  Particles suspended in a fluid exert feedback forces that can significantly
impact the flow, altering the turbulent drag and velocity fluctuations. We
study flow modulation induced by particles heavier than the carrier fluid in
the framework of an Eulerian two-way coupled model, where particles are
represented by a continuum density transported by a compressible velocity
field, exchanging momentum with the fluid phase. We implement the model in
direct numerical simulations of the turbulent Kolmogorov flow, a simplified
setting allowing for studying the momentum balance and the turbulent drag in
the absence of boundaries. We show that the amplitude of the mean flow and the
turbulence intensity are reduced by increasing particle mass loading with the
consequent enhancement of the friction coefficient. Surprisingly, turbulence
suppression is stronger for particles of smaller inertia. We understand such a
result by mapping the equations for dusty flow, in the limit of vanishing
inertia, to a Newtonian flow with an effective forcing reduced by the increase
in fluid density due to the presence of particles. We also discuss the negative
feedback produced by turbophoresis which mitigates the effects of particles,
especially with larger inertia, on the turbulent flow.
