ANISOTROPIC MULTISTAGE FINITE ELEMENT METHOD FOR TWO DIMENSIONAL VISCOUS TRANSONIC FLOW IN TURBOMACHINERY

A new method based on the anisotropic tensor force finite element and Taylor-Galerkin finite element is presented in the present paper.Its application to two-dimensional viscous transonic flow in turbomachinery improves the conver- gence rate and stability of calculation,and the results obtained agree well with the experimental measurements.

Numerical Simulation on Ice Shedding Phenomena in Turbomachinery

In the jet engine, icing phenomena occur primarily on the fan blades, the FEGVs （fan exit guide vanes）, the splitter, and the low-pressure compressor. Accreted ice disturbs the inlet flow and causes large energy losses. In addition, ice accreted on a fan rotor can be shed from the blade surface due to centrifugal force and can damage compressor components. This phenomenon, which is typical in turbomachinery, is referred to as ice shedding. Although existing icing models can simulate ice growth, these models do not have the capability to reproduce ice shedding. In the present study, we develop an icing model that takes into account both ice growth and ice shedding. Furthermore, we have validated the proposed ice shedding model through the comparison of numerical results and experimental data, which include the flow rate loss due to ice growth and the flow rate recovery due to ice shedding. The simulation results for the time at which ice shedding occurred and what were obtained using the proposed ice shedding model were in good agreement with the experimental results.

Dynamic Meta-Modeling Method to Assess Stochastic Flutter Behavior in Turbomachinery

With increasing design demands of turbomachinery,stochastic flutter behavior has become more prominent and even appears a hazard to reliability and safety.Stochastic flutter assessment is an effective measure to quantify the failure risk and improve aeroelastic stability.However,for complex turbomachinery with multiple dynamic influencing factors(i.e.,aeroengine compressor with time-variant loads),the stochastic flutter assessment is hard to be achieved effectively,since large deviations and inefficient computing will be incurred no matter considering influencing factors at a certain instant or the whole time domain.To improve the assessing efficiency and accuracy of stochastic flutter behavior,a dynamic meta-modeling approach(termed BA-DWTR)is presented with the integration of bat algorithm(BA)and dynamic wavelet tube regression(DWTR).The stochastic flutter assessment of a typical compressor blade is considered as one case to evaluate the proposed approach with respect to condition variabilities and load fluctuations.The evaluation results reveal that the compressor blade has 0.95% probability to induce flutter failure when operating 100% rotative rate at t=170 s.The total temperature at rotor inlet and dynamic operating loads(vibrating frequency and rotative rate)are the primary sensitive parameters on flutter failure probability.Bymethod comparisons,the presented approach is validated to possess high-accuracy and highefficiency in assessing the stochastic flutter behavior for turbomachinery.

CALL FOR PAPER The Fourth Chinese International Turbomachinery Conference(CITC 2020)

About CITC CITC (Chinese International Turbomachinery Conference) is sponsored by the Chinese Journal of Turbomachinery which is a reference for Chinese and worldwide industry and research community. CITC focuses on promoting both fundamental and engineering application and is of primary interest to researchers, engineers, students and users in the field of Turbomachinery. It is a key event for technology transfer through the presentation of the latest developments and best practices, with a specific focus concerning China. CITC is becoming a trendsetter conference outlining the roadmap to the future and will be known as one of the most cutting-edge meetings comprising all aspects of Turbomachinery. The conference has been established a platform for exchanging ideas and solutions, encouraging partnerships across academia and industry.

Calculation of three-dimensional transonic flows in turbomachinery with generalized von Mises corrdinate system

An efficient numerical method for calculating the three-dimensional transonic flows in turbomachinery is proposed. Instead of the Euler equation, streamsurface-governing equations are deduced in the generalized von Mises coordinate system to reflect the flow feature in turbomachinery. Its main advantage is that it is easier to specify more reasonable initial values, i.e. initial streamsurface position, thus accelerating the convergence rate of the iteration process. Moreover, to use the generalized von Mises coordinates makes the present method capable of incorporating the calculation of the flow field, design and modification of the blade contour into a unified algorithm. A rotated finite difference scheme for the streamsurface-governing equations is constructed, and a new measure is presented to deal with the double-value problem of the velocity and density caused by the application of the stream functions as coordinates in the transonic flow. Three test cases were considered with the present approach to demonstrate the solution method for 3-D inviscid flow analysis. Numerical results confirm that the present method has rapid convergence and high accuracy.

