RESEARCH ON PARALLEL GRINDING METHOD OF NON-AXISYMMETRIC ASPHERIC LENS

In order to resolve the problems of machining non-axisymmetric aspheric lens,which is short of flexibility in mould grinding and needs high accuracy CNC machine center in globediamond wheel grinding, a new parallel grinding method that utilizes common arc diamond wheel isput forward. Base on the approach calculation of machining locus, the advantages of parallelgrinding that machines non-axisymmetric aspheric lens by 2.5-axis CNC machine center have beenobtained. The results of grinding experiment show the new method can meet the need of grinding highaccuracy non-axisymmetric aspheric lens.

THE NON-AXISYMMETRICAL DYNAMIC RESPONSE OF TRANSVERSELY ISOTROPIC SATURATED POROELASTIC MEDIA

The Blot's wave equations of transversely isotropic saturated poroelastic media excited hy non-axisymmetrical harmonic source were solved by means of Fourier expansion and Hankel transform. Then the components of total stress in porous media are expressed with the solutions of Biot's wave equations. The method of research on non-axisymmetrical dynamic response of saturated porous media is discussed, and a numerical result is presented.

Finite Element Simulation on the Spin-forming of the 3D Non-axisymmetric Thin-Walled Tubes

The roller movement trace for the 3D non-axisymmetric thin-walled tubes is a complex space curve. Besides the roller rotation caused by contact with the blank, the roller rotates around the workpiece together with the main spindle, and also moves simultaneously along the direction of the revolution radius. The method to correctly establish the finite element （FE） models of the metal spinning is based on the MSC. MARC software was introduced. The calculation formulas considering both the revolution and rotation of the roller were obtained by the mathematical deduction. The saving calculation points m should be a multiple of 4 for one revolution of the roller around the workpiece to obtain the maximum forming force for the spinning of the 3D non-axisymmetric thin-walled tubes. The simulation results conform well to the experimental ones for several spinning methods; the maximum error is less than ±15%.

Reconstruction of Emission Coefficients for a Non-axisymmetric Coupling Arc Based on MALDONADO's Method

The reconstruction of emission coefficient is a key factor for the calculation of temperature field.However,most of the researches for determining arc plasmas are based on axisymmetric sources,little has been done to study non-axisymmetric arc plasmas.In order to reveal temperatures of a non-axisymmetric coupling arc,the distribution of emission coefficients must be reconstructed in advance.In this paper,the argon atomic line intensities of the coupling arc are obtained by using the imaging system that involves a high speed camera in conjunction with a neutral and a narrow-band filter.The converted programme between emission coefficients and emitted intensities is programmed based on MALDONADO＇s method.A displaced Gaussian model is used for evaluating the validity of the converted programme.Then,the emission coefficients of a free burning arc are reconstructed by MALDONADO＇s method and an Abel inversion,respectively,and good agreement is obtained.Finally,the emission coefficient profiles of the coupling arc are achieved.The results show that the distribution of emission coefficient for the coupling arc is non-axisymmetric.The emission coefficient profile is similar to an ellipse,and the short axis of the ellipse is in the direction that the two electrodes are arranged along.The peak temperature of the coupling arc is in the middle of both electrodes.There is a strong interaction between both arcs within the coupling arc.The proposed research solves difficulties for determining asymmetric arcs and enlarges the application scope of spectroscopic techniques.

STUDY ON THE NUMERICAL SIMULATION OF MULTI-STAGE ROTARY FORGING OF A NON-AXISYMMETRIC PART AND THE CAE ANALYSIS OF THE DIE STRENGTH

Traditionally a rotary forging process is a kind of metal forming method where a conic upper die, whose axis is deviated an angle from the axis of machine, forges a billet continuously and partially to finish the whole deformation. For the rotary forging process simulation, more researches were focused on simulating the simple stage forming process with axisymmetric part geometry. Whereas in this paper, the upper die is not cone-shaped, and the billet is non-axisymmetric. So the movement of the punch is much more complicated than ever. The 3D FEM simulation models for the preforming ＆ final forming processes are set up aider carefully studying the complicated movement pattern. Deform-3D is used to simulate the material flow, and the boundary nodal resisting forces calculated by the final stage process simulation is used to analyze the final forming die strength. The CAE analysis of the die shows that the design of the final forming die is not reasonable with lower pre-stress which is easy to crack at the critical corners. An optimum die design is also provided with higher pre-stress, and verified by CAE analysis.

