Heinz Stetter

SIMULATION OF 3D-UNSTEADY STATOR/ROTOR INTERACTION IN TURBOMACHINERY STAGES OF ARBITRARY PITCH RATIO

This paper presents a computational method for the calculation of unsteady three-dimensional viscous flow in turbo-machinery stages. The method is based on a Finite-Volume Navier-Stokes solver for structured grids in a multiblock topology. The meshes at the stator/rotor interface are overlapped by two grid cells. An implicit residual smoothing method applicable to global time-stepping is used to accelerate the solution process.The problem of periodic boundary treatment for unequal pitches is handled using a method of time-inclined computational domains for three dimensions. The method applies a time transformation to the stator domain and to the rotor domain and uses different time-steps in the two domains.The results of a numerical simulation of the flow in a transonic turbine stage with a pitch ratio of 1.364 are presented. The time-averaged solution is compared to experimental data and satisfactory agreement is stated. Complex 3D-unsteady flow phenomena (shock motion, vortex shedding) are observed. Unsteady blade pressure fluctuations at various positions in spanwise direction are shown and the fluctuations are found to vary considerably along span. Instantaneous distributions of static pressure, Mach number, and entropy are presented.Copyright

EXPERIMENTAL AND COMPUTATIONAL STUDY OF THE UNSTEADY FLOW IN A 1.5 STAGE AXIAL TURBINE WITH EMPHASIS ON THE SECONDARY FLOW IN THE SECOND STATOR

A study of the unsteady flow in an axial flow turbine stage with a second stator blade row is presented. The low aspect ratio blades give way to a highly three-dimensional flow which is dominated by sec- ondary flow structures. Detailed steady and unsteady measurements throughout the machine and unsteady flow simulations which include all blade rows have been carried out. The presented results focus on the second stator flow. Secondary flow structures and their origins are identified and tracked on their way through the passage. The results of the time-dependent secondary velocity vectors as well as flow angles and Mach number distributions as perturbation from the time-mean flow field are shown in cross-flow sections and azimuthal cuts through- out the domain of the second stator. At each location the experimental and numerical results are compared and discussed. A good overall agreement in the time-dependent flow behaviour as well as in the sec- ondary flow structures is stated. NOMENCLATURE c absolute velocity w relative velocity

Development of a Three-Dimensional Geometry Optimization Method for Turbomachinery Applications

This article describes the development of a method for optimization of the geometry of three-dimensional turbine blades within a stage configuration. The method is based on flow simulations and gradient-based optimization techniques. This approach uses the fully parameterized blade geometry as variables for the optimization problem. Physical parameters such as stagger angle, stacking line, and chord length are part of the model. Constraints guarantee the requirements for cooling, casting, and machining of the blades. The fluid physics of the turbomachine and hence the objective function of the optimization problem are calculated by means of a three-dimensional Navier-Stokes solver especially designed for turbomachinery applications. The gradients required for the optimization algorithm are computed by numerically solving the sensitivity equations. Therefore, the explicitly differentiated Navier-Stokes equations are incorporated into the numerical method of the flow solver, enabling the computation of the sensitivity equations with the same numerical scheme as used for the flow field solution. This article introduces the components of the fully automated optimization loop and their interactions. Furthermore, the sensitivity equation method is discussed and several aspects of the implementation into a flow solver are

Experimental Investigation of Shock-Induced Blade Oscillation at an Elastically Suspended Turbine Cascade in Transonic Flow

Experimental investigations on shock-induced flutter in a linear transonic turbine cascade are presented. To examine the relation between trailing edge shock oscillations on adjacent blades in transonic flow and observed turbine blade vibrations, an elastic suspension system has been developed so that only aerodynamic coupling occurs in the system.The experimental investigations have been performed on a linear test rig with superheated steam as working fluid. The test facility enables Mach and Reynolds numbers to be varied independently.The investigated cascade consists of seven blades which are taken from the tip section of a transonic low pressure steam turbine blade. Each blade is attached by an elastic spring system which allows the respective blade to vibrate in a mode equal to the real blade’s first bending mode. By varying the individual spring stiffness it is possible to either get a tuned or mistuned cascade.The examinations mainly deal with the oscillatory behavior of the blades with respect to a variation in the isentropic outlet Mach number. In addition, the complex shock-boundary-layer interaction on the blades’ suction sides is described.An important result is that the maximum blade oscillation amplitude can be related to a specific outlet Mach number. At this Mach number all seven blades are vibrating with exactly the same frequency. This phenomenon is observed at both the tuned and the mistuned cascades.Spectrum analysis shows that one of the major shock oscillation frequencies corresponds to the flutter frequency.In addition to this frequency the spectrum analysis of the blade oscillation shows the dominant frequencies of the shock oscillation which are not natural blade frequencies.The experimental results show that oscillating shocks in a linear cascade give high potential for aeroelastic excitation of transonic blades under certain flow conditions. Blade oscillations and shock characteristics are discussed in detail.Copyright

