Turbulence can be widely observed in natural environments and engineering systems, where accurate measurements of velocity and scalar fields are essential for understanding flow mechanisms and optimizing engineering designs. Traditional particle image velocimetry (PIV) has become a standard experimental technique in turbulence research. However, its reliance on tracer particles poses significant limitations in enclosed and high-temperature conditions or scenarios requiring multi-field synchronous observation. Specifically, tracer particles may interfere with scalar field measurements, thereby hindering simultaneous spatiotemporal acquisition. Scalar image velocimetry (SIV), based on passive scalar transport, provides a non-intrusive alternative that avoids these issues and offers greater adaptability. Nevertheless, current SIV methods are constrained in high-resolution velocity reconstruction and nonlinear structure perception due to algorithmic limitations. Recent advancements of optical flow neural networks in computer vision, with their powerful feature extraction capabilities, offer new possibilities for flow field estimation. However, most existing networks are built on rigid motion assumptions, making them unsuitable for the continuous deformation characteristics of fluid flows. To resolve this limitation, we proposed a physics-adapted SIV-RAFT (recurrent all-pairs field transforms) neural network architecture that integrated deep learning with fluid dynamic constraints. The model enabled accurate, non-invasive, and synchronized measurement of velocity and concentration fields in complex turbulent flows, demonstrating both theoretical significance and practical engineering applicability.

The proposed SIV-RAFT algorithm was built upon the strengths of the original RAFT framework while introducing systematic architectural enhancements tailored to the deformable fluid motion dynamics. In the feature extraction stage, deformable convolutional networks (DCNs) were employed to replace standard convolutional layers. By dynamically adjusting convolutional kernel sampling positions, the network could adaptively capture geometric deformation features induced by fluid motion. To enhance the optical flow iterative refinement process, an iterative attention feature fusion (iAFF) mechanism was integrated. This mechanism constructed a cross-channel and spatial dual-dimensional attention weight matrix, enabling the network to focus adaptively on multi-scale turbulent structures. Implemented within the gated recurrent unit (GRU) framework, the iAFF mechanism introduced a feature recalibration pathway that dynamically adjusted the contribution of different spatiotemporal scale features during each iteration, thereby improving complex turbulent flow representation. For model training and performance evaluation, a scalar image dataset tailored for the SIV task was constructed. First, the reliability of large eddy simulation (LES) data as a substitute for experimental measurements in jet-related problems was verified through physical comparison experiments. Subsequently, a series of inclined negatively buoyant jet scenarios under various conditions were simulated to generate scalar image sequences with realistic physical evolution, serving as training data. For model validation, both LES results and publicly available direct numerical simulation (DNS) turbulence databases were utilized to conduct rigorous quantitative assessments of the estimation accuracy and robustness of the SIV-RAFT model. These comprehensive evaluations confirmed the proposed model’s adaptability and effectiveness in complex flow velocity reconstruction tasks.

To comprehensively assess the prediction capabilities of the proposed SIV-RAFT algorithm, extensive evaluations have been conducted on both the inclined jet dataset and the DNS turbulence dataset. Figure 8 shows velocity field prediction errors of the proposed SIV-RAFT algorithm, the PWC-Net algorithm, and the Horn?Schunck (HS) method. Quantitative evaluation reveals that SIV-RAFT achieves a maximum error magnitude of less than 0.29 pixel in 95% of the observed region, outperforming the PWC-Net algorithm (0.57 pixel) and the HS method (1.42 pixel). In particular, in high-velocity jet regions, the SIV-RAFT algorithm demonstrates significantly lower local errors than the other two methods, as shown in Fig. 8(a). These comparative results indicate that SIV-RAFT has a distinct advantage in maintaining the spatial consistency of the velocity vector field and capturing local features. Figure 11 presents the velocity profiles across sections perpendicular to the jet centerline at different streamwise locations, namely 20D and 30D downstream from the nozzle, corresponding to Figs. 11(a) and (b), respectively. The results reveal that SIV-RAFT achieves the best overall performance in jet velocity prediction. The root-mean-square errors (RMSEs) of velocity at the 20D and 30D sections are 2.91% and 1.41%, respectively. Furthermore, the predicted velocity profiles exhibit close alignment with the experimental data in both shape and magnitude, confirming that multi-scale feature extraction and spatiotemporal correlation constraints effectively enhance prediction robustness in complex shear flows. Figure 12 shows the instantaneous velocity magnitude at t=30, where Figs. 12(a)?(d) show the ground-truth DNS velocity magnitude and the predictions from the HS, PWC-Net, and SIV-RAFT algorithms, respectively. The HS method exhibits substantial reconstruction errors, with an RMSE approximately 37.14% higher than that of SIV-RAFT. Compared to the PWC-Net, SIV-RAFT reduces the RMSE of the velocity field by 14.10%. Figure 13 illustrates the vorticity fields from the ground-truth value of DNS and those of the other three algorithms. The results show that SIV-RAFT captures fine-scale vortex structures more accurately than PWC-Net and the HS methods, demonstrating enhanced capability in resolving intricate turbulent flow features.

In the present study, a deep learning-based SIV method, SIV-RAFT, is proposed. Based on the RAFT optical flow estimation framework from computer vision, the network is systematically optimized: DCNs are introduced in the feature extraction stage to enhance adaptability to large-scale fluid deformations, while an iAFF mechanism is integrated into the flow update module to improve the ability to capture fine-scale vortical structures. To support model training, a multiphysics benchmark dataset is constructed by performing multi-condition 3D inclined density jet simulations using the open-source CFD software OpenFOAM. The model’s performance is evaluated on both a jet flow dataset and a DNS turbulence dataset. Comparative results show that on the jet dataset, the proposed method reduces velocity magnitude prediction errors by 21.32% and 43.26% compared to the PWC-Net algorithm and the traditional HS method, respectively. On the DNS dataset, corresponding error reductions are 23.02% and 38.99%. Quantitative analysis demonstrates that the SIV-RAFT model effectively captures multi-scale turbulent structures from scalar concentration fields and achieves an accurate velocity field. This study provides a novel and data-driven solution for simultaneous concentration and velocity measurement in complex flow environments, demonstrating potential for deep learning applications in experimental fluid dynamics.