Thermo-electromechanical behavior of functionally graded piezoelectric hollow cylinder under non-axisymmetric loads

This paper presents an analytical solution of a thick walled cylinder composed of a functionally graded piezoelectric material （FGPM） and subjected to a uniform electric field and non-axisymmetric thermo-mechanical loads. All material properties, except Poisson＇s ratio that is assumed to be constant, obey the same power law. An exact solution for the resulting Navier equations is developed by the separation of variables and complex Fourier series. Stress and strain distributions and a displacement field through the cylinder are obtained by this technique. To examine the analytical approach, different examples are solved by this method, and the results are discussed.

BUCKLING AND POST-BUCKLING OF ANNULAR PLATES UNDER NON-AXISYMMETRIC PLANE EDGE FORCES

On the basis of both the general theory[1,2]and the finite element method[4]of perforated thin plates with large deflection,the buckling and post-buckling of annular plates under non-axisymmetric plane edge forces are studied.

Optimal Design of Non-axisymmetric Endwall with Variable-fidelity CFD Model

Non-axisymmetric endwall is numerically investigated to suppress the secondary endwall flow in a HP turbine suction surface.The endwall contour is represented by a non-uniform rational B-spline surface.Two solution spaces are designed by the rule of hypercube sampling through variation of nodal radial extension.Final most effective endwall contour is obtained through screening all available samples with surrogate-based model.Results show that non axisymmetric endwall reduces the turbulence kinetic energy of the passage vortex by 5.5%and the total pressure loss 1.6%.Local heat transfer coefficient is lowered on the afore passage endwall surface with a certain increment on the aft passage endwall.Overall averaged heat transfer coefficient is reduced.

Experimental investigation about the effect of non-axisymmetric wake impact on a low speed axial compressor

Non-axisymmetric wake impact experiments were carried out after the best exciting frequency for a low speed axial compressor had been found by axisymmetric wake impact experiments. When the number and circumferential distribution of inlet guide vanes （IGV） are logical, the wakes of non-axisymmetric IGVs can exert beneficial unsteady exciting effect on their downstream rotor flow fields and improve the compressor＇s performance. In the present paper, four non-axisymmetric wake impact plans were found working better than the axisymmetric wake impact plan. Compared with the base plan, the best non-axisymmetric plan increased the compressor＇s peak efficiency, and the total pressure rise by 1.1 and 2%, and enhanced the stall margin by 4.4%. The main reason why non-axisymmetric plans worked better than the axisymmetric plan was explained as the change of the unsteady exciting signal arising from IGV wakes. Besides the high-frequency components, the nonaxisymmetric plan generated a beneficial low-frequency square-wave exciting signal and other secondary frequency components. Compared with the axisymmetric plan, multifrequency exciting wakes arising from the non-axisymmetric plans are easier to get coupling relation with complex vortices such as clearance vortices, passage vortices and shedding vortices.

INSTABILITY OF HAGEN-POISEUILLE FLOW FOR NON-AXISYMMETRIC MODE

An investigation is described for instability problem of flow through a pipe of circular cross section. As a disturbance motion, we consider a general non-axisym-metric mode. An associated amplitude or modulation equation has been derived for this disturbance motion. This equation belongs to a diffusion type.The coefficient of it can be negative while Reynolds number increases, because of the complex interaction between molecular diffusion and convection. The negative diffusivity, when it occurs, causes a concentration and focussing of energy within decaying slugs, acting as a role of reversing natural decays.

