Experimental study of direct contact condensation of spent vapor in a cocurrent flow packed tower under negative pressure

Condensers are often required in power generation systems to condense the exhaust steam generated at the end of the turbine. This paper will investigate the enhanced condensation process of spent steam in a parallel flow type. The operating parameters of steam temperature (Tcond), steam flow rate (Gin), cooling water temperature (Tin), and cooling water flow rate (Lw) will affect the condensation effect by changing the gas–liquid arrangement in the tower. In this experiment, an orthogonal test was designed in the Raschig ring to investigate the significance of these four operating parameters on the experimental results. Different types of packings have different condensation effects due to different accumulation methods. The same type of packing has a different surface area, resulting in different contact areas between the gas and liquid phases during condensation. In this experiment, four different packings will be investigated to find their condensation performance. This paper uses the size of subcooling (ΔT) as an indicator to evaluate the effectiveness of condensation, and the values of condensation rate (R), number of liquid phase heat transfer units (NTUL), and total volume heat transfer coefficient (Kv) are used as a reference for the effectiveness of condensation. The results show that the overall condensation effect of regular packing is better than that of random packing, The average condensation rate of regular packing is 95%, the average condensation rate of random packing is 90%, the subcooling of regular packing is about three to five smaller than that of random packing, the heat transfer coefficient of regular packing is about 1.5 times of that of random packing. And by fitting the Kv data for different packings, an empirical formula was obtained that can be used to predict the Kv size of other packings.


