In many practical fluid dynamics experiments, measuring variables such as velocity and pressure is possible only at a limited number of sensor locations, or for a few two-dimensional planes in the flow. However, knowledge of the full fields is necessary to understand the dynamics of many flows. Deep learning reconstruction of full flow fields from sparse measurements has recently garnered significant research interest, as a way of overcoming this limitation. This task is referred to as the flow reconstruction (FR) task. In the present study, we propose a convolutional autoencoder based neural network model, dubbed FR3D, which enables FR to be carried out for three-dimensional flows around extruded 3D objects with arbitrary cross-sections. An innovative mapping approach, whereby multiple fluid domains are mapped to an annulus, enables FR3D to generalize its performance to objects not encountered during training. We conclusively demonstrate this generalization capability using a dataset composed of 80 training and 20 testing geometries, all randomly generated. We show that the FR3D model reconstructs pressure and velocity components with a few percentage points of error. Additionally, using these predictions, we accurately estimate the Q-criterion fields as well lift and drag forces on the geometries.

翻译：在许多实际流体动力学实验中，仅能在有限传感器位置或流动中少数二维平面上测量速度和压力等变量。然而，理解众多流动动力学特性需要完整的流场信息。近年来，基于深度学习的稀疏测量全流场重构方法因能克服这一限制而备受关注，该任务被称为流场重构。本研究提出一种基于卷积自编码器的神经网络模型FR3D，能够对任意截面形状的柱状三维物体周围的非定常流进行三维流场重构。通过创新性地将多个流体域映射为环形区域，FR3D可将性能泛化至训练过程中未涉及的物体。我们采用由80个训练几何体和20个测试几何体（均为随机生成）组成的数据集，明确验证了该泛化能力。结果表明，FR3D模型重构的压力和速度分量误差仅为几个百分点。此外，基于这些预测值，我们准确估计了Q准则场以及几何体所受的升力和阻力。