Design and Numerical Investigation to Predict the FlowPattern of Non-axisymmetric Convergent Nozzle:AComponent of Turboexpander

Current work proposes a novel design methodology using curve-fitting approach for a non-axisymmetric airfoil convergent nozzle used in small-sized cryogenic turboexpander.The curves used for designing the nozzle are based on a combination of fifth and third order curve at upper and lower surface respectively.Four different turbulence model such as k-ε,SST,BSL and SSG Reynolds stress turbulence model is used to visualize and compare the fluid flow characteristics and thermal behaviors at various cross-sections.It is interesting to observe that the Mach number obtained at the outlet of the nozzle is highest and temperature drop is maximum for SSG model under similar boundary conditions.It is also observed that the designed nozzle with curve fitting approach is appropriate for impulse type turbine with a small amount of reaction.The key feature of this implementation is to obtain subsonic velocity at the nozzle exit and reduce the irreversible losses through the nozzle,which can affect the performance of a turboexpander.

Effect of Incoming Vortex on Secondary Flows in Turbine Cascades with Planar and Non-Axisymmetric Endwall

Non-Axisymmetric Endwall Profiling(NAEP) is commonly utilized in turbines to eliminate secondary flows.Nevertheless,most of the NAEP methods consider a single-blade row environment without incorporating the effect of the stage environment.This paper aims to investigate the influence mechanism of the incoming vortex on the endwall secondary flow structures of NAEP in a highly loaded turbine cascade.To model the incoming vortex in a stage environment,this study considers a half-delta wing as the vortex generator at the upstream of the turbine cascade.The NAEP is then carried out for a highly loaded turbine cascade with an in-house numerical optimization design platform subject to no incoming vortex.Numerical simulation is also carried out under the influence of the incoming vortex for the turbine cascades with both planar and non-axisymmetric endwall.This paper furthers investigated the pitchwise effect of the incoming vortex on the near endwall secondary flow.The results indicate that the NAEP effectively improves the endwall secondary flow of the turbine cascade,where the total pressure loss coefficient and the secondary kinetic energy(SKE) are reduced by 7.3%,and 45.7%,respectively.It is further seen that with the incoming vortex,the NAEP achieves a considerable control effect on the endwall secondary flow of the turbine cascade.With incoming vortex,the NAEP can still achieve considerable control effect on the endwall secondary flow of the turbine cascade;the averaged reductions of loss coefficient and SKE are 7.8% and 14.2%,respectively.Under some pitchwise locations,incoming vortex can suppress the convection of cross-passage flow toward the suction corner greatly and reduce the loss coefficient of the baseline cascade.The incoming vortex at 4/7 pitch impinged right at the blade leading edge,leading to the generation of low-momentum fluid,which increased the size and the strength of the horseshoe vortex.Under all the pitchwise locations,NAEP can suppress the secondary vortices,e.g.,the passage vortex and the counter vortex,considerably.

Approximate contact solutions for non-axisymmetric homogeneous and power-law graded elastic bodies:A practical tool for design engineers and tribologists

In two recent papers,approximate solutions for compact non-axisymmetric contact problems of homogeneous and power-law graded elastic bodies have been suggested,which provide explicit analytical relations for the force–approach relation,the size and the shape of the contact area,as well as for the pressure distribution therein.These solutions were derived for profiles,which only slightly deviate from the axisymmetric shape.In the present paper,they undergo an extensive testing and validation by comparison of solutions with a great variety of profile shapes with numerical solutions obtained by the fast Fourier transform(FFT)-assisted boundary element method(BEM).Examples are given with quite significant deviations from axial symmetry and show surprisingly good agreement with numerical solutions.

