Deformation modelling of cotton leaf under assisted airflow using bidirectional fluid-structure coupling method

Assisted airflow can cause the deformation of canopy leaf for the wide transport channel of droplets in the air-assisted spray. The uniformity of droplet deposition can be enhanced in the crop canopy. In this study, a mathematical model of cotton leaf deformation was established under the action of assisted airflow using fluid-structure coupling and parameter identification. Firstly, the petiole and leaf surface samples of cotton were collected to obtain the size parameters. A three-point bending was selected to calculate the elastic modulus of petiole and leaf surface. The moisture content of the petiole and leaf surface was measured during drying at 105 ℃. The results showed that the median elastic modulus of leaf surface was 46.5 MPa, where 95% confidence interval was 28.5, 64.5 MPa, whereas the median elastic modulus of petiole was 244.6 MPa, where 95% confidence interval was 215.5, 273.69 MPa, while the average moisture content of petiole was 87.2%, where 95% confidence interval was 82.5%, 91.9%, and the average moisture content of leaf surface was 80.7%, where 95% confidence interval was 72.3%, 89.1%. Then, a bidirectional fluid-structure coupling model was established to characterize the deformation process of cotton leaf. The deflection data were obtained in four monitoring points, including the middle and end of the petiole, as well as the center and tip of leaf surface. A high-speed camera was used to carry out the deformation test of cotton leaf with assisted airflow. The deflection test data of monitoring points were captured to verify the coupling model with the maximum simulation error of 9.85%. Furthermore, an orthogonal test was performed on experimental factors, including the assisted airflow speed, leaf inclination angle, elastic moduli of petiole and leaf. A significant order of experimental factors was obtained: wind speed, elastic modulus, leaf inclination angle. Finally, a mathematical model of cotton leaf deformation was constructed using the nonlinear least square. A trust-region iterative was used to obtain the identification parameters. A systematic evaluation was made on the performance of the mathematical model for cotton leaf deformation. The Mean Absolute Percentage Error (MAPE) of petiole deflection was 5.13%, and the MAPE of main vein deflection was 10.43%. It was found that the bending deformation of cotton leaf mainly occurred at the junction of petiole and leaf surface in the assisted airflow, where the leaf surface basically kept flat with the relatively small curvature. A quantitative analysis was made to obtain the initial parameters of blade inclination and dynamic variation in the frontal area of cotton leaf at different airflow speeds. The frontal area of cotton leaf decreased monotonously with the increase of airflow speed, when the inclination angles of cotton leaf were 0° and 10°. At the inclination angles of 20° and 30°, the frontal area of cotton leaf increased first and then decreased as the airflow speed increased. It infers that the canopy density can increase under the inappropriate assisted airflow. This finding can provide a sound reference to understanding the dynamic changes of cotton canopy density, further optimizing spraying parameters in the air-assisted spray.