Velocity, turbulent flow

Erosion-corrosion of these components was caused by high-velocity turbulent flow resulting from incomplete opening of the valve. In this case, erosion is the dominant factor in the metal loss, corrosion being a minor contributing factor. 

Likewise, Newton s law for terminal velocity (turbulent flow) can be expressed in simplified form as... 

Prandtl velocity ratio t>+ V velocity normalized by friction velocity Turbulent flow near a wall, friction... 

Turbulent flow in contrast with lamiruirflow at lower flow velocities, turbulent flow sets in at higher flow velocities and is characterized by eddies and chaotic motion... 

In situations where a low concentration of suspended solids needs to be separated from a liquid, then cross-flow filtration can be used. The most common design uses a porous tube. The suspension is passed through the tube at high velocity and is concentrated as the liquid flows through the porous medium. The turbulent flow prevents the formation of a filter cake, and the solids are removed as a more concentrated slurry. 

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. 

Most flow meters are designed and caHbrated for use on turbulent flow, by far the more common fluid condition. Measurements of laminar flow rates may be seriously in error unless the meter selected is insensitive to velocity profile or is specifically caHbrated for the condition of use. 

In general, V For laminar Newtonian flow the radial velocity profile is paraboHc and /5 = 3/4. For fully developed turbulent flow the radial... 

Averaging the velocity using equation 50 yields the weU-known Hagen-Poiseuille equation (see eq. 32) for laminar flow of Newtonian fluids in tubes. The momentum balance can also be used to describe the pressure changes at a sudden expansion in turbulent flow (Fig. 21b). The control surface 2 is taken to be sufficiently far downstream that the flow is uniform but sufficiently close to surface 3 that wall shear is negligible. The additional important assumption is made that the pressure is uniform on surface 3. The conservation equations are then applied as follows ... 

In the forced convection heat transfer, the heat-transfer coefficient, mainly depends on the fluid velocity because the contribution from natural convection is negligibly small. The dependence of the heat-transfer coefficient, on fluid velocity, which has been observed empirically (1—3), for laminar flow inside tubes, is h for turbulent flow inside tubes, h and for flow outside tubes, h. Flow may be classified as laminar or... 

Reynolds Number. The Reynolds number, Ke, is named after Osborne Reynolds, who studied the flow of fluids, and in particular the transition from laminar to turbulent flow conditions. This transition was found to depend on flow velocity, viscosity, density, tube diameter, and tube length. Using a nondimensional group, defined as p NDJp, the transition from laminar to turbulent flow for any internal flow takes place at a value of approximately 2100. Hence, the dimensionless Reynolds number is commonly used to describe whether a flow is laminar or turbulent. Thus... 

The minimum velocity requited to maintain fully developed turbulent flow, assumed to occur at Reynolds number (R ) of 8000, is inside a 16-mm inner diameter tube. The physical property contribution to the heat-transfer coefficient inside and outside the tubes are based on the following correlations (39) ... 

One of the most efficient implementations of the slurry process was developed by Phillips Petroleum Company in 1961 (Eig. 5). Nearly one-third of all HDPE produced in the 1990s is by this process. The reactor consists of a folded loop with four long (- 50 m) vertical mns of a pipe (0.5—1.0 m dia) coimected by short horizontal lengths (around 5 m) (58—60). The entire length of the loop is jacketed for cooling. A slurry of HDPE and catalyst particles in a light solvent (isobutane or isopentane) circulates by a pump at a velocity of 5—12 m/s. This rapid circulation ensures a turbulent flow, removes the heat of polymeriza tion, and prevents polymer deposition on the reactor walls. 

The phase Doppler method utilizes the wavelength of light as the basis of measurement. Hence, performance is not vulnerable to fluctuations in light intensity. The technique has been successfully appHed to dense sprays, highly turbulent flows, and combustion systems. It is capable of making simultaneous measurements of droplet size, velocity, number density, and volume flux. 

The physics and modeling of turbulent flows are affected by combustion through the production of density variations, buoyancy effects, dilation due to heat release, molecular transport, and instabiUty (1,2,3,5,8). Consequently, the conservation equations need to be modified to take these effects into account. This modification is achieved by the use of statistical quantities in the conservation equations. For example, because of the variations and fluctuations in the density that occur in turbulent combustion flows, density weighted mean values, or Favre mean values, are used for velocity components, mass fractions, enthalpy, and temperature. The turbulent diffusion flame can also be treated in terms of a probabiUty distribution function (pdf), the shape of which is assumed to be known a priori (1). 

In modem Hquid-fuel combustion equipment the fuel is usually injected into a high velocity turbulent gas flow. Consequently, the complex turbulent flow and spray stmcture make the analysis of heterogeneous flows difficult and a detailed analysis requires the use of numerical methods (9). 

As may be expected, turbulent flow (9,11) is more efficient for droplet formation in low viscosity Hquids. With the average amount of energy dissipated per unit time and volume equal to Z and mass density equal to p, the larger eddies are characterized by a velocity gradient equal to... 

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