Design Optimization of Non-Axisymmetric Vane for an Axial Compressor under Inlet Distortion

The flow field at the inlet of compressors is generally encountered combined total pressure and swirl distortion for either aircraft engine with S-duct or gas turbine with lateral air intake.This inevitably deteriorates compressor aerodynamic performance,including not only the efficiency or pressure ratio but also the operation stability.In order to conquer this issue,appropriate measures such as integrating flow control techniques and modifying inlet or compressor design are of benefits.Due to this motivation,this article develops a full-annular two-dimensional(2D)and a partial-annular three-dimension(3D)optimization strategy for non-axisymmetric vane design.Firstly,two numerical simulation methods for evaluating performance of full-annular 2D vane and compressor with partial-annular 3D vane are developed.The swirl patterns at the inlet of a 1.5-stage axial compressor are analyzed and parametrized,and the parameterization is transferred to characterize the circumferential distribution of geometrical parameters of the vane profile.These approaches dramatically reduce computational simulation costs without violating the non-axisymmetric flow distortion patterns.Then various full-annular 2D sections at different radial locations are constructed as design space.The designed vane is reconstructed and 3D numerical simulations are performed to examine performance of the non-axisymmetric vane and the compressor with it.Also,partial annular 3D optimization is conducted for balancing compressor efficiency and stall margin.Results indicate that the designed non-axisymmetric vane based on full-annular optimization approach can decrease the vane total pressure loss under the considered inlet flow distortion,while those using partial-annular optimization achieve positive effects on compressor stall margin.

Static pressure redistribution mechanism of non-axisymmetric endwall based on radial equilibrium

Non-axisymmetric endwall contouring has been proved to be an effective flow control technique in turbomachinery.Several different flow control mechanisms and qualitative design strategies have been proposed.The endwall contouring mechanism based on the flow governing equations is significant for exploring the quantitative design strategies of the nonaxisymmetric endwall contouring.In this paper,the static pressure redistribution mechanism of endwall contouring was explained based on the radial equilibrium equation.A quantified expression of the static pressure redistribution mechanism was proposed.Compressor cascades were simulated using an experimentally validated numerical method to validate the static pressure redistribution mechanism.A geometric parameter named meridional curvature(Cme)is defined to quantify the concave and convex features of the endwall.Results indicate that the contoured endwall changes the streamline curvature,inducing a centrifugal acceleration.Consequently,the radial pressure gradient is reformed to maintain the radial equilibrium.The convex endwall represented by positive Cme increases the radial pressure gradient,decreasing the endwall static pressure,while the concave endwall represented by negative Cme increases the endwall static pressure.The Cme helps to establish the quantified relation between the change in the endwall radial pressure gradient and the endwall geometry.Besides,there is a great correlation between the distributions of the Cme and the change in the endwall static pressure.It can be concluded that the parameter Cme can be considered as a significant parameter to parameterize the endwall surface and to explore the quantitative design strategies of the nonaxisymmetric endwall contouring.

Non-axisymmetric Flow Characteristics in Centrifugal Compressor

The flow field distribution in centrifugal compressor is significantly affected by the non-axisymmetric geometry structure of the volute.The experimental and numerical simulation methods were adopted in this work to study the compressor flow field distribution with different flow conditions.The results show that the pressure distribution in volute is characterized by the circumferential non-uniform phenomenon and the pressure fluctuation on the high static pressure zone propagates reversely to upstream,which results in the non-axisymmetric flow inside the compressor.The non-uniform level of pressure distribution in large flow condition is higher than that in small flow condition,its effect on the upstream flow field is also stronger.Additionally,the non-uniform circumferential pressure distribution in volute brings the non-axisymmetric flow at impeller outlet.In different flow conditions,the circumferential variation of the absolute flow angle at impeller outlet is also different.Meanwhile,the non-axisymmetric flow characteristics in internal impeller can be also reflected by the distribution of the mass flow.The high static pressure region of the volute corresponds to the decrease of mass flow in upstream blade channel,while the low static pressure zone of the volute corresponds to the increase of the mass flow.In small flow condition,the mass flow difference in the blade channel is bigger than that in the large flow condition.

