Condensation Separation of NO2 with Dimerization Reaction in the Presence of Noncondensable Gas: Critical Assessment and Model Development.

Pure nitrogen dioxide (NO2) has significant economic value and is widely used in many fields, for which condensation technology plays an important role in separation and purification. However, developing cost-effective NO2 condensers remains challenging due to the lack of precise theoretical guidelines and comprehensive understanding of NO2 condensation process. In this work, NO2 condensation at various inlet surface subcoolings, mole fractions of noncondensable gas (NCG), and Re numbers was studied with a visualization experimental system. The influential rules of each parameter on heat transfer coefficients (HTCs) and the NO2 condensate state as the coexistence of droplet, streamlet and film were revealed. A substantial underestimation of experimental data by the classical heat and mass transfer analogy (HMTA) model was quantified. The large discrepancy was found to originate from the uniqueness in heat transfer, mass transfer, and condensate state caused by NO2 dimerization during condensation. A modified HMTA model was developed considering the release heat of dimerization reaction and the promotion of mass transfer by an increased NO2 concentration gradient within the diffusion layer which contribute to improvements of HTCs by ∼6 and ∼49%, respectively. The correction of liquid film roughness regarding potential heterogeneity of dimerization was proposed as a function of the key parameters, contributing to the improvement of HTCs by ∼150%. An accurate theoretical formula for HTCs prediction within an error of ±25% was finally derived, providing the key step for success in practical applications.

Introduction

Nitrogen dioxide (NO2) is a valuable chemical in many fields, which has extensively been used as a multifunctional reagent (nitration agent, nitrosation agent and oxidant), a rocket propellant[1,2] and important ingredients of nitric acid and dimethyl sulfoxide. The high-purity NO2 liquid product has a market price of ∼6000 U.S. dollars/ton in China. The ways of acquiring high-purity NO2 involve separating NO2 from products of ammonia catalytic oxidation as the conventional production process[3] and recycling NO2 from rocket-launching exhaust gases[4] and industrial flue gases.[5,6]

NO2 with a standard boiling point of 294 K can be upgraded and liquefied with high purity and recovery under mild operation conditions, based on which the condensation technology plays an important role in NO2 separation, purification, and storage in each NO2 acquisition process. Zhang et al.[7] demonstrated the condensation process of recycling NO2 from the rocket-launching exhaust gas, achieving a NO2 purity of 99.6% and a recovery of 95.6% under the conditions of 0.12 MPa and 263.15 K. Liu et al.[8] proposed a condensation–distillation process capable of recycling NO2 from iron-ore sintering flue gas and obtained high-purity (>99.5%) NO2 liquid at 0.1 MPa and 263.95 K. Although the NO2 condensation technology has been applied in industry, there remain significant problems such as high investment, operation cost, and safety hazards due to the bulky condenser, equipment corrosion, and high condensation pressure, respectively. Therefore, it is a long-sought-after goal to improve the energy efficiency of NO2 condensation to reduce the size of the condenser and the operation complexity. To meet this goal, precise theoretical guidance is necessary[9,10] for condenser design and optimization, for which effects of processing parameters on NO2 heat and mass transfer during the condensation merit investigations from the following three perspectives. First, coexisting noncondensable gases (NCG including N2, O2, etc.) impair NO2 condensation efficiency, for which studies on water vapor condensation have shown that a 0.5% volume fraction of air can reduce the heat transfer coefficient (HTC) by 50%.[11,12] Second, the conversion of NO2 to N2O4 is favored at lower temperatures via the exothermic dimerization reaction, which may lead to changes in the NO2 gaseous concentration and bulk gas temperature.[13,14] Third, the effect of the condensate film roughness on heat and mass transfer within the diffusion layer (gaseous region between the bulk and the film)[15,16] could not be ignored,[17,18] particularly as the NO2 dimerization is involved.

