HEAT TRANSFER MECHANISM IN NUCLEATE POOL BOILING UNDER HIGH HEAT FLUX CONDITIONS

Abstract

Nucleate boiling is one of the most efficient modes of heat transfer and finds applications in areas such as refrigeration, power generation, chemical processing, nuclear reactors and rocket motors, where quick removal of heat energy from a hot surface is desired. Heat transfer in nucleate pool boiling is a highly complex phenomenon as it depends on several parameters like thermophysical properties of liquid, input heat flux and heating surface conditions. Further the mechanism of boiling heat transfer has been observed to differ. considerably in different regimes. Under low-heat flux conditions a thin liquid layer known as 'microlayer' forms between the isolated vapour bubbles and heated surface and is considered to be responsible for major portion of heat transfer. However, under high heat flux conditions (when heat flux is more than about 60% of critical heat flux), the individual bubbles coalesce due to very high site density and form vapour masses entrapping a relatively thicker film of liquid known as 'macrolayer' between the growing vapour mass and the heating surface. Under these conditions major portion of heat transfer has been thought to be through this liquid layer. Though the existence of a macrolayer under a growing vapour mass at high heat flux has been generally accepted, the mechanism of its evaporation to supply vapour to the vapour mass is still uncertain. The critical examination of literature on pool boiling in high heat flux region reveals that the rate of evaporation due to transient conduction is the most important parameter in determining the heat transfer rate from heated surface. The heat transfer models proposed so far have not been able to satisfactorily explain of heat transfer mechanism under high heat flux conditions. The problem is essentially two-dimensional transient heat conduction due to the presence of vapour stems and the accompanying heat flow to these stems in the lateral direction. In view of the above, the present investigation was undertaken with the following objectives: 1. Critically examining the existing heat transfer models in high heat flux region and to develop a realistic heat transfer model based on transient heat conduction through macrolayer which takes into account the vapour-stems and thinning of macrolayer due to its evaporation. 2. Investigating experimentally the phenomenon of nucleate pool boiling under high heat flux conditions and to collect data on wall heat flux, wall superheat, initial macrolayer thickness and frequency of vapour mass. 3. Comparison of the experimental data of input heat flux with the heat flux obtained from the proposed model to establish the validity and versatility of model. 4. Investigating the effect of parametric variation of input heat flux, initial macrolayer thickness and wall super heat on the resultant heat flux in the macrolayer and to understand the mechanism of macrolayer evaporation, the role of solid-liquid-vapour triple-point and the individual contribution to the total heat transfer through different evaporating surfaces of the macrolayer. A mathematical model for transient two dimensional heat flow through a liquid macrolayer formed between vapour mass and heating surface under high ii heat flux condition has been proposed. A number of vapour stems, supposedly uniformly distributed in the entire area covered by the vapour-mass have been postulated to feed the vapour-mass along with the contribution of vapour as a result of macrolayer evaporation. It has been assumed that each set of vapour stem alongwith corresponding portion of the macrolayer contribute equally towards feeding vapour to the vapour-mass. The present physical model considers the contribution by one such set comprising of a vapour stem and the corresponding area of the macrolayer. The unit size has been determined using the expressions for vapour-stem diameter as related to initial macrolayer thickness. The vapour mass grows with time as vapour is fed into it by way of evaporation of the macrolayer. In the present model this evaporation of macrolayer is assumed to take place from three interfaces namely macrolayer-vapour mass interface, macrolayer-vapour stem interface and solid-vapour stem interface underneath the vapour stem. The heat energy required for the evaporation is determined respectively by evaluating temperature gradient at macrolayer-vapour mass interface, macrolayer-vapour stem interface and utilizing the data available in the literature on departing bubble diameter and frequency at nucleation sites under high heat flux conditions. It is assumed that the macrolayer attains a uniform temperature equal to the superheated wall temperature at the end of waiting period of the vapour mass life cycle and the temperature of the evaporating surfaces of the macrolayer drops to saturation value at the instant of new vapour mass formation. A constant heat flux has been assumed at the heater wall. Using the above assumptions, the governing heat diffusion equation for liquid macrolayer has been solved. iii The exact solution of such heat transfer problem becomes very cumbersome mainly due to decreasing thickness of macrolayer. The heat flow phenomenon being transient and involving two-dimensional cylindrical coordinates, an explicit finite difference technique has been employed in this work. A number of numerical trials were