the Euler code EULQ3D3 was written, which uses unstructured adaptive grids with triangles (Holmes et al, 1983;Holmes, 1989). With such grids high-gradient flow regions can be refined by introducing additional grid cells without affecting the other flow regions.…”

The Simulation of Three-Dimensional Viscous Flow in Turbomachinery Geometries Using a Solution-Adaptive Unstructured Mesh Methodology

“…In three dimensions, published work to date has been restricted to inviscid flows around external aerodynamic configurations (see Bristeau et al (1985), Jameson et al (1987) and Peraire et al (1988) for good examples) and has demonstrated a very impressive degree of flexibility. Application to turbmachinery flows has lagged behind and so far has been limited to two dimensions (see Holmes et al (1988) for inviscid flow and Siden et al (1989) and Hwang et al (1990) for viscous flow).…”