Jürgen F. Mayer

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

Wetness loss prediction for a low pressure steam turbine using computational fluid dynamics

Two-phase computational fluid dynamics modelling is used to investigate the magnitude of different contributions to the wet steam losses in a three-stage model low pressure steam turbine. The thermodynamic losses (due to irreversible heat transfer across a finite temperature difference) and the kinematic relaxation losses (due to the frictional drag of the drops) are evaluated directly from the computational fluid dynamics simulation using a concept based on entropy production rates. The braking losses (due to the impact of large drops on the rotor) are investigated by a separate numerical prediction. The simulations show that in the present case, the dominant effect is the thermodynamic loss that accounts for over 90% of the wetness losses and that both the thermodynamic and the kinematic relaxation losses depend on the droplet diameter. The numerical results are brought into context with the well-known Baumann correlation, and a comparison with available measurement data in the literature is given. The ability of the numerical approach to predict the main wetness losses is confirmed, which permits the use of computational fluid dynamics for further studies on wetness loss correlations.

Modelling and Validation of Wet Steam Flow in a Low Pressure Steam Turbine

Results of numerical investigations of the wet steam flow in a three stage low pressure steam turbine test rig are presented. The test rig is a scale model of a modern steam turbine design and provides flow measurements over a range of operating conditions which are used for detailed comparisons with the numerical results. For the numerical analysis a modern CFD code with user defined models for specific wet steam modelling is used. The effect of different theoretical models for nucleation and droplet growth are examined. It is shown that heterogeneous condensation is highly dependent on steam quality and, in this model turbine with high quality steam, a homogeneous theory appears to be the best choice. The homogeneous theory gives good agreement between the test rig traverse measurements and the numerical results. The differences in the droplet size distribution of the three stage turbine are shown for different loads and modelling assumptions. The different droplet growth models can influence the droplet size by a factor of two. An estimate of the influence of unsteady effects is made by means of an unsteady two-dimensional simulation. The unsteady modelling leads to a shift of nucleation into the next blade row. For the investigated three stage turbine the influence due to wake chopping on the condensation process is weak but to confirm this conclusion further investigations are needed in complete three dimensions and on turbines with more stages.Copyright

The impact of rotor labyrinth seal leakage flow on the loss generation in an axial turbine

Abstract This paper examines the impact of labyrinth seal leakage flow over the rotor shroud on the loss generation in an axial turbine stage. Numerical studies have been carried out with an in-house solver using the Baldwin-Lomax turbulence model to identify the changes in secondary flow structures. The code has been validated for this application using test data from a low-speed axial turbine stage with a simple generic rotor shroud labyrinth seal. Numerical simulations are carried out with different clearance gaps (0, 1, and 3 mm) and without cavity wells. The simulations are used to distinguish the separate interactions of the main flow with the leakage flow and the cavity flow. The leakage flow causes a strong increase in the secondary flow kinetic energy in the downstream stator. Both the leakage flow and the cavity flow lead to an increase in the secondary kinetic energy in the rotor.

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

Unsteady Numerical Study of Wet Steam Flow in a Low Pressure Steam Turbine

In steam power plants condensation already starts in the flow path of the low pressure part of the steam turbine, which leads to a complex three-dimensional two-phase flow. Wetness losses are caused due to thermodynamic and mechanical relaxation processes during condensation and droplet transport.

Three-Dimensional Optimization of Turbomachinery Bladings Using Sensitivity Analysis

This paper presents an approach to optimize the geometry of turbomachinery blades utilizing an automated optimization loop. Optimization examples of turbomachinery blade geometries with selected objective functions and a set of design variables are introduced. The presented optimization examples are performed for a 1.5-stage turbine test case. The blade geometries are fully parameterized, enabling three-dimensional changes to the blade shape during the optimization. Therefore various non-physical and physical parameters such as stacking line or stagger angle can be selected as design variables. Three-dimensional steady-state numerical flow simulations and a sensitivity equation method are part of the optimization process. The design sensitivities used within the optimization are obtained by numerically solving the analytical sensitivity equations. This optimization scheme uses the same numerical method for the flow simulation and for the computation of the sensitivity equation. A Navier-Stokes flow solver, which has especially been designed for turbomachinery applications was used for the implementation of the sensitivity equation method. The focus of this paper is on the application of the described optimization strategy to turbomachinery flows. The presented optimization examples are used to demonstrate and to discuss the capabilities of this approach.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.

Water droplet flow paths and droplet deposition in low pressure steam turbines

The complex three-dimensional two-phase flow in a low pressure steam turbine is investigated with comprehensive numerical flow simulations. In addition to the condensation process, which already takes place in the last stages of steam turbines, the numerical flow model is enhanced to consider the drag forces between the droplets and the vapour phase. The present paper shows the differences in the flow path of the phases and investigates the effect of an increasing droplet diameter. For the flow simulations a performance cluster is used because of the high effort for such multi-momentum two-phase flow calculations. In steam turbines the deposition of small water droplets on the stator blades or on parts of the casing is responsible for the formation of large coarse water droplets and these may cause additional dissipation as well as damage due to blade erosion. A method is presented that uses detailed CFD data to predict droplet deposition on turbine stator blades. This simulation method to detect regions of droplet deposition can help to improve the design of water removal devices.