| INTRODUCTION
Current condenser units in thermal power plants can be divided into two types: surface type and hybrid type. 1,2 In hybrid condensers, the steam condenses through direct contact with cooling water, and in surface condensers, the steam condenses with condensate through heat exchange on metal surfaces. The hybrid condenser has many advantages over the surface condenser. For example, its volume is only 1/3 that of the surface condenser and its subcooling degree ranges from 0.2°C to 0.5°C, which is much smaller than that of the surface condenser. 3,4 The mixing of condensate and cooling water in hybrid condensers increases the cost of condensate treatment, so hybrid condensers are less commonly used. The main type of condenser used at present is the Heller type. However, Heller condensers have disadvantages such as complex water level control and high installation and maintenance costs due to the large number of nozzles. With the development of water treatment technology, the advantages of hybrid condensers are becoming more and more evident as the cost of the condenser decreases, and the importance of its use is gradually gaining emphasis. Studies have shown that the presence of fillers can effectively improve the mass and heat transfer performance of distillation, 5 absorption, 6,7 and other unit operations.
Sun et al. 8 conducted a gas-liquid two-phase condensation experiment in a counterflow tower and showed that steam flow rate, cooling water temperature, and cooling water flow rate can affect the condensation effect. Chen et al. 9 found that high steam temperature, low steam flow rate, low cooling water inlet temperature, and high cooling water flow rate helped to promote steam condensation by conducting condensation experiments in a cocurrent flow tower. Wang et al. 10 conducted an experimental study on the transient condensation of steam containing noncondensable gas in a condensing tower and showed that increasing the cooling water flow rate significantly improved the heat transfer coefficient, but reducing the subcooled water temperature had a limited effect on steam condensation. Ding et al. 11 investigated the effect of water film breakage on condensation by constructing a two-dimensional axisymmetric rotational model in computational fluid dynamics (CFD), and the results showed that cooling water flow rate, cooling water temperature, and steam temperature all had an effect on the breakage length of the water film. Zhou et al. 12 showed that when steam containing noncondensable gas is injected into a cooling water tank, changes in the steam flow rate can affect the heat transfer between the two phases of the steam by changing the plume pattern of the steam. Therefore, in this paper, steam flow rate, steam temperature, cooling water flow rate, and cooling water temperature are selected as the operating conditions to study the effect of their variation on the condensation results.
Segev et al. 13 conducted condensation experiments in a counter-flow tower and found that the turbulence of the liquid film would affect the condensation results. Koirala et al. 14 conducted simulation experiments in a cocurrent flow tower and the results showed that the turbulence of the liquid film would also affect its condensation process. Wei et al. 15 showed that an increase in liquid flow rate in a packed tower promotes turbulence of the liquid film, which in turn promotes condensation. The above experiments only examined the effect of flow rate on condensation and lacked experiments where temperature was used as an operating condition.
The results of Sideman et al. 16 show that the condensation effect of the direct contact condensing system is limited by the size of the contact area of the two phases, while the addition of packing in the tower can increase the specific surface area and improve the heat transfer efficiency. By simulating the condensation process through the packing, Luo et al. 17 found that the inclination angle of different packing surfaces affects the liquid flow; in addition, higher vapor velocity has a significant effect on the width of the liquid film, which affects condensation. 18 Gu et al. 19 established a CFD model of vapor-liquid two-phase counterflow by the VOF method to study the relationship between the surface inclination angle of the gauge packing and the wetting performance of the liquid, and the results showed that as the inclination angle of the packing corrugation increases, the possibility of liquid flooding becomes greater.
Jin et al. 20 compared the evaporation process of the cocurrent flow tower with that of the counterflow tower, and the results showed that, with or without packing, the evaporation effect of the counterflow tower is better than that of the cocurrent flow tower. However, in the industrial production process, the cocurrent flow tower has the advantages of a small footprint and convenient pipe cleaning, so it has a wider development prospect, but unfortunately, there is relatively little research on the heat transfer process of the direct contact cocurrent flow tower.
From the above literature, it is clear that the operating parameters (G in , L w , T cond , T in ) all have an effect on the condensation results. However, the significance of the various influencing factors is not clear. Previous experiments have investigated the effect of the presence of packing on condensation results. For example, the presence of packing can effectively reduce the pressure drop in the tower, 21,22 improve the mass transfer performance of the system, 23 and the texture of the metal packing surface helps the liquid film to travel and thus promotes condensation. 24 However, there is a lack of research on the condensation performance of different fillers in a cocurrent flow tower under negative pressure.
The steam discharged from the tail end of the power plant is less dense and has a coarse tube diameter and interwall heat exchangers have been commonly used in the past. However, their condensation efficiency is lower than that of direct contact heat exchangers. On this basis, this experiment sought to build a new system that could be a direct replacement for the inter-wall heat exchanger. Due to the low density of the steam and the large diameter of the tubes, a counterflow option would require rerouting of the piping and a larger space, but the space at the tail end of the power plant is small, so this experiment was based on this situation and used a downstream direct contact heat exchanger.
In this paper, the influence of each operational property on the significance of the condensation performance will be investigated by means of an orthogonal test in a ceramic Raschig ring and the link between the two will be determined. The other two parts of this paper focus on the comparison of the condensation performance of different packings and the fitting of NTU L to Kv. Four different packings were selected for experiments in a parallel flow condensing tower to obtain the relationship between their packing performance and condensation performance. By comparison, the packing with the best condensation performance was selected. In previous experimental studies, it has been found that conventional heat transfer coefficients do not accurately describe the condensation process due to the complexity of the direct contact condensation process. 25 In this paper, by fitting a large amount of experimental data, an empirical formula is obtained that fits well and can be used to guide the design of condensers.

