Flow regime equilibrium model

It is recommended by DIERS12,81 that an open test cell with a 2.5 mm diameter x 100 mm long vent is used (see Figure A2.8). This diameter has. been chosen to give the best discrimination between inherently foamy and non-inherently foamy behaviour and relates to the use of a test cell with a diameter of approximately 70 mm. The use of a 100 mm long vent ensures that two-phase flow will flash to equilibrium (see 9.3.1) which simplifies any computer modelling of the test to determine the flow regime. 

These models consider either the thermodynamic or mechanical non-equilibrium between the phases. The number of conservation equations in this case are either four or five. One of the most popular models which considers the mechanical non-equilibrium is the drift flux model. If thermal non-equilibrium between the phases is considered, constitutive laws for interfacial area and evaporation/condensation at the interface must be included. In this case, the number of conservation equations is five, and if thermodynamic equilibrium is assumed the number of equations can be four. Well-assessed models for drift velocity and distribution parameter depending on the flow regimes are required for this model in addition to the heat transfer and pressure drop relationships. The main advantage of the drift flux model is that it simplifies the numerical computation of the momentum equation in comparison to the multi-fluid models. Computer codes based on the four or five equation models are still used for safety and accident analyses in many countries. These models are also found to be useful in the analysis of the stability behaviour of BWRs belonging to both forced and natural circulation type. 

It is interesting to note that in chaotic regime, the flow rate outlet stream, which is manipulated by the control valve CVl (see Figure 12), and the reactor volume, are driven by the PI controller to the equilibrium point without chaotic oscillations. However, the other variables have a chaotic behavior as shown in Figure 18. So it is possible to obtain a reactor behavior, in which some variables are in steady state and the others are in regime of chaotic oscillations, due to the decoupling or serial connection phenomena. In this case the control system and the volumetric flow limitation of coolant flow rate through the control valve VC2, are the responsible of this behavior. Similar results can be obtained from model. 

Note that our piecewise linear model corresponds qualitatively to this situation. The condition (7.3.8) is automatically satisfied for all k, and the steady state is stable irrespective of the presence or absence of diffusion. Still, the system may exhibit pulses or kinks under suitable initial conditions. Although such systems are not usually called activator-inhibitor systems, they still retain some similarity to activator-inhibitor systems if the flow in the XY phase space is seen globally beyond the linear regime about the steady state. In fact this similarity to activator-inhibitor systems has some connection with the similarity of the front instability to the conventional diffusion instability. Suppose that a<. If the equilibrium value of X (i.e., the zero value) is perturbed slightly but beyond the small threshold value a, then we have so that X starts to grow... 

---