MULTI-OBJECTIVE OPTIMIZATION DESIGN FOR TRANSONIC TURBINE CASCADES USING SIMULATED ANNEALING ALGORITHM

On the basis of computational of transonic viscid flow, the simulated annealing algorithm, used in statistical mechanics to study solid cooling process, is adaptedfor soving multi-objective cascades design problem. The simulated annealing algorithmdraws an analogy between the energy minimization in physical system and the objectivefunction in the real design problem, To model the multi-objective functions, a minimumdeviation method is used. In this paper, the loss and work are considered as the objectivefunctions. Simulated results indicate that this algorithm can be effectively applied to theimprovement of the design for transonic turbine cascades.

NEW MULTIOBJECTIVE SIMULATED ANNEALING ALGORITHM AND ITS APPLICATION TO TURBINE CASCADES’ DESIGN

A new kind of multiobjective simulated annealing algorithm is proposed,in which the concept of non dominated character is introduced and a new multiobjective acceptance criterion is set up.The optimization example of a typical mathematical problem with two minimum objective functions indicates that all of the solutions contract to the set of the non dominated points,and the variation trend of the optimal solutions is verified to be identical with that obtained using Genetic Algor thms.The new developed algorithm is then applied to the multiobjective optimization design of turbine cascades,in which it is coupled with the aerodynamics computation of the cascade flow fields and performance and the calculated loss coefficient and work potential of the cascade are considered as the objective functions,thus setting up a technique to the engineering optimization design for the cascades.The optimization results,by the view of a group of optimal solutions,show that the algorithm is superior to the traditional technique of multiobjective optimization design and can be applied to more than two objective optimization cascade design problem or other engineering multiobjective optimization designs.

TOPOLOGY AND VORTEX STRUCTURES OF A CURVING TURBINE CASCADE WITH TIP CLEARANCE (Ⅱ)- TOPOLOGICAL FLOW PATTERN AND VORTEX STRUCTURE IN THE TRANSVERSE SECTION OF A BLADE CASCADE

By means of ink trace visualization of the flows in conventional straight, positively curved and negatively curved cascades with tip clearance, and measurement of the aerodynamic parameters in transverse section, and by appling topology theory, the topological structures and vortex structure in the transverse section of a blade cascade were analyzed. Compared with conventional straight cascade, blade positive curving eliminates the separation line of the upper passage vortex, and leads the secondary vortex to change from close separation to open separation, while blade negative curving effects merely the positions of singular points and the intensities and scales of vortex.

TOPOLOGY AND VORTEX STRUCTURES OF A CURVING TURBINE CASCADE WITH TIP CLEARANCE (Ⅰ)- EXPERIMENTAL MODEL AND TOPOLOGICAL FLOW PATTERNS ON BOTH ENDWALLS AND BLADE SURFACES

By means of ink trace visualization of the flows in conventional straight, positively curved and negatively curved cascades with tip clearance, and measurement of the aerodynamic parameters in the transverse section, and by appling topology theory, the structures on both endwalls and blade surfaces were analyzed. Compared with conventional straight cascade, blade positive curving eliminates the separation line of the upper passage vortex and leads the secondary vortex to change from close separation to open separation, while blade negative curving effects merely the positions of singular points and the intensities and scales of vortex.

Near-Wall Flow in the Blade Cascades Representing Last Rotor Root Sections of Large Output Steam Turbines

This paper investigates the flow past two variants of root section profile cascades for a last stage rotor considering three-dimensional flow structures in the near-wall region.Analyses were drawn based on RANS numerical simulations of both variants and on the experimental data obtained by the 3 D traversing in the exit flow field of one of the variants.Extent of 3 D structures at two different regimes and its influence on aerodynamic characteristics of the blade cascades was assessed.The distributions of Mach number along the profiles were compared with 2 D optical measurements and its distortion due to the presence of the sidewall was explored.The interaction between main vortical structures was described and its influence on the loading of the blades,mechanical energy losses and exit flow angle was discussed.The results showed that for a front loaded blade the vortical structures appeared earlier and at a larger extent than for an aft loaded variant.However,due to different Mach number distribution,contribution of end wall flow to the energy losses was lower in the case of the aft loaded variant.The influence of the near wall flow on the loading was found to be rather weak while the deviation of the exit flow angle appeared to be comparable for both of the variants.

Modal Analysis and Vortex Trajectory Description for Tip Leakage Flow of a Transonic Turbine Cascade

