Ivan McBean

Three-Dimensional Aerodynamic Design Optimization of a Turbine Blade by Using an Adjoint Method

This paper presents the application of an adjoint method to the aerodynamic design optimization of a turbine blade. With the adjoint method, the complete gradient information needed for optimization can be obtained by solving the governing flow equations and their corresponding adjoint equations only once, regardless of the number of design parameters. The formulations including imposition of appropriate boundary conditions for the adjoint equations of the Euler equations for turbomachinery problems are presented. Two design cases are demonstrated for a turbine cascade that involves a high tip flare, characteristic of steam turbine blading in low pressure turbines. The results demonstrate that the design optimization method is effective and the redesigned blade yielded weaker shock and compression waves in the supersonic region of the flow while satisfying the specified constraint. The relative effects of changing blade profile stagger, modifying the blade profile shape, and changing both stagger and profile shape at the same time are examined and compared. Navier-Stokes calculations are performed to confirm the performance at both the design and off-design conditions of the designed blade profile by the Euler method.

Turbine Blade Row Optimization Through Endwall Contouring by an Adjoint Method

This paper presents the application of a viscous continuous adjoint method for the optimization of a low-aspect-ratio turbine blade row through endwall contouring. A generalized wall-function method is implemented in a Navier–Stokes flow solver with Menter’s shear-stress transport k-ω turbulence model to simulate the secondary flow with reduced requirements on grid density. Entropy production through the blade row combined with a flow turning constraint is used as the objective function in the optimization. With the viscous adjoint method, at each design cycle, the complete gradient information needed for optimization can be obtained by solving the flow governing equations and their corresponding adjoint equations only once for each cost function, regardless of the number of design parameters. Flow loss through the blade row is minimized while maintaining the same mass-averaged flow turning at the design condition. The performance of the optimized blade at off-design conditions is also evaluated and compa...

The Development of Long Last Stage Steam Turbine Blades

In steam turbine power plants, the appropriate design of the last stage blades is critical in determining the plant efficiency and reliability and competitiveness. A high level of technical expertise combined with many years of operating experience are required for the improvement of last stage designs that increases performance, without sacrificing mechanical reliability. This paper focuses on three main development areas that are key for the development of last stage blades, namely the aerodynamic design, the mechanical design and the validation process. The three different lengths of last stage blade (LSB) were developed of 41in, 45in and 49in (and a number of scaled variants). The aerodynamic design process involves 3D CFD and flow path analysis, considerations such as last stage blade flutter and water droplet erosion, and last stage guide design. The mechanical design includes finite element stress and dynamic analysis, appropriate selection of the blade material, the coupling of the LSB with the rotor and the design of the LSB snubber and shroud. Experimental measurements form a key part of the product validation, from both the mechanical reliability and performance points of view.Copyright

Secondary Flow Reduction by Blade Redesign and Endwall Contouring Using an Adjoint Optimization Method

For low-aspect-ratio turbine blades secondary loss reduction is important for improving performance. This paper presents the application of a viscous adjoint method to reduce secondary loss of a linear cascade. A scalable wall function is implemented in an existing Navier-Stokes flow solver to simulate the secondary flow with reduced requirements on grid density. The simulation result is in good agreement with the experimental data. Entropy production through a blade row is used as the objective function in the optimization of blade redesign and endwall contouring. With the adjoint method, the complete gradient information needed for optimization can be obtained by solving the governing flow equations and their corresponding adjoint equations only once, regardless of the number of design parameters. Three design cases are performed with a low-aspect-ratio steam turbine blade tested by Perdichizzi and Dossena. The results demonstrate that it is feasible to reduce flow loss through the redesign of the blade while maintaining the same mass-averaged turning angle. The effects on the profile loss and secondary loss due to the geometry modification of stagger angle, blade shape and endwall profile are presented and analyzed.Copyright

Numerical and Experimental Investigation of the Aerodynamic Excitation of a Model Low-Pressure Steam Turbine Stage Operating Under Low Volume Flow