A gradient-based method assisted by surrogate model for robust optimization of turbomachinery blades

The design optimization taking into account the impact of uncertainties favors improving the robustness of the design.A Surrogate-Assisted Gradient-Based(SAGB)method for the robust aerodynamic design optimization of turbomachinery blades considering large-scale uncertainty is introduced,verified and validated in the study.The gradient-based method is employed due to its high optimization efficiency and any one surrogate model with sufficient response accuracy can be employed to quantify the nonlinear performance changes.The gradients of objective performance function to the design parameters are calculated first for all the training samples,from which the gradients of cost function can be fast determined.To reveal the high efficiency and high accuracy of SAGB on gradient calculation,the number of flow computations needed is evaluated and compared with three other methods.Through the aerodynamic design optimization of a transonic turbine cascade minimizing total pressure loss at the outlet,the SAGB-based gradients of the base and optimized blades are compared with those obtained by the Monte Carlo-assisted finite difference method.Moreover,the results of both the robust and deterministic aerodynamic design optimizations are presented and compared to demonstrate the practicability of SAGB on improving the aerodynamic robustness of turbomachinery blades.

Computational theory of cavitating flows for hydraulic turbomachinery with consideration of influence of water quality

Previously it was assumed that the pressure within the cavity or on the cavity surface remained constant and the vapor pressure of clean water at 20°C and 0 m altitude was utilized as the computational boundary for cavitating flows in hydraulic turbomachinery. Cavitation was confused with vaporization, and the effect of water quality on cavitation pressure characteristics was not taken into account. In recent years, lots of experiments of cavitation pressure characteristics of different water qualities including different sand concentrations of sand water and different altitudes of clean water have been performed by the authors, and the important influences of water quality on cavitation pressure characteristic have been validated. Thus the water quality should be involved in the cavitating flows computation. In the present paper, the effect of water quality on the cavitation pressure characteristic is analyzed and the computational method and theory of cavitating flows for hydraulic turbomachinery that considers the influence of water quality are proposed. The theory is suitable for both the potential flow method and the two-phase flow method for cavitating flows simulation. Finally, the validation results for cavitating flows in a hydraulic tur- bine indicate the significant influences of water quality on the cavitating flow performance.

Study on Adjoint-Based Optimization Method For Multi-Stage Turbomachinery

Adjoint-based optimization method is a hotspot in turbomachinery.First,this paper presents principles of adjoint method from Lagrange multiplier viewpoint.Second,combining a continuous route with thin layer RANS equations,we formulate adjoint equations and anti-physical boundary conditions.Due to the multi-stage environment in turbomachinery,an adjoint interrow mixing method is introduced.Numerical techniques of solving flow equations and adjoint equations are almost the same,and once they are converged respectively,the gradients of an objective function to design variables can be calculated using complex method efficiently.Third,integrating a shape perturbation parameterization and a simple steepest descent method,a frame of adjoint-based aerodynamic shape optimization for multi-stage turbomachinery is constructed.At last,an inverse design of an annular cascade is employed to validate the above approach,and adjoint field of an Aachen 1.5 stage turbine demonstrates the conservation and areflexia of the adjoint interrow mixing method.Then a direct redesign of a 1+1 counter-rotating turbine aiming to increase efficiency and apply constraints to mass flow rate and pressure ratio is taken.

Synergy Methodology for Internal Flow of Turbomachinery

The complex curvature of turbomachinery rotor blade channels combined with strong rotational effect and clearance leakage brings on intricate internal flow phenomenon.It is necessary to study the internal flow and energy loss mechanism to reveal the influence law of the key parameters and to achieve its optimal design.Considering features of flow and temperature fields in rotor passage,the concept of synergy analysis derived from equation of energy conservation was put forward.Typical NASA low-speed centrifugal compressor(LSCC)rotor was chosen for analysis using CFD.Numerical results showed remarkable agreement with experiment datum in both the tendency of the performance characteristics and quantitative pressure values.Under different flow rates and inlet total temperatures conditions,thermal-fluid interaction effect and losses were studied by synergy analysis.Results showed that peak synergy positive value zones located around blade leading edge,across the shroud wall and hub wall,and at the position where tip-leakage flow was mixing with the bulk flow and high entropy zones existed.Increasing flow rate from design condition,positive and negative synergy areas both changed tiny around leading edge and trailing edge.Reducing flow rate,positive synergy areas tended to increase and negative areas decreased at same positions.The relationship between flow separation,heat transfer and losses in turbomachinery rotor can be revealed based on synergy analyses.

Study on Aerodynamic Design Optimization of Turbomachinery Blades

This paper describes the study on aerodynamics design optimization of turbomachinery blading developed by the authors at the Institute of Engineering Thermophysics, Chinese Academy of Sciences, during the recent few years. The present paper describes the aspects mainly on how to use a rapid approach of profiling a 3D blading and of grid generation for computation, a fast and accurate viscous computation method and an appropriate optimization methodology_ including a blade parameterization algorithm to optimize tm-bomachinery blading aerodynamically. Any blade configuration can be expressed by three curves, they are the camber lines, the thickness distributions and the radial stacking line, and then the blade geometry can be easily parameterized by a number of parameters with three polynomials. A gradient-based parameterization analytical method and a response surface method were applied herein for blade optimization. It was found that the optimization process provides reliable design for turbomachinery with reasonable computing time.