Unsteady Flow Simulation in an Axial Flow Turbine Using a Parallel Implicit Navier-Stokes Method

The unsteady flow in an axial flow turbine stage with a second stator blade row is investigated by means of a Navier-Stokes code especially developed for turbomachinery applications. Due to the low aspect ratio of the blades of the test machine a highly three-dimensional flow dominated by secondary flow structures is observed. Simulations that include all blade rows are carried out. The present investigation focuses on the stator/rotor/stator interaction effects. Secondary flow structures and their origins are identified and tracked on their way through the passage. The time-dependent secondary velocity vectors and total pressure distributions as well as flow angles and Mach number distributions as perturbation from the time-mean flow field are shown in cross-flow sections and azimuthal cuts throughout the turbine. Simulations and measurements show a good overall agreement in the time-dependent flow behaviour as well as in the secondary flow structures.

Unsteady Flow Simulations for Turbomachinery Applications on Dynamic Grids

Preliminary results for the simulation of viscous unsteady transonic flow over oscillating blades in a linear cascade are presented. The experimental setup to be investigated essentially consists of a tip section of a rotor blade of the last stage of a steam turbine that is elastically suspended by cantilevers to allow for oscillations characterized by the first bending mode of the real 3D turbine blade. Time series show Mach number contours for the flow that has been calculated between two blades vibrating with the interblade phase angles 0° and 180°. So far only 2D computations have been performed to further explore and enhance the run-time behaviour of the flow solver ITSM3D on the NEC SX-4 and SX-5 platforms.

Computational Study of the Flow in an Axial Turbine with Emphasis on the Interaction of Labyrinth Seal Leakage Flow and Main Flow

This paper presents a numerical study of the flow in a 1.5 stage lowspeed axial turbine with a straight labyrinth seal on the rotor blade and focuses on the interaction of the leakage flow with the main flow. The influence of the leakage flow on the flow field of the turbine is examined using the Navier-Stokes code ITSM3D. The impact of the re-entering leakage flow on the main flow in dependency of the leakage mass flow rate is studied at two different clearance heights of the labyrinth in the simulations. As demonstrated in this paper, leakage flow not only introduces mixing losses but can also dominate the secondary flow and induce severe losses. In agreement with the experimental data the computational results show that even at realistic clearance heights the leakage flow gives rise to negative incidence over a considerable part of the downstream stator which causes the flow to separate.

Transonic Probe Blockage Effects in a Calibration Wind–Tunnel and Stator Blade Passage

Probe blockage effects are presented for transonic flow through a calibration wind–tunnel as well as through a guide vane row in a three–stage model turbine.Accurate experimental data from measurements in a transonic turbine are needed for the verification of CFD results. The accuracy of etatic pressure measurements in transonic turbine stages is severely affected by the pressure probe stem disturbing the surrounding flow–field. These disturbance effects are present during calibration procedures in wind–tunnels, as well as during measurements in–between turbomachinery blade rows. Therefore, the phenomenon associated with this blockage effect must be investigated for both procedures.The influence of the blockage ratios on the static pressure readings of the four–hole wedge probe during the calibration procedure is investigated for two different wind–tunnels. The aim is to measure the blockage effects on the blade passage flow which are produced by a pneumatic pressure probe immersed in the flow between two adjacent blade rows. In order to measure these effects, two stator blades are instrumented with static pressure taps along the blade chord, as well as along the blade span. During the investigations, the radial and circumferential positions of the probes relative to the blade channel are varied. Pressure probe readings of two four–hole wedge probes with different stem diameters are compared as well as correlated to the static pressure readings of the stator blade pressure taps. The apparent deviations of the different readings are discussed.Copyright

Aerodynamic Excitation of Transonic Turbine Cascade; Description of the Experimental Method

This paper presents the design of a cascade and the experimental method to investigate shock inducted flutter. To examine the interaction between a shock wave and blade oscillation at transonic flow, a cascade with 7 blades, each of them separately elastically mounted, has been developed so that only an aerodynamic coupling can occur in the system. The experimental investigations have been performed at a two-dimensional test rig with superheated steam as working fluid.

Effects of the Rotor Tip Leakage in a Transonic Turbine With Long Blades

A study of the flow in a transonic turbine stage with long and strongly twisted rotor blades is presented. The focus is on the flow in the near tip region of the blade-to-blade passage of the rotor. The flow has been modelled experimentally in a transonic wind tunnel and numerically by means of 2D and 3D Navier-Stokes equation solvers.The profiles of the rotor cascades are characterized by law turning angles and a high-velocity exit flow. Detailed flow measurements have been carried out and analysed. A comparison has been made between the experimental and numerical results, and is discussed in detail.The design and test data of the flow through the upper sections of the span are presented. The effects of the tip leakage flow are evaluated and the three-dimensional patterns of the main flow are estimated. Other points of interest are the results of 3D Navier-Stokes analysis of the stage flow as compared to 2D simulations and wind tunnel experiments, together with the question of the limitations of the individual methods as they all use approximations to the actual flow in the turbine stage.Copyright