| Experimental setup and operation
Packed subatmospheric pressure steam parallel flow condensing experiment system consists of electrically heated steam generator, evacuation system, condenser, circulating water system, and data test acquisition system. The flowchart of the experiment is shown in Figure 1.
The experiments were carried out by means of an electrically heated steam generator to simulate the spent steam at the end of the turbine. It is equipped with six sets of 24 kW electric heating rods inside for three-phase power supply, which can be continuously adjusted from 0 to 144 kW with an electrical efficiency of 97%. During the experiment, the pressure inside the steam generator was reduced by means of an evacuation system, so that the water inside the steam generator evaporated under negative pressure, thus obtaining negative pressure steam. The vacuum pumping system mainly consists of a vacuum pump, a buffer tank and a constant temperature water tank. The speed of the vacuum pump is adjusted by means of a frequency converter to achieve the F I G U R E 1 Schematic diagram of the experimental system. adjustment of the pumping capacity. The ultimate pressure of the vacuum pump is 6 × 10 −2 Pa, the pumping rate is 15 L/s and the speed is 1400 r/min. During the experiment, the PID control system was used to adjust the frequency of the vacuum pump, so that the pressure inside the whole system remained stable and the steam temperature was guaranteed to be stable. The buffer tank is a Φ500 mm × 1500 mm iron tank, which is used to reduce the vacuum fluctuation in the experimental system, and thus reduce the steam temperature change.
A constant temperature water bath is connected to a cold trap to condense any steam that has not yet condensed in the pipework.
The condensing tower is made of stainless steel 304 with an inner diameter of 300 mm and a height of 420 mm. Packing height of 200 mm. The liquid distributor is a 62-hole 4 mm liquid distributor. The volume of condensing heat transfer is the volume between the body distributor and the liquid surface, which is an important parameter for calculating the total volume heat transfer coefficient of the tower. The circulating water system mainly consists of a heat exchanger, circulating water pump, return water pump, and turbine flowmeter. The role of the heat exchanger is to cool the circulating water, which has warmed up after condensation, to the required temperature to ensure that the temperature of the cooling water inlet to the condenser remains stable. The circulating water pump changes the flow rate of the cooling water mainly by changing the number of revolutions of the pump to ensure that the liquid level inside the steam generator and condenser remains stable. A turbine flowmeter is used to determine the cooling water flow with high accuracy.
To reduce heat loss, all transport pipes were wrapped with insulation wool and tested for thermal performance before the experiment to ensure negligible heat loss during the experiment.
The data test acquisition system is a product of Beijing 3D Force control Technology Co 6.1. The tests include system pressure, steam temperature, temperature at the outlet, cooling water flow, cooling water temperature, and so forth. The sensors are located as shown in Figure 1, with three temperature measurement points located at the liquid inlet, steam inlet and condenser outlet, using PT100 temperature thermometers. The steam flow rate, condensate piping and circulating water piping are each equipped with a turbine flowmeter to indicate the condensate flow rate and cooling water flow rate, and a vacuum regular at the outlet of the steam generator is to indicate its internal pressure.
The type and error of each device is shown in Table 1.

| Experimental operating conditions
According to literature, 26 steam flow (G in ), steam temperature (T cond ), cooling water flow (L w ), and cooling water temperature (T in ) have an effect on the condensation effect, but the extent of the effect of these four factors is unclear. Therefore, a L2 5 (5 5 ) orthogonal test was designed using ceramic Raschig rings as packings and used to investigate the significance of the effects of G in , T in , T cond , and L w on ΔT, R, NTU L , and Kv. The results of the experiment were tested using the SNK test and the factors in this experiment had no interaction between each other. The values of the factors and levels of the orthogonal test are shown in Table 2.
Four different packings were used to investigate the effect of packing performance on condensation results. The experimental operating conditions are shown in Table 3 and the properties of each packing are listed in Table 4. Figure 2 shows photographs of the four packings selected.
Before conducting the experiment, the effectiveness of the leakage protector, mechanical safety check, and vacuum tightness test are carried out on the device.
Turn on the circulating water pump to the demanded cooling water flow, turn on the vacuum pump to pump to the specified vacuum level to obtain the required steam temperature, turn on the steam generator after the system stabilizes, set the steam power and start running, observe the steam temperature stabilization and start recording, turn off the vacuum pump and steam generator after the cooling water temperature reaches the demanded value, record the data by computer, change the experimental

| Condensation rate R
The condensation rate is usually used in experiments to characterize the completion of vapor condensation during the condensation process. Its defining equation is: where c pL is the specific heat at a constant pressure (kJ kg −1 K −1 ), L is the mass flow of cooling water (kg/h), T out is the temperature of cooling water at the outlet of the condenser (°C), T in is the temperature of cooling water at the inlet of the condenser (°C), Q is the effective power of the steam generator (kW).

