Liming Song

2D Viscous Aerodynamic Shape Design Optimization for Turbine Blades Based on Adjoint Method

This paper presents an adjoint optimization technique and its application to the design of a transonic turbine cascade. Capable of a quick and exact sensitivity analysis and using little computational resources, the adjoint method has been a focus of research in aerodynamic shape design optimization. The goal of this work is to extend the adjoint method into turbomachinery design applications for viscous and compressible flow, and to further improve the aerodynamic performance. In the work, the minimization of the entropy generation rate with the mass flow rate constraint was considered as the cost function of the optimization, and was applied in the direct design process. The adjoint boundary conditions of the corresponding cost function were derived in detail, using the nonslip boundary condition on the blade wall, while the flow viscous effect on the cascade inlet and outlet was neglected. Numerical techniques used in Computational Fluid Dynamics (CFD) were employed to solve the adjoint linear partial difference equations. With the solved adjoint variables, the final expression of the cost function gradient with respect to the design variables was formulated. Combined with quasi-Newton algorithm, an aerodynamic design approach based on the adjoint method for turbine blades was presented, which was independent of the Navier–Stokes solver being used. Finally, to validate the present optimization algorithm, the aerodynamic design cases of a transonic turbine blade with and without mass flow rate restriction were performed and analyzed.

Investigations on the Discharge and Total Temperature Increase Characteristics of the Labyrinth Seals With Honeycomb and Smooth Lands

The viscous work generated by the rotating components of a seal not only represents a direct loss of power but also causes an increase in the total temperature of fluid (windage effect). In order to study the discharge and total temperature increase characteristics of the stepped labyrinth seals with smooth and honeycomb lands, 3D Reynolds-averaged Navier‐Stokes solutions from CFX is used in this work. At first, the influences of the inlet preswirl, leakage flow rate, and rotational speed on the total temperature increase in the convergent and divergent stepped labyrinth seals with smooth and honeycomb lands are conducted. The obtained 3D numerical results are well in agreement with the referenced experimental data. It shows that the utilized numerical approach has sufficient precision to predict the total temperature increase in seals. Then, a range of pressure ratios and four sizes of sealing clearance are performed to investigate the effects of sealing clearances and pressure ratio impact on the discharge and total temperature increase of the stepped labyrinth seals with honeycomb and smooth liners. DOI: 10.1115/1.3068320 Nowadays, the increasing demands of performance and fuel efficiencies for the gas turbine engine lead to an increase in core flow temperature. In order to protect the turbine airfoil from thermal stress fields created by exposure to the combustion gases, more and more advanced cooling technologies are introduced by the researchers. However, achievements of enhancing cooling for the gas turbine engine will encounter the windage heating effect in seals. In the internal cooling air system, seals serve the purpose of metering the cooling air to prevent hot air ingress. The viscous work generated by the rotating components, the so-called windage heating effect, will induce an increase in the total temperature of the fluid. It degrades the cooling quality and in turn necessitates increasing the quantities of cooling flow extracted from the main gas path. Neglect of such effect will decrease the lifetime of blades working in a high temperature environment. Second, the cooling air is contaminated by the labyrinth seal leakage flow and then passes into the blades or interstage cavities for the purpose of cooling. The heat transfer characteristics in the next gas path are directly affected by the former outlet temperature and exit swirl. As a result, cooling air temperature is the most important information for a gas turbine designer or researcher to evaluate the cooling quality of the components and quantity of the cooling flow. Hence it is crucial to study the total temperature increase characteristic in the seal. There are many factors that can affect windage effect. One of these factors is the inlet preswirl. The positive preswirl will decrease the total temperature difference between seal inlet and outlet 1‐3. Another factor is the swirl development in the seal chamber. Moreover, for interstage seals, the exit swirl can change the incidence angle of the main flow into the downstream blades,

Shape Optimization of Turbine Stage Using Adaptive Range Differential Evolution and Three-Dimensional Navier-Stokes Solver

A new optimization method named as Adaptive Range Differential Evolution (ARDE) is proposed and developed for the turbine stage design. The mathematical tests are used to demonstrate the optimization performance of the present ARDE through compared with the Simple Genetic Algorithms (SGA) and the Differential Evolution (DE). Combined with the ARDE, surface modeling method and Navier-Stokes solver, a low aspect ratio transonic turbine stage is optimized, with 28 design variables in total, for the maximization of the isentropic efficiency. The optimization design of this case is performed on the cluster parallel Personal Computers. The optimal design turbine stage shows a better aerodynamic performance than that of the reference design while meeting the strength requirement. The robustness and reliability of the presented ARDE for the turbomachinery optimization design are also illustrated.Copyright

