DesignOptimizationofAxisymmetricEndwallinAxial.doc

精品论文design optimization of axisymmetric endwall in axialcompressor s-shaped ductjin donghai, zhao weiguang, gui xingmin5(school of energy and power engineering, beihang university, beijing 100191) abstract: this paper presents a numerical investigation on the potential aerodynamic benefits of using endwall contouring in a fairly aggressive duct with six struts based on the platform of the endwall design optimization. the platform was built with adaptive genetic algorithm (aga), design of experiments (doe), response surface methodology (rsm) based on the artificial neural network10(ann) and a 3d navier-stokes solver. visual analysis method based on doe was used to define the design space and analyse the impact of the design parameters on the target function (response).optimization of axisymmetric endwall contouring in the duct has been performed and evaluated. the objective was to minimize the total pressure loss. the optimal duct was found to reduce the hub corner separation and suppress the migration of the low momentum fluid. the axisymmetric endwall15contouring was shown to suppress the separation and reduce the net duct loss by 22%.keywords: s-shaped duct; axisymmetric endwall; design optimization; secondary flow0introductionan s-shaped duct is used to connect the low pressure and high pressure compressors of20aircraft gas turbine engines. within the duct, flow separation should be avoided to minimize the total pressure loss. in addition, a uniform flow filed at the duct exit should also be achieved. however, modern turbo-fan engines demand on improved efficiency and reduced noise level which lead to high by-pass ratio. these demands result in engines with large fans and small high pressure compressors which will bring about a significant radial difference between the25low-pressure and high-pressure systems. the higher by-pass ratio is, the more aggressive s-shaped ducts are needed. this makes duct design increasingly important. firstly, transition ducts play a significant role in determining the overall length and weight of the engine. the advantages are obvious if the duct length could be shorten without other penalties. secondly, if the thickness of the non-turning struts in the duct could be increased, then it would allow improved service access30to the core of engine.several researchers have investigated the flows in s-shaped ducts. bailey1 investigated the aerodynamic performance of a compressor s-shaped duct with a single strut (thickness-to-chord ratio is 0.12). the blockage of strut was found to have a significant effect on pressure field of the duct, which has a direct influence on the turbulent flow field. ortiz duenas et al2 had35experimentally investigated the effect of reducing the duct length and keeping duct inlet height (hin) and inlet to exit radius change ( r ). it was found that the length of original duct without strut reducing to 74% caused a small rise in loss, however, reducing the length to 64% caused a much larger rise in loss. the researches have shown that the limit of the design space of annular s-ductsis set by duct corner separation. reducing the length or increasing the change in radius or the40thickness-to-chord ratio has a similar effect on ducts performance. the streamlines with the highest deceleration occur in the hub-strut corner and the flow might occur to separation. the separation results in a sharp rise in duct loss coefficient, and a large-scale blockage entering the downstream compressor.in order to reduce the extent of the corner separation and avoid higher loss coefficient in45ducts, the focus lie on intermediate s-shaped duct endwall profiling and its influence on the flowbrief author introduction:jin donghai, (1977-), male, associate professor, aerodynamic design optimization of turbomachinery and research of secondary flow mechanism. e-mail: - 11 -field in the 3d annular duct in this paper. a numerical optimization coupling with adaptive genetic algorithm (aga) and response surface methodology (rsm) is undertaken to design the axisymmetric endwall profiling. finally, the performance of optimal endwall profiling is compared with the original s-shaped duct.501endwall design optimization methodthe use of design optimization in turbomachinery is possible today thanks to computational fluid dynamics (cfd) analysis. fig.1 shows the algorithm of the endwall design optimization system. one of its advantages is the use of a response surface model based on an artificial neural network (ann) to approximate the goal-function. it reduces the tremendous computational cost55of evaluating the endwall performance by 3d-cfd.the optimization system consists of three steps. the first one is the training of ann based on the database provided by the orthogonal design of experiment (odoe). the second one is the prediction of the optimal aerodynamic performance of endwall contouring by the combination of aga and ann, as shown in fig.1 with red arrows. finally, comparison of the performance60obtained by cfd with one predicted by the ann is performed. if the design requirements are not achieved, the evaluations computed by cfd are added to the database and the cycle is repeated until the optimal geometry is obtained. for a more detail description of the optimization method,please refer to jin3,4 and ning5. the following subsections summarize some components andtheir application.startodoedesignvariablesend wallcountouringflowsolveragadesignvariablesperformancepredictionannperformanceanalysisdatabasetrainingend65fig. 