Previous studies on gas condensation in the presence of NCG and the effects of liquid film roughness were mainly focused on water vapor. In terms of the effect of NCG, Peterson et al.[15] developed a diffusion layer model and accurately predicted the experimental condensation Nusselt (Nu) number in the presence of NCG with a minimum standard deviation of 4.7%. Dehbi et al.[19] developed a heat and mass transfer analogy (HMTA) model, showing that the increase of NCG from 5 to 10% suppressed heat transfer in water vapor condensation (inlet Nu from 500 to 425). Ge et al.[20] experimentally studied the effects of NCG (CO2) at a wide concentration range on water vapor condensation, showing that the increase of the CO2 mass fraction from 23.3 to 84.0% resulted in the decrease of HTC from 5.5 to 1 kW·m–2·K–1. In terms of the effect of film roughness, a degradation factor defined as the ratio of experimental HTC to theoretical HTC has been commonly employed to correct the error caused by interfacial shear stress while using the conventional models. Lee and Kim[21] showed a satisfactory prediction accuracy with a standard deviation of 19.5–25.8%, by correcting the laminar film model with the degradation factor. Kuhn et al.[22] improved Nusselt film model prediction with the relative standard deviation of 17.6% for HTC by adopting a degradation factor and addressed the heat transfer enhancement due to interfacial shear and surface waviness. Ren et al.[23] used the HMTA model in consideration of film roughness and found that the increase of the inlet mixture mass flux (from 55 to 165 kg·m–2·s–1) increased the heat flux by 110%, indicating the positive effect of film roughness on heat transfer. In terms of gas vapor condensation in consideration of dimerization reaction, Gribkova[13] found that the prediction quantity of condensed N2O4 with the model considering the dimerization reaction was 1.24–1.12 times higher than that without dimerization. Mikhalevich[14] found that NO2 dimerization chemical reactions promoted gas saturation temperature and the heat transfer rate. To sum up, the combined effects of NCG, liquid film roughness, and dimerization reaction on NO2 condensation were rarely studied, which may largely be associated with the difficulties in measuring NO2 condensation variables regarding the narrow condensation temperature range (from a freezing point of 262.15 K to a boiling point of 294.15 K) and the highly corrosive experiments.

In this study, a NO2 condensation experiment apparatus coupled with a sophisticated methodology was set up. The HMTA model in consideration of NO2 dimerization was developed. With the aim of guiding practical application, NO2 condensation at various surface subcoolings, NCG mole fractions, and the inlet mixture Reynolds number (Re) was systematically investigated through a series of condensation tests. The influential rules of each processing parameter on HTCs and the coexistence of droplet, streamlet, and film as the stabilized NO2 condensate state were revealed. The key roles of the NO2 dimerization reaction and the film roughness in condensation were revealed and explored by comparing experimental data and model-predicted results. The friction factor (fr) correlated with the condensate flow rate as a function of Re, inlet surface subcooling, and NCG mole fraction was proposed to gain deeper insights into NO2 condensation and improve the model prediction accuracy for practical use.

Experimental Method

Experimental System

The NO2–air condensation experimental system consisted of a gas supply system, a gas flow rate control system, a refrigerant circulation system, a data acquisition system, and a test section, as shown in Figure a. In current work, the gas supply system used only air as NCG, which is close to the real situation that the concentrations of other NCGs such as NO are much lower as compared with air. The inlet air provided by the air compressor passed through the reducing valve capable of stabilizing the pressure and then entered the dehydration column. The NO2 (purity > 99.9%) was supplied by the gas cylinder, whose pressure was controlled by a reducing valve at the outlet of the tank. The gas flow rates of air and NO2 were controlled by rotameters. The two gases were fully mixed in the mixing tank where a constant temperature of 303.15 K was achieved by heating tape to prevent NO2 condensation. The gas mixture was then fed into the test section for condensation, and the NO2 condensate can be collected using a measuring cylinder.

Figure 1

Schematics of (a) condensation experimental system and (b) test section.

The test section made from 316 stainless steel was the core part of the experimental system. The structure of the test section is shown in Figure b, with detailed information listed in Table . Three T-type patch thermocouples were set for measuring the wall temperature. Another three T-type thermocouples for measuring the bulk mixture temperature were set above the corresponding wall temperature measuring point. In addition, two T-type thermocouples were set in the gas inlet and outlet pipes to measure the temperature of the mixture gas. All thermocouples were connected to an Agilent data collector. Transparent glass sheets were glued around the wall to ensure that the device was sealed. Two high-definition cameras were placed on the front and side of the test section to photograph the condensate. Through this kind of visual design, it was able to ensure that there was no frozen NO2 during the experiment and the data can be measured accurately. A medium tank filled with a coolant was connected directly behind the wall and was covered with insulation material to prevent energy loss. The coolant driven by a centrifugal pump consisted of ethylene glycol and water, circulating between the cooling medium tank and the refrigerator, and providing cold energy to the test section.

