Homogeneous equilibrium model

FIG. 26-69 Ratio of mass flux for inclined pipe flow to that for orifice discharge for flashing liquids by the homogeneous equilibrium model. Leung, J. of Loss Prev. Process Ind. 3 pp. 27-32, with kind peimission of Elsevier Science, Ltd, The Boulevard, Langford Lane, Kidlington, 0X5 IGB U.K., 1990.)... 

For two-phase flow through pipes, an overall dimensionless dis-eharge eoeffieient, /, is applied. Equation 12-11 is referred to as the equilibrium rate model (ERM) for low-quality ehoked flow. Leung [28] indieated that Equation 12-11 be multiplied by a faetor of 0.9 to bring the value in line with the elassie homogeneous equilibrium model (HEM). Equation 12-11 then beeomes... 

Bowers and Mudawar (1994a) performed an experimental smdy of boiling flow within mini-channel (2.54 mm) and micro-channel d = 510 pm) heat sink and demonstrated that high values of heat flux can be achieved. Bowers and Mudawar (1994b) also modeled the pressure drop in the micro-channels and minichannels, using the Collier (1981) and Wallis (1969) homogenous equilibrium model, which assumes the liquid and vapor phases form a homogenous mixture with equal and uniform velocity, and properties were assumed to be uniform within each phase. 

Sutherland (1975). Orifice flow rates are underpredicted by about the same factor with the energy balance method and with the NEM. Discharge predictions for short (0.2-m) pipes are overpredicted by the energy balance method. In this region, the assumption of homogeneous equilibrium is not justified. A model that takes slip velocity into account may improve predictions for short pipes. 

Two-phase flow models allow the calculation of both the two-phase mass flow rate per unit area (G) and also the critical pressure for choking. DIERS recommend the homogeneous equilibrium model (HEM, see 9.4.1) for this calculation. 

The. Homogeneous Equilibrium Model (HEM) assumes uniform mixing of the phases across the. pipe diameter, no phase slip (mechanical equilibrium), thermal equilibrium between, the..phases and complete vapour/ liquid, equilibrium. "Homogenous" in the context of the HEM refers to the flow in the vent line. 

Assumption (f) of isothermal flow means that the method is different to the homogeneous equilibrium model (which assumes adiabatic flow). The difference between the two assumptions is usually small. The isothermal flow assumption gives a slightly simpler method and yields a conservative low value of G for relief sizing purposes. The DIERS Project Manual1111 gives the alternative version of Tangren et al/s method, which assumes adiabatic flow and is therefore equivalent to the HEM. 

A discussion of the different types of assumption that can be made in two-phase flow models is given in Chapter 9. DIERS[8] recommended the use of the homogeneous equilibrium model (HEM) for relief sizing, and so, preferably, a code which implements the HEM should be chosen. The model will need to incorporate sufficiently non-ideal modelling of physical properties and provision for multiple line diameters and potential choke points, as required by the application. 

The Omega method calculates the two-phase flow capacity per unit area, G, of a nozzle or pipe of constant diameter. It evaluates the homogeneous equilibrium model (see 9.4.1) for two-phase flow. The Omega method is particularly convenient, when applicable, because it does not require the use of a computer. All properties can often be evaluated at the conditions in the upstream vessel, (which are known). Most other methods to evaluate G for two-phase flow require the use of appropriate computer codes (see Annex 4). Exceptions are given in 9.4. 

J L Woodward, "An Amended Method for Calculating Omega for a Homogenous Equilibrium Model of Predicting Discharge Rates", J Loss Prev Process Ind, 8 (5), 253-259, 1995... 

The form in which chemical analyses of sea water are given records the history of our thought concerning the nature of salt solutions. Early analytical data were reported in terms of individual salts NaCl, CaSO/i, and so forth. After development of the concept of complete dissociation of strong electrolytes, chemical analyses of sea water were given in terms of individual ions Na+, Ca++, Cl-, and so forth, or in terms of known undissociated and partly dissociated species, e.g., HC03 , In recent years there has been an attempt to determine the thermodynamically stable dissolved species in sea water and to evaluate the relative distribution of these species at specified conditions. Table 1 lists the principal dissolved species in sea water deduced from a model of sea water that assumes the dissolved constituents are in homogeneous equilibrium, and (or) in equilibrium, or nearly so, with solid phases. 

Various nonequilibrium and slip flow models have been proposed as improvements on the homogeneous equilibrium flow model. See, for example, Henry and Fauske (Trans. ASME J. Heat Transfer, 179-187 [May 1971]). Nonequilibrium and slip effects both increase... 

If the puncture occurs on a pipe which is at least 0.5 m from a vessel, it is justifiable to use a homogeneous equilibrium model (HEM) for which an analytical solution is available. The discharge rate pre-... 

The computer code for the electrode equilibration model (EHDRIFT) was written in PASCAL for use on a microcomputer. The program calculates the rest potential which is the EMF value where the currents sum to zero. If the system is in homogeneous equilibrium the rest potential will represent the system Eh. The numerical algorithm uses Eulers method (il) to integrate Equation 2, which involves recalculation of the aqueous concentrations (Equations 4 and 5) at each time step. A full listing of the source code can be found in Kempton (12). 

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