Flows over microscale airfoils are investigated using both particle and continuum approaches. An implementation of the information preservation technique based on the direct simulation Monte Carlo method is used to simulate flows over a flat plate of zero thickness at low Reynolds number (Re < 1 x 10 2 ). The aerodynamics of a flat plate with thickness ratio of 5% at Re = 4 is quite different from that at Re = 4 x 10 3 that were measured experimentally. A continuum approach with slip boundary conditions predicts a similar basic flow pattern as the information preservation method with differences in details, which may indicate that continuum approaches are not suitable for this kind of flow because of rarefied effects

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Numerical Simulation of Gas Flow over Microscale Airfoils

The present work attempts to characterize the flow of shear-thinning power-law fluids past a flat plate as the angle of attack is varied. The effects of Reynolds number, shear-thinning characteristics and angles of attack on drag and lift of the flat plate were investigated, both experimentally and numerically. Carbopol 940 solutions of various strengths were used to approximate purely viscous shear-thinning non-Newtonian fluids for the experiments. An important finding is that at small angles of attack when the wall shear forms the dominant contribution to the drag, the non-Newtonian shear-thinning property leads to drag reduction, whereas for large angles of attack, when pressure-induced form drag is dominant, shear-thinning results in drag augmentation. This is consistent with the trend shown in the present study that lift increases as shear-thinning increases. It is demonstrated that a simple linear model developed for Newtonian creeping flow can be used to estimate the effect of angle on drag given both the drag coefficients corresponding to normal and tangential flow to the plate.

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Non-Newtonian shear-thinning flows past a flat plate

Wall effects on heat losses from hot-wires

In the present work, the flow of Bingham plastic fluids past an elliptical cylinder has been investigated numerically elucidating the effect of yield stress and fluid inertia on the momentum transfer characteristics at finite Reynolds numbers for a 100-fold variation in the aspect ratio. The governing differential equations have been solved over wide ranges of Reynolds number (0.01 ⩽ Re ⩽ 40) and Bingham number (0.01 ⩽ Bn ⩽ 100) in the laminar flow regime employing the finite element method. Furthermore, the effect of the aspect ratio (E) of the elliptical cylinder on the detailed flow characteristics has been studied by varying it from E = 0.1 to E = 10 thereby spanning varying levels of streamlining of the submerged object. In particular, new extensive results on streamline contours, shape and size of yielded/unyielded regions, shear rate profiles, surface pressure distribution and drag coefficient as functions of the Reynolds number, Bingham number and aspect ratio are presented and discussed. The functional dependence of the individual and total drag coefficients on the governing dimensionless parameters, aspect ratio, Reynolds number and Bingham number, is explored. The present results reveal a significant influence of the shape of the cylinder, i.e., aspect ratio on the detailed flow patterns and the overall hydrodynamic flow behavior of elliptical cylinders.

Steady flow of Bingham plastic fluids past an elliptical cylinder

The buoyancy-induced laminar flow and temperature elds associated with a line source of heat in an unbounded environment are described by numerically solving the non-dimensional Boussinesq equations with the appropriate boundary conditions. The solution is given for values of the Prandtl number, the single parameter, ranging from zero to innity. The far-eld form of the solution is well known, including a self-similar thermal plume above the source. The analytical description close to the source involves constants that must be evaluated with the numerical solution. These constants are used when calculating the free convection heat transfer from wires (or cylinders of non-circular shape) at small Grashof numbers. We nd two regions in the flow eld: an inner region, scaled with the radius of the wire, where the eects of convection can be neglected in rst approximation, and an outer region where, also in rst approximation, the flow and temperature elds are those due to a line source of heat. The cases of large and small Prandtl numbers are considered separately. There is good agreement between the Nusselt numbers given by the asymptotic analysis and by the numerical analysis, which we carry out for a wide range of Grashof numbers, extending to very small values the range of existing numerical results; there is also agreement with the existing correlations of the experimental results. A correlation expression is proposed for the relation between the Nusselt and Grashof numbers, based on the asymptotic forms of the relation for small and large Grashof numbers.

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Laminar free convection induced by a line heat source, and heat transfer from wires at small Grashof numbers

Low-Reynolds-number flow past a cylindrical body

In this paper the slip flow of viscous fluid at low Reynolds numbers past a flat plate aligned with the flow is studied theoretically on the basis of Oseen-Stokes equations of motion. An integral equation for the distribution of fundamental singularities representing the plate is derived and solved approximately in the vicinity of the edge and main portion of the plate. A formula for the local skin friction is obtained and discussed numerically. It is also shown that the slippage of the flow gives rise to reduction of the drag force on the plate by an amount O ( K |ln K |), where K is the Knudsen number. The velocity change near the edge of the plate is of particular interest and is found to be logarithmically singular there.

Hiroyuki Miura

Papers

Low-Reynolds-number flow past a cylindrical body

Slip flow past a tangential flat plate at low Reynolds numbers