Table 1

Detailed information of the Test Section

items	details
length of the rectangular channel	0.030 m
width of the rectangular channel	0.015 m
length of the vertical wall	0.075 m
width of the vertical wall	0.030 m
thickness of the vertical wall	0.0008 m
distance between thermocouples on the wall	0.025 m
distance between the bulk mixture temperature measuring point and the wall	0.0075 m

Data Reduction

According to the law of conservation of energy, the total heat flow rate between the bulk mixture and the wall originating from the sensible heat , the latent heat , and the chemical heat from a potential dimerization reaction can be expressed aswhere was calculated by the temperature measured from the inlet and outlet pipes and was calculated by the amount of the condensate and the corresponding time difference in a steady state. The calculation method of was as follows. According to the chemical equation of NO2 and N2O4, the reaction constant[24] can be determined fromwhere pNO and pN are the partial pressures of NO2 and N2O4, respectively. The relationship between the mole fraction of NO2 and Kp at reaction equilibrium is written asAs shown in eq , only Kp of the reaction is required for calculating the mole fraction of NO2 at a constant total pressure P. Chao et al.[25] concluded the correlation between Kp and temperature asAccording to the relation of chemical reaction coefficients (as described in the Section S3 of the Supporting Information), the chemical heat flow rate from the initial state (with pure NO2) to the equilibrium of the reaction isThe reaction heat from equilibrium state A to equilibrium state B can be calculated by the difference between the heat released from the initial state to two states. Figure shows the material flow and energy flow of NO2 above the wall. Thinking of the test section as one node in Figure , the dimerization process in the condenser can be classified into dimerization of gaseous NO2 that is not condensed flowing from the inlet to the outlet and the dimerization of gaseous NO2 that would be condensed from the bulk gas to the wall.

Figure 2

Material flow and energy flow of condensation with the dimerization reaction.

The mass flow rate of NO2 involved in both dimerization processes can, respectively, be expressed aswhere q is the mass flow rate of NO2 at the gas outlet pipe. ρNO is the density of liquid NO2, VNO is the volume of liquid NO2 collected in a steady state, and t is the collection time. The inlet and outlet temperatures were selected as the NO2 saturation temperatures of the equilibrium states at the inlet and the outlet. The average temperatures of the wall and the bulk mixture (eqs and 10) were selected as the NO2 saturation temperatures of the equilibrium states at centroid points of the wall and the gas flow channel, respectively.Based on eq , the chemical heat flow rate is expressed asThe average HTC of the test section is calculated from

Theoretical Model

Classical and modified HMTA condensation models were built in this work. The classical model referred to the conventional diffusion layer model[16,19,21,23] in predicting water vapor condensation, where the total HTC consists of liquid film HTC, sensible HTC, and latent HTC, in terms of the effects of NCG on condensation. The modified model was developed considering the dimerization of NO2 in the diffusion layer on the basis of the classical model. Similar to the correction of enhanced heat transfer due to film roughness in previous studies,[21,22] a degradation factor was introduced to correct the underestimation of experimental HTC. Through the comparisons of two models with experimental data, the effects of dimerization reaction and the film roughness on heat and mass transfer would be demonstrated, for the purpose of accurate prediction of practical NO2 condensation. The detailed derivations for the models were described as follows.

Classical HMTA Model

The classical HMTA model, based on the diffusion layer theory,[15] suggests that condensable gas condenses to form a liquid film with the thickness of δ, and NCG that cannot pass through the film but only accumulates on the film surface forms a stable diffusion layer of mixed gas outside the liquid film. According to the conservation of energy, the heat transfer through the gas diffusion layer is equal to that through the condensate film. Therefore, both the latent heat (the heat flux is qcd) of the condensed vapor and the sensible heat (the heat flux is qs) of the mixed gas first pass through the diffusion layer and then through the film. The equivalent thermal resistance diagram is shown in Figure a.

Figure 3

Equivalent thermal resistance diagrams of (a) classical HMTA model and (b) modified HMTA model.

The heat balance can be expressed aswhere hf is the liquid film HTC and hs is the sensible HTC. The latent HTC can be defined asThe total HTC can be defined asSince the temperatures in eq are the initial values, to calculate the total HTC, the interface temperature should be assumed at first and then calculated hf, hc, and hs. Finally, the steady-state values of all parameters are iteratively calculated.

