Continuous Adjoint-Based Optimization of an Internally Cooled Turbine Blade—Mathematical Development and Application

This paper presents an adjoint-based shape optimization framework and its demonstration in a conjugate heat transfer problem in a turbine blading. The gradient of the objective function is computed based on the continuous adjoint method, which also includes the adjoint to the turbulence model. Differences in the gradient resulting from making the frozen turbulence assumption are discussed. The developed software was used to optimize both the blade shape of the internally cooled linear C3X turbine blade and the position of cooling channels aiming at (a) minimum total pressure drop of the hot gas flow and (b) minimum highest temperature within the blade. A two-step optimization procedure was used. A free-form parameterization tool, based on volumetric NURBS, controls the blade airfoil contour, while the cooling channels are free to move following changes in the coordinates of their centers. Geometric and flow constraints are included in the performed optimizations, keeping the cooling channels away from the airfoil sides and retaining the turbine inlet capacity and flow turning.

Quality Key Numbers of Gas Turbine Combined Cycles

The most relevant quality key numbers for the largest and most efficient Gas Turbine Combined Cycles (GTCC) are not (only) the data published by the original engine manufacturers OEM’s. Additional numbers are here evaluated with educated guesses based on published data of the latest announcements of the “big four OEM’s” [8]. Such data are of interest for potential customers but also for nailing down the current state-of-the-art for all kind of further cycle studies using turbomachinery components and also as a contemporary history record. Making educated guesses means thermodynamic 1D simulation based on additional assumptions for pressure losses and other cycle data, which have a limited influence on the (unpublished) target quality numbers, such as: • Mixed turbine inlet temperature Tmix. This is a key value describing the technology level. It can be derived independently of the (unpublished) TCLA value. It is a quality number for the general cooling design and for the secondary air systems. • Polytropic efficiency of the compressor blading. This number describes the aerodynamic quality of the compressor blading. • Polytropic efficiency of the turbine blading. It describes the quality level of both the blading aerodynamics and of the open air cooling design. • Distribution of the exergy losses within the GT and in the bottoming cycle. The exergy losses describe the remaining opportunities for further improvements in the thermodynamic cycle design. But they also indicate its limits. However already the determination of the Tmix is tricky. It depends on the analysis method and on the fluid data applied. The polytropic efficiency of the turbine blading and the exergy losses will depend both on the used methods and on the Tmix found. Achieving a trustable result therefore requires a transparent and reproducible method. In case of application of the found results for performance prediction of similar cycles the same method has to be applied in order to avoid mistakes. In this paper real gas data with consideration of dissociation in equilibrium are used, while the polytropic efficiencies are determined with an incremental method based directly on the classic definitions of Stodola [3] and Dzung [4]. Therefore the still most used method using semi-perfect gas properties and corresponding formulas is bypassed. In order to keep it as simple as possible the evaluation is limited to base load at ISO ambient condition (15°C, 60% relative humidity, sea level). The fuel is limited to pure methane according to the practice in current catalogue data. The main focus is on the gas turbine with its components. The steam bottoming cycle is captured with its effect on the overall exergy and energy balance of the GTCC, which identifies exhaust and condensation losses.

Finding the Stiffnesses of Interface Contact Elements for the Computational Model of Steam Turbine Blading

A method is proposed for fitting the so-called contact stiffnesses (CSs) of interface elements for a nonlinear dynamic model (NDM) of a bladed disk with integral contact couplings. The method is based on comparison between frequencies of the resonant response of NDM and known natural frequencies in limiting linear cases. For this purpose, an effective approach for calculation of the resonant response NDM is presented allowing CSs to be picked individually. The method is demonstrated for the case of steam turbine bladed disk equipped with 48 inch blades.

