Local Heat Transfer in a Calorimetric Tube with Water Injection

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Article An Experimental Investigation of Water Vapor Condensation from Biofuel Flue Gas in a Model of Condenser, (2) Local Heat Transfer in a Calorimetric Tube with Water Injection

Robertas Poškas 1,*, Arunas¯ Sirvydas 1, Vladislavas Kulkovas 1, Hussam Jouhara 2 , Povilas Poškas 1, Gintautas Miliauskas 3 and Egidijus Puida 3

1 Nuclear Engineering Laboratory, Lithuanian Energy Institute, Breslaujos 3, LT-44403 Kaunas, Lithuania; [email protected] (A.S.); [email protected] (V.K.); [email protected] (P.P.) 2 Heat Pipe and Thermal Management Research Group, College of Engineering, Design and Physical Sciences, Brunel University London, Uxbridge UB8 3PH, UK; [email protected] 3 Department of Energy, Faculty of Mechanical Engineering and Design, Kaunas University of Technology, Studentu 56, LT-51424 Kaunas, Lithuania; [email protected] (G.M.); [email protected] (E.P.) * Correspondence: [email protected]; Tel.: +37-037401893

Abstract: In order for the operation of the condensing heat exchanger to be efficient, the flue gas temperature at the inlet to the heat exchanger should be reduced so that condensation can start from the very beginning of the exchanger. A possible way to reduce the flue gas temperature is the injection of water into the flue gas flow. Injected water additionally moistens the flue gas and increases its level of humidity. Therefore, more favorable conditions are created for condensation and Citation: Poškas, R.; Sirvydas, A.; heat transfer. The results presented in the second paper of the series on condensation heat transfer Kulkovas, V.; Jouhara, H.; Poškas, P.; indicate that water injection into the flue gas flow drastically changes the distribution of temperatures Miliauskas, G.; Puida, E. An along the heat exchanger and enhances local total heat transfer. The injected water causes an increase Experimental Investigation of Water Vapor Condensation from Biofuel in the local total heat transfer by at least two times in comparison with the case when no water is Flue Gas in a Model of Condenser, (2) injected. Different temperatures of injected water mainly have a major impact on the local total heat Local Heat Transfer in a Calorimetric transfer until almost the middle of the model of the condensing heat exchanger. From the middle Tube with Water Injection. Processes part until the end, the heat transfer is almost the same at different injected water temperatures. 2021, 9, 1310. https://doi.org/ 10.3390/pr9081310 Keywords: biofuel flue gas; water vapor condensation; vertical tube; experiments; water injection; total local heat transfer; condensation efficiency Academic Editors: Francesca Raganati and Alessandra Procentese

Received: 23 June 2021 1. Introduction Accepted: 27 July 2021 Published: 29 July 2021 This is the second paper of the series on water vapor condensation from the ﬂue gas in a long vertical tube—model of the condensing heat exchanger. Therefore, the review of the

Publisher’s Note: MDPI stays neutral literature related to water vapor condensation from flue gases has already been presented with regard to jurisdictional claims in in [1]. The results presented in [1] revealed that, under certain inlet flue gas conditions, published maps and institutional affil- the initial part of the condensing heat exchanger is not used efficiently for condensation iations. heat and mass transfer due to the cause that the flue gas has to be cooled down until its temperature reaches the dew point temperature. Usually after that, a significant increase in heat transfer was determined due to condensation of water vapor from the flue gas. Therefore, in order to use such type of heat exchanger more efficiently from its beginning, certain parameters of the flue gas at the inlet to the exchanger should be reached. Copyright: © 2021 by the authors. Licensee MDPI, Basel, Switzerland. The results presented in [1] showed that there is a necessity to reduce the flue gas This article is an open access article temperature prior to the condensing heat exchanger in order to have condensation in the distributed under the terms and heat exchanger from its very beginning. A possible way to reduce the flue gas temperature conditions of the Creative Commons is the injection of water into the flue gas flow [2,3]. The water injected via a nozzle creates Attribution (CC BY) license (https:// water droplets, which in the injection chamber directly contact with the flue gas and the creativecommons.org/licenses/by/ water vapor existing in the flue gas. Then, such a “mixture” is routed into the condensing 4.0/). heat exchanger. In addition, the injected water additionally moistens the flue gas and

Processes 2021, 9, 1310. https://doi.org/10.3390/pr9081310 https://www.mdpi.com/journal/processes Processes 2021, 9, 1310 2 of 18

increases its humidity. Due to this, more favorable conditions for condensation and heat transfer in the condensing heat exchanger should occur. Besides, the injected water allows the recovery of some heat and water due to vapor condensation [4–6] and also reduces the concentration of solid particles [7] in flue gas which, when released into the atmosphere, are the main pollution sources when incinerating biofuel [8]. In addition, the benefit of the injected water is that it can be used for flue gas cleaning from acidic components [9] and for flue gas desulfurization [10]. In boiler plants, condensed moisture is usually collected at the bottom part of condensing heat exchangers. Then a part of it is routed back and injected again into the flue gas flow at the top part of heat exchangers. The efficiency of heat exchangers in boiler houses depends on the rates of injected water and gas flow and also the height and diameter of the heat exchanger [11]. The use of condensing heat exchangers in boiler plants allows significant annual fuel savings [12,13]. One of the ways to achieve better heat and mass transfer results of the condensation process is the use of direct contact condensation [14]. Direct contact condensation is the process when vapor directly contacts with water, which can result in very high heat transfer rates. However, such high heat transfer rates can be obtained only in the case of pure vapor condensation. Meanwhile, in reality there might always be a huge portion of noncondensable gases, especially when incinerating biofuels. The study presented in [15] was dealing with the condensation heat transfer of sat- urated vapor in a stainless-steel cylindrical vessel (158 mm in diameter and 360 mm length), when subcooled water was sprayed into the vessel with a hollow cone nozzle. The measured increase in sprayed water temperature in the flow direction was rather significant up to x/d ≈ 10. After that, the water temperature of the spray was close to the vapor temperature. In another study [16], an analytical model was proposed for the behavior of a water spray in vapor. The spray experiments were performed in a chamber 250 mm in diameter and 300 mm in length with pure vapor. The sprayed droplet sizes used in the experiments were in the range of 0.67–1.32 mm. The water spray pattern determined was divided into several regions. The modeling results compared with the experimental results showed a reasonable agreement. When water was sprayed into the same chamber with air (no condensation) and into the chamber with vapor (with condensation), the structure of the flow streamlines showed a considerable difference between the two cases, and the breakup spray length was shorter in the vapor environment. Moreover, the droplet size was determined to be larger in vapor than in the air environment. However, the authors did not analyze heat transfer. The influence of droplet size on heat transfer was analyzed in [17]. It was determined that the larger the droplet size, the lower the total average heat transfer obtained. The droplet radius increased from ~0.25 mm to ~0.75 mm, resulting in an average total heat transfer decrease of about 3.3 times. In [18], the experiments were carried out in a cylindrical vessel of 610 mm diameter and 915 mm length to observe the characteristics of water spray from full cone-type coarse nozzles into water vapor. The droplet sizes of the sprayed water were in the range between 0.25 and 1 mm. The analysis of the spray photos showed that for the flow of sprayed water, the film and the droplet phases could be distinguished. The results also indicated that increasing the number of the nozzles that generated smaller drops did not have an expected impact on the heat transfer. It was concluded that heat transfer in the film phase is about five times higher than in the droplet phase. A series of experiments on direct contact condensation of an air-vapor mixture on a water surface in a vertical test section with the dimensions of 150W × 100D × 1510L mm was carried out in [19]. The results revealed that the average condensation heat transfer coefficient for a vapor-air mixture decreased when the air mass fraction was increased. The average heat transfer coefficients obtained for different mixture velocities and condensation film Reynolds numbers were in the range between 550 and 2000 W/m2K. Processes 2021, 9, 1310 3 of 18

