Pipe flow scale

Example 2-3 Scale-Up of Pipe Flow. We would like to know the total pressure driving force (AP) required to pump oil (/z = 30 cP, p = 0.85 g/cm3) through a horizontal pipeline with a diameter (D) of 48 in. and a length (L) of 700 mi, at a flow rate (Q) of 1 million barrels per day. The pipe is to be of commercial steel, which has an equivalent roughness (e) of 0.0018 in. To get this information, we want to design a laboratory experiment in which the laboratory model (m) and the full-scale field pipeline (f) are operating under dynamically similar conditions so that measurements of AP in the model can be scaled up directly to find AP in the field. The necessary conditions for dynamic similarity for this system are... 

The scope of coverage includes internal flows of Newtonian and non-Newtonian incompressible fluids, adiabatic and isothermal compressible flows (up to sonic or choking conditions), two-phase (gas-liquid, solid-liquid, and gas-solid) flows, external flows (e.g., drag), and flow in porous media. Applications include dimensional analysis and scale-up, piping systems with fittings for Newtonian and non-Newtonian fluids (for unknown driving force, unknown flow rate, unknown diameter, or most economical diameter), compressible pipe flows up to choked flow, flow measurement and control, pumps, compressors, fluid-particle separation methods (e.g.,... 

The other approach is to scale up the genuine flow, then add the slip flow for the appropriate pipe diameter. Scale up of the genuine flow can be done as described in Section 3.3 or Section 3.4. In order to assess the flow due to wall slip in the pipe, it is necessary to have information about the variation of vs with tw and dt unless it is assumed that the pipe is large enough for the effect of slip to be negligible. If slip velocity data are available, implying that the apparent fluidity plots are also available, then it would be easier to use these plots directly. 

If Reynolds number is useful, it is because flow velocity and Reynolds number are related to the intensity and scale of turbulence in pipe flow. All the measurements... 

In fact, extremum tendencies expressing the dominant mechanisms in systems like turbulent pipe flow (Li et al, 1999), gas-liquid-solid flow (Liu et al, 2001), granular flow, emulsions, foam drainages, and multiphase micro-/nanoflows also follow similar scenarios of compromising as in gas-solid and gas-liquid systems (Ge et al., 2007), and therefore, stability conditions established on this basis also lead to reasonable descriptions of the meso-scale structures in these systems. We believe that such an EMMS-based methodology accords with the structure of the problems being solved, and hence realize the similarity of the structures between the physical model and the problems. That is the fundamental reason why the EMMS-based multi-scale CFD improves the... 

On the bais of an extensive review of experimental results of turbulence modulation in dilute suspension pipe flows and jet flows, Gore and Crowe (1989) proposed a critical ratio of particle diameter to a characteristic integral length scale of turbulence by the following relation... 

A number of kinds of emulsions, foams, and suspensions may be made to flow in tubes or pipes, at scales ranging from the laboratory (e.g., capillary viscometers, Section 6.2.1) to full-scale industry (e.g., transportation pipelines, Sections 10.2 and... 

Chemical engineering in general, and fluid flow in particular, utilises many dimensionless groups, which are discussed in more detail in Chapter 6 11 Scale-up in Chemical Engineering . Since we will use a piping system as an example in this chapter, we will now consider the pertinent dimensionless groups for pipe flow. 

Figure 11.2 (a) Turbulent pipe-flow (open symbols) and GEAE LM-6000 (filled symbols) radial profiles of inlet velocity components (normalized by the peak mean inlet axial velocity) for S = 0.56 1 — axial U 2 — tangential W and 3 — radial V. [b) Sensitivity of LM-6000 normalized centerline velocity to choice of floating inflow boundary condition streamwise variable is scaled with inlet diameter R previous LES [3] 1 — fine grid 2 — coarse grid (fix T and V ) present work 3 — MILES (fix p and V) 4 — MILES (fix Po and float V ) and -5 — OEEV M (fix p and V ). 

Estimating the size of the smallest length scale is relatively simple. One could use computational fluid dynamic modeling techniques or estimate them based on the power input to the system (head loss) and the mass of the fluid being powered. For example, in pipe flow, the energy dissipation rate is a function of the total head loss in the flow h, the volumetric flow rate Q, the density of the solution p, and the mass of the solution m, which in this case is the mass of fluid contained within the pipe [Equation (4.1-3)]... 

For low viscosity process fluids, turbulent pipe flow can usually be established and mixing is then much more quickly and easily achieved than for the laminar mixing of more viscous fluids. In turbulent flow, radial mixing is much stronger and turbulent flow characteristics lead to a rapid reduction in scale of any inhomogeneities present. The characteristics of turbulent flow can... 

A number of kinds of emulsions, foams and suspensions may be made to flow in tubes or pipes, at scales ranging from the laboratory (e.g. capillary viscometers. Section 6.3.1) to full-scale industry (e.g. transportation pipelines. Sections 10.2 and 11.3.4). The pressure drop and pumping requirements are functions of the type of flow and of the rheological properties of the dispersion. If the flow rate in a pipeline falls below the critical deposit velocity (also termed the stationary deposit velocity), then particles or emulsion droplets will either sediment or cream to form a layer on the bottom or top wall, respectively, of the pipe. Some correlations that have been developed for the prediction of critical deposit velocity are discussed by Nasr-El-Din [103] and Shook et /. [104]. 

The interaction of turbulent flow containing regions of high strain rate and high shear rate with polymer molecules can involve both individual molecules and polymer structures. The results of this interaction lead to suppressions of the small scale motions and to production of some large scale motions that do not contribute to turbulent diffusion. Experimental results are interpreted in terms of the interaction of molecules near the wall and movement of the polymeric large scale structures in the center of pipe flows. 

Experiments are reported in which.a concentrated polymer solution is injected into the centre of a turbulent pipe flow. Drag reduction is obtained even if the polymer forms a liquid thread which is conveyed in the core region of the flow, i.e. no significant part of the injected polymer is present in the near-wall region. This type of drag reduction differs from that found in homogeneous solutions and seems to be due to an interaction between the polymer thread and the large-scale structure. 

Gypsum Scale formation Control in Pipe Flow Systems A Systematic Study on the Effects of Process Parameters and Additives... 

---