STUDIES OF SOLID－LIQUID TWO－PHASE TURBULENT FLOWS AND WEAR IN HYDRAULIC TURBOMACHINERY

The Lagrangian equation of motion for solid particles in an arbitrary flow field is derived. The linear differential equation form and the general solution of this equation are obtained. Motion of solid particles in dilute solid-liquid turbulent flows is numerically solved and analysed. The K-εtwo-equation turbulence model, the volume fraction turbulence model, the mixed Eulerian-Lagrangian turbulence model, and the dense mixture turbulence model as well as the erosive wear model are developed. Using these models, the turbulent flows and the erosive wear in some hydraulic turbomachinery ducts are numerically predicted. The numerical results show good agreement with the experiments.

Validation of a novel mixing-plane method for multistage turbomachinery steady flow analysis

The steady calculation based on the mixing-plane method is still the most widely-used three-dimensional flow analysis tool for multistage turbomachines. For modern turbomachines,the trend of design is to reach higher aerodynamic loading but with still further compact size. In such a case, the traditional mixing-plane method has to be revised to give a more physically meaningful prediction. In this paper, a novel mixing-plane method was proposed, and three representative test cases including a transonic compressor, a highly-loaded centrifugal compressor and a highpressure axial turbine were performed for validation purpose. This novel mixing-plane method can satisfy the flux conservation perfectly. Reverse flow across the mixing-plane interface can be resolved naturally, thus making this method numerically robust. Artificial reflection at the mixing-plane interface is almost eliminated, and then its detrimental impact on the flow field is minimized. Generally, this mixing-plane method is suitable to simulate steady flows in highly-loaded multistage turbomachines.

Flow reconstructions and aerodynamic shape optimization of turbomachinery blades by POD-based hybrid models

This study presented a hybrid model method based on proper orthogonal decomposition(POD) for flow field reconstructions and aerodynamic design optimization. The POD basis modes have better description performance in a system space compared to the widely used semi-empirical basis functions because they are obtained through singular value decomposition of the system.Instead of the widely used linear regression, nonlinear regression methods are used in the function response of the coefficients of POD basis modes. Moreover, an adaptive Latin hypercube design method with improved space filling and correlation based on a multi-objective optimization approach was employed to supply the necessary samples. Prior to design optimization, the response performance of POD-based hybrid models was first investigated and validated through flow reconstructions of both single-and multiple blade rows. Then, an inverse design was performed to approach a given spanwise flow turning distribution at the outlet of a turbine blade by changing the spanwise stagger angle, based on the hybrid model method. Finally, the span wise blade sweep of a transonic compressor rotor and the spanwise stagger angle of the stator blade of a single low-speed compressor stage were modified to reduce the flow losses with the constraints of mass flow rate, total pressure ratio, and outlet flow turning.The results are presented in detail, demonstrating the good response performance of POD-based hybrid models on missing data reconstructions and the effectiveness of POD-based hybrid model method in aerodynamic design optimization.

Numerical Investigation of Loss Generation Mechanisms of Flow in Turbomachinery by Using Curved Square Duct

The secondary flow within a passage of turbomachinery exhibits a complex flow pattern by the effect of the centrifugal and the Coriolis forces. The passage vortex in this secondary flow generates a major part of the losses. However, the mechanism of the loss generation has not been fully clarified yet. In this point of view, the passage vortex is closely examined by the computational method using the two-dimensional curved square ducts as fundamental models. The inlet boundary layer thickness and the inlet velocity distortion are considered to be the major parameters affecting the generation of passage vortex in the present study. The computed results revealed that the passage vortex gave the predominant effects for the generation of loss not only in the breakdown process but also in the development process.

Efficient Determination of Turbomachinery Blade Aero-Damping Curves for Flutter Assessment via Trigonometric Interpolation

Proposed in the paper is a trigonometric interpolation method for efficient determination of turbomachinery blade aero-damping curves which are required in a flutter assessment.The trigonometric interpolation method was proposed to be incorporated with the widely used travelling wave method to replace the influence coefficient method.Through analyzing aero-damping/worksum at a few carefully chosen nodal diameters,trigonometric interpolation was applied through existing data points to get aero-damping/worksum at the rest nodal diameters.The proposed approach is much more efficient than the travelling wave method for determining the aero-damping curve of a blade.In principle,the method can be as efficient as the influence coefficient method.Unlike the influence coefficient method,the trigonometric interpolation method does not involve linear superposition,and it can include nonlinear effect and is expected to be more accurate.Two test cases were provided to validate the proposed method and demonstrate its effectiveness.The method is not only effective,but also very easy to be incorporated into existing widely used aero-damping/worksum analysis system using the travelling wave method.