Influence of Non-Axisymmetric Terms on Circumferentially Averaged Method in Fan/Compressor

The governing equations are derived by circumferentially averaging the three-dimensional （3D） Navier-Stokes equations, which are solved using a time marching finite volume approach. Both Euler throughflow model and Navier-Stokes （N-S） throughflow model are employed to investigate the performance and flow fields of a highly loaded transonic single-stage fan ATS-2 and a four-stage fan. The results are compared with the experimental and three-dimensional computational results. It shows that the throughflow models can provide reasonable perform- ance characteristics and N-S throughflow model gives better predictions in endwall regions. A throughflow com- putation in which all the non-axisymmetric terms are included has been performed at off-design condition and the radial distributions of the flow field can be well described.

Influences of Inflow Condition on Non-Axisymmetric Flows in Turbine Exhaust Hoods

The complex 3D flow in a steam turbine exhaust hood model with different inlet swirl and inlet total pressure radial distributions has been simulated by employing CFX-5 and analyzed in this paper. It＇s found that the inlet tangential flow angle at hub has a negative effect on the exhaust hood performance, while a negative gradient of inlet total pressure radial distribution has a positive impact on the hood performances. It＇s also numerically con- firmed that a proper distribution of total pressure at hood inlet can successfully eliminate the negative effects caused by the inappropriate inlet swirl distribution and improve the hood aerodynamic performance.

Investigation of Non-Axisymmetric Endwall Contouring in a Compressor Cascade

The current paper presents experimental and computational results to assess the effectiveness of non-axisymmetric endwall contouring in a compressor linear cascade. The endwaU was designed by an endwall design optimi- zation platform at 0° incidence （design condition）. The optimization method is based on a genetic algorithm. The design objective was to minimize the total pressure losses. The experiments were carried out in a compressor cascade at a low-speed test facility with a Mach number of 0.15. Four nominal inlet flow angles were chosen to test the performance of non-axisymmetric Contoured Endwall （CEW）. A five-hole pressure probe with a head diameter of 2 mm was used to traverse the downstream flow fields of the flat-endwall （FEW） and CEW cascades. Both the measured and predicted results indicated that the implementation of CEW results in smaller comer stall, and reduction of total pressure losses. The CEW gets 15.6% total pressure loss coefficient reduction at design condition, and 22.6% at off-design condition （＋7° incidence）. And the mechanism of the improvement of CEW based on both measured and calculated results is that the adverse pressure gradient （APG） has been reduced through the groove configuration near the leading edge （LE） of the suction surface （SS）.

Numerical Investigation of a High-subsonic Axial-flow Compressor Rotor with Non-axisymmetric Hub Endwall

The major source of loss in modem compressors is the secondary loss. Non-axisymmetric endwall profile contouring is now a well established design methodology in axial flow turbines. However, flow development in axial compressors is differ from turbines, the effects of non-axisymmetric endwall to axial compressors requires flow analysis in detail. This paper presents both experimental and numerical data to deal with the application of a non-axisymmetric hub endwall in a high-subsonic axial-flow compressor. The aims of the experiment here were to make sure the numerically obtained flow fields is the physical mechanism responsible for the improvement in efficiency, due to the non-axisymmetric hub endwall. The computational results were first compared with avail- able measured data of axisymmetric hub endwall. The results agreed well with the experimental data for estima- tion of the global performance. The coupled flow of the compressor rotor with non-axisymmetric hub endwall was simulated by a state-of-the-art multi-block flow solver. The non-axisymmetric hub endwall was designed for a subsonic compressor rotor with the help of sine and cosine functions. This type of non-axisymmetric hub end- wall was found to have a significant improvement in efficiency of 0.45% approximately and a slightly increase for the total pressure ratio. The fundamental mechanisms of non-axisymmetric hub endwall and their effects on the subsonic axial-flow compressor endwall flow field were analyzed in detail. It is concluded that the non-axisymmetric endwall profiling, though not optimum, can mitigate the secondary flow in the vicinity of the hub endwall, resulting in the improvement of aerodynamic performance of the compressor rotor.