Tip leakage vortex(TLV),which develops from the clearance between the turbine blade and casing,has been studied for decades.Nevertheless,some associated phenomena,such as its unsteady behaviors,are still not well understood.In the present work,an unsteady simulation of a transonic turbine cascade was conducted by using a validated unsteady Reynolds averaged Navier-Stokes(URANS)technique with the k-ωshear stress transport(SST)turbulence model.Typical three-dimensional vortical topology in the tip region of this transonic turbine blade was depicted based on the vortex and shock wave identification.Afterwards,quantitative descriptions of TLV transient parameters,including core position,radius,intensity,wandering motion amplitude and their statistical analysis were also provided via an ellipse fitting method.Combined with the turbulent parameters in the tip region,it is recognized that the breakdown of TLV does not occur upstream of the trailing edge,and the TLV wandering,especially the spanwise motion is a dominant unsteady feature as migrating downstream.To mathematically extract underlying flow features of tip leakage flow(TLF),two data-driven modal analysis techniques,namely proper orthogonal decomposition(POD)and dynamic mode decomposition(DMD),are presented to complement one another to reveal underlying flow feature.Observation of modes distribution allowed qualitative identification of shockwaves,vortical cluster and corresponding transient interaction.Results of POD show that the dominant unsteady structures in the tip region exhibit various morphology with moving downstream.In the front part near the leading edge,the oscillation of separation bubble and bifurcation of passage vortex paly a dominant role;while in the middle part of the tip region,the corresponding factors are the wandering of TLV and unsteady interaction between shock waves and TLF/TLV.In the vicinity of the trailing edge,the instability induced by the mixing of large-scale vortices serves as the main factor in the context of flow unsteadiness.Both the POD and DMD methods can decompose the dominant frequency of TLV evolution and its harmonic frequencies;however,the DMD method presents a superiority in segregating the high-frequency components and their corresponding unsteady structures.

Optimization of operating conditions in the steam turbine blade cascade using the black-box method

Water droplets cause corrosion and erosion,condensation loss,and thermal efficiency reduction in low-pressure steam turbines.In this study,multi-objective optimization was carried out using the black-box method through the automatic linking of a genetic algorithm(GA)and a computational fluid dynamics(CFD)code to find the optimal values of two design variables(inlet stagnation temperature and cascade pressure ratio)to reduce wetness in the last stages of turbines.The wet steam flow numerical model was used to calculate the optimization parameters,including wetness fraction rate,mean droplet radius,erosion rate,condensation loss rate,kinetic energy rate,and mass flow rate.Examining the validation results showed a good agreement between the experimental data and the numerical outcomes.According to the optimization results,the inlet stagnation temperature and the cascade pressure ratio were proposed to be 388.67(K)and 0.55(-),respectively.In particular,the suggested optimaltemperature and pressure ratio improved the liquid mass fraction and mean droplet radius by about 32%and 29%,respectively.Also,in the identified optimal operating state,the ratios of erosion,condensation loss,and kinetic energy fell by 76%,32.7%,and 15.85%,respectively,while the mass flow rate ratio rose by 0.68%.

Experimental Investigation of Aerodynamic Performance due to Blade Tip Clearance in a Gas Turbine Rotor Cascade

This study examines how the complex flow structure within a gas turbine rotor affects aerodynamic loss. An unshrouded linear turbine cascade was built, and velocity and pressure fields were measured using a 5-hole probe. In order to elucidate the effect of tip clearance, the overall aerodynamic loss was evaluated by varying the tip clearance and examining the total pressure field for each case. The tip clearance was varied from 0% to 4.2% of blade span and the chord length based Reynolds number was fixed at 2×10^(5). For the case without tip clearance, a wake downstream of the blade trailing edge is observed, along with hub and tip passage vortices. These flow structures result in profile loss at the center of the blade span, and passage vortex related losses towards the hub and tip. As the tip clearance increases, a tip leakage vortex is formed, and it becomes stronger and eventually alters the tip passage vortex. Because of the interference of the secondary tip leakage flow with the main flow, the streamwise velocity decreases while the total pressure loss increases significantly by tenfold in the last 30% blade span region towards the tip for the 4.2% tip clearance case. It was additionally observed that the overall aerodynamic loss increases linearly with tip clearance.

Aerodynamic Comparison between Increasing Cascade Pitch and Turning Angle in the Highly-Loaded Design

Theoretical and numerical study was carried out based on a linear turbine cascade(the Basic cascade)to compare the influences of the increased cascade pitch and turning angle in this paper.On one hand,the two highly-loaded designs both reduced the stability of flow field through enhancing adverse pressure gradient and span-wise pressure gradient of the fluid near suction surface.Therefore,the two highly-loaded designs would both result in thicker boundary layer and stronger secondary flow,so the secondary loss would be increased and more difficult to suppress in the highly-loaded cascades.On the other hand,the two highly-loaded designs showed different influences on the pitch-wise migration of the fluid near the endwall(cross flow)because of the different load enhancing mechanisms.In other words,the increased cascade pitch(TCx highly-loaded design)would delay the pitch-wise migration of the horseshoe vortex because of the increased channel width,while the increased turning angle(Turn highly-loaded design)would do the opposite because of the increased pitch-wise pressure gradient.As a result,the enhancement of the interaction between the fluid near the suction surface and the cross flow would be much stronger in the Turn highly-loaded design than the TCx highly-loaded design,and the span-wise developing tendencies of vortexes and fluid near the suction surface would show much stronger enhancing tendency in the former than the latter.

Study on the Numerical Model of Transonic Wind Tunnel Test Section

The authors consider numerical simulations of transonic flows through various turbine cascades in a confined channel which approximates boundaries of real wind tunnel.The boundaries of the wind tunnel are impermeable or there can be permeable tailboards to diminish shock wave reflections.The mathematical model is based on Favre-averaged Navier-Stokes equations closed by a turbulence model and model of transition to turbulence.The mathematical model is solved by an implicit finite volume method with multi-block grids.Several types of turbine blade cascades with subsonic or supersonic inlet are presented.The results are compared with optical measurements and simulations of periodic cascades.The validity of experimental reference flow parameters in relation to computed flow patterns is discussed.