Thermo-Structural Analysis of Steam Turbine in Pre-Warming Operation With Hot Air

In pursuit of flexibility improvements and extension of lifetime, a concept to pre-warm steam turbines using hot air was developed. In order to further optimize the pre-warming operation, an extensive numerical investigation is conducted to determine the time-dependent temperature and stress fields. In this work, the transient thermal and structural analyses of an IP 19-stage steam turbine in pre-warming operation with hot air are presented. Based on the previous investigations, a hybrid (HFEM - numerical FEM and analytical) approach especially developed for this purpose is applied to efficiently calculate the solid body temperatures of a steam turbine in pre-defined pre-warming scenarios. The HFEM model utilizes the Nusselt number correlations to describe the heat transfer between the hot air and the turbine components in the flow channel. These correlations were developed based on unsteady CHT-simulations of multistage turbine models. In addition, most of the thermal energy in turbine pre-warming operation is transferred through vanes and blades. Therefore, the HFEM approach considers the thermal contact resistance (TCR) on the surfaces between vanes/casing and blades/rotor. After the calibration of the HFEM model with experimental data based on measurements of the natural cooling curve, the pre-warming processes for different pre-warming scenarios are simulated. Subsequently, the obtained temperature fields are imported to an FEM model in order to conduct a structural analysis, which, among other variables, includes the values and locations of highest stresses and displacements.

Uncertainty Quantification of Leakages in a Multistage Simulation and Comparison With Experiments

This paper presents a numerical study of the impact of tip gap uncertainties in a multistage turbine. It is well known that the rotor gap can change the gas turbine efficiency, but the impact of the random variation of the clearance height has not been investigated before. In this paper, the radial seals clearance of a datum shroud geometry, representative of steam turbine industrial practice, was systematically varied and numerically tested by means of unsteady computational fluid dynamics (CFD). By using a nonintrusive uncertainty quantification (UQ) simulation based on a sparse arbitrary moment-based approach, it is possible to predict the radial distribution of uncertainty in stagnation pressure and yaw angle at the exit of the turbine blades. This work shows that the impact of gap uncertainties propagates radially from the tip toward the hub of the turbine, and the complete span is affected by a variation of the rotor tip gap. This amplification of the uncertainty is mainly due to the low-aspect ratio of the turbine, and a similar behavior is expected in high pressure (HP) turbines.

Enhancement to the Traditional Ellipse Law for More Accurate Modeling of a Turbine With a Finite Number of Stages

This paper studies the origin and applicability of the traditional Stodola ellipse law and demonstrates its deficiencies when applied in certain conditions. It extends the equation by Cooke and Traupel through the definition of a semi-ellipse law. This new law produces more accurate results as compared to the ellipse law (EL), especially for turbines with a low number of stages. It does, however, require knowledge of the choking behavior of the turbine, as well as an appropriate pressure ratio exponent. Through numerical studies and careful application of nozzle flow equations, correlations were developed to predict the critical pressure ratio of a multistage turbine, taking nozzle and blade efficiency into account. Correlations are also presented to obtain an appropriate pressure ratio exponent to use in the semi-ellipse law. A methodology is proposed through which the necessary semi-ellipse law terms can be calculated using only design base conditions and estimates of efficiencies. This was successfully validated on a steam turbine. The semi-ellipse law is believed to be the most accurate way of modeling an axial-flow multistage steam or gas turbine from design base conditions, without requiring a stage-by-stage analysis.

Comparison of Numerical Methods for the Prediction of Time-Averaged Flow Quantities in a Cooled Multistage Turbine

An unsteady simulation of a two-stage, cooled, high pressure turbine cascade is achieved by applying the harmonic balance method, a mixed time domain and frequency domain computational fluid dynamic technique for efficiently solving periodic unsteady flows. A comparison of computed temperature and pressure profile predictions generated using the harmonic balance method and a conventional steady mixing plane analysis is presented. The predicted temperature and pressure profiles are also compared to experimental data at the stage exit plane. The harmonic balance solver is able to efficiently model unsteady flows caused by wake interaction and secondary flow effects due to cooling flows. It is demonstrated that modeling the unsteady effects is critical to the accurate prediction of time-averaged flow field quantities, particularly for cooled machines.

Effect of Airfoil Clocking on Noise of LP Turbines: Part II — Modal Structure Analysis

The clocking effect on noise is investigated experimentally in a multistage turbine high speed rig. It consists in a three stages state of the art Low Pressure Turbine (LPT). The work is a continuation of a first part in which efficiency and noise are addressed together for the same test [1]. Due to the large amount of data acquired in the experiment, noise results presented in [1] are based on averaged Sound Pressure Level (SPL) at the exit. The present paper goes beyond that analysis and aims to get the modal structure and its sensitivity to clocking. Noise measurements are taken ‘in-duct’ immediately downstream the LPT by a continuously and slowly rotating device denominated Noise Measurement Module (NMM). Previous experimental studies [2] [3] demonstrate this as an effective way of characterizing the LPT noise source in an engine, provided that the necessary hot to cold conversions and propagation effects are included. The rotation of the NMM allows the identification of the spinning modes responsible of the tone noise. The axial dependence acquired by the different sensors along the duct gives the radial structure of the spinning modes. The modal decomposition allows the estimation of the acoustic energy, which is the proper magnitude for observing the clocking dependence. The data reduction process from time history signals to the acoustic power estimation is described in detail. Special attention is paid on the applicability limits and uncertainty analysis. Results from the first part [1] suggest that efficiency is weakly affected by clocking whereas noticeable influence of some tone noise is observed. The acoustic power and modal structure dependence of the same tones observed in [1] will allow the comprehension of the noise clocking mechanisms in future. Although this is out of the scope, results suggest some physical explanation described here.

The Effect of Airfoil Clocking on Efficiency and Noise of Low Pressure Turbines

The effect of airfoil clocking (stator-stator interaction) on efficiency and noise of low pressure turbines (LPT) was investigated experimentally in a multistage turbine high-speed rig. The rig consisted of three stages of a state-of-the-art LPT. The stages were characterized by a very high wall-slope angle, reverse cut-off design, very high lift, and very high aspect ratio airfoils. The rig had identical blade count for the second and third stators. The circumferential position of the second stator was individually adjusted with respect to the third stator. Eight different circumferential clocking locations over one pitch were back-to-back tested. The rig was heavily instrumented with miniature five hole probes, hot wires, hot films, total pressure and temperature rakes, pressure tappings on the airfoil surface, two array of Kulites in a rotatory module, etc. Every clocking location was tested with the same instrumentation and at the same operating conditions with the intention of determining the impact of the clocking on the overall efficiency and noise. Due to the large amount of data, the results of this test will be reported in several papers. The present paper contains the impact on the overall efficiency, radial traverses, static pressure fields on the airfoils and averaged sound pressure levels in the duct. The comparison of the results suggests that the efficiency is weakly affected by clocking; however the effect on noise is noticeable for some acoustic tones at certain operating conditions.