The direct numerical simulation (DNS) approach is used to understand the flow behavior of Newtonian and viscoelastic fluids in porous materials, four-to-one contraction and the flow of a Newtonian fluid past an airfoil.

In simulations the viscoelastic fluid is modeled by the finitely extensible nonlinear elastic (FENE) dumbbell and Oldroyd-B models. The finite element method (FEM) is used to discretize the flow domain. The DNS results show that the permeability of a periodic porous medium depends on the wavelength used for arranging particles in the direction of flow. Specifically, it is shown that for a given particle size and porosity the permeability varies when the distance between particles in the flow direction is changed. The permeability is locally minimum for kD [approximately equal to] 7.7 and locally maximum for kD [approximately equal to] 5.0; where k is the wave number and D the diameter. A similar behavior holds for a viscoelastic fluid, except that the variation of permeability with kD is larger than for the Newtonian case.

For flow in the four-to-one contraction, it is found that the stress near the 3π/2 comer is singular and that the singularity is stronger than for a Newtonian liquid. In the region away from the walls, the stress varies as r ^-0.47 and near the walls it varies as r ^-0.61. Since the singularity is integrable, the flow away from the comer is not effected [sic] when the flow around the comer is resolved by using a radial mesh with sufficient resolution in the tangential direction at the comer.

The DNS approach is also used to demonstrate that the boundary layer separation on the upper surface of the airfoil can be suppressed by placing injection and suction regions on the upper surface. The simulations are performed for Re ≤ [less than or equal too] 500 and angle of attack up to 40°. Analysis of numerical results shows that the pressure contribution to drag decreases when the boundary layer separation is avoided. The viscous contribution to drag, however, increases and thus there is only a negligible decrease in the total drag for Re ≤ [less than or equal too] 500. Another beneficial effect of suction and injection is that the pressure contribution to the lift increases and the stall is avoided.