| Degree of subcooling ΔT
In condensing systems, the subcooling is the steam temperature T cond minus the mixing water outlet temperature T out and is expressed as: Subcooling is often used to measure the energy loss in a system, a smaller subcooling indicates less energy loss in the system.

| Number of liquid-phase heat transfer units (NTU L )
The number of heat transfer units in the liquid phase is a common dimensionless quantity that characterizes the intensity of heat transfer and is defined at full condensation by the following equation 23 : where L is the mass flow rate of the subcooled water (kg/ h), α L is the liquid phase heat transfer coefficient (kW m −2 K −1 ), S LG is the two-phase heat transfer contact area (m 2 ), c pL is the constant pressure specific heat capacity (kJ kg −1 K −1 ). NTU L is used to describe the heat transfer intensity between two phases and its value is related to the liquid flow rate, the heat transfer coefficient and the contact area between the two phases. In practical experiments, the NTU L is calculated as 27 : where T out is the temperature of the mixture of cooling water and steam condensate at the outlet position of the condensing tower (°C), T in is the temperature of the cooling water at the inlet of the condensing tower, (°C), T cond is the steam temperature (°C).

T A B L E 2 Orthogonal table factors and levels.
Factors level T cond (°C) The value of NTU L can be obtained from experimental results according to Equation (4). With a known NTU L , the actual contact area S LG of the two phases during condensation can be obtained from Equation (3) and a correlation with the equipment scale can be established from this value, which further guides the design of subsequent tower equipment.

| Total volume heat transfer coefficient Kv
The total volume heat transfer coefficient effectively characterizes the overall condensation intensity of the heat exchanger and is an important parameter for measuring the effectiveness of condensation, Kv is expressed as: where V is the volume between the discharge tube liquid distributor and the stable liquid level, indicating the volume used for condensation (m 3 ), ΔT m is the logarithmic mean temperature difference of the condensation process under the parallel flow tower (°C). It is calculated as follows: From the value of Kv, the volume required in the actual condensation process of the condenser can be obtained, which will help in the subsequent optimization of the condenser in terms of design.

| Orthogonal experiments
Analysis of variance (ANOVA) is used to analyze the results of experiments. ANOVA is also known as the "F-test" and is used to test the significance of differences between the means of two or more samples.
The F-value is the statistic of the F-test, which is the ratio of the mean square of the effect value to the mean square of the error term. The larger the F-value, the more significant the effect of the factor on the result.

| the degree of cooling ΔT
As can be seen from Table 5, the F values for steam temperature and cooling water flow are both greater than F0.01 (f1, f2), indicating that these two factors have a significant effect on subcooling at the 0.01 level. By analogy, cooling water inlet temperature and steam flow rate have a significant effect on subcooling at the 0.05 level. The magnitude of the F value shows that the difference between the two factors at the same level is small, and that the cooling water flow rate has the greatest effect of the four factors.

| Condensation rate
As shown in Table 6, the cooling water inlet temperature and steam flow rate have F values greater than F0.25 (f1, f2), so these two factors have a significant effect on the condensation rate at the 0.25 level, and the steam flow rate has the strongest effect. Meanwhile, the smaller F values for cooling water flow rate versus steam temperature indicate a smaller effect on condensation  rate. And all four factors have a limited impact on the condensation rate. Table 6 also indicates that the variation in condensation rate is influenced by a variety of factors, and the distinction between the various factors is not obvious.

