基于伴随方法的涡扇发动机涵道的气动噪声优化设计研究
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摘要
飞机噪声问题对持续增长的航空运输业提出一个重要的问题。其噪声级的大小直接关系到飞机适航签证的获取。这对于我国正在研制的民用客机来说，无疑是巨大的挑战。风扇噪声是现代民用飞机在起飞和降落状态下的主要声源。通过优化发动机涵道外形来降低风扇噪声是一种行之有效的方法。伴随方法具有梯度计算几乎与设计变量数目无关的显著优势,较好地克服了气动噪声优化中计算开销大的问题,使得进行多参数低噪声优化设计成为可能,有着很大的研究价值和广阔应用前景。然而，伴随方法用于发动机涵道减噪优化还处于初步探索阶段，有许多科学问题亟需解决。
本文首次提出并发展了基于连续伴随方法的气动噪声优化设计理论，突破了一般优化算法在多设计变量下的计算效率低的瓶颈问题。研究与发展了非定常伴随方程的高阶有限差分数值求解方法及相应梯度公式的数值求解方法。在此基础上，结合本文发展的减噪设计理论，针对进气道和外涵道减噪问题，分别提出适合各自问题的减噪设计算法，开展了进气道和外涵道减噪问题研究，有效降低了从涵道辐射到远场的噪声，解决了涵道的多参数设计计算量大的难题。从而，为涡扇发动机涵道多参数减噪设计探索出一条高效可靠的新路。
论文的主要研究内容如下：
（1）研究了单音噪声在涡扇发动机进气道中传播和远场辐射过程。通过求解二维轴对称线性欧拉方程(2.5D LEE)研究了单个傅立叶声模态的近场传播过程，然后采用FW-H积分计算远场的声压级。发展了高精度进气道噪声计算工具，通过NASA JT15D静态测试实验的数据验证其正确性，然后详细探究了典型进气道噪声传播机理，得出了衍射和折射效应是两个影响声波传播方向的机制。而且衍射效应是更主要的影响因素。
（2）研究了单音噪声在涡扇发动机外涵道中传播和远场辐射过程。由于外涵道流体与外部流体之间出现剪切层，使得无法直接使用频域有限元、无限元和LEE方法。本文通过求解声扰动方程（2.5D APE）来模拟近场声传播，解决了计算放大的问题，最后利用FW-H积分得到远场指向性特征。发展了高精度外涵道噪声预测工具，其正确性通过使用TURNEX项目的外涵道实验数据得到验证。
（3）首次系统地提出了基于连续伴随方法的气动噪声优化设计理论。提出了合适的减噪设计的目标函数及约束条件，发展了目标函数取在积分线上的减噪优化方法。在计算坐标系下详细推导了LEE的非定常伴随方程，伴随边界条件以及关键的梯度表达式。针对伴随方程的数学性质,研究与发展了伴随方程的高阶有限差分数值求解方法及相应梯度公式的数值求解方法,较好解决了非定常伴随方程和梯度公式的数值求解问题。利用该优化方法，可一次性求出所有设计变量的梯度值，从而大大提高了减噪设计的效率。
(4)提出了基于连续伴随理论和2.5D LEE方程的进气道减噪设计算法。推导了2.5D LEE的伴随方程及边界条件,并给出了最终梯度求解形式。通过利用网格扰动技术,避免了优化设计过程中多次生成计算网格的问题,获得了度量矩阵变分来进行梯度求解。使用Hicks-Henne函数来描述设计变量扰动对进气道表面的影响。优化设计过程使用拟牛顿优化算法,在不同背景流条件和噪声模态下，成功地进行了高达50个设计变量的典型进气道的减噪问题研究，取得显著的减噪效果。
(5)提出了基于连续伴随理论和2.5D APE方程的外涵道减噪设计算法。导出了2.5D APE的非定常伴随方程及相应物面边界条件以及梯度表达式,应用高精度有限差分法对其进行了有效的数值求解。基于最速下降算法,对含实验数据的TURNEX外涵道，在不同背景流条件和噪声模态下，成功进行了含48个设计变量的减噪设计。最优外形取得显著减噪效果。
Aircraft noise problems raised an important question for the air transportindustry with sustained growth. The obtaining of the aircraft airworthinesscertification directly depends on its noise level. It is undoubtedly a hugechallenge to the developing of China's civil aircraft. Fan noise is the primarysound source of modern civil aircraft during takeoff and landing condition.It’s an effective method to reduce the fan noise by optimizing the shape ofengine duct. The major advantage of the adjoint method is that thecomputation of the sensitivity derivatives of cost function with respect todesign variables is nearly independent of the number of design variables,which greatly saves the computational cost and well overcomes largecomputational overhead of the aeroacoustic optimization problem, making itpossible for multi-parameter optimization design for low-noise. It has greatresearch value and broad application prospects. Nevertheless, relevantresearch on this aspect is preliminary, and many scientific issues should befurther investigated.
