Influence of direct contact heat exchange on the vacuum level in horizontal condensers

Abstract

Relevance: the efficient operation of condensers used in industrial enterprises is directly dependent on the internal pressure level. The lower the pressure inside the condenser (the higher the vacuum), the faster and more complete the condensation process occurs. In the winter season, the cooling water temperature is around 10–15 ℃, which allows maintaining the pressure inside the condenser up to 4 kPa. However, in the summer season, when the cooling water temperature rises to 30–40 ℃, the pressure inside the condenser increases to 7 kPa and higher. Such pressure changes lead to incomplete steam condensation, a decrease in the efficiency of the technological process, and an increase in additional energy consumption. Since the radical reconstruction of existing condensers requires large capital investments, studying the possibilities of reducing the pressure inside the condenser using simple and economical methods is an urgent scientific and practical problem.

Aim: to develop the theoretical foundations of the method of additional water spray into the upper part of a horizontal shell-and-tube surface condenser to reduce pressure (improve vacuum) when the cooling water temperature rises, to quantitatively assess its efficiency, and to determine its optimal parameters.

Methods: The study developed a mathematical model of heat transfer processes using the example of a horizontal condenser consisting of 168 tubes (outer diameter 28 mm, inner diameter 25 mm, wall thickness 1,5 mm, length 1 m, steam inlet window 400×600 mm, two-pass). The heat transfer surface area of the condenser based on the outer diameter is 14,78 m². The Nusselt equation was used for surface condensation, heat transfer laws for turbulent flow were applied for the cooling water inside the tubes, and the droplet flow theory was used for the direct contact zone. The relationship between the pressure and saturation temperature of water vapor was modeled using the Antoine equation. The change in pressure inside the condenser was analyzed for various flow rates of the additionally sprayed water.

Results: the calculations showed the following results. Winter mode (cooling water temperature 10 ℃, condenser pressure 4 kPa). The condenser is capable of condensing 0,224 kg/s (806 kg/h) of steam. The required cooling water flow rate is 16,2 kg/s (58,3 m³/h). The outlet cooling water temperature is 18,5 ℃, and the mean logarithmic temperature difference is 12,8 ℃. Summer mode (cooling water temperature 30 ℃, same steam flow rate 0,224 kg/s). The pressure inside the condenser increases from 4 kPa to 9,85 kPa (an increase of 5,85 kPa). The steam condensation temperature rises from 29 ℃ to 45,8 ℃. The outlet cooling water temperature reaches 36,2 ℃. When applying the additional water spray method. The optimal additional water flow rate was found to be in the range of 200–250 kg/h (0,0556–0,0694 kg/s). At this flow rate, the thermal power transferred due to direct contact is 151,5 kW. By spraying additional water, the pressure inside the condenser can be reduced from 9,85 kPa to 7,05 kPa (an improvement of 2,8 kPa). The steam temperature decreases from 45,8 ℃ to 39,2℃. The volumetric heat transfer coefficient for direct contact condensation is in the range of 110,4 kW/(m³∙K), which is 6–8 times higher than that of traditional surface condensation. With an average droplet diameter of 1 mm, the number of droplets formed per second is 123,6 thousand, and their total heat exchange surface area is 0,45–0,52 m²/s. The power required for the pump of the additional water spray system is only 0,0277 kW, indicating the high energy efficiency of the method. Efficiency analysis. Due to additional water spraying, the pressure inside the condenser decreases by 25%. Approximately 16–18 kg/h of additional water is required for every 0,1 kPa reduction in pressure. Increasing the additional water flow rate above 400 kg/h is not advisable, as the pressure reduction slows down and water consumption increases.