The diversification of power generation methods within existing power networks has increased the requirement for operational flexibility of plants employing steam turbines. This has led to the situation where steam turbines may operate at very low volume flow conditions for extended periods of time. Under operating conditions where the volume flow through the last stage moving blades (LSMBs) of a low-pressure (LP) steam turbine falls below a certain limit, energy is returned to the working fluid rather than being extracted. This so-called “ventilation” phenomenon produces nonsynchronous aerodynamic excitation, which has the potential to lead to high dynamic blade loading. The aerodynamic excitation is often the result of a rotating phenomenon, with similarities to a rotating stall, which is well known in compressors. Detailed unsteady pressure measurements have been performed in a single stage model steam turbine operated with air under ventilation conditions. The analysis revealed that the rotating excitation mechanism observed in operating steam turbines is reproduced in the model turbine. A 3D computational fluid dynamics (CFD) method has been applied to simulate the unsteady flow in the air model turbine. The numerical model consists of the single stage modeled as a full annulus, along with the axial-radial diffuser. An unsteady CFD analysis has been performed with sufficient rotor revolutions to obtain globally periodic flow. The simulation reproduces the main characteristics of the phenomenon observed in the tests. The detailed insight into the dynamic flow field reveals information on the nature of the excitation mechanism. The calculations further indicate that the LSMB tip clearance flow has little or no effect on the characteristics of the mechanism for the case studied.

OPTIMIZATION OF ENDWALL CONTOURS OF A TURBINE BLADE ROW USING AN ADJOINT METHOD

This paper presents the application of a viscous adjoint method in the optimization of a low-aspect-ratio turbine blade through spanwise restaggering and endwall contouring. A generalized wall-function method is implemented in a Navier-Stokes flow solver coupled with Menter’s SST k-ω turbulence model to simulate secondary flow with reduced requirements on grid density. Entropy production through the blade row combined with a flow turning constraint is used as the objective function in the optimization. With the viscous adjoint method, the complete gradient information needed for optimization can be obtained by solving the governing flow equations and their corresponding adjoint equations only once, regardless of the number of design parameters. The endwall profiles are contoured alone in the first design case, while it is combined with spanwise restaggering in the second design case. The results demonstrate that it is feasible to reduce flow loss through the blade redesign while maintaining the same mass-averaged flow turning by using the viscous adjoint optimization method. The performance of the redesigned blade is calculated and compared at off-design conditions.

Unsteady Aerodynamics of Low-Pressure Steam Turbines Operating Under Low Volume Flow

Nonsynchronous excitation under low volume operation is a major risk to the mechanical integrity of last stage moving blades (LSMBs) in low-pressure (LP) steam turbines. These vibrations are often induced by a rotating aerodynamic instability similar to rotating stall in compressors. Currently extensive validation of new blade designs is required to clarify whether they are subjected to the risk of not admissible blade vibration. Such tests are usually performed at the end of a blade development project. If resonance occurs a costly redesign is required, which may also lead to a reduction of performance. It is therefore of great interest to be able to predict correctly the unsteady flow phenomena and their effects. Detailed unsteady pressure measurements have been performed in a single stage model steam turbine operated with air under ventilation conditions. 3D computational fluid dynamics (CFD) has been applied to simulate the unsteady flow in the air model turbine. It has been shown that the simulation reproduces well the characteristics of the phenomena observed in the tests. This methodology has been transferred to more realistic steam turbine multistage environment. The numerical results have been validated with measurement data from a multistage model LP steam turbine operated with steam. Measurement and numerical simulation show agreement with respect to the global flow field, the number of stall cells and the intensity of the rotating excitation mechanism. Furthermore, the air model turbine and model steam turbine numerical and measurement results are compared. It is demonstrated that the air model turbine is a suitable vehicle to investigate the unsteady effects found in a steam turbine.

Turbulent Scale Resolving Modelling of Rotating Stall in Low-Pressure Steam Turbines Operated Under Low Volume Flow Conditions

Non-synchronous excitation under low volume operation is a major risk to the mechanical integrity of last stage moving blades (LSMBs) in low-pressure (LP) steam turbines. These vibrations are often induced by a rotating aerodynamic instability similar to rotating stall in compressors. Unsteady computational fluid dynamics (CFD) has been applied to simulate the rotating stall phenomenon in two model turbines. It is shown that the investigated flow field presents a challenge to conventional Reynolds-averaged Navier–Stokes equations simulations. The modelling has been enhanced by applying scale-resolving turbulence modelling, which can simulate large-scale turbulent fluctuations. With this type of simulation a qualitative and quantitative agreement between CFD and measurement for the unsteady and time averaged flow field has been achieved. The results of the numerical investigation allow for a detailed insight into the dynamic flow field and reveal information on the nature of the excitation mechanism. It is concluded that the CFD approach developed can be used to assess LSMB blade designs prior to model turbine tests to check whether they are subjected to vibration under LVF