The suggestion of Nusselt is adopted for hf, and is given byThe theory of diffusion layer is adopted for hc (Sections S4 and S5 of the Supporting Information show more details), and is calculated byThe total length of the test section is too short (0.075 m) to allow the gas to reach the fully developed stage. The Haji-Sheikh’s[26] correlation of forced convection at the entrance of vertical plate is adopted to calculate Shwhere x̂ = (x/a)/Pe, a is half of the flow channel thickness and a = 0.0075 m in this model. Pe is the Peclet number, which is defined as Pe = ReSc for mass transfer.

The hs in the diffusion layer is also calculated by Haji-Sheikh’s correlationFor the heat transfer process, Pe is defined as Pe = RePr.

The suction effect can thin the diffusion layer of the mixed gas, leading to enhancement of the heat and mass transfer.[27] A correction factor has been introduced to correct the enhancement caused by the suction effectwhere mass transfer blowing parameter Bm and heat transfer blowing parameter Bh are defined as

Modified HMTA Model

The modified HMTA model was modified from two aspects of chemical heat and the change of physical properties. During the diffusion of NO2 toward the lower temperature film surface, two NO2 molecules dimerize to form one N2O4, releasing reaction heat energy and reducing the concentration of condensable components in the diffusion layer. Based on the above process, the modified HMTA model is established as follows.

The total heat flux is composed of qcd, qs, and the chemical heat flux qr. Based on the sketch of the modeled systems shown in Figure , the equivalent thermal resistance diagram of the modified model is shown in Figure b. The heat balance between the diffusion layer and the film is expressed asThe modification method of chemical heat in the model is similar to that in Section . A one-dimensional mesh is built for the vertical wall along the direction of gas flow, as shown in Figure . The dimerization reaction is assumed in two directions: direction 1 corresponding to condensed NO2 and N2O4 is perpendicular to the wall, and direction 2 corresponding to uncondensed NO2 and N2O4 is parallel to the wall. The temperature of the gas–liquid interface approximately equals the wall temperature, thus we ignore the reaction in the liquid film and consider that the reaction of direction 1 mainly occurs in the diffusion layer. Accordingly, the dimerization in direction 1 is caused by the temperature difference between the bulk gas and the interface, releasing heat flux qr,. The dimerization reaction in direction 2 is caused by the gas temperature difference between node n and node n+1, releasing heat flux qr,. The qr, and qr, can be calculated fromBoth parts of the heat exchange caused by the dimerization reaction occur at the current node, so the total reaction heat flux of the node n is the sum of the twoAt the steady state of test section’s temperature field and dimerization, parameters of all gases can be calculated from temperature, pressure, and mole fraction. The total HTC of the node can be calculated by eqs ,24 and 27.

Film Roughness Correction

In conventional investigations on water condensation, the uneven condensate surface can inevitably be formed due to the wavy surface caused by a turbulent flow regime, resulting in the film roughness that depends on Re, and needs to be considered into the theoretical model for accurate prediction. For the NO2 condensation in this work, the film roughness for the NO2 condensate may also exist even at a laminar flow, as will be shown in Section , due to the potential inhomogeneity of condensation in terms of the specialty of NO2 dimerization exothermic process that highly depends on temperature (ΔT) and the NCG mole fraction (wnc). Therefore, the correlation of film roughness ought to be conducted.

The classical film roughness correction method for water vapor condensation is as follows[23]The correction for the film roughness fc is given aswhere fs = 16.2/Re, n = Pr0.36 for correcting Nu′, and n = Sc0.36 for correcting Sh′.

The friction factor fr is a degradation factor, the ratio of experimental HTC to the original predicted HTC, which can be used to improve the accuracy of water–NCG condensation model prediction.[21,22] The fr for film roughness of water is as followsAlthough the classical friction factor fr without consideration of dimerization may not be applicable to NO2 condensation, the relationships between the variables above can be adopted to get degradation factor fr for NO2. In this work, fr is assumed to be related not only to Re, indicative of fluid mechanical properties, but also to ΔT and wnc, indicative of NO2 dimerization properties. The friction factor follows the function as f = f(Re, wnc, ΔT), and the detailed relationships among the parameters are derived and validated in Section .

