超声速飞行器烧蚀与结构热耦合计算及气动伺服弹性分析
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摘要
学位论文的主要研究问题是超声速飞行器在气动加热条件下烧蚀防热层与三维结构的耦合热传导分析技术,以及气动-伺服-弹性耦合动力学建模和分析。结构振动引起非定常气动力,而气动力又将影响结构的运动。在热防护系统的保护下,飞行器结构由于气动加热所引起的结构变形与结构振动引起的变形相比非常有限,因此对非定常气动力的影响很小。结构小幅振动时对气动热的影响可以忽略不计,但是气动加热引起的结构升温会明显改变飞行器结构的固有频率和模态,在最为关心的动气动-弹性问题中,为了提高计算效率,计算往往在模态坐标下进行,因此必须考虑气动加热对结构固有频率和固有模态的影响。
结构瞬态温度场随时间的变化导致飞行器结构动力学特性也随时间变化,使得结构成为时变系统,但是由于结构振动的周期远小于结构升温的特征时间,因此在较短时程内分析气动-弹性等结构动力学问题时可以凝固结构温度场。将结构近似地作为时不变系统加以分析,利用该时程内的平均温度场对飞行器结构进行热模态分析,进而利用热模态信息进行气动-弹性耦合系统建模。由此,可以将非定常气动力、气动加热和热防护、飞行器结构和伺服控制系统之间的多场耦合动力学问题,在具体求解的时候分解为两个独立的动力学问题来求解：1)烧蚀热防护-结构耦合传热分析；2)非定常气动力-伺服系统-飞行器结构耦合动力学分析。两者之间通过结构热模态分析串联起来。
学位论文研究的主要内容包括：
1)提出了一种将自行编制用于烧蚀防热层计算的程序与大型通用有限元程序相结合、解决气动加热作用下带有烧蚀热防热层的复杂飞行器结构的传热和温度场分析方法,并在工程中得到应用。首先针对碳化型烧蚀材料进行研究,根据其数学模型推导了用于求解移动边界传热问题的有限差分计算格式,并对移动边界问题的求解进行了验证。以超声速导弹为研究对象,为需要进行热防护的结构表面按结构表面单元加装一定厚度的防热层,编写程序实现两者之间的数据交换,并通过交替算法来实现两者在界面处的热流平衡和温度协调,最终实现烧蚀防热层-结构耦合传热及温度场分析,得到了烧蚀层的消耗情况和结构的升温情况。并对结构进行热模态计算,分析了结构升温引起的飞行器模态频率的变化。
2)提出了一种面向耦合系统稳定性分析的统一的非定常气动力数学表达式,分别将结构振动引起的非定常气动力和伺服控制面偏转引起的控制力进行等效变换,将其表示成这种统一的数学形式,并通过引入辅助变量将这一形式的气动力模型转换成与结构动力学方程一致的二阶常微分的形式,作为结构质量、阻尼和刚度的附加项,便于在结构动力学框架下进行非定常气动力-伺服系统-弹性结构相互耦合情况下的动稳定性分析,即气动-伺服-弹性稳定性分析。首先以一大展弦比机翼颤振边界计算作为验证算例,气动力计算采用经典的Theodorsen模型,验证了这种方法的可行性；再以带伺服控制系统的超声速飞行器作为研究对象,气动力用当地流活塞理论计算。将伺服系统的传递函数做类似的等效变换,将控制面偏转引起的气动力同样用上述统一的气动力模型表示,建立了气动-伺服-弹性耦合的新模型实现在结构动力学框架内通过特征值求解来进行气动-伺服-弹性稳定性分析。给出了在不同马赫数和不同攻角下的超声速飞行器的伺服颤振边界。
The research of this thesis is focused on the heat transfer analysis of ablative thermal protection coupled with structure of the supersonic aircraft with the aerodynamic heating and the modeling and analysis of the aero-servo-elasticity. The vibration of the structure induces the unsteady aerodynamic force, and the aerodynamic force changes the structure deformation. Under the protection of the ablative system, the structure deformation of the aircraft caused by aerodynamic heating is much smaller than that caused by structure vibration, so it has little influence on the unsteady aerodynamic force. When the amplitude of structure vibration is small, the influence of it on aero-heating can be neglected, but the temperature rising caused by aerodynamics changes the natural frequencies and modal shapes of structure. In the analysis of dynamic aero-elasticity problem, the governing equations are always established in the modal coordinates, so the influence of the aero-heating on the natural frequencies and modal shapes cannot be ignored.
