Self-induced velocity correction for improved drag estimation in Euler–Lagrange point-particle simulations

Highlights: • Rigorous analytic derivation of self-induced velocity correction in Euler–Lagrange methodology. • Extension of the low Reynolds number theory to higher Reynolds numbers through numerical simulation. • A composite velocity correction model that has been tested in the context of falling sphere. -- Abstract: In Euler–Lagrange (EL) simulations the force on each particle is obtained from a point-particle model, which is then coupled back to the fluid momentum. The feedback force modifies the flow at the particle location and it is important to evaluate the resulting self-induced velocity disturbance, since the point-particle models are based on the undisturbed flow. An exact solution of the Oseen's equation for flow generated by a steady Gaussian feedback force was obtained, which along with the corresponding finite Reynolds number numerical simulations, provided a steady model for the self-induced velocity disturbance. The unsteady problem of a time dependent Gaussian feedback force was then theoretically investigated in the zero Reynolds number limit. The corresponding finite Reynolds number unsteady results were obtained using companion numerical simulations. Based on these results an unsteady model for predicting the self-induced velocity disturbance was developed. The two main non-dimensional quantities affecting the self-induced velocity disturbance are the Reynolds number based on Gaussian width ${\mathrm{Re}}_{\sigma }$ and the non-dimensional feedback force $\tilde{F}$. The resulting self-induced velocity correction model is general and can be applied in a variety of EL point-particle simulations, with the time history of ${\mathrm{Re}}_{\sigma }$ and $\tilde{F}$ as input. The quasi-steady and unsteady versions of the model were tested in the context of a freely settling particle. The unsteady model was shown to predict the self-induced velocity disturbance to reasonable accuracy for a wide range of Reynolds and Stokes numbers. Issues pertaining to practical implementation and limitations are discussed.