Abstract
We quantify the sensitivity of turbine acoustic impedance to aerodynamic design parameters. Impedance boundary conditions are an influential yet uncertain parameter in predicting the thermoacoustic stability of gas turbine combustors. We extend the semi-actuator disk model to cambered blades, using non-linear time-domain computations of turbine vane and stage cascades with acoustic forcing for validation data. Discretising cambered aerofoils into multiple disks improves reflection coefficient predictions, reducing error by up to an order of magnitude compared to a flat plate assumption. A parametric study of turbine stage designs using the analytical model shows acoustic impedance is a weak function of degree of reaction and polytropic efficiency. The design parameter with the strongest influence is flow coefficient, followed by axial velocity ratio and Mach number. We provide the combustion engineer with improved tools to predict impedance boundary conditions, and suggest thermoacoustic stability is most likely to be compromised by change in turbine flow coefficient.
Highlights
Thermoacoustic instability is a coupling between unsteady heat release and acoustic waves in gas turbine combustors
Predictions of turbine acoustic impedance using a cambered semi-actuator disk model agree with two-dimensional computational fluid dynamics (CFD) simulations to within ±7% and ±16% for incident pressure and entropy waves, an improvement over simpler flat-plate models; For representative coolant flow rates, turbine cooling has a limited effect on acoustic impedance of ±3%
Increasing coolant flow rate reduces entropy–acoustic reflectivity; A parametric study of the turbine design space shows that acoustic impedance is most sensitive to flow coefficient, axial velocity ratio, Mach number, and stage loading coefficient
Summary
Thermoacoustic instability is a coupling between unsteady heat release and acoustic waves in gas turbine combustors. Prediction and mitigation of thermoacoustic instability requires acoustic impedance boundary conditions, characterising reflection of waves from the compressor and turbine back into the combustor. The state of the art for predicting the acoustic impedance of turbomachines is linear models based on the actuator disk approach of Cumpsty and Marble [2]. There is no information available on the sensitivity of acoustic impedance to turbine aerodynamic design This would be useful to a combustion engineer, allowing an assessment of possible thermoacoustic instability problems due to a turbine design change. Improvement of the accuracy of analytical models for turbine acoustic impedance; demonstration of an efficient CFD approach for predicting acoustic impedance; and quantification of the sensitivity of acoustic impedance to a complete set of aerodynamic parameters across the turbine design space
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