A Study on Multidisciplinary Optimization of an Axial Compressor Blade Based on Evolutionary Algorithms

An aerodynamic single disciplinary optimization and an aerodynamic/structural multidisciplinary optimization of an axial compressor blade are performed using evolutionary algorithms in this paper. The blade is optimized for maximizing its isentropic efficiency in the aerodynamic single disciplinary optimization. The isentropic efficiency of the optimum blade obtained from the aerodynamic single disciplinary optimization is 1.65% higher than that of the reference blade, however, the mechanical performance analysis indicates that it has a higher stress distribution and does not satisfy the vibration frequency constraint. In the multidisciplinary optimization, the maximum of the isentropic efficiency and the minimization of the maximum stress are selected as the design objectives. The analysis results indicate that the method of dealing with minimization of the maximum stress as a design objective is proper and that the presented multiobjective and multidisciplinary optimization method is more suitable for the optimization design of a real turbomachinery blade than the traditional heuristic aerodynamic-structural iteration.

Multiobjective Optimization Approach to Multidisciplinary Design of a Three-Dimensional Transonic Compressor Blade

An automatic multiobjective optimization approach to multidisciplinary design of turbomachinery blades is proposed in this paper. Based on this approach, an algorithm named Multiobjective Differential Evolution (MDE) is introduced as an optimizer to find the Pareto solution sets of the multidisciplinary design problem. A typical multiobjective function has been applied to demonstrate the performance of the presented multiobjective optimization algorithm. The Non-uniform B-Spline method is adopted to parameterize the turbomachinery blade profiles. The aerodynamic performance of design blade candidates is predicted by using a three–dimensional Reynolds-Averaged Navier-Stokes (RANS) solution. The blade stresses and vibration frequencies are evaluated by means of a finite element analysis coupled with the surface pressure of blades obtained from CFD calculation. To validate the optimization capability of the multiobjective optimization algorithm, the multidisciplinary design of a typical transonic compressor blade, NASA Rotor 37, is conducted. The blade is optimized for the maximization of the isentropic efficiency and the minimization of the maximum stresses with constraints on mass flow rate, total pressure ratio, and dynamic frequencies. The Pareto solutions are obtained from the multiobjective optimization. Based on the analysis of the design objectives between the Pareto designs and reference design, it is indicated that the overall performance of the optimized designs is improved. The results demonstrate that the presented multiobjective optimization algorithm has a potential in blade performance optimization and it is a promising method for the multidisciplinary design of turbomachinery blades.Copyright

Automated multi-objective and multidisciplinary design optimization of a transonic turbine stage

An automated multi-objective and multidisciplinary design optimization (MDO) of a transonic turbine stage to maximize the isentropic efficiency and minimize the maximum stress of the rotor with constraints on mass flowrate and dynamic frequencies is presented in this article. The self-adaptive multi-objective differential evolution (SMODE) algorithm is studied and developed to seek Pareto solutions of the optimization, and a new constraint-handling method based on multi-objective optimization concept is applied for constraint handling. The optimization performance of the presented SMODE is demonstrated using the typical mathematical tests. By applying SMODE as an optimizer and integrating three-dimensional (3D) blade modelling method based on non-uniform B-spline, load-fitting transfer algorithm in parameter space, 3D Navier–Stokes solution technique, and finite element analysis method as well, seven Pareto solutions are obtained. Two Pareto solutions are analysed in detail. One is the highest isentropic efficiency individual, while the other is a compromise between efficiency and mechanical stress in the blade. The aerodynamic performance and strength characteristics of the optimized turbine stage are significantly improved. The analysis results indicate that the presented multi-objective and MDO method has a potential in the optimization of blade performance and can be applied as a promising method for the optimization design of axial turbomachinery blades

Effects of the layout of film holes near the vane leading edge on the endwall cooling and phantom cooling of the vane suction side surface

ABSTRACT In the current research, effects of the layout of film holes near the first-stage vane leading edge on the endwall cooling and phantom cooling of the vane suction side surface were numerically studied. The computational results indicate that the case with a positive film-hole angle achieves a higher cooling effectiveness level on the endwall and vane suction side surface compared to the case with a corresponding negative film-hole angle. Furthermore, the location of the film hole has a significant influence on the cooling performance of the endwall and vane suction side surface. In addition, the case with a smaller distance from film holes to the vane stagnation also attains a slightly higher cooling effectiveness (phantom cooling effectiveness) on the vane suction side surface.

