Comprehensive study of heat transfer during steam condensation

05014


Introduction
The most common methods of study heat transfer during condensation are based on temperature measurements.Integral temperature measurement (sensors are installed at the inlet and outlet of the measuring section) is used to study the improvement of heat transfer [1][2].This approach allows determining only the heat flux averaged over the heat exchanger surface.Local temperature measurements are used to study the heat transfer during condensation features [3][4][5]: the influence of non-condensable gases, the heat exchange surface orientation, wave formation on the film surface, etc.An experimental approach has unrecoverable disadvantages: the sensors inertia, the technological installation complexity, the high measurement uncertainty of the local heat flux, etc.The method is not applicable to the study of non-stationary processes.
An alternative to the temperature measurement method is the use of optical measurement methods [6][7][8].This approach is based on measuring the thickness of the condensate film and recalculating the local heat transfer coefficient (HTC).Optical methods have high information content, a relatively low measurement uncertainty, but they are applicable only in the study of condensation in optically transparent systems.
The research group of the Science Educational Centre "Energy Thermophysics", Peter the Great St.Petersburg Polytechnic University offers a unique approach -the use of gradient heatmetry [9][10].The applicability of the proposed method to the study of * Corresponding author: zajnullina_er@spbstu.ru condensation heat transfer on the plate surface, the tubes outer and inner surfaces [11][12] confirmed.
An analysis of studies performed using gradient heatmetry revealed that comprehensive techniques [13][14] combined the capabilities of gradient heatmetry, temperature measurements and flow visualization increase the research information content.The presented study combines the possibilities of gradient heatmetry for direct measurement of the heat flux during steam condensation, temperature measurements using L-type thermocouples, and visual observation of the film condensation flow.Experiments carried out during condensation of saturated steam at atmospheric pressure on the outer surface of a vertical tube.

Experimental setup
An experimental model for studying the heat flux distribution during the saturated steam condensation on the outer surface of a vertical tube made according to the "tube in tube" scheme (Figure 1).The inner tube is made of stainless steel with a thermal conductivity of about 15 W/(mK) and the outer diameter of about 20 mm.The case is a prefabricated structure; it consists of four quartz tubes with an inner diameter of 40 mm and a length of about 110 mm.Glass sections are connected through rubber couplings.The stainless-steel tube fixed in the case by rubber plugs.
In the experiments, saturated steam at the atmospheric pressure with a temperature of about 373 К E3S Web of Conferences 459, 05014 (2023) https://doi.org/10.1051/e3sconf/202345905014XXXIX Siberian Thermophysical Seminar was fed into the annular gap between the tubes; its mass flow rate was about 2.22 g/s.Cooling water with a temperature of about 290 K and a flow rate of about 100 g/s entered the stainless-steel tube.The condensate was removed to a condensate collector where its flow rate was determined from the mass of condensate.The length of the measurement section was about 420 mm.The average heat flux during condensation was measured using the integral method.For this, a tachometric flow meter is provided to measure the cooling water rate and two NTC-thermistors installed in the cooling water tube at the inlet and outlet of the measuring section.

Gradient Heatmetry
Gradient heatmetry [9] was developed at for direct measurement of the local heat flux.This method is based on the use of gradient heat flux sensor (GHFS) which is made of materials with anisotropy of thermophysical properties.The GHFSs operating principle is based on thermo-EMF generation under the action of a heat flux on an anisotropic material.The value of thermoEMF (signal generated by the GHFS) is proportional to the heat flux passing through the sensor: where q, W/m 2 is the heat flux; A, m 2 is the GHFS's cross area, and S0, mV/W is the GHFS's volt-watt sensitivity.
Measurement of heat flux during saturated steam condensation were made with the single-bismuth GHFSs (Figure 2). 3 GHFSs with dimensions of 2.9 × 7 × 0.3 mm with a volt-watt sensitivity of 1.18 mV / W were installed in a milled recess flush with the outer tube surface.GHFSs were installed with an angular step of 30° in polar angle on the tube surface at distances of 45, 150, 375 mm from the upper cut of the measuring section.
For the subsequent calculation of the local heat transfer coefficient (HTC), temperature measurements are provided using a thermocouple made of copper + alumel composition at the GHFS installation site.

Temperature Measurement
The local heat flux during condensation was calculated using the equation of stationary heat conduction through a cylindrical wall: where λ, W/(m•K) is the wall heat conduction; t1 and t2, °С are the temperatures on the inner and outer surfaces of the tube, d1 and d2, m are the inner and outer diameters of the tube.
To use this approach type L thermocouples were installed on the inner and outer surfaces of the tube.To install thermocouples on the surface, a segment cut out of the tube (Figure 3) using electric spark cutting.Type L thermocouples were welded to the inner and outer surfaces of the segment, then the segment was soldered in place.
Three measuring segments were made diametrically opposite to the GHFS installation site at distances of x = 45, 150, 375 mm from the upper cut of the measuring section.

