Local Pressure Drop

The pressure drop between two locations in a bioreactor is an important hydro-dynamic characteristic because the actual measure is needed to size pumps and compressors. Average and transient pressure drop measures can also be analyzed to quantify phase holdup or identify flow regime. 

Local pressure drop measurements with flush-mounted sensors are an easy way to determine gas holdup in the region in which the pressure drop was measured 

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The flow patterns (expansion of the bubbly, slug and annular regions of flow) affect the local pressure drop, as well as the pressure oscillations in micro-channels (Kandlikar et al. 2001 Wu and Cheng 2003a,b, 2004 Qu and Mudawar 2003 Hetsroni et al. 2005 Lee and Mudawar 2005a). 

Since the pressure drop in two-phase flow is closely related to the flow pattern, most investigations have been concerned with local pressure drop in well-characterized two-phase flow patterns. In reality, the desired pressure drop prediction is usually over the entire flow channel length and covers various flow patterns when diabatic condition exist. Thus, a summation of local Ap values is necessary, assuming the phases are in thermodynamic equilibrium. The addition of heat in the case of single-component flow causes a phase change along the channel consequently, the vapor void increases and the phase (also velocity) distribution as well as the momentum of the flow vary accordingly. 

The transport velocity can also be evaluated from the variations of the local pressure drop per unit length (Ap/Az) with respect to the gas velocity and the solids circulation rate, Jp. An example of such a relationship is shown in Fig. 10.4. It is seen in the figure that, along the curve AB, the solids circulation rates are lower than the saturation carrying capacity of the flow. Particles with low particle terminal velocities are carried over from the riser, while others remain at the bottom of the riser. With increasing solids circulation rate, more particles accumulate at the bottom. At point B in the curve, the solids fed into the riser are balanced by the saturated carrying capacity. A slight increase in the solids circulation rate yields a sharp increase in the pressure drop (see curve BC in Fig. 10.4). This behavior reflects the collapse of the solid particles into a dense-phase fluidized bed. When the gas... 

Figure 10.4. Local pressure drop as a function of solids circulation rate at various gas velocities (after Yerushalmi and Cankurt, 1979).

The common interpretation of pumping test data is based on the assumption that only one aquifer is pumped and tested. However, the intensive pumping during the test causes a significant local pressure drop in the pumped aquifer that may cause water from an adjacent aquifer to breach in (Fig. 4.14). If the pumping test is done in a phreatic aquifer, water of a lower confined aquifer may flow in. Similarly, in pumping tests in confined aquifers, an overlying phreatic aquifer may be drawn in. 

Re-entrainment of liquid droplets that are captured can also occur as a result of squeezing when the local pressure drop is increased to overcome the capillary resistance force. The shape of the liquid droplets depends on the wettability of the rock. On the basis of this physical picture, Soo and Radke 12) proposed a model to describe the flow of dilute, stable emulsion flow in a porous medium. The flow redistribution phenomenon and permeability reduction are included in the model. Both low and high interfacial tension were considered. 

Local pressure drop in the subassemblies (for instance that due to spacing elements) can make significant contribution to the total pressure drop [6.7, 6.8]. It is unlikely, that spacing elements used in the fuel subassemblies of sodium cooled reactors (wire, etc.) could be applied for lead cooled reactors. Therefore, if the new spacers are designed, the available data cannot be applied. This would require special-purpose experiments not only for determining hydrodynamics, but to test structure for vibration and attrition. 

Evaluation of local pressure drop in LCFR core (spacing grids and other structural elements of SA) requires additional studies to be carried out on each modification stage. 

The side wall of the confining container is assumed to be a macroscopically homogeneous membrane with permeability Bq (in particular, Bq = 0 corresponds to the impermeable membrane i.e. the FBR). The flow rate through the membrane depends on both, permeability and the local pressure drop across the membrane (by Darcy s law). Local gas density (and pressure) is assumed to be constant at the membrane shell-side. In addition, fluid flow through the packed bed is assumed to be isothermal, nonreactive and nonturbulent, while gas kinematic viscosity is assumed to be independent on gas density. The following boundary conditions have been imposed to simulate the pressure and velocity fields in the fixed bed ... 

Hydrodynamics in gas-liquid systems have been studied extensively in the past due to their wide range of applications. Characteristics of interest include flow regimes, local pressure drop, gas residence time, axial diffusion coefficients, bubble size, bubble rise velocity, gas holdup, and power consumption. This section will summarize various experimental techniques to quantify some of these characteristics. 

The foam factor FFmax is a scaling factor that weighs the overall foam effects. FFmax is related to the foam mobility reduction factor MRF , but there exists no straightforward correlation between the two factors. In the STARS formulation, the single capillary number Nep is based on the local pressure drop, and the length over which the pressure drop is effective ... 

Because the resistance to flow in the pipeline and local pressure drop of the PAM fluid are similar to the behavior of Newtonian fluids, the cause of the above phenomena should therefore not be the high viscosity of the PAM fluid (when doing the designs, the high viscosity was already considered) rather, it was the elasticity of the fluid, which was not considered. 

For reference purposes, selected results obtained at Chalk River Laboratories (Pioro and Duffey, 2007) are shown in Fig. A4.14. In these experiments, the local pressure drop due to obstructions along the heated length was 0 because of a smooth test section. Therefore, the measured pressure drop consists only of three components ... 

The dry packing pressure drop APo was presented as a sum of two terms - pressure drcqp in the straight section (the rows) and local pressure drop between the rows APof. 

The local pressure drop in tiie packing APoi is described the expression ... 

The irrigated packing pressure drop under the loading point must be dbscrilxd [163] witib uation of two terms, first for the channel with a (instant oross-section, and second for the local pressure drop. Taking into account, that the liquid holdup changes not only the free cross-section in the chaimels of the... 

The exponent 6.8 is obtained theoretically from the well known equation for the local pressure drop at an abrupt change of a tube cross-section. 

The gas velocity in the zones of local pressure drops considerably exceeds the velocity in the straight channels. Thus, the additional retention in the channels could be neglected. Introducing AA in Eq.(17SX it is obtained ... 

The value of Kk depends not only on e qterimental data but also on fte relations used to estimate Ag and AA in Eq. (46). In [34, 160], Eq. (259) -Chapter 1 is used, ha this equation the power at (1-A) is 3, while Eq. (46) is derived from Eq. (178), where the power in the egression the local pressure drop is 6.8. In frurt, the loadmg point is that at idiich the pressure drop... 

If the friction losses are taken into account, the calculated value is higher and depends on the ratio of friction losses to local pressure drop. 

As it should be expected, packings with long channels and thin walls, i.e. xicMngs with relatively lower local pressure drop in comparison to friction losses, Imve the hipest values of Kk (see Fig. SS). 

The experimental data fit friirly well to the line calculated with Kk =1.1. It proves tfrst it is not necessary to account for the additional effects associated with the local pressure drop to friction loss ratio. 

APot - local pressure drop because of flow contraction between two neighbour packing rows, Pa r. 2... 

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