In this thesis, the aeroacoustic optimization design theory based on theadjoint method has been proposed for the first time. Not like the generaloptimization method, the bottlenecks of the inefficiency of calculating thegradient is broke through by this method.The numerical algorithms of solvingthe unsteady adjoint equations for LEE have been developed by using high-order finite difference methodology. The numerical solution of thecorresponding gradient formula also has been exploited. Base on theaeroacoustic optimization design theory developed in this paper, theaeroacoustic optimization algorithms of turbofan engine inlet and bypass duct are proposed and the multi-parameter aeroacoustic optimization designexamples for ducts have been done successfully. The noise radiated to the far-field is reduced effectively and the intensive computational cost of the multi-parameter noise design problems is solved.Thereby, a novel optimizationapproach with high efficiency and reliability has been devised for low-noisedesign of turbofan engine inlet and bypass duct.
The main work and contributions of the present thesis are as follows:
(1) The near field propagation mehanisim and far-field radiationdirectivity of a tone noise at the inlet of the turbofan engine is studied. Thenear field propagation is studied by solving the two-dimensionalaxisymmetric linear Euler equation (2.5D LEE), then the far-field soundpressure level is calculated through the FW-H integration. The high-precisionnoise calculation tool of inlet is developed. And its correctness is validated bythe experimental data of NASA JT15D static testing. Base on that, thepropagation mechanisms of a tone noise at a typical intake are explored indetail. It’s obtained that diffraction and refraction effects are two mechanismsaffecting the direction of wave propagation. And diffraction effects are moreimportant factors.
(2) The near field propagation mechanisim and far-field radiationdirectivity of a tone noise at the bypass duct of the turbofan engine is studied.The prediction of aft radiated fan noise from turbofan aero-engines ischallenging for conventional numerical schemes, more so than for thecorresponding intake problem. The major complicating factor in the case ofthe bypass duct is the presence of a mixing shear layer between the bypassstream and the external flow. This precludes the straightforward use offrequency-domain finite, infinite element (FE/IE) method and LEE.The meanflow field is calculated using the FLUENT before the simulation of the near-field sound propagation by solving the acoustic perturbation equations (2.5DAPE), avoiding the problem of numerical amplification, and finally far-fielddirectivity characteristics is obtained by the use of FW-H integration. Thenoise prediction tool of bypass duct with high-precision is further developed. The predicted results compared very well with the correspondingexperimental data of TURNEX bypass duct.
(3) The aeroacoustic optimization design theory based on the adjointmethod is put forward creatively. After the noise cost function and constraintsare properly proposed, the adjoint-based optimization method for noisereduction is developed with the acoustic objective function defined on theintegral line. The corresponding unsteady adjoint equation of LEE, adjointboundary conditions and critical gradient expression are derived in Cartesiancoordinate system in detail. The numerical algorithm of solving the unsteadyadjoint equations for LEE have been developed by using high-order finitedifference methodology after analysing the mathematical nature of unsteadyadjoint equation. The numerical solution of the corresponding gradientformula also has been exploited. With this optimization theory, one can obtainall the gradient value of the design variables once, thus greatly improving theefficiency of the low-noise design.
(4) The aeroacoustic optimization algorithms of turbofan engine inletbased on the2.5D LEE and its adjoint formular is proposed. Thecorresponding adjoint equations and boundary conditions of2.5D LEE arederived first, and the final forms of the gradient expression are given. Thegrid perturbation technique is adopted, avoiding the repeat generation of thecomputational grid during the design process, and the metrics are obtained forthe solution of Gradient. The influence of perturbation of the design variableson the inlet surface is described by Hicks-Henne function. The quasi-Newtonoptimization algorithm is used and some practical design tests for inlet ductsshow that, for the different flow condition and modal noise condition, thecontinuous adjoint approach is highly effective and useful for multi-parameteraeroacoustic optimization design with up to50design variables.
