Fluid flow Reynolds number

Fig. 1. Flow profiles, where N is velocity (a) laminar, and (b) turbulent for fluids having Reynolds numbers of A, 2 x 10, and B, 2 x 10 .

Laminar and Turbulent Flow, Reynolds Number These terms refer to two distinct types of flow. In laminar flow, there are smooth streamlines and the fuiid velocity components vary smoothly with position, and with time if the flow is unsteady. The flow described in reference to Fig. 6-1 is laminar. In turbulent flow, there are no smooth streamlines, and the velocity shows chaotic fluctuations in time and space. Velocities in turbulent flow may be reported as the sum of a time-averaged velocity and a velocity fluctuation from the average. For any given flow geometry, a dimensionless Reynolds number may be defined for a Newtonian fluid as Re = LU p/ I where L is a characteristic length. Below a critical value of Re the flow is laminar, while above the critical value a transition to turbulent flow occurs. The geometry-dependent critical Reynolds number is determined experimentally. 

Since the process is more complex, the proposed method may not be valid for scale-up calculation. The combination of power and Reynolds number was the next step for correlating power and fluid-flow dimensionless number, which was to define power number as a function of the Reynolds number. In fact, the study by Rushton summarised various geometries of impellers, as his findings were plotted as dimensionless power input versus impeller... 

The behavior of a rotating sphere or hemisphere in an otherwise undisturbed fluid is like a centrifugal fan. It causes an inflow of the fluid along the axis of rotation toward the spherical surface as shown in Fig. 1(a). Near the surface, the fluid flows in a spirallike motion towards the equator as shown in Fig. 1(b) and (c). On a rotating sphere, two identical flow streams develop on the opposite hemispheres. The two streams interact with each other at the equator, where they form a thin swirling jet toward the bulk fluid. The Reynolds number for the rotating sphere or hemisphere is defined as ... 

Equation (2.20) also assumes laminar flow (Reynolds numbers less than about 0.1), i.e., low particle velocities, and a dilute suspension of particles that are large compared with the molecules of the fluid. For Reynolds numbers greater than about 0.1 but less than 1, Oseen s law is approximately ... 

Segmentation in fluids with Reynolds numbers below 1 is only possible by the way in which two fluids are merged. Since the width of the microfabricated channels on the planer wafers is usually larger than the depth, a method for reducing mixing time is to stack the two flow streams as thin layers in one... 

The choice of equation to use for cross flow over cylinders is subject to some conjecture. Clearly, Eq. (6-17) is easiest to use from a computational standpoint, and Eq. (6-21) is the most comprehensive. The more comprehensive relations are preferable for computer setups because of the wide range of fluids and Reynolds numbers covered. For example, Eq. (6-21) has been successful in correlating data for fluids ranging from air to liquid sodium. Equation (6-17) could not be used for liquid metals. If one were making calculations for air either relation would be satisfactory. 

Reynolds number A dimensionless number characterizing the flow of a fluid. The Reynolds Number is defined as... 

Flowrates expected for fluids and Reynolds number of fluids. Hence, the expected diameter of the tubing to and from the flowmeter must be chosen. Are flows steady or pulsating Pressures range to be monitored. Pressures may vary greatly. A pressure drop is often experienced in the flowmeter, but pressure increases occur if metering pumps are employed. 

The changes in heat transfer coefficient due to vibration are strongly dependent on the initial flow Reynolds number. This means that the effects of vibration are strongly influenced by the initial turbulence level of the liquid. Therefore, subsequent studies of the effects of vibration on convective heat transfer phenomena should give close attention to initial or residual turbulence levels in the fluid. 

If we accept this as the definition of the laminar-flow Reynolds number, then for any constitutive equation which can be integrated twice to give the nonnewtonian equiyalent of the Poiseuille equation, Eq. 15.9 cian be used to define a working Reynolds number. For example, for power-law fluids (Eq. 15.7) this leads (Prob. 15.7) to... 

In turbulent flow of time-independent fluids the Reynolds number at which turbulent flow occurs varies with the flow properties of the non-Newtonian fluid. Dodge and Metzner (D2) in a comprehensive study derived a theoretical equation for turbulent flow of non-Newtonian fluids through smooth round tubes. The final equation is plotted in Fig. 3.5-3, where the Fanning friction factor is plotted versus the generalized Reynolds... 

