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首页> 外文会议>AHS Specialists Conference on Aeromechanics Design for Transformative Vertical Flight >Practical Application of Adjoint Variables to Real-Time Computation of Off-Rotor Induced Velocities
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Practical Application of Adjoint Variables to Real-Time Computation of Off-Rotor Induced Velocities

机译：伴随变量对偏离转子诱导速度的实时计算的实际应用

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The finite-state inflow model is widely used in real-time simulations. Coupling such a model with rotor blade flapping requires that the induced velocity be computed at the rotor disk, but the model also allows the flow to be computed at any location in the flow field above the rotor plane. However, to compute the flow field below the rotor disk (such as is required for co-axial rotors) requires computation of the adjoint variables (along with the normal state variables) including a time delay. Since the adjoint variables must be marched backwards in time, this can pose a problem in real time analysis. In this paper, computation of the adjoint variables (and flow below the disk) is addressed in the time domain. For illustrative purposes, the parameters for the two-blade Harrington coaxial rotor are used. A step input is given to collective pitch in hover. The blade sectional lift is then calculated based on combined blade-element theory and on dynamic wake modeling (including blade flapping). These equations are first time-marched forward to give the conventional state variables in the time domain. The co-state theorem is then introduced to calculate the co-states and the induced velocity below the rotor. Two alternatives methods are explored in order to compute the adjoint variables with time-delay. The first is the convolution method (in which at every time steps the adjoint variables are computed by a closed-form convolution). The second method is to march backwards in time for the co-states (i.e., adjoint variables). Two methods are considered for this second method: 1.) time marching bacwards at every three time steps, and 2.) time-marching backwards once at the end of the domain of interest. The various methods are compared for computational efficiency and numerical accuracy.
机译：有限状态流入模型广泛用于实时仿真。使用转子刀片耦合这样的模型要求在转子盘处计算感应速度，但是该模型还允许在转子平面上方的流场中的任何位置计算流动。然而，为了计算转子盘下方的流场（例如用于共轴转子所需的），需要计算伴随变量（以及正常状态变量），包括时间延迟。由于伴随变量必须在时间向后行进，因此这可能会在实时分析中提出问题。在本文中，在时域中寻址伴随变量的计算（和磁盘下方的流程）。出于说明性目的，使用了双叶片Harrington同轴转子的参数。步进输入被悬停在悬停中的集体间距。然后基于组合的刀片元素理论和动态唤醒建模（包括刀片拍打）计算叶片截面升降。这些方程首次向前行进，以在时域中提供传统状态变量。然后引入共态定理以计算转子下方的共态和诱导的速度。探索了两个替代方法，以便在暂时延迟计算伴随变量。首先是卷积方法（在每次步骤时，伴随变量通过闭合形式卷积计算）。第二种方法是在共同（即伴随变量）的时间后向后3月。这两种方法考虑了两种方法：1。比较各种方法以进行计算效率和数值精度。

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