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.

Two-Dimensional Riemann Problems:Transonic Shock Waves and Free Boundary Problems

We are concerned with global solutions of multidimensional(M-D)Riemann problems for nonlinear hyperbolic systems of conservation laws,focusing on their global configurations and structures.We present some recent developments in the rigorous analysis of two-dimensional(2-D)Riemann problems involving transonic shock waves through several prototypes of hyperbolic systems of conservation laws and discuss some further M-D Riemann problems and related problems for nonlinear partial differential equations.In particular,we present four different 2-D Riemann problems through these prototypes of hyperbolic systems and show how these Riemann problems can be reformulated/solved as free boundary problems with transonic shock waves as free boundaries for the corresponding nonlinear conservation laws of mixed elliptic-hyperbolic type and related nonlinear partial differential equations.

TIME MARCHING INTEGRAL EQUATION METHOD FOR UNSTEADY TRANSONIC FLOWS

In this paper,we have proposed a time marching intregral equation method which does not have the limitation of the time linearized integral equation method in that the latter method can not satisfac- torily simulate the shock-wave motions.Firstly,a model problem——one dimensional initial and boundary value wave problem is treated to clarify the basic idea of the new method.Then the method is implemented for 2-D and 3-D unsteady transonic flow problems.The introduction of the concept of a qua- si-velocity-potential simplifies the time marching integral equations and the treatment of trailing vortex sheet condition.The numerical calculations show that the method is reasonable and reliable.

NUMERICAL METHOD FOR SOLVING THE EULER EQUATION FOR UNSTEADY TRANSONIC FLOWS OVER OSCILLATING AIRFOILS

Through transformations, the time-dependent boundary condition on the airfoil contour and the boundary condition at infinity are brought fixed to the boundaries of a finite domain. The boundary conditions can thus be satisfied exactly without increasing the computational time. The novel scheme is useful for computing transonic, strong disturbance, unsteady flows with high reduced frequencies. The scheme makes use of curvefitted orthogonal meshes and the lattice control technique to obtain the optimal grid distribution. The numerical results are satisfactory.

Fourier time spectral method for subsonic and transonic flows

The time accuracy of the exponentially accurate Fourier time spectral method（TSM） is examined and compared with a conventional 2nd-order backward difference formula（BDF） method for periodic unsteady flows. In particular, detailed error analysis based on numerical computations is performed on the accuracy of resolving the local pressure coefficient and global integrated force coefficients for smooth subsonic and non-smooth transonic flows with moving shock waves on a pitching airfoil. For smooth subsonic flows, the Fourier TSM method offers a significant accuracy advantage over the BDF method for the prediction of both the local pressure coefficient and integrated force coefficients. For transonic flows where the motion of the discontinuous shock wave contributes significant higherorder harmonic contents to the local pressure fluctuations,a sufficient number of modes must be included before the Fourier TSM provides an advantage over the BDF method.The Fourier TSM, however, still offers better accuracy than the BDF method for integrated force coefficients even for transonic flows. A problem of non-symmetric solutions for symmetric periodic flows due to the use of odd numbers of intervals is uncovered and analyzed. A frequency-searching method is proposed for problems where the frequency is not known a priori. The method is tested on the vortex shedding problem of the flow over a circular cylinder.

Generation of Dynamic Grids and Computation of Unsteady Transonic Flows around Assemblies

Algebraic methods and rapid deforming techniques are used to generate three-dimensional boundary-fitted dynamic grids for assemblies. The conservative full-potential equation is solved by a time-accurate approximate factorization algorithm and internal Newton iterations. An integral boundary layer method based on the dissipation integral is used to account for viscous effects. The computational results about unsteady transonic forces on wings, bodies and control surfaces are in agreement with experimental data.

Hierarchical Evolutionary Algorithms and Its Application in Transonic Airfoil Optimization in Aerodynamics

Hierarchical evolutionary algorithms based on genetic algorithms (GAs) and Nash strategy of game theory are proposed to accelerate the optimization process and implemented in transonic aerodynamic shape optimization problems Inspired from the natural evolution history that different periods with certain environments have different criteria for the evaluations of individuals’ fitness, a hierarchical fidelity model is introduced to reach high optimization efficiency The shape of an NACA0012 based airfoil is optimized in maximizing the lift coefficient under a given transonic flow condition Optimized results are presented and compared with the single model results and traditional GA

Unsteady Inverse Problem of Type B for 2-D Transonic Flow: A Variational Formulation

A family of variational principles (VP) has been developed for the unsteady inverse problem of the second type I B. It opens new ways for the inverse shape design of unsteady airfoils and can serve as key basis of multipoint inverse shape design of steady airfoils and cascades.