The changing of the transient temperature field of the structure with time results that the structural dynamic characteristics also changes with time, which make the structure a time-varying system. It is known that the cycle of the structural vibration is much shorter than the characteristic time of the temperature changing of the structure, so the temperature field can be solidified when the time period of the structural dynamic analysis is short. The structure can be regarded as a time-invariant system approximatively, and the modal analysis with aero-heating can be carried out with the average temperature in that time period. Therefore, the multi-physics coupling dynamic problem considering unsteady aerodynamic force, aerodynamic heating&thermal protection, aircraft structure and servo control system can be divided into two individual dynamic problems:1) thermal protection-structure coupled heat transfer analysis; 2) unsteady aerodynamic force-servo-aircraft structure coupled dynamic analysis. Two problems are connected by modal analysis with aero-heating.
The main work includes these following sections.
1).The thesis presents a method which combines the ablative thermal protection program with commercial FEM program. It provides an approach that can handle heat transfer and temperature field analysis of complex aircraft with ablative thermal protection. The method has been used in some engineering applications. First, the finite difference schemes of the moving boundary heat transfer problem of ablative material are deduced, and the finite difference program is validated by a simple heat transfer problem. Taking a supersonic missile as the research object, the ablative layers are installed on the surface elements of the structure where need, computer programs have been designed to exchange the data between two programs. A alternate algorithm is used to ensure that interface temperature and heat flux can satisfy the thermal equilibrium condition. After the coupled analysis of ablative protection layer and structure, the temperature rising of the structure and consumption of the ablative material are gotten. The changing of structural natural frequencies are analyzed resulting from the temperature rising.
2).An unsteady aerodynamic force expression is presented and used in the aero-servo-elasticity analysis of a supersonic aircraft. Using equivalent transformation to transform some general aerodynamic models into a uniform mathematical model. By introducing some instrumental variables, this kind of mathematical model can be converted into second order differential equations as the addition items of the mass, damping, and stiffness in structural dynamic equations. Through this transformation, the aero-servo-elasticity problem can be studied by the structural dynamic methods. Taking a high-aspect ratio wing as the research object, the aerodynamic force is calculated by Theodorsen model, and the critical velocity of flutter is obtained and the equivalent transformation of the aerodynamic force is validated. Taking a supersonic aircraft with servo control system as the research object, aeordynamic force are computed by local piston theory. Through the transformation of the transfer function, the control force induced by the deflection of the control surface is converted into that uniform expression. The new coupled model of aero-servo-elasticity is obtained and stability analysis is studied by the complex eigenvalues of the system. The servo-flutter boundaries of this supersonic aircraft with different Mach numbers and different angles of attack are calculated.
结构瞬态温度场随时间的变化导致飞行器结构动力学特性也随时间变化,使得结构成为时变系统,但是由于结构振动的周期远小于结构升温的特征时间,因此在较短时程内分析气动-弹性等结构动力学问题时可以凝固结构温度场。将结构近似地作为时不变系统加以分析,利用该时程内的平均温度场对飞行器结构进行热模态分析,进而利用热模态信息进行气动-弹性耦合系统建模。由此,可以将非定常气动力、气动加热和热防护、飞行器结构和伺服控制系统之间的多场耦合动力学问题,在具体求解的时候分解为两个独立的动力学问题来求解：1)烧蚀热防护-结构耦合传热分析；2)非定常气动力-伺服系统-飞行器结构耦合动力学分析。两者之间通过结构热模态分析串联起来。
学位论文研究的主要内容包括：
1)提出了一种将自行编制用于烧蚀防热层计算的程序与大型通用有限元程序相结合、解决气动加热作用下带有烧蚀热防热层的复杂飞行器结构的传热和温度场分析方法,并在工程中得到应用。首先针对碳化型烧蚀材料进行研究,根据其数学模型推导了用于求解移动边界传热问题的有限差分计算格式,并对移动边界问题的求解进行了验证。以超声速导弹为研究对象,为需要进行热防护的结构表面按结构表面单元加装一定厚度的防热层,编写程序实现两者之间的数据交换,并通过交替算法来实现两者在界面处的热流平衡和温度协调,最终实现烧蚀防热层-结构耦合传热及温度场分析,得到了烧蚀层的消耗情况和结构的升温情况。并对结构进行热模态计算,分析了结构升温引起的飞行器模态频率的变化。
2)提出了一种面向耦合系统稳定性分析的统一的非定常气动力数学表达式,分别将结构振动引起的非定常气动力和伺服控制面偏转引起的控制力进行等效变换,将其表示成这种统一的数学形式,并通过引入辅助变量将这一形式的气动力模型转换成与结构动力学方程一致的二阶常微分的形式,作为结构质量、阻尼和刚度的附加项,便于在结构动力学框架下进行非定常气动力-伺服系统-弹性结构相互耦合情况下的动稳定性分析,即气动-伺服-弹性稳定性分析。首先以一大展弦比机翼颤振边界计算作为验证算例,气动力计算采用经典的Theodorsen模型,验证了这种方法的可行性；再以带伺服控制系统的超声速飞行器作为研究对象,气动力用当地流活塞理论计算。将伺服系统的传递函数做类似的等效变换,将控制面偏转引起的气动力同样用上述统一的气动力模型表示,建立了气动-伺服-弹性耦合的新模型实现在结构动力学框架内通过特征值求解来进行气动-伺服-弹性稳定性分析。给出了在不同马赫数和不同攻角下的超声速飞行器的伺服颤振边界。