The injection of water droplets in the range of 0.3–2.8 mm to humid hot air of relative humidity 80% and temperature 65–85 ◦C using a hollow cone nozzle was studied in [20]. The results showed that, due to direct contact condensation, vapor condenses on the surface of droplets because the temperature of water droplets is less than the dew point of air. Although condensing heat exchangers are widely used in boiler plants, there is not much analysis done on local distributions of temperatures and processes of condensation heat and mass transfer when water is injected into the flue gas flow. The study described in [21] presented a numerical simulation of a quench tower (2.5 m in diameter and 10 m in height) for high inlet temperature (>500 ◦C) flue gas purification in the case of water droplets of 0.1 mm diameter injected using one to four nozzles located in the upper part of the quench tower. The temperature distribution in the center of the tower indicated that after the spraying, a large amount of flue gas heat was absorbed due to droplet evaporation. With the downward movement of the flue gas, the gas temperature was continuously decreasing and the droplets were gradually evaporating. At about 4 m from the top of the tower, the temperature of flue gas and water vapor were almost the same, and therefore the evaporation of the injected water droplets was negligible. It was determined that the gas with a high temperature was concentrated in the central part of the tower. The flue gas temperature change rates obtained using one to four nozzles for water injection showed that the highest temperature change rate in the case of one nozzle was between 1 and 3 m from the top of the tower, in the case of two, three and four nozzles it was between 2 and 4 m from the top of the tower. From almost the middle of the tower, the flue gas temperature change rate was negligible and this did not depend on the number of nozzles used. In general, spray cooling is an efficient way to reduce gas temperature, especially in confined spaces [22]. Experiments with a water spray for air cooling were carried out in a heat exchanger located in a channel with a rectangular cross section of 36 × 25 cm and a length of 1.7 m with the purpose of improving heat transfer [23]. An increase in the heat transfer of up to three times was reached for a counter-flow injection with the injected droplets smaller than 0.025 mm in diameter. A co-flow injection was found not to be very effective due to bad dispersion of the droplets. Such dispersion resulted in very heterogeneous cooling. Heat transfer analysis in a flat tube heat exchanger showed that the heat transfer was increasing with an increasing water spraying rat; however, only up to a certain water spray flow rate. It was found that in the case of a high spraying rate, parts of the flow passage of the heat exchanger can be blocked by water droplets and this may result in regions with poor heat transfer. Thus, an optimum water spray rate should be achieved to give an increase in total heat transfer [24]. Flue gas might contain some components in vapor form, which, when condensed on the surfaces of the heat exchanger, can cause corrosion of the surfaces of heat exchanger. In such cases, it is necessary to make heat exchangers from corrosions resistant materials (stainless steel, various corrosion resistant alloys, etc.). Moreover, some reagents could be injected in order to decrease the acidity of vapors. The literature review showed that a lot of studies are devoted to investigating pure vapor condensation when water is injected into short vessels, as well as flue gas cleaning from gaseous pollutants, solid particles and for the reduction of the temperature of the flow. In the case of biofuel incineration, the flue gas contains a significant amount of noncondensable gases with the remaining portion of water vapor, which, if condensed in an efficiently operating economizer, could increase the efficiency of the boiler station and guarantee huge fuel savings. Although condensing heat exchangers are widely used, there are no studies devoted to the local total heat transfer characteristics of condensing heat exchangers with water injection [25]. Therefore, the aim of this study was to investigate the influence of water injected into the flue gas flow on the distribution of temperatures and total local heat transfer along the model of the condensing heat exchanger. Processes 2021, 9, x FOR PEER REVIEW 4 of 17

Therefore, the aim of this study was to investigate the influence of water injected into the flue gas flow on the distribution of temperatures and total local heat transfer along the model of the condensing heat exchanger.

2. Experimental Setup The experimental setup (Figure 1) which was used for the investigations was the

Processes 2021, 9, 1310 same as described in [1]. However, some minor changes necessary for water injection4 were of 18 introduced and are described further. To generate flue gas from incinerated wood pellets, the automatic boiler Kostrzewa (Poland) from the first experiments (without water injection) was used. The boiler has a 2.maximum Experimental power Setup of 50 kW. The power can be adjusted in a certain range according to the needs.The Flue experimental gas generated setup with (Figure a temperatur1) which wase of used about for the180–190 investigations °C at the wasexit thefrom same the asboiler described was routed in [1]. into However, the experimental some minor section. changes Using necessary the economizer for water of injectionthe boiler, were dif- introducedferent temperatures and are described of the flue further. gas could be obtained at the inlet to the test section.

FigureFigure 1.1. (1)(1) boiler; boiler; (2) (2) flue flue gas gas pipe; pipe; (3) (3) heat heat exchanger exchange (fan-coilr (fan-coil type); type); (4) flue (4) gas flue exhauster; gas exhauster; (5) water (5) injectionwater injection supply supply pump; pump; (6) injection (6) injection water water tank; (7)tank; bypass (7) bypass pipe; (8)pipe; damper; (8) damper; (9) inlet (9) flueinlet gas flue flow gas rate,flow temperaturerate, temperature and humidity and humidity measurement measurement point (before point test(before section); test (10)section); water (10) injection water chamber;injection (11)chamber; water (11) mixer; water (12) mixer; vertical (12) calorimetric vertical calorimetric tube—the modeltube—the of flue model gas condensingof flue gas condensing heat exchanger heat exchanger (economizer); (13) cooling water discharge line; (14) cooling water supply line; (15) col- (economizer); (13) cooling water discharge line; (14) cooling water supply line; (15) collection tank. lection tank. To generate flue gas from incinerated wood pellets, the automatic boiler Kostrzewa (Poland) from the first experiments (without water injection) was used. The boiler has a maximum power of 50 kW. The power can be adjusted in a certain range according to the needs. Flue gas generated with a temperature of about 180–190 ◦C at the exit from the boiler was routed into the experimental section. Using the economizer of the boiler, different temperatures of the flue gas could be obtained at the inlet to the test section. Dampers were used for flue gas flow rate adjustment. After that, the flue gas was supplied to the top of the test section, flowed via the internal vertical calorimetric tube, passed it, flew to the flue gas chimney and discharged into the atmosphere. Processes 2021, 9, 1310 5 of 18

The test section was made of stainless steel. It was composed of an internal calorimetric tube (length x ≈ 5.8 m, inner diameter d = 0.034 m, wall thickness δ = 2 mm, x/d ≈ 170) where condensation takes place on its internal surface and an outer tube (length x ≈ 5.9 m, inner diameter D = 0.108 m) [1]. A water injection chamber with one nozzle was installed just before the inlet into the calorimetric tube. The internal diameter of the chamber was 100 mm and the height 250 mm. The nozzle for water injection was mounted in the middle of the chamber’s height at its side surface. Therefore, the directions of flue gas flow and water injection to the gas flow were perpendicular to each other. The distilled water was supplied to the nozzle via a flexible hose from the water tank with a pump. The hose was insulated using 6 mm thick polyethylene insulation. All of the experimental section as well as flue gas chimney were also insulated using 5 cm thick rockwool insulation. For cooling the calorimetric tube, water from a municipal water supply network was supplied in the space between the inner and outer tubes. Flow rate of the cooling water was measured at its discharge line by weighing, and the necessary rate was adjusted by the valve. To have uniform inlet temperature before entering the experimental section at its bottom, the water was mixed in the water mixer. When leaving the experimental section, the water was also mixed in the same type of mixer. During the experiments, the condensed and injected water was collected in a collection tank.

