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Chapter 4: Modeling For the initialization phase, two options are left to the user: 1. Imposed initial tank level: this allows a good control of the initial refrigerant charge in the cycle since the latter is mainly defined by the volume of liquid in each cycle component. 2. Imposed initial pressure: this can make the initialization process less iterative and easier to solve. The only parameter of the liquid receiver model is its internal volume. It should be noted that, the higher this volume, the easier the solving process since the tank acts as a damper and reduces the pressure fluctuations. 3.4 Valve model The pressure drop in the valve is modeled by a quadratic expression using the incompressible flow hypothesis. This is typically written: M ̇ =Xopen⋅Afull⋅√(2⋅ρ⋅Δp) (58) where X open⋅A full is the actual valve cross-sectional area. This formulation may cause numerical issues when M ̇ and Δp are small because the derivative d M ̇ / d Δ p tends to infinity. The actual physical flow characteristic does not show this singularity because the flow becomes laminar (Casella et al., 2006). To avoid numerical issues, Eq 58 is replaced by the following expression, proposed by (Richter, 2008), ensuring the continuity of both the pressure drop function and its first derivative: A⋅√(2⋅ρ⋅Δp) for Δp>Δp0 M ̇ ={−A⋅√(2⋅ρ⋅Δp) for Δp<−Δp0 (59) Δp Δp2 A⋅(Δp)⋅ ⋅(5−( )) for −Δp<Δp<Δp √ 0 4⋅Δp Δp 00 0 0 Figure 62: Valve model parameters 36PDF Image | Organic Rankine Cycles for Waste Heat Recovery and Solar Uses
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