Sensitivity Analysis and Uncertainty Quantification for Rim Seal Ingestion With 1-D Network Models

Accurate prediction of turbine rim seal ingestion remains a challenge, even sophisticated unsteady computational models have had limited success due to the complexity and uncertainties present in this type of problems. For this reason, it is of interest to perform stochastic analysis taking into account the variability in the input parameters as well as uncertainties and assumptions associated with a given model of choice.  In the present work several statistical methods are applied to a 1D gas network model in order to evaluate the impact of the tolerances of the main geometrical parameters in the model with respect to uncertain operating conditions. This study focus on a Secondary Air System (SAS) of a gas turbine, considering a generic cavity in a high pressure turbine (HPT) in which hot gas ingestion occurs.

The network model was built using a proprieatery software, it includes the main annulus flow, a damping cavity and a wheel space cavity in which a coolant flow is added to prevent ingestion. The system is represented as a network of "nodes" and "bits" connected by "links". Mass flow rates are calculated taking into account the boundary conditions and the pressure drops stated by the "bits", solutions are obtained using a Newton-Rhapson iterative algorithm that solves the system of equations defined by mass and energy conservation laws and the flow link characteristics.

The temperature in the wheel-space cavity is used as a quantity of interest (QoI) for all the methods, serving as an indicator of when ingestion is present. An initial sensitivity analysis is performed using both the "Morris" method and Sobol indices to analyse the main drivers of the system's behaviour and variable dependency. This is complemented by the application of second order Sobol indices to analyse the variance caused by each variable and its interactions. Results show, that for some parameters, their interactions are the dominant cause of the ingestion variability observed.

Monte Carlo simulations are performed to propagate the variability forward, preserving any correlations present in the model. Histograms and the main statistical moments are obtained to quantify the effect of the variability in input parameters. The data obtained is also segregated in terms of ingestion present or absent, to identify trends and corroborate information obtained by sensitivity analysis.

Results obtained indicate that the main geometrical parameter in terms of ingestion is the minimum gap for the wheel-space cavity, followed by the minimum gap of the damping cavity. Those parameters have the most influential effect in the variance of the model output. In terms of design this implies that reducing the manufacturing tolerance for those gaps would greatly reduce the uncertainty in the solution obtained.

The final paper will include the theoretical details of the sensitivity analysis and uncertainty quantification methods employed, along with numerical solutions obtained with the model. Previous studies focusing on parametric studies and uncertainty quantification for 1D models will also be discussed. The results of this work will provide insights regarding the critical geometrical parameters driving ingestion subject uncertainties and assess potential trade-offs that result in minimizing ingestion and uncertainty.