3. Materials and Methods The investigations were performed using different inlet flue gas temperatures and for two different Reynolds numbers at the inlet into the calorimetric tube. The water vapor mass fraction in the flue gas of about 17% was achieved when incinerating biofuel pellets in the boiler and additionally spraying water into the furnace of the boiler due to the reasons indicated in [1]. Calibrated chromel-copel thermocouples (wire diameter 0.2 mm, accuracy ±0.3%) were installed to measure flue gas (20 pieces), inner wall of the calorimetric tube (20 pieces) and cooling water temperatures (10 pieces) along the model of the condensing heat exchanger. The same type of thermocouples (3 pieces) was also installed in each of the water mixers. For details see [1]. During the experiments, all the thermocouple data were collected using the Keithley ◦ data acquisition system. Flue gas inlet temperature (tin, C) and inlet relative humidity (RHin, %) were measured using a KIMO C310 sensor installed before the inlet to the water injection chamber (250 mm before inlet into the calorimetric tube). Therefore, Rein and dew point temperatures indicated in the Figures presented in this article were calculated based on these parameters. Bellmouth with installed Pitot and Prandtl tubes connected to a differential micromanometer [1] was used to measure the inlet flue gas flow rate. The flow rate of the cooling water was determined using weighing method. Ex- periments were carried out for a cooling water flow rate of 60 kg/h. The cooling water temperature at the inlet to the test section was about 9–10 ◦C. The flow rate of the water injected into the flue gas stream was defined by the water level change in the distilled water tank, applying the weighing method. During experiments, the flow rate of the injected water was 33.6 kg/h (or 0.56 kg/min). According to the manufacturer of the injector, the injector used in experiments was the full cone injector and the droplets generated by it are in the range of 36–864 µm. The Sauter mean diameter of the droplet is 481 µm and the surface mean diameter is 361 µm. The temperature of the injected water was measured by two thermocouples installed at the bottom of the distilled water tank—in the zone where the water take-up by the pump was realized. The distilled water tank was equipped with electric heating coils, and a mixer installed in the tank allowed to have a uniform temperature of the water. The temperature of the water injected into the injection chamber was about 25 ◦C. For the purpose of comparison between the heat transfer results, it was also increased to about 40 ◦C. Processes 2021, 9, 1310 6 of 18

In the formulas presented further the properties (cp, λ, etc.) of the flue gas and water vapor mixture were calculated using formulas presented in [26]. The properties were calculated based on the flow temperature measured in the center of the calorimetric tube. The total local heat flux was obtained as

mH2O · cpH2O dtH2O q = i i · i , (1) ti π·d dx

where mH2O is inlet mass flow rate of the cooling water, kg/s, cpH2O is specific heat of the ◦ water, kJ/kg· C, dtH2O/dx is the slope of the cooling water temperature gradient, determined as the least squares polynomial fit of the coolant temperature as a function of the length of the heat exchanger model, and d is the inner diameter of the calorimetric tube, m. The local total heat transfer coefﬁcient was calculated as

αti = qti /(tc − tw)i, (2)

◦ where tc is the temperature measured in the center of the calorimetric tube, C, tw is the measured inner wall temperature of the calorimetric tube, ◦C. The total Nusselt number:

Nuti = αti ·d/λi (3) To evaluate the performance of the condensing heat exchanger, the condensation efﬁciency (%) was used [27]. Condensation efﬁciency was calculated as

mcd ncd = ·100, (4) mH2Oin

where mcd is the mass flow rate of the condensate, kg/s, mH2Oin is the inlet flow rate of the water vapor, kg/s. The condensate mass flow rate was obtained:

mΣ − minj m = , (5) cd h

where mΣ is the total water mass collected in the collection tank, kg, minj is the mass of the injected water, kg and h is the time, s. Flue gas Reynolds number at the inlet to the calorimetric tube was calculated based on the ﬂue gas parameters before the water injection section:

Rein = uin·d/νin, (6)

where uin is the ﬂue gas bulk velocity in the calorimetric tube, m/s, d is the inner diameter 2 of the calorimetric tube, m, νin is the kinematic viscosity, m /s. The uncertainty of the data evaluated by using the methodology presented in [28] showed that for the Nusselt number the uncertainty is 6–14%.

4. Results and Discussions Experiments with water injection were carried out for different injected water temperatures, and different ﬂue gas temperatures (tin) and Reynolds numbers (Rein) at the inlet into the calorimetric tube.

4.1. Water Injection with a Temperature of 25 ◦C Figure2 presents typical distribution of temperatures along the model of the condensing heat exchanger at the same inlet Reynolds number (Rein), different inlet flue gas temperatures and in cases when no water was injected and when water was injected into the flue gas flow. The dew point temperature at the inlet to the test section for the cases presented was calculated according to tin, RHin and using the equations presented in [29] Processes 2021, 9, x FOR PEER REVIEW 7 of 17

4.1. Water Injection with a Temperature of 25 °C Figure 2 presents typical distribution of temperatures along the model of the condensing heat exchanger at the same inlet Reynolds number (Rein), different inlet flue gas temperatures and in cases when no water was injected and when water was injected into the flue gas flow. The dew point temperature at the inlet to the test section for the cases presented was calculated according to tin, RHin and using the equations presented in [29] and was in the range of ~58–64 °C (the dew point temperature was calculated according to tin, RHin, i.e., results before injection section). If the condenser wall temperature from the flue gas flow side is lower than the dew point temperature, water vapor should start to condensate on the wall of a calorimetric Processes 2021, 9, 1310 tube. If the temperature of the flue gas in the center of a calorimetric tube reaches the7 dew of 18 point temperature, water vapor should start to condense in all its volume. For all the cases shown in Figure 2, the tube wall temperature (curve 2) is much lower than the dew point temperature. Therefore, condensation on the wall of the calorimetric and was in the range of ~58–64 ◦C (the dew point temperature was calculated according to tube should start from the beginning of the tube and the results of heat transfer presented t , RH , i.e., results before injection section). inin Figurein 3 (curve 1) confirm that.

Figure 2. Temperature distribution along the model of the condensing heat exchanger at Rein ≈ 9500, different flue gas inlet Figure 2. Temperature distribution along the model of the condensing heat exchanger at Rein ≈ 9500, different ﬂue gas inlet temperatures and in the case when water is not injected (a) Rein ≈ 9500, tin≈ 80 °C, (c◦) Rein ≈ 9500, tin ≈ 115 °C and is◦ injected temperatures and in the case when water is not injected (a) Rein ≈ 9500, tin≈ 80 C, (c) Rein ≈ 9500, tin ≈ 115 C and is (b) Rein ≈ 9500, tin ≈ 87 °C, (d) Rein ≈ 9500, tin ≈ 122 °C: (1) center of the calorimetric tube, (2) inner wall of the calorimetric injected (b) Re ≈ 9500, t ≈ 87 ◦C, (d) Re ≈ 9500, t ≈ 122 ◦C: (1) center of the calorimetric tube, (2) inner wall of the tube, (3) coolingin water inin the middle of thein inner andin the outer tubes, (4) dew point temperature at the inlet to the calorimetric tube, (3) cooling water in the middle of the inner and the outer tubes, (4) dew point temperature at the inlet to calorimetric tube. the calorimetric tube.

If the condenser wall temperature from the flue gas flow side is lower than the dew point temperature, water vapor should start to condensate on the wall of a calorimetric tube. If the temperature of the flue gas in the center of a calorimetric tube reaches the dew point temperature, water vapor should start to condense in all its volume. For all the cases shown in Figure2, the tube wall temperature (curve 2) is much lower than the dew point temperature. Therefore, condensation on the wall of the calorimetric tube should start from the beginning of the tube and the results of heat transfer presented in Figure3 (curve 1) confirm that. The flue gas temperature measured in the center of the calorimetric tube rather rapidly and almost linearly decreases from x/d = 0 to x/d ≈ 20 for about 20 ◦C (Figure2a, curve 1), then some stabilization of the temperature between x/d ≈ 20–40 is observed and after that, until the end of the tube, it decreases gradually. The stabilization of temperature (Figure2a, curve 1) could mean that the condensation of vapor occurred in the whole cross section of the calorimetric tube, and due to this, a sudden increase in the total heat transfer was obtained in the x/d range between 20–40 (Figure3, curve 1). Further on, as some vapor is condensed and the difference between the flue gas and the tube wall temperature is decreasing (Figure2a, curves 1 and 2), heat transfer is also gradually decreasing; however, Processes 2021, 9, 1310 8 of 18

Processes 2021, 9, x FOR PEER REVIEW the results show that it is still rather high and at the end of the calorimetric8 of 17 tube Nut is

≈ 140 (Figure3, curve 1).