| NTU L
As can be seen from Table 7, the F values for cooling water inlet temperature and cooling water flow rate are greater than F0.05 (f1, f2), so these two factors have a significant effect on NTU L at the 0.05 level. The effect of cooling water flow is greater than the effect of cooling water inlet temperature and is the most significant of all the influencing factors. The F values for steam temperature and steam flow rate show that these two factors have a significant effect on NTU L at the 0.1 level. Table 8 shows the results of the ANOVA for Kv. From the data in the table, it can be seen that steam temperature, steam flow, and other four factors have a more significant effect on Kv. The cooling water inlet temperature and steam flow rate have a significant effect on Kv at the 0.05 level as their F values are greater than F0.05 (f1, f2). Similarly, it can be seen that cooling water flow rate and steam temperature have a significant effect on the magnitude of Kv at the 0.1 level. And of these four factors, the steam flow rate has the greatest effect.

| Kv
From the above orthogonal experiments and correlation analysis, it can be seen that the factors that have a significant effect on the cooling degree (ΔT), the condensation rate (R), the number of liquid phase heat transfer units (NTU L ), and the total volume heat transfer coefficient (Kv) are different. The cooling water flow rate has the greatest influence on ΔT and NTU L , while the steam flow rate has the greatest influence on Kv, the effect of each factor on R is largely similar. The experiments can be changed by adjusting the corresponding operating conditions for the ΔT, NTU L versus Kv.
3.2 | Effect of the operating parameters on ΔT and R

| Steam temperature
As the temperature of the steam rises during the experiment, the temperature difference between the two phases gradually becomes greater and the condensation push becomes greater. At the same time, as the steam temperature increases, the steam density increases, which leads to the flow rate decreasing and the residence time of the vapor in the tower becomes longer, which improves the condensation efficiency.
As shown in Figure 3, the condensation rates of the four packings show a general upward trend as the steam temperature rises. In Figure 3A the condensation rate of the regular packing is approximately 95%, which is the same as the empty tower, with no significant difference between the two packings. In Figure 3B, the condensation rate for the random packing is approximately 90%, which is lower than that of the empty tower. This indicates that the condensation rate can be increased by changing the type of packing to increase the specific surface area. However, for the same type of packing with different specific surface areas, the effect of specific surface area on the condensation rate is limited.
Comparing Figure 3A,B, we can find that the subcooling degree of the regular packing is basically the same as that of the empty tower, but the subcooling degree of the random packing is greater than that of the empty tower.
Considering the uneven distribution of gas and liquid in the random packing, the increase in temperature does not improve the distribution of vapor and liquid in the packing. However, it leads to an increase in driving force, and the specific surface area is smaller than that of the regular packing, which does not provide a larger contact area and is not conducive to condensation. As can be seen from Figure 3B, the trend in subcooling tends to flatten out in the pall ring compared to the Raschig ring, which has a somewhat larger operating range considering its 50% increase in gas flux.

| Cooling water flow
The condensation rates of the four fillings and the empty tower in Figure 4 all increase with the cooling water flow rate, and this variation follows the same trend as in Equation (1). The reason for this is that as the cooling water flow rate increases, the increase in liquid flow rate helps to accelerate the turbulence and renewal of the interface between the vapor and liquid phases, thus increasing the heat transfer efficiency. Regular packing provides a larger specific surface area and thus a higher condensation rate than the empty tower and random packing, but for the same type of regular packing, the increase in specific surface area has a more limited effect on condensation when the cooling water flow rate is increased. It is worth noting that in Figure 4B the Raschig ring with a smaller surface area shows better condensation as the cooling water flow rate increases. This is because the pall ring provides a larger specific surface area at lower cooling water flow rates, but as the cooling water flow rate increases the liquid spray density gradually increases and its value approaches the minimum spray density of the Raschig ring, and the larger pathway of the Raschig ring helps to redistribute the liquid within the tower, resulting in a larger condensation rate. 28 The graph shows that as the cooling water flow rate increases, the subcooling degree of all four types of packing and empty tower increases. This is because as the cooling water flow rate (L w ) increases, the liquid phase processing capacity in the tower equipment increases under the same steam load, and the outlet water temperature must decrease resulting in an increase in subcooling. And from the figure can be seen: Figure 4A in the regular packing subcooling degree of change in the range of 0.3-7°C, Figure 4B in the random packing range of 1-8°C. The overall subcooling degree of the random packing is higher than that of the regular packing and both are smaller than that of the empty tower, indicating that the presence of the packing can promote the heat exchange between the two phases, reduce the subcooling degree of the tower equipment and improve the waste heat utilization rate.