UNSTEADY TRANSONIC AERODYNAMIC LOADINGS ON THE AIRFOIL CAUSED BY HEAVING, PITCHING OSCILLATIONS AND CONTROL SURFACE

An implicit upwind finite volume solver for the Euler equations using the improved flux - splitting method is established and used to calculate the transonic flow past the airfoils with heaving, pitching oscillations and the control surface. Results are given for the NACA64A - 10 airfoil which is in harmonic heaving and pitching oscillation and with the control surface in the transonic flow field. Some computational results are compared with the experiment data and the good agreements are shown in the paper.

Multiple solutions and stability of the steady transonic small-disturbance equation

Numerical solutions of the steady transonic small-disturbance（TSD） potential equation are computed using the conservative Murman-Cole scheme. Multiple solutions are discovered and mapped out for the Mach number range at zero angle of attack and the angle of attack range at Mach number 0.85 for the NACA 0012 airfoil. We present a linear stability analysis method by directly assembling and evaluating the Jacobian matrix of the nonlinear finite-difference equation of the TSD equation. The stability of all the discovered multiple solutions are then determined by the proposed eigen analysis. The relation of stability to convergence of the iterative method for solving the TSD equation is discussed. Computations and the stability analysis demonstrate the possibility of eliminating the multiple solutions and stabilizing the remaining unique solution by adding a sufficiently long splitter plate downstream the airfoil trailing edge. Finally, instability of the solution of the TSD equation is shown to be closely connected to the onset of transonic buffet by comparing with experimental data.

An improved deviation model for transonic stages in axial compressors

Deviation model is an important model for through-flow analysis in axial compressors.Theoretical analysis in classical deviation models is developed under the assumption of onedimensional flow,which is controlled by the continuity equation.To consider three-dimensional characteristics in transonic flow,this study proposes an improved theoretical analysis method combining force analysis of the blade-to-blade flow with conventional analysis of the continuity equation.Influences of shock structures on transverse force,streamwise velocity and streamline curvature in the blade-to-blade flow are analyzed,and support the analytical modelling of density flow ratio between inlet and outlet conditions.Thus,a novel deviation model for transonic stages in axial compressors is proposed in this paper.The empirical coefficients are corrected based on the experimental data of a linear cascade,and the prediction accuracy is validated with the experimental data of a three-stage transonic compressor.The novel model provides accurate predictions for meridional flow fields at the design point and performance curves at design speed,and shows obvious improvements on classical models by Carter and C¸etin.

叶片开缝和边界层抽吸耦合控制压气机失速裕度的数值研究

为了进一步优化压气机的整体性能,提出三种叶片开缝和边界层抽吸的耦合流动控制方案。首先,利用数值模拟的方法,研究叶片开缝或边界层抽吸对跨声速轴流压气机流场结构的影响机理。然后,详细研究了边界层抽吸分别与三种不同叶片开缝的耦合流动控制方案对压气机整体性能的影响。研究结果表明,与叶片开缝或边界层抽吸的单独应用相比,三种耦合流动控制方案都使压气机实现了更宽的稳定裕度。全叶片开缝与边界层抽吸的耦合方案稳定裕度改进量为1.27%,中间叶高开缝的耦合方案和上半叶高开缝的耦合方案稳定裕度改进量分别为1.67%和1.35%;在近失速点处,相比较全叶片开缝与边界层抽吸的耦合方案,局部开缝与边界层抽吸的耦合方案应用后,总压损失和效率降低;上半叶高开缝的耦合方案在三种耦合方案中稳定裕度最高,所以叶片开缝和边界层抽吸的耦合方案是可行的。

Double-decoupled inverse design of natural laminar flow nacelle under transonic conditions

The inverse design based on the pressure distribution is an essential approach to realize the improvement of Natural Laminar Flow(NLF) performance for nacelles. However, the direct definition of target pressure distribution at design point is challenging for the dilemma to consider the constraints of shock wave and laminar flow at the same time. In addition, the universality of method will be limited when the inverse design is strongly coupled with the solver. Thus, a double-decoupled methodology based on the relationship of pressure distributions between design and off-design points is proposed in this paper, which realizes the decoupling of constraints in shock wave and laminar flow on target pressure distribution as well as the decoupling of flow field solution and inverse design method. Aimed at an isolated flow-through-nacelle of high bypass ratio, the target pressure distribution with appropriate favorable gradient and shock-free feature is defined according to physical principles at the off-design point of Ma = 0.80 while the transonic and laminar performance are examined at the design point of Ma = 0.85. The solution of flow field is based on γ-Re_(θ) transition model and the inverse design is based on residual-correction method. With the inverse design starting from off-design point, the performance of shock wave and laminar flow at design point are both improved. The local shock wave after the lip of nacelle is eliminated effectively while the streamwise length of laminar flow region is doubled and exceeds to 30% of the chord length. The percentage of drag reduction for outboard surface is 12.7% for friction drag, 7.8%for pressure drag and 10.5% for total drag. The effects of inverse design on the process of transition are analyzed with detailed flow features. The robustness of laminar flow is examined under different variation factors of freestream which are deviated from the design point.