(5) At the same time, we have done the research of aeroacousticoptimum design for bypass ducts by using2.5D APE.The aeroacousticoptimization algorithms of turbofan engine bypass duct based on the2.5DAPE and its adjoint formular is also proposed.The corresponding unsteady adjoint equations and boundary conditions of2.5D APE are derived, and theexpressions of the gradient expression are given. The adjoint equations aresolved by using high-order finite difference scheme. The steepest descentmethod is used and with up to48design variables, the multi-parameteraeroacoustic optimization design examples for TURNEX bypass ducts havebeen done successfully for the different flow condition and modal noisecondition.
本文首次提出并发展了基于连续伴随方法的气动噪声优化设计理论，突破了一般优化算法在多设计变量下的计算效率低的瓶颈问题。研究与发展了非定常伴随方程的高阶有限差分数值求解方法及相应梯度公式的数值求解方法。在此基础上，结合本文发展的减噪设计理论，针对进气道和外涵道减噪问题，分别提出适合各自问题的减噪设计算法，开展了进气道和外涵道减噪问题研究，有效降低了从涵道辐射到远场的噪声，解决了涵道的多参数设计计算量大的难题。从而，为涡扇发动机涵道多参数减噪设计探索出一条高效可靠的新路。
论文的主要研究内容如下：
（1）研究了单音噪声在涡扇发动机进气道中传播和远场辐射过程。通过求解二维轴对称线性欧拉方程(2.5D LEE)研究了单个傅立叶声模态的近场传播过程，然后采用FW-H积分计算远场的声压级。发展了高精度进气道噪声计算工具，通过NASA JT15D静态测试实验的数据验证其正确性，然后详细探究了典型进气道噪声传播机理，得出了衍射和折射效应是两个影响声波传播方向的机制。而且衍射效应是更主要的影响因素。
（2）研究了单音噪声在涡扇发动机外涵道中传播和远场辐射过程。由于外涵道流体与外部流体之间出现剪切层，使得无法直接使用频域有限元、无限元和LEE方法。本文通过求解声扰动方程（2.5D APE）来模拟近场声传播，解决了计算放大的问题，最后利用FW-H积分得到远场指向性特征。发展了高精度外涵道噪声预测工具，其正确性通过使用TURNEX项目的外涵道实验数据得到验证。
（3）首次系统地提出了基于连续伴随方法的气动噪声优化设计理论。提出了合适的减噪设计的目标函数及约束条件，发展了目标函数取在积分线上的减噪优化方法。在计算坐标系下详细推导了LEE的非定常伴随方程，伴随边界条件以及关键的梯度表达式。针对伴随方程的数学性质,研究与发展了伴随方程的高阶有限差分数值求解方法及相应梯度公式的数值求解方法,较好解决了非定常伴随方程和梯度公式的数值求解问题。利用该优化方法，可一次性求出所有设计变量的梯度值，从而大大提高了减噪设计的效率。
(4)提出了基于连续伴随理论和2.5D LEE方程的进气道减噪设计算法。推导了2.5D LEE的伴随方程及边界条件,并给出了最终梯度求解形式。通过利用网格扰动技术,避免了优化设计过程中多次生成计算网格的问题,获得了度量矩阵变分来进行梯度求解。使用Hicks-Henne函数来描述设计变量扰动对进气道表面的影响。优化设计过程使用拟牛顿优化算法,在不同背景流条件和噪声模态下，成功地进行了高达50个设计变量的典型进气道的减噪问题研究，取得显著的减噪效果。
(5)提出了基于连续伴随理论和2.5D APE方程的外涵道减噪设计算法。导出了2.5D APE的非定常伴随方程及相应物面边界条件以及梯度表达式,应用高精度有限差分法对其进行了有效的数值求解。基于最速下降算法,对含实验数据的TURNEX外涵道，在不同背景流条件和噪声模态下，成功进行了含48个设计变量的减噪设计。最优外形取得显著减噪效果。
Aircraft noise problems raised an important question for the air transportindustry with sustained growth. The obtaining of the aircraft airworthinesscertification directly depends on its noise level. It is undoubtedly a hugechallenge to the developing of China's civil aircraft. Fan noise is the primarysound source of modern civil aircraft during takeoff and landing condition.It’s an effective method to reduce the fan noise by optimizing the shape ofengine duct. The major advantage of the adjoint method is that thecomputation of the sensitivity derivatives of cost function with respect todesign variables is nearly independent of the number of design variables,which greatly saves the computational cost and well overcomes largecomputational overhead of the aeroacoustic optimization problem, making itpossible for multi-parameter optimization design for low-noise. It has greatresearch value and broad application prospects. Nevertheless, relevantresearch on this aspect is preliminary, and many scientific issues should befurther investigated.