| Steam flow
As the steam flow rate increases, the increased steam load will affect the condensation effect when the cooling water flow rate is a constant value. It is known from the literature 29 that the increase in steam flow rate will be accompanied by an increase in vapor atomization in the tower, resulting in a reduction in the condensation rate. However, as the steam flow rate increases, the steam velocity becomes larger within a certain range, which helps to promote turbulence at the gas-liquid interface and improves the condensation effect. Figure 5A shows that the condensation rate of the regular packing fluctuates less with increasing steam flow rate, remaining at around 93% overall. However, in Figure 5B the two different types of random packing show a large difference as the steam flow rate increases. As the steam flow rate increases, the condensation rate of the smaller specific surface area of the four packings in the Raschig ring with screen corrugated 250Y is greater. The two different types of packing exhibit the same condensation behavior. This is due to the fact that as the steam flow rate increases, the vapor path in the larger surface area packing is smaller, which is not conducive to vapor-liquid contact and thus affects condensation.
With increased steam flow rate G in , the amount of steam absorbed by the cooling water becomes greater for the same cooling water flow rate and therefore the subcooling decreases.
As can be seen from the subcooling curves in Figure 5, as the steam flow rate increases, the subcooling of all four fillings and the empty tower decreases. This is because when the steam flow rate increases, the amount of steam condensed by the cooling water increases and the outlet temperature increases, so the subcooling decreases. Figure 5 indicates that the subcooling degree of all four packings is greater than that of the empty tower. However, the packing provides a large specific surface area, making the contact area between the two phases of gas and liquid larger. However, with an increased steam flow rate, accompanied by a higher steam velocity, the channels in the packing instead impede the flow of steam. This is detrimental to heat transfer and condensation, resulting in a packed tower with greater subcooling than an empty tower. Figure 6 depicts the variation curve of condensation rate and subcooling with increasing cooling water inlet temperature for four types of packing and empty tower. As can be seen from the condensation rate curves in the figure, the condensation rates of the four packings and the empty tower show an overall increasing trend as the cooling water inlet temperature increases, and the condensation rate of the regular packing is greater than that of the empty tower and the random packing. This indicates that the random packing has a limited effect on increasing the condensation rate when the cooling water inlet temperature is increased. The regular packing provides a larger specific surface area, which helps to improve condensation efficiency.

| Cooling water inlet temperature
As can be seen from the subcooling curves in the graph, the subcooling of all four fillings is greater than that of the empty tower. The reason for this is that as the inlet temperature of the cooling water rises, its viscosity decreases and the flow rate becomes greater, resulting in a shorter residence time in the tower, which is not conducive to condensation. It is also known from the literature 30 that the main condensation zone in a packed tower decreases as the temperature of the liquid rises. Considering the limited height of the packed tower in this experiment, it will have an effect on the condensation effect of the packing, making the subcooling in the packed tower higher than that in the empty tower.