1 endwall design optimization system1.1endwall parameterizationfig.2presentstheparameterizationof axisymmetric endwallcontouring.the70parameterization was performed using a b-spline curve controlled by six points in axial direction.the axial direction represents the direction of engine axis. in order to maintain c0 continuity of endwall contouring in axial direction, points 1 and 6 are fixed. second point from each end of the curve is used to maintain an approximate c1 continuity. for instance, height of the dependent control point 2, as shown in fig. 2, is set in the way that the slop of line passing through points 175and 2 is close to the slope of starting of contoured. the independent control points 3 and 4 canmove freely. so, there are four design variables for each endwall.12fitted b-spline control polygon fixed control pointsdependent control points3independent control points456fig. 2 axisymmetric endwall parameterization1.2design of experiment80it is well known that the purpose of using rsm is to construct an approximation of the true goal-function (response) from training datas. the accuracy of rsm mostly depends on the quality of the training data selection. in order to minimize the size of training data, a reasonable strategy for training data selection needs to be application. this theory of choosing suitable designs for exploring the entire design space efficiently is known as the design of experiments (doe). it is to85investigate the effective method of establishing database and synthetically analyze to reachoptimal project. there are many different doe approaches. in the present work an orthogonal design of experiment (odoe) has been used. odoe is an efficient method for analyzing multiple factors experiment, which can provide essential information with smallest quantity of samples. after the number of design parameters has been determined, the orthogonal array in90which the factors (design parameters) are orthogonal to each other can be used to organize the experiment. fig. 3 illustrates the odoe strategy for a case of three design parameters (x1, x2, x3)with two levels.1x3 0-1-1-1001 1951.3flow sloverfig. 3 a odoe of three design parameter100the numerical simulation was performed using the commercial cfd package of numeca. the code is based on a cell-centered finite-volume approach to solve the governing compressible rans equations where the one-equation model of spoalart-allmaras was used for turbulence modeling. a five-step runge-kutta algorithm was used for the time-marching. in order to speed up convergence, local time stepping, residual smoothing and multigrid techniques were applied.105110the computational mesh was generated with grid generation tool of numeca/igg software package. for fulfilment the requirement of turbulence model, y+ was controlled within 10.to confirm the accurate prediction of numerical simulation in s-shaped duct with curvatures and pressure gradients, the simulated duct performance was compared with the experiment2. the geometry is shown in fig. 4. the duct without strut was two-dimension. the turbulence model used was spalart-allmaras model. the computational mesh was 541 (axial) by 57 (spanwise) nodes.fig. 4 s-shaped duct rig schematic2the two coefficients used to evaluate the performance of the duct in the paper are the static pressure coefficient and the total pressure loss coefficient. the static pressure coefficient isdefined asc p =p prefp pref(1)115where pref is the static pressure at the reference location, the total pressure loss coefficient is defined asp p = pin pexrefref(2)here p*in and p*ex are the stagnation pressures at inlet and exit respectively.0.40.20-0.2outer wall10.8span0.6expcfd ,spalcp-0.4 inner wall-0.60.4-0.8-1expcfd,spal0.20-0.5 0 0.5 11.5x/l0 0.2 0.4 0.6 0.8 1120125(a) static pressure coefficient distribution (b) exit total pressure loss coefficientfig. 5 comparison of calculation with experimenttwo figures comparing experiments with the calculations are shown in fig. 5. fig. 5(a) shows the static pressure coefficient distribution on the duct walls, fig. 5(b) shows the duct exit spanwise profile of total pressure loss coefficient. for the inner wall, fig. 5(a) and 5(b) show a good agreement between the calculations and the measured static pressure coefficient and profiles of stagnation pressure coefficient at exit. for the outer wall, fig.5(a) shows that the static pressure130135140145150155160165170coefficient is accurately predicted by the spalart-allmaras turbulence model except in the region close to peak where its magnitude is under predicted. fig. 5(b) shows a significant difference between the inner wall and the outer wall. the order of the concave and convex wall curvatures in which the boundary layer experiences and pressure gradients has a significant effect on the development of the boundary layer on each wall. between 65% and 85% height the calculations under predict the loss, while between 85% and 98% height they over predict the loss, as shown infig. 