Condensation visual observation
To analyse the results of gradient heatmetry and temperature measurements, visual observation of the condensation course was provided.The purpose of video recording was to confirm the formation of a condensate film on the tube surface.The video was recorded on a DJI Action 2 camera with a macro lens, the recording frequency was 30 Hz.The video was divided into frames which were performed to evaluate the distribution of condensate over the tube surface.
The relative uncertainty of measuring the heat flux using the GHFS is less than 6 %, the uncertainty of calculation using the stationary heat conduction equation reaches 14.5 %.The relative uncertainty of the local HTC calculation when using gradient heatmetry is about 8%, when using temperature measurements it increases to 16%.

Results
Figure 5 shows the time heat flux graphs, built according to the GHFS readings.The GHFS 1 was installed at the distance x = 45 mm from the upper cut of measurement section, the GHFS 2 was installed at the distance of x = 150 mm and the distance at which the GHFS 3 was installed is x = 375 mm.The experimental results confirm the heat transfer during film condensation being an essentially unsteady process.The Reynolds number is about Re = 46 at the distance of x = 45 mm from the upper cut of the measuring section, and at the distance of x = 150 mm increases to about Re =120.The obtained Reynolds number correspond to a laminar wavy film flow.We assume that the heat flux fluctuations recorded by the GHFS 1 and GHFS 2 are associated with the complex nature of the condensate flow.
Table 1 shows the values of the time average local heat flux, obtained using gradient heatmetry and calculated by the equation of stationary heat conduction from temperature measurements through a cylindrical wall.The difference between the results does not exceed 11%.
The largest deviations between the results were observed at the distance of x = 375 mm from the upper cut of the measuring section.The reason for this difference apparently determined by the nature of the condensate flow.
The video confirms that a laminar wave flow regime was organized on the tube surface at distances x = 45 mm and x = 150 mm.The condensate film was destroyed at the distance of x = 375 mm from the upper cut of the measuring section.Figure 6 shows a frame from the video, which indicates the absence of a condensate film in the tube lower section.Separate streams and drops of condensate observed in the lower sector of the tube.The heat flux fluctuations observed in Figure 5 according to the readings of the GHFS № 3 explained by the individual condensate streams flow in the lower section of the tube.We assume that this effect is because the condensate flow rate is not enough to form a condensate film at a significant distance from the tube top.Figure 7 shows the local HTC depending on the distance from the upper cut of the measuring section.
The graphs plotted according to the readings of the GHFS, according to the results of calculated by the equation of stationary heat conduction through the cylindrical wall and according to the Nusselt theory of film condensation on the vertical surface (3) where r, J/kg is latent heat of vaporization, ρl, kg/m 3   The experimental results are in good agreement with the HTC values calculated by the Nusselt model when the condensate is combined into a single film.But changes in the flow of condensate in the lower part of the tube lead to a difference in the experimental results from the calculated ones by 48%.The reasons for the film mode destruction and a decrease in the HTC require additional studies with a steam mass flow rate extension and an assessment of the non-condensable gases presence in the measuring section.

Conclusions
A comprehensive approach was applied to the study of heat transfer during saturated steam condensation on the outer surface of a vertical tube.The approach combines the capabilities of gradient heatmetry, temperature measurement and visualization of the condensate flow.The combined use of gradient heatmetry and temperature measurements made it possible to compare the heat flux measured by the GHFS and calculated by the equation of stationary heat conduction through a cylindrical wall.The difference in values did not exceed 11%.At the same time, a segment cut out of the tube to mount the thermocouple on the inner surface of the tube, which is not always acceptable and possible.The use of temperature measurement leads to technological difficulties.The accuracy comparison of the approaches also indicates the gradient heatmetry advantage, which makes it possible to reduce the relative uncertainty of the local heat flux to 6%.
Combining the capabilities of the gradient heatmetry and temperature measurements made it possible to determine the distribution of local HTCs during condensation on vertical tube; the relative uncertainty of the calculations was about 8%.
The application of condensation optical observation made it possible to reveal the non-film mode of condensation.When saturated water steam condenses on the surface of a stainless steel tube, film condensation can switch from a mixed mode -areas with separate streams and drops of condensate can form on the surface.

Fig. 2 .
Fig. 2. The GHFS installed on the outer surface of the tube.

Fig. 5 .
Fig. 5. Heat flux graph during steam condensation on the vertical tube.

Fig. 6 .
Fig. 6.Photos of the condensate flow at the distance of x = 375 mm from the upper cut of the measuring section.

Fig. 7 .
Fig. 7. Local HTC during steam condensation on the vertical tube.

Table 1 .
The time average local heat flux.