Non-Axisymmetric Turbine Endwall Aerodynamic Optimization Design: Part I — Turbine Cascade Design and Experimental Validations

The non-axisymmetric endwall profiling has been proven to be an effective tool to reduce the secondary flow loss in turbomachinery. In this work, the aerodynamic optimization for the non-axisymmetric endwall profile of the turbine cascade and stage was presented and the design results were validated by annular cascade experimental measurements and numerical simulations. The parametric method of the non-axisymmetric endwall profile was proposed based on the relation between the pressure field variation and the secondary flow intensity. The optimization system combines with the non-axisymmetric endwall parameterization method, global optimization method of the adaptive range differential evolution algorithm and the aerodynamic performance evaluation method using three-dimensional Reynolds-Averaged Navier-Stokes (RANS) and k–ω SST turbulent with transition model solutions. In the part I, the optimization method is used to design the optimum non-axisymmetric endwall profile of the typical high loaded turbine stator. The design objective was selected for the maximum total pressure coefficient with constrains on the mass flow rate and outlet flow angle. Only five design variables are needed for one endwall to search the optimum non-axisymmetric endwall profile. The optimized non-axisymmetric endwall profile of turbine cascade demonstrated an improvement of total pressure coefficient of 0.21% absolutely, comparing with the referenced axisymmetric endwall design case. The reliability of the numerical calculation used in the aerodynamic performance evaluation method and the optimization result were validated by the annular vane experimental measurements. The static pressure distribution at midspan was measured while the cascade flow field was measured with the five-hole probe for both the referenced axisymmetric and optimized non-axisymmetric endwall profile cascades. Both the experimental measurements and numerical simulations demonstrated that both the secondary flow losses and the profile loss of the optimized non-axisymmetric endwall profile cascade were significantly reduced by comparison of the referenced axisymmetric case. The weakening of the secondary flow of the optimized non-axisymmetric endwall profile design was also proven by the secondary flow vector results in the experiment. The detailed flow mechanism of the secondary flow losses reduction in the non-axisymmetric endwall profile cascade was analyzed by investigating the relation between the change of the pressure gradient and the variation of the secondary flow intensity.Copyright

Optimization and Knowledge Discovery of a Three-Dimensional Parameterized Vane with Nonaxisymmetric Endwall

The optimization and knowledge discovery of a low-aspect-ratio cascade was conducted. The techniques of nonaxisymmetric endwall contouring, section profiling, and compound lean were combined for ca...

Multi-Objective and Multi-Disciplinary Optimization of Gas Turbine Blade Profile and Cooling System Using Conjugate Heat Transfer Analysis

This paper presents a multi-objective and multi-disciplinary design optimization and data mining of gas turbine blade profile and cooling system by using conjugate heat transfer analysis. A 3D multi-disciplinary aerothermal optimization and data mining is proposed and developed by integrating the global optimization method of self-adaptive multi-objective differential evolution (SMODE) algorithm based on constraint-handling method, the CHT method for aerothermal performance evaluation of gas turbine blade, the 3D blade parameterization method and the self-organization map (SOM) based data mining technique. Using CHT, a numerical investigation was carried out to evaluate the aerothermal performance of C3X model, which consists of the blade passage, the blade solid domain and the internal coolant flow passages. The results calculated by the CHT method were validated by the experimental results. A new parameterization method for modeling the blade profile and cooling system has been developed. The optimization is intended to minimize the maximum blade temperature and the temperature gradient with constraints on the coolant mass flow rate, total mass flow rate and total pressure recovery coefficient of the blade. 27 Pareto solutions are obtained after the multidisciplinary design optimization for the gas turbine blade. Detailed aerothermal analysis shows that the thermal performance of the blade is significantly improved without deteriorating the related aerodynamic performance, thereby the correctness and effectiveness of our proposed optimization method are demonstrated. The SOM-based data mining on optimization design space is also applied to explore the trade-off relations between objective functions and correlations among design variables and objective function.Copyright