Figure 3. DistributionFigure 3. ofDistribution the total local of the Nusselt total numberlocal Nusselt along numb the modeler along of the the condensing model of heatthe condensing exchanger atheat Re in ≈ 9500, different flueexchanger gas inlet temperaturesat Rein ≈ 9500, and different for the flue cases gas when inlet notemperatures water was injectedand for the into cases the flue when gas no flow water and was when it was injected ◦into the flue gas flow and when ◦it was injected: (1) tin ≈ 80 °C without◦ injection, (2) tin ≈ 87 ◦ injected: (1) tin ≈ 80 C without injection, (2) tin ≈ 87 C with injection, (3) tin ≈ 115 C without injection, (4) tin ≈ 122 C °C with injection, (3) tin ≈ 115 °C without injection, (4) tin ≈ 122 °C with injection. with injection.

The flue gas temperatureThe cooling watermeasured temperature in the ce (Figurenter of2 thea, curve calorimetric 3) from thetube inlet rather into rap- the model of the idly and almostcondensing linearly decreases heat exchanger from x/d (x/d = 0 to≈ x/d170) ≈ until20 for the about outlet 20 °C (x/d (Figure = 0) is 2a, gradually curve increasing. 1), then some Initially,stabilization the increaseof the temperature from the inlet between until x/dx/d ≈ 20–4070 is slightis observed and from and x/dafter≈ 70 until the that, until theoutlet end of it isthe more tube, pronounced. it decreases Thisgradually. means The that stabilization the heating ofof water temperature in thissection of the (Figure 2a, curvemodel 1) could of the mean condensing that the heat condensation exchanger of (x/d vapor≈ 0–70) occurred is more in the intense whole due cross to the prevailing section of the calorimetriccondensation tube, process. and due In total,to this via, a sudden all of the increase test section, in the thetotal cooling heat transfer water temperature was obtained increasesin the x/d byrange about between 20 ◦C—from 20–40 (Figure ~10 ◦C 3, to curve ~30 ◦ 1).C. Further on, as some vapor is condensed and Whenthe difference water of between about 25 the◦C startedflue gas to and be injectedthe tube into wall the temperature flue gas flow, is the character decreasing (Figureof the 2a, temperatures curves 1 and presented 2), heat tr inansfer Figure is2 alsob is differentgradually in decreasing; comparison however, to those presented in the results showFigure that2 ait when is still no rather water high was and injected. at the end of the calorimetric tube Nut is ≈ 140 (Figure 3, curveAlthough 1). the flue gas temperature before the water injection chamber was about The cooling87 ◦ waterC, after temperature mixing with (Figure the injected 2a, curve water, 3) from at the the beginning inlet into of the the model calorimetric of tube the the condensingflue heat gas exchanger temperature (x/d decreases≈ 170) until to the ~52 outlet◦C (Figure (x/d = 20)b, is curve gradually 1). The increasing. results show that the Initially, the increaseflue gas from temperature the inlet fromuntil thex/d beginning≈ 70 is slight until and the from end x/d of ≈ the 70 tubeuntil is the constantly outlet decreasing it is more pronounced.and at the This exit frommeans the that tube the it isheating about of 30 water◦C. Therefore, in this section the injection of the ofmodel water reduces the of the condensingflue gasheat temperature, exchanger (x/d and ≈ it0–70) is likely is more that intense at the same due time,to thedue prevailing to the evaporation con- of the densation process.injected In water,total, via an increaseall of the in test the humiditysection, the of thecooling flue gaswater flow temperature occurs. These in- factors ensure creases by aboutbetter 20 °C—from conditions ~10 for °C condensation to ~30 °C. in the calorimetric tube. When water ofThe about characteristics 25 °C started of the to tubebe inje wallcted temperature into the flue and gas cooling flow, waterthe character temperature variation of the temperaturesalong thepresented tube (Figure in Figure2b, curves 2b is different 2 and 3) arein comparison almost the same to those as the presented characteristic of flue in Figure 2a whengas temperature. no water was Figure injected.2b also shows that the temperature differences between flue gas Althoughand the tube flue wall,gas temperature and between before tube wall the andwater cooling injection water, chamber are almost was constant about 87 through all the ◦ °C, after mixinglength with of the the injected model ofwater, the condensing at the beginning heat exchanger of the calorimetric and are in tube the range the flue of 7–10 C. gas temperature decreases to ~52 °C (Figure 2b, curve 1). The results show that the flue gas temperature from the beginning until the end of the tube is constantly decreasing and at the exit from the tube it is about 30 °C. Therefore, the injection of water reduces the flue

Processes 2021, 9, 1310 9 of 18

Water injection had a significant impact on total local heat transfer (Figure3, curve 2). The heat transfer starts to increase from the beginning of the tube from Nut ≈ 400 until Nut ≈ 550 at x/d ≈ 60. The intensification could be related to the conditions suitable for condensation, i.e., a low flue gas temperature, and a possibly increased amount of vapor in the flue gas. Later, the heat transfer starts to decrease. This is related to the fact that some water vapor is condensed and such a tendency remains almost until the end of the tube. In general, the injection of water in comparison with experimental results when no water was injected allowed the increase of the local total heat transfer at least by two times. Condensation efficiencies for the cases when no water was injected and when it was injected did not differ very much—they were 64 and 76%, respectively. In the case of a higher inlet flue gas temperature (Figure2c), the flue gas temperature decreases rather sharply until x/d ≈ 90. Then, until the flue gas exits the tube, the decrease in the flue gas temperature becomes smaller (Figure2c, curve 1). Comparing this with the case presented in Figure2a, it is obvious that the point of a more sudden flue gas temperature decrease extends farther from the beginning of the tube, i.e., from x/d ≈ 30 to x/d ≈ 90. In this case, the characteristic of the tube wall temperature is also similar to that of the cooling water temperature (Figure2c, curves 2 and 3). The cooling water temperature increases slightly from the inlet (x/d ≈ 170) until x/d ≈ 90, and from x/d ≈ 90 until the exit, the increase in the cooling water temperature is bigger, which indicates that the water is receiving more heat due to vapor condensation. The comparison of local total heat transfer in cases of lower and higher inlet flue gas temperatures (Figure3, curves 1 and 3) without water injection indicates that the main differences are at the beginning of the tube. In the case of a higher inlet flue gas temperature, lower heat transfer was obtained due to conditions unfavorable for intense condensation heat transfer. Further, as the flue gas cooled down, there were almost no differences in heat transfer from x/d > 80 for both inlet flue gas temperatures. When the flue gas inlet temperature was increased to ~122 ◦C and water was injected into the flow, all the temperatures (Figure2d) measured in the test section increased only by about 3–4 ◦C in comparison with the case presented in Figure2b. The decreasing characteristics and temperature differences (Figure2d, curves 1–3) remained almost constant and in the range of 8–12 ◦C along the tube. Water injection in this case resulted in much higher total heat transfer in comparison to the case when no water was injected (Figure3, cf. curves 3 and 4). Because the flue gas inlet temperature at the injection chamber (Figure2d) is rather high and exceeds 100 ◦C, some injected water in the injection chamber evaporates, and the flue gas with possibly increased water vapor content enters the calorimetric tube. In the tube, it starts to condense, resulting in very high heat transfer (Figure3, curve 4, Nu t ≈ 600 in x/d range between 0 and ~30). As some water vapor is condensed initially in the calorimetric tube, heat transfer starts to decrease gradually along the tube. This means that the influence of condensation also decreases yet is still dominant. The comparison of total heat transfer in cases when no water was injected and when it was injected (Figure3, curves 3 and 4) indicates that water injection results in a local total heat transfer increase by at least about four times. In this case, water injection allowed an increase in the condensation efficiency by about 12%—from 52% (without water injection) to about 64% (with water injection). Temperature distributions in the case of a higher inlet flue gas Reynolds number (Rein ≈ 21,000) are presented in Figure4. It should be noticed that in this case, the characteristics of the temperature distributions differ from those obtained for lower Rein numbers (Figure2). For all the cases presented in Figure4, the tube wall temperature (Figure4, curve 2) is also lower the dew point temperature. Processes 2021, 9, x FOR PEER REVIEW 10 of 17

Temperature distributions in the case of a higher inlet flue gas Reynolds number (Rein ≈ 21,000) are presented in Figure 4. It should be noticed that in this case, the characteristics Processes 2021, 9, 1310of the temperature distributions differ from those obtained for lower Rein numbers (Figure 10 of 18 2). For all the cases presented in Figure 4, the tube wall temperature (Figure 4, curve 2) is also lower the dew point temperature.

