Intensification of heat transfer during condensation of water vapor on a vertical tube

. A review of the scientific literature on the intensification of the heat exchange process during condensation of water vapor on the surface of a vertical tube is carried out and the main results of the study are presented. The work on the study of heat transfer during laminar condensation of water vapor in the form of a laminar-flowing liquid in the form of a film both inside and on the outer surfaces of vertical tubes with an ascending steam flow is analyzed. The numerical values of Nusselt and Reynolds, which are also known and proposed for the case under consideration, have been studied. Methods of intensification of the heat exchange process are presented by improving the geometric configuration of the heat exchange surface from the side of the heating steam, on which its condensation occurs during heat transfer, which consists in reducing the thermal resistance of the wall molecular layers of the liquid. This method helps to increase the coefficient of heat transfer from steam to the wall surface by increasing the surface area of heat exchange. Based on the study of the results of well-known works, the authors have developed an experimental laboratory installation to study the increase in the efficiency of water vapor condensation processes on the outer surface of a vertical tube. An important scientific problem to be solved is the breakdown of the laminar-flowing liquid of condensed steam from the heat exchange surface, which leads to the admission and contact of steam directly from the cold surface of the tube.


Introduction
In the world, special attention is paid to research in the field of creating competitive technologies that meet international requirements, efficient designs of heat exchange plants for various industries of heat power, chemistry, food and oil refining industries.The intensification of heat exchange processes leads to a decrease in the size and mass of heat exchangers with an increase in their thermal power, which is a very relevant issue.The work in question is devoted to the development of a laboratory stand for the study of the condensation of water vapor in a shell-and-tube heat exchanger.This issue is considered in many published works, where various methods and methods are proposed that lead to improved heat transfer during condensation of heating steam in tubular apparatuses [1][2][3][4][5][6][7].It is known that with abundant condensation of heating steam, the condensate forms a liquid film on the surface of a vertically positioned tube and, as it flows down, the thickness of the condensate layer increases, which increases the thermal resistance affecting the heat transfer process [8][9][10][11][12][13][14][15][16][17].Heat exchange during the laminar flow of the condensate film inside vertical tubes with an ascending steam flow has been theoretically investigated in [9][10][11][12][13].The condensation of the return flow inside a closed thermosiphon is analytically considered in [9].In these papers, the results obtained were compared with the classical Nusselt theory for the case of a stationary steam.A number of works are devoted to the condensation of steam in the form of a laminar film inside a pipe for the cases of ascending and descending turbulent steam flow [9], the theoretical study of the condensation of an ascending steam flow in the form of a laminar-fluid in a vertical tube [14], analytical study of condensation of the reverse flow of steam in a two-phase closed thermosiphon taking into account the influence of interphase shear stress [15], mathematical model of heat transfer during steam condensation taking into account mass transfer, steam velocity and interphase shear [16], mathematical model for condensation of the reverse flow of current vapors taking into account non-condensable gases which are present in real operating conditions of heat exchangers and with this the results of the work are of interest to specialists [17][18][19][20][21].

Materials and Methods
The purpose of this work is to develop an improved laboratory installation to increase the efficiency of heat exchange processes during condensation of water vapor on a vertical heat exchange tube with various geometric intensifying surface shapes.Intensification, in essence, consists in reducing the thermal resistance of the wall layers, which contributes to an increase in the heat transfer coefficient by increasing the heat exchange surface area.Finned surfaces, which are used in most heat exchangers, provide an effective increase in the heat transfer surface area.The use of a peculiar design of finned surfaces also allows you to influence the flow of the coolant, disturbing it.Figure 1 shows the developed scheme of an experimental laboratory stand for the study of heat exchange processes during condensation of heating steam on the surface of vertically arranged tubes.

Results and Discussion
Some generalized results of experimental studies are shown in Fig. 2 and 3. From Fig. 2 it can be seen that with an increase in the thickness of the condensate film δ along the length of the tube, the heat transfer coefficient α decreases.The intersection point of the condensate film thickness and the heat transfer coefficient can be taken as the most effective parameters.Analysis of a series of experiments has shown that the effective values of the parameters that intensify the thermal processes adopted for research vary in the following intervals: -the distance between the edges with an improved surface, S2 = 0,05 m; -film thickness, δ = 0,1 -0,11 mm; -heat transfer coefficient, α = 10583÷6640 Wt / (m 2 ‧ 0 C).
Based on the graphs shown in Fig. 2, the empirical equation of the change in the thickness of the condensate film δ along the length of the tube is obtained by the least squares method: According to the above method, an empirical equation of the change in the heat transfer coefficient α along the length of the tube is obtained: The average relative error of equations ( 1) and ( 2) is 3.7%.According to the Fisher criterion, the adequacy of the results of calculations based on empirical equations and corresponding experimental data was assessed.For (1) equation, calculated Fr = 5.0821, tabular Ft = 7.71, for equation (2)calculated Fr = 5.0821, tabular Ft = 7.71, i.e. with Fr < Ft, the probability of reliability is adequate with an accuracy of 95%.The change in the condensate output on a smooth tube, a tube with fins in the form of a truncated cone and a tube with fins with an improved surface is shown in Fig. 3., where it can be seen that under the same experimental conditions, the condensate output on the proposed vertical tubes with an improved fin surface is greater.

Fig. 1 .
Fig. 1.Schematic diagram of the experimental laboratory stand: 1cylindrical glass container, 2smooth copper tube, 3fins, 4 steam tube, 5steam inlet, 6cold water, 7steam generator, 8condensate, 9condensate tube, 10condensate collector, 11water inlet, 12water outlet, 13steam generator water supply, 14, 15rotameters, 16water supply, 17water pump, 18valve, 19drainage, p1, p2differential pressure gauge (testo 510), t1, t2, t3, t4, tk1, tk2, tk3, tk4temperature measurement pointsThe main element of the experimental setup is a glass bulb with a diameter of 56/64 mm, respectively, a smooth copper tube is installed vertically inside 2. Fins are installed on the surface of a smooth copper tube after a certain distance 3. The diameter of a smooth copper tube is 10/12 mm, the length of the working section is ℓ = 300 mm.The steam generator 7, equipped with a laboratory autotransformer (LATR), with an electric power of 690 Watts, produces steam for a cylindrical flask, with the parameters set for experiments.Since cooling water is supplied to the vertical tube, condensate 8 forms on the surface of the tube, which flows down the pipe 9 and collects in the condensate collector 10.The cooling water flow rate is regulated by the valve 18.All temperature values in the laboratory unit were measured with a DS18B20 electronic thermometer with a measurement accuracy of 0,01 0 C. DS18B20 electronic thermometers are connected to an Arduino board, programmed with a C++ program.Every second, the Excel program automatically registers readings.The flow rate of cooling water and condensate is measured by rotameters 14 and 15, of the RS-5 brand.

Fig. 2 .Fig. 3 .
Fig. 2. Change in the thickness of the condensate film  and the heat transfer coefficient α along the length of the tube

Table 1 .
Geometric parameters of a vertical tube with an edge with an improved surface