Results and Discussion

Effects of Various Parameters on Average HTC

Effects of Surface Subcooling on HTC

Figure shows the dependence of average HTC on surface subcooling at a 500 mL·min–1 inlet mixture volume flow and NCG concentrations of 50, 60, and 70%, respectively. In the range of surface subcooling (6–20 K), the average HTC decreases with increasing surface subcooling. For the lower NCG mole fraction, the decreasing trend is sharper: an increase in the surface subcooling by 20 K causes HTC to drop by about 200 W·m–2·K–1.

Figure 4

Effect of surface subcooling on the average HTC.

According to Figure b, total HTC is composed of hf, hc, and hs and the equivalent HTC of chemical heat. Generally, hf and hc involving latent heat as the major contribution to total heat transfer dominate the value of HTC.[16] For hf, the increase in surface subcooling promotes NO2 condensation and thus increases the thickness of the liquid film, leading to the decrease of hf. For hc, the main thermal resistance that deteriorates the condensation heat transfer is in the diffusion layer.[20] The higher NO2 condensation rate with the increased surface subcooling promotes the accumulation of NCG at the gas–liquid interface, thus increasing the mass transfer resistance according to the diffusion layer theory,[15] and resulting in the decrease of hc. The sharper decreasing trend of HTC versus surface subcooling at a lower NCG mole fraction is associated with more significant inhibition of heat and mass transfer caused by a greater increase in the NCG accumulation.

Effect of the NCG Concentration on HTC

Figure shows the effects of the NCG mole fraction on average HTC when the surface subcooling is 13 K, and the inlet flow rates of the mixture are 250, 500, and 700 mL·min–1, respectively. The average HTC decreased exponentially with the inlet NCG mole fraction, and there are no significant differences in decreasing trends under different flow rates.

Figure 5

Effect of the NCG mole fraction on the average HTC.

The negative effect of NCG on NO2 condensation heat transfer can be explained as follows. With the continuous condensation of NO2, the air gathered on the film surface and formed the diffusion layer.[28,29] Vapor molecules can only reach the film surface by diffusion. The increase in the inlet air mole fraction increases the concentration of NCG in the diffusion layer, suppressing the mass transfer process. Moreover, NO2 saturation temperature decreases with increasing NCG partial pressure, which also has a negative effect on condensation.

Effect of Re on HTC

Figure shows the variation of HTC with inlet Re at a constant pressure when the concentration of NCG is 40, 50, and 60%, respectively. It can be seen from the figure that the HTC increases with inlet Re, and the dependence of HTC on Re is almost linear in the entire range.

Figure 6

Effect of Re on the average HTC.

The positive effect of Re on NO2 condensation heat transfer can be explained as follows. With other parameters constant, the increase of Re accompanied by the increase of the inlet volume flow rate means that more condensable gas (NO2 and/or N2O4) flows into the test section. With a sufficient supply of cold energy, the heat released from the phase change of the condensable gas increases the heat transfer flow rate and HTC. In terms of the heat and mass transfer, hc and hf are the major contributors to HTC and both increase with Re. In the aspect of hc, the increase of Re reduces the thickness of the boundary layer and promotes the diffusion rate of NO2 toward the liquid film. In the aspect of hf, the increase of Re results in a more significant shear force between the gas and the film and perturbs the liquid film,[18,30] making the film thin and reducing the heat transfer resistance of the liquid film.

Effect of Dimerization on Heat Transfer

Figure a,b compares the results of HTC varying with the NCG mole fraction and Re from experiments, model predictions from classical and modified HMTA models. As can be seen from the figures, the HTC resulted from the modified HMTA model is closer to the experimental data as compared to that from the classical model. These results indicate the positive effect of NO2 dimerization on heat transfer. As shown in Figure a, with the increase in the NCG mole fraction from 0.4 to 0.8, the HTC calculated by the modified HMTA model is decreased by 61.4%, from 202.2 to 78.0 W·m–2·K–1, whereas the HTC calculated by the classical model is decreased by 47.3%. Obviously, the influence of NCG is more distinct in the former case, and the difference in calculated HTCs between two models (ΔHTC) decreases exponentially with the inlet NCG mole fraction. The reason for this trend could be explained by the fact that the increase in the inlet NCG mole fraction causes less NO2/N2O4 flow over the wall, leading to the decrease in NO2 molecules involved in the dimerization. However, the proportion of NO2 in condensable components increases exponentially with the decrease of the partial pressure of the condensable NO2/N2O4 mixture (as described in Section S6 of the Supporting Information). This mechanism can to some extent impede the decrease of dimerization caused by the increase of NCG.