5(b). ortiz2, britchford1pointed that the development of boundary layer is effected byendwall curvatures. the flow in highly curved surface is particularly difficult to model accurately by turbulence models. so, one potential cause for the difference between the predicted and measured spanwise profile of outer wall losses is the lack of modelling of curvature effects in the spalart-allmaras turbulence model.although there is difference between the calculation and the experiment in outer wall, the main flow features of the s-shaped duct could be captured by the numerical model used by this research. according to previous simulation experience, comparative difference between each simulated configuration could still present the information that the mechanism of endwall contouring. therefore, the numerical model was acceptable for this research.1.4numerical optimization methodit is well known that optimization methods can be divided into local and global optimization algorithms. local search algorithms based on gradient techniques are efficient in terms of convergence rate, but are not guaranteed to find the global optimum and can not carry through when the design space is discontinuity. in contrast, global search methods such as genetic algorithms offer the advantage of enhancing the probability of reaching the global optimum. unfortunately, they may require thousands of iterations to obtain the global optimum. it is very time consuming for the 3d numerical simulation of flow field in turbomachinery. therefore, in order to reduce the computational time the optimization approach presented here is performed using the artificial neural network partial substitute for the calculation of flow field. theoptimization method is summarized by jin3 as: firstly, selection of the samples for the ann.the accuracy of the optimization depends on the neural network constructed by the database of design samples. the initial database is provided by an odoe in this research to select the essential information with smallest quantity of samples in design space. secondly, training of the ann. after a sufficiently initial database of samples has been generated, a training process is used to build the neural network. the network contains free parameters to fit database samples. a fitting process is performed by back-propagation of the errors also called learning process. the weight of each node is adjusted to minimize the overall error between the input and the output. after training, the network response surface model is defined. thirdly, searching the global optimum of rsm. the searching process is performed by genetic algorithm. finally, validation for the optimal design. the optimal endwall is evaluated by the 3d flow computation and added to the database. the comparison of the performance obtained by cfd with the one predicted by the neural network response surface model is performed. if there is not a good correlation, another design iteration is started, repeating the same process until the optimum endwall is obtained. at the same time, the database grows after each iteration to provide more information of the design space and therefore to a better prediction of the real optimum.2optimization test caseoptimization case of axisymmetric contouring in s-shaped duct based on the endwall175180185optimization system has been investigated. the aim of the optimization in the present work is to minimize the exit total pressure loss with the duct length constant. the total pressure loss coefficient has been defined by equation (2).2.1original ductthe duct with six struts is investigated in this paper. the meridional channel is shown in fig.6. the non-dimensional parameters of annular s-ducts are r/l, hin/l, aex/ain, rin/hin and t/c. a summary of the main parameters is given in table 1. the last column shows the typical values of parameters of ducts used in current engines according to karakasis6. adopting this classification would reveal the investigated duct to be fairly aggressive.for the calculation of the duct, a long parallel section was used upstream and downstream of the duct to allow for the development of the boundary of layer and to minimize the interference between the duct static pressure filed and the boundary conditions, thus the cfd inlet plane is located 3hin upstream of the duct inlet plane. the total number of mesh grids is 444543. the original duct is shown along with the surface mesh used for cfd analysis in fig. 7. the inlet condition was given total pressure, total temperature and angles of velocity. at the outlet boundary, radial equilibrium was applied with the static pressure being specified.instrutex190fig. 6 the meridional channel of s-shaped ductfig. 7 surface mesh of the original ducttab. 1 main geometric parameters of annular s-ductparameters original typical values of parametersr/l 0.60.30-0.45hin/l 0.3 0.1-0.3 rin/l 1.5 1.5-1.7 t/c0.24 0.14-0.30aex/ain 1.0 0.6-0.7195200fig. 8 shows the calculated pressure distribution around strut at 5% and 50% span in the original duct. there is a change in gradient at rear of strut in both lines. this indicates that the strut has a hub corner separation. the computed near wall streamlines on the strut is shown in fig. 9, from which the size and location of hub corner separation can be obtained. the separation occurs at approximately 45% of chord after the maximum strut thickness (40% chord). another significant phenomenon is the radial migration of the low momentum fluid because of the radial pressure gradient generated by wall curvatures. the low momentum fluid migrates to 70% of span. the separation results in a large-scale blockage in the duct and a rise in loss coefficient. the calculation of total pressure loss coefficient was 0.096. the loss coefficient distribution at exit surface is shown in fig. 13(a). the effect of the strut hub corner separation can be observed as thehigh loss region between 50% and 80% span.20510.5cp0-0.5-15% span50% span-1.500.20.