The unsteady drag force on a cylinder immersed in a dilute granular flow

Abstract

This paper presents results from hard-particle discrete element simulations of a two-dimensional dilute stream of particles accelerating past an immersed fixed cylinder. Simulation measurements of the drag force Fd are expressed in terms of a dimensionless drag coefficient, Cd=Fd∕[12ρνU2(D+d)], where ρ is the particle density, ν is the upstream solid fraction, U is the upstream instantaneous velocity, and D and d are the cylinder and particle diameters, respectively. Measurements indicate that the cylinder’s unsteady drag coefficient does not vary significantly from its steady (nonaccelerating) drag coefficient for both frictionless and frictional particles implying that the added mass for the flow is negligible. However, the drag coefficient is larger than its nominal value during an initial transient stage, during which a shock wave develops in front of the cylinder. Once the shock has developed, the drag coefficient remains constant despite the stream’s acceleration. The duration of the shock development transient stage is a function of the number of particle/cylinder collisions.

Equation for the force experienced by a wall overflowed by a granular avalanche: Experimental verification

“…The quasi-static regime, from the pioneering work of Wieghardt [4] to more recent studies [5][6][7][8][9], has been investigated. The rapid-dilute regime has been also studied [10][11][12][13][14][15][16]. Besides quasi-static (solid) and rapid-dilute (gazeous) regimes, granular flows can exhibit an intermediate dense regime [17] referring to the so-called granular liquid regime [18].…”

Time-varying force from dense granular avalanches on a wall

“…Granular drag on objects was approached by the pioneering work of Wieghardt [7,8] and was followed by several studies in a relatively quasi-static granular regime on the one hand [9][10][11][12][13][14] and in the rapid-dilute-granular regime on the other hand [15][16][17][18] interstitial gas effects [19,20]. Many studies on granular flows around obstacles focused on the shock waves occurring in front of the obstacles in the rapid regime [17,18,[21][22][23][24][25][26].…”

Mean steady granular force on a wall overflowed by free-surface gravity-driven dense flows

“…Furthermore, free-surface curvatures and large flow-depth gradients are observed in the vicinity of the obstacle. All these conditions result in a mean force on the obstacle that cannot be expressed as (i) a simple function of the incoming depth-averaged velocity of the flow, as is usually observed for granular flows around small immersed obstacles in the dilute regime [8,9,12,13] or (ii) a simple function of a depth of insertion (equal to the flow depth when the small object is located at the base of the flow) in the quasi-static regime [25,27,28,30].…”

“…Many recent studies have focused on the drag force on small obstacles such as cylinders in the case of rapid -dilute -granular flows [8,9], including interstitial gas effects [10,11].…”