Figure 7

Variation of experimental and theoretical HTCs with (a) NCG mole fraction and (b) Re.

As shown in Figure b, with the increase of Re from 100 to 300, the HTCs from the modified HMTA model increase at a higher rate (by up to 160.4%) as compared with those from the classical model (127.9%). Meanwhile, the ΔHTC shows an increasing trend with the increase of Re. This might be associated with the reduced temperature of the thinned boundary layer at increased Re.[31] The lower temperature facilitates the NO2 dimerization that further promotes the heat transfer.

Figure shows the contributors (latent heat, sensible heat, chemical heat) to the NO2 condensation heat flow rate predicted by the modified model, and the HTCs predicted by modified and classical models and their differences (ΔHTC) at varying inlet flow rates. Under the inlet surface subcooling of 20 K and the NCG mole fraction of 50%, the total heat flow rate increases from 6.41 to 9.32 J·s–1, as the inlet flow rate increases from 450 to 750 mL·min–1. The latent heat of condensation is found to be the majority (∼86%) of the total heat flow, while the dimerization chemical heat and the sensible heat merely account for ∼6 and ∼8%, respectively. In contrast to the slight effect of dimerization on the heat flow rate, HTC was greatly influenced by dimerization, as evidenced by the relative increase in HTC from the classical model prediction to the modified counterpart (ΔHTC/HTCclassical model = 50.95–53.95%).

Figure 8

Effect of dimerization on the heat flow rate and HTC.

It can be clearly found that the relative increase in HTC due to dimerization is much greater than that in the dimerization chemical reaction heat, indicating underlying influences of NO2 dimerization on condensation heat transfer as compared to the direct influence caused by the reaction heat. Considering the process that NO2 molecules diffuse to the wall and dimerize to N2O4, the first underlying influence of NO2 dimerization might be associated with more gaseous NO2 driven to the film by a greater concentration gradient of NO2 between the bulk mixture and the interface due to a reduced number of NO2 molecules at the interface. As a result, NO2 condensation and the release of latent and chemical heat would be promoted. In addition, the reduction in NO2 partial pressure leads to a decrease in the temperature of the bulk mixture, which is assumed to be equal to the saturation temperature of gaseous NO2. According to Newton’s cooling law (eq ), an increased heat flow and a reduced temperature difference between the bulk and the surface synergistically increase HTC. Note that the average surface subcooling was different at different inlet flow rates though the inlet surface subcooling was kept constant. As a result, the increase in HTC is much greater than the increase in the total heat flow, as shown in Figure .

It can be inferred that the influence of dimerization on condensation ought to involve several aspects. In addition to the above heat release or mass transfer effect, the dimerization would also cause other indirect effects from the perspective of a fluid mechanism, as indicated by the remarkable discrepancy between experimental and modified HMTA model results. For instance, as mentioned in Section , the film roughness for the NO2 condensate may also exist due to the potential inhomogeneity of NO2 dimerization, which will be discussed in the following section.

Liquid Film Roughness Correction

Figure shows the images of the liquid film taken at 2, 7, and 15 min during the condensation under a volume flow rate of 650 mL·min–1, an air mole fraction of 70%, and a surface subcooling of 17 K. At different times in the condensation, the mixture of the film, droplets, and streamlets as marked in the figure can be constantly observed, directly leading to the liquid film roughness that differs from the traditional smooth film. On the basis of the above relationship between dimerization and HTC, it is reasonable to speculate that the inhomogeneity of NO2 dimerization due to an uneven component concentration and temperature profiles in the condensation region is one of the reasons for uneven heat transfer distribution over the wall surface. The resultant heterogeneity of heat transfer contributes to varying existence of the condensate and thus the film roughness, which could be likely the reason for the values of experimental HTCs that are greatly underestimated by the theoretical model (Figure ). On the one hand, the surfaces of droplets and streamlets exposed to the gas flow can increase the heat transfer area between the liquid film and the diffusion layer. On the other hand, with the condensate flowing downward, the surface morphology of the film changes constantly, causing disturbance to the gas diffusion layer.

Figure 9

Condensate states (film, droplets, and streamlets marked by green, blue, and white dashed lines, respectively) visualized at different times during condensation.

