A Study of the Impact of Variations on Aerodynamic Flow in Gas Turbine Engines via Monte-Carlo Simulations

The unsteady compressible inviscid flow is characterized by the conservations of mass, momentum, and energy; or simply the Euler equations. In this paper, a study of the subsonic one-dimensional Euler equations with local preconditioning is presented with a modal analysis approach. Specifically, this study investigates the behavior of airflow in a gas turbine engine using the specified conditions at the inflow and outflow boundaries of the compressor, combustion chamber, and turbine, under the impact of variations in pressure, velocity, temperature, and density at low Mach numbers. Two main questions that motivate this research are: 1) Is there any aerodynamic problem with the existing gas turbine engines that could impact aircraft performance? 2) If yes, what aspect of a gas turbine engine could be improved via design to alleviate that impact and to optimize aircraft performance. This paper presents an initial attempt to the flow behavior in terms (perturbation) using simulation outputs from a customer-deck model obtained from Pratt&Whitney, (i.e., pressure, temperature, velocity, density) about their mean states at the inflow and outflow boundaries of the compressor, combustion chamber, and turbine. Flow behavior is analyzed for the high pressure compressor and combustion chamber employing the conditions on their left and right boundaries. In the same fashion, similar analyses are carried out for the high and low-pressure turbines. In each case, the eigenfrequencies that are obtained for different boundary conditions are examined closely based on their probabilistic distributions, a result of a Monte Carlo 10,000-sample simulation. Furthermore, the characteristic waves and eave response are analyzed and contrasted among different cases, with and without preconditioners. The results reveal the existence of flow instabilities due to the combined effect of variations and excessive pressures; which are clearly the case in the combustion chamber and high-pressure turbine. Finally a discussion is presented on potential impacts of the instabilities and what can be improved via design to alleviate them for a better aircraft performance.