In this thesis, the aeroacoustic optimization design theory based on theadjoint method has been proposed for the first time. Not like the generaloptimization method, the bottlenecks of the inefficiency of calculating thegradient is broke through by this method.The numerical algorithms of solvingthe unsteady adjoint equations for LEE have been developed by using high-order finite difference methodology. The numerical solution of thecorresponding gradient formula also has been exploited. Base on theaeroacoustic optimization design theory developed in this paper, theaeroacoustic optimization algorithms of turbofan engine inlet and bypass duct are proposed and the multi-parameter aeroacoustic optimization designexamples for ducts have been done successfully. The noise radiated to the far-field is reduced effectively and the intensive computational cost of the multi-parameter noise design problems is solved.Thereby, a novel optimizationapproach with high efficiency and reliability has been devised for low-noisedesign of turbofan engine inlet and bypass duct.
The main work and contributions of the present thesis are as follows:
(1) The near field propagation mehanisim and far-field radiationdirectivity of a tone noise at the inlet of the turbofan engine is studied. Thenear field propagation is studied by solving the two-dimensionalaxisymmetric linear Euler equation (2.5D LEE), then the far-field soundpressure level is calculated through the FW-H integration. The high-precisionnoise calculation tool of inlet is developed. And its correctness is validated bythe experimental data of NASA JT15D static testing. Base on that, thepropagation mechanisms of a tone noise at a typical intake are explored indetail. It’s obtained that diffraction and refraction effects are two mechanismsaffecting the direction of wave propagation. And diffraction effects are moreimportant factors.
(2) The near field propagation mechanisim and far-field radiationdirectivity of a tone noise at the bypass duct of the turbofan engine is studied.The prediction of aft radiated fan noise from turbofan aero-engines ischallenging for conventional numerical schemes, more so than for thecorresponding intake problem. The major complicating factor in the case ofthe bypass duct is the presence of a mixing shear layer between the bypassstream and the external flow. This precludes the straightforward use offrequency-domain finite, infinite element (FE/IE) method and LEE.The meanflow field is calculated using the FLUENT before the simulation of the near-field sound propagation by solving the acoustic perturbation equations (2.5DAPE), avoiding the problem of numerical amplification, and finally far-fielddirectivity characteristics is obtained by the use of FW-H integration. Thenoise prediction tool of bypass duct with high-precision is further developed. The predicted results compared very well with the correspondingexperimental data of TURNEX bypass duct.
(3) The aeroacoustic optimization design theory based on the adjointmethod is put forward creatively. After the noise cost function and constraintsare properly proposed, the adjoint-based optimization method for noisereduction is developed with the acoustic objective function defined on theintegral line. The corresponding unsteady adjoint equation of LEE, adjointboundary conditions and critical gradient expression are derived in Cartesiancoordinate system in detail. The numerical algorithm of solving the unsteadyadjoint equations for LEE have been developed by using high-order finitedifference methodology after analysing the mathematical nature of unsteadyadjoint equation. The numerical solution of the corresponding gradientformula also has been exploited. With this optimization theory, one can obtainall the gradient value of the design variables once, thus greatly improving theefficiency of the low-noise design.
(4) The aeroacoustic optimization algorithms of turbofan engine inletbased on the2.5D LEE and its adjoint formular is proposed. Thecorresponding adjoint equations and boundary conditions of2.5D LEE arederived first, and the final forms of the gradient expression are given. Thegrid perturbation technique is adopted, avoiding the repeat generation of thecomputational grid during the design process, and the metrics are obtained forthe solution of Gradient. The influence of perturbation of the design variableson the inlet surface is described by Hicks-Henne function. The quasi-Newtonoptimization algorithm is used and some practical design tests for inlet ductsshow that, for the different flow condition and modal noise condition, thecontinuous adjoint approach is highly effective and useful for multi-parameteraeroacoustic optimization design with up to50design variables.
(5) At the same time, we have done the research of aeroacousticoptimum design for bypass ducts by using2.5D APE.The aeroacousticoptimization algorithms of turbofan engine bypass duct based on the2.5DAPE and its adjoint formular is also proposed.The corresponding unsteady adjoint equations and boundary conditions of2.5D APE are derived, and theexpressions of the gradient expression are given. The adjoint equations aresolved by using high-order finite difference scheme. The steepest descentmethod is used and with up to48design variables, the multi-parameteraeroacoustic optimization design examples for TURNEX bypass ducts havebeen done successfully for the different flow condition and modal noisecondition.
引文
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