Two-phase flow Calculations

Monsanto and other companies are working independently on design methods to size vents more rigorously using two-phase flow calculations in complex computer programs. Several assumptions have been made in an effort to allow a wide range of application. Most notable is the use of the correlations of Martinelli and co-workers for pressure drop H) and hold-up( ). 

Two-phase flow calculations are relatively complex, especially when conditions change rapidly, as in a runaway reaction scenario. As a result of this complexity, special methods have... 

Flashing two-phase flow calculations are appropriate for vapour pressure systems. Possible methods for calculating G for two-phase flashing flow are ... 

The capacity of the relief system can be obtained from a two-phase flow calculation for nozzle flow. If the flow is not choked, then the Omega method (see Annex 8) or suitable computer code must be used to calculate flow capacity. For choked flow a larger range of methods may be applicable, e.g. ERM for vapour pressure systems (see 9.4.2) or Tangren et al. s method for gassy systems (see 9.4.3), together with the application of a discharge coefficient. The capacity can then be obtained from ... 

Stand-alone codes for two-phase flow calculations also exist. TPHEM , a code for evaluating the HEM, is provided with a CCPS publication131. Another possible code is IN PLANT from Simulation Sciences191. 

Two-phase flow calculations are complex when conditions change rapidly as in runaway reactions. Because of this complexity, several... 

A safety factor is, therefore, usually applied to the calculated vent area, the calculated vent area being multiplied by the safety factor which ranges between 1 and 2. The choice of the safety factor depends on the individual situation. A figure of 2 is often used due to uncertainties in the two-phase flow calculations. As a minimum, the calculated vent discharge pipe diameter should be increased to the next available standard pipe size and never reduced. 

Two-Phase Flow Calculations. Some useful empirical correlations at ambient conditions have been developed by Martinelli and Nelsonand Martinelli and Lockhartfor frictional pressure drop resulting from two-phase flow in pipes. The two assumptions made in developing the correlations are that (1) the static pressure drop for the liquid phase equals that of the vapor phase and (2) the sum of the liquid and vapor volumes always equals the total volume of the pipe. Thus, the correlations are not valid for slug or stratified flow. 

Aluminum-containing propellants deflver less than the calculated impulse because of two-phase flow losses in the nozzle caused by aluminum oxide particles. Combustion of the aluminum must occur in the residence time in the chamber to meet impulse expectations. As the residence time increases, the unbumed metal decreases, and the specific impulse increases. The soHd reaction products also show a velocity lag during nozzle expansion, and may fail to attain thermal equiUbrium with the gas exhaust. An overall efficiency loss of 5 to 8% from theoretical may result from these phenomena. However, these losses are more than offset by the increase in energy produced by metal oxidation (85—87). 

In the macroscopic heat-transfer term of equation 9, the first group in brackets represents the usual Dittus-Boelter equation for heat-transfer coefficients. The second bracket is the ratio of frictional pressure drop per unit length for two-phase flow to that for Hquid phase alone. The Prandd-number function is an empirical correction term. The final bracket is the ratio of the binary macroscopic heat-transfer coefficient to the heat-transfer coefficient that would be calculated for a pure fluid with properties identical to those of the fluid mixture. This term is built on the postulate that mass transfer does not affect the boiling mechanism itself but does affect the driving force. 

There are no precise formulas for calculating orifice area for two-phase flow. The common convention is to calculate the area required for the gas flow as if there were no liquid present and the area required for the liquid flow as if there were no gas present. The two areas are then added to approximate the area required for two-phase flow. 

Calculation of condensate piping by two-phase flow techniques is recommended however, the tedious work per line can often be reduced by using empirical methods and charts. Some of the best are proprietary and not available for publication however, the Sarco method [42] has been used and found to be acceptable, provided no line less than VA" is used regardless of the chart reading. Under some circumstances, w hich are too random to properly describe, the Sarco method may give results too small by possibly a half pipe size. Therefore, latitude is recommended in selecting either the flow rates or the pipe size. 

Because flashing steam-condensate lines represent two-phase flow, with the quantity of liquid phase depending on die system conditions, these can be designed following the previously described two-phase flow methods. An alternate by Ruskin [28] uses the concept but assumes a single homogeneous phase of fine liquid droplets dispersed in the flashed vapor. Pressure drop was calculated by the Darcy equation ... 

This metliod calculates the dry tray pressure drop and allows for correcting the two-phase flow effects at various entrainment ratios. 

This calculation is not accurate, because it does not account for two-phase flow. 

Equations (5) and (15) yield another important equation a formula for calculating point coordinates along the channel, where two-phase flow originates — 1CI [20] ... 

Sudden eniargement/contraction, 70, 80 Total line, 64 Two-phase flow, 124-127 Vacuum lines, 128-134 Velocities, 83, 89, 90 Velocities, chart, 91 Velocity head, 71 Water flow calculations, 96 Water flow, table, 93, 97, 98 Pressure level relationships,... 

Total head, centrifugal pumps, 180, 183 Discharge, 205 Head curve, 198 Suction head, 184, 186 Suction lift, 184, 186 Type, 184 Tubing, 63, 64 Two-phase flow, 124 Calculations, 125-127 Flow patterns, chart, 124 System pressure drop, 125 Types of flow, 124, 125 Utilities check list, process design, 34 Vacuum,... 

The pressure drop due to acceleration is important in two-phase flow because the gas is normally flowing much faster than the liquid, and therefore as it expands the liquid phase will accelerate with consequent transfer of energy. For flow in a vertical direction, an additional term — AZ y must be added to the right hand side of equation 5.5 to account for the hydrostatic pressure attributable to the liquid in the pipe, and this may be calculated approximately provided that the liquid hold-up is known. 

Two-phase flow pattern maps, observed by Revellin et al. (2006), are presented in Fig. 2.31 in mass flux versus vapor quality, and superficial liquid velocity versus superficial vapor velocity formats calculated from the test results as follows ... 

Beattie DRH, Whalley PB (1982) A simple two-phase flow frictional pressure drop calculation method. Int J Multiphase Flow 8 83-87... 

Chapter 9 consists of the following in Sect. 9.2 the physical model of two-phase flow with evaporating meniscus is described. The calculation of the parameters distribution along the micro-channel is presented in Sect. 9.3. The stationary flow regimes are considered in Sect. 9.4. The data from the experimental facility and results related to two-phase flow in a heated capillary are described in Sect. 9.5. 

In this section we present the system of quasi-one-dimensional equations, describing the unsteady flow in the heated capillary tube. They are valid for flows with weakly curved meniscus when the ratio of its depth to curvature radius is sufficiently small. The detailed description of a quasi-one-dimensional model of capillary flow with distinct meniscus, as well as the estimation conditions of its application for calculation of thermohydrodynamic characteristics of two-phase flow in a heated capillary are presented in the works by Peles et al. (2000,2001) and Yarin et al. (2002). In this model the set of equations including the mass, momentum and energy balances is ... 

Design of vessel and vent line pipe supports is very important because very large forces can be encountered as soon as venting begins. Figure 4 shows the equations and nomenclature to calculate forces on pipe bends. The authors have heard of situations where vent line bends have been straightened, lines broken off, or vent catch tanks knocked off their foundations by excessive forces. For bends, the transient effects of the initial shock wave, the transition from vapor flow to two-phase flow, and steady state conditions should be considered. Transient conditions, however, are likely to be so rapid as to not have enough dura-... 

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