跨声速自然层流标模CRM-NLF风洞试验快速转捩预测

中国商飞北研中心开发了快速CFD分析工具CFAST进行层流基本流场计算,单工况的计算时间仅为200 s,然后耦合转捩预测模块进行转捩预测分析,大幅缩减了计算周期,从而实现跨声速民机典型后掠机翼三维边界层的快速转捩预测。转捩预测模块基于线性稳定性理论的双e^(N)方法,可以同时考虑横流驻波不稳定模态和Tollmien-Schlichting波不稳定模态对转捩的影响。目前,公开的跨声速高雷诺数民机自然层流试验数据十分稀缺,本文以NASA公开的跨声速高雷诺数自然层流标模CRM-NLF为研究对象,研究了迎角、雷诺数和马赫数对转捩的影响。计算结果与试验结果以及基于RANS的转捩计算结果吻合很好,说明开发的快速转捩预测工具高效可靠,可以用于跨声速民机层流机翼设计和优化。

Numerical method for sound propagation with acoustic shock waves in transonic flow ducts

The fourth order MacCormack scheme with fourth viscous term is used to improve the shocked solutions for sound propagation in varying cross area and hard-wall ducts with transonic flow. The artificial viscous coefficient is given out by an empirical formula. It is shown from three calculation examples of acoustic shock waves that the new method is much better than the second order MacCormack method which is the best one of second order schemes. Moreover, CPU times of both methods are almost the same.

基于黏性伴随方法的跨声速机翼气动优化设计

进行了基于黏性伴随方法和Navier-Stokes方程的跨声速机翼气动优化设计研究。分别推导了适用于三维跨声速机翼气动反设计和减阻设计的黏性伴随方程、边界条件和梯度求解表达式,并研究了伴随方程的数值求解方法。通过将网格生成、流场计算、黏性伴随方程数值求解、梯度求解和拟牛顿优化算法等几方面的有效结合,发展了一种跨声速机翼气动优化设计方法。为了提高计算效率,将多重网格方法应用到方程的数值求解中来加速收敛。跨声速机翼反设计和减阻设计算例验证了本文所发展的方法的正确性。采用本文的方法进行优化设计,一般通过20～30次迭代就能得到满意的结果。

跨音速透平扭叶片的气动优化设计研究

以并行自适应差分进化算法为核心,耦合曲面造型方法以及计算流体动力学求解技术,发展了一种适用于叶轮机械三维气动优化设计的全局自动气动优化算法.利用该算法,以等熵效率最高为目标,在满足流量约束的条件下对跨音速扭叶片进行了气动优化设计.对优化结果的详细分析表明,最优叶栅的等熵效率比原始叶栅提高了1.1%,气动性能有显著的改善,算法具有良好的优化性能.在跨音速条件下,载荷分布对叶栅的气动性能有着巨大的影响,采用前加载设计可有效地减弱斜激波的强度,减少激波损失,提高流动效率.因此,通过优化叶栅型线来改变叶栅的载荷分布可有效地提高叶栅的气动性能.

人参总皂苷超声提取工艺的研究

目的优选人参总皂苷的超声波提取工艺。方法采用正交设计通过比色法对不同超声处理条件下的人参总皂苷含量进行测定。结果超声-比色法测人参总皂苷的最佳工艺为:水饱和正丁醇提取、超声时间60分钟、超声2次、不萃取。结论该方法简便、准确,可用于人参总皂苷含量评价。

一种跨声速翼型设计方法及设计诸例

本文采用正反迭代、余量修正的设计思想,发展了一种能迅速达到指定目标压力分布的跨声速翼型设计方法。提出了推导各积分的解析表达式取代数值积分、加权光顺过程、直接含粘性迭代和进行矩阵状态分析等有效的改进措施,克服了现有设计方法中的主要缺陷。在设计软件中,正计算程序作为一个“插件”与反设计部分耦合,因此可以方便地与新的正计算方法组合以提高整个设计系统的先进性。对多种超临界、无激波、自然层流压力分布及低速翼型的设计实例表明,本方法只需少数几次设计迭代即可以设计出准确收敛于目标的新翼型。

跨声速多级轴流压气机特性预估及分析

为了研究跨声速轴流压气机的性能分析问题,采用流线曲率法结合损失落后角模型,发展了一种利用反问题方程求解正问题的数值方法。在NASA低速平面叶栅试验数据的基础上考虑三维效应的修正,根据激波结构随工况的变化发展了一种新的激波损失计算方法,整理了一套适合跨声速轴流压气机的损失落后角模型。对两级跨声速轴流风扇进行了数值模拟研究,进行了设计工况的校核计算和全工况特性预测,并将计算结果与NASA试验值进行了比较分析。结果显示,设计点计算误差在1.1%以下,非设计点也能得到与试验值吻合的趋势,表明所建立的方法和模型可以有效地对跨声速多级轴流压气机进行全工况特性预测。