Interfacial instability as a trigger for dryout inception in two-phase CO2 flow

Abstract

Progress in particle physic leads to increasing in detector luminosity and a consequent increasing overheating induced by Joule effect. An effective cooling strategy is the exploitation of CO\textsubscript{2} heat latency in phase-change. An additional challenge, relevant to detectors for High Energy Particles, is the consequent geometrical constrain due to the limited space avialable for the cooling system within the detector arrangement, leading to the implementation of cooling system by means of millichannels. In this context, at relative high vapour quality the liquid phase exhibits annular flow, anticipating the dryout. Dryout is a critical condition where the heat transfer coefficient dramatically drops and dangerous temperature levels can be reached, potentially leading to catastrophic consequences. Experimental evidences reveal that its behavior in two-phase annular flows differs from conventional refrigerants and the fundamental inception-mechanism is not yet understood. This study aims at investigating the key new idea whereby dryout inception is triggered by instability of the liquid-vapour interface. A mathematical model for two-phase annular flow is presented and the stability of the interface between the two fluids is studied through the linear theory. The stability analysis reduces to solving a coupled forth-order differential eigenvalue problem that is treated numerically with an in-house code based on the Chebyshev-$τ$ method. Numerical investigations identify a critical value for the vapour quality, named $x_{dry}$, that leads to interface instability. The resulting predictions on $x_{dry}$ are confirmed by experimental data collected from two independent experimental campaigns, validating the hypothesis that dryout inception is governed by interfacial instabilities.

Figures (8)

• Figure 1: Sketch of distinct viewpoints for a cylindrical configuration. Streamwise point of view is adopted in this study.
• Figure 2: Sketch of physical configuration, where the liquid film is attached to the pipe wall, while the bulk is occupied by the vapour phase. The sloping interface between the two fluids is identified by $\delta(z)$. External heat is provided to the system via the heat flux $q$.
• Figure 3: Comparison between the spectrum obtained in Figure 7 in DongarraStraughWalker1996 and the numerical results obtained with the in-house code.
• Figure 4: Value of the real and imaginary part of the leading eigenvalue as a function of $N$, with $T_{sat} = -15 ^\circ C, q = 30 kW/m^2, G =1200 kg/m^2, x = 0.7$ and $k=0.1$.
• Figure 5: Spectrum obtained with Chebyshev-$\tau$ method with $N=20$ polynomials, for $T_{sat} = -15^\circ C, q = 30 kW/m^2, G =1200 kg/m^2, x = 0.7$ and $k=0.1$.