State observer techniques are investigated for the assimilation of three-dimensional velocity measurements into computational fluid dynamics simulations based on Reynolds-averaged Navier–Stokes (RANS) equations. The method relies on a forcing term, or observer, in the momentum equation, stemming from the difference between the computed velocity and the reference value, obtained by measurements or high-fidelity simulations. Two different approaches for the forcing term are considered: proportional and integral-proportional. This technique is demonstrated considering an experimental database that describes the time-average three-dimensional flow behind a generic car-mirror model. The velocity field is obtained by means of Robotic Volumetric PIV measurements. The effects of the different forcing terms and the spatial density of the measurement input to the numerical simulation are studied. The state observer approach forces locally the solution to comply with the reference value and the extent of the region modified by the forcing input is discussed. The velocity distribution and flow topology obtained with data assimilation are compared with attention to the object wake and the reattachment point where the largest discrepancy is observed between the different approaches. The results show that the integral term is more effective than the proportional one in reducing the mismatch between simulation and the reference data, with increasing benefits when the density of forced points, or forcing density, is increased.

对状态观察器技术进行了研究，以将三维速度测量值吸收到基于雷诺平均Navier-Stokes（RANS）方程的计算流体动力学模拟中。该方法依赖于动量方程中的强迫项或观察者，其源于通过测量或高保真模拟获得的计算速度与参考值之间的差异。考虑了两种不同的强迫项方法：比例法和积分比例法。考虑到一个实验数据库证明了该技术，该实验数据库描述了通用汽车镜模型背后的时间平均三维流。速度场是通过机器人体积PIV测量获得的。研究了不同强迫项和数值输入的空间密度对数值模拟的影响。状态观察器方法在本地强制解决方案符合参考值，并讨论了由强制输入修改的区域的范围。比较了通过数据同化获得的速度分布和流动拓扑，并着眼于对象尾流和重新连接点，其中在不同方法之间观察到最大差异。结果表明，积分项在减少仿真和参考数据之间的不匹配方面比比例项更有效，并且随着强制点密度或强制密度的增加，收益也会增加。状态观察器方法在本地强制解决方案符合参考值，并讨论了由强制输入修改的区域的范围。比较了通过数据同化获得的速度分布和流动拓扑，并着眼于对象尾流和重新连接点，其中在不同方法之间观察到最大差异。结果表明，积分项在减少仿真和参考数据之间的不匹配方面比比例项更有效，并且随着强制点密度或强制密度的增加，收益也会增加。状态观察器方法在本地强制解决方案符合参考值，并讨论了由强制输入修改的区域的范围。比较了通过数据同化获得的速度分布和流动拓扑，并着眼于对象尾流和重新连接点，其中在不同方法之间观察到最大差异。结果表明，积分项在减少仿真和参考数据之间的不匹配方面比比例项更有效，并且随着强制点密度或强制密度的增加，收益也会增加。比较了通过数据同化获得的速度分布和流动拓扑，并着眼于对象尾流和重新连接点，其中在不同方法之间观察到最大差异。结果表明，积分项在减少仿真和参考数据之间的不匹配方面比比例项更有效，并且随着强制点密度或强制密度的增加，收益也会增加。比较了通过数据同化获得的速度分布和流动拓扑，并着眼于对象尾流和重新连接点，其中在不同方法之间观察到最大差异。结果表明，积分项在减少仿真和参考数据之间的不匹配方面比比例项更有效，并且随着强制点密度或强制密度的增加，收益也会增加。