An analytical scaling law model framework for short-time dust emission from belt conveyor

Aiming at explaining the short-time dust emission from belt conveyors, an analytical scaling law model framework is introduced, employing the same assumptions and wall models as traditional numerical simulations. Further, assuming a piecewise mean velocity profile, the Lagrangian mean velocity of dust particles can be written as a general expression. This expression is validated in various cases, including the 2D Belt, 3D Belt, 2D Tire, and 3D Tire cases. Numerical results show that the theoretical prediction, with key parameters fixed at $u_s=5,\kappa =0.4187$, and $E=9.793$, fits well with the simulated Lagrangian mean velocity profiles. For example, in the 2D Belt case, short-time agreement is achieved within $t⩽1$ s, indicating the model’s effectiveness in predicting dust dispersion within this time frame.