Numerical Simulation of Boiling Heat Transfer

It’s considered that pool boiling heat transfer is closely related to the intermittent behavior of vapor mass and the consumption of macro-layer on the heated surface. Many experiments have been carried out to support the macrolayer evaporation model, however, little has been done in the numerical simulation of boiling heat transfer. This paper reports a method to simulate heat transfer near the boiling surface by using time dependent dry-patterns of macro-layer. Employing one-dimensional heat conduction model, the processes of heat transfer for nucleate boiling, critical heat flux condition and transition boiling were simulated. In addition, the boiling curve for water and FC-72(C6F14) were predicted. The predictions agree reasonably well with experimental data. Moreover, the wall temperature fluctuations for different regimes were examined. The change of initial macrolayer thickness with wall superheat was explored. It could be believed that the numerical simulation is useful for understanding the mechanism of boiling heat transfer more clearly. INTRODUCTION It’s believed that the macro-layer is important to heat transfer in nucleate and transition boiling at high heat flux. There are several modeling efforts which focus on the instabilities in the tiny vapor passages that are postulated to intersperse the liquid-rich macro-layer immediately adjacent to the heater surface. Historically, macro-layer evaporation model was firstly proposed by Katto & Yokoya(1970). They considered that the evaporation of the macro-layer under the coalesced bubble was the primary mechanism of heat transfer from the surface. In the nucleate boiling regime, the film doesn’t dry out. When critical heat flux is reached, the film evaporates away just at the time when the bubble leaves. In the transition-boiling regime, after the film evaporates away, the vapor bubble still hovers, the surface remains dry for a period of time. Haramura & Katto(1983) and Pan(1989) suggested an alternate CHF theory based on the role of the macro-layer. Their model still retained the basic element of Zuber model that hydrodynamic instabilities dictate the occurrence of CHF. However, they proposed that the controlling instabilities occured not at the walls of large vapor columns but rather at the walls of the tiny vapor stems around active nucleate cavities that intersperse the liquid macro-layer on the heater surface itself. Another representative model was reported by Dhir & Liaw(1989). They deduced an area and time-averaged model from the experimental measurements of void fraction close to the heater surface. They considered that the energy from the wall was conducted into liquid macro/micro layer surrounding the stems and was utilized in evaporation at the stationary liquid-vapor interface. The total length of vaporliquid interface (periphery of vapor stems) determined the effectiveness of evaporation. The analysis is based on the assumption that all dissipation of liquid occurs on the walls of the vapor stems. Currently, Shoji & Kuroki (1994) did experimental observations and modeling efforts. They claimed that the formation of the macro-layer for moderately wetting fluids might be a result of the lateral coalescence of bubbles before their escape from the boiling surface. It suggests one way in which active site density might play a role in high heat-flux nucleate boiling and CHF. Although these models can explain critical heat flux and transition boiling fairly well. They appear to be some discrepancies among them. In order to investigate whether the heat transfer mechanism of nucleate boiling, critical heat flux and transition boiling could be explained by a unified model, Maruyama et al. (1992) presented a model still basing on the theory of evaporation of macrolayer. The model postulated that vapor stems were formed on the active cavity sites in a certain contact angle and the evaporation phenomena also occur at the liquid-vapor interface. The simulated results showed favorable agreements with the spatially averaged and the time averaged model. However, in this model, one of the most important parameters, the macrolayer thickness, was correlated empirically, which affected the prediction of boiling curve greatly. In this paper, a developed numerical simulation based on the model of Maruyama et al. is presented. In this simulation, we employed the bisection method to obtain the boiling curves without using empirical correlation about macrolayer thickness. Additionally, we included the analysis of the heater to obtain the temporal variations of wall temperature. Results of this study could be a good supplement to the previous simulation. METHOD OF NUMERICAL SIMULATION Fig. 1 shows the schematic of the top and side views of a vapor bubble over a heated surface. In this model, the macrolayer containing vapor stems occupies the region immediately next to the wall. The vapor stems are formed on the active cavity sites. The most important feature of this model is the introduction of a liquid-vapor stem interface evaporation phenomenon, which means that not only does the evaporation occur at the vapor bubble-macrolayer interface but also at the stem interface. In this study, we assumed that the temperature of heated surface was uniform. From the heater surface heat is conducted into the macrolayer and is utilized in evaporation at the macrolayer-bubble interface. Therefore, the heat balance is written as