J. A. Rodríguez

Numerical Analysis of the Blade Forces Caused by Wake/Blade Interaction in the Last Stage of a Steam Turbine

In a steam turbine stage there is an interaction between blades and the flow field. The blades are subjected to the forces caused by the flow field, but also the flow field is affected by the blades and its movement. The nozzle wakes cause uneven pressure field downstream and produce alternating forces on blades which lead to blade vibrations. Some of the vibrations originated in this way may damage the blades and affect the turbine performance. The results of numerical computations about the forces acting on the blades as a result of the variations in the flow field in the axial clearance rotor-stator in the last stage of a 110 MW steam turbine are presented. The analysis is focused on discussing the pressure field because it is necessary for further computation of the useful life time. The flow field was resolved using computational fluids dynamics and the computed pressure field was integrated around the blades to get the forces acting on blades. These computed dynamical forces will be used in the blade useful life estimation and in the investigation to the failure causes of these blades. The Navier-Stokes equations are resolved in two and three dimensions using a commercial program based on finite-volume method. 2-D and 3-D geometry models were built to represent the dimensional aspects of the last stage of the turbine. Periodic boundary conditions were applied to both sides of a periodic segment of the 2-D and 3-D models with the purpose of reducing computational efforts. The computations were conducted in steady state and transient conditions. The results show that the force magnitude acting on blades has an harmonic pattern. Finally a Fourier analysis was used to determine the coefficients and frequency of a Fourier equation which can be used to calculate the alternating stresses on the blade in order to predict the useful life of the blades. Also, the pressure and velocity fields are shown between the diaphragm and rotor blades along the axial clearance.Copyright

Flexibility in Biopharmaceutical Manufacturing Using Particle Swarm Algorithms and Genetic Algorithms

Pharmaceutical researchers and biotechnology companies are devoted to developing medicines, such as: therapeutic proteins, human insulin , vaccines for hepatitis , food grade protein, chymosin detergent enzyme, and cryophilic protease. This allows patients to live longer, healthier, and more productive. Within this context, there is a high degree of consensus in the biomanufacturing industry that product quality, customer service, and cost efficiency are fundamental for success. Based on our knowledge there has not been an adequate flexibility strategy to manufacture different multiproduct drug substances, such as designing a plant, determining the number of units for a specific task, assigning raw materials to different production processes, and deciding the production planning. The aim of this work is to minimize the investment cost and find out the number and size of parallel equipment units in each stage of multiproduct batch plant design (MBPD). For this purpose, it is proposed to solve the problem in two different ways: the first way is by using a particle swarm algorithm (PSA) and the second way is by a genetic algorithm (GA). This paper presents the effectiveness and performance comparison of PSA and GA for optimal design of a MBPD. The experimental results (given by investment cost, number and size of equipment, computational time, and idle times within the plant) obtained by the GA are better than those found by the PSA. This methodology can help the decision makers, and constitutes a very promising framework for finding a set of good solutions.

Film cooling optimization on leading edge gas turbine blade using differential evolution

This article reports the optimization of film cooling on a leading edge of a gas turbine blade model, with showerhead configuration, it is based on five input parameters, which are hole diameter, hole pitch, column holes pitch, injection angle, and velocity at plenum inlet. This optimization increased the Area-Averaged Film Cooling Effectiveness ( η Aav ) and reduced the consumption of coolant flow. Differential Evolution assisted by artificial neural networks was used as optimization algorithm. Reynolds Averaged Navier–Stokes computations were carried out to getting the net database and to evaluate the optimized models predicted by artificial neural network. The results show an effective increment of η Aav by 36% and a mass flow reduction by 66%. These results were reached by means of a better distribution of cooling flow at blade surface as function of the input parameters. To assure the reliability of the numerical model, particle image velocimetry technique was used for its validation.

An Approach to Codification Power on the Behavior of Genetic Algorithms

Genetics Algorithms (GAs) are based on the principles of Darwins evolution which are applied to the minimization complex function successfully. Codification is a very important issue when GAs are designed to dealing with a combinatorial problem. An effective crossed binary method is developed. The GAs have the advantages of no special demand for initial values of decision variables, lower computer storage, and less CPU time for computation. Better results are obtained in comparison the results of traditional Genetic Algorithms. The effectiveness of GAs with crossed binary coding in minimizing the complex function is demonstrated.