Figure 4. TemperatureFigure 4. distributionTemperature along distribution the model along of the the condensing model of the heat condensing exchanger atheat Re inexchanger≈ 21,000, at different Rein ≈ ﬂue gas 21,000, different flue gas inlet temperatures and in the case when water is◦ not injected (a) Rein ≈ ◦ inlet temperatures and in the case when water is not injected (a) Rein ≈ 21,000, tin ≈ 97 C, (c) Rein ≈ 21,000, tin ≈ 97 C 21,000, tin ≈ 97 °C, (c) Rein ≈ 21,000,◦ tin ≈ 97 °C and is injected (◦b) Rein ≈ 21,000, tin ≈ 129 °C, (d) Rein ≈ and is injected (b) Rein ≈ 21,000, tin ≈ 129 C, (d) Rein ≈ 21,000, tin ≈ 135 C: (1) center of the calorimetric tube, (2) inner 21,000, tin ≈ 135 °C: (1) center of the calorimetric tube, (2) inner wall of the calorimetric tube, (3) wall of the calorimetric tube, (3) cooling water in the middle of the inner and the outer tubes, (4) dew point temperature at cooling water in the middle of the inner and the outer tubes, (4) dew point temperature at the inlet the inlet into the calorimetric tube. into the calorimetric tube.

Figure4a,c shows that with the increase in flue gas Re in, the part of the calorimetric Figure 4a,c shows that with the increase in flue gas Rein, the part of the calorimetric tube where a sharp flue gas temperature decrease is noticed (Figure4a,c, curve 1) extends tube where a sharp flue gas temperature decrease is noticed (Figure 4a,c, curve 1) extends farther, i.e., until x/d ≈ 120–130 in comparison with lower Rein numbers (Figure2a,c). farther, i.e., until x/d ≈ 120–130 in comparison with lower Rein numbers (Figure 2a,c). After After that, a not so sharp decrease in temperature is observed. The tube wall and the that, a not so sharp decrease in temperature is observed. The tube wall and the cooling cooling water temperatures demonstrate identical changes with position in the model water temperaturesof the condensingdemonstrate heat identical exchanger. changes The with cooling position water in the temperature model of the increases con- intensively densing heat fromexchanger. the inlet The (x/d cooling≈ 170) water until temperature x/d ≈ 40, fromincreases 15 ◦C intensively until 46 ◦C, from then the the in- increase is less let (x/d ≈ 170)intense, until x/d and ≈ 40, finally, from at 15 the °C outlet until 46 the °C, cooling then the water increase temperature is less intense, is about and 52 ◦ C (Figure4a, finally, at thecurve outlet 3). the Although cooling water the tube temperature wall temperature is about is52 less°C (Figure than the 4a, dew curve point 3). temperature, Although thethe tube difference wall temperature between is these less th temperaturesan the dew point in comparison temperature, with the the difference results presented in between theseFigure temperatures2a,c is not in comparison significant: with 2–4 ◦ theC. Dueresults to this,presented the condensation in Figure 2a,c at is thenot beginning of significant: 2–4the °C. tube Due is to not this, intensive the condensation (Figure5, curve at the 1).beginning As the temperatureof the tube is difference not inten- (the driving sive (Figure 5,force curve of 1). the As condensation the temperature heat transfer)difference between (the driving the dew force point of the temperature condensa- and the tube tion heat transfer)wall temperatures between the increasesdew point with temperature x/d (Figure and4a), the the tube Nusselt wall number temperatures also increases until increases withx/d x/d≈ (Figure130 (Figure 4a), the5, Nu curvesselt 1). number Further also on, increases the Nusselt until number x/d ≈ 130 decreases (Figure 5, slightly, pos- curve 1). Furthersibly on, due the to Nusselt a decrease number in the decreases water vapor slightly, mass possibly fraction due in to the a decrease flue gas flow,in and thus, the water vaporcondensation mass fraction also in becomes the flue weaker. gas flow, and thus, condensation also becomes weaker.

Processes 2021, 9, 1310 11 of 18 Processes 2021, 9, x FOR PEER REVIEW 11 of 17

Figure 5. Distribution of the total local Nusselt numbernumber along the model of thethe condensingcondensing heatheat exchanger at Rein ≈ 21,000, different flue gas inlet temperatures and for the cases when no water was exchanger at Rein ≈ 21,000, different flue gas inlet temperatures and for the cases when no water injected into the flue gas flow and when it was injected: (1) tin ≈ 97 °C without◦ injection, (2) tin ≈ 97 was injected into the flue gas flow and when it was injected: (1) tin ≈ 97 C without injection, °C with injection,◦ (3) tin ≈ 129 °C without injection,◦ (4) tin ≈ 135 °C with injection.◦ (2) tin ≈ 97 C with injection, (3) tin ≈ 129 C without injection, (4) tin ≈ 135 C with injection.

In the case with water injection at higher flue gas Rein, the characteristics of temper- In the case with water injection at higher flue gas Rein, the characteristics of tempera- ature variations (Figure 4b) are different in comparison to those obtained for a lower Rein ture variations (Figure4b) are different in comparison to those obtained for a lower Re in number with water injection (Figure2 2b).b). DueDue toto waterwater injection,injection, thethe flueflue gasgas temperaturetemperature decreases from 97 ◦°CC to 58 ◦°C.C. Further, in the calorimetriccalorimetric tube, the flueflue gasgas temperaturetemperature decreases slightlyslightly fromfrom the the inlet inlet until until x/d x/d≈ ≈110 110 (Figure (Figure4b, 4b, curve curve 1). After1). After that, that, a more a more pro- nouncedpronounced decrease decrease is observed. is observed. The The distribution distribution of the of coolingthe cooling water water temperature temperature indicates indi- thatcates the that water the water is gaining is gaining heat ratherheat rather intensively intensively from thefrom inlet the (x/dinlet ≈(x/d170) ≈ 170) until until x/d x/d≈ 50 ≈ (Figure50 (Figure4b, curve4b, curve 2). In 2). this In region, this region, the water the temperaturewater temperature increases increases by about by 35 about◦C (from 35 °C 15 to(from 50 ◦ 15C). to From 50 °C). x/d From≈ 50 x/d until ≈ the50 until outlet, the the outlet, water the temperature water temperature increased increased insignificantly, insig- i.e.,nificantly, by ~5 ◦ i.e.,C, up by to~5 ~ °C, 55 up◦C. to The ~ 55 tube °C. wall The temperaturetube wall temperature characteristic characteristic (Figure4b, curve(Figure 3) 4b, is similarcurve 3) to is the similar cooling to the water cooling temperature water temperature characteristic. characteristic. In general, general, from from the the temperature temperature distribution distribution results results presented presented in Figure in Figure 4b 4itb is it evi- is evidentdent that that from from x/d x/d ≈ 50≈ till50 tillthe the end end of ofthe the model model of of the the condensing condensing heat heat exchanger, exchanger, the differences between flueflue gas, tubetube wallwall andand waterwater temperaturestemperatures increaseincrease significantly.significantly. Heat transfer data presented in Figure5 5 (curves (curves 11 andand 2)2) indicate indicate that that condensation condensation occurs at the beginning of the calorimetric tube, and here thethe NuNutt obtained when no water was injectedinjected andand when when it it was was injected injected are are almost almost the same.the same. However, However, in the in case the with case water with injectionwater injection (Figure (Figure5, curve 5, 2),curve the 2), heat the transfer heat transfer increases increases rapidly rapidly until x/d until≈ x/d60 and≈ 60 Nuandt reachesNut reaches ~1450. ~1450. Then, Then, it decreases it decreases gradually gradually until the until end the of theend tube. of the The tube. increase The indicatesincrease thatindicates the injection that the ofinjection water intensifiesof water intensifies heat transfer heat due transfer to the due influence to the influence of condensation, of con- anddensation, then, as and the then, water as vapor the water is being vapor condensed, is being the condensed, heat transfer the graduallyheat transfer decreases. gradually At thedecreases. end of theAt the tube, end Nu oft isthe still tube, high—about Nut is still 1000.high—about 1000. Condensation efficiencies efficiencies for the cases withoutwithout and with water injection were 52% and 73%, respectively. In general, the results of condensation efficiencyefficiency show that higher efficiencyefficiency is is obtained obtained at at lower lower Re Rein numbers.in numbers. At lower At lower Rein, Rethein time, the of time the offlue the gas flue travel- gas travellingling through through the calorimetric the calorimetric tube tubeis longer, is longer, and thus and thusmore more water water vapor vapor is condensed. is condensed. At a higher flueflue gas inlet temperature (Figure(Figure4 4c,d),c,d), thethe distributiondistribution ofof temperaturestemperatures obtained are very similar to the case of a lower inlet flueflue gasgas temperaturetemperature for thethe casescases without and with with water water injection injection (Figure (Figure 4a,b),4a,b), respectively. respectively. The The difference difference is that is that the the ab- absolutesolute values values of ofthe the temperatures temperatures in in the the case case of of a a higher higher flue flue gas gas inlet temperature are slightly higher.

