Application of a Riemann Solver Unstructured Finite Volume Method to Combustion Instabilities

Abstract

Combustion instabilities are a common difficulty in the design of combustion systems for applications from power generation gas turbines to gas and liquid fuel rockets. Many low-order models have been developed for quick turnaround prediction of trends, while high-fidelity, large-eddy simulations are becoming a viable tool with the increasing availability of computing resources. In this paper, a three-dimensional linear thermoacoustic solver is developed to fill the void in design tools between the low-order modeling techniques and the expensive high-fidelity approach. The solver uses the finite volume method with a second-order Riemann solver flux calculation to solve the linearized Euler equations with unsteady heat release. The code is written for unstructured grids in order to easily accommodate the complex geometries of industrial combustors. Because the application requires the ability to resolve the effects of sharp gradients of mean density, a method for treating variable-coefficient hyperbolic systems is developed within the Riemann solver approach for unstructured grids. The code is tested with three verification cases with comparison to exact solution and three validation cases with comparison to experimental data. The code is shown to predict the frequencies and limit-cycle amplitudes of the validation experiments well, comparing favorably to lower-order models. In the final validation case, the code predicts the frequency and limit-cycle amplitude within 5% for a realistic gas turbine combustor design. More important, the code predicts the subsequent stability of the mode after a change in the operating conditions.