| Steam temperature
As can be seen from Figure 7, NTU L and Kv of the four fillings and the empty tower both decrease as the steam temperature increases. The NTU L and Kv of the regular packing are greater than those of the random packing, while the NTU L and Kv of the empty tower are between those of the regular and random packing. Although the presence of random packing increases the specific surface area, the uneven vapor-liquid distribution inside the packing will affect the condensation effect. As the vapor temperature increases, packed tower may be varying degrees of atomization within the packing, affecting condensation. 31 As the temperature of the vapor rises, the atomization increases, preventing the liquid from coming into contact with the vapor for condensation and affecting condensation. The increase in temperature of saturated steam is accompanied by an increase in density. Steam at 40°C has a density of 0.05 kg/m 3 and when it is heated to 50°C, the density increases by 1.5 times and the dynamic viscosity 1.0 times, which is not conducive to steam condensation in the tower, resulting in a lower condensation coefficient. As can be seen from the curves of the four different packings in the graph, the uneven distribution is not apparent within the same type of packing. Indicates that this uneven distribution is more pronounced between the different types of packing and therefore may be caused by the stacking method.

| Cooling water flow
According to Equation (3), the NTU L is inversely proportional to the liquid phase flow rate L w and directly proportional to the two-phase contact area S LG . Therefore, as the cooling water flow rate L w increases the number of liquid phase heat transfer units decreases. The defining equation for Kv shows that the magnitude of Kv is proportional to the magnitude of NTU L , so as the cooling water flow rate increases, Kv follows the same downward trend as NTU L . It should also be noted that an increase in the cooling water flow rate will result in an increase in the flow rate and a decrease in the residence time in the tower. This becomes the main limiting condition for condensation, which is reflected in the fact that a filler with a larger specific surface area has a higher heat transfer coefficient.
As shown in Figure 8, the difference between regular and random packing is mainly reflected in the lower cooling water flow rate in the tower. The need for more surface areas is more pronounced at lower cooling water flow rates. NTU L is larger as the regular packing provides a larger specific surface area, which facilitates a more uniform distribution of the liquid. The graph shows that the screened corrugated 700Y has a larger NTU L and Kv than its 250Y counterpart, and that the loose packed pall ring has a larger NTU L and Kv than the Raschig ring, but given the uneven distribution of the liquid within the loose packed material at low water flow rates, the NTU L and Kv are smaller than in an empty tower at low subcooled water flow rates. However, as the subcooled water flow rate increases, the effect of redistribution of liquid between the packings becomes apparent and the difference in NTU L and Kv between the four packings decreases and is greater than that of the empty tower. This indicates that the presence of packings can expand the operating conditions, and with the increase in water flow, the uneven distribution of random packing, trench flow and wall flow is alleviated.

| Steam flow
As the steam flow rate increases, the flow velocity of the vapor becomes greater and the degree of turbulence increases, helping to improve heat transfer. Therefore, as the steam flow rate increases, the NTU L and Kv of all four packings and the empty tower in Figure 9 increase.
When the steam flow rate is small, all four types of packing can make the vapor in the tower evenly distributed. However, as the steam flow rate increases, the smaller surface area of the Raschig ring and the screen corrugated 250Y exhibit larger NTU L and Kv. This is because the smaller vapor paths within the larger surface area packing are not conducive to steam flow, which leads to a smaller heat transfer coefficient.

| Cooling water temperature
As the temperature of the cooling water increases, the temperature difference between the two phases of the vapor and liquid decreases and the driving force is weakened, which is not conducive to condensation. However, the increase in liquid temperature leads to a decrease in its viscosity and an increase in turbulence, which promotes the renewal of the cooling water surface and improves the condensation efficiency.
As can be seen from Figure 10, the NTU L and Kv of all four types of packed and empty towers increase with the increase in cooling water temperature, but the NTU L and Kv of packed towers are smaller than those of empty towers. This is because as the cooling water temperature increases, the driving force between the gas and liquid phases gradually decreases, and the turbulence between the two phases gradually becomes the main influencing factor. The presence of packing does not facilitate the turbulence of the liquid phase, thus reducing the condensation efficiency, which is reflected in the fact that the number of liquid phase heat transfer units NTU L and the total volume heat transfer coefficient Kv are both greater in empty towers than in packed towers.