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The characteristics of the local total Nusselt numbers in the case of a higher flue gas The characteristics of the local total Nusselt numbers in the case of a higher flue gas inletinlet temperaturetemperature without without and and with with water water injection injection (Figure (Figure5, curves5, curves 3 and 3 and 4) are4) are similar similar to theto the Nusselt Nusselt numbers numbers in in the the case case of of a lowera lower flue flue gas gas inlet inlet temperature temperature without without and and withwith waterwater injectioninjection (Figure(Figure5 5,, curves curves 1 1 and and 2). 2). The The difference difference is is that that in in the the case case of of a a higher higher flue flue gas inlet temperature and using water injection, the maximum value of Nut was ≈ 1500, gas inlet temperature and using water injection, the maximum value of Nut was ≈ 1500, andand withwith aa lowerlower flueflue gasgas inletinlet temperaturetemperature itit waswas lower,lower, i.e.,i.e., aboutabout 12001200 (Figure(Figure5 5,, curves curves 22 andand 4).4). However,However, condensation condensation efficiency efficiency does does not not differ differ very very much, much, as it as is 42%it is 42% and 49%and for49% the for cases the cases when when no water no water was injectedwas injected and when and when it was it injected,was injected, respectively. respectively. FromFrom thethe resultsresults presentedpresented inin FigureFigure5 5 for for the the cases cases without without water water injection injection (curves (curves 1 1 andand 3),3), itit isis evidentevident thatthat thethe flueflue gasgas inletinlet temperature,temperature, especiallyespecially inin thethe beginningbeginning ofof thethe tubetube (x/d(x/d = = 0–80), 0–80), has has a a definite definite influenceinfluence on heatheat transfer.transfer. TheThe lowerlower thethe flueflue gasgas inletinlet temperature,temperature, thethe higherhigher thethe heatheat transfertransfer obtainedobtained in in thethe beginningbeginning of of thethe tube.tube. ThisThis meansmeans thatthat atat aa lower flueflue gas inlet temperature, aa betterbetter conditioncondition forfor moremore intenseintense condensationcondensation heatheat transfertransfer isis created.created. FartherFarther onon (x/d(x/d = 80–170), as the flueflue gas temperature decreases,decreases, thethe heatheat transfertransfer remainsremains almostalmost thethe samesame independentlyindependently ofof thethe flueflue gasgas inletinlet temperaturetemperature (Figure(Figure5 5,, curves curves 1 1 and and 3), 3), i.e., i.e., the the same same tendencies tendencies exist exist as as for for the the lower lower Re Reinin numbernumber (see(see FigureFigure3 3,, curves curves 1 1 and and 3). 3). InIn thethe casecase ofof waterwater injection,injection, thethe oppositeopposite cancan bebe noticed:noticed: thethe higherhigher flueflue gasgas inletinlet temperature,temperature, thethe higherhigher heatheat transfertransfer (see(see FiguresFigures3 3and and5, 5, curves curves 2 and2 and 4). 4).

◦ 4.2.4.2. Water InjectionInjection withwith aa TemperatureTemperature ofof 4040 °CC ◦ TheThe temperaturetemperature ofof thethe injectedinjected waterwater waswas chosenchosen toto bebe 4040 °CC becausebecause itit isis aa typicaltypical temperaturetemperature ofof condensed condensed water water vapor vapor obtained obtained at theat bottomthe bottom of condensing of condensing heat exchang-heat ex- erschangers in heating in heating power power plants. plants. Condensed Condensed water water in power in power plants plants is routed is routed back back to the to flue the gasflue inlet gas inlet into theinto condensing the condensing heat exchangerheat exchanger and injectedand injected into theinto flue the gasflue flow. gas flow. TemperatureTemperature distributionsdistributions forfor differentdifferent flueflue gasgas inletinlet temperaturestemperatures whenwhen waterwater waswas injectedinjected intointo thethe calorimetriccalorimetric tubetube areare presentedpresented inin FigureFigure6 6.. In In general, general, the the characteristics characteristics ◦ ofof thethe curvescurves areare thethe samesame asas presentedpresented forfor thethe casecase whenwhen waterwater ofof 2525 °CC waswas injectedinjected (Figure2b,d). The difference is that all the temperatures obtained for the current case are (Figure 2b,d). The difference◦ is that all the temperatures obtained for the◦ current case are higherhigher byby aboutabout 3–53–5 °CC inin comparisoncomparison withwith thethe casecase whenwhen waterwater ofof 2525 °CC waswas injected.injected.

FigureFigure 6.6. TemperatureTemperature distribution distribution along along the the model model of of the the condensing condensing heat heat exchanger exchanger at at Re Reinin≈ ≈ 9500, different ﬂueflue gasgas inletinlet temperatures (a) tin ≈ 88 °C,◦ (b) tin ≈ 125 °C◦ and water injection of 40 °C:◦ (1) center of the calorimetric tube, (2) the inner temperatures (a) tin ≈ 88 C, (b) tin ≈ 125 C and water injection of 40 C: (1) center of the calorimetric tube, (2) the inner wallwall ofof thethe calorimetric calorimetric tube, tube, (3) (3) cooling cooling water water in in the the middle middle of of the the inner inner and and the the outer outer tubes, tubes, (4) (4) dew dew point point temperature temperature at at the inlet to the calorimetric tube. the inlet to the calorimetric tube.