The Reynolds number is a characterizer of flow type, being proportional to the ratio of the momentum of the fluid to the viscosity of the fluid. The Reynolds number also accounts for the fact that, whereas increases in momentum tend to push the fluid into turbulent flow, increases in viscosity or increases in viscous forces tend to slow up and straighten out the flow pattern. 

The skin friction decreases in the flow direction as the boundary layer thickness increases in the downstream x-direction. The wall shear stress and hence the skin friction can be obtained from the known velocity field, which is defined by the continuity and momentum equations of fluid motion. The skin frictions are generally expressed in the form of a correlation as a function of characteristics flow Reynolds number as... 

The mesh geometry file is imported into Fluent 3D solver the imported grid is checked and scaled to actual units of measurements. Segregated solver (default) was selected for the incompressible resin flow through fabric dining RTM process (low velocities of the fluid-low Reynolds number). order implicit, physical velocity porous formulation for 3D unsteady flow was opted in the model-solver options. Viscous laminar model was selected for physical model (laminar flow). 

The complex flow was simplified by the assumption that the screw chaimel is fully filled with a steady isothermal flow of an incompressible fluid. The Reynolds number of the flow is very small. We ignored the mass force and inertia force, since they are not to be compared with the big viscous force. 

The simplest case of fluid modeling is the technique known as computational fluid dynamics. These calculations model the fluid as a continuum that has various properties of viscosity, Reynolds number, and so on. The flow of that fluid is then modeled by using numerical techniques, such as a finite element calculation, to determine the properties of the system as predicted by the Navier-Stokes equation. These techniques are generally the realm of the engineering community and will not be discussed further here. 

The Reynolds number for flow in a tube is defined by dvpirj, where d is the diameter of the tube, V is the average velocity of the fluid along the tube, p is the density of the fluid, and rj is its dynamic viscosity. At flow velocities corresponding with values of the Reynolds number of greater than 2000, turbulence is encountered. 

Reynolds dumber. One important fluid consideration in meter selection is whether the flow is laminar or turbulent in nature. This can be deterrnined by calculating the pipe Reynolds number, Ke, a dimensionless number which represents the ratio of inertial to viscous forces within the flow. Because... 

A low Reynolds number indicates laminar flow and a paraboHc velocity profile of the type shown in Figure la. In this case, the velocity of flow in the center of the conduit is much greater than that near the wall. If the operating Reynolds number is increased, a transition point is reached (somewhere over Re = 2000) where the flow becomes turbulent and the velocity profile more evenly distributed over the interior of the conduit as shown in Figure lb. This tendency to a uniform fluid velocity profile continues as the pipe Reynolds number is increased further into the turbulent region. 

Flow Past Bodies. A fluid moving past a surface of a soHd exerts a drag force on the soHd. This force is usually manifested as a drop in pressure in the fluid. Locally, at the surface, the pressure loss stems from the stresses exerted by the fluid on the surface and the equal and opposite stresses exerted by the surface on the fluid. Both shear stresses and normal stresses can contribute their relative importance depends on the shape of the body and the relationship of fluid inertia to the viscous stresses, commonly expressed as a dimensionless number called the Reynolds number (R ), EHp/]1. The character of the flow affects the drag as well as the heat and mass transfer to the surface. Flows around bodies and their associated pressure changes are important. 

Flow Past Deformable Bodies. The flow of fluids past deformable surfaces is often important, eg, contact of Hquids with gas bubbles or with drops of another Hquid. Proper description of the flow must allow for both the deformation of these bodies from their shapes in the absence of flow and for the internal circulations that may be set up within the drops or bubbles in response to the external flow. DeformabiUty is related to the interfacial tension and density difference between the phases internal circulation is related to the drop viscosity. A proper description of the flow involves not only the Reynolds number, dFp/p., but also other dimensionless groups, eg, the viscosity ratio, 1 /p En tvos number (En ), Api5 /o and the Morton number (Mo),giJ.iAp/plG (6). 

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