| Fitting of NTU L and Kv
In Equations (3) and (5), the values of NTU L and Kv are related to the cross-sectional area and volume of condensation. Therefore, predicting the experimental values of NTU L and Kv is useful in determining the cross-sectional area and volume of condensation and thus guiding the design of the condenser. Jacimovic 32 carried out predictions regarding NTU L in counterflow packed towers, but did not show a good fit with the experimental results. On this basis, Chen et al. 18 introduced a comparison temperature (T r ) for the fitting and obtained better fitting results, so their fitting method is followed in this paper.
F LG is the kinetic energy factor, and the formula is as follows: LG in G L where ρ G is the density of the vapor (kg/m 3 ), ρ L is the density of the subcooled water (kg/m 3 ), r cond is the latent heat and c pL is the constant pressure specific heat capacity, kJ kg −1 K −1 . T r is the comparison temperature and the equation is: The fit is evaluated by adjusted R 2 , the closer the value is to 1, the better the fit is. The formula is as follows (Figures 11 and 12): n p n y y n p y y n The results of the fitting of T r and F LG for NTU L and Kv with different packings are as follows (Tables 9  and 10): From the above fitting results, it can be seen that in this experiment, the results of fitting experiments with different packings are similar, and the difference between different packings is more obvious when T r × F LG is small, when T r × F LG is greater than 1.0, the experimental data for the different fillings converge, indicating that the difference between the different fillings mainly arises when the subcooled water flow rate is small.
A fit on NTU L versus Kv combining the above data points is shown below.: The empirical equation for NTU L versus Kv is obtained from the experimentally obtained data points as follows: To verify the reliability of the fitted results, the experimental values obtained for the four different packings were fitted to their theoretical values as shown below: Figure 13 shows that the experimental values for the different packings fit well with the theoretical values of the above empirical equations within a ±20% error range.

| Verify the empirical formula for NTU L and Kv
To further verify the reliability of the above empirical formula, the orifice plate corrugated 250Y was chosen to verify the simulation results, and the verification results are as follows: The experimental results show that the empirical equations (8) and (9)   ±20% ( Figure 14). It shows that the above empirical equations can be used to predict the experimental results and can further guide the design of the condenser by predicting the unit volume heat transfer coefficient (NTU L ) and the total volume heat transfer coefficient (Kv) to determine the condensing volume V and the twophase contact area S LG .

| CONCLUSION
(1) Operating parameters that can have a significant effect on different condensation characteristics vary. The cooling water flow rate has a significant effect on the magnitude of ΔT and NTU L , and the steam flow rate has a significant effect on the magnitude of Kv. For R, however, the difference between the parameters is not significant. Therefore, the desired condensation coefficient can be obtained by varying the different operating parameters. (2) When the cooling water flow is low or the steam flow is high, the regular packing has a greater condensation rate and less subcooling than an empty tower and a random stack packed tower. Under both operating conditions, increasing the specific surface area improves the condensation effect. When the steam temperature rises, the random packing will lead to uneven distribution of the vapor and liquid due to the way it is stacked, resulting in a higher subcooling than in an empty tower. The graph shows that the overall performance of condensation rate and subcooling is better with regular packing than with random packing. (3) As the cooling water inlet temperature rises, the NTU L and Kv of the empty tower is greater than that of the packed tower, due to the smaller porosity of the packed tower which is not conducive to steam flow. In experiments where the cooling water flow has not yet reached the minimum spray density of the bulk stack filler, the heat transfer coefficient is less than that of the empty tower and the heat transfer is poorer. (4) For the same type of regular packing, the increase in specific surface areas has a limited effect on condensation. For bulk packing, however, the differences between the different types of packing are more pronounced. (5) From the fitting results, it is found that different packing Kv expressions tend to be the same and gradually converge as T r × F LG rises, the difference between different fillings is mainly reflected in the smaller cooling water flow rate, when T r × F LG is greater than 1, it gradually merges into a curve. Therefore, all data points can be fitted to a curve, and its formula is verified by orifice plate corrugation (250Y) to find that the formula has good predictability and can be used to guide engineering practice in the future.