Tubes transitional flow

ESDU 93018 (2001) Forced convection heat transfer in straight tubes. Part 2 laminar and transitional flow. ESDU 98003-98007 (1998) Design and performance evaluation of heat exchangers the effectiveness-NTU method. 

As the pressure is lowered, slip occurs, and the flow mechanism is referred to as transition flow. At pressures so low that collisions between gas molecules are rare compared to the collisions between the gas and the tube wall, the flow is said to be Knudsen flow or free molecular flow. Free molecular flow prevails when Lla > 1. For air at 25°C, this condition means that we have free molecular flow when aPm on < 5. We now consider an intuitive derivation of the result for Fc in the free molecular flow region. 

Knudsen s result for free molecular flow in a tube is given by Eq. (73). With/ = 1, Knudsen s result and the second term in Eq. (84) differ only by a numerical factor. In Knudsen s result, the numerical factor is 2/3 in Eq. (84), the corresponding factor is n/8. Thus, except for a modest difference in the numerical factor, the slip term in Eq. (84) is the Knudsen free molecular flow term, and transition flow in a tube appears as a mixture of free molecular flow and viscous flow. That is, the total flow behaves approximately as a sum of two parallel flow mechanisms. 

Kaiampokis, A., Argyrakis, P., Macheras, P., Heterogeneous tube model for the study of small intestinal transit flow, Pharm. Res. 1999, 16, 87-91. 

When running a CFD simulation, a decision must be made as to whether to use a laminar-flow or a turbulent-flow model. For many flow situations, the transition from laminar to turbulent flow with increasing flow rate is quite sharp, for example, at Re — 2100 for flow in an empty tube. For flow in a fixed bed, the situation is more complicated, with the laminar to turbulent transition taking place over a range of Re, which is dependent on the type of packing and on the position within the bed. 

The well was flowed for 5 hours at some 60C b/d corresponding to transition flow. The flow tubes were then replaced and the well flowed at some 2000 b/d for 5 hours to see the eroslonal effect of turbulent flow on wax deposits. 

Wax deposits were recovered rcm all flow tubes and the rate of deposition at the wall under transition flow conditions was estimated at some 0.003 imi/hr. Turbulent appeared to erode wax deposits, reducing accumulation on the pipe wall. 

Chapter 8 now has the Topic of Special Interest Transitional Flow in Tubes contributed by Dr. Afshin Ghajar of Oklahoma State University. 

In transitional flow, the flow switches between laminar and turbulent randomly (Fig. 8-5). It should be kept in mind that laminar flow can be maintained at much higher Reynolds numbers in very smooth pipes by avoiding flow disturbances and tube vibrations. In such carefully controlled experiments, laminar flow has been maintained at Reynolds numbers of up to 100,000. 

ESDU 93018 (2001) Forced convection heat transfer in straight tubes. Part 2 laminar and transitional flow. 

Phenomenologically, dispersion occurs because different solute molecules take different times to move from point A to point 5 in a convective flow. The difference in transit times is attributed to a combination of kinematic and dynamic effects. Kinematic effects stem from tortuosity and the splitting and joining of stream tubes during flow, so that different particles traverse paths of different length. Dynamic effects stem from the distribution of velocities that a particle encounters on its path. Mechanical dispersion consists of the combined effects associated purely with convection (i.e., velocity variations due to hydrodynamics). Nonmechanical effects are associated with the diffusion of solutes from one streamline to another and into stagnant regions. 

What models should be used either for scaleup or to correlate pilot plant data Section 9.1 gives the preferred models for nonisothermal reactions in packed beds. These models have a reasonable experimental basis even though they use empirical parameters D, hr, and Kr to account for the packing and the complexity of the flow field. For laminar flow in open tubes, use the methods in Chapter 8. For highly turbulent flows in open tubes (with reasonably large L/dt ratios) use the axial dispersion model in both the isothermal and nonisothermal cases. The assumption D = E will usually be safe, but do calculate how a PFR would perform. If there is a substantial difference between the PFR model and the axial dispersion model, understand the reason. For transitional flows, it is usually conservative to use the methods of Chapter 8 to calculate yields and selectivities but to assume turbulence for pressure drop calculations. 

J. G. Withers, Tube-Side Heat Transfer and Pressure Drop for Tubes Having Helical Internal Ridging With Turbulent/Transitional Flow of Single-Phase Fluid. Pt. 1. Single-Helix Ridging, Heat Transfer Eng. (2/1) 48-58,1980. 

The transition flow and fully developed turbulent flow Nusselt number correlation for a circular tube is given by Gnielinski as reported in Bhatti and Shah [46] as... 

The full-scale analogue of tube flocculation is in flocculation in pipes, although the flow would be turbulent, not laminar this is discussed later in section 4.10.3. It may also be considered that flocculation in inclined tube modules is similar, as these are often in laminar or transitional flow. 

Interestingly, in tube flow the Reynolds number clearly indicates the range of a given type of flow. For example, for Reynolds numbers up to 2100 the flow is laminar from 2100 to about 4000 we have transition flow and from 4000 on up, the flow is turbulent. Actually, it is possible to extend laminar flow beyond 2100 if done in carefully controlled experiments. This, however, is not the usual situation found in nature. Furthermore, it should be mentioned that the boundary between transition and turbulent flow is not always clearly defined. The ranges given above are considered to hold for most situations that would be encountered. 

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