Omega method

FIG. 26-65 Comp arison of predictions for two-phase specific volume as a function of pressure by the omega method for two alternative formulas to calculate omega. 

Omega Method Model for Compressible Flows The factored momentum balance, Eq. (23-42), can be analytically integrated after first relating the dimensionless specific volume 8 to the dimensionless pressure ratio r. A method to do this, designated the omega method, was suggested by Leung (1986) ... 

The omega method HEM solution for orifice flow is plotted in Fig. 23-36. The solution for flashing liquids without noncondensables is to the right of = 1, and the solution for frozen flow with subcooled liquids plus noncondensables is to the left. The omega method HEM solution for horizontal pipe flow is plotted in Fig. 23-37 as the ratio ot pipe mass flux to orifice mass flux. 

FIG. 23-36 Omega method solution for orifice flow of flashing liquids and for noncondensable gas plus subcooled liquids. 

FIG. 23-37 Omega method solution for flashing liquid horizontal pipe flow. 

FIG. 23-38 Omega method HEM solution for inclined pipe flow at Fj = 0.1. 

Nonequilibrium Extension of Omega Method The omega method HEM tends to produce discharge rates that are low, particularly for short pipes. To correct this deficiency, Diener and Schmidt proposed a modification they term the nonequilibrium compressibility factor N, defined by... 

FIG. 23-41 Accuracy of Omega method HEM and NEM correction compared with saturated water data by Uchaida and Narai. 

In order to find the relief area, it is necessary to calculate G. This will be done using Tangren et al. s method for frictionless flow, and correcting for the effects of friction using the Omega method. 

A value of G has been calculated using the Omega method. This is shown as a worked example in A8.5 and G is calculated as 3792 kg/m2s at the relief pressure of... 

In this case, G is estimated as 2990 kg/mzs using the Omega method (calculation not shown). 

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 ... 

In the absence of a discharge coefficient, the most accurate way of estimating a flow reduction factor is to use the Omega method (see Annex 8). Alternatively, a discharge coefficient can be estimated from the following equation which applies for single-phase non-choked flow ... 

Alternatively, equation (9.10) (jives an approximate value for the correction factor. For the ERM, Fauskef17] gave a Table of friction correction factors as a function of the equivalent length to diameter ratio. These are given inTable5.1 and tend to be quite conservative compared with values estimated using the Omega method. 

The Omega method is intended for constant diameter relief lines. However, it is possible to use the Omega method in an iterative calculation procedure if the use of a hand calculation method is preferred. A suggested procedure for using the... 

Omega method to find the capacity of a bursting disc line with two sections having different pipe diameters is given in A8.4.5,... 

An alternative, more rigorous procedure than equation (9.12) above, using the Omega method, is given by Leung[4].. -... 

The back pressure on the safety, valve due to the flow through the discharge line can be calculated using a suitable computer program (see Annex 4). However, the Omega method (see Annex 8). ban also be used to check that the back pressure is not excessive, if it is applicable and if the discharge piping from a safety valve is of constant diameter. 

J C Leung, "The Omega Method for Discharge Rate Calculations", International Symposium on Runaway Reactions and Pressure Relief Design, 367-393, AlChE, 1995, ISBN 0-8169-0676-9... 

Gl is determined by test (see Annex 2). The calculation of GT using the Omega method for turbulent flow is described in Annex 8. 

This can be evaluated using the Omega method, if applicable (see Annex 8) or other HEM model (see Annex 4). The Omega method can be used to obtain G and the exit choke pressure, PE for the upstream pipe. An isenthalpic flash calculation can then be performed from the stagnation pressure at the start of the pipe to the choke pressure, PE, in order to evaluate the mass fraction of vapour, x, at the pipe exit. If the flow is not choked, then the term (PE - Pa) becomes zero. 

DIERS[1) presented a series of design charts, based on the Omega method, which can be used to evaluate the thrust force. These charts do not include the dynamic load factor, FD. If a load is suddenly applied, as will be the case following operation of a relief system, the piping will. experience a dynamic load of approximately twice the applied load. It is therefore usual to use a dynamic load factor of 2 in equation (12.1). Leung121 also discusses the use of the Omega method to calculate reaction forces. 

It is difficult to use the Omega method to obtain the pressure at a bend, but some estimate can be made knowing the upstream pressure and downstream choke pressure. 

---