A Numerical Modeling of the Vortex-induced Vibration of Cascade in Turbomachinery using Immersed Boundary Method

Based on the immersed boundary method,a fast simulation for solving unsteady,incompressible,viscous flow associated with the oscillating cascade is established on a quasi-three-dimensional coordinate system.The numerical method is applied to the simulation of the flow passing an oscillating circular cylinder which is forced to move in X direction under prescribed motions in water at rest at low Keulegan-Carpenter numbers.Then vor-tex-induced vibration of a cylinder with two degrees of freedom which oscillates in in-line direction and transverse direction is simulated using this method.The results are in good agreement with the previous research.Then the method is extended to the oscillating cascade simulation of making various comparisons.It is found that the IBPA(inter blade phase angle) will change as the time goes on,because of the non-uniformity of the flow in the circumferential direction,until the oscillating cascade goes to a stable situation.The reduced velocity and the number of blades are chosen to investigate the effects of them on IBPA.The results indicate that both the reduced velocity and the number of blades are the main factors which influence IBPA.It is worth noting that the coupling process is not necessary to generate any body-fitting grids,which makes it much faster in computational process for such a complicated fluid-structure interaction problem.

PSEUDOSTREAM FUNCTION FORMULATION——A METHOD OF SOLVING THREE-DIMENSIONAL AERODYNAMIC ANALYSIS AND DESIGN PROBLEMS IN TURBOMACHINERY

In this paper two pseudostream functions are defined in view of the characteristic featuresof the momentum equations and the requirement of continuity. The principal equationsof eiher pseudostream functions only contain the terms of its own second-order partial deriv-atives and do not include those of the other, and these equations can be easily solved. Theentire three-dimensional solution is then obtained through solving the principal equations ofboth pseudostream functions separately and iterating the two solutions. The principal equa-tions of the pesudostream functions in a nonorthogonal curvilinear coordinates and thecorresponding boundary conditions are given. The three-dimensional aerothermodynamicanalysis problem and design problem are discussed, some calculations are conducted and theresults are compared with the analytical solution and with that of other methods. It is seenthat this method is accurate in theory and simple in computation, and may be widely usedin three-dimensional flow calculations.

CONCERNING A BASIC ASSUMPTION FOR AEROELASTICITY IN TURBOMACHINERY

One of the basic assumptions for aeroelasticity in turbomachinery that the interbladephase angle along a blade row is constant has been proved to be invalid by the fact that nei-ther dynamic stresses nor interblade phase angles are constant along a blade row when thestall flutter occurs. With this assumption abandoned, a new model and the correspondingnumerical method have been developed. Comparisons between calculations and measurementsshowed that the main cause which makes blade dynamic stresses unequal along a blade rowin the unstable aeroelastic process is inequable interblade phase angle distribution along theblade row.

Aerodynamic adjoint optimization of turbomachinery with direct control on blade design parameters

Nowadays,the adjoint method has become a popular approach in the optimization of turbomachinery to further improve its aerodynamic performance.However,design variables in these adjoint optimization applications are generally not direct design parameters of blade(such as wedge angles or maximum thickness),making the geometric variation by adjoint optimization can hardly be re-extracted as the change of each design parameter.By giving considerations to the G1 continuity constraint of adjoint method on its parameterization method,this manuscript shows how to apply a parameterization method in 3D blade design process into adjoint optimization.Nearly all design parameters can therefore be treated as design variables in the adjoint method and then participate in the sensitivity-based optimization.Finally,a fitted Rotor 67 blade is optimized and the adiabatic efficiency is significantly improved by nearly 0.91%.

Numerical Calculation of Flowsin Turbomachinery with Threedimensional Viscous Codes

Afast and accurate three dimensional (3 D) viscous code for calculating flows in turbomachinery has been established.In this code, H meshes are adopted to build the discrete equations, and the conservation equationsare solved on grid nodes atthe corners of cuboid elements.In orderto accelerate convergence,local time stepping,residualsmoothing and multigrid method are also applied,andthe viscous effects are approximatedby a very simple mixing length model.For verification ofthe accuracy and applicability ofthe method,transonicflowsthrough compressor cascades of NASArotor 37 and flows through a turbine stator of NASAhave been calculated.The good agreementbetween experimentalresults and design data has demonstratedthereliability and applicability ofthe present method,which can be usedforsimulatingthe complex 3 Dviscousflow phenomenonin turbomachinery.