Transitional flow friction coefficient

The isothermal friction coefficients for the three inlet types showed that the range of the Reynolds number values at which transition flow exists is strongly inlet-geometry dependent. Furthermore, healing caused an increase in the laminar and turbulent friction coefficients and an increase in the lower and upper limits of the isothermal transition regime boundaries. The friction coefficient transition Reynolds number ranges for the isothermal and nonisotliermal (three different heating rates) and the three different inlets used in their study are summarized in Table 8-6. 

The plot below shows how Re and the location of the transition from the laminar flow to the turbulent flow affect the skin friction coefficient. 

As seen in the previous section, flow is considered to be laminar when Re < 2300 and turbulent when Re > 104. Transition flow occurs in the range of 2300 < Re < 104. Few correlations or formulas for computing the friction factor and heat transfer coefficient in transition flow are available. In this section, the formula developed by Bhatti and Shah [45] is presented to compute the friction factor. It follows ... 

In this work are obtained generalized Reynolds and Hedstrom numbers connected with a three parameter rheological model to correlate the friction coefficient for the laminar, transitional and turbulent regime in annular flow. The use at experimental data covering a considerable range of dimensionless numbers for the flow of bentonite suspensions leads to a calculation technique for the transition velocity and pressure drop of these suspensions in annular geometries. 

The semi-empirical analysis of many experimental data collected in two different pilot plants led to satisfactory correlations for the turbulent friction coefficient and to the prediction of laminar-turbulent transition velocity for the flow of viscoplastic suspensions in annuli. 

Because most applications for micro-channel heat sinks deal with liquids, most of the former studies were focused on micro-channel laminar flows. Several investigators obtained friction factors that were greater than those predicted by the standard theory for conventional size channels, and, as the diameter of the channels decreased, the deviation of the friction factor measurements from theory increased. The early transition to turbulence was also reported. These observations may have been due to the fact that the entrance effects were not appropriately accounted for. Losses from change in tube diameter, bends and tees must be determined and must be considered for any piping between the channel plenums and the pressure transducers. It is necessary to account for the loss coefficients associated with singlephase flow in micro-channels, which are comparable to those for large channels with the same area ratio. 

FIGURE 17.4 Surface friction drag coefficient vs. Reynolds number transition location from the turbulent to the laminar flow. 

However, the curve of the sphere drag coefficient has some marked differences from the friction factor plot. It does not continue smoothly to higher and higher Reynolds numbers, as does the / curve instead, it takes a sharp drop at an of about 300,000. Also it does not show the upward jump that characterizes the laminar-turbulent transition in pipe flow. Both differences are due to the different shapes of the two systems. In a pipe all the fluid is in a confined area, and the change from laminar to turbulent flow affects all the fluid (except for a very thin film at the wall). Around a sphere the fluid extends in all directions to infinity (actually the fluid is not infinite, but if the distance to the nearest obstruction is 100 sphere diameters, we may consider it so), and no matter how fast the sphere is moving relative to the fluid, the entire fluid cannot be set in turbulent flow by the sphere. Thus, there cannot be the sudden laminar-turbulent transition for the entire flow, which causes the jump in Fig. 6.10. The flow very near the sphere, however, can make the sudden switch, and the switch is the cause of the sudden drop in Q at =300,(300. This sudden drop in drag coefficient is discussed in Sec. 11.6. Leaving until Chaps. 10 and 11 the reasons why the curves in Fig. 6.22 have the shapes they do, for now we simply accept the curves as correct representations of experimental facts and show how to use them to solve various problems. 

The performance of an extruder is determined as much by the characteristics of the feedstock as it is by the machine. Feedstock properties that affect the extrusion process inciude buik properties, meit flow properties, and thermal properties. Important buik flow properties are the buik density, compressibility, particle size, particle shape, external and internal coefficient of friction, and agglomeration tendency. Important melt flow properties are the shear and eiongational viscosity as a function of strain rate and temperature. The commonly used melt indexer provides only limited information on the meit viscosity. Important thermal properties include the specific heat, the glass transition temperature, the crystalline melting point, the latent heat of fusion, the thermal conductivity, the density, the degradation temperature, and the induction time as a function of temperature. 

The coefficient f depends on the Reynolds number for flow within the tube. In laminar flow, the Hagen-Poiseuille law can be applied. In turbulent flow the Blasius equation is used. The main difficulty is the evaluation of water pressure drop during transition boiling. The pressure drop consists of three components friction (APf), acceleration (APJ and static pressure (APg). In once-through horizontal tubes boiler APg=0. The Lockard-Martinelli formulation is used to estimate the friction term. 

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