hr. J. Hrar Mm\ Tmmfir Vol. 36. No. 6. pp. 1677-1686. 1993 Prmied ,n Cre;,~ Bnwm 0017-93m/93fmo+o.oo f 1993 Perpmon Press Ltd Flow dynamics and heat transfer of a condensate film on a vertical wall-l. Numerical analysis and flow dynamics ERICH STUHLTRAGER BALZERS Ltd. FL-9496 Balzers, Liechtenstein YUTAKA NARIDOMI Mitsubishi Heavy Industries Ltd. 2-l-l. Shinhama, Arai-machi. Takasago-shi 676, Japan and AK10 MIYARA and HARUO UEHARA Saga University. I, Honjo-machi Saga-shi, Saga 840, Japan Abstract-The flow dynamics and heat transfer characteristics of the condensate film on a vertical wall is analysed by solving the time-dependent Navier-Stokes and the energy equation as well as the Poisson equation for the pressure with finite difference schemes and non-periodic boundary conditions. The simulation shows the evolution of the condensate film from the leading edge until 0.6 m by the low frequency surface fluctuation upstream of the line of wave-inception. Downwards. the time-averaged film thickness is decreasing with the flowing of big short waves. which are merging afterwards into individual long waves. The strong influence of the wave on the flow is shown by the pressure and vorticity field. 1. INTRODUCTION THIN FILM condensation heat transfer is widely used in power plant systems, refrigeration equipment and many other industrial process equipment. The con- densate film flow is divided into three regions such as laminar, wavy and turbulent regions. The heat trans- fer coefficient in the wavy and turbulent regions is much higher than in the laminar region, forcing the falling film as early as possible into the state of big roll wave lumps gliding on a thin substrate layer. This is one of the most efficient means of increasing the heat flux. Contrary to existing opinion that there exists a waveless region immediately after the initiation of the condensate film, Marschall and Lee [I] showed by the stability analysis that the distance from the leading edge of the condensation film until the location where the film is unstable is negligibly small for practical situations. The understanding of the development of the condensate flow from the leading edge, the very beginning of the falling film, down to the wavy state is therefore, important and since it has not been covered by publications until now, lead to the inves- tigations presented herewith. Flow visualization studies of Dukler and Bergelin [2] reveal a thin laminar condensate film growing from the top of the plate. By flowing downward, small ripple waves can be seen on the instable surface at Reynolds numbers Re > 20, which are growing to distorted sinusoidal waves. The straight crests gradu- ally bend and get higher to form intermediate waves at Re > 100. These waves steepen on their front at Re > 1500 and merge into lumps of roll waves, gliding on the thin film substrate, which may also be turbulent 131. The heat flux through the film at constant wall and vapor temperature is on the one hand determined by the film thickness of the substrate, and on the other hand by the flow state. either laminar, wavy or tur- bulent with roll waves. The theoretical calculations of the laminar flow part at the beginning of the gravity driven condensate film [4] and the calculations includ- ing the effects of subcooling and the variation of the physical properties with temperature [5] have also been confirmed by the experiments of Grigull [6]. As for the wavy and turbulent falling film without condensation, not only the time averaged film thick- ness and Reynolds number but also the statistics of the wave frequencies as well as wave amplitudes, length and celerity were determined in comprehensive experimental studies [7-131, covering the range up to Re = 13000. In order to calculate the How and heat Hux of the falling film in the wavy state, many different theories have been established. The results fit the experimental data to a certain extent, since the calculation schemes are restricted by periodicity, space and time averaging and linearization. Penev et al. [I41 used an integral method to solve the Navier-Stokes equation and lin- earized it for the approximation of small wave ampli- tudes. The wave numbers, wavelengths and phase- velocity can be predicted for small Weber numbers. 1677