HeatHeat transfertransfer resultsresults indicateindicate thatthat inin thethe casecase ofof aa lowerlower ﬂueflue gasgas inletinlet temperaturetemperature (Figure(Figure7 7,, curve curve 1), 1), heat heat transfer transfer at at the the beginning beginning of of the the tube tube is is higher higher by by at at least least 1.3 1.3 times times andand inin thethe casecase ofof aa higherhigher ﬂueflue gasgas inletinlet temperaturetemperature (Figure(Figure7 7,, curve curve 2), 2), it it is is higher higher by by at at

Processes 2021, 9, x FOR PEER REVIEW 13 of 17

least 1.5 times in comparison with the results when water of 25 °C was injected (Figure 3, curves 2 and 4). Heat transfer data obtained for different flue gas inlet temperatures (Figure 7) show a decreasing trend along the calorimetric tube. From about the middle of the tube (x/d > 100) there are almost no differences in heat transfer for different flue gas inlet temperatures, and from x/d > 150 heat transfer is almost the same (Nut ≈ 350–380), as obtained for Processes 2021, 9, 1310 the case when the injected water temperature was 25 °C (Figure 3, curves 2 and 4). 13 of 18 The same trends of heat transfer were obtained in the calorimetric tube as described previously for the cases with water injection: the higher the flue gas inlet temperature, the higher the heat transfer. However, it should be noticed that for the case with injected wa- ◦ leastter of 1.5 40 °C, times higher in comparison heat transfer with for the different results flue when gas water inlet temperatures of 25 C was injectedremains (Figureonly over3, curvesa short 2distance and 4). along the calorimetric tube (up to x/d ≈ 50, then the difference lessen).

Figure 7.7. Distribution of the total local Nusselt numbernumber along thethe modelmodel ofof thethe condensingcondensing heatheat exchanger at Re inin ≈≈ 9500,9500, different different flue flue gas gas inlet inlet temperatures temperatures and and for for the the case case when when water water was was inin ◦ in ◦ injectedjected into into the the flue flue gas gas flow: flow: (1) (1) t t in≈ 88≈ °C,88 (2)C, (2)t ≈ t in125≈ °C.125 C.

HeatAlthough transfer the datadistribution obtained of for Nu differentt shows some flue gas differences inlet temperatures in Figure 7, (Figure the condensa-7) show ation decreasing efficiencies trend obtained along for the different calorimetric flue gas tube. inlet From temperatures about the tin middle≈ 88 °C and of the tin ≈ tube 125 (x/d°C do > not 100) differ there very are much almost and no are differences about 77–78%. in heat transfer for different flue gas inlet temperatures,The characteristics and from of x/d temperature > 150 heat distributions transfer is almost at a higher the same inlet (Nu fluet ≈ gas350–380), Reynolds as obtainednumber (Figure for the 8) case do whennot differ the injectedfrom those water presented temperature in the wascase 25 of ◦aC higher (Figure inlet3, curves flue gas 2 andReynolds 4). number and using a lower injected water temperature (Figure 4b,d); the tem- peraturesThe same obtained trends are of higher heat transfer by a few were degrees. obtained in the calorimetric tube as described previouslyThe influence for the cases of flue with gas water inlet temperature injection: the on higher total thelocal flue heat gas transfer inlet temperature, is presented the in higherFigure the9. For heat both transfer. flue gas However, inlet temperatures, it should be noticed the heat that transfer for the is case almost with the injected same waterup to ◦ ofx/d 40 ≈ 20.C, After higher that, heat the transfer heat transfer for different is about flue 1.2 gas times inlet higher temperatures in the case remains of the onlyhigher over flue a shortgas inlet distance temperature. along the This calorimetric tendency tube and (updist toribution x/d ≈ characteristic50, then the difference remain almost lessen). until the endAlthough of the calorimetric the distribution tube of for Nu botht shows flue some gas inlet differences temperatures. in Figure 7, the condensation ◦ ◦ efficienciesCondensation obtained efficiency for different in this flue case gas almo inletst temperatures does not differ tin ≈ and88 isC about and t in48–49%≈ 125 forC doboth not flue differ gas veryinlet muchtemperatures. and are about 77–78%. The characteristics of temperature distributions at a higher inlet flue gas Reynolds number (Figure8) do not differ from those presented in the case of a higher inlet flue gas Reynolds number and using a lower injected water temperature (Figure4b,d); the temperatures obtained are higher by a few degrees. The influence of flue gas inlet temperature on total local heat transfer is presented in Figure9. For both flue gas inlet temperatures, the heat transfer is almost the same up to x/d ≈ 20. After that, the heat transfer is about 1.2 times higher in the case of the higher flue gas inlet temperature. This tendency and distribution characteristic remain almost until the end of the calorimetric tube for both flue gas inlet temperatures. Processes 2021, 9, 1310 14 of 18 Processes 2021, 9, x FOR PEER REVIEW 14 of 17

Processes 2021, 9, x FOR PEER REVIEW 14 of 17

Figure 8. Temperature distribution along the model of the condensing heat exchanger at Rein ≈ 21,000, different flue gas Figure 8. Temperature distribution along the model of the condensing heat exchanger at Rein ≈ 21,000, different ﬂue gas inlet temperatures (a) tin ≈ 103 °C,◦ (b) tin ≈ 138 °C ◦and water injection of 40 °C: ◦(1) center of the calorimetric tube, (2) the inlet temperatures (a) tin ≈ 103 C, (b) tin ≈ 138 C and water injection of 40 C: (1) center of the calorimetric tube, (2) Figureinner wall 8. Temperature of the calorimetric distribution tube, (3) along cooling the modelwater inof thethe middlecondensing of the heat inner exchanger and the oute at Rer tubes,in ≈ 21,000, (4) dew different point fluetemper- gas the inner wall of the calorimetric tube, (3) cooling water in the middle of the inner and the outer tubes, (4) dew point inletature temperatures at the inlet to (thea) t incalorimetric ≈ 103 °C, ( btube.) tin ≈ 138 °C and water injection of 40 °C: (1) center of the calorimetric tube, (2) the temperatureinner wall of atthe the calorimetric inlet to the tube, calorimetric (3) cooling tube. water in the middle of the inner and the outer tubes, (4) dew point temperature at the inlet to the calorimetric tube.

Figure 9. Distribution of the total local Nusselt number along the model of the condensing heat exchanger at Rein ≈ 21,000, different flue gas inlet temperatures: (1) tin ≈ 103 °C, (2) tin ≈ 138 °C. Figure 9. Distribution of of the total local Nusselt numb numberer along the model of the condensingcondensing heat exchanger at Rein ≈ 21,000, different flue gas inlet temperatures: (1) tin ≈ 103 °C,◦ (2) tin ≈ 138 °C. ◦ 4.3.exchanger Comparison at Rein of≈ Heat21,000, Transfer different Results flue gas for inlet Different temperatures: Injected Water (1) tin ≈ Temperatures103 C, (2) tin ≈ 138 C. 4.3. ComparisonHeatCondensation transfer of Heat data efficiency Transfer obtained in Results thisat almost case for Different almostthe same does Injected flue not gas Water differ inlet Temperatures andtemperature is about ( 48–49%≈87–88 °C) for but different injected water temperature in the case of Rein ≈ 9500 show (Figure 10, curves bothHeat flue gastransfer inlet data temperatures. obtained at almost the same flue gas inlet temperature (≈87–88 °C) 1 and 2) that a higher temperature of the injected water results in a substantial increase in but different injected water temperature in the case of Rein ≈ 9500 show (Figure 10, curves heat4.3. Comparisontransfer along of Heat the tube. Transfer The Results increase for is Different especially Injected pronounced Water Temperatures in the initial part of the 1 and 2) that a higher temperature of the injected water results in a substantial increase in tube (x/d = 0–60). At the end of the tube (x/d > 150) heat transfer data in case≈ for both◦ heat transferHeat transfer along data the tube. obtained The atincrease almost is the especially same flue pronounced gas inlet temperature in the initial ( part87–88 of theC) injected water temperatures do not differ very much. ≈ tubebut different (x/d = 0–60). injected At waterthe end temperature of the tube in (x/d the case > 150) of Reheatin transfer9500 show data (Figure in case 10 for, curves both In the case of a higher flue gas inlet temperature (≈122–125 °C) the same tendencies injected1 and 2) water that a highertemperatures temperature do not of differ the injected very much. water results in a substantial increase in inheat heat transfer transfer along (Figure the tube. 10, curves The increase 3 and 4) is for especially different pronounced injected water in the temperatures initial part of were the In the case of a higher flue gas inlet temperature (≈122–125 °C) the same tendencies noticed:tube (x/d the = higher 0–60). Atthe the injected end of water the tube temperat (x/dure, > 150) the heat higher transfer the heat data transfer in case obtained for both in heat transfer (Figure 10, curves 3 and 4) for different injected water temperatures were ininjected the tube, water especially temperatures in its initial do not part. differ The very results much. also show that heat transfer for both noticed: the higher the injected water temperature, the higher the heat transfer obtained cases decreases along the tube and from x/d > 105 there are almost no differences in heat in the tube, especially in its initial part. The results also show that heat transfer for both transfer for different injected water temperatures. cases decreases along the tube and from x/d > 105 there are almost no differences in heat transfer for different injected water temperatures.