performed to determine the grid size and the time step required for the numerical solution to become stable and grid size independent. A computer programme in FORTRAN has been developed and run to obtain the results. An experimental setup was designed and fabricated for the measurement of wall heat flux, wall super heat, initial macrolayer thickness and vapour mass frequency for water and two organic. liquids, ethanol and methanol boiling on copper surface under atmospheric pressure conditions for the high heat flux region (heat flux ranging from 60 % of the critical heat flux value to the critical value). Range of experimental observations is as follows: Fluid Heat Flux, MW/m2 Wall Superheat K Initial Macrolayer thickness, um Vapour mass Frequency, Hz Water 0.849 - 1.170 19.0 - 27.1 88- 153 4.0 - 7.7 Ethanol 0.394 - 0.601 21.0 - 36.9 72 - 112 6.3 - 14.9 Methanol 0.374 - 0.551 22.1 - 36.0 78 - 122 7.0 - 13.4 Using experimental data, a simple relationship between wall superheat DT in terms of input heat flux q has been proposed in the form of AT = C1 qal for the high heat flux region. The values of constant C1 and index al have been determined for water, ethanol and methanol boiling on copper surface at atmospheric pressure. Similar type of relationships were also obtained for the initial iv macrolayer thickness &, and vapour mass frequency F as a function of input heat flux q, for the above fluids. Experimental value of input heat flux in case of water, ethanol and methanol have been compared with out-put heat flux predicted by present heat transfer model. An average absolute deviation of 1.7%, 3.8% and 3.6% has been found in case of water, ethanol and methanol respectively. The radial and vertical temperature and resulting heat flow transients as predicted by the proposed heat transfer model have been presented and discussed. The role of vapour stems present in the macrolayer and solid-liquid-vapour contact point called 'triple point' has been studied. The relative contribution of energy conducted through the macrolayer-vapour mass interface (axial heat flow), macrolayer-vapour stem interface (radial heat flow) are found to be as follows: Liquid Range of heat flux. MW/m2 Ratio of axial heat flow to total heat output. % Ratio of radial heat flow to total heat output. % Water 0.8 - 1.3 77.7 - 84.1 21.4 - 14.8 Ethanol 0.4 - 0.6 74.9 - 81.8 23.9 - 17.3 Methanol 0.375 - 0.55 75.8 - 82.7 23.3 - 16.3 while latent heat transport underneath the vapour stem is found to be nearly 1%. The temperature transients in macrolayer shows that at locations very close to vapour stem-macrolayer interface, the temperature profile differ considerably from those at locations away form the vapour stem (higher value of non-dimensional radial distance) and do not tend towards linearity that decrease the axial heat flow. This departure is obviously due to the radial heat flow. The heat transfer transients showing the instantaneous ratio of heat output „ ,w, to heat input latotal /a 1 over the entire surface shows this ratio is initially very high, and then it drops down rapidly to a minimum value and finally attains a unity value. Ratio drops to a lower value in case of lower input heat flux. Therefore the deviation of output energy from input energy is found to be higher at lower heat flux values. The value of instantaneous ratio of heat output to heat input attains a value of unity early under very high flux conditions, presumably due to lower value of initial thickness of macrolayer and high initial wall superheat resulting in high rate of evaporation of macrolayer. Plots of radial heat flow show a concentration of very high heat flux near the solid-liquid-vapour contact point called 'triple point'. This indicates a high evaporation rate associated with triple point. In the present model the vapour stems act as an efficient heat dissipating source. A base area of 11% of the vapour stem contributes about 15 to 23% (depends upon input heat flux) of total heat flow. Although the individual contribution of direct vapour stem is small but the importance of vapour stem lies in the fact that its presence triggers a very fast heat transfer process in the form of macrolayer evaporation in radial direction. The rate of heat flow resulting from the present two-dimensional heat transfer model has been compared with the one-dimensional model proposed earlier. It is found that the axial heat flux produced by 2-D model is, although, lower as compared to that predicted by 1-D model, but overall heat output rate in 2-D model is higher and closer to the actual input heat flux. This increment is due to enhanced lateral evaporating area of vapour stem as well as higher rate of evaporation at triple point visualized in 2-D model. vi To summarise, it can be stated that on the basis of critical examination of mechanism of heat transfer phenomena in nucleate pool boiling under high heat flux conditions, a new heat transfer model has been developed. The heat flow rate predicted by this model have been compared with the experimental data collected in this work on water, ethanol and methanol boiling under high heat flux conditions. The temperature and heat flow transients predicted by this model have been critically examined and the role of vapour stem present in the macrolayer and solid-liquid-vapour contact point called 'triple point' has been studied leading to a batter understanding of the mechanism of heat transfer through macrolayer.