To address the degradation factor for film roughness correction that follows fr = f(Re,wnc,ΔT) assumed in this work, the relationships of fr with Re, ΔT, and wnc can be established based on properties of the liquid film. Apparently, the roughness of liquid film depends on the proportion and distribution of the condensate film, streamlets, and droplets. Nevertheless, it is not easy to quantify the specific liquid amount and spatial distribution of each condensate state. The liquid amounts of the three condensate states constitute the total condensate amount that can be recorded in tests. Similarly to the film roughness, the flow rate of the total condensate (q, calculated via eq ) varies with the status (proportion and distribution) of three condensates present at a specific moment. Therefore, there ought to be a certain correlation between liquid film roughness and q. Based on the experimental data at a NO2–air mixture flow rate of 500 mL·min–1 and the relation of equations in Section , the curve of fr versus q can be depicted (Figure ) and fitted with an equation showing a good correlation (R2 = 0.81) asThe value of q representative of the macroscopic condensation efficacy varies with HTC that has close relationships with surface subcooling, Re, and NCG mole fraction, as shown in Sections and 4.2. Therefore, the variation of q with Re, ΔT, and wnc as independent variables, can be fitted based on the experimental data at a NO2–air mixture flow rate of 500 mL·min–1, as listed in Table S3, rendering the correlation asTherefore, q is introduced as a bridge between fr and Re, ΔT, and wnc to derive friction factor fr = f(Re, wnc, ΔT) based on eqs and 33. Aiming to validate the accuracy of proposed fr, eq is replaced by eqs and 33, and the product of fc (eq ) and HTC calculated from the modified model are compared with the experimental HTC. Note that the data used for verification, as shown in Table , and those for fitting eqs and 33 (500 mL·min–1) are independent. The verification results are shown in Figure : the horizontal axis represents the HTC calculated from the experimental data and the vertical axis represents the product of fc and HTC calculated from the modified model. All of the calculated values fall within ±25% of the experimental HTC, indicating the accuracy of the film roughness-corrected model prediction.

Figure 10

Experimental data and the fitting curve of fr versus q.

Table 2

Details of Experimental Data Used to Verify the Correlation between fr and Re, ΔT, and wnc

items	details
NCG	air
NCG mole fraction (%)	40, 50, 60, 70
inlet volume flow (mL·min–1)	250, 320, 650, 750
inlet Re number	60–360
surface subcooling (K)	8.4–20.5
pressure	0.1 MPa

Figure 11

Comparison of calculated HTC with experimental HTC.

In eq , the exponent of each term reflects the effect of the corresponding variable on q, indicative of the condensation rate. Both Re and surface subcooling are positively correlated with q, while the NCG mole fraction is negatively correlated with q. The degree of the variable effect on q, indicated by the absolute value of the exponent, follows the order ΔT > wnc > Re (0.95 > 0.49 > 0.3). Similarly, for film roughness correction that is described by the combination of eqs and 33 and Section , the order of the degree of the variable effect follows Re > ΔT > wnc (0.8 > 0.5 > 0.25). These results may indicate the mixed contributions from multiple factors to the NO2 condensation heat transfer. The modified HMTA model in consideration of NO2 dimerization and liquid film roughness correction would provide the key step for success in practical applications of NO2 condensation.

Conclusions

In this paper, the condensation HTC of NO2 was investigated using an experimental apparatus with a visualization system. The rough film of a NO2 condensate with the coexistence of droplet, streamlet, and liquid film was observed. It was found that HTC increased with the decreases in surface subcooling and NCG mole fraction, and the increase in Re. There exist large discrepancies between experimental and classical HMTA model prediction results. The reasons lie in the effects of NO2 dimerization on condensation, including the release of chemical reaction heat, the promotion of the mass transfer by increasing the NO2 concentration gradient within the diffusion layer, and the liquid film roughness related to the heterogeneity of dimerization. A modified HMTA model considering changes in heat and mass transfer due to NO2 dimerization was built. The effect of liquid film roughness on condensation was further corrected, improving the HTCs by 55 and 150%, respectively. In particular, the relationship between the liquid film roughness and each key parameter (inlet surface subcooling, NCG mole fraction, and Re) under NO2 dimerization was addressed using the flow rate of the total condensate as an intermediary factor. Finally, an accurate prediction model for NO2 condensation HTC in the presence of NCG within an error of ±25% was obtained, providing the key step for success in practical applications.