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FigureFigure 10.10. DistributionDistribution of of the the total total local local Nusselt Nusselt number numb alonger thealong model the ofmodel the condensing of the condensing heat exchanger heat in ◦ in atexchanger Rein ≈ 9500 at Re for the ≈ 9500 different for the inlet different flue gas andinlet injected flue gas water and temperatures:injected water (1) temperatures: tin ≈ 87 C and (1) injected t ≈ 87 °C and injected water◦ temperature 25◦ °C, (2) tin ≈ 88 °C and injected water temperature◦ 40 °C,◦ (3) tin water temperature 25 C, (2) tin ≈ 88 C and injected water temperature 40 C, (3) tin ≈ 122 C and ≈ 122 °C and injected water temperature◦ 25 °C,◦ (4) tin ≈ 125 °C and injected water temperature◦ 40 °C. injected water temperature 25 C, (4) tin ≈ 125 C and injected water temperature 40 C.

InFor the higher case ofRe ain highernumbers, flue heat gas transfer inlet temperature results presented (≈122–125 in Figure◦C) the 11 same show tendencies that at the inbeginning heat transfer of the (Figure calorimetric 10, curves tube, 3 heat and transfer 4) for different does not injected differ very water much temperatures for the cases were of noticed:different theinlet higher flue gas the and injected injected water water temperature, temperatures. the higher However, the heatin this transfer case, the obtained distri- inbution the tube, of total especially heat transfer in its along initial the part. tube The differs results very also much show from that distributions heat transfer presented for both casesfor lower decreases Rein numbers along the (Figure tube and 10).from x/d > 105 there are almost no differences in heat transfer for different injected water temperatures. For higher Rein numbers, heat transfer results presented in Figure 11 show that at the beginning of the calorimetric tube, heat transfer does not differ very much for the cases of different inlet flue gas and injected water temperatures. However, in this case, the distribution of total heat transfer along the tube differs very much from distributions presented for lower Rein numbers (Figure 10). For the lower flue gas inlet temperature (≈97–103 ◦C), results show that for both injected water temperatures (Figure 11, curves 1 and 2), heat transfer increases rather steeply until x/d ≈ 55–65. The maximum total heat transfer in the case of a higher injected water temperature is about 1.2 times higher in comparison with data at the lower injected water temperature. After both heat transfer curves reach their maximum values (at x/d ≈ 65 and 55, respectively), then heat transfer starts to decrease and from x/d > 100 only an insignificant difference in heat transfer is observed. For the higher flue gas inlet temperature (≈135–138 ◦C), the characteristics of the heat transfer distribution along the tube (Figure 11, curves 3 and 4) for different injected water temperatures are very similar to those described before. However, the maximum heat transfer obtained in this case is higher in comparison with data from the lower flue gas inlet temperature. After the maximum heat transfer is reached (at x/d ≈ 55), then both curves (Figure 11, curves 3 and 4) show decreasing heat transfer along the tube: i.e., the tendency is the same as for the lower flue gas inlet temperature. From x/d > 110, heat transferFigure 11. along Distribution the tube of for the both total injectedlocal Nusselt water numb temperatureser along the remains model of almost the condensing the same. heat exchanger at Rein ≈ 21,000 for the different inlet flue gas and injected water temperatures: (1) tin ≈ 97 °C and injected water temperature 25 °C, (2) tin ≈ 103 °C and injected water temperature 40 °C, (3) tin ≈ 135 °C and injected water temperature 25 °C, (4) tin ≈ 138 °C and injected water temperature 40 °C.

For the lower flue gas inlet temperature (≈97–103 °C), results show that for both injected water temperatures (Figure 11, curves 1 and 2), heat transfer increases rather steeply

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Figure 10. Distribution of the total local Nusselt number along the model of the condensing heat exchanger at Rein ≈ 9500 for the different inlet flue gas and injected water temperatures: (1) tin ≈ 87 °C and injected water temperature 25 °C, (2) tin ≈ 88 °C and injected water temperature 40 °C, (3) tin ≈ 122 °C and injected water temperature 25 °C, (4) tin ≈ 125 °C and injected water temperature 40 °C.

For higher Rein numbers, heat transfer results presented in Figure 11 show that at the beginning of the calorimetric tube, heat transfer does not differ very much for the cases of Processes 2021, 9, 1310 different inlet flue gas and injected water temperatures. However, in this case, the 16distri- of 18 bution of total heat transfer along the tube differs very much from distributions presented for lower Rein numbers (Figure 10).

FigureFigure 11.11. DistributionDistribution of of the the total total local local Nusselt Nusselt number numb alonger thealong model the ofmodel the condensing of the condensing heat exchanger heat ◦ atexchanger Rein ≈ 21,000 at Re forin ≈ the 21,000 different for the inlet different flue gas andinlet injected flue gas water and temperatures:injected water (1) temperatures: tin ≈ 97 C and (1) injected tin ≈ 97 °C and injected water◦ temperature 25 ◦°C, (2) tin ≈ 103 °C and injected water temperature◦ 40 °C,◦ (3) tin water temperature 25 C, (2) tin ≈ 103 C and injected water temperature 40 C, (3) tin ≈ 135 C and ≈ 135 °C and injected water temperature◦ 25 °C,◦ (4) tin ≈ 138 °C and injected water temperature◦ 40 °C. injected water temperature 25 C, (4) tin ≈ 138 C and injected water temperature 40 C. 5. ConclusionsFor the lower flue gas inlet temperature (≈97–103 °C), results show that for both in- jectedAfter water analysis, temperatures the following (Figure conclusions11, curves 1 haveand 2), been heat made: transfer increases rather steeply 1. Performed investigations revealed the regularities of the local heat transfer during operation of condensing heat exchangers with water injection. 2. Water injection drastically changes the distribution of temperatures and has a significant effect on heat transfer along the calorimetric tube. ◦ 3. In the case of the water injection with a temperature of 25 C, at lower Rein numbers, the local total heat transfer along the tube increased by at least four times, and at higher Rein numbers, at least by two times in comparison with the case without water injection. ◦ 4. In the case of water injection with a temperature of 40 C, at lower Rein numbers, the local total heat transfer increased by at least 2.3 times and at higher Rein numbers, by at least 1.7 times in comparison with the case without water injection. 5. At higher flue gas inlet temperatures, the effect of water injection on heat transfer is also stronger. For lower Rein, the effect is more pronounced in the initial part of the tube (up to x/d ≈ 60), and for higher Rein, it is in the x/d range between 20 and 110. 6. Condensation efficiency increases with decreasing Rein number, flue gas temperature and injected water temperature. 7. To optimize the operation of condensing heat exchangers with water injection, it is necessary to perform wider investigations on the effect of different flue gases, cooling water and injected water parameters.

Author Contributions: Conceptualization, R.P.; methodology, A.S. and P.P.; formal analysis, A.S. and V.K.; experimental investigation, A.S. and V.K.; resources, A.S., R.P., G.M., E.P.; writing—original draft preparation, A.S.; writing—review and editing, P.P., H.J., G.M. and E.P.; supervision, R.P. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by Research Council of Lithuania (LMTLT), grant number S-MIP-20-30. Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Processes 2021, 9, 1310 17 of 18

Data Availability Statement: Not applicable. Conﬂicts of Interest: The authors declare no conﬂict of interest.

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