Fluid dynamics Reynolds experiment

In fluid dynamics the behavior in this system is described by the full set of hydrodynamic equations. This behavior can be characterized by the Reynolds number. Re, which is the ratio of characteristic flow scales to viscosity scales. We recall that the Reynolds number is a measure of the dominating terms in the Navier-Stokes equation and, if the Reynolds number is small, linear terms will dominate if it is large, nonlinear terms will dominate. In this system, the nonlinear term, (u V)u, serves to convert linear momentum into angular momentum. This phenomena is evidenced by the appearance of two counter-rotating vortices or eddies immediately behind the obstacle. Experiments and numerical integration of the Navier-Stokes equations predict the formation of these vortices at the length scale of the obstacle. Further, they predict that the distance between the vortex center and the obstacle is proportional to the Reynolds number. All these have been observed in our 2-dimensional flow system obstructed by a thermal plate at microscopic scales. ... 

The CFD model described above has been used by Liu and Fox (2006) to simulate the experiments of Johnson and Prud homme (2003a) in a confined impinging-jets reactor. In these experiments, two coaxial impinging jets with equal flow rates are used to introduce the two reactant-streams. The jet Reynolds number Re, determines the fluid dynamics in the reactor. Typical CFD results are shown in Fig. 6 9 for a jet Reynolds number of Re, = 400 and a reaction time of tr — 4.8 msec. The latter is controlled by fixing the inlet concentrations of the reactants. Further, details on the reactor geometry and the CFD model can be found in Liu and Fox (2006). 

The data trend of the above presented analytical study has been verified by computational fluid dynamics (CFD) analysis. Moreover, some microscale-specific effects could be seen for the initial part of the process, the pressure drop is confined over a short distance (between stations 2 and 3 in Fig. 5a) as the shockwave travels further from the left to the right, the pressure gradient dissipates more and more continuously over a longer range. Instead of a well-defined shockwave, a set of conpres-sion waves can then be seen distributed over more than a half of the length of the channel (Fig. 5b). This effect has already been noted in experiments with microscale shock tubes [9], originating from the stronger influence of the viscous forces at low Reynolds numbers. In the den-... 

We have considered a one-dimensional flow case for a Newtonian fluid (Newton s Law of Viscosity) as well as a phenomenological consideration of fluid dynamics (the Reynolds experiment, the Reynolds number, velocity profiles). Now, let us direct our attention to the concepts of the multidimensional cases. 

It is known that the resin behaves as an incompressible and Newtonian fluid (7), at least for a significant portion of the lamination process during which resin flow occurs. The Reynolds number of the flow is usually so small that the inertia temis in the equations of motion can be neglected. Also, because the aspect ratio, R/h (h being the thickness of the lay-up), is much greater or greater than unity in our experiments, we assume v, > > v and (dp/dr) > > (dp/dz) w here v, is the lateral velocity (in the r direction), v is the axial velocity (in the z direction) and p is dynamic pressure defined as the pressure above the ambient. Under these conditions, the resin flow satisfies... 

Fluid flow around a hair in an array depends on the relative importance of inertial and viscous forces, as represented by the Reynolds number (Re = ulp/p), where u is velocity, 1 is hair diameter, p is fluid density, and p is the dynamic viscosity of the fluid (viscosity is the resistance of the fluid to being sheared a fluid is sheared when neighboring layers of fluid move at different velocities). We humans are big (high 1), rapidly moving (large u) organisms who experience high Re turbulent flow dominated by inertia. In contrast, very small (low 1) structures such as aesthetascs operate at low Re, where fluid motion is smooth and laminar because viscous forces damp out disturbances to the flow. 

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