The research of this thesis is focused on the heat transfer analysis of ablative thermal protection coupled with structure of the supersonic aircraft with the aerodynamic heating and the modeling and analysis of the aero-servo-elasticity. The vibration of the structure induces the unsteady aerodynamic force, and the aerodynamic force changes the structure deformation. Under the protection of the ablative system, the structure deformation of the aircraft caused by aerodynamic heating is much smaller than that caused by structure vibration, so it has little influence on the unsteady aerodynamic force. When the amplitude of structure vibration is small, the influence of it on aero-heating can be neglected, but the temperature rising caused by aerodynamics changes the natural frequencies and modal shapes of structure. In the analysis of dynamic aero-elasticity problem, the governing equations are always established in the modal coordinates, so the influence of the aero-heating on the natural frequencies and modal shapes cannot be ignored.
The changing of the transient temperature field of the structure with time results that the structural dynamic characteristics also changes with time, which make the structure a time-varying system. It is known that the cycle of the structural vibration is much shorter than the characteristic time of the temperature changing of the structure, so the temperature field can be solidified when the time period of the structural dynamic analysis is short. The structure can be regarded as a time-invariant system approximatively, and the modal analysis with aero-heating can be carried out with the average temperature in that time period. Therefore, the multi-physics coupling dynamic problem considering unsteady aerodynamic force, aerodynamic heating&thermal protection, aircraft structure and servo control system can be divided into two individual dynamic problems:1) thermal protection-structure coupled heat transfer analysis; 2) unsteady aerodynamic force-servo-aircraft structure coupled dynamic analysis. Two problems are connected by modal analysis with aero-heating.
The main work includes these following sections.
1).The thesis presents a method which combines the ablative thermal protection program with commercial FEM program. It provides an approach that can handle heat transfer and temperature field analysis of complex aircraft with ablative thermal protection. The method has been used in some engineering applications. First, the finite difference schemes of the moving boundary heat transfer problem of ablative material are deduced, and the finite difference program is validated by a simple heat transfer problem. Taking a supersonic missile as the research object, the ablative layers are installed on the surface elements of the structure where need, computer programs have been designed to exchange the data between two programs. A alternate algorithm is used to ensure that interface temperature and heat flux can satisfy the thermal equilibrium condition. After the coupled analysis of ablative protection layer and structure, the temperature rising of the structure and consumption of the ablative material are gotten. The changing of structural natural frequencies are analyzed resulting from the temperature rising.
2).An unsteady aerodynamic force expression is presented and used in the aero-servo-elasticity analysis of a supersonic aircraft. Using equivalent transformation to transform some general aerodynamic models into a uniform mathematical model. By introducing some instrumental variables, this kind of mathematical model can be converted into second order differential equations as the addition items of the mass, damping, and stiffness in structural dynamic equations. Through this transformation, the aero-servo-elasticity problem can be studied by the structural dynamic methods. Taking a high-aspect ratio wing as the research object, the aerodynamic force is calculated by Theodorsen model, and the critical velocity of flutter is obtained and the equivalent transformation of the aerodynamic force is validated. Taking a supersonic aircraft with servo control system as the research object, aeordynamic force are computed by local piston theory. Through the transformation of the transfer function, the control force induced by the deflection of the control surface is converted into that uniform expression. The new coupled model of aero-servo-elasticity is obtained and stability analysis is studied by the complex eigenvalues of the system. The servo-flutter boundaries of this supersonic aircraft with different Mach numbers and different angles of attack are calculated.
引文
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