Accelerating unsteady aerodynamic simulations using predictive reduced-order modeling
Accelerating unsteady aerodynamic simulations using predictive reduced-order modeling
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DOI：
10.1016/j.ast.2023.108412
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发表时间：
2023-05
影响因子：
5.6
通讯作者：
Zilong Li;Pingjing He
中科院分区：
文献类型：
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作者：
Zilong Li;Pingjing He
非定常计算流体力学(CFD)模拟在航空航天工程中是必不可少的，因为它们可以提供高保真的流场，以更好地理解瞬变物理，如涡流脱落。然而，非定常的全阶CFD模拟必须以小的时间步长重复推进流动解，并且计算量很大。降阶模型通过将非定常流动的解分解为空间模式和时间系数，使非定常流动更易于模拟，是缓解上述问题的有力手段。现有的只读模型研究大多集中在使用大量仿真样本训练离线模型的参数问题(参数只读)。尽管训练后的模型可以快速预测参数空间内的任意流场，但生成大量非定常模拟样本的计算代价仍然很高，特别是当参数数量及其范围增加时。为了进一步解决高成本问题，我们开发了一种有效的预测只读存储器方法来加速个人非定常气动模拟。我们使用Galerkin投影方法来简化雷诺平均的N-S方程，并使用离散经验插值法(DEIM)来降低非线性项的计算量。此外，我们开发了一种有效的只读存储器公式，该公式将动量、压力和湍流方程之间的时间系数关联起来，允许在预测阶段求解较少的只读存储器方程。预测只读存储器的侵入性使得能够使用非恒定流数据的第一部分来加速其余的模拟；不需要大量的离线样本。我们使用NACA0012翼型上的失速湍流作为基准，并评估了预测只读存储器的速度和精度，以挑战由流动条件的大突然变化引起的非平衡场景。CFD和ROM之间的运行时间比(包括基向量和投影矩阵的计算)在13到45之间。在不同时刻，用ROM法模拟的压力、阻力、升力、俯仰力矩和流场与CFD参考数据吻合得很好。所提出的预测ROM法原则上适用于不同的翼型几何形状和流动条件，并可集成到加速非定常气动模拟的设计优化过程中。
Unsteady computational fluid dynamics (CFD) simulations are essential in aerospace engineering because they can provide high-fidelity flow fields to better understand transient physics, such as vortex shedding. However, unsteady full-order CFD simulations must repeatedly march the flow solution with a small time step and are computationally expensive. Reduced-order modeling (ROM) is a powerful approach to alleviate the above issue by decomposing the unsteady flow solutions into spatial modes and temporal coefficients, making the unsteady flow easier to simulate. Existing ROM studies mostly focused on parametric problems that use a large number of simulation samples to train an offline model (parametric ROM). Although the trained model can quickly predict any flow fields within the parameter space, the computational cost for generating the massive unsteady simulation samples is still high, especially when the number of parameters and their ranges increase. To further address the high-cost issue, we develop an efficient predictive ROM approach to accelerate individual unsteady aerodynamic simulations. We use the Galerkin projection approach to reduce the Reynolds-averaged Navier–Stokes equations, along with the discrete empirical interpolation method (DEIM) for decreasing the computation cost for nonlinear terms. In addition, we develop an efficient ROM formulation that correlates the temporal coefficients between the momentum, pressure, and turbulence equations, allowing solving fewer ROM equations at the prediction stage. The intrusive nature of the predictive ROM enables using the first portion of unsteady flow data to accelerate the rest of the simulation; no massive offline samples are needed. We use the stalled turbulent flow over the NACA0012 airfoil as the benchmark and evaluate the predictive ROM's speed and accuracy for challenging non-equilibrium scenarios caused by a large sudden change in flow conditions. The run time ratios between CFD and ROM (including the calculation of basis vectors and projection matrices) range between 13 and 45. The pressure, drag, lift, pitching moment, and flow fields simulated by the ROM approach agree reasonably well with the CFD references at various times. The proposed predictive ROM approach is, in principle, applicable to different airfoil geometries and flow conditions and can be integrated into a design optimization process for accelerating unsteady aerodynamic simulations.