Effect of Rotor Diameter on the Thermal Stresses of a Turbine Rotor Model

Abstract Thermal stresses in a simplified steam turbine rotor model during a cold startup are analyzed using finite element analysis (FEA). In order to validate the numerical model, an experimental array is developed in which a hollow cylinder is heated with hot air in the external surface. At the thick wall of the cylinder, temperature distribution is measured in real time, while at the same time an algorithm computes thermal stresses. Additional computational fluid dynamics (CFD) calculations are made to obtain magnitudes of velocity and pressure in order to compute convective heat transfer coefficient. The experimental results show good agreement with the FEA computations. To evaluate the effect of rotor diameter size, FEA computations with variation in external and internal diameters are performed. Results show that thermal stresses are proportional to rotor diameter size. Also, zones of higher stress concentration are found in the external and internal surfaces of the rotor.

Effect of the Modification of the Start-Up Sequence on the Thermal Stresses for a Microgas Turbine

Microgas turbines (MGT) are an alternative for small-scale energy production; however, their small size becomes a drawback since it enhances the heat transfer among their components. Moreover, heat transfer drives to temperature gradients which become higher during transient cycles like start-up. The influence of different start-up curves on temperature and thermal stresses of a microgas turbine was investigated. Stationary and rotational blades of the turbine were numerically simulated using CFD and FEM commercial codes. Conjugated heat transfer cases were solved for obtaining heat transfer from fluid toward the blades. Changes of temperature gradients within the blades during the start-ups were calculated under transient state with boundary conditions according to each curve to assess accurate thermal stresses calculations. Results showed that the modification of the start-up curves had an impact on the thermal stresses levels and on the time when highest stresses appeared on each component. Furthermore, zones highly stressed were located near the constraints of blades where thermal strains are restricted. It was also found that the curve that had a warming period at the beginning of the start-up allowed reducing the peaks of stresses making it more feasible and safer for the turbine start-up operation.

Reliability Assessment and Useful Life of Turbine Blades Using Probabilistic Methods

Steam turbines have numerous applications in various sectors of industry and it is known by experience that blade failures are the most common origin of breakdown in these machines, causing significant economic losses in turbomachinery industry. The turbines are designed to work in stable conditions of operation; nevertheless, failure in blades could appear after a short time of work. Failures are attributed to resonance of the blades to certain excitation frequencies. The vibration stresses reached by resonance conditions and the combination of other random variables could determine the useful life of the blades. In the deterministic design of turbines, the failure possibility is reduced in acceptable small levels by means of safety factors based on the good judgment. However, the possibility of failure could be reduced by using probabilistic methods. In the probabilistic approach, the variability in the properties of the material, tolerances in manufacture and uncertainties in the load are considered with statistical methods. The probabilistic method allows to evaluate the uncertainty or randomness present in some variables which translates in a high level of reliability in the results and a better operation analysis of the turbines. There are a lot of variables in the operation of the turbomachineries, in its design and construction. These variables are conceived under a certain degree of uncertainty, that is to say, these cannot be totally controlled. Generally, repeated measurements of mechanical phenomena generate a lot of input variables each one with certain instability in their magnitude that contributes to increase the probability of failure before the estimated time. In this work the reliability and useful life of blade steam turbines of 110 MW of the L-0 stage are analyzed using deterministic numerical methods and a probabilistic approach. Curves of the useful life for both cases are obtained. The probabilistic approach shows that failure occurs when a combination of variables and the presence of failure are combined.Copyright

Numerical Analysis of Crack Propagation and Life Estimation of Curtis Stage Blade of a Steam Turbine

During the operation of a turbomachine the parts most exposed to the alternative forces are the blades. The Curtis stage blades are then subjected to high alternative loads which may cause forced vibrations and these may fracture and fatigue the blades, affecting the integrity of the machine and causing its consequential shut down. In this paper the numerical analysis of crack propagation in Curtis stage blade subject to forced vibrations is presented. A finite element model of the Curtis stage blade was constructed. The natural frequencies, the steady and dynamic stresses were calculated according to life estimation. The stresses due to forced vibration were estimated using the alternative forces based in computed numerical fluid dynamics from a previous study.Copyright