Single phase flow

The calculation of the pressure drop in a single-phase pipeline begins with the Bernoulli equation  

The integral term is evaluated differently depending upon the nature of the fluid. If it is a liquid, and hence incompressible (constant density), then  

So for a horizontal pipeline, where the fluid is of constant density and the change in kinetic energy is small (a good assumption for most pipelines), equation (8.2) can be integrated to obtain  

If the pressure drop is small, then even the flow of a gas can be consider incompressible and the above equations can be applied to estimate the pressure drop. However, if there is a significant pressure drop then a different approach is required. 

In the engineering community there are two types of friction factors - Fanning and Darcy. Although basically the same, they differ by a factor of four /nn = 4 ffm. The Darcy factor is used here. 

In Section 2 several nuclear reactor designs as well as natural circulation applications have been described.The single phase natural circulation flow is driven by a gravity head induced by coolant density differences the mass flow is established according to the balance between driving head and flow resistance losses. Because the (one component) density is a ftinction of the temperature there is a functional interaction between heat exchange and natural circulation flow. 

In general, the determination of the main parameters, e.g. average velocities, pressure drops, heat transfer and 1-D temperature fields for flow inside pipes or around structures, is based on established engineering practise. These parameters can be calculated with industrial codes as well as with thermal hydraulic codes used for nuclear reactor system behaviour. 

Some uncertainties exist if two natural circulation flows with different densities caused by different temperatures are mixed. Then diffusion processes, turbulences and other mixing processes become important. Specific experiments would be capable to reduce the uncertainties in some cases related experiments are necessary for a design. 

If 2-D or 3-D flow fields can establish, the use of capable codes isnecessary the codes listed in Section 3.2.2.2 can be used for calculations of this type. 

Mixing processes and 3-D natural convection flow is important for deboration accidents for PWRs. For BWRs similar complicated flow fields exist for sequences with boron injection. For these processes experiments with detailed instrumentation are underway the data can be used also for code validation. 

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In addition to the reduction in performance, flow maldistribution may result in increased corrosion, erosion, wear, fouling, fatigue, and material failure, particularly for Hquid flows. This problem is even more pronounced for multiphase or phase change flows as compared to single-phase flows. Flow distribution problems exist for almost all types of exchangers and can have a significant impact on energy, environment, material, and cost in most industries. 

Rapid approximate predictions of pressure drop for fully developed, incompressible horizontal gas/fiquid flow may be made using the method of Lockhart and MartineUi (Chem. Eng. Prog., 45, 39 8 [1949]). First, the pressure drops that would be expected for each of the two phases as if flowing alone in single-phase flow are calculated. The LocKhart-Martinelli parameter X is defined in terms of the ratio of these pressure drops ... 

As for any incompressible single-phase flow, the equivalent pressure P = p + pgz where g = acceleration of gravity z = elevation, may be used in place of p to account for gravitational effects in flows with vertical components. 

For isotropic homogeneous porous media (uniform permeability and porosity), the pressure for creeping incompressible single phase-flow may be shown to satisfy the LaPlace equation ... 

Shielding electromagnetic radiation, conducting composites for 143-145 Single-phase flows 109 Statistical systems, distribution of fillers 130 Structurized systems, distribution of fillers 130... 

The two models commonly used for the analysis of processes in which axial mixing is of importance are (1) the series of perfectly mixed stages and (2) the axial-dispersion model. The latter, which will be used in the following, is based on the assumption that a diffusion process in the flow direction is superimposed upon the net flow. This model has been widely used for the analysis of single-phase flow systems, and its use for a continuous phase in a two-phase system appears justified. For a dispersed phase (for example, a bubble phase) in a two-phase system, as discussed by Miyauchi and Vermeulen, the model is applicable if all of the dispersed phase at a given level in a column is at the same concentration. Such will be the case if the bubbles coalesce and break up rapidly. However, the model is probably a useful approximation even if this condition is not fulfilled. It is assumed in the following that the model is applicable for a continuous as well as for a dispersed phase in gas-liquid-particle operations. 

Methods for determining the drop in pressure start with a physical model of the two-phase system, and the analysis is developed as an extension of that used for single-phase flow. In the separated flow model the phases are first considered to flow separately and their combined effect is then examined. 

In Chap. 3 the problems of single-phase flow are considered. Detailed data on flows of incompressible fluid and gas in smooth and rough micro-channels are presented. The chapter focuses on the transition from laminar to turbulent flow, and the thermal effects that cause oscillatory regimes. 

Pressure Drop and Heat Transfer in a Single-Phase Flow 33... 

One drawback of a micro-channel heat sink is a relatively high temperature rise along the micro-channel compared to that for the traditional heat sink designs. In the direction of the flow, the wall temperature rises in a single-phase flow even when the wall heat flux is uniform. In a micro-channel heat sink, the large amount... 

Calame JP, Myers RE, Binari SC, Wood FN, Garven M (2007) Experimental investigation of micro-channel coolers for the high heat flux thermal management of GaN-on-SiC semiconductor devices. Int J Heat Mass Transfer 50 4767-4779 Celata GP, Cumo M, Zummo G (2004) Thermal-hydraulic characteristics of single- phase flow in capillary pipes. Exp Thermal Fluid Sci 28 87-95 Celata GP (2004). Heat transfer and fluid flow in micro-channels. Begell House, N.Y. 

Velocity Field and Pressure Drop in Single-Phase Flows... 

The problems of micro-hydrodynamics were considered in different contexts (1) drag in micro-channels with a hydraulic diameter from 10 m to 10 m at laminar, transient and turbulent single-phase flows, (2) heat transfer in liquid and gas flows in small channels, and (3) two-phase flow in adiabatic and heated microchannels. The smdies performed in these directions encompass a vast class of problems related to flow of incompressible and compressible fluids in regular and irregular micro-channels under adiabatic conditions, heat transfer, as well as phase change. 

We attempt here to reveal the acmal reasons of disparity between the theoretical predictions and measurements obtained for single-phase flow in micro-channels. For this purpose, we consider the effect of different factors (roughness, energy dissipation, etc.) on flow characteristics. Some of these factors were also discussed by Sharp et al. (2001), and Sharp and Adrian (2004). 

The experimental results of single-phase flow in smooth micro-channels are summarized in Table 3.3. 

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