Comparison of 2D and 3D Airfoils in Combination With Non Axisymmetric End Wall Contouring: Part 1 — Experimental Investigations

Tangential end wall contouring is intended to improve turbomachinery blading efficiency. This paper is the first of a series of two papers. It summarizes the experimental investigation of a test turbine with end wall contoured vanes and blades. Constant section airfoils as well as optimized 3D high pressure steam turbine blading in baseline and end wall contoured configurations have been examined in a 2 stage axial turbine test rig at the Institute of Power Plant Technology, Steam and Gas Turbines (IKDG) of RWTH Aachen University. The test rig is driven with air. Brush seals are implemented within the casing sided cavities to minimize the leakage flow near the tip end walls, where the contouring is also applied. The pressure and temperature data that is recorded in three axial measuring planes are plotted to visualize the change in flow structure. This has shown that the efficiency is increased for 2D airfoils by means of end wall contouring, which is caused by a homogenized inflow to the second stage. However the efficiency of the first stage suffers, the end wall contouring is beneficial for the performance of the engine. Both phenomena (an efficiency loss in stage one and an improvement of the performance in stage two) have also been measured for the optimized 3D configurations thus it can be expected that end wall contouring has also a beneficial impact on the performance of multi row turbines. The second part of this paper presents the results of numerical investigations of end-wall contoured blades. It will demonstrate how the secondary flow phenomena are influenced by end-wall contours. The simulations are validated with measured data from the test rig.

Some Unresolved Features in the Physics of Quasi Two-Dimensional Flows Over Turbine Blading

Even for the ostensibly two-dimensional flow through cascades of blades, many details of the flow physics are neither well-understood nor well-predicted. Gaps in knowledge are identified that cover entire blade and nozzle vane surfaces from leading edge to trailing edge and beyond. To give improved prediction capability these gaps require improved understanding. The goal of this work is to draw attention to five most significant internal aerodynamic phenomena that affect turbomachinery blade performance and design. By drawing together important experimental results awareness can be raised of these features in blading aerodynamics that are not yet clearly understood. The emphasis is on quasi two-dimensional flows. As well as work on blade cascades this research draws on fundamental investigations over flat plates and circular cylinders. Similar behavior was observed between tests under strong adverse pressure gradients on triggered spots, wake-disturbed flat plate boundary layers, and on turbine blading.

Successful Power Limit Increase Testing of SGT5/6-2000E Gas Turbines on the Basis of Si3D Turbine Blading

One of the most innovative solutions for making SGTx-2000E gas turbines more competitive and more cost-effective is the Si3D upgrade product. The profile of the Si3D turbine blades and vanes is aerodynamically optimized. Based on this new Si3D design optimization, a Power Limit Increase (PLI) upgrade was developed in close cooperation with customers. The Power Limit Increase upgrade is a change of the engines rating which allows operating the engine at a higher maximum electrical power output. The PLI not only shows a much higher power output of up to 16 % but also a significant increase in efficiency at low ambient temperatures — especially for district heating power plants. In 2011/2012 at a Finnish SGT5-2000E an opportunity arose to carry out an extensive program of measurements for testing and validating how the power limit can be increased in parallel with the blading upgrade (no compressor modification). The essential feature of this campaign was a non-intrusive stress measurement of blade vibration by means of optical probes. The campaign was successfully completed, and the Finnish customer is able to take advantage of optimized winter operation. The main benefit is operation of the engine at base load, especially at very low ambient temperatures with a higher power output and efficiency potential. On the basis of these encouraging results, Siemens prepared a fleet release for a power limit increase of all SGT5-2000E gas turbines with Si3D airfoils in stages 1 to 4 from 173 MW to 186 MW (with compressor mass flow increase) or even up to 196.5 MW. In addition, a second opportunity arose 2013 to execute the similar test campaign in the USA for the 60 Hz Si3D turbine blading with a compressor mass flow increase. Thereby not only the same test equipment was used, but several additional investigations had to be done prior to the test campaign. This publication describes details of the technical evaluation and conversions required to perform these tests and accomplish an increase of the power limit of the SGTx-2000E fleet.