A combined experimental and numerical study is performed to investigate the flow field and associated aerodynamic forces on a cambered airfoil. The Reynolds number is low enough to ensure importance of viscous dynamics, and high enough so that instability and transition to turbulence can occur. The flow fields are complex and their correct description is essential in understanding the nonlinear curves describing the variation of lift and drag coefficients with angle of attack, α. As α is increased from 0, the flow states go through a number of qualitatively distinct phases. At low to moderate α, the laminar boundary layer separates before the trailing edge, and as the separation point moves forward, instabilities of the detached shear layer form coherent vortices over the upper (suction) surface. At a critical angle, α_crit, instabilities in the shear layer grow fast enough to transition to turbulence, which then leads to reattachment before the trailing edge. In this flow state, lift is increased and drag decreases. Hence, in order to understand the aerodynamics at this scale, we need to understand the viscous dynamics of the boundary layer, as elegantly described and analyzed by Frank White.

This paper discusses the particle-laden flow development from a cloud of particles in an accelerated flow behind a normal moving shock. The effects of the aspect ratio of a rectangular and ellipsoidal cloud and the cloud’s angle of attack with respect to the carrier flow are studied. Computations are performed with an in-house high-order weighted essentially non-oscillatory (WENO-Z) finite-difference scheme-based Eulerian-Lagrangian solver that solves the conservation equations in the Eulerian frame, while particles are traced in the Lagrangian frame. Streamlined elliptically shaped clouds exhibit a lower dispersion than blunt rectangular clouds. The averaged and root-mean-square locations of the particle coordinates in the cloud show that the cloud’s streamwise convection velocity increases with decreasing aspect ratio. With increasing rotation angle, the cross-stream dispersion increases if the aspect ratio is larger than unity. The particle-laden flow development of an initially moderately rotated rectangle is qualitatively and quantitatively comparable to the dispersion of an initially triangular cloud.

A Lagrangian particle cloud model is proposed that accounts for the effects of Reynolds-averaged particle and turbulent stresses and the averaged carrier-phase velocity of the subparticle cloud scale on the averaged motion and velocity of the cloud. The SPARSE (subgrid particle averaged Reynolds stress equivalent) model is based on a combination of a truncated Taylor expansion of a drag correction function and Reynolds averaging. It reduces the required number of computational parcels to trace a cloud of particles in Eulerian–Lagrangian methods for the simulation of particle-laden flow. Closure is performed in an a priori manner using a reference simulation where all particles in the cloud are traced individually with a point-particle model. Comparison of a first-order model and SPARSE with the reference simulation in one dimension shows that both the stress and the averaging of the carrier-phase velocity on the cloud subscale affect the averaged motion of the particle. A three-dimensional isotropic turbulence computation shows that only one computational parcel is sufficient to accurately trace a cloud of tens of thousands of particles.